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https://blogs.ifas.ufl.edu/osceolaco/2020/06/24/negative-effects-of-overwatering-plants/
Skip Navigation or Skip to Content Home Blog Directory Blogs.IFAS Negative Effects of Overwatering Plants Email2Facebook1Twitter0Reddit1 X Linkedin0 Stumbleupon0 Central Florida experiences most of its annual rain between June 1st and September 30th. Water is a very important component for good plant health but for most people it is very difficult to find a balance. Too little water is bad, likewise too much water. I recommend that plants should only be irrigated in early morning before 10 am and not in the late evenings. I am aware that we cannot control when rain will fall which can make it a little difficult for plant health. When watering, only wet the soil where the roots are located and avoid wetting the leaves of the plant. Wet leaves will encourage foliar diseases. For disease to survive, the pathogen that will cause the disease must be present, the environment such as wet leaves must be conducive, and there must be a host plant that is susceptible to a specific disease. Leaving wet plant leaves overnight is perfect for disease development. At UF/IFAS Extension/Osceola County office we receive many samples of unhealthy plants each year. Most of these samples of diseased plants show signs of root rot diseases in many cases. Overwatering contributes to root rot diseases. Root rot affects a wide range of plants including turfgrasses, roses, liriope, marigolds, verbenas, hollies, box woods, azaleas and rhododendrons. The problem with root rot is that the symptoms often cause plants to wilt, leaves become yellow, growth is stunted, and people naturally think the problem is lack of water. They apply water and the problem becomes worse. One thing to keep in mind is that plant diseases such as take all root rot, pythium and rhizoctonia are very aggressive pathogens that thrive in wet soil. Foliar leaf spot is also a major issue that is triggered by prolonged leaf wetness. Another key to minimize the occurrence of root rot is to carefully check new plants before introducing them to the landscape. Take one or two plants out of a flat of bedding plants and observe the roots. Roots should be white or silvery, if they are dark, soft or sparse, then the plant is probably infected with a root rot-causing pathogen. Avoid introducing sick plants into the landscape. Diseases are not the only negative impact of overwatering. Overwatering and excess rainfall over a short period causes leaching of fertilizer and pesticides through the soil profile down into the underground water. Leaching is bad in that it causes non-point source pollution to our water resources. Soil erosion and nutrient runoff are also results of excess watering. During the rainy season do not fertilize the lawn if rain is in forecast within 24 hours. Excess rainfall will move fertilizer off site leading to pollution. For more information on lawn and landscape related topics, contact Grantly Ricketts with UF/IFAS Extension in Osceola County at 321-697-3000 or email gricketts@ufl.edu. 3 by Grantly Ricketts Posted: June 24, 2020 Category: Horticulture, Lawn, Pests & Disease, Pests & Disease, Turf, Tags: Bahiagrass More From Blogs.IFAS Holiday Gift Plants What To Do in the Yard in May Raised Garden Bed Is it OK to plant a veggie garden now?
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https://www.ahajournals.org/doi/10.1161/circimaging.109.921791
The Role of Multimodality Imaging in the Management of Pericardial Disease | Circulation: Cardiovascular Imaging Skip to main content Advertisement Become a member Volunteer Donate Journals BrowseCollectionsSubjectsAHA Journal PodcastsTrend Watch ResourcesCMEAHA Journals @ MeetingsJournal MetricsEarly Career ResourcesDEIA Resources InformationFor AuthorsFor ReviewersFor SubscribersFor International Users Alerts 0 Cart Search Sign inREGISTER Quick Search in Journals Enter search term Quick Search anywhere Enter search term Quick search in Citations Journal Year Volume Issue Page Searching: This Journal This JournalAnywhereCitation Advanced SearchSearch navigate the sidebar menu Sign inREGISTER Quick Search anywhere Enter search term Publications Arteriosclerosis, Thrombosis, and Vascular Biology Circulation Circulation Research Hypertension Stroke Journal of the American Heart Association Circulation: Arrhythmia and Electrophysiology Circulation: Cardiovascular Imaging Current Issue Archive Journal Information About Circulation: Cardiovascular Imaging Author Instructions Editorial Board Information for Advertisers Features Teaching Files Webinars Special Issues Circulation: Cardiovascular Interventions Circulation: Cardiovascular Quality & Outcomes Circulation: Genomic and Precision Medicine Circulation: Heart Failure Stroke: Vascular and Interventional Neurology Annals of Internal Medicine: Clinical Cases Information For Authors For Reviewers For Subscribers For International Users Submit & Publish Submit to the AHA Editorial Policies Open Science Diversity, Equity, Inclusion, and Accessibility Publishing with the AHA Open Access Information Resources AHA Journals CME AHA Journals @ Meetings Metrics AHA Journals Podcast Network Early Career Resources Trend Watch Professional Heart Daily AHA Newsroom Current Issue Archive Journal Information About Circulation: Cardiovascular Imaging Author Instructions Editorial Board Information for Advertisers Features Teaching Files Webinars Special Issues Submit Reference #1 Research Article Originally Published 1 May 2010 Free Access The Role of Multimodality Imaging in the Management of Pericardial Disease David Verhaert, MD, Ruvin S.Gabriel, MBChB, Douglas Johnston, MD, Bruce W.Lytle, MD, Milind Y.Desai, MD, and Allan L.Klein, MDAuthor Info & Affiliations Circulation: Cardiovascular Imaging Volume 3, Number 3 29,551 159 Metrics Total Downloads 29,551 Last 12 Months 1,084 Total Citations 159 Last 12 Months 7 View all metrics Track CitationsAdd to favorites PDF/EPUB Contents Pericardial Disease: Which Imaging Test to Choose? When to Consider Added Imaging? When to Consider Added Imaging? When to Consider Added Imaging? When to Consider Added Imaging? When to Consider Added Imaging? When to Consider Added Imaging? Conclusion Acknowledgments Footnote Supplemental Material References eLetters Information & Authors Metrics & Citations View Options References Figures Tables Media Share Pericardial pathology is commonly encountered in clinical practice and may present either as an isolated process or in association with other systemic disorders. Recognizing pericardial pathology can be relatively straightforward, particularly if the clinical manifestation is typical (eg, the patient with acute pericarditis and an audible friction rub reporting retrosternal pain, exacerbated by inspiration or in the supine position) or when an associated disease process gives a direct clue to the diagnosis (eg, the finding of a complex pericardial effusion in a patient with a known malignancy). In these situations, the diagnostic pathway can be limited to a relatively small sequence of tests to basically confirm the initial clinical suspicion.1 However, pericardial disease can also result in nonspecific symptoms and equivocal physical findings. When the initial tests of choice turn out to be nondiagnostic or the course of the disease is prolonged, pericardial disease may cause considerable diagnostic dilemmas. Furthermore, established diagnostic techniques may not visualize the full extent of the pericardial disease process. In such difficult clinical situations, an integrated multimodality imaging approach may provide incremental value. Unfortunately, current guidelines do not address the role of a multimodality approach in the difficult to manage pericardial patient.1 This review will therefore discuss the potential role of different imaging modalities in the diagnosis and management of pericardial disorders, with a specific focus on what constitutes a rational multimodality imaging approach. Pericardial Disease: Which Imaging Test to Choose? The 3 imaging modalities most commonly used for evaluation of pericardial disease are echocardiography, cardiac computed tomography (CT), and cardiac MRI (CMR). The main indications and limitation for each test are summarized in Table 1. Echocardiography remains the initial imaging method of choice for the majority of patients with pericardial disease, but in many clinical scenarios, a transthoracic echocardiogram (TTE) alone is insufficient. Under those circumstances, many clinicians experience difficulties deciding which test to choose as the best next step in the diagnostic process. Each patient scenario tends to be unique, mandating a highly individualized approach from the clinician but unfortunately also explains the complete absence of consensus or general recommendations to assist clinicians in making these decisions. Sometimes it is even unclear whether patients may benefit at all from additional imaging. As a consequence, patients may get referred for an exhaustive battery of imaging tests when it is not absolutely needed. The first important role of the imaging expert is therefore to ensure that patients do not get inappropriate or unnecessary tests and avoid incomplete or nondiagnostic studies. Subsequently, he should decide when and how to combine different tests to answer important clinical questions. Table 2 offers an example of pericardial disease-specific protocols for each imaging modality; adhering to standardized protocols would potentially maximize the information derived from an imaging test and probably avoid incomplete studies. Open in Viewer Table 1. Strengths and Limitations of Various Imaging Modalities in the Evaluation of Pericardial Disease | Echocardiography | Cardiac CT | CMR | --- | Main indications/advantages | | | | • First-line diagnostic imaging test in the evaluation and follow-up of pericardial disease | • Need for better anatomic description | • Need for better anatomic description | | • Evaluation of associated/extracardiac disease | • Superior tissue characterization | | • Preoperative planning | | | • Widely available • Low cost • Safe • Can be performed bedside or in hemodynamically unstable patients | • Detection of pericardial calcification | | | Main limitations/disadvantages | | | | • Limited windows, narrow field of view | • Use of ionizing radiation | • Time consuming, high cost | | • Technical difficulties in case of obesity, obstructive lung disease or immediately post- cardiothoracic surgery | • Use of iodinated contrast (unless visualization of related anatomy is not needed) | • Preferably stable heart rhythms | | • Contraindicated in case of pacemaker or defibrillators | | • Lung tissue less well visualized | | • Functional evaluation only possible with retrospectively gated studies (higher radiation dose, suboptimal temporal resolution) | • Calcifications less well visualized | | • Operator dependent | • Use of Gadolinium contrast contra-indicated in case of advanced renal dysfunction (glomerular filtration rate <30 mL/min) | | • Low signal-to-noise ratio of the pericardium | | • Limited tissue characterization | • Difficulties in case of tachycardia or unstable heart rhythm (particularly for prospectively gated studies) | • Use of some breath-hold sequences | | | • Hemodynamically stable patients only | | | • Need for breath-hold | | | | • Hemodynamically stable patients only | | Expand Table Open in Viewer Table 2. Protocols and Findings for the Evaluation of Pericardial Disease by Different Imaging Modalities | Echocardiography | Prospectively ECG-Triggered or Retrospectively ECG-Gated Multidetector CT | CMR | --- | SSTSE indicates single-shot turbo spin-echo; SSFP, steady-state free precession sequence; and STIR, short tau inversion recovery. | | Doppler measurements should be repeated in the sitting position (reducing preload) in case of nondiagnostic findings and suspicion for constriction. | | †Orientation short-axis slice with diaphragm in view. | | 2D Echocardiography | Axial imaging | Bright blood single-shot SSFP and black blood axial stacks (half Fourier SSTSE, ECG-gated) | | • Effusion (size, location, echogenic vs serous, suitability for needle pericardiocentesis) | • Pericardial thickening, calcification | | • Localization and characterization of pericardial effusions, cysts, or masses | • Presence of pleural effusion, ascites, distension of the inferior vena cava, assessment of pericardial thickening | | • Pericardial thickness (particularly TEE) | • Evaluation of lungs (pleural effusion, postradiation fibrosis, malignancy) and liver (cirrhosis, ascites) | | • Collapse of right-sided chambers (duration of diastole and relation with respiration) | | • Proximity of bypass grafts and/or other vital structures to the sternum (preoperative planning) | | | • Early diastolic septal bounce, respiratory shift of the ventricular septum | | | | • Inferior vena cava plethora | | | | • Pleural effusion/ascites | | | | • Right atrial tethering (best seen by TEE) | | | | • Stasis of agitated saline contrast in right atrium (sluggish flow) | | | | Doppler+simultaneous respirometry | Multiplanar reconstruction | Black blood images (T1+T2-weighted fast spin-echo) Optional: T2-weighted STIR (edema weighted) fast spin-echo | | • Restrictive mitral inflow pattern | • Chamber dimensions (right atrial enlargement, conical ventricular deformity) | | • Reciprocal respiratory changes of mitral (and tricuspid) inflow | | | | • Assess coronary patency | • Tissue characterization, measurement of pericardial thickness | | • Reciprocal respiratory changes of diastolic forward flow velocity and end-diastolic flow reversal in hepatic veins | | • Assessment of pericardial inflammation and masses (STIR sequence) | | • Tissue-Doppler velocities of mitral and tricuspid annuli, color Doppler M-mode of mitral inflow | | | | • 2D Strain of longitudinal and circumferential deformation | | | | M-Mode | Volume-rendered imaging | Tagged cine images (T1-weighted gradient echo) | | • Flattening of the posterior wall during diastole | • Extent and distribution of pericardial calcification | • Epicardial/pericardial tethering | | • Respiratory variation of ventricular size | Cine imaging (retrospectively gated study only) | Bright blood cine images (SSFP) | | | • Functional evaluation (septal bounce, pericardial tethering) | • Atrial/ventricular size and function | | | | • Diastolic restraint | | | | • Conical deformity of the ventricles | | | | • Myocardial tethering | | | | • Diastolic septal bounce | | | | • Pericardial thickening and/or effusion | | | | Late gadolinium enhancement images (phase-sensitive inversion recovery sequence) | | | | • Detection of pericardial inflammation | | | | Real-time gradient echo cine image† | | | | • Monitor respiratory variation of ventricular septal motion | Expand Table The role and value of specific imaging modalities for the recognition and characterization of a variety of pericardial disorders will subsequently be discussed and illustrated. Pericarditis Clinical Scenario A 37-year-old man with a history of recurrent pericarditis is referred with a new episode of chest pain. During the last 2 years, the patient experienced multiple flare-ups of pericarditis affecting his ability to work and perform daily activities. He has previously been treated with intermittent courses of nonsteroidal antiinflammatory drugs and short trials of prednisone therapy. Echocardiography shows only a trivial pericardial effusion. Before initiating therapy with high-dose nonsteroidal antiinflammatory medication and colchicine, a CMR is performed, confirming the presence of active pericardial inflammation. Six weeks later, it is eventually decided to gradually taper the medication dose based on the results of a new CMR scan documenting a dramatic response to therapy (Figure 1). No serious recurrences have been noted since. Open in Viewer Figure 1.CMR and TTE before and after 6 weeks of high-dose ibuprofen and colchicine. Before treatment, thickened, inflamed pericardium (arrows) appears as low to intermediate signal intensity adjacent to the high signal intensity epicardial fat in black blood T2-weighted turbo spin-echo (A), intermediate signal intensity in steady-state free precession sequence cine images (B), and enhances bright on late gadolinium enhancement imaging (C). Posttreatment is associated with resolution of pericardial thickening (D and E) and inflammation on late gadolinium enhancement imaging (F). By comparison, the parasternal long-axis echocardiographic image of the same patient before and after treatment is shown in G and H. Although a small, organized effusion (black arrows) could be noted posteriorly before therapy (G, arrow), the presence and resolution of pericardial inflammation are much better demonstrated by CMR. Acute pericarditis implies an inflammatory reaction of the pericardium, often presenting as a sudden, pleuritic-type retrosternal chest pain, typically worsening with inspiration or when supine.1–5 As an isolated problem, acute pericarditis is usually caused by viral infections or considered idiopathic when the viral agent cannot be identified. Less common etiologies include pericardial inflammation after a transmural myocardial infarction (either acute or delayed, then referred to as Dressler syndrome); uremia; hypothyroidism; systemic autoimmune disease; or more uncommon infections (eg, tuberculosis). Pericarditis can also occur in association with acute dissection of the ascending aorta (hemopericardium) or as a result of neoplastic invasion of the pericardium.1–5 History, physical examination, ECG, and serological evidence of systemic inflammation will usually guide the clinician to the right diagnosis. When there is a clear diagnosis of uncomplicated idiopathic pericarditis, additional imaging is usually unnecessary because of the self-limited nature of the disease. However, TTE is still widely used as a screening tool for the presence of an associated pericardial effusion, visualized as an echo-free space adjacent to the myocardium. TTE can semiquantify the size of pericardial effusions into trivial (only in systole), small (<1 cm), moderate (1 to 2 cm), and large (>2 cm) or very large (>2 cm with compression of the heart).1 Our threshold for ordering a TTE is usually low, particularly when pericarditis is associated with indicators of worse outcome (fever >38�, subacute course, or failure of initial response to standard therapy).6 TTE is certainly indicated when there is concern for features of constrictive physiology or to exclude cardiac tamponade but also to detect associated heart disease or to guide diagnostic or therapeutic pericardiocentesis. When to Consider Added Imaging? Figure 2 illustrates a suggested pathway for situations in which sequential imaging generally is indicated, usually after a baseline TTE has been obtained. In summary, tomographic imaging (CT or CMR) for the evaluation of pericarditis should be considered in case of: Open in Viewer Figure 2.Suggested diagnostic approach to investigate acute pericarditis and its complications from an imaging perspective. ESR indicates erythrocyte sedimentation rate; NSAIDs, nonsteroidal antiinflammatory drugs; TTE, transthoracic echocardiogram; and TEE, transesophageal echocardiogram. (1) Therapeutic difficulties or complications after acute pericarditis (failure to respond to aspirin or nonsteroidal antiinflammatory drugs and evolution toward recurrent or chronic pericarditis with possible constrictive features). (2) Traumatic etiology (penetrating injury, esophageal, or gastric perforation). (3) Pericarditis associated with a specific disease (eg, neoplastic disorders) or with involvement of adjacent anatomic structures (aortic dissection, empyema, acute pancreatitis). One good example of the complimentary role of both CT and CMR is their ability to clearly visualize pericardial thickening and to demonstrate inflammatory changes involving the pericardium and/or epicardial fat. As illustrated by the introductory case scenario and Figure 1, CMR may thus confirm the presence of pericarditis when the diagnosis is uncertain by TTE alone. However, it should be emphasized that TTE is frequently unremarkable in acute pericarditis, and the majority of these patients do not need additional imaging unless they present with atypical features or there is concern for a complicated course. Similarly, CMR can be used to monitor the inflammatory process in patients with recurrent pericarditis or effusive constrictive pericarditis, thereby identifying patients with persistence of pericardial inflammation despite courses of medical therapy. Tapering or stopping antiinflammatory therapy (particularly corticosteroids) in these patients is often troublesome, as a balance needs to be made between the risk of recurrence and the risk of possible side effects related to continuation of therapy. Clinicians will often try to obtain proof of stable remission before therapy is reduced or stopped, usually by reassuring that symptoms have resolved or C-reactive protein has normalized. In case of doubt, we typically perform CMR and if active inflammation is still present, tapering of the antiinflammatory medication is reconsidered regardless of symptomatic improvement. Small or loculated effusions may not always be evident on TTE; CT or CMR may then be useful, particularly when there is concern for penetrating injury (eg, a patient presenting with chest pain shortly after implantation of a transvenous pacer wire). CT attenuation values may occasionally give a clue to the etiology of an effusion. Serous fluid typically has a density close to water (<10 Hounsfield Units [HU]), whereas higher attenuation values are more suggestive of an exudate (20 to 60 HU, as in purulent pericarditis or malignancy) or acute hemopericardium (>60 HU, as secondary to penetrating injury or acute dissection). It can occasionally be challenging to differentiate thickened pericardium from a small effusion by CT, precisely because of similar attenuation coefficients. In contrast, CMR breath-hold steady-state free precession sequence cine imaging will demonstrate a change in the distribution of pericardial fluid between systole and diastole, thereby distinguishing small effusions from pericardial thickening.7 CMR may also allow further characterization of a pericardial effusion. Simple transudative effusions typically have a low signal intensity on T1-weighted images, whereas hemorrhagic or exudative effusions often have a medium or high signal intensity on T1 sequences.7 Cardiac Tamponade Clinical Scenario A 61-year-old patient receiving chemotherapy for metastatic non–small cell lung carcinoma is admitted to the emergency department because of worsening shortness of breath, excessive cough, and chest discomfort in the last few days. His blood pressure is 80/40 mm Hg, his heart rate is 110 bpm, and physical examination reveals a markedly elevated jugular venous pressure. Urgent bedside TTE demonstrates a large pericardial effusion with features of tamponade (supplemental Movie Clips 1 and 2). An echo-guided pericardiocentesis is subsequently performed before more definite treatment by surgical pericardial window formation is offered the next day. Cardiac tamponade is a potentially fatal compression of the heart due to an accumulation of fluid in the intrapericardial space.1,2,5,8 The fluid accumulation can occur rapidly or more gradually, but once the limits of parietal pericardial stretch are exceeded, intrapericardial pressure will rise quickly and compromise diastolic filling.8,9 Patients are often anxious and may report dyspnea and chest discomfort. The classic findings in tamponade known as Beck’s triad include hypotension, jugular venous distension, and muffled heart sounds. Tachycardia is the rule, acting as a compensatory mechanism in the setting of a decreased stroke volume. Cardiac tamponade ultimately is a clinical diagnosis and must be considered in every patient with unexplained cardiogenic shock or pulseless electric activity.1 Because the clinical diagnosis can be challenging, echocardiography should be performed without further delay once a patient is suspected of having tamponade. Supplemental Movie Clips 1 and 2 highlight an important feature of cardiac tamponade, which is the collapse of right-sided chambers once the intrapericardial pressure exceeds the intracavitary pressure. Because intracardiac pressures vary throughout the cardiac cycle, inversion of these chambers can be transient, typically at end-diastole for the right atrium or early diastole for the right ventricle (the latter being more specific for tamponade).10 Right-sided collapse will be most prominent during expiration when right heart filling is reduced. When the intrapericardial pressure continues to rise, duration and severity of collapse will further increase, eventually resulting in circulatory failure. Distension of the inferior vena cava with absent reduction in diameter during inspiration is another very sensitive, albeit nonspecific sign of tamponade.11 When the intrapericardial volume becomes fixed due to pericardial constraint, filling of one side of the heart will occur at the expense of the other. This mechanism leads to substantial reciprocal respiratory variation in mitral (>25%) and tricuspid (>50%) inflow, reflecting the accentuated ventricular interdependence.12 Similar reciprocal respiratory changes in flow velocity can be identified in the hepatic and pulmonary veins. Pulmonary vein diastolic forward flow will decrease with inspiration and increase with expiration. In contrast, the hepatic vein diastolic forward flow will decrease on expiration and have a large atrial reversal. An additional manifestation of increased ventricular interdependence is the leftward shift of the septum with inspiration, reversing on expiration. When to Consider Added Imaging? Once the presence of cardiac tamponade has been established by echocardiography, there is basically no need for confirmatory testing by CT or CMR as any delay in appropriate treatment could be harmful to the patient. Occasionally TTE is inconclusive, in our experience particularly during the early postoperative period when the acoustic windows can be very poor. However, in these situations, transesophageal echocardiography (TEE) will almost always allow exclusion of a postoperative loculated pericardial effusion or intrapericardial clot.13 Occasionally, a significant effusion is initially detected first on postoperative CT or CMR. In this case, the multimodality imaging specialist must be able to recognize signs of imminent tamponade, which are essentially similar to those outlined above. Constrictive Pericarditis Clinical Scenario A 44-year-old man presents with increasing shortness of breath since the last 8 months. More recently he also noticed worsening leg edema and abdominal girth. His medical history is insignificant except for mild asthma, and he has no risk factors for coronary artery disease. An echocardiogram shows normal left ventricular systolic function (ejection fraction, 60%) but restrictive diastolic filling. Mild biatrial enlargement and a plethoric inferior vena cava are also seen. An abnormal septal bounce is noted (supplemental Movie Clip 3), but in the absence of significant respiratory variation of mitral or tricuspid inflow, further evidence is deemed necessary to confidently make the diagnosis of constrictive pericarditis. A cardiac CT is then ordered, excluding obstructive coronary artery disease and additionally demonstrating extensive circumferential pericardial calcification (Figure 3C and 3D). The patient is subsequently referred for surgical pericardiectomy. Open in Viewer Figure 3.Classic anatomic findings of pericardial constriction by CMR and CT. CMR findings of constriction demonstrated in black blood T2-weighted spin-echo (A) and steady-state free precession sequence cine sequence (B) in the horizontal long-axis view. Pericardial thickening (6 mm) is seen adjacent to the right atrium and ventricle (arrow), with characteristic tubular deformity of the right and left ventricles (RV/LV) and dilation of the right atrium. Other contributory findings by CMR (not illustrated here) are tethering of the underlying myocardium to the pericardium (demonstrated on tagged gradient echo cine sequences), a diastolic septal bounce, and subjective abrupt cessation of diastolic filling on steady-state free precession sequence cine images. C, Cardiac CT demonstrating the presence of circumferential pericardial calcification on a multiplanar reconstructed short-axis image (arrows). D, Three-dimensional volume-rendered imaging showing the extent and anatomic distribution of pericardial calcium. Chronic inflammation can occasionally result in fibrous thickening and calcification of the pericardium and lead to a condition where ventricular filling is severely impaired due to loss of pericardial compliance.1–3,5,14 The etiology of constrictive pericarditis is most commonly idiopathic; however, it can be associated with prior cardiac surgery, mediastinal radiation, or scarring related to tuberculous pericarditis.15 Although constriction occasionally develops acutely (within days) or subacutely (3 to 12 months)—mainly after cardiac surgery—a long delay between the initial insult and the onset of constriction is the more common scenario.2,3 The diagnosis of constriction remains challenging and although clinical clues (related to the presence of unexplained systemic venous congestion) are important in considering the disease, further confirmation by other tests is always necessary. No single diagnostic approach can or should be used to diagnose all cases of constrictive pericarditis, and clinicians therefore must tailor their diagnostic strategy according to each patient. The algorithm shown in Figure 4 suggests an investigative strategy in case of clinical suspicion for constrictive pericarditis and will subsequently be discussed in more detail. Open in Viewer Figure 4.Suggested diagnostic approach for the evaluation of patients with constrictive pericarditis. LV indicates left ventricular; RV, Right ventricular; TEE, transesophageal echocardiogram; and TTE, transthoracic echocardiogram. An important reason to use echocardiography early in the diagnostic process is to rule out other more common causes of right-sided heart failure, including left or right ventricular systolic dysfunction, severe pulmonary hypertension, or unrecognized left-sided valvular disease. Encasement of the heart by a stiff pericardium leads to an abrupt termination of ventricular diastolic filling due to pericardial constraint, isolates the heart from respiratory changes in intrathoracic pressure, and causes exaggerated ventricular interdependence.16 These pathophysiologic abnormalities are represented in typical 2D and Doppler findings (Figure 5), and their recognition is pivotal not only to make a correct diagnosis but also to differentiate constrictive pericarditis from restrictive cardiomyopathy as both conditions share many clinical features. A precise measurement of pericardial thickness may be difficult (particularly by TTE), but an early diastolic “septal bounce,” a respiratory shift in the position of the interventricular septum, inferior vena cava plethora, and the presence of myocardial tethering are all classic 2D features associated with pericardial constriction (none of them particularly sensitive or specific, however).3 Doppler interrogation of transmitral flow velocity shows early rapid restrictive filling, but the difference with restrictive cardiomyopathy is often made by demonstrating reciprocal respiratory changes between transmitral and transtricuspid flow (or between pulmonary vein and hepatic vein flow) using simultaneous respirometry in constriction.17,18 Color M-mode imaging (measuring early diastolic flow propagation velocity, Vp) and tissue Doppler (measuring the early diastolic mitral annular velocity E′ [Figure 5D]) allow further differentiation from restrictive cardiomyopathy by documenting preserved myocardial relaxation in constrictive pericarditis (Vp >45 cm/s or E′ >8 cm/s).19,20 These methods are especially useful when no substantial respiratory variation of Doppler recordings is observed; for instance, in patients with atrial fibrillation having irregular R-R intervals or in patients with markedly elevated filling pressures when respiration has only little effect on the transmitral driving pressure, even with head-up tilt.21 Open in Viewer Figure 5.A, M-mode recording in the parasternal long-axis view showing a respiratory shift of the interventricular septum toward the left ventricle with inspiration and toward the right ventricle with expiration as a result of exaggerated ventricular interdependence. Small yellow arrow denotes the early diastolic septal bounce, typically seen in constrictive pericarditis. There is flattening of the posterior left ventricular wall during diastole (white arrows). B, Pulsed wave Doppler echocardiography of the mitral valve with simultaneous respirometry. Constrictive pericarditis is characterized by dissociation of intrathoracic and intracardiac pressures, resulting in an increase in diastolic driving pressure into the left ventricle with expiration, and a decrease with inspiration. This leads to marked (>25%) respiratory changes of early mitral inflow velocity (E). C, Tricuspid inflow velocity, showing the opposite changes. Tricuspid valve early diastolic velocity E increases with inspiration and decreases with expiration. D, The early diastolic septal mitral annular velocity E′ (in this case 14 cm/s) is usually increased in patients with constriction because diastolic filling occurs predominantly by longitudinal relaxation. However, adherence of the pericardium to the basolateral wall may occasionally inhibit normal or decreased motion of the lateral mitral annulus. A′ indicates late diastolic mitral annular velocity; E′, early diastolic mitral annular velocity; EXP, expiration; INSP, inspiration; IVS, interventricular septum; LV, left ventricle; PW, posterior wall; RV, right ventricle; and S′, systolic mitral annular velocity. When to Consider Added Imaging? Remaining Diagnostic Uncertainty When the picture is complete, comprehensive echocardiography may provide conclusive evidence of constrictive pericarditis. Unfortunately, echocardiographic findings are not uncommonly equivocal in patients with a possible diagnosis of pericardial constriction. In these situations additional testing is needed to make the diagnosis with more confidence. CT Versus MRI Both CT and CMR provide excellent anatomic delineation of the pericardium from adjacent tissue and enable a precise measurement of pericardial thickness. A thickened pericardium (>4 mm) in the proper clinical setting certainly adds further support to the diagnosis and is a valuable piece of information if the echocardiography was inconclusive (although absence of pericardial thickening does not necessarily rule out constrictive pericarditis).22 Other important features are abnormalities in the contour of the pericardium; conical deformity (“tubing”) of the ventricles; right atrial (sometimes biatrial) enlargement; and inferior vena cava plethora. Compared with CMR, CT is far superior in detecting calcification (Figure 3C), but calcification can occur without constriction and vice versa. CMR, on the other hand, better differentiates small effusions from pericardial thickening; has a better temporal resolution (enabling detection of rapid hemodynamic processes such as a septal bounce or respirophasic variation in septal excursion (Figure 5A and supplemental Movie Clip 4); and may reveal ongoing pericardial inflammation. CMR myocardial tagging sequences can demonstrate pericardial-myocardial adherence, whereas abrupt cessation of diastolic filling can be visually appreciated on steady-state free precession sequence cine images as another (subjective) sign of a stiff pericardium. Phase encoding velocimetry provides information similar to Doppler echocardiography, although flow curves are averaged over several cardiac cycles precluding assessment of respirophasic variation. For these reasons, CMR is sometimes preferred over CT for patients with a high clinical suspicion of constriction and a nondiagnostic echo. Multimodality Imaging Versus Catheterization As illustrated in the case scenario above, cardiac catheterization can sometimes be avoided by the rational use of multimodality imaging. Nevertheless, despite the availability of CT and CMR, constrictive pericarditis continues to be a diagnostic challenge, particularly in patients presenting after prior radiation therapy or open heart surgery who may have combined pericardial, myocardial, and valvular disease. As recently shown by Talreja et al,23 in this difficult subgroup of patients, catheterization may offer valuable diagnostic information by showing dynamic respiratory changes of the ventricular pressure curves reflecting enhanced ventricular interaction. Ultimately, cardiologists need to make a synthesis of the available (and occasionally discrepant) pieces of information to make a clinical judgment whether or not a patient is likely to benefit from pericardiectomy. Preoperative Planning in Patients With a Definite Diagnosis of Constrictive Pericarditis Even if a diagnosis of constrictive pericarditis has unequivocally been established by routine testing, cardiac CT can assist in preoperative planning in the following situations: (1) Patients with history of prior cardiothoracic surgery: Sternal reentry and dissection of mediastinal structures can be a major challenge due to the formation of dense adhesions. The proximity of bypass grafts, the ascending aorta, innominate vein, and right ventricle to the back of the sternum pose an additional risk factor for catastrophic hemorrhaging during resternotomy. These high-risk findings are readily detected by preoperative CT and allow the surgeon to adopt preventive surgical strategies and thus potentially improve outcomes in these patients.24 (2) Radiation-induced constrictive pericarditis: CT will also determine the extent of associated lung injury due to radiation. (3) Preoperative evaluation of the localization and extent of pericardial calcification (Figure 5C and 5D): The presence of circumferential or severe posterolateral calcification may push the surgical approach toward a bilateral thoracotomy. Particularly in patients with circumferential constriction, the left ventricular pericardium should be removed first to prevent provocation of sudden pulmonary edema. (4) The occasional patient with constrictive pericarditis and a low-to-intermediate probability of underlying coronary artery disease, to obviate the need for preoperative coronary angiography. Effusive Constrictive Pericarditis Clinical Scenario A patient presents with symptoms of right-sided heart failure shortly after an episode of acute pericarditis that was complicated by a large pericardial effusion requiring pericardiocentesis. A postprocedure echocardiogram shows a normal right ventricular systolic function, but now there is a septal bounce and increased respiratory variation of the transmitral (30%) and transtricuspid Doppler flow velocity (50%), suggesting presence of constrictive physiology. Subsequently, CMR is performed, which confirms inflammatory thickening of the pericardial layers (Figure 6A). Based on these findings, antiinflammatory therapy is initiated with gradual improvement of the patient’s symptoms. Open in Viewer Figure 6.A, Basal short-axis steady-state free precession sequence cine image demonstrating a complex organized pericardial effusion with stranding (arrow), separating the thickened visceral and parietal pericardium. B, Multiplanar reconstruction of a basal short-axis slice on a postcontrast cardiac CT in a patient with severe postpericardiectomy Dressler syndrome. CT was performed because of ongoing chest pain, shortness of breath, and echocardiographic features suggesting constriction. There is an organized pericardial effusion (CT attenuation values 35 to 50 HU), measuring 8 mm in thickness (asterisk), with enhancement of the pericardial layers (arrows) indicating subacute pericarditis. RV indicates right ventricle; LV, left ventricle; and RVOT, right ventricular outflow tract. Effusive constrictive pericarditis is a relatively uncommon pericardial syndrome, characterized by impaired diastolic filling due to concomitant tamponade caused by a tense effusion and constriction by the visceral pericardium.25,26 Constrictive hemodynamics typically persist in these patients after the pericardial fluid has been removed or resolved. Based on the results of a consecutive series reported by Sagrista-Sauleda,27 effusive constrictive pericarditis may have a prevalence close to 8% in patients presenting with cardiac tamponade. Most commonly associated with idiopathic pericarditis, effusive constrictive pericarditis can also be caused by malignancies or radiation. Effusive constrictive pericarditis is difficult to diagnose by echocardiography at the time of presentation with tamponade. The diagnosis is therefore traditionally made by cardiac catheterization (either after but ideally at the time of pericardiocentesis). Failure of the right atrial pressure to fall ≥50% after the intrapericardial pressure has been lowered to near 0 mm Hg (in other words, an increase in right atrial transmural pressure after pericardiocentesis) and the finding of a diastolic ventricular dip and plateau morphology have been considered diagnostic hemodynamic criteria.26 When to Consider Added Imaging? Catheterization at the time of pericardiocentesis is not always feasible. The diagnosis of effusive constrictive pericarditis is therefore increasingly being made by noninvasive imaging techniques. Echocardiography performed after pericardiocentesis will not only confirm effective removal of pericardial fluid but will also enable screening for the presence of residual constrictive physiology. However, the presence of abnormal pericardial thickening or inflammation on the other hand is best demonstrated by CT or CMR (Figure 6). Similar to transient constrictive pericarditis, patients with idiopathic effusive constrictive pericarditis may experience gradual improvement of their symptomatic process (either spontaneously or after treatment with antiinflammatory agents).26 By documenting resolution of the inflammatory process, CMR may potentially provide important prognostic information with respect to the need for future pericardiectomy. However, this remains to be tested in subsequent studies. Pericardial Cysts Pericardial cysts are encapsulated structures most commonly located in the right anterior cardiophrenic angle, although they can be found throughout the mediastinum. Generally congenital in origin, pericardial cysts are also occasionally seen after previous cardiac surgery. These cystic structures are usually asymptomatic unless they cause compression of adjacent structures. When to Consider Added Imaging? Pericardial cysts are commonly detected first by plain chest radiography or echocardiography, but additional imaging by CT or CMR is often helpful to obtain a better idea of their exact size, location, and relation with the surrounding anatomy, particularly when a decision needs to be made whether to intervene on these lesions. Pericardial cysts typically appear as thin-walled, unilocular nonenhancing structures, with near water attenuation values by CT (Figure 7). On CMR, they usually demonstrate a low signal intensity on T1-weighted images (unless the content of the cyst is proteinaceous)27 and a high signal intensity on T2-weighted STIR images (Figure 7). Pericardial cysts are generally benign, although it is important to recognize possible associated soft-tissue components that can be related to a malignant process. Open in Viewer Figure 7.Pericardial cysts can be diagnosed on both CT and CMR. Simple cysts have a characteristic Hounsfield unit range (0 to 20 HU) on cardiac CT imaging (A). Simple cysts are typically of low to intermediate signal intensity on T2-weighted black blood spin-echo images (B), high signal intensity on T2-weighted STIR sequences, or fat-suppressed images (C) and have no gadolinium uptake on late gadolinium enhancement imaging (D). Pericardial Tumors Neoplastic involvement of the pericardium in patients with an established malignancy can occur by hematogenous or lymphatic spread but also by direct invasion from the lung or mediastinum. Although commonly detected during autopsy, pericardial metastatic disease frequently goes unnoticed until late in the disease process when patients may present with symptoms related to pericarditis or even tamponade. The most common causes of metastatic pericardial disease are breast and lung cancers, followed by renal cell carcinomas, lymphomas, and melanomas. Primary pericardial tumors are much more uncommon, with mesothelioma (usually presenting as a pericardial effusion accompanied by pericardial nodules or plaques) and sarcomas (appearing as heterogeneous masses often associated with a serosanguineous effusion) being the most frequent. Benign tumors include fibromas, lipomas, hemangiomas, and benign teratomas. When to Consider Added Imaging? Although echocardiography may be appropriate to screen for malignant involvement of the pericardium or to monitor serial changes in the size of a malignant effusion, CT or CMR is generally necessary to accurately delineate the tumor implantation and to better evaluate the extent of tumor spread (Figure 8). Disruption of the pericardial lining, presence of an associated hemorrhagic effusion, and invasion of the tumor into the epicardial fat tissue, myocardium, or into a cardiac chamber (rather than causing displacement of these structures) are characteristics of a lesion with an aggressive nature. Associated lymphadenopathy is another important finding suggesting malignancy. Open in Viewer Figure 8.A 20-year-old man with a previous resection of cardiac synovial cell sarcoma of the left and right ventricles presents with a recurrence in his pericardium (arrow). The mass has intermediate signal intensity on black blood T2 spin-echo (A) and steady-state free precession sequence cine images (B) and has high signal intensity on T2 STIR spin-echo images (C). Tissue characterization with cardiac CMR is superior to cardiac CT and echocardiography. CMR can differentiate tumor from thrombus; characterize fatty tumors such as lipomas or liposarcomas (high signal intensity both on T1- and T2-weighted images with a characteristic signal reduction by fat suppressed inversion recovery sequences); and is often helpful to assess the perfusion of a pericardial mass with the use of gadolinium contrast. Sites of malignant disease usually demonstrate high signal intensity on T2-weighted STIR imaging and late gadolinium enhancement images (Figure 8). Conclusion Clinicians increasingly rely on cardiac imaging in the diagnostic workup of patients with pericardial disease. Continuous advances in cardiac CT and CMR technology allow for an excellent visualization and characterization of pericardial pathology, making these tomographic techniques complimentary to echocardiography. An integrated multimodality imaging strategy is sometimes needed to answer specific clinical questions, but the rational use of such an approach also requires good knowledge of the strengths and limitations of each technique. Given the paucity of evidence-based guidelines, more clinical studies are needed to better define the role of cardiac imaging in the management of patients with pericardial disease. Acknowledgments The authors would like to thank Marie Campbell for her assistance with this manuscript. Disclosures None. Footnote The online-only Data Supplement is available at Supplemental Material File(hci200137-role_of_multimodality_imaging_movie_clip_four_3-12-2010.avi) Download 6.76 MB File(hci200137-role_of_multimodality_imaging_movie_clip_one_3-12-2010.avi) Download 3.72 MB File(hci200137-role_of_multimodality_imaging_movie_clip_three_3-12-2010.avi) Download 4.72 MB File(hci200137-role_of_multimodality_imaging_movie_clip_two_3-12-2010.avi) Download 5.35 MB File(verhaert_333.pdf) Download 2.93 MB References 1. Maisch B, Seferović PM, Ristić AD, Erbel R, Rienmüller R, Adler Y, Tomkowski WZ, Thiene G, Yacoub MH. Task Force on the Diagnosis and Management of Pericardial Diseases of the European Society of Cardiology. Guidelines on the diagnosis and management of pericardial diseases executive summary. Eur Heart J . 2004; 25: 587–610. Crossref PubMed Google Scholar a [...] confirm the initial clinical suspicion. b [...] difficult to manage pericardial patient. c [...] worsening with inspiration or when supine. d [...] of neoplastic invasion of the pericardium. e [...] (>2 cm with compression of the heart). f [...] of fluid in the intrapericardial space. g [...] shock or pulseless electric activity. h [...] due to loss of pericardial compliance. 2. Spodick DH. Pericarditis, pericardial effusion, cardiac tamponade, and constriction. Crit Care Clin . 1989; 5: 455–476. Go to Citation Crossref PubMed Google Scholar 3. Troughton RW, Asher CR, Klein AL. Pericarditis. Lancet . 2004; 363: 717–727. Go to Citation Crossref PubMed Google Scholar 4. Lange RA, Hillis LD. Clinical practice: acute pericarditis. N Engl J Med . 2004; 351: 2195–2202. Crossref PubMed Google Scholar 5. Little WC, Freeman GL. Pericardial disease. Circulation . 2006; 113: 1622–1632. Crossref PubMed Google Scholar 6. Imazio M, Cecchi E, Demichelis B, Ierna S, Demarie D, Ghisio A, Pomari F, Coda L, Belli R, Trinchero R. Indicators of poor prognosis of acute pericarditis. Circulation . 2007; 115: 2739–2744. Go to Citation Crossref PubMed Google Scholar 7. Breen JF. Imaging of the pericardium. J Thorac Imaging . 2001; 16: 47–54. Crossref PubMed Google Scholar a [...] effusions from pericardial thickening. b [...] or high signal intensity on T1 sequences. 8. Spodick DH. Acute cardiac tamponade. N Engl J Med . 2003; 349: 684–690. Go to Citation Crossref PubMed Google Scholar 9. Shabetai R. Pericardial effusion: haemodynamic spectrum. Heart . 2004; 90: 255–256. Crossref PubMed Google Scholar 10. Reydel B, Spodick DH. Frequency and significance of chamber collapses during cardiac tamponade. Am Heart J . 1990; 119: 1160–1163. Go to Citation Crossref PubMed Google Scholar 11. Himelman RB, Kircher B, Rockey DC, Schiller NB. Inferior vena cava plethora with blunted respiratory response: a sensitive echocardiographic sign of cardiac tamponade. J Am Coll Cardiol . 1988; 12: 1470–1477. Go to Citation Crossref PubMed Google Scholar 12. Appleton CP, Hatle LK, Popp RL. Cardiac tamponade and pericardial effusion: respiratory variation in transvalvular flow velocities studied by Doppler echocardiography. J Am Coll Cardiol . 1988; 11: 1020–1030. Go to Citation Crossref PubMed Google Scholar 13. Berge KH, Lanier WL, Reeder GS. Occult cardiac tamponade detected by transesophageal echocardiography. Mayo Clin Proc . 1992; 67: 667–670. Go to Citation Crossref PubMed Google Scholar 14. Oh KY, Shimizu M, Edwards WD, Tazelaar HD, Danielson GK. Surgical pathology of the parietal pericardium: a study of 344 cases (1993–1999). Cardiovasc Pathol . 2001; 10: 157–168. Crossref PubMed Google Scholar 15. Bertog SC, Thambidorai SK, Parakh K, Schoenhagen P, Ozduran V, Houghtaling PL, Lytle BW, Blackstone EH, Lauer MS, Klein AL. Constrictive pericarditis: etiology and cause-specific survival after pericardiectomy. J Am Coll Cardiol . 2004; 43: 1445–1452. Go to Citation Crossref PubMed Google Scholar 16. Shabetai R, Fowler NO, Guntheroth WG. The hemodynamics of cardiac tamponade and constrictive pericarditis. Am J Cardiol . 1970; 26: 480–489. Go to Citation Crossref PubMed Google Scholar 17. Hatle LK, Appleton CP, Popp RL. Differentiation of constrictive pericarditis and restrictive cardiomyopathy by Doppler echocardiography. Circulation . 1989; 79: 357–370. Go to Citation Crossref PubMed Google Scholar 18. Oh JK, Hatle LK, Seward JB, Danielson GK, Schaff HV, Reeder GS, Tajik AJ. Diagnostic role of Doppler echocardiography in constrictive pericarditis. J Am Coll Cardiol . 1994; 23: 154–162. Crossref PubMed Google Scholar 19. Garcia MJ, Rodriguez L, Ares M, Griffin BP, Thomas JD, Klein AL. Differentiation of constrictive pericarditis from restrictive cardiomyopathy: assessment of left ventricular diastolic velocities in longitudinal axis by Doppler tissue imaging. J Am Coll Cardiol . 1996; 27: 108–114. Go to Citation Crossref PubMed Google Scholar 20. Rajagopalan N, Garcia MJ, Rodriguez L, Murray RD, Apperson-Hansen C, Stugaard M, Thomas JD, Klein AL. Comparison of new Doppler echocardiographic methods to differentiate constrictive pericardial heart disease and restrictive cardiomyopathy. Am J Cardiol . 2001; 87: 86–94. Crossref PubMed Google Scholar 21. Oh JK, Tajik AJ, Appleton CP, Hatle LK, Nishimura RA, Seward JB. Preload reduction to unmask the characteristic Doppler features of constrictive pericarditis: a new observation. Circulation . 1997; 95: 796–799. Go to Citation Crossref PubMed Google Scholar 22. Talreja DR, Edwards WD, Danielson GK, Schaff HV, Tajik AJ, Tazelaar HD, Breen JF, Oh JK. Constrictive pericarditis in 26 patients with histologically normal pericardial thickness. Circulation . 2003; 108: 1852–1857. Go to Citation Crossref PubMed Google Scholar 23. Talreja DR, Nishimura RA, Oh JK, Holmes DR. Constrictive pericarditis in the modern era: novel criteria for diagnosis in the cardiac catheterization laboratory. J Am Coll Cardiol . 2008; 51: 315–319. Go to Citation Crossref PubMed Google Scholar 24. Kamdar AR, Meadows TA, Roselli EE, Gorodeski EZ, Curtin RJ, Sabik JF, Schoenhagen P, White RD, Lytle BW, Flamm SD, Desai MY. Multidetector computed tomographic angiography in planning of reoperative cardiothoracic surgery. Ann Thorac Surg . 2008; 85: 1239–1245. Go to Citation Crossref PubMed Google Scholar 25. Hancock EW. Subacute effusive-constrictive pericarditis. Circulation . 1971; 43: 183–192. Go to Citation Crossref PubMed Google Scholar 26. Sagrista-Sauleda J, Angel J, Sanchez A, Permanyer-Miralda G, Soler-Soler J. Effusive-constrictive pericarditis. N Engl J Med . 2004; 350: 469–475. Crossref PubMed Google Scholar a [...] considered diagnostic hemodynamic criteria. b [...] treatment with antiinflammatory agents). 27. Wang ZJ, Reddy GP, Gotway MB, Yeh BM, Hetts SW, Higgins CB. CT and MR imaging of pericardial disease. Radiographics . 2003; 23: S167–S180. Crossref PubMed Google Scholar a [...] series reported by Sagrista-Sauleda, b [...] the content of the cyst is proteinaceous) Show all references eLetters eLetters should relate to an article recently published in the journal and are not a forum for providing unpublished data. Comments are reviewed for appropriate use of tone and language. Comments are not peer-reviewed. Acceptable comments are posted to the journal website only. Comments are not published in an issue and are not indexed in PubMed. Comments should be no longer than 500 words and will only be posted online. References are limited to 10. Authors of the article cited in the comment will be invited to reply, as appropriate. Comments and feedback on AHA/ASA Scientific Statements and Guidelines should be directed to the AHA/ASA Manuscript Oversight Committee via its Correspondence page. Sign In to Submit a Response to This Article Information & Authors Information Authors Information Published In Circulation: Cardiovascular Imaging Volume 3 • Number 3 • May 2010 Pages: 333 - 343 PubMed: 20484113 Copyright © 2010. History Published online: 1 May 2010 Published in print: May 2010 Permissions Request permissions for this article. Request permissions Keywords pericardial disease echocardiography CT CMR multimodality imaging Subjects Computerized Tomography (CT) Echocardiography Pericardial Disease Notes Received November 12, 2009; accepted March 19, 2010. Authors Affiliations Expand All David Verhaert, MD From the Cleveland Clinic, Cleveland, Ohio. View all articles by this author Ruvin S.Gabriel, MBChB From the Cleveland Clinic, Cleveland, Ohio. View all articles by this author Douglas Johnston, MD From the Cleveland Clinic, Cleveland, Ohio. View all articles by this author Bruce W.Lytle, MD From the Cleveland Clinic, Cleveland, Ohio. View all articles by this author Milind Y.Desai, MD From the Cleveland Clinic, Cleveland, Ohio. View all articles by this author Allan L.Klein, MD From the Cleveland Clinic, Cleveland, Ohio. View all articles by this author Notes Correspondence to Allan L. Klein, MD, Center for the Diagnosis and Treatment of Pericardial Diseases, Heart and Vascular Institute, Department of Cardiovascular Medicine, Cleveland Clinic, 9500 Euclid Ave, Desk J1-5, Cleveland, OH 44195. E-mail kleina@ccf.org Metrics & Citations Metrics Citations 158 Metrics Article Metrics View all metrics Downloads Citations No data available. 29,551 159 Total 6 Months 12 Months Total number of downloads and citations See more details Posted by 1 X users Referenced in 3 clinical guideline sources 127 readers on Mendeley Citations Download Citations If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Select your manager software from the list below and click Download. Please select your download format: [x] Direct Import Hanyun Yi, Yongnan Li, Qiming Zhao, Xiangyang Wu, Commando procedure in cardiac surgery: a narrative review, General Thoracic and Cardiovascular Surgery, (2025). Crossref Felipe Aluja‐Jaramillo, Omar Andrés Pantoja‐Burbano, Fernando R. Gutiérrez, Carlos Previgliano, Sanjeev Bhalla, Radiological Insights Into the Pericardium: A Comprehensive Review, Journal of Medical Imaging and Radiation Oncology, 69, 4, (468-475), (2025). Crossref Pouya Ebrahimi, Homa Taheri, Pegah Bahiraie, Florian Rader, Robert J. Siegel, Mohammad Hosein Mandegar, Kaveh Hosseini, Farhan Shahid, Incidence of secondary pericardial effusions associated with different etiologies: a comprehensive review of literature, Journal of Cardiothoracic Surgery, 20, 1, (2025). Crossref K. M. Beseliia, Z. M. Magomedova, F. Kh. Eldzharkieva, M. S. Dolgaya, D. Yu. Shchekochikhin, E. S. Pershina, A. A. Bogdanova, A. N. Volovchenko, D. A. Andreev, Potential of Magnetic Resonance Imaging in Diagnostics of Transient Constrictive Pericarditis, Kardiologiia, 65, 1, (67-72), (2025). Crossref Nawaf Alotaibi, Faisal Almutawa, Alwaleed Alhazzaa, Ihab Suliman, Tuberculous Pericarditis in an Immunocompromised Patient: A Case Report, Cureus, (2024). Crossref Rehan Karmali, Tahir S. Kafil, Aqieda Bayat, Bianca Honnekeri, Osamah Badwan, Felix Berglund, Paul Cremer, Allan L. Klein, Recurrent Pericarditis and Paradigm Shift in Cardiovascular Imaging and Targeted Therapeutics, JACC: Advances, 3, 9, (101194), (2024). Crossref Allan L. Klein, Tom Kai Ming Wang, Paul C. Cremer, Antonio Abbate, Yehuda Adler, Craig Asher, Antonio Brucato, Michael Chetrit, Brian Hoit, Christine L. Jellis, Deborah H. Kwon, Martin LeWinter, David Lin, Sushil Allen Luis, Vartan Mardigyan, Jae K. Oh, Karen G. Ordovas, E. Rene Rodriugez, Aldo L. Schenone, Carmela D. Tan, Brittany Weber, Massimo Imazio, Pericardial Diseases, JACC: Cardiovascular Imaging, 17, 8, (937-988), (2024). Crossref Muhammad Hamza Tahir, Sidra Sohail, Daniyal Shahid, Iqbal Hussain, Jahanzeb Malik, Syeda Iqra, Maria Faraz, Postcardiac Injury Syndrome After Cardiac Surgery: An Evidence-Based Review, Cardiology in Review, (2024). Crossref Ujjwal K. Chowdhury, Lakshmi Kumari Sankhyan, Ujjwal K. Chowdhury, Lakshmi Kumari Sankhyan, Diseases Mimicking Constrictive Pericarditis: Salient Features and Novel Strategies of Management, Surgical Treatment of Chronic Constrictive Pericarditis, (143-185), (2023). Crossref Ujjwal K. Chowdhury, Lakshmi Kumari Sankhyan, Ujjwal K. Chowdhury, Lakshmi Kumari Sankhyan, Management of Chronic Constrictive Pericarditis, Surgical Treatment of Chronic Constrictive Pericarditis, (199-215), (2023). Crossref See more Loading... View Options View options PDF and All Supplements Download PDF and All Supplements Download is in progress PDF/EPUB View PDF/EPUB Figures Open all in viewer Figure 1.CMR and TTE before and after 6 weeks of high-dose ibuprofen and colchicine. Before treatment, thickened, inflamed pericardium (arrows) appears as low to intermediate signal intensity adjacent to the high signal intensity epicardial fat in black blood T2-weighted turbo spin-echo (A), intermediate signal intensity in steady-state free precession sequence cine images (B), and enhances bright on late gadolinium enhancement imaging (C). Posttreatment is associated with resolution of pericardial thickening (D and E) and inflammation on late gadolinium enhancement imaging (F). By comparison, the parasternal long-axis echocardiographic image of the same patient before and after treatment is shown in G and H. Although a small, organized effusion (black arrows) could be noted posteriorly before therapy (G, arrow), the presence and resolution of pericardial inflammation are much better demonstrated by CMR. Go to FigureOpen in Viewer Figure 2.Suggested diagnostic approach to investigate acute pericarditis and its complications from an imaging perspective. ESR indicates erythrocyte sedimentation rate; NSAIDs, nonsteroidal antiinflammatory drugs; TTE, transthoracic echocardiogram; and TEE, transesophageal echocardiogram. Go to FigureOpen in Viewer Figure 3.Classic anatomic findings of pericardial constriction by CMR and CT. CMR findings of constriction demonstrated in black blood T2-weighted spin-echo (A) and steady-state free precession sequence cine sequence (B) in the horizontal long-axis view. Pericardial thickening (6 mm) is seen adjacent to the right atrium and ventricle (arrow), with characteristic tubular deformity of the right and left ventricles (RV/LV) and dilation of the right atrium. Other contributory findings by CMR (not illustrated here) are tethering of the underlying myocardium to the pericardium (demonstrated on tagged gradient echo cine sequences), a diastolic septal bounce, and subjective abrupt cessation of diastolic filling on steady-state free precession sequence cine images. C, Cardiac CT demonstrating the presence of circumferential pericardial calcification on a multiplanar reconstructed short-axis image (arrows). D, Three-dimensional volume-rendered imaging showing the extent and anatomic distribution of pericardial calcium. Go to FigureOpen in Viewer Figure 4.Suggested diagnostic approach for the evaluation of patients with constrictive pericarditis. LV indicates left ventricular; RV, Right ventricular; TEE, transesophageal echocardiogram; and TTE, transthoracic echocardiogram. Go to FigureOpen in Viewer Figure 5.A, M-mode recording in the parasternal long-axis view showing a respiratory shift of the interventricular septum toward the left ventricle with inspiration and toward the right ventricle with expiration as a result of exaggerated ventricular interdependence. Small yellow arrow denotes the early diastolic septal bounce, typically seen in constrictive pericarditis. There is flattening of the posterior left ventricular wall during diastole (white arrows). B, Pulsed wave Doppler echocardiography of the mitral valve with simultaneous respirometry. Constrictive pericarditis is characterized by dissociation of intrathoracic and intracardiac pressures, resulting in an increase in diastolic driving pressure into the left ventricle with expiration, and a decrease with inspiration. This leads to marked (>25%) respiratory changes of early mitral inflow velocity (E). C, Tricuspid inflow velocity, showing the opposite changes. Tricuspid valve early diastolic velocity E increases with inspiration and decreases with expiration. D, The early diastolic septal mitral annular velocity E′ (in this case 14 cm/s) is usually increased in patients with constriction because diastolic filling occurs predominantly by longitudinal relaxation. However, adherence of the pericardium to the basolateral wall may occasionally inhibit normal or decreased motion of the lateral mitral annulus. A′ indicates late diastolic mitral annular velocity; E′, early diastolic mitral annular velocity; EXP, expiration; INSP, inspiration; IVS, interventricular septum; LV, left ventricle; PW, posterior wall; RV, right ventricle; and S′, systolic mitral annular velocity. Go to FigureOpen in Viewer Figure 6.A, Basal short-axis steady-state free precession sequence cine image demonstrating a complex organized pericardial effusion with stranding (arrow), separating the thickened visceral and parietal pericardium. B, Multiplanar reconstruction of a basal short-axis slice on a postcontrast cardiac CT in a patient with severe postpericardiectomy Dressler syndrome. CT was performed because of ongoing chest pain, shortness of breath, and echocardiographic features suggesting constriction. There is an organized pericardial effusion (CT attenuation values 35 to 50 HU), measuring 8 mm in thickness (asterisk), with enhancement of the pericardial layers (arrows) indicating subacute pericarditis. RV indicates right ventricle; LV, left ventricle; and RVOT, right ventricular outflow tract. Go to FigureOpen in Viewer Figure 7.Pericardial cysts can be diagnosed on both CT and CMR. Simple cysts have a characteristic Hounsfield unit range (0 to 20 HU) on cardiac CT imaging (A). Simple cysts are typically of low to intermediate signal intensity on T2-weighted black blood spin-echo images (B), high signal intensity on T2-weighted STIR sequences, or fat-suppressed images (C) and have no gadolinium uptake on late gadolinium enhancement imaging (D). Go to FigureOpen in Viewer Figure 8.A 20-year-old man with a previous resection of cardiac synovial cell sarcoma of the left and right ventricles presents with a recurrence in his pericardium (arrow). The mass has intermediate signal intensity on black blood T2 spin-echo (A) and steady-state free precession sequence cine images (B) and has high signal intensity on T2 STIR spin-echo images (C). Go to FigureOpen in Viewer Tables Open all in viewer Table 1. Strengths and Limitations of Various Imaging Modalities in the Evaluation of Pericardial Disease Go to TableOpen in Viewer Table 2. Protocols and Findings for the Evaluation of Pericardial Disease by Different Imaging Modalities Go to TableOpen in Viewer Media Share Share Share article link Copy Link Copied! Copying failed. Share FacebookX (formerly Twitter)LinkedInemail References References 1. Maisch B, Seferović PM, Ristić AD, Erbel R, Rienmüller R, Adler Y, Tomkowski WZ, Thiene G, Yacoub MH. Task Force on the Diagnosis and Management of Pericardial Diseases of the European Society of Cardiology. Guidelines on the diagnosis and management of pericardial diseases executive summary. Eur Heart J . 2004; 25: 587–610. Crossref PubMed Google Scholar a [...] confirm the initial clinical suspicion. b [...] difficult to manage pericardial patient. c [...] worsening with inspiration or when supine. d [...] of neoplastic invasion of the pericardium. e [...] (>2 cm with compression of the heart). f [...] of fluid in the intrapericardial space. g [...] shock or pulseless electric activity. h [...] due to loss of pericardial compliance. 2. Spodick DH. Pericarditis, pericardial effusion, cardiac tamponade, and constriction. Crit Care Clin . 1989; 5: 455–476. Go to Citation Crossref PubMed Google Scholar 3. Troughton RW, Asher CR, Klein AL. Pericarditis. Lancet . 2004; 363: 717–727. Go to Citation Crossref PubMed Google Scholar 4. Lange RA, Hillis LD. Clinical practice: acute pericarditis. N Engl J Med . 2004; 351: 2195–2202. Crossref PubMed Google Scholar 5. Little WC, Freeman GL. Pericardial disease. Circulation . 2006; 113: 1622–1632. Crossref PubMed Google Scholar 6. Imazio M, Cecchi E, Demichelis B, Ierna S, Demarie D, Ghisio A, Pomari F, Coda L, Belli R, Trinchero R. Indicators of poor prognosis of acute pericarditis. Circulation . 2007; 115: 2739–2744. Go to Citation Crossref PubMed Google Scholar 7. Breen JF. Imaging of the pericardium. J Thorac Imaging . 2001; 16: 47–54. Crossref PubMed Google Scholar a [...] effusions from pericardial thickening. b [...] or high signal intensity on T1 sequences. 8. Spodick DH. Acute cardiac tamponade. N Engl J Med . 2003; 349: 684–690. Go to Citation Crossref PubMed Google Scholar 9. Shabetai R. Pericardial effusion: haemodynamic spectrum. Heart . 2004; 90: 255–256. Crossref PubMed Google Scholar 10. Reydel B, Spodick DH. Frequency and significance of chamber collapses during cardiac tamponade. Am Heart J . 1990; 119: 1160–1163. Go to Citation Crossref PubMed Google Scholar 11. Himelman RB, Kircher B, Rockey DC, Schiller NB. Inferior vena cava plethora with blunted respiratory response: a sensitive echocardiographic sign of cardiac tamponade. J Am Coll Cardiol . 1988; 12: 1470–1477. Go to Citation Crossref PubMed Google Scholar 12. Appleton CP, Hatle LK, Popp RL. Cardiac tamponade and pericardial effusion: respiratory variation in transvalvular flow velocities studied by Doppler echocardiography. J Am Coll Cardiol . 1988; 11: 1020–1030. Go to Citation Crossref PubMed Google Scholar 13. Berge KH, Lanier WL, Reeder GS. Occult cardiac tamponade detected by transesophageal echocardiography. Mayo Clin Proc . 1992; 67: 667–670. Go to Citation Crossref PubMed Google Scholar 14. Oh KY, Shimizu M, Edwards WD, Tazelaar HD, Danielson GK. Surgical pathology of the parietal pericardium: a study of 344 cases (1993–1999). Cardiovasc Pathol . 2001; 10: 157–168. Crossref PubMed Google Scholar 15. Bertog SC, Thambidorai SK, Parakh K, Schoenhagen P, Ozduran V, Houghtaling PL, Lytle BW, Blackstone EH, Lauer MS, Klein AL. Constrictive pericarditis: etiology and cause-specific survival after pericardiectomy. J Am Coll Cardiol . 2004; 43: 1445–1452. Go to Citation Crossref PubMed Google Scholar 16. Shabetai R, Fowler NO, Guntheroth WG. The hemodynamics of cardiac tamponade and constrictive pericarditis. Am J Cardiol . 1970; 26: 480–489. Go to Citation Crossref PubMed Google Scholar 17. Hatle LK, Appleton CP, Popp RL. Differentiation of constrictive pericarditis and restrictive cardiomyopathy by Doppler echocardiography. Circulation . 1989; 79: 357–370. Go to Citation Crossref PubMed Google Scholar 18. Oh JK, Hatle LK, Seward JB, Danielson GK, Schaff HV, Reeder GS, Tajik AJ. Diagnostic role of Doppler echocardiography in constrictive pericarditis. J Am Coll Cardiol . 1994; 23: 154–162. Crossref PubMed Google Scholar 19. Garcia MJ, Rodriguez L, Ares M, Griffin BP, Thomas JD, Klein AL. Differentiation of constrictive pericarditis from restrictive cardiomyopathy: assessment of left ventricular diastolic velocities in longitudinal axis by Doppler tissue imaging. J Am Coll Cardiol . 1996; 27: 108–114. Go to Citation Crossref PubMed Google Scholar 20. Rajagopalan N, Garcia MJ, Rodriguez L, Murray RD, Apperson-Hansen C, Stugaard M, Thomas JD, Klein AL. Comparison of new Doppler echocardiographic methods to differentiate constrictive pericardial heart disease and restrictive cardiomyopathy. Am J Cardiol . 2001; 87: 86–94. Crossref PubMed Google Scholar 21. Oh JK, Tajik AJ, Appleton CP, Hatle LK, Nishimura RA, Seward JB. Preload reduction to unmask the characteristic Doppler features of constrictive pericarditis: a new observation. Circulation . 1997; 95: 796–799. Go to Citation Crossref PubMed Google Scholar 22. Talreja DR, Edwards WD, Danielson GK, Schaff HV, Tajik AJ, Tazelaar HD, Breen JF, Oh JK. Constrictive pericarditis in 26 patients with histologically normal pericardial thickness. Circulation . 2003; 108: 1852–1857. Go to Citation Crossref PubMed Google Scholar 23. Talreja DR, Nishimura RA, Oh JK, Holmes DR. Constrictive pericarditis in the modern era: novel criteria for diagnosis in the cardiac catheterization laboratory. J Am Coll Cardiol . 2008; 51: 315–319. Go to Citation Crossref PubMed Google Scholar 24. Kamdar AR, Meadows TA, Roselli EE, Gorodeski EZ, Curtin RJ, Sabik JF, Schoenhagen P, White RD, Lytle BW, Flamm SD, Desai MY. Multidetector computed tomographic angiography in planning of reoperative cardiothoracic surgery. Ann Thorac Surg . 2008; 85: 1239–1245. Go to Citation Crossref PubMed Google Scholar 25. Hancock EW. Subacute effusive-constrictive pericarditis. Circulation . 1971; 43: 183–192. Go to Citation Crossref PubMed Google Scholar 26. Sagrista-Sauleda J, Angel J, Sanchez A, Permanyer-Miralda G, Soler-Soler J. Effusive-constrictive pericarditis. N Engl J Med . 2004; 350: 469–475. Crossref PubMed Google Scholar a [...] considered diagnostic hemodynamic criteria. b [...] treatment with antiinflammatory agents). 27. Wang ZJ, Reddy GP, Gotway MB, Yeh BM, Hetts SW, Higgins CB. CT and MR imaging of pericardial disease. Radiographics . 2003; 23: S167–S180. Crossref PubMed Google Scholar a [...] series reported by Sagrista-Sauleda, b [...] the content of the cyst is proteinaceous) Advertisement Recommended July 2016 A Rare Pericardial Malignancy Urooj Fatima, Sarika Gupta, Dennis J. Firchau, Alan H. Stolpen, and [...] Rajan Sah +1 authors June 2002 Management of Effusive and Constrictive Pericardial Heart Disease [...] Brian D. Hoit +0 authors March 2006 Pericardial Disease William C. Littleand [...] Gregory L. 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https://www.ucd.ie/mathstat/t4media/NotesProblemsinCombinatoricsOliverNash.pdf
UCD Maths Enrichment: The ‘double counting trick’ for combinatorial problems. Oliver Nash March 28, 2020 1 Bipartite graphs A graph is a set of vertices connected by edges. Figure 1 gives two examples of graphs. For some counting-type problems, it can help to organise data using what’s called a bipartite graph. A bipartite graph is just a graph where the vertices are split into two different groups and the edges only connect vertices from one group to the other, i.e., there is never an edge between two vertices of the same group. The graph on the right-hand side in figure 1 has a bipartite grouping. It is often very convenient to represent a finite bipartite using a rectangu-lar grid of numbers, called its matrix, with rows corresponding to one set of vertices and columns corresponding to the other set of vertices. For example the following matrix represents the bipartite graph on the right-hand side of Figure 1: the graph on the right has a bipartite grouping 1 figure 1, taking the five vertices grouped as U for rows and the four vertices grouped as V for columns:       1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1       Sometimes the edges naturally come with labels (often called colours) and this fits nicely with the matrix representation. Useful questions to ask yourself when faced with counting problems like the ones discussed below are: 1. What am I being asked to count? 2. If I were to represent the things I am being asked to count as the edges of a bipartite graph, what would be the rows and columns of its matrix? If you manage to provide answers to the above then the ‘trick’ is that you can often make progress by noting that a row-wise count is the same as a column-wise count. 2 Handshaking lemma Suppose we have a graph G with E edges and vertices v1, v2, . . . , vn, then: d(v1) + d(v2) + · · · + d(vn) = 2E, (1) where d(vi) is the number of edges through vertex vi. rows: vertices of G columns: edges of G 3 Counting solutions Example 3.1. Suppose that 17 contestants took part in a mathematics com-petition with 9 problems. Each problem was solved by exactly 11 contestants. Show that there exists a pair of contestants who, between them, solved all 9 problems1. 1These examples are based on 2 rows: problems columns: unordered pairs of contestants Exercise 3.2. Suppose that c contestants took part in a mathematics com-petition with p problems, and that each problem was solved by at least k contestants. Show that there exists a pair of contestants who, between them, solved all p problems provided: p < c(c −1) d(d −1), where d = c −k. Example 3.3. Suppose that 15 contestants took part in a mathematics com-petition with 15 problems. Each contestant solved exactly 6 problems. Show that there exists a pair of contestants who solved at least 3 problems in com-mon. Exercise 3.4. Suppose that c contestants took part in a mathematics com-petition with p problems. Each contestant solved at least s problems, and p divides evenly into cs. Show that there exists a pair of contestants who solved at least k problems in common, for some: k ≥s(cs −p) p(c −1) . Exercise 3.5. What about when p does not divide evenly into cs? 4 IMO 1998 Q2 Example 4.1. In a competition, there are a contestants and b judges, where b ≥3 is an odd integer. Each judge rates each contestant as either ‘pass’ or ‘fail’. Suppose k is a number such that, for any two judges, their ratings coincide for at most k contestants. Prove that k/a ≥(b −1)/(2b). rows: contestants columns: unordered pairs of judges Exercise 4.2. State and prove the corresponding statement if b is even. It is useful to look at the results of this question to see how contestants performed when the exam took place back in 1998. The vast majority of contestants scored either 0 or 7! Surely this is because each contestant either knew the ‘double counting trick’ or they didn’t2. 2Knowing how contestants performed can be quite useful when practicing with past IMO questions. Try exploring 3 Figure 2: how many contestants got each score between 0 and 7 5 IMO 2001 Q3 Example 5.1. Twenty-one girls and twenty-one boys took part in a mathe-matical contest. • Each contestant solved at most six problems. • For each girl and each boy, at least one problem was solved by both of them. Prove that there was a problem that was solved by at least three girls and at least three boys. rows: girls columns: boys Exercise 5.2. Suppose that a girls and a boys took part in mathematical contest and that: • each each contestant solved at most n problems, • n > 1, • for each girl and each boy, at least one problem was solved by both of them. 4 Prove that there was a problem solved by at least x girls and at least x boys for some: x ≥ a 2(n −1). Exercise 5.3. Suppose that g girls and b boys took part in mathematical contest and that: • each girl solved at most n problems, • each boy solved at most m problems, • for each girl and each boy, at least one problem was solved by both of them. Prove that there was a problem solved by at least x girls and at least x boys for some: x ≥ gb gn + bm −min(gn, bm, g + b). Exercise 5.4. State and prove the corresponding statement if we wish to find a problem solved by at least x girls and at least y boys. Sketch the results in the x-y-plane. 6 IMO 2005 Q6 Example 6.1. In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2 5 of the contestants. Moreover, no contestant solved all the 6 problems. Show that there are at least 2 contestants who solved exactly 5 problems each. rows: contestants columns: unordered pairs of problems 7 Average number of divisors For a natural number n, let d(n) be the number of divisors of n, and let ¯ d(n) = 1 n (d(1) + d(2) + · · · d(n)) , 5 be the average of the number of divisors of all natural numbers up to n. Then3 we have: ¯ d(n) ∼Hn ∼ln n. where: Hn = 1 + 1 2 + · · · + 1 n, is the nth harmonic number (in fact we can be more precise). rows: the numbers 1, 2, . . . , n columns: the numbers 1, 2, . . . , n 8 Higher dimensions Exercise 8.1. Suppose we have a d-dimensional cube of natural numbers of shape: 100 × 400 × 900 × · · · × (10d)2, and any line parallel to an axis of the cube contains at most 21 different natural numbers. Show that the cube contains a number which appears at least 4 times in each of the d lines passing through it. You may use without proof the fact that π2 < 10. This is really a generalisation of IMO 2001 Q3. For d = 2, it is close to the original problem but don’t be confused: it’s just a coincidence the number 21 appears in both statements and it plays a different role. 3This example is taken from: Aigner M., Ziegler G.M., ‘Proofs from THE BOOK’, third edition, chapter 22, section 4, pages 142–143. 6
4003
https://www.vedantu.com/question-answer/define-skew-lines-using-only-the-vector-approach-class-12-maths-cbse-5f47ccdf7daf4560449eb83a
Talk to our experts 1800-120-456-456 Define skew lines. Using only the vector approach, find the shortest distance between the following two skew lines. $\begin{align} & \vec{r}=\left( 8+3\lambda \right)\hat{i}-\left( 9+16\lambda \right)\hat{j}+\left( 10+7\lambda \right)\hat{k} \ & \vec{r}=15\hat{i}+29\hat{j}+5\hat{k}+\mu \left( 3\hat{i}+8\hat{j}-5\hat{k} \right) \ \end{align}$ © 2025.Vedantu.com. All rights reserved
4004
https://www.emathhelp.net/calculators/calculus-2/integral-calculator/?f=4x%5E2
Integral of 4x^2 - eMathHelp | | | | | Math Calculator Calculators Notes Games Algebra Geometry Pre-Calculus Calculus Linear Algebra Discrete Math Probability/Statistics Linear Programming Home Calculators Calculators: Calculus II Calculus Calculator Integral of 4 x 2 4 x^{2}4 x 2 The calculator will find the integral/antiderivative of 4 x 2 4 x^{2}4 x 2, with steps shown. Related calculator: Definite and Improper Integral Calculator Function: Please write without any differentials such as d x dx d x, d y dy d y etc. Variable: Leave empty for autodetection. If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us. Your Input Find ∫4 x 2 d x\int 4 x^{2}\, dx∫4 x 2 d x. Solution Apply the constant multiple rule ∫c f(x)d x=c∫f(x)d x\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx∫c f(x)d x=c∫f(x)d x with c=4 c=4 c=4 and f(x)=x 2 f{\left(x \right)} = x^{2}f(x)=x 2: ∫4 x 2 d x=(4∫x 2 d x){\color{red}{\int{4 x^{2} d x}}} = {\color{red}{\left(4 \int{x^{2} d x}\right)}}∫4 x 2 d x=(4∫x 2 d x) Apply the power rule ∫x n d x=x n+1 n+1\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}∫x n d x=n+1 x n+1​(n≠−1)\left(n \neq -1 \right)(n=−1) with n=2 n=2 n=2: 4∫x 2 d x=4 x 1+2 1+2=4(x 3 3)4 {\color{red}{\int{x^{2} d x}}}=4 {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}=4 {\color{red}{\left(\frac{x^{3}}{3}\right)}}4∫x 2 d x=4 1+2 x 1+2​=4(3 x 3​) Therefore, ∫4 x 2 d x=4 x 3 3\int{4 x^{2} d x} = \frac{4 x^{3}}{3}∫4 x 2 d x=3 4 x 3​ Add the constant of integration: ∫4 x 2 d x=4 x 3 3+C\int{4 x^{2} d x} = \frac{4 x^{3}}{3}+C∫4 x 2 d x=3 4 x 3​+C Answer ∫4 x 2 d x=4 x 3 3+C\int 4 x^{2}\, dx = \frac{4 x^{3}}{3} + C∫4 x 2 d x=3 4 x 3​+C A Related Notes:Substitution (Change of Variable) Rule , Integration by Parts , Concept of Antiderivative and Indefinite Integral , Integrals Involving Trig Functions , Trigonometric Substitutions In Integrals , Integrals Involving Rational Functions , Integration Formulas (Table of Indefinite Integrals) , Properties of Indefinite Integrals , Table of Antiderivatives About Contact Terms of use Privacy Policy Copyright (c) 2025. All rights reserved.
4005
https://math.stackexchange.com/questions/1897169/function-that-describes-the-approach-of-1-1-nn-to-eulers-number-what-is-t
Function that describes the approach of (1 + 1/n)^n to Euler's number. What is the limit? - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community Mathematics helpchat Mathematics Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Function that describes the approach of (1 + 1/n)^n to Euler's number. What is the limit? Ask Question Asked 9 years, 1 month ago Modified7 years, 11 months ago Viewed 2k times This question shows research effort; it is useful and clear 1 Save this question. Show activity on this post. I will try to state the function in simple parts. First, take lim n→∞(1+1 n)n lim n→∞(1+1 n)n, then subtract e from each value of n. Make the reciprocal of this function. What is the limit of the derivative of this function? d d n lim n→∞1/(e−(1+1 n)n)d d n lim n→∞1/(e−(1+1 n)n), One way of defining Euler's number is the limit as n approaches infinity of (1 + 1/n)^n. I have used Excel to compute each value up to n = 1,000. I then calculated the inverse of the difference of e for each value of n. For n= 1, we find (1+1/1)^2=2. Then, 1/(e - 2) = 1.3922... For n = 2, we have (1+1/2)^2= 2.25. Then, (1/e-2.25) = 2.1355... This value increases as n increases, as expected. I then calculated the difference between the value and the one before it. I found that this value decreases to a point, but does not do so smoothly. When graphed after about n = 250 there is an erratic but downward trend. However, I'm not sure if this erratic behaviour is due to successive rounding errors by Excel.The average value from n = 900 to n= 1000 is 0.735758909. The series appears to converge very quickly, at just n = 5 we have 0.736817183. What is exact value of this limit? Is it related to any important constants? limits exponential-function approximation Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications edited Oct 12, 2017 at 6:09 Martin Sleziak 56.3k 20 20 gold badges 211 211 silver badges 391 391 bronze badges asked Aug 19, 2016 at 14:19 AspectionsAspections 45 5 5 bronze badges 1 3 The question as stated makes no sense (the derivative and the limit should be permuted) but lim x→∞d d x(1 e−(1+1/x)x)=2 e lim x→∞d d x(1 e−(1+1/x)x)=2 e The proof is direct using the Taylor expansion log(1+u)=u−u 2/2+o(u 2)log⁡(1+u)=u−u 2/2+o(u 2) when u→0 u→0.Did –Did 2016-08-19 14:28:55 +00:00 Commented Aug 19, 2016 at 14:28 Add a comment| 1 Answer 1 Sorted by: Reset to default This answer is useful 1 Save this answer. Show activity on this post. Basically, what you need is to quantify in a precise sense "at which rate (1+1 n)n(1+1 n)n does approach its limit e e." To do so, one of the preferred and very useful methods is to use Taylor expansions(†)(†) (1+1 n)n=e n ln(1+1 n)=e n(1 n−1 2 n 2+o(1 n 2))=e 1−1 2 n+o(1 n)=e⋅e−1 2 n+o(1 n)=e⋅(1−1 2 n+o(1 n))=e−e 2 n+o(1 n)(1+1 n)n=e n ln⁡(1+1 n)=e n(1 n−1 2 n 2+o(1 n 2))=e 1−1 2 n+o(1 n)=e⋅e−1 2 n+o(1 n)=e⋅(1−1 2 n+o(1 n))=e−e 2 n+o(1 n) so we get (1+1 n)n−e∼n→∞−e 2 n.(1+1 n)n−e∼n→∞−e 2 n. (Which means, in a formal sense, that "the difference behaves like −e 2 n−e 2 n when n n tends to ∞∞") In particular, what you appear to be considering (the way you wrote it is slightly off, the derivative should not be outside the limit) is 1 n⋅1 e−(1+1 n)n−→−−n→∞2 e.1 n⋅1 e−(1+1 n)n→n→∞2 e. Note that 2 e≃0.73575888 2 e≃0.73575888, so this is indeed consistent with your numerical experiments. (†)(†) Namely, two standard ones, to low order: ln(1+x)=x−x 2 2+o(x 2)ln⁡(1+x)=x−x 2 2+o(x 2) and e x=1+x+o(x)e x=1+x+o(x) when x→0 x→0. Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications edited Aug 19, 2016 at 14:35 answered Aug 19, 2016 at 14:28 Clement C.Clement C. 68.5k 8 8 gold badges 82 82 silver badges 171 171 bronze badges Add a comment| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions limits exponential-function approximation See similar questions with these tags. 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4006
https://math.stackexchange.com/questions/779790/alternative-characterization-max-eigenvalue
linear algebra - Alternative characterization max eigenvalue - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community Mathematics helpchat Mathematics Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Alternative characterization max eigenvalue Ask Question Asked 11 years, 5 months ago Modified11 years, 5 months ago Viewed 280 times This question shows research effort; it is useful and clear 2 Save this question. Show activity on this post. I want to see if my line of thinking is correct on the following problem (given that A A is Hermitian, the eigenvalues are in non decreasing order λ min λ min to λ max λ max, and A A has at least one positive eigenvalue): Show that λ max=max{1 x∗x∣x∗A x=1,x∈C n}.λ max=max{1 x∗x∣x∗A x=1,x∈C n}. My thought was to use the Rayleigh Quotient. We know λ max=max{x∗A x x∗x∣x∈C n}λ max=max{x∗A x x∗x∣x∈C n}. Since we know λ max λ max is positive then the first set contains the eigenvector y λ max√y λ max corresponding to λ max λ max, since y∗A y y∗y=1 y∗A y y∗y=1 . Then since the first set is a subset of {x∗A x x∗x∣x∈C n}{x∗A x x∗x∣x∈C n} and contains the maximum of that set then its maximum is λ max λ max as well. linear-algebra matrices Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications edited May 3, 2014 at 16:44 Michael Hardy 1 asked May 3, 2014 at 16:28 JonathanJonathan 21 2 2 bronze badges Add a comment| 1 Answer 1 Sorted by: Reset to default This answer is useful 1 Save this answer. Show activity on this post. Your thought is of course valid. The first observation is that we do not need to maximise all the Rayleigh quotients but only the positive ones, then it's just a simple manipulation (substitution): λ max=max y≠0 y∗A y y∗y=max y∗A y>0 y∗A y y∗y=max y∗A y>0(y∗y∗A y−−−−√y y∗A y−−−−√)−1=max x∗A x=1 1 x∗x.λ max=max y≠0 y∗A y y∗y=max y∗A y>0 y∗A y y∗y=max y∗A y>0(y∗y∗A y y y∗A y)−1=max x∗A x=1 1 x∗x. Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered May 4, 2014 at 2:45 Algebraic PavelAlgebraic Pavel 23.9k 5 5 gold badges 42 42 silver badges 66 66 bronze badges Add a comment| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions linear-algebra matrices See similar questions with these tags. Featured on Meta Introducing a new proactive anti-spam measure Spevacus has joined us as a Community Manager stackoverflow.ai - rebuilt for attribution Community Asks Sprint Announcement - September 2025 Report this ad Related 7Show that the minimum eigenvalue of a Hermitian matrix A A is less than or equal to the smallest diagonal element of A A 5Relation between Rayleigh quotient and eigenvalues for non-Hermitian matrices? 0Maximum eigenvalue of product of two matrices 0Rayleigh quotients being the diagonal entry of a matrix after orthogonal transformation 1Given A∈R n×n A∈R n×n real, symmetric, positive semidefinite matrix, find all eigenvalue and eigenvector pairs 1Lower bound on minimal eigenvalue of B(A+B)−1 A B(A+B)−1 A 0On the Rayleigh quotient of two matrices 0If A,B A,B are Hermitian, how to show that λ max(A B−1)=max x≠0 x∗A x x∗B x λ max(A B−1)=max x≠0 x∗A x x∗B x if A,B have only positive eigenvalues? 3Maximum eigenvalue of the hermitian part of a matrix Hot Network Questions What's the expectation around asking to be invited to invitation-only workshops? Determine which are P-cores/E-cores (Intel CPU) Matthew 24:5 Many will come in my name! Copy command with cs names What is a "non-reversible filter"? Direct train from Rotterdam to Lille Europe Discussing strategy reduces winning chances of everyone! Can you formalize the definition of infinitely divisible in FOL? Alternatives to Test-Driven Grading in an LLM world Is direct sum of finite spectra cancellative? alignment in a table with custom separator What were "milk bars" in 1920s Japan? Proof of every Highly Abundant Number greater than 3 is Even Checking model assumptions at cluster level vs global level? What happens if you miss cruise ship deadline at private island? The geologic realities of a massive well out at Sea Any knowledge on biodegradable lubes, greases and degreasers and how they perform long term? Repetition is the mother of learning Can I go in the edit mode and by pressing A select all, then press U for Smart UV Project for that table, After PBR texturing is done? For every second-order formula, is there a first-order formula equivalent to it by reification? If Israel is explicitly called God’s firstborn, how should Christians understand the place of the Church? Passengers on a flight vote on the destination, "It's democracy!" Triangle with Interlacing Rows Inequality [Programming] In Dwarf Fortress, why can't I farm any crops? more hot questions Question feed Subscribe to RSS Question feed To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Why are you flagging this comment? It contains harassment, bigotry or abuse. This comment attacks a person or group. Learn more in our Code of Conduct. It's unfriendly or unkind. This comment is rude or condescending. Learn more in our Code of Conduct. Not needed. This comment is not relevant to the post. Enter at least 6 characters Something else. A problem not listed above. Try to be as specific as possible. 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4007
https://www.youtube.com/watch?v=f4WvNUDSvIw
Giancoli Chapter 4 #39 Chuen-Wei Ng 325 subscribers 1 likes Description 176 views Posted: 31 Oct 2018 Transcript: hello ap physics one it's mr. Inge and a lot of you asked me about number 39 out of your homework set um it's actually not as hard as you think let's hop right into it so here is the question what is the maximum acceleration of a car that a car can undergo if the coefficient of static friction between the tires and the ground is 0.8 so um I think one of the things that really bothered us is the lack of information there's only one number does the static friction coefficient so how am I supposed to find all this other stuff you're used to a lot more numbers and that makes you feel uncomfortable you do know enough so and usually when you don't know a lot so a lot of things must cancel typically in physics the masses will cancel so for me I'm already going in here thinking like mmm I think masses might cancel so let's draw a Freebody diagram so this is about tires the this is a tire moving forward there's going to be a force of static friction alright this is the force applied or we have mg like always and then we have F normal whose magnitude is also mg right the same thing that means F of s is going to be the coefficient of static kinetic the coefficient of static friction times mg right that's the same thing as friction that's just a definition that we know so now we have a lot more to work with um and I think one of the biggest misunderstandings here is how to set it up so watch what I'm going to do I'm going to say the sum of forces is gonna equal to FS and I'm gonna make the static friction the maximum static friction is going to equal to the force applied does that make sense so I know the car is already moving forward but this static friction is talking about the grip of the tire on the ground and if the force applied is past that then the tire will slip right and sometimes that does happen we definitely seen cars kind of peel out so the highest force that can be applied is going to be that static friction it's about the tire not slipping right and then let's just make that into the MA so now we're talking about the maximum force applied is basically equal to the force of the friction right because this is before it slips and that's going to equal to MA you know I don't even need this F of a part so let's just work with the force of static friction is gonna equal to MA okay I hope that wasn't I hope that's understandable right the static friction is is equal to MA because that's the maximum force available before it starts slipping okay so now all we got to do is plug in this equation so the static coefficient times mg is equal to M a alright that makes it pretty easy the MS cancel out so all we need is the coefficient of static friction and gravity which we know is 9.8 and that is equal to our acceleration so that's gonna equal to 0.8 times 9.8 Newton's which is equal to no 9.8 not Newtons meters per second squared so let's punch this endpoint eight times nine point eight so I got seven point eight four meters per second squared see the units are correct its acceleration and and it gave me two sig figs so I might write it as seven point eight meters per second squared good okay so biggest thing that messed you guys up is probably just setting it up so we need to set up the friction the force of friction as mass times acceleration because we're we're imagining that force applied that max force applied where it equals the static friction alright I hope that helps out and thank you again for watching
4008
https://www.firerescue1.com/fire-service-culture
facebook twitter instagram linkedin youtube REGISTER MY ACCOUNT Trending Topics Fire Service Culture The FireRescue1 fire service culture resource page encompasses the cultural aspects of firefighter life, from the traditions that make the fire service such a proud profession to the kitchen table conversations that develop a brotherhood and sisterhood among members, to critical discussions about firefighter health and safety, focusing on the impact of culture on behavior and decision-making, both on and off the fireground. Fire Service Culture Is your crew bonded, or just sharing Wi-Fi? Downtime together is becoming the rarest call firefighters answer September 19, 2025 12:49 PM · Linda Willing Women in Firefighting ‘I have always been treated with respect’: My story of inclusion As a woman in the fire service, I am so grateful for my extended family and this group of role models for my son September 16, 2025 05:41 PM · FireRescue1 Special Contributors Book Excerpt Book Excerpt: ‘The Fire She Fights’ Ruby has been assigned to Minneapolis Fire Station 7 for three months when she finally responds to her first house fire September 16, 2025 04:36 PM · FireRescue1 Special Contributors Load More Women in Firefighting The only guy on the crew: Lessons in strength, teamwork and positivity The crew’s wealth of experience and dedication set a high bar in an environment where all-women crews were often scrutinized September 16, 2025 11:27 AM · Aaron Zamzow Level Up Your Mayday Training Developing a culture of mayday training within your department From prevention to data-driven decision-making, department leaders must set the tone for mayday-minded training September 15, 2025 02:41 PM Brotherhood and Sisterhood Retired Minn. firefighters gather regularly to tell stories, stay connected Veteran firefighters with nearly 300 years of combined service to swap stories, honor past fires and stay connected to today’s department September 13, 2025 12:00 PM September 11, 2001 9/11 Stair Climb events: Everything you need to know to participate Participants climb or walk the equivalent of 110 stories to honor the 343 FDNY firefighters killed on September 11, 2001 September 09, 2025 05:13 PM · Rachel Engel Social Media The ‘Taylor Swift Effect’ and fire service personalities on social media High-profile firefighters are using social media, podcasts and livestreams to sway tactics and culture, offering fresh learning — and new risks for inexperienced crews September 05, 2025 03:35 PM · Bill Carey First Responder Wellness Week 6 steps to adding a therapy dog to your organization The benefits are clear, but where to start? 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What makes a fire department enthusiast — and how to be one, the right way August 04, 2025 02:51 PM · FireRescue1 Staff Fire Service Culture The importance of firehouse meals The firehouse kitchen table has long been the place to continue traditions and share lessons learned August 04, 2025 11:09 AM · Gordon Graham Fire Service Culture Fire station groceries: Tracking the cost of a fire company meal — July 2025 update Shop and price compare a chicken dinner for 12 firefighters in San Diego and Pennsylvannia August 02, 2025 05:18 PM · Dryw Keltz Firefighting History Mich. firefighters return to historic firehouse for 3-day shift For the first time in decades, Ypsilanti firefighters responded to calls from their original 1898 station, sliding down fire poles and backing modern trucks through barn doors August 02, 2025 08:00 AM Fire Service Culture ‘Now serving #47’: We’re not tickets at a deli counter If our leaders can’t see that, then it’s on us, especially those in the middle, to bring some humanity back into the firehouse July 30, 2025 11:24 AM · FireRescue1 Special Contributors Fire Service Culture Okla. firefighters share special bond in honor guard Enid Fire Department’s Honor Guard proudly represents the department at ceremonies and funerals, blending tradition, teamwork and deep respect for service July 26, 2025 12:00 PM Fire Department Management Depreciating assets: How unchecked negativity costs your crew Great leaders know when to coach, when to cut and how to build a growth-focused culture July 24, 2025 01:12 PM · Brycen Garrison Safety In the age of ICE, fire departments must maintain their apolitical identity Community trust can erode quickly when firefighters are mistaken for enforcers July 23, 2025 11:45 AM · Linda Willing Leadership From briefing to buy-in: 5 ways fire officers can lead with purpose Go beyond check-the-box communication to build real trust with firefighters who need more than information July 22, 2025 04:19 PM · Kristopher T. 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https://en.wikipedia.org/wiki/Von_Neumann_neighborhood
Von Neumann neighborhood - Wikipedia Jump to content [x] Main menu Main menu move to sidebar hide Navigation Main page Contents Current events Random article About Wikipedia Contact us Contribute Help Learn to edit Community portal Recent changes Upload file Special pages Search Search [x] Appearance Appearance move to sidebar hide Text Small Standard Large This page always uses small font size Width Standard Wide The content is as wide as possible for your browser window. Color (beta) Automatic Light Dark This page is always in light mode. Donate Create account Log in [x] Personal tools Donate Create account Log in Pages for logged out editors learn more Contributions Talk [x] Toggle the table of contents Contents move to sidebar hide (Top) 1 Von Neumann neighborhood of range r 2 See also 3 References 4 External links Von Neumann neighborhood [x] 9 languages Чӑвашла Deutsch Español Français עברית Polski Português Русский Українська Edit links Article Talk [x] English Read Edit View history [x] Tools Tools move to sidebar hide Actions Read Edit View history General What links here Related changes Upload file Permanent link Page information Cite this page Get shortened URL Download QR code Expand all Edit interlanguage links Print/export Download as PDF Printable version In other projects Wikidata item From Wikipedia, the free encyclopedia Cellular automaton neighborhood consisting of four adjacent cells Manhattan distance r = 1 Manhattan distance r = 2 In cellular automata, the von Neumann neighborhood (or 4-neighborhood) is classically defined on a two-dimensional square lattice and is composed of a central cell and its four adjacent cells. The neighborhood is named after John von Neumann, who used it to define the von Neumann cellular automaton and the von Neumann universal constructor within it. It is one of the two most commonly used neighborhood types for two-dimensional cellular automata, the other one being the Moore neighborhood. This neighbourhood can be used to define the notion of 4-connectedpixels in computer graphics. The von Neumann neighbourhood of a cell is the cell itself and the cells at a Manhattan distance of 1. The concept can be extended to higher dimensions, for example forming a 6-cell octahedral neighborhood for a cubic cellular automaton in three dimensions. Von Neumann neighborhood of range r [edit] An extension of the simple von Neumann neighborhood described above is to take the set of points at a Manhattan distance of r>1. This results in a diamond-shaped region (shown for r=2 in the illustration). These are called von Neumann neighborhoods of range or extent r. The number of cells in a 2-dimensional von Neumann neighborhood of range r can be expressed as r 2+(r+1)2{\displaystyle r^{2}+(r+1)^{2}}. The number of cells in a d-dimensional von Neumann neighborhood of range r is the Delannoy numberD(d,r). The number of cells on a surface of a d-dimensional von Neumann neighborhood of range r is the Zaitsev number (sequence A266213 in the OEIS). See also [edit] Moore neighborhood Neighbourhood (graph theory) Taxicab geometry Lattice graph Pixel connectivity Chain code References [edit] ^Toffoli, Tommaso; Margolus, Norman (1987), Cellular Automata Machines: A New Environment for Modeling, MIT Press, p.60. ^Ben-Menahem, Ari (2009), Historical Encyclopedia of Natural and Mathematical Sciences, Volume 1, Springer, p.4632, ISBN9783540688310. ^Wilson, Joseph N.; Ritter, Gerhard X. (2000), Handbook of Computer Vision Algorithms in Image Algebra (2nd ed.), CRC Press, p.177, ISBN9781420042382. ^ Jump up to: abBreukelaar, R.; Bäck, Th. (2005), "Using a Genetic Algorithm to Evolve Behavior in Multi Dimensional Cellular Automata: Emergence of Behavior", Proceedings of the 7th Annual Conference on Genetic and Evolutionary Computation (GECCO '05), New York, NY, USA: ACM, pp.107–114, doi:10.1145/1068009.1068024, ISBN1-59593-010-8. External links [edit] Weisstein, Eric W."von Neumann Neighborhood". MathWorld. Tyler, Tim, The von Neumann neighborhood at cell-auto.com | show v t e Conway's Game of Life and related cellular automata | | Structures | Breeder Garden of Eden Glider Gun Methuselah Oscillator Puffer train Rake Reflector Replicator Sawtooth Spacefiller Spaceship Spark Still life | | Life variants | Day and Night Highlife Lenia Life without Death Seeds | | Concepts | Moore neighborhood Speed of light Von Neumann neighborhood | | Implementations | Golly Life Genesis Video Life Anonymous;Code | | Key people | John Conway Martin Gardner Bill Gosper Richard Guy | | Websites | LifeWiki | | Popular culture | Bloom Wake | P≟NPThis theoretical computer science–related article is a stub. You can help Wikipedia by expanding it. v t e Retrieved from " Categories: Cellular automata Theoretical computer science stubs Hidden categories: Articles with short description Short description is different from Wikidata All stub articles This page was last edited on 26 August 2020, at 10:47(UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Code of Conduct Developers Statistics Cookie statement Mobile view Edit preview settings Search Search [x] Toggle the table of contents Von Neumann neighborhood 9 languagesAdd topic
4010
https://www.yulan-lightings.com/info/what-is-the-distance-between-outdoor-lights-93171270.html
What is the distance between outdoor lights? - Knowledge Tel:+8618705299363 Email:info@yulanlighting.com Language English Türkçe Português Deutsch 日本語 Việt Nam Español русский Français 한국어 عربي Italiano Čeština ไทย Eesti Gaeilgenah Éireann Bai Miaowen íslenska Cymraeg Български اردو Polski hrvatski українська bosanski فارسی Lietuvių Latviešu עברית România limbi Ελληνικά dansk magyar Norsk suomi Nederlands Svenska slovenčina slovenščina हिंदी Indonesia Melayu Malti Kreyòl Ayisyen Català বাংলা Srbija jezik (latinica) O'zbek Home About Us Exhibition and Customer Visit Equipment and Warehouse Certificate Service Products Street Light Led Street Light HPS Street Light Solar Light All in One Solar Light All in Two Solar Light Garden Light Traditional Garden Light Led Garden Light Bollard Light Light Pole Aluminum Light Pole Iron Light Pole Decrotative Pole Tempered Glass Lamp Cover Flat Tempered Glass Lamp Cover Domed Tempered Glass Lamp Cover News Knowledge Contact Us Solution Feedback Home / Knowledge / Content Knowledge Related Industry China outdoor led garden light What is an in-depth analysis of high-pressure sodium lamps? Why will DOB become the core direction of LED lighting driving future develop... How to comprehensively improve the lumen output of LED lighting fixtures? Contact Us Tel+8613023139863 (Nancy) +8618705299363 (Zoe) +8613928285391 (Sunny) E-mail:info@yulanlighting.com Office address: No.1 Huangxing Road, 200090, Shanghai, China Factory address: Jiepai, Danyang Zhenjiang City, Jiangsu Province What is the distance between outdoor lights? Mar 07, 2024 View: 134 The distance interval of outdoor lighting depends on the type, height, and type of light source used, as well as the specific requirements of the courtyard for lighting brightness. For example, a diffuse reflection courtyard light without a mask will scatter light everywhere. Generally, a 150W high-pressure sodium lamp is used, with a height of 3.5m to 4.5m and a spacing of 18m to 20m. A courtyard lamp with a face shield does not emit light everywhere, so sodium lamps and metal halide lamps can be used, suitable for 150W, with a spacing of about 16m. In urban road lighting, the spacing between lamp posts can be determined based on the width of the road and the required lighting level. If the road is wide and requires high illumination, the distance between lamp posts will be relatively close, usually between 8-10 meters. If the road is narrow, the distance between lamp posts can be appropriately reduced, usually between 5 to 6 meters. In short, the distance between outdoor lights needs to be reasonably arranged according to the usage scenario and the required lighting level. Our goal should be to minimize energy consumption and environmental impact while ensuring lighting quality. Our company has a variety of high-quality outdoor lighting products, including LED street lights, courtyard lights ,solar street lights and lamp poles, which can meet the needs and preferences of different customers. We provide solutions for customer projects (above industry average, non-standard products, products from 0 to 1, etc.) Contact us Previous: How to choose HPS outdoor street light? Next: How to judge the quality of a solar street light source? Send Inquiry Leave a message You Might Also Like Separate Commercial Solar Powered S... All In Two Solar Led Street Light W... 20 Foot Aluminum 4 Inch Square Ligh... ​3-5mm Customizable Flat Tempered G... 6m-12m Galvanized pole steel material Commercial Street Lights 150w Fixture Quick Navigation Home About Us Products News Knowledge Contact Us Solution Showroom Feedback Sitemap Categories Street Light Solar Light Garden Light Light Pole Tempered Glass Lamp Cover Contact Us Tel:+8618705299363 Fax: Email:info@yulanlighting.com Address: Office address:No.1 Huangxing Road, 200090, Shanghai, China Factory address:Jiepai, Danyang Zhenjiang City, Jiangsu Province ###### QR Code Copyright © Yulan Electrical Co., Ltd. All Rights Reserved.Privacy Policy whatsapp Phone E-mail Inquiry 0 正在输入中... Send a file Send a picture Your name E-mail Phone/WhatsApp Message SUBMIT upload percent: 0% WhatsApp WhatsApp E-Mail Wechat WhatsApp Cookie Usage In order to provide you with a better browsing experience, this website will use cookies. By clicking "Accept" or continuing to browse this website, you agree to our use of cookies.Learn More Reject - click here to reject the cookies Accept
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https://stackoverflow.com/questions/63756779/simulating-computation-of-the-expected-value-of-random-variable-y
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Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Simulating computation of the expected value of random variable Y Ask Question Asked 5 years ago Modified5 years ago Viewed 2k times Part of R Language Collective This question shows research effort; it is useful and clear 1 Save this question. Show activity on this post. I have been given the following task: Compute the expected value of Y=e^{-X}(X is uniform between 0 and 1) with a simulation in R. Plot the expected value as a function of the number of simulations where n is an integer between 1 and 10000 The pdf of this function is: f(y) = 1/y, for 1/e < y < 1. The formula of finding expect value is of course: E[Y] = integrate(y 1/y dy) How do you simulate something likes this ? I expect you draw random sample between (1/e < y < 1) but the pdf of the distribution has different probabilities depending on what you draw it seems. I thought about using the "sample" or "runif" functions but i can't figure out how to make those functions work with different probabilities. R Language Collective r statistics data-science probability probability-theory Share Share a link to this question Copy linkCC BY-SA 4.0 Improve this question Follow Follow this question to receive notifications edited Sep 5, 2020 at 18:06 Steinar Ágúst SteinarssonSteinar Ágúst Steinarsson asked Sep 5, 2020 at 17:37 Steinar Ágúst SteinarssonSteinar Ágúst Steinarsson 15 7 7 bronze badges Add a comment| 1 Answer 1 Sorted by: Reset to default This answer is useful 3 Save this answer. Show activity on this post. You could use the fact that the random variable U = F(Y) is uniform, where F is the cumulative density function of the random variable Y (with pdf 1/y). You then have that Y = F^-1(U). This means that you can sample from a uniform variable and then transform it through F^-1(U) to get a sample from Y. You can then take the mean of your sample. This is known as inverse sampling transformation. For your example you have F(y) = ln(y) + 1 and F^-1(u) = exp(u - 1). It is then easy to get a sample: r n = 1000 u = runif(n) y = exp(u - 1) mean(y) 0.6342477 which is very near the true mean of 0.6321206 (1 - 1/e). EDIT To see how the estimated mean changes with how many samples you simulate you could do something like this: ```r sample_y = function(n){ u = runif(n) y = exp(u - 1) mean(y) } n = seq(10, 20000, 10) res = sapply(n, sample_y) ts.plot(res) ``` It stabilizes around the true mean very quickly and the variation around the mean gets smaller and smaller as n grows. Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications edited Sep 6, 2020 at 8:28 answered Sep 5, 2020 at 18:07 J.C.WahlJ.C.Wahl 1,664 2 2 gold badges 11 11 silver badges 16 16 bronze badges 4 Comments Add a comment Steinar Ágúst Steinarsson Steinar Ágúst SteinarssonOver a year ago Thanks a lot, very well explained! 2020-09-05T19:15:15.06Z+00:00 0 Reply Copy link Steinar Ágúst Steinarsson Steinar Ágúst SteinarssonOver a year ago Maybe one thing I was wondering about. The inverse of the CDF: F(y) = ln(y) - 1, i don't understand how you get exp(u-1) as the inverse of ln(y)-1. I get exp(u+1), and as you can see so does the calculator online: emathhelp.net/calculators/algebra-2/inverse-function-calculator/… im wondering if I'm missing something? @J.C.Wahl 2020-09-05T22:26:01.983Z+00:00 0 Reply Copy link J.C.Wahl J.C.WahlOver a year ago You are correct, the CDF is ln(y) + 1, since the int 1/y, 1/e < y < 1, is equal to ln(y) - ln(1/e) = ln(y) + 1. I'll update my answer. 2020-09-06T08:28:14.427Z+00:00 0 Reply Copy link Steinar Ágúst Steinarsson Steinar Ágúst SteinarssonOver a year ago Thanks. Yes but you rather that you take the integral: 1/e -> y, to end up with exactly ln(y) - ln(1/e) = ln(y) + 1 which is exactly the cdf: F(Y <= y). 2020-09-06T13:45:55.377Z+00:00 0 Reply Copy link Add a comment Your Answer Thanks for contributing an answer to Stack Overflow! Please be sure to answer the question. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. 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https://www.youtube.com/watch?v=DGSIRbZnF_0
Proving the Laws of Logarithms Math and Science 1650000 subscribers 155 likes Description 3495 views Posted: 14 Jan 2024 This educational video meticulously guides viewers through the process of proving the laws of logarithms, an essential topic in mathematics. Understanding and proving these laws not only solidifies one's grasp of logarithms but also enhances overall algebraic reasoning and problem-solving skills. The tutorial begins with a brief introduction to logarithms, explaining their basic concept and why they are significant in mathematics. We then delve into the three fundamental laws of logarithms: the product law, the quotient law, and the power law. Each law is addressed individually, detailing its statement and the rationale behind it. With a focus on clarity and thoroughness, the video demonstrates how to prove each of these laws, using fundamental algebraic properties and exponential rules. These proofs provide a deeper insight into how logarithms operate and their practical applications in simplifying complex algebraic expressions. This tutorial is ideal for students who are studying algebra and logarithms, educators looking for teaching resources, or anyone interested in enhancing their mathematical understanding. By the end of this video, viewers will not only comprehend the laws of logarithms but also be capable of proving and applying them in various mathematical contexts. Join us to deepen your understanding and mastery of logarithms. More Lessons: Twitter: 4 comments Transcript: so we're going to prove three laws of logarithms here the first one we're going to prove is the following we're going to prove uh the one that we use all the time we'll use all of these but this one probably used the most logarithm base B of the product M times n and we now know because we've been using this so much that it's the same thing as log base B of M plus log base B of n so why is it that when you have two things multiplied in the logarithm operating on it why does that become the addition of two logarithms it's almost like multiplication when you're dealing with logarithms you take the log of multiplication it kind of gets transformed into addition of logarithms so the multiplication operation becomes addition which is very useful for more advanced math when we're trying to simplify things sometimes multiplying things gets tricky and dicey you can change it to addition if you just take the logarithm of the thing so we're trying to prove this thing here also one more thing I'm going to say probably in the beginning you might say oh that proof was neat but I never would have thought of that that's okay none of us think of the stuff to begin with right you have to see it right as long as you understand what I'm doing that's all I care about I don't expect you to know how to prove this I don't expect you to feel you know like you should already know how to do this I just want you to follow it that's all I want you to do so that you can sharpen your skills all right so in order to do this we know we want to add these guys together so to make things easier let's let the following things be true let's let some new variable x equal the log base B of M and let's let a new variable y be log base B of n you might say why am I introducing new variables well that happens all the time in proofs the proof is like it's like a blank canvas for you to paint on you can paint anything I I can paint what I want I can paint Jupiter or Saturn I can paint cows or chickens it's whatever I want to do in the proof I can do what I want as long as it's mathematically legal so I'm just going to let the variable x equal to this and this equal to this that's fine the rest of it I'm going to try to logically connect the dots and make this thing be true okay but if I let these things true then the following things are true because this is a logarithm Then I then know because of this first line B to the power of X is n equal to m b to the power of X is M that's the definition of a logarithm and also B to the power of Y is equal to n so because of what I let these variables equal then these variables are equal you might say this is not at all looking like that that's fine that's what I said you probably you know unless you're a math you know Guru you probably wouldn't know to do this I mean none of us would but as long as you can follow what I'm doing that's all I care about all right then or I should say thus you can use words like thus and a proof If I let this true then this become is true because of the definition of a logarithm then I know I want to multiply these things together M times n okay but now I know what M and N are they came from these definitions you see now I have equations for what M and N are so then M times n is this times this which means that's B to the x times B to the Y you see because I know what imminent are those things multiplied together but because these have the same base and different exponents I can then say that this is B to the power of X Plus y because I can add these exponents anytime I have the same base I can take uh those exponents there I can I can add those exponents now ultimately I have M times n and I'm trying to take the logarithm of that and I want to see what it equals now I have an expression for what M times n actually is so in order to to figure out if this is going to work out I'm going to take logarithm of both sides so I'll take log of Base B both sides because I can do anything I want to an equation as long as I do it to both sides so I'm going to work with this one I'm going to say log base B of M times n is equal to I'm going to have to take the log of this log base B of B to the power of X Plus y now this B to the power of X Plus y this is what the logarithm is operating on but remember we talked about 90 million times about the idea that a logarithm with a base B is the inverse function of an exponential with a base B they're inversive so when they operate on each other they annihilate each other that is what the definition of the inverse does the inverse function undoes what the parent function or what the other function did in the first place so since we have an exponential here it raised to the power B to the power of this but the logarithm undoes that so on the right hand side the logarithm cancels with the base B and all I have left is X Plus y on the left hand side I have the logarithm base B of M times n so you might say great but I don't care about X Plus y but then you remember wait a minute I've defined what X and Y were up here this X and Y are the same ones that are Rippling through the problem statement so then you know that the logarithm base B of M times n is equal to X but X is the logarithm base B of M log base B of M there's a plus sign here y y is log base B of n and if you look back and compare these things these are exactly the same thing all right because log base B of the product becomes the the logarithm of the first one plus the logarithm of the second one that's exactly what we set out to prove do I expect that you would have known how to do that no most teachers are not going to tell you prove the first law of logarithms but what does it do it allows you to understand how to get this from the definition that's a property of logarithms when you multiply them you add exponents when I take the log of both sides the annihilation that happens here that's a property of logarithms so in the process of learning how to prove these things you actually sharpen your skills with dealing with logs that's really all I care about in this lesson okay let's go and prove the uh the one about exponents next so we're going to prove log base B of M to the power of K some number to the power of K and we're we know that that's equal from our laws of logarithms to K log B of M like that okay K log B uh a base B of the number M so we basically we can take an exponent we can bring it out in front of the logarithm that's all this is telling us how do we prove that so we need to do we're going to do the similar kinds of assumptions okay we're gonna have to let some things happen okay in this case we're going to let we're going to let x equal to log B of n okay now we could let y equal to log B of n but you see in this property of logs there is no n anywhere else so we don't really need to Define that here we had an m and an N so we had to kind of have a term for each one of them but here there is no in anywhere so there's no reason to really do that but from this single definition here something pops out the same exact thing as before B to the power of X is equal to M so so far it's just a rewrite of what we did on the other board but we have a conclusion that we can draw here I should say thus right ultimately what do I want I want m to the power of K okay m to the power of K so this thing m to some power of K is what's on this side B to the X raised to the sum power of K all I've done is I said hey this gives me a definition for what m is I want to raise it to a power because that's what's in my proof so I raise it to a power so I have to raise this side to the power because that's what it's equal to but this means that m to the power of K is B to the uh how do I want to write it KX because this is a exponent raised to an exponent so I'm going to multiply those things together all right and what do we do in the last uh thing once we had it all kind of written out like this we wanted to get M times n to match our problem statement here we have m to the power of K to match what's in our proof so now we want to take log of both sides so we'll take the logarithm we'll take a base B logarithm of M to the power of K logarithm base B of what's on the right hand side B to the power of k x like this but then you know that on the right hand side you're going to get the same Annihilation here you have a log of an exponent those two things are going to cancel just like we had a log of an exponential here we have a log of an exponential here on the right hand side all you're going to have is K times X on the left hand side you're going to have log base B of M to the power of K and you have K times x and you say well wait a minute I know what x is X was log base B of M so you're going to have log base B of M to the power of K is K multiplied by X but I know what that is it's log base B of M you see you take the logarithm of something with an exponent you could just take that exponent right out front and then multiply by the log of of that of that base there so that is the proof of the uh one of the three laws of logarithms the one that deals with exponents now the one that I say for last is the one that looks kind of like this remember there's one that talks about multiplying things becomes addition of logs and then there's another one that talks about division of things becomes subtraction of logs so our last one that we're going to do and that's this will be the last thing we'll prove in this lesson isn't want to prove let me flip my page here just to make sure I don't mess anything up let's prove this last one prove the following thing log base B of the division M over n is equal to log base B of M minus sine log base B of n so I want to do the subtraction there so ultimately this proof is going to be very very similar to what we did before but let me show you um how we're going to get there the first thing we're going to do is we're going to recognize that this statement right here is really the same as log base B of M multiplied by 1 over n right multiply by 1 over n that's how you get a division here you multiply by 1 over n and since we know what happens when we multiply things we can use a similar proof to go in fact we could even use that thing we could just substitute in and use it but that's no fun let's do it let's do it the real way let's let's do it the right way let's let the following things happen let's say let's let x equal to the log base B of something called M and we'll let y equal log base B of something called 1 over n 1 over n like this why am I doing that because I know I'm going to need an m and I know I'm going to need a 1 over n it's different than the other one big and then we're just multiplied together I'm going to need some fraction with an m on the bottom here foreign okay so we'll do the same thing again then the following things are true B to the power of X is m and then from this one B to the power of Y is 1 over n so we're going to need those all right now ultimately what I'm trying to do is I'm trying to form the product of these things so I can take the logarithm right so what I'm going to have is M times 1 over n because I'm trying to make M over n is M over n but I know what these things are equal to it's B to the x times B to the Y because that's M and that's 1 over n okay but what is this B to the X Plus y so what I figured out is M over n is exactly the same thing as B to the X Plus y so I'm going to take and write that down separately M over n is B to the X Plus Y and now I want to take the logarithm of both sides why because I want the logarithm of this quotient of this division that's what I'm trying to get to I'm trying to take the logarithm of that so I had to kind of do all of this to get to where I had an expression for this and so I'll take the logarithm of both sides so it has to be a base B logarithm base B of M over n equals log base B of B to the X Plus y all of this is wrapped up inside that logarithm I have the same thing happening on the right the logarithm of an exponential annihilate each other all I'm going to have on the right hand side is X Plus y on the left hand side I'll have log base B M over n like this all right so what am I going to have next I know what X and Y are so let's substitute for that log base B M over n is equal to X Plus y but I know what X and Y are X is log base B log of M log base B of M and then the Y is this guy log base b 1 over n so it's plus sign from this log base b 1 over n ah it's hard to read I'm sorry about that this is a capital N right here like this so X Plus y so I'm just plugging what I have now you think well this isn't quite right and this is a plus sign this is a minus sign it's not quite right but we're going to get there how are we going to get there let's go well if you think about it let me go over here let me just write a note over here this is the same thing as the logarithm base B of n to the minus 1. how do I know that because 1 over n is the same thing as n to the minus 1. so this is an exponent so this exponent can come out in front here so then I have log base B of M over n equals log base B of M and because of this the exponent can come down it's going to be a minus sign log and then you have an N right here and this is exactly what we're trying to prove the log of the division of n m divided by n is the log of M minus the log of n it's exactly what we have right here it all comes from this little exponent and it comes from having to Define things this way so I can make the product of M and N so or the division of M divided by n do I expect you to know this no of course not the first time you see this nobody knows how to do this stuff all I care about is that you can follow through so that it serves two purposes it sharpens your skills so that you know where things come from I mean you know how to use these laws of logarithms to in order to make logical conclusions and it also shows you that these laws of logarithms don't just come from the sky they come from logical progression of thought we start from here we let this equal to this notice how nobody I don't want to say nobody on this Earth there's some pretty brilliant math guys out there but not very many people can look at this and say oh yeah I know how to prove that no problem I can see all the steps almost nobody can do that but what we can say is if we let this equal to this and this equal to this then this must be true then if we if we multiply this and this it must be this times this and then we just Ripple through every little step is an incremental uh step towards the Finish Line that's all I care that you understand so make sure you understand this if you want to grab a sheet of paper and prove these yourself it definitely can't hurt you and then follow me on to the next lesson we're going to start to learn more about the applications of logarithms and exponentials in math learn anything at mathandscience.com
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https://clinicalinfo.hiv.gov/sites/default/files/guidelines/archive/adult-adolescent-oi-2024-10-08.pdf
Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV How to Cite the Adult and Adolescent Opportunistic Infection Guidelines: Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV. National Institutes of Health, Centers for Disease Control and Prevention, HIV Medicine Association, and Infectious Diseases Society of America. Available at guidelines/adult-and-adolescent-opportunistic-infection. Accessed (insert date) [include page numbers, table number, etc., if applicable]. It is emphasized that concepts relevant to HIV management evolve rapidly. The Panels have a mechanism to update recommendations on a regular basis, and the most recent information is available on the Clinicalinfo website ( Developed by the National Institutes of Health, the Centers for Disease Control and Prevention, and the HIV Medicine Association of the Infectious Diseases Society of America Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV—A Working Group of the NIH Office of AIDS Research Advisory Council (OARAC) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV i Table of Contents What’s New in the Guidelines .................................................................................................................................... iii Introduction ............................................................................................................................................................. A-1 Bacterial Infections ....................................................................................................................................................B-1 Bartonellosis ...............................................................................................................................................................C-1 Candidiasis (Mucocutaneous).................................................................................................................................. D-1 Chagas Disease ........................................................................................................................................................... E-1 Coccidiodomycosis ..................................................................................................................................................... F-1 Community-Acquired Pneumonia .......................................................................................................................... G-1 Cryptococcosis .......................................................................................................................................................... H-1 Cryptosporidiosis ........................................................................................................................................................ I-1 Cystoisosporiasis ......................................................................................................................................................... J-1 Cytomegalovirus Disease ......................................................................................................................................... K-1 Hepatitis B Virus Infection ....................................................................................................................................... L-1 Hepatitis C Virus Infection ...................................................................................................................................... M-1 Herpes Simplex Virus Disease ................................................................................................................................. N-1 Histoplasmosis........................................................................................................................................................... O-1 Human Herpesvirus 8 Disease .................................................................................................................................. P-1 Human Papillomavirus Disease ............................................................................................................................... Q-1 Immunizations for Preventable Diseases in Adults and Adolescents With HIV ...................................................R-1 Leishmaniasis ............................................................................................................................................................. S-1 Malaria ....................................................................................................................................................................... T-1 Microsporidiosis ....................................................................................................................................................... U-1 Mpox .......................................................................................................................................................................... V-1 Mycobacterium avium Complex Disease ................................................................................................................ W-1 Mycobacterium tuberculosis Infection and Disease ................................................................................................ X-1 Pneumocystis Pneumonia ......................................................................................................................................... Y-1 Progressive Multifocal Leukoencephalopathy/JC Virus Infection ....................................................................... Z-1 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV ii Syphilis ................................................................................................................................................................... AA-1 Talaromycosis (Penicilliosis) .................................................................................................................................. BB-1 Toxoplasmosis ......................................................................................................................................................... CC-1 Varicella-Zoster Virus Diseases ........................................................................................................................... DD-1 Tables Table 1. Prophylaxis to Prevent First Episode of Opportunistic Disease ..................................................... EE-1 Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Chronic Suppressive/Maintenance Therapy) ......................................................................... FF-1 Table 3. Indications for Discontinuing and Restarting Opportunistic Infection Prophylaxis in Adults and Adolescents With HIV ............................................................................................................... GG-1 Table 4. Significant Pharmacokinetic Interactions for Drugs Used to Treat or Prevent Opportunistic Infections ...................................................................................................................................................... HH-1 Table 5. Common or Serious Adverse Reactions Associated With Drugs Used for Preventing or Treating Opportunistic Infections ...................................................................................................................................II-1 Table 6. Dosing Recommendations for Drugs Used in Treating or Preventing Opportunistic Infections Where Dosage Adjustment is Needed in Patients With Renal Insufficiency ............................................................... JJ-1 Appendix A. List of Abbreviations ...................................................................................................................... KK-1 Appendix B. Panel Roster and Financial Disclosures ......................................................................................... LL-1 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV iii What’s New in the Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV The Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV document is published in an electronic format and updated as relevant changes in prevention and treatment recommendations occur. All changes are developed by the subject-matter groups listed in the document. (Changes in group composition also are posted promptly.) These changes are reviewed by the editors and relevant outside reviewers before the document is altered. Major revisions within the last 6 months are as follows: October 8, 2024 Bacterial Enteric Infections • Updated information on antimicrobial resistance among bacterial enteric pathogens. • Updated recommended regimens for empiric therapy pending susceptibility results, including a recommendation to consider empiric carbapenem therapy in people with advanced HIV and severe diarrhea where campylobacter bacteremia is suspected. • Updated information on the use of antibiotics for bacterial enteric infections during pregnancy. September 16, 2024 Candidiasis • Added information on the role of ibrexafungerp in the treatment of vulvovaginal candidiasis and recurrent vulvovaginal candidiasis and the approval of ibrexafungerp by the U.S. Food and Drug Administration (FDA). • Added information on the role of oteseconazole for the treatment of recurrent vulvovaginal candidiasis and the approval of oteseconazole by the FDA. Pneumocystis Pneumonia • Simplified indications for starting primary prophylaxis. • Added intermittent intravenous pentamidine as an alternative regimen for primary or secondary prophylaxis. • Provided more detailed recommendations for management during pregnancy. Toxoplasma gondii Encephalitis • Recommended primarily limiting baseline serologic screening and measures to prevent exposure to individuals with CD4 T lymphocyte cell counts <200 cells/mm3. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV iv • Added trimethoprim-sulfamethoxazole as a preferred regimen for acute infection. • Provided more detailed recommendations for management during pregnancy. August 15, 2024 Disseminated Mycobacterium avium Complex Disease • Updated information to prioritize the initiation of effective antiretroviral therapy and to refrain from primary prophylaxis for Mycobacterium avium Complex (MAC) except for people with HIV who are not receiving antiretroviral therapy (ART), remain viremic on ART, or have no options for a fully suppressive ART regimen. • Added new information indicating that drugs demonstrating substantive in vitro activity against MAC might be considered for the treatment of refractory MAC disease (e.g., bedaquiline, tedizolid, linezolid, omadacycline), acknowledging that there is insufficient observational or clinical trial data to support formal recommendations in this setting. • Updated information on drug–drug interactions between anti-MAC therapies, particularly rifabutin, and antiretroviral drugs and provided a link to the Adult and Adolescent Antiretroviral Guidelines on drug–drug interactions. July 29, 2024 Leishmaniasis • Updated information on prevalence, including transmission in the United States. • Updated information on the use of polymerase chain reaction, or PCR, and serological tests for the diagnosis of leishmanial diseases. • Updated treatment regimens for each of the leishmanial diseases, including regimens that reduce the likelihood of recurrence. • Added new information about special considerations in pregnancy. July 9, 2024 Human Papillomavirus Disease • A brief summary of this update is available here from the NIH Office of AIDS Research. • Based on the ANCHOR study results, provided new screening and treatment recommendations for anal cancer prevention. • Provided new anal cancer screening algorithms. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV v May 2, 2024 Mycobacterium tuberculosis Infection and Disease • Recommended a 4-month regimen of daily rifapentine, isoniazid, pyrazinamide, and moxifloxacin as an alternative treatment for active pulmonary tuberculosis (TB) in people receiving efavirenz-based antiretroviral therapy. • Recommended a regimen consisting of bedaquiline, pretomanid, linezolid, and moxifloxacin (BPaLM) as the preferred treatment for rifampin-resistant TB. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-1 Introduction Updated: June 14, 2023 Reviewed: January 10, 2024 Opportunistic infections (OIs), which in the context of HIV have been defined as infections that are more frequent or more severe because of HIV-mediated immunosuppression,1 were the first clinical manifestations that alerted clinicians to the occurrence of AIDS. Pneumocystis pneumonia, toxoplasma encephalitis, cytomegalovirus retinitis, cryptococcal meningitis, tuberculosis, disseminated Mycobacterium avium complex (MAC) disease, and pneumococcal respiratory disease, as well as certain cancers such as Kaposi sarcoma and central nervous system lymphoma, have been hallmarks of AIDS. These OIs and many more occurred on average 7 to 10 years after infection with HIV.2,3 Until effective antiretroviral therapy (ART) was developed, patients generally survived only 1 to 2 years after the initial manifestation of AIDS.4 Starting in the late 1980s, the use of chemoprophylaxis, immunization, and better strategies for managing OIs improved quality of life and lengthened survival of people with HIV.5 Early antiretroviral drugs and treatment strategies added further benefit.6 However, the most profound reduction in OI-related morbidity and mortality in people with HIV resulted from the introduction of highly effective combination ART in the mid-1990s.7-13 Despite the availability of multiple safe, effective, and simple ART regimens that, when used widely, have led to corresponding population-level declines in the incidence of OIs,11,14,15 the Centers for Disease Control and Prevention (CDC) estimates that more than 13% of people with HIV are unaware of their HIV infection and that 34% of Americans who are aware of their HIV infection are not effectively virally suppressed.16 As a result, OIs continue to cause preventable morbidity and mortality in the United States. Achieving and maintaining durable viral suppression in all people with HIV, and thus preventing or substantially reducing the incidence of HIV-related OIs, remains challenging for three main reasons: • Not all HIV infections are diagnosed, and once diagnosed many people have already experienced substantial immunosuppression. CDC estimates that in 2019, among those with diagnosed HIV, approximately 20% had a CD4 T lymphocyte (CD4) cell count <200 cells/mm3 (or <14%) at the time of diagnosis.16 • Not all people with diagnosed HIV receive timely, continuous HIV care or are prescribed ART. CDC estimates that in 2019, 81% of people with newly diagnosed HIV had been linked to care within 1 month. However, only 58% of people with HIV were adequately engaged in continuous care.16 • Not all people greater than 13 years old treated for HIV achieve durable viral suppression. CDC estimates that in 2019, only 68% of people had durable viral suppression within 6 months of HIV diagnosis.17 Causes for the suboptimal response to treatment include poor adherence, unfavorable pharmacokinetics, or unexplained biologic factors.18,19 Thus, some people with HIV infection will continue to present with an OI as the sentinel event leading to a diagnosis of HIV infection or present with an OI as a complication of unsuccessful viral suppression.17 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-2 Durable viral suppression eliminates most but not all OIs. Tuberculosis, pneumococcal disease, and dermatomal zoster are examples of infectious diseases that occur at higher incidence in people with HIV regardless of CD4 count. The likelihood of each of these OIs occurring does vary inversely with the CD4 count, however.20-26 Certain OIs—most notably tuberculosis and syphilis—can increase plasma viral load,27-31 which both accelerates HIV progression and increases the risk of HIV transmission if patients are not virally suppressed by ART. Thus, clinicians continue to need to be knowledgeable about the prevention and management of HIV-related OIs. History of These Guidelines In 1989, the Guidelines for Prophylaxis Against Pneumocystis carinii Pneumonia for Persons Infected with the Human Immunodeficiency Virus became the first HIV-related treatment guideline published by the U.S. government.32 This guideline was published in the Morbidity and Mortality Weekly Report (MMWR), which was the most rapid mode of publication at the time. It was followed by a guideline on prevention of MAC disease in 1993.33 In 1995, these guidelines were expanded to include the treatment of 18 HIV-related OIs. In 2004, information about the prevention of HIV-related OIs was incorporated into the guidelines. The National Institutes of Health (NIH), CDC, and the HIV Medicine Association of the Infectious Diseases Society of America (HIVMA/IDSA) now jointly co-sponsor these guidelines,1,34,35 which have been published in peer-reviewed journals and/or the MMWR in 1997, 1999, and 2002.35-44 Since 2009, the guidelines have been managed as a living document on the web with each chapter reviewed quarterly by the guidelines committee. Updates are published as often and as promptly as deemed appropriate by the guidelines committee. Data regarding the use of these guidelines demonstrate that the document is a valuable reference for HIV health care providers. In 2021, there were approximately 417,000 page views of the online version of the guidelines and approximately 19,600 PDF downloads. All guideline recommendations regarding therapy and prevention are rated in terms of the quality of supporting evidence; comments about diagnosis are not rated. These ratings allow readers to assess the relative importance of each recommendation. This document focuses on adults and adolescents; recommendations for children with HIV can be found in separate documents on the Clinicalinfo website. These guidelines are intended for clinicians, other health care providers, patients with HIV, and policymakers in the United States. Guidelines pertinent to other regions of the world, especially resource-limited countries, may differ with respect to the spectrum of relevant OIs and the diagnostic and therapeutic options that are available to clinicians. Snapshot of Guidelines Development Process These guidelines were prepared by the OI Working Group under the auspices of the Office of AIDS Research Advisory Council (OARAC), an authorized Federal Advisory Committee to the U.S. Department of Health and Human Services established in 1994. Co-chairs who are selected and appointed by their respective agencies or organizations (i.e., NIH, CDC, IDSA, HIVMA) convene Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-3 OI-specific working groups of clinicians and scientists with subject matter expertise in those specific OIs. The co-chairs appoint a leader for each working group. The working groups review in real time the relevant literature published since the last review, with the help of quarterly literature searches for articles relevant to their section that are provided by guidelines support staff. The working groups propose revisions to their section as appropriate. The co-chairs, HIVMA/IDSA, and CDC review each proposed revision to recommendations and/or ratings. The co-chairs and working group leaders have a teleconference quarterly to discuss updates to sections. The co-chairs also convene a meeting each year with members of the Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV to review guidelines content and format and set an agenda for the coming year. The names and affiliations of all contributors, as well as their financial disclosures, are provided in Appendix B: Panel Roster and Financial Disclosures. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-4 Guidelines Development Process Topic Comment Goal of the guidelines Provide guidance to HIV care practitioners and others on the optimal prevention and management of HIV-related opportunistic infections (OIs) for adults and adolescents in the United States. Panel members The Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV (the Panel) is composed of co-chairs who represent the National Institutes of Health (NIH), the Centers for Disease Control and Prevention (CDC), and the HIV Medicine Association of the Infectious Disease Society of America (HIVMA/IDSA), plus Panel members with expertise in HIV clinical care, infectious disease management, and research. Co-chairs are appointed by their respective agencies or organizations. Each working group is led by a Panel member selected by the co-chairs. Panel members are selected from government, academia, and the health care community by the co-chairs and working group leaders based on the member’s area of subject matter expertise. Members serve on the Panel for a 4-year term, with an option to be reappointed for additional terms. Prospective Panel members may self-nominate at any time. When specific or unique subject matter expertise is required, the co-chairs together with working group leaders may solicit advice from individuals with such specialized knowledge. The list of the current Panel members can be found in Appendix B: Panel Roster and Financial Disclosures. Financial disclosure and management of conflicts of interest All members of the Panel submit a written financial disclosure annually reporting any associations with manufacturers of drugs, vaccines, medical devices, or diagnostics used to manage HIV-related OIs. A list of these disclosures and their last update is available in Appendix B: Panel Roster and Financial Disclosures. The co-chairs review each reported association for potential conflicts of interest and determine the appropriate action: disqualification from the Panel, disqualification or recusal from topic review and discussion, or no disqualification needed. A conflict of interest is defined as any direct financial interest related to a product addressed in the section of the guideline to which a Panel member contributes content. Financial interests include direct receipt by the Panel member of payments, gratuities, consultancies, honoraria, employment, grants, support for travel or accommodation, or gifts from an entity having a commercial interest in that product. Financial interests also include direct compensation for membership on an advisory board, data safety monitoring board, or speakers’ bureau. Compensation and support provided to a Panel member’s university or institution (e.g., grants, research funding) is not considered a financial conflict of interest. The co-chairs strive to ensure that 50% or more of the members of each working group have no conflicts of interest. Primary users of the guidelines HIV treatment providers Developer Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV—a working group of the Office of AIDS Research Advisory Council (OARAC). See Appendix B: Panel Roster and Financial Disclosures. Funding source Office of AIDS Research (OAR), NIH Evidence collection The recommendations in the guidelines are based on studies published in peer-reviewed journals. On some occasions, particularly when new information may affect patient safety, unpublished data presented at major conferences or information prepared by the U.S. Food and Drug Administration or manufacturers (e.g., warnings to the public) may be used as evidence to revise the guidelines. Members of each working group are responsible for identifying relevant literature and conducting a systematic comprehensive review of that literature that is provided to them on a quarterly basis. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-5 Method of synthesizing data and formulating recommendations Each section of the guidelines is assigned to a working group of Panel members with expertise in the area of interest. The members of the working group synthesize the available data. Recommendations are reviewed and updated by each working group after an assessment of the quality and impact of the existing and any new data. Aspects of evidence that are considered include but are not necessarily limited to the type of study (e.g., case series, prospective cohort, randomized controlled trial), the quality and appropriateness of the methods, and the number of participants and effect sizes observed. Finally, all proposed recommendations and supporting evidence are reviewed by the co-chairs and subject matter experts at CDC and HIVMA/IDSA before final approval and publication. OAR reviews all proposed recommendations and gives final approval. Recommendation rating Recommendations are rated according to the information in the table below, “Rating System for Prevention and Treatment Recommendations,” and accompanied, as needed, by explanatory text that reviews the evidence and the working group’s assessment. All proposed changes are discussed during teleconferences and by email and then assessed by the Panel’s co-chairs and reviewed by OAR, CDC, and HIVMA/IDSA before being endorsed as official recommendations. Other guidelines These guidelines focus on prevention and treatment of HIV-related OIs for adults and adolescents. A separate guideline outlines similar recommendations for children who have HIV infection. These guidelines are also available on the Clinicalinfo website. Update plan Each working group leader and the co-chairs meet every 3 months by teleconference to review interim data that may warrant modification of the guidelines. Updates may be prompted by approvals of new drugs, vaccines, medical devices, or diagnostics; by new information regarding indications or dosing; by new safety or efficacy data; or by other information that may affect prevention and treatment of HIV-related OIs. How to Use the Information in These Guidelines Recommendations in this report address— • Preventing exposure to opportunistic pathogens; • Preventing disease; • Discontinuing primary prophylaxis after immune reconstitution; • Treating disease; • When to start ART in the setting of an acute OI; • Monitoring for adverse effects (including immune reconstitution inflammatory syndrome); • Managing treatment failure; • Preventing disease recurrence (secondary prophylaxis or chronic maintenance therapy); • Discontinuing secondary prophylaxis or chronic maintenance therapy after immune reconstitution; and • Special considerations during pregnancy. Recommendations are rated according to the criteria in the table below and accompanied, as needed, by explanatory text that reviews the evidence and the working group’s assessment. In this system, the letters A, B, or C signify the strength of the recommendation for or against a preventive or therapeutic measure, and the Roman numerals I, II, or III indicate the quality of the evidence Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-6 supporting the recommendation. In cases where there are no data for the prevention or treatment of an OI based on studies conducted in people with HIV, but there are data derived from studies in people without HIV that could plausibly guide management of patients with HIV, the recommendation is rated II or III but is assigned A, B, or C depending on the strength of the recommendation. Rating System for Prevention and Treatment Recommendations Strength of Recommendation Quality of Evidence for the Recommendation A: Strong recommendation for the statement B: Moderate recommendation for the statement C: Weak recommendation for the statement I: One or more randomized trials with clinical outcomes and/or validated laboratory endpoints II: One or more well-designed, non-randomized trials or observational cohort studies with long-term clinical outcomes III: Expert opinion This document also includes tables in each section pertinent to the prevention and treatment of the OI(s) in that section, as well as seven summary tables at the end of the document (Tables 1–7) and a figure of the latest Advisory Committee of Immunization Practices immunization recommendations adapted to adults and adolescents with HIV. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-7 References 1. Kaplan JE, Masur H, Holmes KK, et al. USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus: an overview. USPHS/IDSA Prevention of Opportunistic Infections Working Group. Clin Infect Dis. 1995;21 Suppl 1:S12-31. Available at: 2. Bacchetti P, Moss AR. Incubation period of AIDS in San Francisco. Nature. 1989;338(6212):251-253. Available at: 3. Alcabes P, Munoz A, Vlahov D, Friedland GH. Incubation period of human immunodeficiency virus. Epidemiol Rev. 1993;15(2):303-318. Available at: 4. Bacchetti P, Osmond D, Chaisson RE, et al. Survival patterns of the first 500 patients with AIDS in San Francisco. J Infect Dis. 1988;157(5):1044-1047. Available at: 5. Palella FJ, Jr., Delaney KM, Moorman AC, et al. Declining morbidity and mortality among patients with advanced human immunodeficiency virus infection. HIV Outpatient Study Investigators. N Engl J Med. 1998;338(13):853-860. Available at: 6. Detels R, Munoz A, McFarlane G, et al. Effectiveness of potent antiretroviral therapy on time to AIDS and death in men with known HIV infection duration. Multicenter AIDS Cohort Study Investigators. JAMA. 1998;280(17):1497-1503. Available at: 7. Mocroft A, Vella S, Benfield TL, et al. Changing patterns of mortality across Europe in patients infected with HIV-1. EuroSIDA Study Group. Lancet. 1998;352(9142):1725-1730. Available at: 8. McNaghten AD, Hanson DL, Jones JL, Dworkin MS, Ward JW. Effects of antiretroviral therapy and opportunistic illness primary chemoprophylaxis on survival after AIDS diagnosis. Adult/Adolescent Spectrum of Disease Group. AIDS. 1999;13(13):1687-1695. Available at: 9. Miller V, Mocroft A, Reiss P, et al. Relations among CD4 lymphocyte count nadir, antiretroviral therapy, and HIV-1 disease progression: results from the EuroSIDA study. Ann Intern Med. 1999;130(7):570-577. Available at: 10. Mocroft A, Ledergerber B, Katlama C, et al. Decline in the AIDS and death rates in the EuroSIDA study: an observational study. Lancet. 2003;362(9377):22-29. Available at: 11. Buchacz K, Lau B, Jing Y, et al. Incidence of AIDS-defining opportunistic infections in a multicohort analysis of HIV-infected persons in the United States and Canada, 2000–2010. J Infect Dis. 2016;214(6):862-872. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-8 12. Gardner EM, McLees MP, Steiner JF, Del Rio C, Burman WJ. The spectrum of engagement in HIV care and its relevance to test-and-treat strategies for prevention of HIV infection. Clin Infect Dis. 2011;52(6):793-800. Available at: 13. Ives NJ, Gazzard BG, Easterbrook PJ. The changing pattern of AIDS-defining illnesses with the introduction of highly active antiretroviral therapy (HAART) in a London clinic. J Infect. 2001;42(2):134-139. Available at: 14. Coelho L, Veloso VG, Grinsztejn B, Luz PM. Trends in overall opportunistic illnesses, Pneumocystis carinii pneumonia, cerebral toxoplasmosis and Mycobacterium avium complex incidence rates over the 30 years of the HIV epidemic: a systematic review. Braz J Infect Dis. 2014;18(2):196-210. Available at: 15. Rubaihayo J, Tumwesigye NM, Konde-Lule J. Trends in prevalence of selected opportunistic infections associated with HIV/AIDS in Uganda. BMC Infect Dis. 2015;15:187. Available at: 16. Centers for Disease Control and Prevention. HIV surveillance report: diagnoses of HIV infection in the United States and dependent areas, 2019. 2021. Available at: 17. Centers for Disease Control and Prevention. Monitoring selected national HIV prevention and care objectives by using HIV surveillance data—United States and 6 dependent areas, 2019. 2021. Available at: 18. Panel on Antiretroviral Guidelines for Adults and Adolescents. Limitations to treatment safety and efficacy. Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents Living with HIV. 2022. Available at: 19. Kelly C, Gaskell KM, Richardson M, Klein N, Garner P, MacPherson P. Discordant immune response with antiretroviral therapy in HIV-1: a systematic review of clinical outcomes. PLoS One. 2016;11(6):e0156099. Available at: 20. Sonnenberg P, Glynn JR, Fielding K, Murray J, Godfrey-Faussett P, Shearer S. How soon after infection with HIV does the risk of tuberculosis start to increase? A retrospective cohort study in South African gold miners. J Infect Dis. 2005;191(2):150-158. Available at: 21. Wood R, Maartens G, Lombard CJ. Risk factors for developing tuberculosis in HIV-1-infected adults from communities with a low or very high incidence of tuberculosis. J Acquir Immune Defic Syndr. 2000;23(1):75-80. Available at: 22. Wallace JM, Hansen NI, Lavange L, et al. Respiratory disease trends in the Pulmonary Complications of HIV Infection Study cohort. Pulmonary Complications of HIV Infection Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-9 Study Group. Am J Respir Crit Care Med. 1997;155(1):72-80. Available at: 23. Hirschtick RE, Glassroth J, Jordan MC, et al. Bacterial pneumonia in persons infected with the human immunodeficiency virus. Pulmonary Complications of HIV Infection Study Group. N Engl J Med. 1995;333(13):845-851. Available at: 24. Engels EA, Rosenberg PS, Biggar RJ. Zoster incidence in human immunodeficiency virus-infected hemophiliacs and homosexual men, 1984–1997. District of Columbia Gay Cohort Study. Multicenter Hemophilia Cohort Study. J Infect Dis. 1999;180(6):1784-1789. Available at: 25. Gebo KA, Kalyani R, Moore RD, Polydefkis MJ. The incidence of, risk factors for, and sequelae of herpes zoster among HIV patients in the highly active antiretroviral therapy era. J Acquir Immune Defic Syndr. 2005;40(2):169-174. Available at: 26. Vanhems P, Voisin L, Gayet-Ageron A, et al. The incidence of herpes zoster is less likely than other opportunistic infections to be reduced by highly active antiretroviral therapy. J Acquir Immune Defic Syndr. 2005;38(1):111-113. Available at: 27. Toossi Z, Mayanja-Kizza H, Hirsch CS, et al. Impact of tuberculosis (TB) on HIV-1 activity in dually infected patients. Clin Exp Immunol. 2001;123(2):233-238. Available at: 28. Sadiq ST, McSorley J, Copas AJ, et al. The effects of early syphilis on CD4 counts and HIV-1 RNA viral loads in blood and semen. Sex Transm Infect. 2005;81(5):380-385. Available at: 29. Bentwich Z. Concurrent infections that rise the HIV viral load. J HIV Ther. 2003;8(3):72-75. Available at: 30. Kublin JG, Patnaik P, Jere CS, et al. Effect of Plasmodium falciparum malaria on concentration of HIV-1-RNA in the blood of adults in rural Malawi: a prospective cohort study. Lancet. 2005;365(9455):233-240. Available at: 31. Abu-Raddad LJ, Patnaik P, Kublin JG. Dual infection with HIV and malaria fuels the spread of both diseases in sub-Saharan Africa. Science. 2006;314(5805):1603-1606. Available at: 32. Centers for Disease Control and Prevention. Guidelines for prophylaxis against Pneumocystis carinii pneumonia for persons infected with human immunodeficiency virus. MMWR Suppl. 1989;38(5):1-9. Available at: 33. Masur H. Recommendations on prophylaxis and therapy for disseminated Mycobacterium avium complex disease in patients infected with the human immunodeficiency virus. Public Health Service Task Force on Prophylaxis and Therapy for Mycobacterium avium Complex. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-10 N Engl J Med. 1993;329(12):898-904. Available at: 34. USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus: a summary. MMWR Recomm Rep. 1995;44(RR-8):1-34. Available at: 35. USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus: disease-specific recommendations. USPHS/IDSA Prevention of Opportunistic Infections Working Group. Clin Infect Dis. 1995;21 Suppl 1:S32-43. Available at: 36. 1997 USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with HIV: part I. prevention of exposure. U.S. Department of Health and Human Services, Public Health Service, Centers for Disease Control and Prevention. Am Fam Physician. 1997;56(3):823-834. Available at: 37. 1999 USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus. U.S. Public Health Service (USPHS) and Infectious Diseases Society of America (IDSA). MMWR Recomm Rep. 1999;48(RR-10):1-59, 61-56. Available at: 38. Kaplan JE, Masur H, Holmes KK, USPHS, Infectious Disease Society of America. Guidelines for preventing opportunistic infections among HIV-infected persons—2002. Recommendations of the U.S. Public Health Service and the Infectious Diseases Society of America. MMWR Recomm Rep. 2002;51(RR-8):1-52. Available at: 39. Kaplan JE, Masur H, Jaffe HW, Holmes KK. Preventing opportunistic infections in persons infected with HIV: 1997 guidelines. JAMA. 1997;278(4):337-338. Available at: 40. 1999 USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus. Clin Infect Dis. 2000;30 Suppl 1:S29-65. Available at: 41. USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus: a summary. Ann Intern Med. 1996;124(3):349-368. Available at: 42. 1997 USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with human immunodeficiency virus. Ann Intern Med. 1997;127(10):922-946. Available at: 43. 1999 USPHS/IDSA guidelines for the prevention of opportunistic infections in persons infected with HIV: part I. prevention of exposure. Am Fam Physician. 2000;61(1):163-174. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV A-11 44. Antiretroviral therapy and medical management of pediatric HIV infection and 1997 USPHS/IDSA report on the prevention of opportunistic infections in persons infected with human immunodeficiency virus. Pediatrics. 1998;102(4 Pt 2):999-1085. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-1 Bacterial Enteric Infections Updated: October 8, 2024 Reviewed: October 8, 2024 Epidemiology HIV-associated alterations in mucosal immunity or intestinal integrity and treatment with acid-suppressive agents may increase the risk of enteric bacterial infections. Rates of Gram-negative bacterial enteric infections are at least 10 times higher among adults with HIV than in the general population, but these rates are lower among people with HIV who are treated with antiretroviral therapy (ART).1 The risk of bacterial diarrhea varies according to CD4 T lymphocyte (CD4) cell count and is greatest in individuals with clinical AIDS or CD4 counts <200 cells/mm3. The bacteria most frequently isolated by culture from adults with HIV in the United States are Shigella, Campylobacter, and nontyphoidal Salmonella spp. (particularly Salmonella enterica serotypes Typhimurium and Enteritidis).1-6 Diarrheagenic Escherichia coli, particularly enteroaggregative E. coli, may contribute to the burden of diarrheal disease,7 but their role is understood poorly because reporting to public health systems is not required. Data on Helicobacter pylori infection in HIV infection are limited and do not suggest excess risk in people with HIV.8 Clostridioides difficile–associated infection (CDI) is common in people with HIV9; in addition to traditional risk factors, such as exposure to a health care facility or to antibiotics, data10 suggest that low CD4 count (<50 cells/mm3) is an independent risk factor. Incidence of community-onset CDI is increasing, and clinicians also should consider CDI in the evaluation of outpatient diarrheal illnesses in people with HIV. Other enteric infections that may cause diarrhea—such as Mycobacterium avium complex (MAC), cytomegalovirus, and various protozoa—are discussed elsewhere in these guidelines. As with bacterial enteric infections in people without HIV, the probable source for most bacterial enteric infections in people with HIV is ingestion of contaminated food or water.11 Sexual activity with the potential for direct or indirect fecal-oral exposure also increases risk of infections, especially with Shigella12 and Campylobacter.3,13-16 Clinical Manifestations Three major clinical syndromes of infection are associated with Gram-negative enteric bacteria among people with HIV: • Self-limited gastroenteritis; • Severe and prolonged diarrheal disease, potentially associated with fever, bloody diarrhea, and weight loss; and • Bacteremia associated with extra-intestinal involvement, with or without concurrent or preceding gastrointestinal (GI) illness.6,17,18 Severe community-associated diarrhea often is defined as six or more loose stools (loose stool is defined as defecated material that takes the shape of a container) per day with or without other signs of systemic illness, such as fecal blood, orthostatic hypotension, or fever. In people with HIV, the risk of more profound illness increases with the degree of immunosuppression but risk diminishes Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-2 with ART therapy.1,4,5,11,18,19 Relapses in infection with Salmonella and other Gram-negative bacterial enteric pathogens after appropriate treatment have been well documented in people with HIV.11,20,21 As in other populations, CDI can cause a variety of syndromes, from watery diarrhea to toxic megacolon.10 Although enteric pathogens can be associated with clinical proctitis (e.g., pain with defecation, tenesmus, bloody discharge),22 other infections that may be transmitted during intimate contact (e.g., Chlamydia trachomatis including lymphogranuloma venereum, Neisseria gonorrhoeae, herpes simplex virus, Treponema pallidum, and mpox) more commonly cause this syndrome, especially in those with relevant exposures (e.g., condomless receptive anal intercourse).23 Proctocolitis with diarrhea caused by STIs is less common but may occur; relevant exposures should be queried.24 Diagnosis Assessment of patients with diarrhea should include a complete exposure history (i.e., ingestion of contaminated food or water, including through recreational exposure to water, sexual history or other fecal-oral exposures, animal/pet exposures, travel-related exposures, exposure to antibiotics or chemotherapies, use of acid-suppressing medications, recent hospitalization); a medication review, because diarrhea is a common side effect of some ART and antibiotics; quantification of the diarrheal illness by stool frequency, consistency, volume, duration, and presence of blood; and associated signs and symptoms, such as presence and duration of fever. Physical examination should include measurement of temperature and assessment of intravascular volume and nutritional status. The diagnosis of Gram-negative bacterial enteric infection is established through cultures of stool and blood or stool molecular methods (i.e., culture-independent diagnostic tests [CIDTs]), ideally before antibiotics are given. Although stool molecular methods rapidly diagnose enteric infections, stool cultures are required to obtain phenotypic antibiotic sensitivity testing for isolated enteric pathogens and may also be helpful during outbreak investigations to identify the source. Thus, the Centers for Disease Control and Prevention (CDC) recommends reflex stool cultures and antibiotic sensitivity testing for specimens with positive CIDT reports given increasing resistance detected in enteric bacterial infections.25 Because incidence of bacteremia associated with Salmonella gastroenteritis is high in people with HIV—particularly those with advanced disease—blood cultures should be obtained from any patient who has diarrhea and fever. For shigellosis, blood cultures may be helpful but are less likely to be positive than in salmonellosis.18 Other infections for which people with HIV are at risk, albeit at a lower rate, are non-jejuni, non-coli Campylobacter spp.—such as C. fetus, C. upsaliensis, and C. lari—and the enterohepatic Helicobacter spp. (H. cineadi and H. fennelliae), which were described originally as Campylobacter spp. Blood culture systems typically will grow these bacteria, but they are unlikely to be identified on routine stool cultures performed by most laboratories because growing these fastidious organisms requires special stool culture conditions. The diagnosis of CDI can be made only through careful selection of the correct population for testing and a correlation of clinical and laboratory findings. Populations at risk for C. difficile diarrhea include individuals who recently received or currently are receiving antibiotics (including antimicrobial prophylaxis) or cancer chemotherapy; those who have been hospitalized in the past 4 to 6 weeks (or currently are hospitalized); those who reside in a long-term care facility; those with CD4 counts <200 cells/mm3; those taking acid-suppressive medications; and those with moderate-to-severe community-acquired diarrhea.26 Only people with diarrhea (defined as three or more loose stools in 24 hours) should be tested for CDI to limit detection of asymptomatic colonization, and only stool samples that take the shape of the container (i.e., diarrheal) should be tested.27 Detection of Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-3 either the C. difficile toxin B gene (using nucleic acid amplification testing [NAAT]) or the C. difficile toxin B protein (using an enzyme immunoassay [EIA]) is required for diagnosis. Current EIAs suffer from low sensitivity, whereas polymerase chain reaction (or PCR) assays have high sensitivity and can detect asymptomatic carriers. Glutamate dehydrogenase (GDH) antigen enzyme immunoassays, which detect an antigen common to C. difficile strains, whether or not toxigenic, must be combined with a second confirmatory test for stool C. difficile toxin B.28,29 Based on the criteria above (i.e., person meets the definition of diarrhea and the stool sample is diarrhea, taking the shape of the container), Infectious Diseases Society of America (IDSA) and Society for Healthcare Epidemiology of America (or SHEA) guidelines for CDI support using an NAAT alone or a multiple-step algorithm (e.g., GDH plus toxin B assay) versus an EIA alone for C. difficile testing.29 Endoscopy generally should be reserved for patients in whom stool culture, microscopy, C. difficile toxin B assay, and blood culture fail to reveal an etiology or in whom treatment for an established diagnosis fails. Endoscopy with biopsy may be required for diagnosing etiologies other than bacterial enteric infections—including cryptosporidiosis, microsporidiosis, cytomegalovirus, or MAC gastroenteritis—and noninfectious causes of GI symptoms. Clinicians should remain alert to the possibility of sexually transmitted infections (STIs). In patients with relevant exposures and symptoms of proctitis or proctocolitis, diagnostic evaluation and treatment for STIs should are recommended.30 Preventing Exposure Multiple epidemiologic exposures can place people at risk for enteric illnesses. The most common are ingestion of contaminated food or water and fecal-oral exposures. Providing advice and education about such exposures is the responsibility of the health care provider. The clinical condition and CD4 count of a person with HIV can help the provider determine what prevention recommendations are most appropriate. People with HIV with CD4 counts <200 cells/mm3 or a history of AIDS-defining illness31 are at the greatest risk of enteric illnesses; however, excess risk of undetermined magnitude or duration may persist in those with lesser degrees of immune impairment, including individuals treated with ART. Individuals in the community should be advised to wash their hands regularly with soap and water or alcohol-based cleansers to reduce the risk of enteric infection (AIII). To prevent enteric infections, soap and water are preferred over alcohol-based cleansers, which do not kill C. difficile spores and are active only partially against norovirus and Cryptosporidium (AIII). People with HIV should be advised to wash their hands with soap and water after potential contact with human feces (e.g., through defecation, sexual exposures, cleaning feces from infants, contact with a person who has diarrhea), after handling pets or other animals, after gardening or other contact with soil, and before preparing food and eating (AIII). In addition to handwashing, use of barriers (e.g., condoms, dental dams, and gloves) can reduce exposure to feces when engaging in sex practices such as anal sex and oral-anal contact (AIII).22,30,32 Avoiding sex while any partner has diarrhea may further reduce risk of transmission. Travelers to relevant locations may be counseled on food and water hygiene (see the CDC Travelers’ Health webpage).33 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-4 Preventing Disease Recommendations for Preventing Bacterial Enteric Infections Preventing Bacterial Enteric Illness • Immunizations (e.g., against Salmonella serotype Typhi) should be recommended in advance of travel to relevant locations (see Immunizations for Preventable Diseases in Adults and Adolescents With HIV in the Adult and Adolescent Opportunistic Infection Guidelines) (AIII). • Antimicrobial prophylaxis to prevent bacterial enteric illness is not routinely recommended, including for travelers (AIII). • In rare cases—such as for immunosuppressed travelers (depending on their level of immunosuppression, the region of travel, and the trip’s duration)—antimicrobial prophylaxis with rifaximin or azithromycin should be offered (CIII). • Because of toxicity associated with fluoroquinolone use (e.g., CDI, tendinitis) and increasing rates of antimicrobial resistance among enteric bacterial pathogens outside of the United States, routine use of fluoroquinolones for prophylaxis is discouraged (AIII). • For pregnant people, azithromycin is the preferred agent for prophylaxis (BIII). Key: CDI = Clostridioides difficile–associated infection Antimicrobial prophylaxis to prevent bacterial enteric illness is not routinely recommended, including for travelers (AIII). Prophylactic antimicrobial treatment can elicit adverse reactions, promote the emergence of resistant organisms, and increase the risk of CDI. In rare cases, however, antimicrobial prophylaxis (e.g., with rifaximin or azithromycin) should be considered—such as for immunosuppressed travelers, depending on their level of immunosuppression, the region of travel, and the trip’s duration (CIII).34,35 In addition, immunizations, (e.g., against Salmonella serotype Typhi), should be recommended in advance of travel to relevant locations (see Immunizations for Travel in the Immunizations section of the Adult and Adolescent Opportunistic Infection Guidelines) (AIII). For people with HIV already taking trimethoprim-sulfamethoxazole (TMP-SMX) (e.g., for Pneumocystis jirovecii pneumonia prophylaxis), TMP-SMX may offer limited protection against traveler’s diarrhea.36 For pregnant people, azithromycin would be the preferred agent for prophylaxis (BIII). Clinicians should be aware of concerns about fluoroquinolone safety. Given increased recognition of fluoroquinolone toxicities, as well as increasing rates of antimicrobial resistance among enteric bacterial pathogens outside the United States, routine use of fluoroquinolones for prophylaxis is discouraged (AIII).37 Treating Disease Recommendations for Treating Bacterial Enteric Infections General Considerations When Managing Patients With Bacterial Enteric Infections • Oral or IV rehydration therapy (if indicated) should be given to patients with diarrhea (AIII). • Antimotility agents should be avoided if concern about inflammatory diarrhea, including CDI, exists (BIII). • Diagnostic fecal specimens should be obtained before initiation of empiric antimicrobial therapy. • If a pathogen is identified in stool, antibiotic susceptibilities should be performed to confirm and inform antibiotic choice given increased reports of antibiotic resistance. Reflexively culturing the stool of patients diagnosed using PCR-based methods can facilitate antibiotic susceptibility testing among these patients. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-5 • Risk of a bacterial enteric infection increases as CD4 count declines, with the greatest risk in people with CD4 counts <200 cells/mm3. Risk of bacteremia also increases with decreasing CD4 count. If no clinical response occurs after 3 to 4 days of therapy, consider follow-up stool culture with antibiotic susceptibility testing and other methods to detect enteric pathogens (e.g., toxin assays, molecular methods), alternative diagnosis, antibiotic resistance, or drug–drug interactions (BIII). • Effective ART may reduce the frequency, severity, and recurrence of bacterial enteric infections. Empiric Treatment of Bacterial Enteric Infections (Pending Diagnostic Studies and Antimicrobial Resistance Testing) For People With HIV and CD4 >500 cells/mm3, With 1–2 Days of Loose Stools Without Fever or Blood • Oral hydration; no further work-up and no treatment is needed. For People With HIV and CD4 Count 200–500 cells/mm3, With Diarrhea Severe Enough to Compromise Quality of Life or Ability to Work • Azithromycin 500 mg PO daily for 5 days (BIII), or • Ciprofloxacin 500–750 mg PO every 12 hours for 5 days (BIII) For People With HIV and Severe Disease (e.g., people with CD4 count <200 cells/mm3 or concomitant AIDS-defining illnesses), With Clinically Severe Diarrhea (≥6 liquid stools/day or bloody stool and/or accompanying fever or chills) • Hospitalization for inpatient diagnostic evaluation and IV antibiotics • Ceftriaxone 1–2 g IV every 24 hours (BIII)a until antimicrobial susceptibility is available, then treatment can be changed based on sensitivity results. o If Campylobacter or Shigella bacteremia is suspected, a carbapenem is preferred for empiric therapy (BIII). Duration of Therapy • Therapy and its duration should be adjusted depending on stool microbiology results and antibiotic sensitivity testing. See recommendations for specific bacteria below. If no pathogen is identified and the patient recovers quickly, 5 days of therapy is recommended. Other Considerations • MSM may be at increased risk for antibiotic-resistant enteric infections. • Diarrhea is a common illness of international travelers. Antimicrobial resistance among enteric bacterial pathogens outside the United States is common. Clinicians should consider the possibility of resistant infections when prescribing empiric antibiotic therapy for travelers with HIV while traveling or upon return to the United States, particularly among travelers to South and Southeast Asia or Africa. • For patients with persistent diarrhea (>14 days) but no other severe clinical signs (e.g., dehydration, blood in stool), antibiotic therapy can be withheld until a diagnosis is confirmed. Noninfectious etiologies of persistent diarrhea (e.g., inflammatory bowel disease) also can be considered in the differential diagnosis (BIII). • Azithromycin should not be used to treat bacteremia. • Before susceptibilities are known, empiric IV ceftriaxone is recommended, although given the rise of antimicrobial resistance in enteric pathogens, updated outbreak information, local susceptibility patterns, and travel history should always be considered. Treating Nontyphoidal Salmonellosis All people with HIV and salmonellosis should receive antibiotic treatment due to the increased risk of bacteremia (by 20- to 100-fold) and mortality (by as much as sevenfold) compared with people without HIV (AIII). For Invasive Disease (Suspected or Confirmed) Pending Susceptibilities • Ceftriaxone 1–2 g IV every 24 hours pending susceptibilities (BIII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-6 Preferred Therapy for Nontyphoidal Salmonella Gastroenteritis With or Without Bacteremia (If Susceptible) • Ciprofloxacin 500–750 mg PO (or 400 mg IV) every 12 hours (AIII) Alternative Therapy (If Susceptible) • Levofloxacin 750 mg (PO or IV) every 24 hours (BIII), or • Moxifloxacin 400mg (PO or IV) every 24 hours (BIII), or • Trimethoprim 160 mg/sulfamethoxazole 800 mg (PO or IV) every 12 hours (BIII), or • Ceftriaxone 1–2 g IV every 24 hours (BIII) Duration of Therapy for Gastroenteritis Without Bacteremia • If CD4 count ≥200 cells/mm3: 7–14 days (BIII) • If CD4 count <200 cells/mm3, minimum of 2 weeks (may extend to up to 6 weeks if with severe disease or bacteremia) (BIII) Duration of Therapy for Gastroenteritis With Bacteremia • If CD4 count ≥200 cells/mm3: 14 days; longer duration if bacteremia persists or if the infection is complicated (e.g., metastatic foci of infection are present) (BIII) • If CD4 count <200 cells/mm3: 2–6 weeks (BIII) Secondary Prophylaxis • The role of long-term, secondary prophylaxis for patients with recurrent bacteremia or gastroenteritis is not well established. Clinicians must weigh the benefit against the risks of long-term antibiotic exposure (BIII). Antibiotic choices for secondary prophylaxis are the same as for primary treatment and are dependent on the sensitivity of the Salmonella isolate. • HIV suppression with ART is expected to decrease the risk of recurrent illnesses. • Clinicians should be aware that recurrence may represent development of antimicrobial resistance during therapy. Indication • Patients with recurrent bacteremia (BIII), or • Patients with recurrent gastroenteritis (with or without bacteremia) with CD4 count <200 cells/mm3 and severe diarrhea (BIII) Discontinuing Secondary Prophylaxis • After resolution of Salmonella infection and response to ART with sustained viral suppression and CD4 count >200 cells/mm3, secondary prophylaxis likely can be discontinued (CII). Treating Shigellosis Therapy should be considered because it may slightly shorten the duration of illness and help prevent spread of the infection to others (AIII); however, antibiotic selection should be guided by the results of antibiotic susceptibility testing. Because antimicrobial resistance of Shigella spp. is increasing and limited data demonstrate that antibiotic therapy limits transmission, antibiotic treatment may be withheld in people with HIV and CD4 >500 cells/mm3 whose diarrhea resolves before culture confirmation of Shigella infection (CIII). In Severely Ill Patients Requiring Empiric Parenteral Therapy While Awaiting Susceptibility • Initiate a carbapenem until antimicrobial susceptibilities are available (BIII). Preferred Therapy (If Susceptible) • Ciprofloxacin 500–750 mg PO (or 400 mg IV) every 12 hours if MIC <0.12 µg/mL for 5 to 10 days (AIII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-7 Alternative Therapy (If Susceptible) • Levofloxacin 750 mg (PO or IV) every 24 hours if MIC <0.12 ug/mL for 5 to 10 days (BIII), or • Trimethoprim 160 mg/sulfamethoxazole 800 mg PO or IV every 12 hours for 5 to 7 days (BIII), or o Note: TMP-SMX is not recommended for bacteremia. • Azithromycin 500 mg PO daily for 5 days (BIII) o Note: Azithromycin is not recommended for bacteremia (AIII) • Ceftriaxone 1–2 g IV every 24 hours (BIII) Duration of Therapy • Gastroenteritis: 5–7 days (AIII) (except ciprofloxacin [5 to 10 days] and azithromycin [5 days]) o 7–10 days of therapy may be reasonable in patients who are severely immunosuppressed with poor clinical response to antibiotics. • Bacteremia: ≥14 days (BIII) • Recurrent infections: up to 6 weeks (BIII) Chronic Maintenance or Suppressive Therapy • Not recommended for first-time Shigella infections (BIII) Treating Campylobacteriosis • Optimal treatment is poorly defined and multidrug resistance may occur. • Antimicrobial therapy should be modified based on susceptibility reports. Mild Disease If CD4 Count >200 cells/mm3 • If diarrhea resolves before culture confirmation of Campylobacter infection, antibiotic treatment can be withheld (CIII). If symptoms persist for more than several days, consider antibiotic therapy (CIII). Mild-to-Moderate Disease • Preferred Therapy (If Susceptible) o Azithromycin 500 mg PO daily for 5 days (BIII) (not recommended for bacteremia [AIII]), or o Ciprofloxacinb 500–750 mg PO (or 400 mg IV) every 12 hours for 7–10 days (BIII) (if susceptible) • Alternative Therapy (If Susceptible) o Levofloxacinc 750 mg PO or IV every 24 hours (BIII), or Bacteremia • Ciprofloxacinb 500–750 mg PO (or 400 mg IV) every 12 hours for ≥14 days (BIII) (if susceptible) plus an aminoglycoside (BIII) to limit the emergence of antibiotic resistance Duration of Therapy • Gastroenteritis: 7–10 days (except azithromycin, which is 5 days) (BIII) • Bacteremia: ≥14 days (BIII) • Recurrent disease: 2–6 weeks (BIII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-8 Chronic Maintenance or Suppressive Therapy • Not recommended for first-time Campylobacter infections (BIII) b The rate of fluoroquinolone resistance in the United States is increasing (29% resistance in 2018 among C. jejuni isolates). Third generation cephalosporins are not reliably active and use of alternative cell-wall active agents such as carbapenems may be necessary in severely ill people requiring empiric parenteral therapy until antimicrobial susceptibilities return. Treating Clostridioides difficile–Associated Infection Preferred Therapy (Severe or Nonsevere CDIc) • Fidaxomicin 200 mg PO two times per day for 10 days (AI) Alternative Therapy • Vancomycin 125 mg PO four times per day for 10 days (AI) • For severe, life-threatening CDI, see C. difficile and references for additional information. Alternative Therapy for Nonsevere CDIc • If neither fidaxomicin nor vancomycin is available: metronidazole 500 mg PO three times per day for 10 days (CI). Note: Based on clinical trials, vancomycin is superior to metronidazole for therapy of CDI (discussed in text). Recurrent CDI • Use of fidaxomicin over oral vancomycin is recommended, in agreement with the 2021 IDSA CDI Guidelines, as it has a greater likelihood for a sustained clinical response at 30 days (AI). • Vancomycin is an acceptable option (see IDSA Guideline for tapered and pulsed regimens) (AI). • FMT may be considered after three CDI episodes (i.e., an initial and two recurrent episodes) (CIII). c Severe CDI: white blood cell count ≥15,000 cells/mL or serum creatinine concentrations >1.5 mg/dL; nonsevere CDI: white blood cell count <15,000 cells/mL and serum creatinine concentrations <1.5 mg/dL Treating Bacterial Enteric Infections During Pregnancy • Based on their safety profile, expanded-spectrum cephalosporins (such as ceftriaxone and cefotaxime) or azithromycin should be the first-line therapy for bacterial enteric infections during pregnancy if antimicrobials are required, depending on the organism and the results of susceptibility testing (BIII). • Other commonly prescribed antimicrobials during pregnancy include vancomycin and metronidazole. Fidaxomicin, quinolones, and TMP-SMX should be prescribed using shared decision-making. • Quinolones can be used for bacterial enteric infections in pregnant people with HIV if indicated by susceptibility testing or failure of first-line therapy (BIII). • TMP-SMX use in the first trimester should be avoided, if possible, because of an association with an increased risk of birth defects, specifically neural tube, cardiovascular, and urinary tract defects (BIII). Clinicians should consider giving supplemental folic acid 4 mg/day to people who are on TMP-SMX if they are capable of becoming pregnant prior to pregnancy or as soon as possible in their first trimester (BIII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CDI = Clostridioides difficile–associated infection; FMT = fecal microbiota therapy; IDSA = Infectious Diseases Society of America; IV = intravenously; MIC = minimum inhibitory concentration; MSM = men who have sex with men; PCR = polymerase chain reaction; PO = orally; TMP­SMX = trimethoprim-sulfamethoxazole Empiric Therapy In most situations, treatment of diarrheal disease in people with HIV does not differ significantly from that in immunocompetent individuals. Decisions on therapy are based on an assessment of diarrhea severity and hydration status. Patients should be informed of the importance of maintaining Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-9 hydration and be given oral or intravenous (IV) rehydration, if indicated (AIII). Because diarrheal disease can produce temporary malabsorption or lactose intolerance, consuming a bland diet and avoiding fat, dairy, and complex carbohydrates are likely to be useful and are therefore recommended (BIII). The effectiveness and safety of probiotics or antimotility agents have not been studied adequately in people with HIV who have diarrheal illnesses.38 Antimotility agents should be avoided if concern about inflammatory diarrhea, including CDI, exists (BIII). After obtaining stool samples for diagnostic evaluation, the initiation and duration of empiric antimicrobial therapy depend on the patient’s CD4 count and clinical appearance. If stool samples are obtained, antibiotic susceptibility testing should be performed to confirm and inform antibiotic choice. For example, in patients with CD4 counts >500 cells/mm3 who have had 1 to 2 days of loose stools without fever or blood, no further work-up and no treatment other than oral rehydration may be required. However, a short course of antibiotics (e.g., ciprofloxacin for 5 days [BIII]) may be indicated in people with HIV and CD4 counts of 200 to 500 cells/mm3 who have diarrhea severe enough to compromise quality of life or ability to work. Patients with severe disease (advanced HIV disease [i.e., CD4 counts <200 cells/mm3 or concomitant AIDS-defining illness] and clinically severe diarrhea [i.e., ≥6 liquid stools per day or bloody stools or a lower number of liquid stools per day but accompanied by fever or chills concerning for invasive bacterial disease]) should undergo inpatient diagnostic evaluation to determine the etiology of the diarrheal illness and receive parenteral antimicrobial treatment (AIII). In stable patients, empiric therapy with oral ciprofloxacin (BIII) or azithromycin (BIII) is recommended, particularly if the infection is not associated with international travel. However, even in the United States, all patients should have careful follow-up since rates of resistance to ciprofloxacin and (to a lesser extent) azithromycin in common enteric pathogens are substantial, and therefore treatment failure may occur. In patients with severe disease, treatment with empiric IV ceftriaxone is recommended until antimicrobial susceptibility results are available (BIII). Given the rise of antimicrobial resistance in enteric pathogens, however, updated outbreak information, local susceptibility patterns and travel history always should be considered. For example, if Campylobacter or Shigella bacteremia is suspected, a carbapenem is preferred for empiric therapy (BIII). Therapy should be adjusted based on the results of the diagnostic work-up. For diarrhea that is persistent (i.e., lasting >14 days) in the absence of other clinical signs of severity—such as bloody stool or dehydration—antibiotic therapy can be withheld and directed therapy initiated once a diagnosis is confirmed. Noninfectious etiologies of persistent diarrhea (e.g., inflammatory bowel disease) also should be considered in the differential diagnosis (BIII). International travel: Diarrhea is one of the most common illnesses affecting international travelers. Antimicrobial resistance among enteric bacterial pathogens outside the United States is an important public health problem. For example, traveler’s diarrhea caused by fluoroquinolone-resistant C. jejuni in South and Southeast Asia or Africa is common.39,40 Clinicians should consider the possibility of a resistant infection when prescribing empiric therapy for travelers with HIV who experience diarrhea or a syndrome consistent with a systemic infection while traveling or upon returning to the United States, given reports of multidrug-resistant Enterobacteriaceae acquisition during travel.41-45 Pathogen-Specific Therapy Nontyphoidal Salmonella Species Immunocompetent hosts who do not have HIV often do not require antibiotic treatment for Salmonella gastroenteritis (typically caused by nontyphoidal Salmonella spp.) because the condition is usually self-limited, and treatment may prolong the carrier state. In contrast, all people with HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-10 and salmonellosis should be treated (AIII), even though no clinical trials have compared antimicrobial therapy with placebo. Notably, HIV infection increases the risk of Salmonella bacteremia 20 to 100 times and mortality as much as seven times compared to people who do not have HIV.19,46 The treatment of choice for susceptible nontyphoidal Salmonella spp. infection is a fluoroquinolone (AIII). Ciprofloxacin is the preferred agent (AIII).47 Other fluoroquinolones—such as levofloxacin and moxifloxacin are recommended as alternatives to ciprofloxacin (BIII). Although they have not been well evaluated in clinical trials, they likely would be effective in treating salmonellosis in people with HIV. Depending on antibiotic susceptibility, alternatives to the fluoroquinolones include TMP-SMX or expanded-spectrum cephalosporins, such as ceftriaxone (BIII). Fluoroquinolone resistance in nontyphoidal Salmonella spp. appears to be increasing, with preliminary CDC data showing genetic markers of fluoroquinolone resistance among 19% of 20,831 nontyphoidal Salmonella spp. isolates tested in the United States in 2023.48 In agreement with IDSA guidelines, the Panel recommends ceftriaxone over ciprofloxacin if invasive disease is suspected or confirmed, at least until susceptibilities return (BIII).47,48 The optimal duration of therapy for HIV-related nontyphoidal Salmonella infection has not been defined. For patients with CD4 counts ≥200 cells/mm3 who have mild gastroenteritis without bacteremia, 7 to 14 days of treatment is recommended (BIII). For the same patients with bacteremia, 14 days is appropriate provided clearance of bacteremia is documented. Longer treatment is recommended if bacteremia persists or if the infection is complicated (i.e., if metastatic foci are present) (BIII). For any patients with advanced HIV disease (CD4 count <200 cells/mm3) and Salmonella infection, a minimum of 2 weeks with extension up to 6 weeks of antibiotics in severe disease or bacteremia is often recommended (BIII).49 People with HIV and Salmonella bacteremia, which typically occurs in those with advanced HIV disease, should be monitored clinically for recurrence after treatment (BIII). As people with HIV age, it is also important to remember that rates of invasive Salmonella infections increase with age in each age group beyond infancy.50,51 Recurrence may present as bacteremia or as an anatomically localized infection, including intraabdominal, endothelial, urinary tract, soft tissue, bone and joint, lung, or meningeal foci. Secondary prophylaxis should be considered for patients with recurrent Salmonella bacteremia (BIII), and it also might be considered for patients with recurrent gastroenteritis (with or without bacteremia), and in those with CD4 counts <200 cells/mm3 with severe diarrhea (BIII). The value of this secondary prophylaxis has not been established and must be weighed against the risks of long-term antibiotic exposure. Recurrent Salmonella bacteremia constitutes an AIDS-defining illness,31 and HIV suppression with ART appears to decrease the risk of recurrent illnesses. In patients whose Salmonella infection is resolved and who have responded to ART with sustained viral suppression and CD4 counts >200 cells/mm3, secondary prophylaxis for salmonellosis likely can be discontinued (CII). Clinicians also should be aware that recurrence may indicate development of antimicrobial resistance during therapy. Shigella Species Therapy for Shigella infections should be considered because it may slightly shorten the duration of illness and help prevent transmission to others (AIII); however, because antimicrobial resistance of Shigella spp. is increasing and limited data demonstrate that antibiotic therapy limits transmission, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-11 antibiotic treatment may be withheld in people with HIV and CD4 >500 cells/mm3 with mild symptoms or whose diarrhea is resolving before culture confirmation of Shigella infection (CIII). When treatment is offered, antibiotic selection should be guided by the results of antibiotic susceptibility testing.43,52-55 Preferred treatment for susceptible shigellosis is a fluoroquinolone, preferably ciprofloxacin, for 5 to 10 days (AIII) with levofloxacin serving as an alternative (BIII). Importantly, preliminary CDC data estimate 60% of Shigella spp. isolated among the general U.S. population in 2023 harbored genetic markers of resistance to ciprofloxacin, and 55% of such isolates tested in 2022 had a ciprofloxacin minimum inhibitory concentration (MIC) of ≥0.12 µg/mL.48 Although current Clinical and Laboratory Standards Institute criteria categorize Shigella isolates with a ciprofloxacin MIC of 0.12 and 0.25 µg/mL as susceptible and a MIC of 0.5 µg/mL as intermediate, these isolates typically harbor a fluoroquinolone resistance gene or mutation. Until the clinical significance of these findings can be determined, alternative antibiotics should be considered to treat patients whose isolates have ciprofloxacin MICs ≥0.12 µg/mL (BIII).56 In general, automated antimicrobial susceptibility test panels do not have doubling dilutions that span the MIC range to determine susceptibility to ciprofloxacin based on the CDC recommendation of ≤0.06. As such, a clinically validated manual antimicrobial susceptibility testing method such as reference broth microdilution or a gradient diffusion method would be required to confirm susceptibility at the lower MIC range. Ciprofloxacin-resistant S. sonnei and S. flexneri infections in the United States are associated with international travel, homelessness, and men who have sex with men (MSM); ciprofloxacin-resistant shigellosis among MSM appears to be acquired predominantly within the United States, rather than during travel.43 Depending on antibiotic susceptibilities, in stable patients without concern for bacteremia, azithromycin (5 days) or TMP-SMX (5–7 days) may be alternatives (BIII). Azithromycin has not been evaluated in people with HIV and shigellosis, and the therapy suggested is extrapolated from limited data in immunocompetent hosts.56 Azithromycin susceptibility testing is not widely available in clinical laboratories but can be performed by many state public health laboratories. Preliminary CDC data estimate 34% of Shigella spp. isolated among the general U.S. population in 2023 harbored genetic markers of resistance to azithromycin.48 Azithromycin-resistant Shigella spp. infections in MSM with HIV have been reported.57-59 Multidrug resistance is common among shigellae, and clinicians should be aware that rates of infections caused by extensively drug resistant Shigella strains (strains resistant to azithromycin, ciprofloxacin, ceftriaxone, trimethoprim-sulfamethoxazole, and ampicillin) are increasing in the United States.60 Therefore, while IV ceftriaxone is recommended therapy for susceptible Shigella, in severely ill people requiring empiric parenteral therapy, carbapenems can be initiated before antimicrobial susceptibilities are available (BIII). Treatment for people with Shigella bacteremia is less well defined but extending treatment to at least 14 days is recommended (BIII). Azithromycin is not recommended for treatment of Shigella spp. bacteremia (AIII). Chronic suppressive or maintenance therapy is not recommended for first-time Shigella infections (BIII). Recurrent infections can occur, particularly in individuals with CD4 counts <200 cells/mm3, in which case, extending antimicrobial therapy for up to 6 weeks is recommended (BIII). Because of Shigella’s extremely low infectious dose, patients with shigellosis should be counseled about transmission prevention. As with Salmonella infections, suppression of HIV replication with ART is expected to decrease the risk of recurrent shigellosis. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-12 Campylobacter Species The optimal treatment of campylobacteriosis in people with HIV is poorly defined and multidrug resistance might occur.61,62 Culture and testing for the antibiotic susceptibility of Campylobacter isolates is recommended (BIII). In the United States in 2018, 29% of C. jejuni isolates were resistant to ciprofloxacin, and 2% were resistant to azithromycin; among C. coli isolates, 41% of isolates were resistant to fluoroquinolones, and 13% were resistant to azithromycin.48 For people with mild disease and CD4 counts >200 cells/mm3, therapy should be withheld unless symptoms persist for more than several days (CIII). For mild-to-moderate campylobacteriosis, initiating therapy with azithromycin for 5 days or a fluoroquinolone—such as ciprofloxacin—for 7 to 10 days (if the organism is sensitive) is recommended (BIII). Azithromycin has not been evaluated in people with HIV and campylobacteriosis, and the therapy suggested is extrapolated from limited data in immunocompetent hosts.39 Azithromycin susceptibility testing, however, is not widely available in clinical laboratories but can be performed by many state public health laboratories. Campylobacter bacteremia should be treated for at least 14 days using a fluoroquinolone if the isolate is sensitive (BIII).63 Adding a second active agent—such as an aminoglycoside—may be prudent in patients with bacteremia to limit the emergence of antibiotic resistance (BIII). Third generation cephalosporins are not reliably active and use of alternative cell-wall active agents such as carbapenems may be necessary in severely ill people requiring empiric parenteral therapy until antimicrobial susceptibilities return. Antibiotic choice should be guided by antibiotic susceptibility tests. Azithromycin is not recommended for treatment of Campylobacter bacteremia (AIII). Chronic suppressive or maintenance therapy is not recommended for first-time Campylobacter infections in people with HIV (BIII). However, recurrent infections can occur, particularly in people with CD4 counts <200 cells/mm3. In recurrent disease, extending the length of antimicrobial therapy for 2 to 6 weeks is reasonable (BIII). As with Salmonella infections, suppression of HIV replication with ART is expected to decrease the risk of recurrent Campylobacter spp. infections.64 Clostridioides difficile No randomized controlled trials have been conducted for CDI therapy in people with HIV. Available data suggest that people with HIV respond to treatment of CDI similarly to people without HIV.9 Thus, treatment of CDI in people with HIV is the same as in people without HIV. Guidelines and subsequent updates for treatment of CDI have been published29,65 and should be consulted for further information. Treatment of an Initial Episode of Clostridioides difficile–Associated Infection Four randomized clinical trials all conducted in the general population (two identical studies with ~60% hospitalized patients; two studies restricted to hospitalized patients)66-69 have revealed that, when compared to oral vancomycin, fidaxomicin increased the likelihood of a sustained clinical response of CDI (at 28 days) in the initial therapy of CDI (relative risk [RR] 1.16; 95% confidence interval [CI], 1.09–1.24).65 Fidaxomicin was equivalent to oral vancomycin in initial clinical cure, serious adverse events and all-cause mortality. Given these data, the 2021 IDSA CDI Clinical Practice Guideline update65 for adults suggests treatment with fidaxomicin rather than oral vancomycin, for initial CDI whether CDI is severe or nonsevere. Fidaxomicin remains very expensive but should be considered in people with HIV and CDI, if available (AI). Oral vancomycin is also an acceptable option for initial CDI (AI). Earlier multicenter, randomized, double-blind studies identified that oral vancomycin is superior to metronidazole for treatment of CDI.70,71 Thus, metronidazole is to be considered as an alternative drug for CDI therapy only if fidaxomicin or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-13 vancomycin are unavailable and CDI is nonsevere (white blood cell count <15,000 cells/mL and serum creatinine concentrations <1.5 mg/dL) (CI).29 Treatment of Recurrent Clostridioides difficile–Associated Infection Treatment of recurrent CDI is complex and, in part, defined by the specific circumstances of the patient with recurrent CDI and the number of prior CDI episodes. Brief guidance is provided here; the 2017 and 2021 IDSA CDI guidelines should be consulted for a full discussion of this topic.29,65 Risk factors for CDI recurrence are age ≥65 years, history of CDI, compromised immunity, severe CDI, and certain virulent strains (ribotypes 027/078/244). Similar to an initial episode of CDI and also based on the randomized clinical trials cited above,66-69 the Panel recommends administering fidaxomicin, instead of oral vancomycin, to adults with recurrent CDI (AI), consistent with the 2021 IDSA CDI Clinical Practice Guideline update.65 Fidaxomicin therapy increased the likelihood of a sustained clinical response for recurrent CDI at 30 days (RR 1.27; 95% CI, 1.05–1.54). For treatment of an initial CDI recurrence, fidaxomicin was equivalent to oral vancomycin in initial clinical cure, serious adverse events, and all-cause mortality. Vancomycin is also an acceptable option for recurrent CDI (see the IDSA Guideline for tapered and pulsed regimens) (AI). Bezlotoxumab is a humanized monoclonal antibody against C. difficile toxin B approved for prevention of recurrent CDI in high-risk adults when used in conjunction with standard-of-care (SOC) antibiotic therapy. The 2021 IDSA CDI Clinical Practice Guideline update suggests use of bezlotoxumab as a cointervention along with vancomycin as the SOC antibiotic in patients with a history of CDI in the last 6 months or other risk factors for recurrence (i.e., age ≥65 years, compromised immunity, severe CDI, or certain virulent strains (ribotypes 027/078/244).65 However, data on the benefit of bezlotoxumab therapy when fidaxomicin is used as the SOC antibiotic are limited. Limited case reports suggest that fecal microbiota therapy (FMT) (i.e., fecal transplant) may be successful and safe to treat recurrent CDI in people with HIV.72-74 However, it is important to note that complications of FMT, including transmission of enteric pathogens and antibiotic-resistant bacteria with deaths, have been reported.75,76 FMT for treatment of recurrent CDI may be considered after three total CDI episodes (initial and two recurrent CDI episodes) (CIII).29,65 The effect of ART on recurrence of CDI is unknown, but ART initiation should follow standard guidelines, similar to other enteric infections (see the Special Considerations Regarding ART Initiation section below). Special Considerations Regarding ART Initiation ART initiation should follow standard guidelines. The presence of an enteric infection should not delay ART initiation (AIII). The presence of a diarrheal illness is relevant only in terms of a patient’s ability to ingest and absorb ART. If recurrent enteric infections are documented or Salmonella bacteremia occurs, prompt initiation of ART should be considered regardless of CD4 count. Monitoring of Response to Therapy and Adverse Events (Including Immune Reconstitution Inflammatory Syndrome) Patients should be monitored closely for response to treatment, defined clinically by improvement in systemic signs and symptoms, resolution of diarrhea, and sterilization of infected tissues or body fluids, such as blood. Follow-up stool testing may be required when public health considerations and state policies dictate the need to ensure microbiologic cure, such as in health care or food service workers. Follow-up stool culture and antibiotic susceptibility testing should be considered for patients with incomplete clinical response to appropriate antimicrobial therapy. In patients with persistent or recurrent diarrhea despite therapy, clinicians should consider other enteric infections (including STIs; see the Diagnosis section above) in the context of the patient’s immune status and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-14 exposures, as well as the possibility of C. difficile or the development of antimicrobial resistance (BIII). Observational studies suggest that plasma drug concentrations in people with HIV may be decreased as a result of severe diarrhea or malabsorption.77,78 Coadministration of fluoroquinolones with magnesium- or aluminum-containing antacids or with calcium, zinc, or iron should be avoided because these agents interfere with fluoroquinolone absorption (AII).79 Although larger prospective studies are needed to determine the impact of severe diarrhea on antibiotic absorption, it is prudent to use IV antibiotics in clinically unstable patients (AIII). Immune reconstitution inflammatory syndrome has not been described in association with treatment for typical bacterial enteric pathogens. Preventing Recurrence The pharmacologic approach to recurrent enteric infections is covered in the section on directed therapy for each bacterial species. As noted above, secondary prophylaxis should be considered for patients with recurrent Salmonella bacteremia (BIII) and, in some circumstances, for those with recurrent shigellosis (BIII) or campylobacteriosis (BIII). Special Considerations During Pregnancy The diagnosis of bacterial enteric infection in pregnant people with HIV is the same as in people who are not pregnant and should be managed the same, with several considerations. Based on their safety profile, expanded-spectrum cephalosporins or azithromycin should be the first-line therapy for bacterial enteric infections during pregnancy if antimicrobials are required, depending on the organism and the results of susceptibility testing (BIII).80 Arthropathy has been noted in the offspring of animals treated with quinolones during pregnancy. However, studies evaluating quinolone use in pregnant people did not find an increased risk of birth defects or musculoskeletal abnormalities.81-83 Thus, quinolones can be used for bacterial enteric infections in pregnant people with HIV if indicated by susceptibility testing or failure of first-line therapy, as listed above with a shared medical decision-making decision model in discussion with the patient. (BIII). TMP-SMX use in the first trimester should be avoided, if possible, because of an association with an increased risk of birth defects, specifically neural tube, cardiovascular, and urinary tract defects (BIII).84-86 However, a review of potential risks related to TMP-SMX use cites the low quality of current data and supports the use of TMP-SMX in pregnant people with HIV as clinically indicated.87 Clinicians should consider giving supplemental folic acid 4 mg/day to people who are on TMP-SMX if they are capable of becoming pregnant prior to pregnancy or as soon as possible in their first trimester (BIII).84,85,88 Neonatal care providers should be informed if maternal sulfa therapy was used near delivery because of the theoretical increased risk of hyperbilirubinemia and kernicterus in the newborn. Because oral rifaximin and fidaxomicin are not absorbed systemically, these can be used in pregnancy as in nonpregnant individuals. However, pregnant people should have a shared medical decision with their providers and be made aware about the limited data about Fidaxomicin in pregnancy (BIII). Vancomycin and metronidazole are two antimicrobials that have been utilized in the perinatal period in the United States. Intravenous vancomycin has been utilized as intrapartum prophylaxis in the penicillin allergic patient colonized with group B streptococcus,89 and minimal absorption is expected with oral therapy. Although vancomycin for enteric disease is recommended for use only in its oral formulation, which is not absorbed in meaningful concentrations from the gastrointestinal tract,90 it should be noted that with intravenous use, vancomycin readily crosses the placenta.91 A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-15 study of 10 infants evaluated after the second or third trimester for in utero exposure of maternal intravenous vancomycin therapy for serious staphylococcal infections found no hearing loss or renal toxicity attributed to vancomycin.91 A review of metronidazole use in pregnancy for treatment of trichomoniasis or bacterial vaginosis found no increase in risk of birth defects.92 Studies on the use of metronidazole for CDI in pregnancy were not found. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-16 References 1. 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Foodborne Pathog Dis. 2010;7(11):1393-1399. Available at: 47. Shane AL, Mody RK, Crump JA, et al. 2017 Infectious Diseases Society of America clinical practice guidelines for the diagnosis and management of infectious diarrhea. Clin Infect Dis. 2017;65(12):e45-e80. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-20 48. Centers for Disease Control and Prevention. National Antimicrobial Resistance Monitoring System (NARMS) Now: human data. 2023. Available at: 49. Gordon MA, Banda HT, Gondwe M, et al. Non-typhoidal Salmonella bacteraemia among HIV-infected Malawian adults: high mortality and frequent recrudescence. AIDS. 2002;16(12):1633-1641. Available at: 50. Hsu RB, Tsay YG, Chen RJ, Chu SH. Risk factors for primary bacteremia and endovascular infection in patients without acquired immunodeficiency syndrome who have nontyphoid salmonellosis. Clin Infect Dis. 2003;36(7):829-834. Available at: 51. Nielsen H, Gradel KO, Schonheyder HC. High incidence of intravascular focus in nontyphoid Salmonella bacteremia in the age group above 50 years: a population-based study. APMIS. 2006;114(9):641-645. Available at: 52. Eikmeier D, Talley P, Bowen A, et al. Decreased susceptibility to azithromycin in clinical Shigella isolates associated with HIV and sexually transmitted bacterial diseases, Minnesota, USA, 2012–2015. Emerg Infect Dis. 2020;26(4):667-674. Available at: 53. Hoffmann C, Sahly H, Jessen A, et al. High rates of quinolone-resistant strains of Shigella sonnei in HIV-infected MSM. Infection. 2013;41(5):999-1003. Available at: 54. Murray K, Reddy V, Kornblum JS, et al. Increasing antibiotic resistance in Shigella spp. from infected New York City residents, New York, USA. Emerg Infect Dis. 2017;23(2):332-335. Available at: 55. Gharpure R, Friedman CR, Fialkowski V, et al. Azithromycin and ciprofloxacin treatment outcomes during an outbreak of multidrug-resistant Shigella sonnei infections in a retirement community-Vermont, 2018. Clin Infect Dis. 2022;74(3):455-460. Available at: 56. Centers for Disease Control and Prevention. CDC recommendations for diagnosing and managing Shigella strains with possible reduced susceptibility to ciprofloxacin. 2017. Available at: 57. Heiman KE, Karlsson M, Grass J, et al. Notes from the field: Shigella with decreased susceptibility to azithromycin among men who have sex with men - United States, 2002– 2013. MMWR Morb Mortal Wkly Rep. 2014;63(6):132-133. Available at: 58. Hassing RJ, Melles DC, Goessens WH, Rijnders BJ. Case of Shigella flexneri infection with treatment failure due to azithromycin resistance in an HIV-positive patient. Infection. 2014. Available at: 59. Baker KS, Dallman TJ, Ashton PM, et al. Intercontinental dissemination of azithromycin-resistant shigellosis through sexual transmission: a cross-sectional study. Lancet Infect Dis. 2015;15(8):913-921. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-21 60. Centers for Disease Control and Prevention. Increase in extensively drug-resistant shigellosis in the United States. 2023. Available at: 61. Gaudreau C, Rodrigues-Coutlee S, Pilon PA, Coutlee F, Bekal S. Long-lasting outbreak of erythromycin- and ciprofloxacin-resistant Campylobacter jejuni subspecies jejuni from 2003 to 2013 in men who have sex with men, Quebec, Canada. Clin Infect Dis. 2015;61(10):1549-1552. Available at: 62. Greninger AL, Addetia A, Starr K, et al. International spread of multidrug-resistant Campylobacter coli in men who have sex with men in Washington state and Quebec, 2015– 2018. Clin Infect Dis. 2020;71(8):1896-1904. Available at: 63. Fernandez-Cruz A, Munoz P, Mohedano R, et al. Campylobacter bacteremia: clinical characteristics, incidence, and outcome over 23 years. Medicine (Baltimore). 2010;89(5):319-330. Available at: 64. Larsen IK, Gradel KO, Helms M, et al. Non-typhoidal Salmonella and Campylobacter infections among HIV-positive patients in Denmark. Scand J Infect Dis. 2011;43(1):3-7. Available at: 65. Johnson S, Lavergne V, Skinner AM, et al. Clinical practice guideline by the Infectious Diseases Society of America (IDSA) and Society for Healthcare Epidemiology of America (SHEA): 2021 focused update guidelines on management of Clostridioides difficile infection in adults. Clin Infect Dis. 2021;73(5):e1029-e1044. Available at: 66. Louie TJ, Miller MA, Mullane KM, et al. Fidaxomicin versus vancomycin for Clostridium difficile infection. N Engl J Med. 2011;364(5):422-431. Available at: 67. Cornely OA, Crook DW, Esposito R, et al. Fidaxomicin versus vancomycin for infection with Clostridium difficile in Europe, Canada, and the USA: a double-blind, non-inferiority, randomised controlled trial. Lancet Infect Dis. 2012;12(4):281-289. Available at: 68. Guery B, Menichetti F, Anttila VJ, et al. Extended-pulsed fidaxomicin versus vancomycin for Clostridium difficile infection in patients 60 years and older (EXTEND): a randomised, controlled, open-label, phase 3b/4 trial. Lancet Infect Dis. 2018;18(3):296-307. Available at: 69. Mikamo H, Tateda K, Yanagihara K, et al. Efficacy and safety of fidaxomicin for the treatment of Clostridioides (Clostridium) difficile infection in a randomized, double-blind, comparative phase III study in Japan. J Infect Chemother. 2018;24(9):744-752. Available at: 70. Johnson S, Louie TJ, Gerding DN, et al. Vancomycin, metronidazole, or tolevamer for Clostridium difficile infection: results from two multinational, randomized, controlled trials. Clin Infect Dis. 2014;59(3):345-354. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-22 71. Zar FA, Bakkanagari SR, Moorthi KM, Davis MB. A comparison of vancomycin and metronidazole for the treatment of Clostridium difficile-associated diarrhea, stratified by disease severity. Clin Infect Dis. 2007;45(3):302-307. Available at: 72. Di Bella S, Gouliouris T, Petrosillo N. Fecal microbiota transplantation (FMT) for Clostridium difficile infection: focus on immunocompromised patients. J Infect Chemother. 2015;21(4):230-237. Available at: 73. Serrano-Villar S, Talavera-Rodriguez A, Gosalbes MJ, et al. Fecal microbiota transplantation in HIV: a pilot placebo-controlled study. Nat Commun. 2021;12(1):1139. Available at: 74. Kelly CR, Ihunnah C, Fischer M, et al. Fecal microbiota transplant for treatment of Clostridium difficile infection in immunocompromised patients. Am J Gastroenterol. 2014;109(7):1065-1071. Available at: 75. Food and Drug Administration. Fecal microbiota for transplantation: safety alert - risk of serious adverse events likely due to transmission of pathogenic organisms. 2020. Available at: 76. DeFilipp Z, Bloom PP, Torres Soto M, et al. Drug-resistant E. coli bacteremia transmitted by fecal microbiota transplant. N Engl J Med. 2019;381(21):2043-2050. Available at: 77. Gurumurthy P, Ramachandran G, Hemanth Kumar AK, et al. Malabsorption of rifampin and isoniazid in HIV-infected patients with and without tuberculosis. Clin Infect Dis. 2004;38(2):280-283. Available at: 78. Sahai J, Gallicano K, Swick L, et al. Reduced plasma concentrations of antituberculosis drugs in patients with HIV infection. Ann Intern Med. 1997;127(4):289-293. Available at: 79. Highlights of prescribing information. CIPRO® (ciprofloxacin hydrochloride) tablet, for oral use CIPRO® (ciprofloxacin), for oral suspension [package insert]. U.S. Food and Drug Administration. 2021. Available at: 80. Bérard A, Sheehy O, Zhao J, Nordeng H. Use of macrolides during pregnancy and the risk of birth defects: a population-based study. Pharmacoepidemiology and Drug Safety. 2015;24(12):1241-1248. Available at: 81. Padberg S, Wacker E, Meister R, et al. Observational cohort study of pregnancy outcome after first-trimester exposure to fluoroquinolones. Antimicrob Agents Chemother. 2014;58(8):4392-4398. Available at: 82. Schaefer C, Amoura-Elefant E, Vial T, et al. Pregnancy outcome after prenatal quinolone exposure. Evaluation of a case registry of the European Network of Teratology Information Services (ENTIS). Eur J Obstet Gynecol Reprod Biol. 1996;69(2):83-89. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV B-23 83. Loebstein R, Addis A, Ho E, et al. Pregnancy outcome following gestational exposure to fluoroquinolones: a multicenter prospective controlled study. Antimicrob Agents Chemother. 1998;42(6):1336-1339. Available at: 84. Czeizel AE, Rockenbauer M, Sorensen HT, Olsen J. The teratogenic risk of trimethoprim-sulfonamides: a population based case-control study. Reprod Toxicol. 2001;15(6):637-646. Available at: 85. Hernandez-Diaz S, Werler MM, Walker AM, Mitchell AA. Folic acid antagonists during pregnancy and the risk of birth defects. N Engl J Med. 2000;343(22):1608-1614. Available at: 86. Hernandez-Diaz S, Werler MM, Walker AM, Mitchell AA. Neural tube defects in relation to use of folic acid antagonists during pregnancy. Am J Epidemiol. 2001;153(10):961-968. Available at: 87. Ford N, Shubber Z, Jao J, Abrams EJ, Frigati L, Mofenson L. Safety of cotrimoxazole in pregnancy: a systematic review and meta-analysis. J Acquir Immune Defic Syndr. 2014;66(5):512-521. Available at: 88. Bortolus R, Filippini F, Cipriani S, et al. Efficacy of 4.0 mg versus 0.4 mg folic acid supplementation on the reproductive outcomes: a randomized controlled trial. Nutrients. 2021;13(12). Available at: 89. Puopolo KM, Lynfield R, Cummings JJ, et al. Management of infants at risk for group B streptococcal disease. Pediatrics. 2019;144(2). Available at: 90. Rao S, Kupfer Y, Pagala M, Chapnick E, Tessler S. Systemic absorption of oral vancomycin in patients with Clostridium difficile infection. Scand J Infect Dis. 2011;43(5):386-388. Available at: 91. Bourget P, Fernandez H, Delouis C, Ribou F. Transplacental passage of vancomycin during the second trimester of pregnancy. Obstet Gynecol. 1991;78(5 Pt 2):908-911. Available at: 92. Sheehy O, Santos F, Ferreira E, Berard A. The use of metronidazole during pregnancy: a review of evidence. Curr Drug Saf. 2015;10(2):170-179. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-1 Bartonellosis Updated: November 14, 2023 Reviewed: January 10, 2024 Epidemiology Bartonella species cause infections that include cat scratch disease, retinitis, trench fever, relapsing bacteremia, culture-negative endocarditis, bacillary angiomatosis (BA), and bacillary peliosis hepatis.1 The latter two manifestations occur almost exclusively in individuals who are immunocompromised. Thirty-seven species and three subspecies of Bartonella have been described and are officially recognized (see Bartonella on the List of Prokaryotic Names with Standing in Nomenclature); fourteen of these Bartonella species have been implicated in human infections. BA most often occurs late in HIV infection2 in patients with median CD4 T lymphocyte (CD4) cell counts <50 cells/mm3. In people with HIV, bartonellosis is often a chronic illness, lasting for months to more than a year, with BA lesions and intermittent bacteremia. Development of BA lesions caused by B. henselae is statistically linked to cat exposure in people with HIV.2 In contrast, BA caused by B. quintana is associated with body louse infestation and homelessness.2 The body louse serves as the vector of B. quintana to humans. To avoid exposure to B. quintana, people with HIV should avoid body lice exposure and have prompt eradication of lice if infestation occurs. The cat flea is the vector of B. henselae in cats. Cats are the most common vector (via a scratch) responsible for transmitting B. henselae to humans, most likely when their claws become contaminated with feces from B. henselae-infected fleas. In some areas of the United States, the prevalence of B. henselae bacteremia in pet cats approaches 50%;3 infection is more common among kittens and feral cat populations. Controlling cat flea infestation and avoiding cat scratches are therefore critical strategies for preventing B. henselae infections in people with HIV. Clinical Manifestations BA lesions have been associated with nearly every organ system, but cutaneous lesions are the most readily identified. These lesions can be clinically indistinguishable from Kaposi sarcoma, pyogenic granuloma, and other skin conditions. BA also can cause subcutaneous nodules. Osteomyelitis is usually caused by B. quintana, and only B. henselae causes bacillary peliosis hepatis.2 Although isolated organs can appear to be the principal focus of disease, BA represents a hematogenously disseminated infection, and systemic symptoms of fever, night sweats, and weight loss often accompany BA. Bartonella infection is a major cause of unexplained fever in patients with advanced HIV and should be considered in the differential diagnosis of patients with CD4 counts <100 cells/mm3 and fever.4 Bartonella is a frequent cause of culture-negative endocarditis in immunocompetent and immunocompromised humans and is most commonly caused by B. quintana, less frequently by B. henselae, and rarely by other Bartonella species.5 Immune complex disease (such as glomerulonephritis) may complicate endocarditis or other systemic Bartonella infections; assessment for immune complex formation may be warranted in such cases so that nephrotoxic agents can be avoided. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-2 Diagnosis Diagnosis of BA can be confirmed by histopathologic examination of biopsied tissue.6 BA lesions are characterized by vascular proliferation, and a modified silver stain (such as Warthin-Starry stain) usually demonstrates numerous bacilli. Tissue Gram staining and acid-fast staining are negative. A well-characterized indirect fluorescent antibody (IFA) serologic test was developed at the Centers for Disease Control and Prevention (CDC)7 and is available at the CDC Infectious Diseases Laboratories. In addition, several private laboratories offer IFA serological testing, but the performance characteristics of these tests have not been validated for people with HIV. In immunocompetent patients, anti-Bartonella antibodies might not be detectable for 6 weeks after acute infection; in contrast, by the time Bartonella infection is suspected in patients with late-stage HIV infection, they usually have been infected with Bartonella for months or even >1 year. However, as many as 25% of Bartonella culture-positive patients never develop antibodies in the setting of advanced HIV infection.4 In those patients who do develop anti-Bartonella antibodies, monitoring of antibody levels can be useful in following treatment response of Bartonella infection to antibiotics, reflecting resolution8 or recrudescence. Because of interlaboratory variability, longitudinal testing should be conducted at the same laboratory to enable direct comparison of titers over time. Because of their fastidious nature, Bartonella organisms can be isolated only with difficulty from blood (drawn into ethylenediaminetetraacetic acid [EDTA] tubes, centrifuged, and then plated directly onto fresh chocolate agar). Bartonella has been cultured directly from tissue in only a few laboratories.2 Removing samples from blood culture bottles after 8 days of incubation, followed by staining with acridine orange, has facilitated identification and subsequent culture of Bartonella species.9 Additionally, the CDC can perform polymerase chain reaction (PCR) amplification with universal and/or specific primers to detect Bartonella in EDTA blood samples (see Bartonella quintana Molecular Detection); these molecular detection tests also are increasingly available through private laboratories. Finally, molecular detection of Bartonella in BA skin lesions or other vascular lesions, lymph nodes, or resected cardiac valves from unfixed tissue biopsy samples (at the University of Washington) or from formalin-fixed tissue (at the CDC Infectious Disease Pathology Branch) can be performed.8,10 Bartonella species may also be detected from blood or plasma using metagenomic next generation sequencing.11-13 Clinicians should be aware that results from the CDC may take longer—several weeks to months—for serologic and molecular testing, respectively, compared with some private laboratories. A notable update was published in the 2023 Duke-ISCVID Criteria for Infective Endocarditis, indicating that an IFA immunoglobulin G (IgG) titer of ≥1:800 for B. quintana or B. henselae or identification of a Bartonella sp. by PCR or other nucleic acid–based techniques (including metagenomic sequencing) from blood are now considered major criteria for the diagnosis of Bartonella endocarditis.14 In summary, diagnosis of bartonellosis may require multiple testing modalities, including serologic testing (which is the most accessible test, and when positive, is helpful both for diagnosis and subsequent monitoring of treatment response), histopathology, and, especially, molecular testing for biopsied or resected tissue (e.g., BA lesion tissue or heart valve tissue). Preventing Exposure People with HIV, specifically those who are severely immunocompromised (CD4 counts <100 cells/mm3), are at high risk of severe disease when infected by B. quintana or B. henselae. The Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-3 major risk factors for acquisition of B. henselae are contact with cats infested with fleas and receiving cat scratches. Immunocompromised individuals should consider the potential risks of cat ownership (AIII). People with HIV who want cats should acquire animals that are older than 1 year of age and in good health (BII). Cats should be acquired from a known environment, have a documented health history, and be free of fleas. Stray cats and cats with flea infestation should be avoided. Declawing is not advised, but individuals with HIV should avoid rough play with cats and situations in which scratches are likely (AII). People with HIV should avoid contact with flea feces (i.e., flea dirt), and any cat-associated wound should be washed promptly with soap and water (BIII). Care of cats should include a comprehensive, ongoing flea-control program under the supervision of a veterinarian (BIII). No evidence indicates any benefits to cats or their owners from routine culture or serologic testing of the pet for Bartonella infection or from antibiotic treatment of healthy, serologically positive cats (BII). The major risk factor for B. quintana infection is body lice infestation. People with HIV who are experiencing homelessness or are in marginal housing should be informed that body louse infestation can be associated with serious illness and should be provided with appropriate measures to eradicate body lice, if present (AII). Regardless of CD4 count, people with both HIV and solid organ transplantation may be at risk of developing more severe Bartonella infections, similar to transplant recipients without HIV.15 Preventing Disease Primary chemoprophylaxis for Bartonella-associated disease is not recommended (BIII). However, note that in a retrospective case-control study, use of a macrolide (such as for Mycobacterium avium complex prophylaxis) was protective against developing Bartonella infection.2 Treating Disease Recommendations for Treating Bartonella Infections Preferred Therapy For Cat Scratch Disease, Bacillary Angiomatosis, Peliosis Hepatis, Bacteremia, and Osteomyelitis o Doxycycline 100 mg PO or IV every 12 hours (AII), or o Erythromycin 500 mg PO or IV every 6 hours (AII) For Infections Involving the CNS o Doxycycline 100 mg PO or IV every 12 hours +/– rifampin 300 mg PO or IV every 12 hours (AIII) For Confirmed Bartonella Endocarditis o (Doxycycline 100 mg IV every 12 hours + rifampin 300 mg IV or PO every 12 hours) for 6 weeks, then continue with doxycycline 100 mg IV or PO every 12 hours for ≥3 months (BII), or For Other Severe Infections (Multifocal Disease or with Clinical Decompensation) o Doxycycline 100 mg PO or IV every 12 hours + rifampin 300 mg PO or IV every 12 hours (BIII), or o Erythromycin 500 mg PO or IV every 6 hours + rifampin 300 mg PO or IV every 12 hours (BIII) Note: IV therapy may be needed initially (AIII). Alternative Therapy For Confirmed Bartonella Endocarditis Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-4 o (Doxycycline 100 mg IV every 12 hours + gentamicin 1 mg/kg IV every 8 hours) for 2 weeks, then continue with doxycycline 100 mg IV or PO every 12 hours for ≥3 months (BII) For Bartonella Infections Other than Endocarditis or CNS Infections • Azithromycin 500 mg PO daily (BIII), or • Clarithromycin 500 mg PO twice daily (BIII) Duration of Therapy • At least 3 months for all manifestations of Bartonella infection in patients with HIV Long-Term Suppressive Therapy Indication for Long-Term Suppressive Therapy If a relapse occurs after a ≥3-month course of primary treatment: • A macrolide or doxycycline as long as the CD4 count remains <200 cells/mm3 (AIII) Indications for Discontinuing Long-Term Suppressive Therapy (CIII) • Received at least 3–4 months of treatment, and • CD4 count >200 cells/mm3 for at least 6 months • Some specialists would discontinue therapy only if Bartonella titers have also decreased by 4-fold (CIII). Other Considerations • Rifamycin class antibiotics are potent hepatic enzyme inducers and may lead to significant interaction with many drugs, including ARV agents (see the Dosing Recommendations for Anti-TB Drugs table in the Mycobacterium tuberculosis Infection and Disease section for dosing recommendations). • In pregnancy, erythromycin or an alternative macrolide should be used as first-line therapy (AIII) rather than tetracyclines (such as doxycycline) due to toxicity profile; third-generation cephalosporins may have efficacy but are second line. First- and second-generation cephalosporins are not recommended because of their lack of efficacy against Bartonella (AII). Key: +/− = with or without; ARV = antiretroviral; CD4 = CD4 T lymphocyte; CNS = central nervous system; IV = intravenously; PO = orally All patients with HIV and Bartonella infection should receive antibiotic treatment (AII). No randomized, controlled clinical trials have evaluated antimicrobial treatment of bartonellosis in patients with HIV. Erythromycin and doxycycline have been used successfully to treat BA, peliosis hepatis, bacteremia, and osteomyelitis; either drug is considered first-line treatment for bartonellosis on the basis of reported experience in case series (AII).1,2 Anecdotal and limited published case reports16 suggest that other macrolide antibiotics (such as azithromycin or clarithromycin) are effective in treating Bartonella infections in patients with HIV and may be better tolerated than erythromycin; either of these can be an alternative therapy for Bartonella infections (except for endocarditis or central nervous system [CNS] infections) (BIII). Therapy should be administered for at least 3 months (AII). Doxycycline, preferably in combination with a rifamycin class antibiotic, is the treatment of choice for bartonellosis infection involving the CNS (AIII). For severe Bartonella infections (i.e., patients with multifocal disease or evidence of clinical decompensation), combination therapy using erythromycin or doxycycline with a rifamycin class antibiotic is recommended (BIII); intravenous therapy may be needed initially (AIII). Treatment of Bartonella endocarditis should include doxycycline with the addition of a rifamycin class antibiotic for a minimum of 6 weeks (BII). Doxycycline for 6 weeks plus gentamicin for the first 2 weeks may also be considered but is less Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-5 preferred due to the intrinsic nephrotoxicity of gentamicin and the frequency of vasculitis-induced renal dysfunction complicating Bartonella endocarditis (BII).17 Penicillins and first-generation cephalosporins have no in vivo activity and should not be used for treatment of bartonellosis (AII).18 Bartonella species have been isolated from patients with HIV during documented treatment or prophylaxis with trimethoprim-sulfamethoxazole (TMP-SMX);2 quinolones and TMP-SMX also have variable in vitro activity and an inconsistent clinical response in case reports and are not recommended (AIII). Monitoring of Response to Therapy and Adverse Effects (Including IRIS) The potential exists for immune reconstitution inflammatory syndrome (IRIS) in association with bartonellosis treatment and initiation of antiretroviral therapy (ART) in people with HIV. In ART-naive patients, ART generally can be initiated at the same time as Bartonella-directed treatment; however, patients with Bartonella CNS or ophthalmic lesions probably should be treated with doxycycline and a rifamycin class antibiotic for 2 to 4 weeks before instituting ART (CIII). Because of the propensity for relapse of Bartonella infection, patients should have anti-Bartonella IFA IgG antibody titers checked at the time of diagnosis (Note: It is important to specify to the receiving lab that the sample must be diluted to endpoint.) and, if positive, should be followed with sequential endpoint titers every 6 to 8 weeks during treatment, preferably until at least a fourfold decrease is documented (CIII).8 Patients treated with oral doxycycline should be cautioned about pill-associated esophagitis and photosensitivity. Adverse effects associated with macrolides include nausea, vomiting, abdominal pain, and elevations of liver transaminase levels; potential QT interval prolongation also should be considered. Serious side effects can occur during treatment with rifamycin class antibiotics, including hypersensitivity reactions (thrombocytopenia, interstitial nephritis, and hemolytic anemia) and hepatitis. Administration of rifamycin class antibiotics strongly induces the cytochrome P450 enzyme system, which is an important consideration when other medications, including many antiretroviral drugs, are taken simultaneously. Managing Treatment Failure Relapse of Bartonella infections occurs frequently, especially in patients with BA. Among patients who fail to respond to initial treatment, switching to a different preferred regimen (for example, from doxycycline to erythromycin) may be considered, again with treatment duration of ≥3 months (AIII). For severe infections, the addition of a rifamycin class antibiotic is indicated (AIII). For patients with positive or increasing antibody titers, but with clinical improvement, treatment should continue until at least a fourfold decrease in the antibody titers is documented (CIII).8 Preventing Recurrence After a primary course of treatment (minimum of 3 months), treatment may be discontinued, with close monitoring for evidence of relapse (e.g., symptoms, increase in antibody titers). If a relapse occurs, an additional course of treatment is recommended, followed by long-term suppression of infection with doxycycline or a macrolide (AIII). Long-term suppression can be discontinued after the patient has received at least 3 to 4 months of therapy and when the CD4 count remains >200 cells/mm3 on effective ART for ≥6 months (CIII).8 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-6 Some specialists would discontinue therapy only if the Bartonella titers also have decreased at least fourfold (CIII). Special Considerations During Pregnancy Infection with B. bacilliformis in immunocompetent patients during pregnancy has been associated with increased complications and risk of death, but no data are available on the effect of B. quintana or B. henselae infection during pregnancy. The approach to diagnosis of Bartonella infections in pregnant people is the same as in nonpregnant people. Erythromycin treatment (or an alternative macrolide) should be used as first-line therapy (AIII) rather than tetracyclines (such as doxycycline) during pregnancy because of the increased risk of hepatotoxicity and the accumulation of tetracycline in fetal teeth and bones, resulting in dark, permanent staining of fetal teeth. Third-generation cephalosporins, such as ceftizoxime19 or ceftriaxone, may have efficacy against Bartonella in pregnant people with HIV, but it should be considered second-line therapy after a macrolide. First- and second-generation cephalosporins are not recommended because of their lack of efficacy against Bartonella (AII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-7 References 1. Rose SR, Koehler J. Bartonella, including cat-scratch disease. In: Mandell, Douglas, and Bennett's Principles and Practice of Infectious Disease. J. E. Bennett, R. Dolin and M. J. Blaser. 9th ed. Philadelphia, PA: Elsevier Press; 2020. 2. Koehler JE, Sanchez MA, Garrido CS, et al. Molecular epidemiology of bartonella infections in patients with bacillary angiomatosis-peliosis. N Engl J Med. 1997;337(26):1876-1883. Available at: 3. Koehler JE, Glaser CA, Tappero JW. Rochalimaea henselae infection. A new zoonosis with the domestic cat as reservoir. JAMA. 1994;271(7):531-535. Available at: 4. Koehler JE, Sanchez MA, Tye S, et al. Prevalence of Bartonella infection among human immunodeficiency virus-infected patients with fever. Clin Infect Dis. 2003;37(4):559-566. Available at: 5. Fournier PE, Thuny F, Richet H, et al. Comprehensive diagnostic strategy for blood culture-negative endocarditis: a prospective study of 819 new cases. Clin Infect Dis. 2010;51(2):131-140. Available at: 6. LeBoit PE, Berger TG, Egbert BM, Beckstead JH, Yen TS, Stoler MH. Bacillary angiomatosis. The histopathology and differential diagnosis of a pseudoneoplastic infection in patients with human immunodeficiency virus disease. Am J Surg Pathol. 1989;13(11):909-920. Available at: 7. Regnery RL, Olson JG, Perkins BA, Bibb W. Serological response to "Rochalimaea henselae" antigen in suspected cat-scratch disease. Lancet. 1992;339(8807):1443-1445. Available at: 8. Lee SA, Plett SK, Luetkemeyer AF, et al. Bartonella quintana aortitis in a man with AIDS, diagnosed by needle biopsy and 16S rRNA gene amplification. J Clin Microbiol. 2015;53(8):2773-2776. Available at: 9. Larson AM, Dougherty MJ, Nowowiejski DJ, et al. Detection of Bartonella (Rochalimaea) quintana by routine acridine orange staining of broth blood cultures. J Clin Microbiol. 1994;32(6):1492-1496. Available at: 10. Dumler JS, Carroll KS, Patel R. Bartonella. In: Manual of Clinical Microbiology. K. C. Carroll, M. A. Pfaller and M. Landry. 12th ed. Washington, DC: American Society for Microbiology; 2019. 11. Li M, Yan K, Jia P, Wei E, Wang H. Metagenomic next-generation sequencing may assist diagnosis of cat-scratch disease. Front Cell Infect Microbiol. 2022;12:7. Available at: 12. Flurin L, Wolf MJ, Fisher CR, et al. Pathogen detection in infective endocarditis using targeted metagenomics on whole blood and plasma: a prospective pilot study. J Clin Microbiol. 2022;60(9):e0062122. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV C-8 13. Downey RD, Russo SM, Hauger SB, et al. Identification of an emergent pathogen, Bartonella vinsonii, using next-generation sequencing in a patient with culture-negative endocarditis. J Pediatric Infect Dis Soc. 2021;10(2):213-216. Available at: 14. Fowler VG, Durack DT, Selton-Suty C, et al. The 2023 Duke-ISCVID Criteria for infective endocarditis: updating the modified Duke Criteria. Clin Infect Dis. 2023. Available at: 15. Psarros G, Riddell Jt, Gandhi T, Kauffman CA, Cinti SK. Bartonella henselae infections in solid organ transplant recipients: report of 5 cases and review of the literature. Medicine (Baltimore). 2012;91(2):111-121. Available at: 16. Guerra LG, Neira CJ, Boman D, et al. Rapid response of AIDS-related bacillary angiomatosis to azithromycin. Clin Infect Dis. 1993;17(2):264-266. Available at: 17. Raybould JE, Raybould AL, Morales MK, et al. Bartonella endocarditis and Pauci-immune glomerulonephritis: a case report and review of the literature. Infect Dis Clin Pract (Baltim Md). 2016;24(5):254-260. Available at: 18. Koehler JE, LeBoit PE, Egbert BM, Berger TG. Cutaneous vascular lesions and disseminated cat-scratch disease in patients with the acquired immunodeficiency syndrome (AIDS) and AIDS-related complex. Ann Intern Med. 1988;109(6):449-455. Available at: 19. Riley LE, Tuomala RE. Bacillary angiomatosis in a pregnant patient with acquired immunodeficiency syndrome. Obstet Gynecol. 1992;79(5, Part 2):818-819. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-1 Candidiasis (Mucocutaneous) Updated: September 16, 2024 Reviewed: September 16, 2024 Epidemiology Oropharyngeal and esophageal candidiasis are common in people with HIV.1 The vast majority of such infections are caused by Candida albicans, although infections caused by non–C. albicans species have been increasingly reported worldwide, in part due to increased selection pressure from increased use of azoles.2-9 The occurrence of oropharyngeal or esophageal candidiasis is recognized as an indicator of immune suppression and is most often observed in people with CD4 T lymphocyte (CD4) cell counts <200 cells/mm3, with esophageal disease typically occurring at lower CD4 counts than oropharyngeal disease.10,11 In contrast, vulvovaginal candidiasis—whether a single episode or recurrent—is common in healthy adults and does not suggest HIV. Clinical Manifestations Oropharyngeal candidiasis (oral thrush) is characterized by painless, creamy white, plaque-like lesions that can occur on the buccal surface, hard or soft palate, gums, oropharynx, or tongue surface. In many cases, lesions can be scraped off with a tongue depressor or other instrument. Less commonly, erythematous patches without white plaques can be seen on the anterior or posterior upper palate or diffusely on the tongue. Angular cheilosis also can be caused by Candida. Because a proportion of people with HIV who have oropharyngeal candidiasis also manifest esophageal involvement, clinicians should ascertain whether there are symptoms suggestive of esophageal disease in people with oropharyngeal candidiasis. Esophageal candidiasis generally presents with retrosternal burning pain or discomfort along with odynophagia; occasionally, esophageal candidiasis can be asymptomatic. Endoscopic examination reveals whitish plaques similar to those observed with oropharyngeal disease. On occasion, the plaques may progress to superficial ulcerations of the esophageal mucosa with central or peripheral whitish exudates. In contrast to oropharyngeal candidiasis, vulvovaginal candidiasis is less common in people with HIV and when it occurs, it is uncommonly refractory to azole therapy unless caused by non-C. albicans species. In people with HIV, Candida vulvovaginitis usually presents with white adherent vaginal discharge associated with mucosal burning and itching of mild-to-moderate severity and sporadic recurrences. In those with advanced immunosuppression, episodes may be more severe and recur more frequently. Diagnosis Oropharyngeal candidiasis is usually diagnosed clinically based on the characteristic appearance of lesions. In contrast to oral hairy leukoplakia, the white plaques of oropharyngeal candidiasis can be scraped off the mucosa. If laboratory confirmation is required, scrapings can be examined microscopically for characteristic yeast or hyphal forms, using a potassium hydroxide preparation. Cultures of clinical exudative material yield the species of Candida present. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-2 Esophageal candidiasis should be suspected in people with low CD4 count with substernal chest pain, dysphagia, and odynophagia, especially if there is oral thrush present (though the absence of oral thrush does not rule out esophageal involvement). The diagnosis of esophageal candidiasis is often made empirically based on symptoms plus response to therapy. The definitive diagnosis of esophageal candidiasis requires direct endoscopic visualization of lesions with histopathologic demonstration of characteristic Candida yeast forms in tissue and confirmation by fungal culture and speciation. Vulvovaginal candidiasis usually is diagnosed based on clinical presentation coupled with the demonstration of characteristic blastosphere and hyphal yeast forms in vaginal secretions when examined microscopically after potassium hydroxide preparation. Culture confirmation is rarely required but may provide supportive information. Self-diagnosis of vulvovaginitis is unreliable; microscopic and culture confirmation is required to avoid unnecessary exposure to treatment and to assess for other potential pathogens including those that cause sexually transmitted infections (STIs). Preventing Exposure Candida organisms are common commensals on mucosal surfaces in healthy individuals. No measures are available to reduce exposure to these fungi. Preventing Disease Routine primary prophylaxis is not recommended because mucosal disease is associated with very low attributable morbidity and mortality and, moreover, acute therapy is highly effective.12,13 Primary antifungal prophylaxis can lead to infections caused by drug-resistant Candida strains and introduce significant drug–drug interactions and QTc (QT corrected for heart rate) prolongation. In addition, long-term oral prophylaxis is expensive. Therefore, routine primary prophylaxis is not recommended (AIII). Administration of antiretroviral therapy (ART) and immune restoration is the most effective means to prevent disease. Treating Disease Treating Mucosal Candidiasis Oropharyngeal Candidiasis: Initial Episodes (Duration of Therapy: 7–14 Days) Preferred Therapy • Fluconazole 200-mg loading dose, followed by 100–200 mg PO once daily (AI) Alternative Therapy • One 50-mg miconazole mucoadhesive buccal tablet once daily: Apply to mucosal surface over the canine fossa (do not swallow, chew, or crush tablet). Refer to the product label for more detailed application instructions. (BI), or • One 10-mg clotrimazole troche PO five times a day (BI), or • Nystatin suspension 4–6 mL PO four times daily (BII), or • Itraconazole oral solution 200 mg PO daily (BI), or • Posaconazole oral suspension 400 mg (10 mL) PO twice daily for 1 day, then 400 mg daily (BI), or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-3 • Posaconazole tablet 300 mg PO twice daily for 1 day, then 300 mg daily (BI) Esophageal Candidiasis (Duration of Therapy: 14–21 Days) Note: Systemic antifungals are required for effective treatment of esophageal candidiasis (AI); topical therapy alone is not recommended (AI). Preferred Therapy • Fluconazole 200-mg loading dose, followed by 100–200 mg (up to 400 mg) PO or IV daily (AI); consider oral suspension for people with severe symptoms and difficulty swallowing. Alternative Therapy • Itraconazole oral solution 200 mg PO daily (AI), or • Isavuconazole 400 mg PO as a loading dose, followed by isavuconazole 100 mg PO daily (BI), or • Isavuconazole 400 mg PO once weekly (BI), or • Voriconazole 200 mg PO or IV twice daily (BI), or • Posaconazole oral suspension 400 mg (10 mL) PO twice daily for 1 day, then 400 mg daily (BI), or • Posaconazole tablet 300 mg PO twice daily for 1 day, then 300 mg daily (BI), or • Lipid formulation of amphotericin B 3–4 mg/kg IV daily (BI) • Caspofungin 70-mg loading dose IV, followed by 50 mg IV daily (BI), or • Micafungin 150 mg IV daily (BI), or • Anidulafungin 100 mg IV for one dose, then anidulafungin 50 mg IV daily (BI) Note: A higher rate of esophageal candidiasis relapse has been reported with echinocandins than with fluconazole. Uncomplicated Vulvovaginal Candidiasis • Fluconazole 150 mg PO for one dose (AII), or • Topical azoles (i.e., clotrimazole, butoconazole, miconazole, tioconazole, or terconazole) for 3–7 days (AII), or • Ibrexafungerp 300 mg PO twice daily for 1 day (BI), or • For azole-refractory Candida glabrata vaginitis, boric acid 600 mg vaginal suppository once daily for 14 days (BII) Severe or Recurrent Vulvovaginal Candidiasis • Oral fluconazole (100–200 mg) PO daily or topical antifungals for ≥7 days (AII) • For recurrent only (the following regimens include treatment for the acute episode plus treatment to reduce incidence of recurrent episodes): o Oteseconazole 600 mg PO at Day 1, 450 mg at Day 2, followed by once weekly 150 mg dosing starting at Day 14 for 11 weeks (AI) (for those who are not of reproductive potential); or o Fluconazole 150 mg PO at Days 1, 4, and 7, followed by oteseconazole 150 mg PO daily at Days 14 through 20, followed by oteseconazole 150 mg once weekly starting at Day 28 for 11 weeks (Weeks 4–14) (AI) (for those who are not of reproductive potential); or o Fluconazole 150 mg PO every 72 hours x 3 doses, followed by ibrexafungerp 300 mg PO twice daily 1 day per month for 6 months (BI) (use an effective form of contraception during treatment and for 4 days after the last dose) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-4 Other Considerations • Systemic azoles may have significant drug–drug interactions with ARV drugs (refer to Drug–Drug Interactions section of the Adult and Adolescent Antiretroviral Guidelines) and other drugs used for the treatment of opportunistic infections (refer to Table 4: Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections). Consider TDM if prolonged use is indicated. • Fluconazole, itraconazole, posaconazole, and voriconazole can increase the risk for QTc prolongation, especially when co-administered with other QTc prolonging drugs that are cleared by CYP3A4. • Chronic or prolonged use of azoles might promote development of resistance. Considerations During Pregnancy and Lactation • Topical therapy is preferable for treatment of oral candidiasis and vulvovaginal candidiasis in pregnancy. Oral fluconazole should be avoided when treating vulvovaginal candidiasis in the first trimester (AIII). • For pregnant people, substitution of amphotericin B for fluconazole in the first trimester is recommended for invasive or refractory esophageal Candida infections (AIII). • Human data are not available for micafungin, anidulafungin, caspofungin, thus their use in human pregnancy is not recommended (AIII). Human data on the use of voriconazole are also not available, so its use is not recommended. • Oteseconazole is contraindicated in pregnant and lactating individuals as animal studies have shown fetal malformations including ocular toxicity. Due to its long half-life, it is also contraindicated in females of reproductive potential despite the use of oral or other contraception. • Ibrexafungerp is teratogenic in animal studies. Use in pregnant or lactating individuals is contraindicated. Key: ARV = antiretroviral; CYP = cytochrome P450; IV = intravenous; PO = orally; QTc = QT corrected for heart rate; TDM = therapeutic drug monitoring Oropharyngeal Candidiasis Oral fluconazole is as effective as or superior to topical therapy for oropharyngeal candidiasis.14 In addition, oral therapy is more convenient than topical therapy and usually better tolerated. Oral therapy has the additional benefit over topical regimens of being efficacious in treating esophageal candidiasis. Oral fluconazole at 100 to 200 mg once a day is considered the drug of choice to treat oropharyngeal candidiasis except during pregnancy (AI).14 One to 2 weeks of therapy until resolution of infection is recommended for oropharyngeal candidiasis.14 Using topical agents to treat oropharyngeal candidiasis includes several advantages: it reduces systemic drug exposure, diminishes the risk of drug–drug interactions and systemic adverse events, and may reduce the likelihood that antifungal resistance develops. As an alternative to oral fluconazole, once-daily miconazole in 50-mg mucoadhesive buccal tablets (BI) or five-times-per-day clotrimazole troches can be used to treat oropharyngeal candidiasis (BI); these regimens were shown to be equivalent in a multicenter, randomized study. Nystatin suspension four times daily remains an additional alternative (BII).15 Unfavorable taste and multiple daily dosing, such as in the cases of clotrimazole and nystatin, may lead to decreased tolerability of and adherence to these topical therapies. If esophageal involvement is suspected, topical therapy alone is not recommended (AI). Itraconazole is formulated as an oral solution or capsules, which differ in dosing and efficacy. Oral itraconazole for 7 to 14 days is as effective as oral fluconazole for oropharyngeal candidiasis but less well tolerated.16 Posaconazole oral suspension17 is also as effective as fluconazole and generally better tolerated than itraconazole solution, but it is more expensive. Although both posaconazole and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-5 itraconazole have more drug–drug interactions than fluconazole, there are a few situations, such as in vitro resistance or poor clinical response, that would suggest these drugs be used in preference to fluconazole solely to treat mucosal candidiasis (BI). In a multicenter, randomized study, posaconazole was found to be more effective than fluconazole in sustaining clinical success after antifungal therapy was discontinued.17 A oral delayed-release tablet formulation of posaconazole, which exhibits less variable absorption than the oral suspension, has been available.18 Whether it offers any advantage for the treatment of oropharyngeal candidiasis has not been formally tested; however, it has been shown that switching from the oral suspension to the tablet formulation of posaconazole results in greater serum concentrations.19 Itraconazole capsules are less effective than fluconazole because of their more variable absorption, and they are associated with more drug–drug interactions than fluconazole. Esophageal Candidiasis Systemic antifungals are required for effective treatment of esophageal candidiasis (AI). A 14-day to 21-day course of either fluconazole (oral or intravenous [IV]) or oral itraconazole solution is highly effective and therefore recommended (AI). As with oropharyngeal candidiasis, however, itraconazole capsules for esophageal candidiasis may be less effective than fluconazole because of variable absorption Therefore, oral or IV fluconazole remains the preferred therapy for esophageal candidiasis (AI). People with severe symptoms initially may have difficulty swallowing oral drugs; oral fluconazole suspension is available and should be considered in such patients. A 2-week course of isavuconazole, given orally at an initial loading dose of 400 mg followed by 100 mg once daily (BI) or 400 mg once weekly, is as effective as fluconazole for uncomplicated esophageal candidiasis and is recommended as an alternative regimen (BI); however, a higher rate of gastrointestinal adverse effects was seen with the 100-mg, once-daily isavuconazole regimen than with fluconazole and the other isavuconazole regimens.20 Posaconazole, voriconazole, amphotericin B (lipid formulations), and the echinocandins caspofungin, micafungin, and anidulafungin all effectively treat esophageal candidiasis and also can be administered as alternatives (BI); however, esophageal candidiasis appears to have a higher relapse rate after treatment with the echinocandins.21,22 Cost and insurance coverage also might be issues for the newer therapies. Although infection with other pathogens that can cause esophagitis (e.g., cytomegalovirus, herpes simplex virus) can result in symptoms that mimic those of esophageal candidiasis, a diagnostic and therapeutic trial of antifungal therapy is usually warranted before endoscopy. In those who do not respond to antifungal therapy within 7 days, endoscopy is recommended to identify other potential causes of esophagitis or drug-resistant Candida (AII). Vulvovaginal Candidiasis In most people with HIV, vulvovaginal candidiasis is uncomplicated and responds readily to short-course oral or topical treatment with any of several therapies, including the following: • Oral fluconazole (AII) • Topical azoles (i.e., clotrimazole, butoconazole, miconazole, tioconazole, or terconazole) (AII) • Oral ibrexafungerp (BI) Severe or recurrent episodes of vaginitis should be treated with oral fluconazole or topical antifungal therapy for ≥7 days (AII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-6 There are now additional options for recurrent vulvovaginal candidiasis that include treatment for the acute episode plus treatment to reduce incidence of recurrent episodes. One option for people who are not of reproductive potential is oteseconazole, a new tetrazole antifungal that was U.S. Food and Drug Administration (FDA)–approved in 2022. It exhibited efficacy when administered as 600 mg on Day 1 and 450 mg on Day 2, followed by once-weekly 150 mg dosing starting at Day 14 for 11 weeks or when it was administered after three fluconazole 150-mg doses administered at Days 1, 4, and 7, followed by oteseconazole 150 mg daily dosing at Days 14 through 20, followed by oteseconazole 150 mg once weekly starting at Day 28 for 11 weeks (Weeks 4 through 14) (AI).23,24 Ibrexafungerp is an oral b-glucan synthase inhibitor that belongs in the class of triterpenoids. It was effective in Phase 2 and Phase 3 clinical trials of uncomplicated vulvovaginal candidiasis and was approved by the FDA in 2021.25,26 In December 2022, ibrexafungerp was approved by the FDA for women with recurrent vulvovaginal candidiasis. Specifically, administration of fluconazole 150 mg every 72 hours for three doses, followed by ibrexafungerp 300 mg twice daily 1 day per month for 6 months was associated with absence of recurrent infection through week 24 in 65.4% of women compared to 53.1% of women who received placebo. These findings have been reported only in a press release,27 with results available at ClinicalTrials.gov and on the FDA label,28 and are thereby less compelling than peer-reviewed publication. Therefore, ibrexafungerp can be administered for recurrent vulvovaginal candidiasis (BI). Given the potential teratogenic effects of ibrexafungerp, treatment of women with recurrent vulvovaginal candidiasis who may become pregnant requires institution and documentation of effective contraception during treatment and for 4 days after the last dose.29 For additional advice on managing Vulvovaginal Candidiasis, see the section in the STI Treatment Guidelines from the Centers for Disease Control and Prevention. Special Considerations with Regard to Starting ART There are no special considerations regarding initiation of ART in people with mucocutaneous candidiasis. Specifically, there is currently no evidence that treatment with ART needs to be delayed until treatment for candidiasis has been completed. For information about drug–drug interactions between azoles and ARV agents, see the Drug–Drug Interactions section in the Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents with HIV. For information about drug–drug interactions between azoles and other drugs used for the treatment of opportunistic infections, see Table 4: Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections. Monitoring of Response to Therapy and Adverse Events (Including IRIS) For most people with mucocutaneous candidiasis, response to antifungal therapy is rapid; signs and symptoms improve within 48 to 72 hours. Short courses of topical therapy rarely result in adverse effects, although people may experience cutaneous hypersensitivity reactions characterized by rash and pruritus. Oral azole therapy can be associated with nausea, vomiting, diarrhea, abdominal pain, or transaminase elevations. Liver function and the QTc interval should be monitored if azole therapy is anticipated for >21 days, especially in people with other hepatic comorbidities or on concomitant hepatotoxic drugs (AII). The echinocandins appear to be associated with very few adverse reactions: histamine-related infusion toxicity, transaminase elevations, and rash have been attributed to these drugs. No dose adjustments are required in renal failure.30 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-7 Immune reconstitution inflammatory syndrome (IRIS) with ART has rarely been reported for mucocutaneous candidiasis in people with HIV. Indeed, ART is associated with a markedly reduced incidence of candidiasis.31,32 Managing Treatment Failure Antifungal treatment failure is typically defined as the persistence of signs or symptoms of oropharyngeal or esophageal candidiasis within 7 days of appropriate antifungal therapy. Refractory disease occurs in approximately 4% to 5% of people with HIV who have oral or esophageal candidiasis, typically those with CD4 counts <50 cells/mm3 who have received multiple courses of azole antifungals.4 Confirmatory culture with drug susceptibilities and, in the case of esophageal candidiasis, endoscopy, are necessary to assess for treatment failure due to azole resistance or other causes of esophagitis, especially if these procedures were not initially performed. Posaconazole immediate-release oral suspension (400 mg twice daily for 28 days) is effective in 75% of people with azole-refractory oropharyngeal or esophageal candidiasis and is therefore recommended (AI).33 Again, although the delayed-release tablet formulation of posaconazole is now available, it is not known whether it offers an advantage over the suspension for treating this particular disease. Alternatively, oral itraconazole solution is effective, at least transiently, in approximately two-thirds of people with fluconazole-refractory mucosal candidiasis and can be used as alternative therapy (BII).16 If necessary, azole-refractory esophageal candidiasis also can be treated with anidulafungin (BII), caspofungin (BII), micafungin (BII), or voriconazole (BII).21,22,34,35 IV amphotericin B (BII), amphotericin B deoxycholate (BII), and the lipid preparations of amphotericin B (BII) are usually effective for treating azole-refractory disease and are therefore recommended. Amphotericin B oral suspension (1 mL of the 100-mg/mL suspension four times daily) can be administered to people with refractory oropharyngeal candidiasis who cannot take other oral options (BII), but this product is not commercially available in the United States and requires compounding by pharmacies.36 Patients with refractory vaginal candidiasis may benefit from intravaginal boric acid suppositories, which are commercially available at 600 mg.37,38 Preventing Recurrence Preventing Recurrence • Chronic suppressive therapy for recurrent oropharyngeal or vulvovaginal candidiasis is usually not recommended unless people have frequent or severe recurrences (CIII). • If used, it is reasonable to discontinue therapy if CD4 count increased to >200 cells/mm3 following initiation of ART (AIII). If the Decision Is to Use Suppressive Therapy Because of Frequent or Severe Recurrences Oropharyngeal Candidiasis • Fluconazole 100 mg PO once daily or three times weekly (BI) Esophageal Candidiasis • Fluconazole 100–200 mg PO daily (BI), or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-8 • Posaconazole oral suspension 400 mg PO twice daily (BII), or • Posaconazole tablet 300 mg PO daily (BII) Vulvovaginal Candidiasis • Fluconazole 150 mg PO once weekly (BII) or • Oteseconazole 600 mg at Day 1, 450 mg at Day 2 for treatment of the acute episode, followed by once-weekly 150-mg doses starting at Day 14 for 11 weeks (AI) (for those who are not of reproductive potential); or • Fluconazole 150 mg at Days 1, 4, and 7 for treatment of the acute episode, followed by oteseconazole 150 mg daily at Days 14–20, followed by oteseconazole 150 mg once weekly starting at Day 28 for 11 weeks (Weeks 4–14) (AI) (for those who are not of reproductive potential); or • Ibrexafungerp 300 mg twice daily 1 day per month for 6 months (BI) (use an effective form of contraception during treatment and for 4 days after the last dose.) Considerations During Pregnancy and Lactation • Chemoprophylaxis, either chronic maintenance therapy or secondary prophylaxis, against oropharyngeal, esophageal, or vaginal candidiasis using systemically absorbed azoles should not be initiated during pregnancy (AIII). Furthermore, prophylaxis with systemic azoles should be discontinued in people with HIV who become pregnant (AIII). • Oteseconazole is contraindicated in pregnant and lactating individuals as animal studies have shown fetal malformations including ocular toxicity. Due to its long half-life, it is also contraindicated in females of reproductive potential despite the use of oral or other contraception. • Ibrexafungerp is teratogenic in animal studies. Use in pregnancy or during lactation is contraindicated. Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; PO = orally When to Start Suppressive Therapy A randomized clinical trial39 of people with HIV who had CD4 counts <150 cells/mm3 documented significantly fewer episodes of oropharyngeal candidiasis and other invasive fungal infections with continuous fluconazole therapy (three times a week) than with episodic fluconazole treatment for recurrences. This clinical trial also demonstrated no difference in the risk of developing clinically significant fluconazole resistance between the two fluconazole-treated groups among patients who were receiving ART. However, secondary prophylaxis (chronic suppressive therapy) for recurrent oropharyngeal or vulvovaginal candidiasis is not recommended by most HIV specialists unless people have frequent or severe recurrences (CIII) because therapy for acute disease is effective, mortality associated with mucocutaneous disease is low, potential exists for drug interactions and for the development of antifungal-resistant Candida, and prophylaxis is costly. If recurrences are frequent or severe, oral fluconazole can be used as suppressive therapy for oropharyngeal (BI), esophageal (BI), or vulvovaginal (AII) candidiasis.40-42 Oral posaconazole twice daily is also effective for esophageal candidiasis (BII).43 The potential for development of secondary azole resistance should be considered when contemplating chronic maintenance therapy using azoles in people with HIV who are severely immunocompromised.44 Several important factors should be considered when making the decision to use secondary prophylaxis. These factors include the effect of recurrences on the person’s well-being and quality of life, the need for prophylaxis against other fungal infections, cost, adverse events, and, most importantly, drug–drug interactions.45 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-9 Rates of relapse are high in people with azole-refractory oropharyngeal or esophageal candidiasis who have initially responded to echinocandins, voriconazole, or posaconazole therapy. In such people, secondary prophylaxis should be instituted until immune reconstitution is achieved with the use of ART (AIII). For information regarding oteseconazole and ibrexafungerp, see the Vulvovaginal Candidiasis Treatment Section above. When to Stop Suppressive Therapy In situations where secondary prophylaxis has been instituted, no data exist to guide recommendations regarding its discontinuation. Based on experience with other opportunistic infections, it would be reasonable to discontinue secondary prophylaxis when the CD4 count has increased to >200 cells/mm3 following initiation of ART (AIII). Special Considerations During Pregnancy Pregnancy increases the risk of vaginal colonization with Candida species. Diagnosis of oropharyngeal, esophageal, and vulvovaginal candidiasis is the same in pregnant people as in those who are not pregnant. Topical therapy is preferable for treatment of oral candidiasis and vulvovaginal candidiasis in pregnancy. Oral fluconazole should be avoided when treating vulvovaginal candidiasis in the first trimester (AIII). Data derived from women with vulvovaginal candidiasis suggest that fluconazole should not be used at any dose (including a single 150-mg dose) in the first trimester due to the risk of spontaneous abortion, while higher exposures (>150 mg dosing) during the first trimester are associated with cardiac septal closure defects.46-50 A recent analysis of registry data from Sweden and Denmark did not find any increase in stillbirth or neonatal death associated with exposure to fluconazole at any dose during pregnancy.51 Five cases of a syndrome consisting of craniosynostosis, characteristic facies, digital synostosis, and limb contractures (fluconazole embryopathy) have been reported in women chronically prescribed fluconazole at doses of 400 mg daily or higher in pregnancy.48 A report from a national cohort register in Denmark found an increased hazard ratio (HR) of 1.48 for spontaneous pregnancy loss with any exposure to oral fluconazole from 7 to 22 weeks of pregnancy compared to unexposed, matched controls.49 An increased HR of 1.47 was also noted with low-dose (150–300-mg cumulative dose) exposure. No increase in stillbirth was seen with fluconazole exposure broadly, but an increase in risk of stillbirth (HR, 4.10) was noted with fluconazole doses >300 mg. Based on these data, substitution of amphotericin B for fluconazole in the first trimester is recommended for invasive or refractory esophageal Candida infections (AIII). Neonates born to those receiving chronic amphotericin B at delivery should be evaluated for renal dysfunction and hypokalemia. Other azoles are similarly not recommended in pregnancy. Itraconazole at high doses has been shown to be teratogenic in animals,52 but the metabolic mechanism accounting for these defects is not present in humans, so the data supporting this finding are of uncertain significance to human pregnancy. Case series in humans do not suggest an increased risk of birth defects with itraconazole,53 but experience is limited. Human data are not available for posaconazole; however, the drug was associated with skeletal abnormalities in rats and was embryotoxic in rabbits when Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-10 given at doses that produced plasma levels equivalent to those seen in humans.54 Evidence is inconclusive or inadequate for determining fetal risk associated with voriconazole use during pregnancy. An association with cleft palate and renal defects has been seen in rats, as well as embryotoxicity seen in rabbits.55 Human data on the use of voriconazole are not available, so its use is not recommended. In animals, multiple anomalies have been seen with exposure to micafungin, and ossification defects have been seen with the use of anidulafungin and caspofungin.56 Human data are not available for these drugs, thus their use in human pregnancy is not recommended (AIII). The recently FDA-approved drugs for the treatment of vulvovaginal candidiasis, ibrexafungerp and oteseconazole, are contraindicated in pregnancy as animal studies have shown fetal malformations including ocular toxicity from oteseconazole.29,57 Chemoprophylaxis, either chronic maintenance therapy or secondary prophylaxis, against oropharyngeal, esophageal, or vaginal candidiasis using systemically absorbed azoles should not be initiated during pregnancy (AIII). Furthermore, prophylaxis with systemic azoles should be discontinued in people with HIV who become pregnant (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-11 References 1. Boesecke C, Schellberg S, Schneider J, Schuettfort G, Stocker H. Prevalence, characteristics and challenges of late HIV diagnosis in Germany: an expert narrative review. Infection. 2023;51(5):1223-1239. Available at: 2. Martins MD, Lozano-Chiu M, Rex JH. Point prevalence of oropharyngeal carriage of fluconazole-resistant Candida in human immunodeficiency virus-infected patients. Clin Infect Dis. 1997;25(4):843-846. Available at: 3. Maenza JR, Merz WG, Romagnoli MJ, Keruly JC, Moore RD, Gallant JE. Infection due to fluconazole-resistant Candida in patients with AIDS: prevalence and microbiology. Clin Infect Dis. 1997;24(1):28-34. Available at: 4. Fichtenbaum CJ, Koletar S, Yiannoutsos C, et al. Refractory mucosal candidiasis in advanced human immunodeficiency virus infection. Clin Infect Dis. 2000;30(5):749-756. Available at: 5. Rex JH, Rinaldi MG, Pfaller MA. Resistance of Candida species to fluconazole. Antimicrob Agents Chemother. 1995;39(1):1-8. Available at: 6. Patel PK, Erlandsen JE, Kirkpatrick WR, et al. The changing epidemiology of oropharyngeal candidiasis in patients with HIV/AIDS in the era of antiretroviral therapy. AIDS Res Treat. 2012;2012:262471. Available at: 7. Thanyasrisung P, Kesakomol P, Pipattanagovit P, Youngnak-Piboonratanakit P, Pitiphat W, Matangkasombut O. Oral Candida carriage and immune status in Thai human immunodeficiency virus-infected individuals. J Med Microbiol. 2014;63(Pt 5):753-759. Available at: 8. Mushi MF, Mtemisika CI, Bader O, et al. High oral carriage of non-albicans Candida spp. among HIV-infected individuals. Int J Infect Dis. 2016;49:185-188. Available at: 9. Clark-Ordóñez I, Callejas-Negrete OA, Aréchiga-Carvajal ET, Mouriño-Perez RR. Candida species diversity and antifungal susceptibility patterns in oral samples of HIV/AIDS patients in Baja California, Mexico. Med Mycol. 2016. Available at: 10. Klein RS, Harris CA, Small CB, Moll B, Lesser M, Friedland GH. Oral candidiasis in high-risk patients as the initial manifestation of the acquired immunodeficiency syndrome. N Engl J Med. 1984;311(6):354-358. Available at: 11. Bonacini M, Young T, Laine L. The causes of esophageal symptoms in human immunodeficiency virus infection. A prospective study of 110 patients. Arch Intern Med. 1991;151(8):1567-1572. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-12 12. Brion LP, Uko SE, Goldman DL. Risk of resistance associated with fluconazole prophylaxis: systematic review. J Infect. 2007;54(6):521-529. Available at: 13. Salem M, Reichlin T, Fasel D, Leuppi-Taegtmeyer A. Torsade de pointes and systemic azole antifungal agents: analysis of global spontaneous safety reports. Glob Cardiol Sci Pract. 2017;2017(2):11. Available at: 14. Pappas PG, Kauffman CA, Andes DR, et al. Clinical practice guideline for the management of candidiasis: 2016 update by the Infectious Diseases Society of America. Clin Infect Dis. 2016;62(4):e1-50. Available at: 15. Vazquez JA, Patton LL, Epstein JB, et al. Randomized, comparative, double-blind, double-dummy, multicenter trial of miconazole buccal tablet and clotrimazole troches for the treatment of oropharyngeal candidiasis: study of miconazole Lauriad(R) efficacy and safety (SMiLES). HIV Clin Trials. 2010;11(4):186-196. Available at: 16. Vazquez JA. Optimal management of oropharyngeal and esophageal candidiasis in patients living with HIV infection. HIV AIDS (Auckl). 2010;2(1):89-101. Available at: 17. Vazquez JA, Skiest DJ, Nieto L, et al. A multicenter randomized trial evaluating posaconazole versus fluconazole for the treatment of oropharyngeal candidiasis in subjects with HIV/AIDS. Clin Infect Dis. 2006;42(8):1179-1186. Available at: 18. Krishna G, Ma L, Martinho M, Preston RA, O’Mara E. A new solid oral tablet formulation of posaconazole: a randomized clinical trial to investigate rising single- and multiple-dose pharmacokinetics and safety in healthy volunteers. J Antimicrob Chemother. 2012;67(11):2725-2730. Available at: 19. Jung DS, Tverdek FP, Kontoyiannis DP. Switching from posaconazole suspension to tablets increases serum drug levels in leukemia patients without clinically relevant hepatotoxicity. Antimicrob Agents Chemother. 2014;58(11):6993-6995. Available at: 20. Viljoen J, Azie N, Schmitt-Hoffmann AH, Ghannoum M. A phase 2, randomized, double-blind, multicenter trial to evaluate the safety and efficacy of three dosing regimens of isavuconazole compared with fluconazole in patients with uncomplicated esophageal candidiasis. Antimicrob Agents Chemother. 2015;59(3):1671-1679. Available at: 21. de Wet N, Llanos-Cuentas A, Suleiman J, et al. A randomized, double-blind, parallel-group, dose-response study of micafungin compared with fluconazole for the treatment of esophageal candidiasis in HIV-positive patients. Clin Infect Dis. 2004;39(6):842-849. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-13 22. Krause DS, Simjee AE, van Rensburg C, et al. A randomized, double-blind trial of anidulafungin versus fluconazole for the treatment of esophageal candidiasis. Clin Infect Dis. 2004;39(6):770-775. Available at: 23. Martens MG, Maximos B, Degenhardt T, et al. Phase 3 study evaluating the safety and efficacy of oteseconazole in the treatment of recurrent vulvovaginal candidiasis and acute vulvovaginal candidiasis infections. Am J Obstet Gynecol. 2022;227(6):880 e881-880 e811. Available at: 24. Sobel JD, Donders G, Degenhardt T, et al. Efficacy and safety of oteseconazole in recurrent vulvovaginal candidiasis. NEJM Evid. 2022;1(8):1-13. Available at: 25. Schwebke JR, Sobel R, Gersten JK, et al. Ibrexafungerp versus placebo for vulvovaginal candidiasis treatment: a phase 3, randomized, controlled superiority trial (VANISH 303). Clin Infect Dis. 2022;74(11):1979-1985. Available at: 26. Nyirjesy P, Schwebke JR, Angulo DA, Harriott IA, Azie NE, Sobel JD. Phase 2 randomized study of oral ibrexafungerp versus fluconazole in vulvovaginal candidiasis. Clin Infect Dis. 2022;74(12):2129-2135. Available at: 27. SCYNEXIS presents positive data from its pivotal phase 3 CANDLE study of oral ibrexafungerp for prevention of recurrent vaginal yeast infections during the 2022 IDSOG annual meeting [press release]. Jersey City, NJ. SCYNEXIS, Inc. 2022. Available at: 2022-08-04_SCYNEXIS_Presents_Positive_Data_from_Its_Pivotal_298.pdf. 28. BREXAFEMME® (ibrexafungerp tablets), for oral use [package insert]. U.S. Food and Drug Administration. 2021. Available at: 29. Sucher AJ, Thai A, Tran C, Mantena N, Noronha A, Chahine EB. Ibrexafungerp: a new triterpenoid antifungal. Am J Health Syst Pharm. 2022;79(24):2208-2221. Available at: 30. Chang YL, Yu SJ, Heitman J, Wellington M, Chen YL. New facets of antifungal therapy. Virulence. 2017;8(2):222-236. Available at: 31. Thambuchetty N, Mehta K, Arumugam K, Shekarappa UG, Idiculla J, Shet A. The epidemiology of IRIS in southern India: an observational cohort study. J Int Assoc Provid AIDS Care. 2017;16(5):475-480. Available at: 32. Ramirez-Amador V, Patton LL, Naglik JR, Nittayananta W. Innovations for prevention and care of oral candidiasis in HIV-infected individuals: are they available?-A workshop report. Oral Dis. 2020;26 Suppl 1:91-102. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-14 33. Skiest DJ, Vazquez JA, Anstead GM, et al. Posaconazole for the treatment of azole-refractory oropharyngeal and esophageal candidiasis in subjects with HIV infection. Clin Infect Dis. 2007;44(4):607-614. Available at: 34. Villanueva A, Gotuzzo E, Arathoon EG, et al. A randomized double-blind study of caspofungin versus fluconazole for the treatment of esophageal candidiasis. Am J Med. 2002;113(4):294-299. Available at: 35. Ally R, Schurmann D, Kreisel W, et al. A randomized, double-blind, double-dummy, multicenter trial of voriconazole and fluconazole in the treatment of esophageal candidiasis in immunocompromised patients. Clin Infect Dis. 2001;33(9):1447-1454. Available at: 36. Dentinger PJ, Swenson CF, Anaizi NH. Stability of amphotericin B in an extemporaneously compounded oral suspension. Am J Health Syst Pharm. 2001;58(11):1021-1024. Available at: 37. Powell A, Ghanem KG, Rogers L, et al. Clinicians’ use of intravaginal boric acid maintenance therapy for recurrent vulvovaginal candidiasis and bacterial vaginosis. Sex Transm Dis. 2019;46(12):810-812. Available at: 38. Nyirjesy P, Brookhart C, Lazenby G, Schwebke J, Sobel JD. Vulvovaginal candidiasis: a review of the evidence for the 2021 Centers for Disease Control and Prevention of sexually transmitted Infections treatment guidelines. Clin Infect Dis. 2022;74(Suppl_2):S162-S168. Available at: 39. Goldman M, Cloud GA, Wade KD, et al. A randomized study of the use of fluconazole in continuous versus episodic therapy in patients with advanced HIV infection and a history of oropharyngeal candidiasis: AIDS Clinical Trials Group Study 323/Mycoses Study Group Study 40. Clin Infect Dis. 2005;41(10):1473-1480. Available at: 40. Powderly WG, Finkelstein D, Feinberg J, et al. A randomized trial comparing fluconazole with clotrimazole troches for the prevention of fungal infections in patients with advanced human immunodeficiency virus infection. NIAID AIDS Clinical Trials Group. N Engl J Med. 1995;332(11):700-705. Available at: 41. Schuman P, Capps L, Peng G, et al. Weekly fluconazole for the prevention of mucosal candidiasis in women with HIV infection. A randomized, double-blind, placebo-controlled trial. Terry Beirn Community Programs for Clinical Research on AIDS. Ann Intern Med. 1997;126(9):689-696. Available at: 42. Havlir DV, Dube MP, McCutchan JA, et al. Prophylaxis with weekly versus daily fluconazole for fungal infections in patients with AIDS. Clin Infect Dis. 1998;27(6):1369-1375. Available at: 43. Vazquez JA, Skiest DJ, Tissot-Dupont H, Lennox JL, Boparai N, Isaacs R. Safety and efficacy of posaconazole in the long-term treatment of azole-refractory oropharyngeal and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-15 esophageal candidiasis in patients with HIV infection. HIV Clin Trials. 2007;8(2):86-97. Available at: 44. Johnson EM, Warnock DW, Luker J, Porter SR, Scully C. Emergence of azole drug resistance in Candida species from HIV-infected patients receiving prolonged fluconazole therapy for oral candidosis. J Antimicrob Chemother. 1995;35(1):103-114. Available at: 45. Marty F, Mylonakis E. Antifungal use in HIV infection. Expert Opin Pharmacother. 2002;3(2):91-102. Available at: 46. Alsaad AM, Kaplan YC, Koren G. Exposure to fluconazole and risk of congenital malformations in the offspring: a systematic review and meta-analysis. Reprod Toxicol. 2015;52:78-82. Available at: 47. Molgaard-Nielsen D, Pasternak B, Hviid A. Use of oral fluconazole during pregnancy and the risk of birth defects. N Engl J Med. 2013;369(9):830-839. Available at: 48. Lopez-Rangel E, Van Allen MI. Prenatal exposure to fluconazole: an identifiable dysmorphic phenotype. Birth Defects Res A Clin Mol Teratol. 2005;73(11):919-923. Available at: 49. Molgaard-Nielsen D, Svanstrom H, Melbye M, Hviid A, Pasternak B. Association between use of oral fluconazole during pregnancy and risk of spontaneous abortion and stillbirth. JAMA. 2016;315(1):58-67. Available at: 50. Berard A, Sheehy O, Zhao JP, et al. Associations between low- and high-dose oral fluconazole and pregnancy outcomes: 3 nested case-control studies. CMAJ. 2019;191(7):E179-E187. Available at: 51. Pasternak B, Wintzell V, Furu K, Engeland A, Neovius M, Stephansson O. Oral fluconazole in pregnancy and risk of stillbirth and neonatal death. JAMA. 2018;319(22):2333-2335. Available at: 52. SPORANOX® (itraconazole) oral solution [package insert]. U.S. Food and Drug Administration. 2003. Available at: 53. De Santis M, Di Gianantonio E, Cesari E, Ambrosini G, Straface G, Clementi M. First-trimester itraconazole exposure and pregnancy outcome: a prospective cohort study of women contacting teratology information services in Italy. Drug Saf. 2009;32(3):239-244. Available at: 54. NOXAFIL Highlights of prescribing information [package insert]. U.S. Food and Drug Administration. 2015. Available at: 004,0205596s001s003lbl.pdf. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV D-16 55. VFEND® [package insert]. U.S. Food and Drug Administration. 2010. Available at: 56. Pilmis B, Jullien V, Sobel J, Lecuit M, Lortholary O, Charlier C. Antifungal drugs during pregnancy: an updated review. J Antimicrob Chemother. 2015;70(1):14-22. Available at: 57. Oteseconazole. Am J Health Syst Pharm. 2022;79(23):2083-2085. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-1 Chagas Disease Updated: June 14, 2023 Reviewed: January 10, 2024 Epidemiology Chagas disease (American trypanosomiasis) is caused by the protozoan parasite Trypanosoma cruzi. It is transmitted to humans by infected triatomine bugs (“kissing bugs”), and less commonly by transfusion, organ transplant, from mother to infant, and, in rare instances, by ingestion of contaminated food or drink.1-4 Vector-borne transmission occurs only in the Americas, where an estimated 6 million people have Chagas disease.5,6 Historically, transmission occurred largely in rural areas in Latin America, where houses built of mud brick are vulnerable to colonization by the triatomine vectors.4 In such areas, Chagas disease usually is acquired in childhood. In the last several decades, successful vector control programs have substantially decreased transmission rates in much of Latin America.4,7,8 Infected triatomine vectors and T. cruzi–infected domestic and wild animals are found across the southern half of the United States, and rare cases of autochthonous vector-borne transmission have been documented.9-11 However, the risk of vector-borne infection within the United States appears to be very low.12 T. cruzi can also be transmitted in blood; screening of blood donations for anti-T. cruzi antibodies was introduced in 2007 after the U.S. Food and Drug Administration approved a serological test for that purpose.13,14 In people chronically infected with T. cruzi as a result of prior infection, profound immunosuppression (e.g., due to advanced HIV) may lead to reactivation of the disease, characterized by parasitemia, which is associated with increased intracellular parasite replication and lack of immunological control of the infection.15-17 Clinical Manifestations Acute Phase. The acute phase of T. cruzi infection, which typically goes unrecognized, lasts up to 90 days and is characterized by circulating trypomastigotes detectable on microscopy of fresh blood or buffy coat smears.2,4 If the portal of infection was the conjunctiva, patients may develop the characteristic Romaña’s sign—unilateral painless swelling of the upper and lower eyelids—which usually lasts several weeks. The other symptoms of acute infection are usually limited to a non-specific febrile illness. In a small proportion of patients, however, acute, life-threatening myocarditis or meningoencephalitis may occur.2,4 At the end of the acute phase, typically 60 to 90 days after infection, parasitemia falls below levels detectable by microscopy, and in the absence of effective antitrypanosomal treatment, T. cruzi infection passes into the chronic phase.2,4 Chronic Phase. Most patients with chronic T. cruzi infection have no signs or symptoms and are said to have the indeterminate form of the disease. Over the course of their lives, 20% to 30% of these patients will progress to clinically evident Chagas disease—most commonly, cardiomyopathy.2,4 The earliest manifestations are usually conduction system abnormalities, such as right bundle branch block, alone or in combination with frequent premature ventricular contractions, which may develop years to decades after infection.4,18 Over time, the disease may progress to Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-2 higher-grade heart block and complex ventricular arrhythmias. In patients with more advanced cardiomyopathy, poor prognostic factors include congestive heart failure, ventricular aneurysm, and complete heart block; these are associated with short-term mortality, including sudden death.19 Chagas digestive disease is much less common than cardiomyopathy.20 Dysphagia is the characteristic symptom of megaesophagus, and prolonged constipation is the most common complaint associated with megacolon. T. cruzi reactivation during the chronic phase of Chagas disease is characterized by a return to high levels of parasite replication and parasitemia, which are usually detectable by microscopy. Reactivation can occur in individuals on immunosuppressive medications or cancer chemotherapy and in people with HIV.16,21-25 Even in the absence of symptoms, people with HIV and chronic Chagas disease have significantly higher levels of T. cruzi parasitemia than their immunocompetent counterparts.24 Most cases of clinically apparent reactivation occur with CD4 T lymphocyte cell counts <200 cells/mm3, a history of prior opportunistic infections, or both.16 The clinical features of reactivated Chagas disease in people with HIV differ from those observed in individuals who are immunosuppressed for other reasons. The most common manifestations consist of T. cruzi meningoencephalitis, with or without brain abscesses (chagomas).15,16,26,27 The presentation in people with HIV may be confused with central nervous system (CNS) toxoplasmosis and should be considered in the differential diagnosis of CNS symptoms or mass lesions on imaging. The second most frequently reported manifestation of reactivation in people with HIV is acute myocarditis, sometimes superimposed on pre-existing chronic Chagas heart disease.16,17 Patients may present with new arrhythmias, pericardial effusion, acute cardiac decompensation, or rapid progression of existing chronic cardiomyopathy.16,28 Less frequent manifestations of reactivation include skin lesions, erythema nodosum, and parasitic invasion of the peritoneum, stomach, or intestine.16,28 Diagnosis Screening with serological testing is recommended for all individuals who have lived in Mexico or Central or South America for greater than 6 months.29 Most persons infected with T. cruzi are in the chronic phase and are typically unaware of their infection. Screening for infection to identify persons with the indeterminate or early clinical forms of chronic Chagas disease is important to identify those who might benefit from antiparasitic treatment and counseling regarding potential transmission of T. cruzi to others (e.g., blood donation, organ donation). This is particularly important for people with HIV because of the risk of reactivation disease. Diagnosis of chronic infection relies on serological methods to detect immunoglobulin G antibodies to T. cruzi, most commonly enzyme-linked immunosorbent assay (ELISA) and immunofluorescent antibody assay (IFA). No available assay has sufficient sensitivity and specificity to be used alone; a single positive result does not constitute a confirmed diagnosis. Two serological tests based on different antigens (i.e., whole parasite lysate and recombinant antigens) and/or techniques (e.g., ELISA and IFA) should be used for individuals with suspected Chagas. In some cases, the infection status remains difficult to resolve even after a third test, because there is no true gold standard assay for chronic T. cruzi infection.29,30 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-3 Data suggest that the sensitivity of serological assays varies by geographical location, possibly because of T. cruzi strain differences and resulting antibody responses.31,32 Options for T. cruzi serological testing in the United States include diagnostic ELISA kits based on parasite lysate or recombinant antigens.29,33 In general, polymerase chain reaction (PCR) is not a useful diagnostic test for chronic T. cruzi infection, as its sensitivity is highly variable.30,34,35 In people with HIV and epidemiologic risk factors for Chagas disease, coinfection with T. cruzi and reactivation disease should be considered in the differential diagnosis of CNS mass lesions, meningoencephalitis, arrhythmias or heart failure.16,25,26 The imaging pattern of brain chagoma is similar to that of cerebral toxoplasmosis, although chagomas tend to be larger than Toxoplasma lesions.17,26,27 Computed tomography and magnetic resonance imaging show subcortical hypodense lesions that enhance with contrast or gadolinium. These lesions most often involve brain white matter. Histopathology shows inflammation and the presence of T. cruzi amastigotes in glial cells and, less often, in neurons. Cerebrospinal fluid (CSF) typically shows a mild pleocytosis (lymphocyte predominance), increased protein, and T. cruzi trypomastigotes.16,17,26,27 In a case series that included 15 people coinfected with HIV and T. cruzi with clinical meningoencephalitis, trypomastigotes were visualized in CSF in 85%.36 A definitive diagnosis of reactivation is established by identification of the parasite or its products in tissue, such as on brain biopsy, in CSF, or in blood.16 In chronically infected patients who are immunocompetent or who have HIV coinfection in the absence of reactivation, trypomastigotes typically are undetectable in the circulating blood.24 If observed in a coinfected patient, circulating parasites suggest reactivation and the need for treatment. Testing to identify T. cruzi should be considered in all at-risk individuals with suspected reactivation of chronic Chagas disease. Initial assessment can be done by evaluation of a peripheral blood smear. Blood concentration techniques, such as capillary centrifugation, can improve sensitivity.34 In centrifuged blood, T. cruzi trypomastigotes are found just above the buffy coat. Parasites also may be observed in lymph nodes, bone marrow, skin lesions, or pericardial fluid. Hemoculture is somewhat more sensitive than direct methods but takes 2 to 8 weeks to demonstrate parasites. Quantitative PCR assays performed on serial blood specimens that show rising parasite numbers over time provide the earliest and most sensitive indicator of reactivation.37,38 As such, clinicians should consider obtaining PCR testing in all individuals in whom there is high clinical suspicion and blood and/or tissue tests are negative. In people with HIV who have suspected CNS Chagas disease, centrifugation and microscopic examination of CSF should be conducted. Few published data exist on PCR of CSF, but it would be expected to have high sensitivity for the diagnosis of reactivation in the CNS.39 In the United States, Chagas disease molecular detection (PCR testing for T. cruzi DNA) is available at the Centers for Disease Control and Prevention (CDC); consultations and testing requests should be addressed to Parasitic Diseases Hotline for Healthcare Providers (404-718-4745, parasites@cdc.gov, hours: 8 a.m.–4 p.m. ET/Monday–Friday) or through the CDC Emergency Operations Center (770-488-7100) for emergencies after business hours, on weekends, and federal holidays. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-4 Preventing Exposure Travelers to endemic countries may be at risk of infection with T. cruzi if they visit rural areas and stay in rustic lodging. The triatomine vector typically infests cracks in walls and roofing of poor-quality buildings that are constructed of adobe brick, mud, or thatch.40 Because the insects feed at night, individuals who live in or visit Chagas disease–endemic areas should avoid sleeping in such dwellings or outdoors. Control programs in endemic areas rely on spraying infested dwellings with residual-action insecticide. If sleeping outdoors or in suspect dwellings cannot be avoided, sleeping under insecticide-treated bed nets provides significant protection.41 In the United States, all blood donors are screened for Chagas disease when they first donate blood. Universal screening of blood donors has been implemented in 21 Chagas disease–endemic Latin American countries.42 Although transfusion-acquired cases have been uncommon in the United States, transfusion with infected blood products remains a risk for acquiring Chagas disease. No drugs or vaccines for preventing T. cruzi infection are available. Preventing Disease All people with HIV with epidemiologic risk factors for Chagas disease should be tested for antibody to T. cruzi to detect latent infection.29,43 For people living with HIV, a single course of treatment with benznidazole or nifurtimox should be offered to individuals with T. cruzi infection who have not been previously treated and who do not have advanced Chagas cardiomyopathy, with a discussion of potential risks and benefits and shared decision making (BIII). However, the efficacy of currently available drugs in the chronic phase is suboptimal, there is no useful test of cure, and treated individuals are still considered at risk for reactivation.32,44 There are no direct studies evaluating interactions between antiretroviral medications and either benznidazole or nifurtimox. However, as benznidazole may be partially metabolized by the cytochrome P450 (CYP) system, medications that inhibit this system may increase benznidazole toxicity and those that induce CYP enzymes may reduce benznidazole efficacy.43,45 Although direct data are lacking, optimization of antiretroviral therapy (ART) may help prevent Chagas reactivation in coinfected patients. Most symptomatic reactivation cases have occurred in people with HIV who were not virologically suppressed on ART.16,43 Treating Disease Therapy for Chagas disease with benznidazole or nifurtimox is effective in reducing parasitemia and preventing clinical manifestations or slowing progression in patients with acute and reactivated disease.44,46 These drugs have limited efficacy, however, in achieving parasitological cure. As both drugs are U.S. Food and Drug Administration (FDA)–approved only for children, use for the treatment of adults in the United States is off-label. Individuals with advanced Chagas cardiomyopathy will not benefit from treatment. Consultation with a specialist should be sought. Consultations with experts at the CDC can be addressed to the Parasitic Diseases Hotline for Healthcare Providers (404-718-4745, parasites@cdc.gov). Benznidazole (commercially available at is approved by the FDA for use in children 2 to 12 years of age. The use of benznidazole to treat a patient outside of the Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-5 FDA-approved age range is based on clinical diagnosis and decision by a treating physician under practice of medicine. The regimen of 5 to 8 mg/kg/day in two divided doses taken with or without food for 60 days is the recommended treatment (BIII); a daily maximum dose of 300 mg is recommended by most experts.47,48 Nifurtimox (Lampit®) is also FDA approved for children less than 18 years of age and is available from retail sources.49,50 Use of nifurtimox to treat a patient outside of the FDA-approved age range is based on clinical diagnosis and decision by the treating physician under practice of medicine. The recommended regimen is 8 to 10 mg/kg/day in three divided doses with food for 60 days (BIII).51 Treatment of patients outside of the FDA-approved age ranges for either drug is based on clinical diagnosis and decision by the treating physician under practice of medicine. The duration of therapy with either of these agents has not been studied in people with HIV. Mortality is high for symptomatic reactivated T. cruzi infection, even in patients who receive chemotherapy.16,26 Limited data suggest that early recognition and treatment of reactivation may improve prognosis.16 Special Considerations with Regard to Starting Antiretroviral Therapy As with other parasitic infections that localize in the CNS, the decision to initiate ART must be carefully considered in people with HIV and reactivated T. cruzi infection involving the brain. Only anecdotal information exists on the consequences of starting ART after a diagnosis of CNS Chagas disease, but there are no cases of Chagas-related immune reconstitution inflammatory syndrome (IRIS) that have been well described. Therefore, there is no known contraindication to starting or optimizing ART in patients with CNS Chagas disease. ART should be initiated in all patients with concomitant T. cruzi (AIII). In general, as IRIS is not recognized as a common manifestation in the setting of coinfection, treatment of T. cruzi does not warrant delay in ART. Monitoring for Adverse Events Patients undergoing treatment should be monitored closely because both benznidazole and nifurtimox are associated with significant toxicities.46 Benznidazole-associated adverse drug reactions include abdominal symptoms (abdominal pain, nausea, vomiting, diarrhea), reversible peripheral neuropathy, rash, and granulocytopenia. Comprehensive metabolic panel (CMP) and complete blood count (CBC) should be monitored before initiation and during therapy. Co-administration of benznidazole with disulfiram, alcohol, and products that contain propylene glycol should be avoided. Nifurtimox-associated adverse drug reactions include anorexia, nausea, vomiting, abdominal pain and weight loss, rash, restlessness, tremors, and dose-dependent peripheral neuropathy. Alcohol consumption with nifurtimox should be avoided. CMP and CBC should be monitored before initiation and during treatment with nifurtimox. The frequency of monitoring CMP and CBC during treatment, though not standardized, is generally every 2 weeks. The adverse effects of both drugs wane when the drugs are discontinued. For more information, refer to the Adverse Drug Reactions table. As stated above, there are no reports at this time regarding T. cruzi infection and IRIS. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-6 Managing Treatment Failure People with HIV are at risk for clinical manifestations because of intermittent reactivation of chronic infection.43 Benznidazole and nifurtimox are only partially effective in the chronic phase of T. cruzi infection and may be suppressive rather than curative.44 Because the drugs are toxic and experience with their use in people with HIV is limited, expert advice should be sought.46 Whether secondary prophylaxis or chronic maintenance therapy should be used in people with HIV with latent Chagas disease is unclear, particularly when potent ART is used. There are no current recommendations for monitoring for reactivation after treatment. T. cruzi antibodies may persist after treatment. Reactivation after treatment is diagnosed based on compatible clinical symptoms and identification of the parasite in blood or CNS fluid/tissue by microscopy or PCR. Although no efficacy data are available, retreatment with benznidazole or nifurtimox is recommended for people with HIV and T. cruzi reactivation who fail to respond or who reactivate again after initial antitrypanosomal therapy (AIII). Special Considerations During Pregnancy As recommended for all individuals with epidemiologic risk of Chagas disease, screening of pregnant persons who have lived in endemic areas should be considered to identify maternal infection and possible risk of infection in their offspring. See the CDC resource for congenital Chagas disease for more information. Between 1% to 10% of infants of mothers with T. cruzi are born with acute T. cruzi infection.52 Most congenital T. cruzi infections are asymptomatic or cause non-specific signs; laboratory screening is required for detection of these cases.53 In a small proportion of patients, congenital infection causes severe morbidity, including low birthweight, hepatosplenomegaly, anemia, meningoencephalitis, and/or respiratory insufficiency, with high risk of mortality.52,54 Limited data suggest that the rate of congenital transmission is higher for women with HIV than in immunocompetent women.16,55 Infants with HIV and concomitant T. cruzi also may be more likely to have symptoms, especially neurologic symptoms.56,57 Minimal data are available on the potential reproductive toxicity of benznidazole and nifurtimox, although both drugs have been associated with increased detection of chromosomal aberrations in children being treated for Chagas disease.58,59 Benznidazole crosses the placenta in rats.60 Due to the toxicity and limited experience with use of these drugs in pregnancy, treatment of acute T. cruzi infection in pregnant people should only be undertaken in consultation with a specialist in this area, and treatment of chronic disease should be considered only after completion of the pregnancy and breastfeeding. For pregnant people with HIV with symptomatic reactivation of T. cruzi infection, ART should be initiated (AIII) as initial treatment. Only two cases of treatment of Chagas disease in pregnancy with benznidazole have been reported in people with HIV.61,62 One infant was born with a low birthweight.62 All infants born to people with T. cruzi should undergo appropriate testing for congenitally acquired T. cruzi infection and be treated promptly if infection is confirmed.63,64 Refer to the Opportunistic Infection Drugs During Pregnancy table for additional information. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-7 Recommendations for Preventing and Treating Chagas Disease (American Trypanosomiasis) Preventing Manifestations of Chagas Disease • All people with HIV who have epidemiologic risk factors for Chagas disease should be tested for antibody to T. cruzi using at least two serological tests based on different antigens (e.g., whole parasite lysate and recombinant antigens) and/or techniques (e.g., ELISA and IFA). Indication • Individuals with epidemiological risk factors for Chagas disease who have tested positive for antibody to T. cruzi, have not been previously treated, and do not have advanced Chagas cardiomyopathy Therapy • A single course of benznidazole or nifurtimox is recommended by some experts (doses and duration same as for treatment of acute or reactivated infection). o Benznidazole 5–8 mg/kg/day PO in 2 divided doses for 60 days (BIII) (commercially available at Most experts recommend a daily maximum of 300 mg. o Nifurtimox (Lampit®) 8–10 mg/kg/day PO in 3 divided doses for 60 days (BIII) (commercially available through retail sources) Note: Efficacy of both therapies is suboptimal, and treated patients are still at risk of reactivation. Treating Acute or Reactivated T. cruzi Infection Indication • Individuals with acute or reactivated T. cruzi infection as manifested by presence of parasitemia should be treated (AII). Therapy • Benznidazole 5–8 mg/kg/day PO in 2 divided doses for 60 days (BIII) (commercially available at Most experts recommend a daily maximum of 300 mg. • Nifurtimox (Lampit®) 8–10 mg/kg/day PO in 3 divided doses for 60 days (BIII) (commercially available through retail sources) • Initiation or optimization of ART is recommended for all people with HIV with concomitant T. cruzi (AIII). Note: Treatment is not recommended for patients with advanced chagasic cardiomyopathy. Key: ART = antiretroviral therapy; CDC = Centers for Disease Control and Prevention; ELISA = enzyme-linked immunosorbent assays; IFA = immunofluorescence assays; PO = orally Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-8 References 1. Messenger LA, Bern C. Congenital Chagas disease: current diagnostics, limitations and future perspectives. Curr Opin Infect Dis. 2018;31(5):415-421. Available at: 2. Maguire J. Trypanosoma. Vol. 2nd ed. Philadelphia, PA: Lippincott, Williams, & Wilkins; 2004. 3. Benchimol Barbosa PR. The oral transmission of Chagas' disease: an acute form of infection responsible for regional outbreaks. Int J Cardiol. 2006;112(1):132-133. Available at: 4. Rassi A, Jr., Rassi A, Marin-Neto JA. Chagas disease. Lancet. 2010;375(9723):1388-1402. Available at: 5. World Health Organization. Chagas disease in Latin America: an epidemiological update based on 2010 estimates. Wkly Epidemiol Rec. 2015;90(6):33-43. Available at: 6. Pan American Health Organization. Chagas disease. 2022. Available at: 7. Gascon J, Bern C, Pinazo MJ. Chagas disease in Spain, the United States and other non-endemic countries. Acta Trop. 2010;115(1-2):22-27. Available at: 8. Moncayo A. Chagas disease: current epidemiological trends after the interruption of vectorial and transfusional transmission in the Southern Cone countries. Mem Inst Oswaldo Cruz. 2003;98(5):577-591. Available at: 9. Lynn MK, Bossak BH, Sandifer PA, Watson A, Nolan MS. Contemporary autochthonous human Chagas disease in the USA. Acta Trop. 2020;205:105361. Available at: 10. Bern C, Messenger LA, Whitman JD, Maguire JH. Chagas disease in the United States: a public health approach. Clin Microbiol Rev. 2019;33(1). Available at: 11. Kjos SA, Snowden KF, Craig TM, Lewis B, Ronald N, Olson JK. Distribution and characterization of canine Chagas disease in Texas. Vet Parasitol. 2008;152(3-4):249-256. Available at: 12. Klotz SA, Dorn PL, Klotz JH, et al. Feeding behavior of triatomines from the southwestern United States: an update on potential risk for transmission of Chagas disease. Acta Trop. 2009;111(2):114-118. Available at: 13. Bern C, Montgomery SP, Katz L, Caglioti S, Stramer SL. Chagas disease and the U.S. blood supply. Curr Opin Infect Dis. 2008;21(5):476-482. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-9 14. Centers for Disease Control Prevention. Blood donor screening for chagas disease—United States, 2006-2007. MMWR. 2007;56(7):141-143. Available at: 15. Rocha A, de Meneses AC, da Silva AM, et al. Pathology of patients with Chagas' disease and acquired immunodeficiency syndrome. Am J Trop Med Hyg. 1994;50(3):261-268. Available at: 16. Sartori AM, Ibrahim KY, Nunes Westphalen EV, et al. Manifestations of Chagas disease (American trypanosomiasis) in patients with HIV/AIDS. Ann Trop Med Parasitol. 2007;101(1):31-50. Available at: 17. Vaidian AK, Weiss LM, Tanowitz HB. Chagas' disease and AIDS. Kinetoplastid Biol Dis. 2004;3(1):2. Available at: 18. Nunes MCP, Beaton A, Acquatella H, et al. Chagas cardiomyopathy: an update of current clinical knowledge and management: a scientific statement from the American Heart Association. Circulation. 2018;138(12):e169-e209. Available at: 19. Rassi A, Jr., Rassi SG, Rassi A. Sudden death in Chagas' disease. Arq Bras Cardiol. 2001;76(1):75-96. Available at: 20. de Oliveira RB, Troncon LE, Dantas RO, Menghelli UG. Gastrointestinal manifestations of Chagas' disease. Am J Gastroenterol. 1998;93(6):884-889. Available at: 21. Radisic MV, Repetto SA. American trypanosomiasis (Chagas disease) in solid organ transplantation. Transpl Infect Dis. 2020;22(6):e13429. Available at: 22. Czech MM, Nayak AK, Subramanian K, et al. Reactivation of Chagas disease in a patient with an autoimmune rheumatic disease: case report and review of the literature. Open Forum Infect Dis. 2021;8(2):ofaa642. Available at: 23. Riarte A, Luna C, Sabatiello R, et al. Chagas' disease in patients with kidney transplants: 7 years of experience 1989-1996. Clin Infect Dis. 1999;29(3):561-567. Available at: 24. de Freitas VL, da Silva SC, Sartori AM, et al. Real-time PCR in HIV/Trypanosoma cruzi coinfection with and without Chagas disease reactivation: association with HIV viral load and CD4 level. PLoS Negl Trop Dis. 2011;5(8):e1277. Available at: 25. Sartori AM, Lopes MH, Benvenuti LA, et al. Reactivation of Chagas' disease in a human immunodeficiency virus-infected patient leading to severe heart disease with a late positive direct microscopic examination of the blood. Am J Trop Med Hyg. 1998;59(5):784-786. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-10 26. Almeida EA, Ramos Junior AN, Correia D, Shikanai-Yasuda MA. Co-infection Trypanosoma cruzi/HIV: systematic review (1980–2010). Rev Soc Bras Med Trop. 2011;44(6):762-770. Available at: 27. Diazgranados CA, Saavedra-Trujillo CH, Mantilla M, Valderrama SL, Alquichire C, Franco-Paredes C. Chagasic encephalitis in HIV patients: common presentation of an evolving epidemiological and clinical association. Lancet Infect Dis. 2009;9(5):324-330. Available at: 28. Ferreira MS, Nishioka Sde A, Silvestre MT, Borges AS, Nunes-Araujo FR, Rocha A. Reactivation of Chagas' disease in patients with AIDS: report of three new cases and review of the literature. Clin Infect Dis. 1997;25(6):1397-1400. Available at: 29. Forsyth CJ, Manne-Goehler J, Bern C, et al. Recommendations for screening and diagnosis of Chagas disease in the United States. J Infect Dis. 2021. Available at: 30. Whitman JD, Bulman CA, Gunderson EL, et al. Chagas disease serological test performance in U.S. blood donor specimens. J Clin Microbiol. 2019;57(12). Available at: 31. Sosa-Estani S, Gamboa-Leon MR, Del Cid-Lemus J, et al. Use of a rapid test on umbilical cord blood to screen for Trypanosoma cruzi infection in pregnant women in Argentina, Bolivia, Honduras, and Mexico. Am J Trop Med Hyg. 2008;79(5):755-759. Available at: 32. Tarleton RL, Reithinger R, Urbina JA, Kitron U, Gurtler RE. The challenges of Chagas disease—grim outlook or glimmer of hope. PLoS Med. 2007;4(12):e332. Available at: 33. Verani JR, Seitz A, Gilman RH, et al. Geographic variation in the sensitivity of recombinant antigen-based rapid tests for chronic Trypanosoma cruzi infection. Am J Trop Med Hyg. 2009;80(3):410-415. Available at: 34. Gorlin J, Rossmann S, Robertson G, et al. Evaluation of a new Trypanosoma cruzi antibody assay for blood donor screening. Transfusion. 2008;48(3):531-540. Available at: 35. Junqueira AC, Chiari E, Wincker P. Comparison of the polymerase chain reaction with two classical parasitological methods for the diagnosis of Chagas disease in an endemic region of north-eastern Brazil. Trans R Soc Trop Med Hyg. 1996;90(2):129-132. Available at: 36. Cordova E, Boschi A, Ambrosioni J, Cudos C, Corti M. Reactivation of Chagas disease with central nervous system involvement in HIV-infected patients in Argentina, 1992-2007. Int J Infect Dis. 2008;12(6):587-592. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-11 37. Ramirez JD, Guhl F, Umezawa ES, et al. Evaluation of adult chronic Chagas' heart disease diagnosis by molecular and serological methods. J Clin Microbiol. 2009;47(12):3945-3951. Available at: 38. Duffy T, Bisio M, Altcheh J, et al. Accurate real-time PCR strategy for monitoring bloodstream parasitic loads in chagas disease patients. PLoS Negl Trop Dis. 2009;3(4):e419. Available at: 39. Schijman AG, Vigliano C, Burgos J, et al. Early diagnosis of recurrence of Trypanosoma cruzi infection by polymerase chain reaction after heart transplantation of a chronic Chagas' heart disease patient. J Heart Lung Transplant. 2000;19(11):1114-1117. Available at: 40. Qvarnstrom Y, Schijman AG, Veron V, Aznar C, Steurer F, da Silva AJ. Sensitive and specific detection of Trypanosoma cruzi DNA in clinical specimens using a multi-target real-time PCR approach. PLoS Negl Trop Dis. 2012;6(7):e1689. Available at: 41. Mott KE, Muniz TM, Lehman JS, Jr., et al. House construction, triatomine distribution, and household distribution of seroreactivity to Trypanosoma cruzi in a rural community in northeast Brazil. Am J Trop Med Hyg. 1978;27(6):1116-1122. Available at: 42. Kroeger A, Villegas E, Ordonez-Gonzalez J, Pabon E, Scorza JV. Prevention of the transmission of Chagas' disease with pyrethroid-impregnated materials. Am J Trop Med Hyg. 2003;68(3):307-311. Available at: 43. Perez-Molina JA, Rodriguez-Guardado A, Soriano A, et al. Guidelines on the treatment of chronic coinfection by Trypanosoma cruzi and HIV outside endemic areas. HIV Clin Trials. 2011;12(6):287-298. Available at: 44. Rodriques Coura J, de Castro SL. A critical review on Chagas disease chemotherapy. Mem Inst Oswaldo Cruz. 2002;97(1):3-24. Available at: 45. Perez Montilla CA, Moroni S, Moscatelli G, et al. Major benznidazole metabolites in patients treated for Chagas disease: mass spectrometry-based identification, structural analysis and detoxification pathways. Toxicol Lett. 2023;377:71-82. Available at: 46. Bern C, Montgomery SP, Herwaldt BL, et al. Evaluation and treatment of chagas disease in the United States: a systematic review. JAMA. 2007;298(18):2171-2181. Available at: 47. U.S. Food and Drug Administration. Benznidazole tablets [package insert]. Exeltis USA, Inc. 2021. Available at: 48. Altcheh J, Moscatelli G, Mastrantonio G, et al. Population pharmacokinetic study of benznidazole in pediatric Chagas disease suggests efficacy despite lower plasma Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-12 concentrations than in adults. PLoS Negl Trop Dis. 2014;8(5):e2907. Available at: 49. Abbott A, Montgomery SP, Chancey RJ. Characteristics and adverse events of patients for whom nifurtimox was released through CDC-sponsored investigational new drug program for treatment of Chagas disease—United States, 2001–2021. MMWR Morb Mortal Wkly Rep. 2022;71(10):371-374. Available at: 50. Falk N, Berenstein AJ, Moscatelli G, et al. Effectiveness of nifurtimox in the treatment of Chagas disease: a long-term retrospective cohort study in children and adults. Antimicrob Agents Chemother. 2022;66(5):e0202121. Available at: 51. U.S. Food and Drug Administration. LAMPIT (nifurtimox) tablets, for oral use [package insert]. Bayer HealthCare Pharmaceuticals Inc. 2023. Available at: 52. Torrico F, Alonso-Vega C, Suarez E, et al. Maternal Trypanosoma cruzi infection, pregnancy outcome, morbidity, and mortality of congenitally infected and non-infected newborns in Bolivia. Am J Trop Med Hyg. 2004;70(2):201-209. Available at: 53. Klein MD, Proano A, Noazin S, Sciaudone M, Gilman RH, Bowman NM. Risk factors for vertical transmission of Chagas disease: a systematic review and meta-analysis. Int J Infect Dis. 2021;105:357-373. Available at: 54. Chancey RJ, Edwards MS, Montgomery SP. Congenital Chagas disease. Pediatr Rev. 2023;44(4):213-221. Available at: 55. Scapellato PG, Bottaro EG, Rodriguez-Brieschke MT. Mother-child transmission of Chagas disease: could coinfection with human immunodeficiency virus increase the risk? Rev Soc Bras Med Trop. 2009;42(2):107-109. Available at: 56. Freilij H, Altcheh J. Congenital Chagas' disease: diagnostic and clinical aspects. Clin Infect Dis. 1995;21(3):551-555. Available at: 57. Freilij H, Altcheh J, Muchinik G. Perinatal human immunodeficiency virus infection and congenital Chagas' disease. Pediatr Infect Dis J. 1995;14(2):161-162. Available at: 58. Gorla NB, Ledesma OS, Barbieri GP, Larripa IB. Assessment of cytogenetic damage in chagasic children treated with benznidazole. Mutat Res. 1988;206(2):217-220. Available at: 59. Gorla NB, Ledesma OS, Barbieri GP, Larripa IB. Thirteenfold increase of chromosomal aberrations non-randomly distributed in chagasic children treated with nifurtimox. Mutat Res. 1989;224(2):263-267. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV E-13 60. de Toranzo EG, Masana M, Castro JA. Administration of benznidazole, a chemotherapeutic agent against Chagas disease, to pregnant rats. Covalent binding of reactive metabolites to fetal and maternal proteins. Arch Int Pharmacodyn Ther. 1984;272(1):17-23. Available at: 61. Correa VR, Barbosa FG, Melo Junior CA, D'Albuquerque e Castro LF, Andrade Junior HF, Nascimento N. Uneventful benznidazole treatment of acute Chagas disease during pregnancy: a case report. Rev Soc Bras Med Trop. 2014;47(3):397-400. Available at: 62. Bisio M, Altcheh J, Lattner J, et al. Benznidazole treatment of chagasic encephalitis in pregnant woman with AIDS. Emerg Infect Dis. 2013;19(9):1490-1492. Available at: 63. Oliveira I, Torrico F, Munoz J, Gascon J. Congenital transmission of Chagas disease: a clinical approach. Expert Rev Anti Infect Ther. 2010;8(8):945-956. Available at: 64. Edwards MS, Stimpert KK, Bialek SR, Montgomery SP. Evaluation and management of congenital Chagas disease in the United States. J Pediatric Infect Dis Soc. 2019;8(5):461-469. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-1 Coccidioidomycosis Updated: February 16, 2021 Reviewed: January 10, 2024 Epidemiology Coccidioidomycosis is caused by either of two soil-dwelling dimorphic fungi: Coccidioides immitis and Coccidioides posadasii. Most cases of coccidioidomycosis in people with HIV have been reported in the areas in which the disease is highly endemic.1 Cases also may be identified outside of these areas when a person gives a history of having traveled through an endemic region. In the United States, these areas include the lower San Joaquin Valley and other arid regions in southern California; much of Arizona; the southern regions of Utah, Nevada, and New Mexico; and western Texas.2 Several cases of coccidioidomycosis in individuals who acquired the infection in eastern Washington state have been reported. One of these cases was phylogenetically linked to local Coccidioides immitis isolates.2 These observations suggest that the coccidioidal endemic range may be expanding. The risk of developing symptomatic coccidioidomycosis after infection is increased in patients with HIV who have CD4 T lymphocyte (CD4) counts <250 cells/mm3, those who are not virologically suppressed, or those who have AIDS.3 The incidence and severity of HIV-associated coccidioidomycosis have declined since the introduction of effective antiretroviral therapy (ART).4,5 Clinical Manifestations Four common clinical syndromes of coccidioidomycosis have been described: focal pneumonia; diffuse pneumonia; extrathoracic involvement, including meningitis, osteoarticular infection, and other extrathoracic sites; and positive coccidioidal serology tests without evidence of localized infection.6 In patients with HIV, lack of viral suppression and CD4 count <250 cells/mm3 are associated with increased severity of the presentation of coccidioidomycosis.7 Focal pneumonia is most common in patients with CD4 counts ≥250 cells/mm3. Focal pneumonia can be difficult to distinguish from a bacterial community-acquired pneumonia; patients present with symptoms that include cough, fever, and pleuritic chest pain.7,8 However, coccidioidomycosis may present with hilar or with a persistent headache and progressive lethargy. The cerebrospinal fluid (CSF) profile in meningitis demonstrates low glucose levels, elevated protein levels, and a lymphocytic pleocytosis. mediastinal adenopathy, upper lobe infiltrates, nodules, and peripheral blood eosinophilia—all of which are uncommon in bacterial pneumonia and should make one think of coccidioidomycosis, particularly in patients who reside in, previously resided in, or have travelled to a known endemic area. Diffuse pneumonia and extrathoracic disease usually occur in more immunocompromised patients. Diffuse pulmonary disease presents with fever and dyspnea with a diffuse reticulonodular pattern on chest imaging, and in some instances may be difficult to distinguish clinically from Pneumocystis pneumonia.9 Hypoxemia may be severe and serological tests are frequently negative at presentation. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-2 Patients with meningitis present with a persistent headache and progressive lethargy. The cerebrospinal fluid (CSF) profile in meningitis demonstrates low glucose levels, elevated protein levels, and a lymphocytic pleocytosis. Elevated coccidioidal antibody titers even without symptoms can indicate risk of subsequent symptomatic disease in patients with advanced HIV. A study conducted prior to the advent of potent ART described 13 patients with HIV who had CD4 counts <350 cells/mm3 and positive coccidioidal serologic tests without an anatomic site of infection. Five patients subsequently developed clinical illness when their median CD4 count fell to 10 cells/mm3.10 Diagnosis The diagnosis of coccidioidomycosis is based on serology, histology, culture, and clinical presentation. Culture of the organism from clinical specimens or by demonstration of spherules on histopathological examination of infected tissue confirms the diagnosis. Positive blood cultures are rare and usually found only in those with diffuse pulmonary disease. CSF cultures are positive in fewer than one-third of patients with coccidioidal meningitis. Unlike other endemic fungi, Coccidioides spp. grow relatively rapidly at 37°C on routine bacterial media, especially blood agar. Growth of a non-pigmented mold may be observed in as few as 3 to 7 days and can be confirmed as Coccidioides by gene probe. Coccidioides growth on an agar plate is a significant laboratory biosafety hazard because of the risk of inhalation of dislodged arthroconidia. When a specimen is sent for culture, laboratory personnel should be alerted to the possibility that Coccididoides spp. may be present, and in the laboratory, the culture plate lid should be kept secured with tape.11 Identification of the fungus should be performed only in a biosafety level 3 containment laboratory. Most commonly, the diagnosis of coccidioidomycosis is based on a positive coccidioidal serological test and a compatible clinical syndrome. However, it may take several weeks for antibodies to develop, and negative serology cannot be used to rule out disease. Repeat testing every 1-2 weeks should be considered if the patient is ill and the diagnosis has not been established. Patients with past coccidioidal infection and without disease activity usually have negative serological tests. Screening with an enzyme immunoassay (EIA) for IgM and IgG antibody is recommended. It has a rapid turnaround time and is available in many clinical laboratories. These tests are very sensitive but occasionally have been associated with false positive results, particularly for IgM.12 If either EIA test is positive, antibody assays by immunodiffusion (ID) and by complement fixation (CF) should be obtained to confirm the result and be used for further follow-up. A lateral flow assay (LFA) recently has become available but is far less sensitive than EIA.13 A coccidioidomycosis-specific antigen assay is commercially available. It has been shown to detect antigen in urine,14 serum,15 and other body fluids in samples from individuals with active coccidioidomycosis. The assay is most useful in diagnosing extrathoracic disseminated coccidioidomycosis. A recent study suggests that detection of coccidioidal antigen in CSF has a very high sensitivity and specificity for diagnosing coccidioidal meningitis.16 In addition, real-time polymerase chain reaction (RT-PCR) testing, if available, can be used on unfixed clinical specimens and on formalin-fixed tissue to aid in the diagnosis of coccidioidomycosis. A Coccidioides RT-PCR assay is commercially available but not Food and Drug Administration (FDA)-approved nor tested in patients with HIV.17 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-3 Preventing Exposure Individuals with HIV living in or visiting areas in which Coccidioides spp. are endemic cannot avoid exposure to the fungus. They should, however, avoid extensive exposure to disturbed native soil, such as at building excavation sites, and they should stay inside during dust storms (BIII). No evidence indicates that gardening in cultivated soil in the coccidioidal endemic region increases the risk of acquiring coccidioidomycosis. Preventing Disease Preventing Coccidioidomycosis Primary antifungal prophylaxis for individuals with negative serologic tests for Coccididoides is not recommended (AIII) except for the following indications: Indication for Primary Prophylaxis • New positive IgM and/or IgG test for Coccidioides; and • No sign of active coccidioidomycosis; and • CD4 count <250 cells/mm3 Preferred Therapy • Fluconazole 400 mg PO once daily (AIII) Discontinuation of Primary Prophylaxis • CD4 count ≥250 cells/mm3 with virologic suppression on ART (BIII) • Close clinical follow-up is recommended (BIII) Key: CD4 = CD4 T lymphocyte cell; IgG = immunoglobulin G; IgM = immunoglobulin M; PO = orally Primary antifungal prophylaxis (i.e., prophylaxis for individuals with negative results on serological tests for Coccidioides) does not appear to benefit patients with HIV with low CD4 counts who live in regions in which Coccidioides spp. are endemic,4 and it is not recommended (AIII). Yearly or twice-yearly serological testing for coccidioidomycosis is reasonable for serologically negative individuals with HIV who live in endemic areas. Testing is advised also for individuals who have previously traveled to or lived in endemic areas. Both IgM and IgG antibody testing using either an EIA or immunodiffusion technique are recommended. In patients who have CD4 counts <250 cells/mm3 and who previously tested negative for Coccidioides, a new positive serology test suggests possible active disease10 and should prompt further clinical evaluation. If no signs, symptoms, or laboratory abnormalities compatible with active coccidioidomycosis are identified, antifungal therapy with fluconazole 400 mg daily is recommended for those with a new positive serological test and CD4 counts <250 cells/mm3 (AIII). This regimen should be continued until the CD4 count is ≥250 cells/mm3 and virological suppression is documented (BIII). For those with CD4 counts already ≥250/mm3 and with viral suppression on antiretrovirals, close clinical follow-up without antifungal therapy is recommended (BIII). For asymptomatic patients who have not lived in or travelled to endemic regions, routine testing does not appear useful and should not be performed (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-4 Treating Disease Treating Coccidioidomycosis Treating Mild-to-Moderate Pulmonary Infections Indications for Treatment • Patients who have clinically mild infection, such as focal pneumonia; • Patients with positive coccidioidal serologies but with mild or without clinical illness. Preferred Therapy • Fluconazole 400 mg PO once daily (AII), or • Itraconazole 200 mg PO three times daily for 3 days then twice daily (AII) Alternative Therapy (For Patients Who Failed to Respond to Fluconazole or Itraconazole) • Voriconazole loading dose of 400 mg twice daily for the first day followed by 200 mg PO twice daily (BIII); or • Posaconazole (extended-release tablet) 300 mg PO twice daily for the first day and then 300 mg daily (BIII) Treating Severe Pulmonary or Extrapulmonary Infection (Except Meningitis) Preferred Therapy • Lipid formulation amphotericin B 3–5 mg/kg IV daily (AIII), or • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV daily (AII) • Use until clinical improvement, then switch to triazole (BIII). Alternative Therapy • Some specialists recommend combining amphotericin B with a triazole (fluconazole or itraconazole 400mg daily) and continue the triazole once amphotericin B is stopped (CIII). Treatment for Meningeal Infections (Consultation with a Specialist Is Advised) Preferred Therapy • Fluconazole 400–800 mg IV or PO once daily (AII) Alternative Therapy • Itraconazole 200 mg PO two to three-times daily (BII), or • Voriconazole 200–400 mg PO twice daily (BIII), or • Posaconazole (delayed-release tablet) 300 mg PO once daily after a loading dose (CIII), or • Isavuconazole 372 mg every 8 hr for 6 doses, then 372 mg daily (CIII). • Intrathecal amphotericin B (AIII) when triazole antifungals are not effective. Use in consultation with a specialist and ensure administration by a clinician experienced in this drug delivery technique. Treatment in Pregnancy • Azole antifungal agents are contraindicated and should be avoided in the first trimester of pregnancy because of potential teratogenic effect and risk of spontaneous abortion (AIII). • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV daily (AIII), or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-5 • Lipid formulation amphotericin B 3–5 mg/kg IV daily (AIII) Discontinuing Therapy Focal Coccidioidal Pneumonia, Therapy Can Be Stopped If (AII) • Clinically responded to 3 to 6 months of antifungal therapy, and • CD4 count ≥250 cells/mm3, and • Virologic suppression on ARVs, and • Continued monitoring for recurrence can be performed using serial chest radiograph and coccidioidal serology. Diffuse Pulmonary Disease or Non-Meningeal Disseminated Coccidioidomycosis • Relapse can occur in 25% to 33% of patients without HIV and can occur in patients with HIV who have CD4 count >250 cells/mm3. • Therapy duration is at least 12 months and usually much longer; discontinuation is dependent on clinical and serological response and should be made in consultation with experts (BIII). Coccidioidal Meningitis • Relapse has been reported in 80% of patients after stopping triazoles; therefore, suppressive therapy should be lifelong (AII). Other Considerations • Certain patients with meningitis may develop hydrocephalus and require CSF shunting in addition to antifungal therapy. • All the triazole antifungals have the potential to interact with certain ARV agents and other anti-infective agents. These interactions are complex and can be bidirectional. The Adult and Adolescent Antiretroviral Guidelines DDI Tables list these interactions and recommend dosage adjustments where feasible. Key: ARVs = antiretrovirals; CD4 = CD4 T lymphocyte cell; CSF = cerebrospinal fluid; DDI = drug–drug interaction; IV = intravenous; PO = orally Treatment of mild-to-moderate pulmonary coccidioidal infection: Therapy with a triazole antifungal agent given orally is appropriate for patients who have clinically mild infection, such as focal pneumonia (AII). Fluconazole should be given as 400 mg daily (AII); itraconazole should be given in divided doses of 200 mg three times daily for 3 days, followed by 200 mg twice daily (AII).18,19 Itraconazole is preferred for those who have bone or joint disease (AI).20 Serum itraconazole concentrations should be measured after the drug reaches steady state at 2 weeks to ensure adequate absorption. Target serum concentration (the sum of the parent itraconazole and hydroxyl itraconazole metabolite levels) is at least >1mcg/mL and preferably >2mcg/mL. Data to support clinical efficacy for treatment with posaconazole21,22 and voriconazole are limited, but these agents are useful for patients who do not respond to fluconazole or itraconazole (BIII). Voriconazole is given as a loading dose of 400 mg twice daily on Day 1, followed thereafter by 200 mg twice daily. Trough serum voriconazole concentrations should be measured to ensure efficacy and avoid toxicity; a concentration of 1 to 5 mcg/mL is desired. Several dosage formulations of posaconazole have been studied for coccidioidomycosis. A dose of 400 mg twice daily of the older liquid formulation of posaconazole has been used (BIII),22 but the current extended-release tablet formulation of posaconazole at a dosage of 300 mg twice daily for the first day, then 300mg once daily is better tolerated by patients and provides more reliable serum concentrations. Recently, a Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-6 syndrome of mineralocorticoid excess manifesting as hypertension with hypokalemia was reported in some patients taking posaconazole.23 Monitoring of blood pressure and serum potassium levels is appropriate in patients taking posaconazole. No data have been published on the use of the antifungal isavuconazole for coccidioidomycosis in patients with HIV. Among nine patients with pulmonary disease without HIV, initial therapy with isavuconazole resulted in complete or partial treatment success in five patients (56%).24 All triazole antifungals have the potential for complex and possibly bidirectional interactions with certain antiretroviral agents and other anti-infective agents. Drug–drug interaction (DDI) tables in the Adult and Adolescent ARV Guidelines list such interactions and recommendations for therapeutic drug monitoring and dosage adjustments, where feasible. Treatment of severe pulmonary coccidioidal infection or extrapulmonary infection: Amphotericin B is the preferred initial therapy for patients who have diffuse pulmonary involvement or who are severely ill with extrathoracic disseminated disease (AII).19 Most experience has been with the deoxycholate formulation using a dose of amphotericin B of 0.7 to 1.0 mg/kg intravenously (IV) daily. There are only anecdotal reports25 from studies that used lipid formulations of amphotericin B for the treatment of coccidioidomycosis. Lipid formulations are likely to be as effective as the deoxycholate formulation and should be considered as equivalent alternative initial therapy, particularly in patients with underlying renal dysfunction (AIII). For lipid formulations, a daily dose of amphotericin B of 3 to 5 mg/kg is appropriate. Therapy with amphotericin B should continue until clinical improvement is observed and then changed to an oral triazole antifungal (BIII). Some specialists recommend combining amphotericin B with a triazole antifungal (400 mg of fluconazole or itraconazole daily) at initiation of therapy, and then continuing the triazole once amphotericin B is stopped (CIII).19 Treatment of patients with coccidioidal meningitis: Treatment of coccidioidal meningitis requires consultation with a specialist (AIII). Intravenous amphotericin B alone is ineffective as treatment for coccidioidal meningitis. Treatment with a triazole antifungal is recommended. Fluconazole (400 to 800 mg daily) is the preferred regimen (AII),18,26 but itraconazole 400 to 600 mg daily also has been successfully used (BII).27 Therapy with voriconazole (BIII),28-30 posaconazole (CIII),22,31 and isavuconazole (CIII) has been described in individual cases and has been successful.32 Despite appropriate antifungal therapy, some patients may develop hydrocephalus and require CSF shunting. In some instances, triazole antifungals are ineffective and intrathecal amphotericin B is recommended (AIII). When required, intrathecal therapy should be administered by someone very experienced in this drug delivery technique. Monitoring of Response to Therapy and Adverse Events (Including IRIS) Monitoring the CF antibody titer is useful to assess response to therapy, and this titer should be measured every 12 weeks. More than a twofold rise suggests recurrence or worsening of clinical disease and should prompt reassessment of management. Immune reconstitution inflammatory syndrome (IRIS) has been reported infrequently in patients with HIV and coccidioidomycosis.33-35 In general, delaying initiation of ART while treating coccidioidomycosis is not recommended (AIII). Conversely, a recent case series36 and a single case report37 suggested that, in highly immunosuppressed patients (i.e., CD4 counts <100 cells/mm3) with disseminated disease, clinical Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-7 decline may occur with initiation of ART. These findings suggest that it might be prudent to delay ART for 4 to 6 weeks after initiating antifungal therapy in severely immunosuppressed patients who have disseminated or central nervous system disease (BIII). However, delay may not prevent IRIS, as reported in at least one patient with disseminated disease, who had received treatment with fluconazole for 28 days but who still had worsening symptoms within a week after starting ART.38 Close monitoring for clinical worsening, particularly if meningitis is present, is essential when treating highly immunosuppressed people who have HIV and who have disseminated coccidioidomycosis.13 Managing Treatment Failure Serum drug concentrations should be checked in patients with severe coccidioidomycosis who do not respond to treatment with itraconazole. In case of confirmed treatment failure with adequate serum concentrations of the azole, treatment should be changed to IV amphotericin B, either deoxycholate or a lipid formulation for patients who are severely ill (AIII). For those who are not severely ill, posaconazole (BIII) and voriconazole (BIII) are appropriate alternatives. Drug interactions may limit the use of voriconazole in patients who are taking non-nucleoside reverse transcriptase inhibitors or ritonavir- or cobicistat-boosted regimens (see the DDI tables in the Adult and Adolescent Antiretroviral Guidelines). Posaconazole and isavuconazole have fewer known drug interactions with antiretrovirals than voriconazole. In certain situations, surgical intervention may be indicated.18 Therapy After Immune Reconstitution Patients with peripheral blood CD4 count ≥250 cells/mm3 appear capable of maintaining their coccidioidal-specific cellular immune response.39 Moreover, a prospective study has demonstrated that coccidioidomycosis is less severe in those with lower HIV RNA and higher CD4 counts.5 Given these facts, in patients with HIV who have undetectable HIV RNA on potent ART and who have CD4 count ≥250cells/mm3, coccidioidomycosis should be managed no differently than it is in patients in the general population (AII). For patients with focal pulmonary disease who meet the above criteria, treatment with a triazole antifungal agent should continue for a minimum of 3 to 6 months (AII). For patients with diffuse pulmonary disease and those with extrathoracic dissemination, antifungal therapy should continue for at least 12 months and usually much longer. Therapy should be discontinued based on clinical and immunological response and in consultation with an expert. For patients with detectable HIV viremia or CD4 count <250/mm3, antifungal therapy at full dose should continue (BIII). Preventing Relapse Relapse of coccidioidomycosis occurs in 25% to 33% of individuals without HIV who have diffuse pulmonary coccidioidomycosis or nonmeningeal disseminated coccidioidomycosis40,41 and may occur in people with HIV who have CD4 counts ≥250 cells/mm3 and are virologically suppressed on antiretrovirals.1,36 During and after coccidioidomycosis therapy, patients should have serial chest radiographs and coccidioidal serology tests every 3 to 6 months. Relapses have been reported in >80% of patients with meningitis in whom triazoles have been discontinued.42 Therefore, therapy for coccidioidal meningitis should be continued for life (AII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-8 Special Considerations During Pregnancy Women are generally at lower risk than men for severe coccidioidomycosis, and disease does not appear to reactivate or worsen in women with prior coccidioidomycosis during pregnancy. However, when coccidioidomycosis is acquired during the second or third trimester of pregnancy, the infection is more likely to be severe and disseminated.43 Congenital malformations, including craniofacial and limb abnormalities, similar to those observed in animals exposed to fluconazole, have been reported in infants born to mothers who received fluconazole through or beyond the first trimester of pregnancy.44 A recent systematic review and meta-analysis of cohort or case control studies (n = 6 studies) that analyzed more than 16,000 exposures and reported fetal outcomes after exposure to fluconazole used in the first trimester of pregnancy, found a marginal association with increased risk of congenital malformations (odds ratio 1.09; 95% CI, 0.99–1.2, P = 0.088), including heart defects, as well as spontaneous abortion; exposure to more than 150 mg was associated with an overall increase in congenital malformations. One registry-based cohort study (included in the systematic review)5,37 and a more recent large population-based case-control study45 specifically noted an increase in conotruncal heart defects. The latter study also suggested an increase in cleft lip with cleft palate. A nationwide cohort study in Denmark reported that the risk of spontaneous abortion was greater in women exposed to oral fluconazole in pregnancy than in women who had not been exposed or those with topical azole exposure only.46 A cohort study using Swedish and Norwegian registry data (n = 1,485,316 pregnancies) found no association between fluconazole use in pregnancy and risk of stillbirth or neonatal death.47 Most of the studies regarding effects of fluconazole in pregnancy have involved low doses and short-term exposure. Responding to the reported birth defects, the FDA has changed the pregnancy category for fluconazole from C to D for any use other than a single 150 mg dose of fluconazole to treat vaginal candidiasis.48 Although cases of birth defects in infants exposed to itraconazole have been reported, prospective cohort studies of >300 women with first trimester exposure did not show an increased risk of malformation.49,50 However, in general, all azole antifungals should be avoided during the first trimester of pregnancy (BIII). One problematic area is coccidioidal meningitis, for which the only alternative treatment to triazole antifungals is IV or intrathecal amphotericin B. In such situations, the decision regarding choice of treatment should be based on considerations of benefit versus potential risk and made in consultation with the mother, the infectious diseases consultant, and the obstetrician.43 Voriconazole and posaconazole are teratogenic and embryotoxic in animal studies; for voriconazole, these occurred at doses lower than recommended for humans; however, adequately controlled studies in humans have not been conducted. Therefore, use of voriconazole and posaconazole should be avoided in pregnancy, especially in the first trimester (AIII). Intravenous amphotericin B, formulated with deoxycholate or as a lipid preparation, is the preferred treatment for non-meningeal coccidioidomycosis during the first trimester of pregnancy (AIII). Extensive clinical use of amphotericin B has not been associated with teratogenicity. At delivery, infants born to women treated with amphotericin B should be evaluated for renal dysfunction and hypokalemia. One study suggested that the treatment regimen for women who develop coccidioidomycosis in the second or third trimester can be similar to that for nonpregnant women with coccidioidomycosis (CIII).18 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-9 References 1. Jones JL, Fleming PL, Ciesielski CA, Hu DJ, Kaplan JE, Ward JW. Coccidioidomycosis among persons with AIDS in the United States. J Infect Dis. 1995;171(4):961-966. Available at: 2. Litvintseva AP, Marsden-Haug N, Hurst S, et al. Valley fever: finding new places for an old disease: Coccidioides immitis found in Washington State soil associated with recent human infection. Clin Infect Dis. 2015;60(1):e1-3. Available at: 3. Ampel NM, Dols CL, Galgiani JN. Coccidioidomycosis during human immunodeficiency virus infection: results of a prospective study in a coccidioidal endemic area. Am J Med. 1993;94(3):235-240. Available at: 4. Woods CW, McRill C, Plikaytis BD, et al. Coccidioidomycosis in human immunodeficiency virus-infected persons in Arizona, 1994-1997: incidence, risk factors, and prevention. J Infect Dis. 2000;181(4):1428-1434. Available at: 5. Masannat FY, Ampel NM. Coccidioidomycosis in patients with HIV-1 infection in the era of potent antiretroviral therapy. Clin Infect Dis. 2010;50(1):1-7. Available at: 6. Fish DG, Ampel NM, Galgiani JN, et al. Coccidioidomycosis during human immunodeficiency virus infection. A review of 77 patients. Medicine (Baltimore). 1990;69(6):384-391. Available at: 7. Valdivia L, Nix D, Wright M, et al. Coccidioidomycosis as a common cause of community-acquired pneumonia. Emerg Infect Dis. 2006;12(6):958-962. Available at: 8. Kim MM, Blair JE, Carey EJ, Wu Q, Smilack JD. Coccidioidal pneumonia, Phoenix, Arizona, USA, 2000-2004. Emerg Infect Dis. 2009;15(3):397-401. Available at: 9. Mahaffey KW, Hippenmeyer CL, Mandel R, Ampel NM. Unrecognized coccidioidomycosis complicating Pneumocystis carinii pneumonia in patients infected with the human immunodeficiency virus and treated with corticosteroids. A report of two cases. Arch Intern Med. 1993;153(12):1496-1498. Available at: 10. Arguinchona HL, Ampel NM, Dols CL, Galgiani JN, Mohler MJ, Fish DG. Persistent coccidioidal seropositivity without clinical evidence of active coccidioidomycosis in patients infected with human immunodeficiency virus. Clin Infect Dis. 1995;20(5):1281-1285. Available at: 11. Stevens DA, Clemons KV, Levine HB, et al. Expert opinion: what to do when there is Coccidioides exposure in a laboratory. Clin Infect Dis. 2009;49(6):919-923. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-10 12. Blair JE, Ampel NM, Hoover SE. Coccidioidomycosis in selected immunosuppressed hosts. Med Mycol. 2019;57(Supplement_1):S56-s63. Available at: 13. Donovan FM, Ramadan FA, Khan SA, et al. Comparison of a Novel Rapid Lateral Flow Assay to Enzyme Immunoassay Results for Early Diagnosis of Coccidioidomycosis. Clin Infect Dis. 2021;73(9):e2746-e2753. Available at: 14. Durkin M, Connolly P, Kuberski T, et al. Diagnosis of coccidioidomycosis with use of the Coccidioides antigen enzyme immunoassay. Clin Infect Dis. 2008;47(8):e69-73. Available at: 15. Durkin M, Estok L, Hospenthal D, et al. Detection of Coccidioides antigenemia following dissociation of immune complexes. Clin Vaccine Immunol. 2009;16(10):1453-1456. Available at: 16. Kassis C, Zaidi S, Kuberski T, et al. Role of Coccidioides Antigen Testing in the Cerebrospinal Fluid for the Diagnosis of Coccidioidal Meningitis. Clin Infect Dis. 2015;61(10):1521-1526. Available at: 17. Dizon D, Mitchell M, Dizon B, Libke R, Peterson MW. The utility of real-time polymerase chain reaction in detecting Coccidioides immitis among clinical specimens in the Central California San Joaquin Valley. Med Mycol. 2019;57(6):688-693. Available at: 18. Galgiani JN, Ampel NM, Catanzaro A, Johnson RH, Stevens DA, Williams PL. Practice guideline for the treatment of coccidioidomycosis. Infectious Diseases Society of America. Clin Infect Dis. 2000;30(4):658-661. Available at: 19. Galgiani JN, Ampel NM, Blair JE, et al. Coccidioidomycosis. Clin Infect Dis. 2005;41(9):1217-1223. Available at: 20. Galgiani JN, Catanzaro A, Cloud GA, et al. Comparison of oral fluconazole and itraconazole for progressive, nonmeningeal coccidioidomycosis. A randomized, double-blind trial. Mycoses Study Group. Ann Intern Med. 2000;133(9):676-686. Available at: 21. Anstead GM, Corcoran G, Lewis J, Berg D, Graybill JR. Refractory coccidioidomycosis treated with posaconazole. Clin Infect Dis. 2005;40(12):1770-1776. Available at: 22. Stevens DA, Rendon A, Gaona-Flores V, et al. Posaconazole therapy for chronic refractory coccidioidomycosis. Chest. 2007;132(3):952-958. Available at: 23. Thompson GR, 3rd, Beck KR, Patt M, Kratschmar DV, Odermatt A. Posaconazole-Induced Hypertension Due to Inhibition of 11beta-Hydroxylase and 11beta-Hydroxysteroid Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-11 Dehydrogenase 2. J Endocr Soc. 2019;3(7):1361-1366. Available at: 24. Thompson GR, 3rd, Rendon A, Ribeiro Dos Santos R, et al. Isavuconazole Treatment of Cryptococcosis and Dimorphic Mycoses. Clin Infect Dis. 2016;63(3):356-362. Available at: 25. Stewart ER, Eldridge ML, McHardy I, Cohen SH, Thompson GR, 3rd. Liposomal Amphotericin B as Monotherapy in Relapsed Coccidioidal Meningitis. Mycopathologia. 2018;183(3):619-622. Available at: 26. Galgiani JN, Catanzaro A, Cloud GA, et al. Fluconazole therapy for coccidioidal meningitis. The NIAID-Mycoses Study Group. Ann Intern Med. 1993;119(1):28-35. Available at: 27. Tucker RM, Denning DW, Dupont B, Stevens DA. Itraconazole therapy for chronic coccidioidal meningitis. Ann Intern Med. 1990;112(2):108-112. Available at: 28. Cortez KJ, Walsh TJ, Bennett JE. Successful treatment of coccidioidal meningitis with voriconazole. Clin Infect Dis. 2003;36(12):1619-1622. Available at: 29. Proia LA, Tenorio AR. Successful use of voriconazole for treatment of Coccidioides meningitis. Antimicrob Agents Chemother. 2004;48(6):2341. Available at: 30. Freifeld A, Proia L, Andes D, et al. Voriconazole use for endemic fungal infections. Antimicrob Agents Chemother. 2009;53(4):1648-1651. Available at: 31. Schein R, Homans J, Larsen RA, Neely M. Posaconazole for chronic refractory coccidioidal meningitis. Clin Infect Dis. 2011;53(12):1252-1254. Available at: 32. Heidari A, Quinlan M, Benjamin DJ, et al. Isavuconazole in the Treatment of Coccidioidal Meningitis. Antimicrob Agents Chemother. 2019;63(3). Available at: 33. Mortimer RB, Libke R, Eghbalieh B, Bilello JF. Immune reconstitution inflammatory syndrome presenting as superior vena cava syndrome secondary to Coccidioides lymphadenopathy in an HIV-infected patient. J Int Assoc Physicians AIDS Care (Chic). 2008;7(6):283-285. Available at: 34. D'Avino A, Di Giambenedetto S, Fabbiani M, Farina S. Coccidioidomycosis of cervical lymph nodes in an HIV-infected patient with immunologic reconstitution on potent HAART: a rare observation in a nonendemic area. Diagn Microbiol Infect Dis. 2012;72(2):185-187. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-12 35. Trible R, Edgerton N, Hayek S, Winkel D, Anderson AM. Antiretroviral therapy-associated coccidioidal meningitis. Emerg Infect Dis. 2013;19(1):163-165. Available at: 36. Mathew G, Smedema M, Wheat LJ, Goldman M. Relapse of coccidioidomycosis despite immune reconstitution after fluconazole secondary prophylaxis in a patient with AIDS. Mycoses. 2003;46(1-2):42-44. Available at: 37. Molgaard-Nielsen D, Pasternak B, Hviid A. Use of oral fluconazole during pregnancy and the risk of birth defects. N Engl J Med. 2013;369(9):830-839. Available at: 38. Lin AY, Chun V, Dhamija A, Bordin-Wosk T, Kadakia A. Immune reconstitution inflammatory syndrome in an HIV-infected patient with disseminated coccidioidomycosis. Int J STD AIDS. 2019;30(9):923-926. Available at: 39. Ampel NM. Delayed-type hypersensitivity, in vitro T-cell responsiveness and risk of active coccidioidomycosis among HIV-infected patients living in the coccidioidal endemic area. Med Mycol. 1999;37(4):245-250. Available at: 40. Graybill JR, Stevens DA, Galgiani JN, Dismukes WE, Cloud GA. Itraconazole treatment of coccidioidomycosis. NAIAD Mycoses Study Group. Am J Med. 1990;89(3):282-290. Available at: 41. Catanzaro A, Galgiani JN, Levine BE, et al. Fluconazole in the treatment of chronic pulmonary and nonmeningeal disseminated coccidioidomycosis. NIAID Mycoses Study Group. Am J Med. 1995;98(3):249-256. Available at: 42. Dewsnup DH, Galgiani JN, Graybill JR, et al. Is it ever safe to stop azole therapy for Coccidioides immitis meningitis? Ann Intern Med. 1996;124(3):305-310. Available at: 43. Bercovitch RS, Catanzaro A, Schwartz BS, Pappagianis D, Watts DH, Ampel NM. Coccidioidomycosis during pregnancy: a review and recommendations for management. Clin Infect Dis. 2011;53(4):363-368. Available at: 44. Pursley TJ, Blomquist IK, Abraham J, Andersen HF, Bartley JA. Fluconazole-induced congenital anomalies in three infants. Clin Infect Dis. 1996;22(2):336-340. Available at: 45. Howley MM, Carter TC, Browne ML, Romitti PA, Cunniff CM, Druschel CM. Fluconazole use and birth defects in the National Birth Defects Prevention Study. Am J Obstet Gynecol. 2016;214(5):657.e651-659. Available at: 46. Mølgaard-Nielsen D, Svanström H, Melbye M, Hviid A, Pasternak B. Association Between Use of Oral Fluconazole During Pregnancy and Risk of Spontaneous Abortion and Stillbirth. Jama. 2016;315(1):58-67. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV F-13 47. Pasternak B, Wintzell V, Furu K, Engeland A, Neovius M, Stephansson O. Oral Fluconazole in Pregnancy and Risk of Stillbirth and Neonatal Death. Jama. 2018;319(22):2333-2335. Available at: 48. U.S. Food and Drug Administration. FDA Drug Safety Communication:Use of long-term, high-dose Diflucan (fluconazole) during pregnancy may be associated with birth defects in infants. 2011. Available at: 49. De Santis M, Di Gianantonio E, Cesari E, Ambrosini G, Straface G, Clementi M. First-trimester itraconazole exposure and pregnancy outcome: a prospective cohort study of women contacting teratology information services in Italy. Drug Saf. 2009;32(3):239-244. Available at: 50. Bar-Oz B, Moretti ME, Bishai R, et al. Pregnancy outcome after in utero exposure to itraconazole: a prospective cohort study. Am J Obstet Gynecol. 2000;183(3):617-620. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-1 Community-Acquired Pneumonia Updated: September 7, 2022 Reviewed: January 10, 2024 Epidemiology Bacterial respiratory diseases, including sinusitis, bronchitis, otitis, and pneumonia, are among the most common infectious complications in people with HIV, occurring with increased frequency at all CD4 T lymphocyte cell (CD4) counts.1 This chapter will focus on the diagnosis, prevention, and management of bacterial community-acquired pneumonia (CAP) in people with HIV. While viral pneumonias are a frequent cause of CAP, particularly influenza and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), the management of coronavirus-19 (COVID-19) disease is outside the scope of these guidelines (refer to NIH COVID-19 Treatment Guidelines for updated treatment recommendations). These guidelines also do not consider hospital acquired pneumonia and ventilator-associated pneumonia; limited data suggest that these do not differ in terms of microbiology, clinical course, treatment, or prevention in people with HIV as compared to in people without HIV with similar HIV-unrelated comorbidities. Bacterial pneumonia is a common cause of HIV-associated morbidity. Recurrent pneumonia, considered two or more episodes within a 1-year period, is an AIDS-defining condition. The incidence of bacterial pneumonia in individuals with HIV has decreased progressively with the advent of combination antiretroviral therapy (ART).2-7 In one study, the incidence of bacterial pneumonia declined from 22.7 episodes per 100 person-years before the introduction of ART to 9.1 episodes per 100 person-years by 1997 after ART was introduced. Since then, the incidence of bacterial pneumonia among people with HIV in developed countries has continued to drop. In the Strategic Timing of AntiRetroviral Treatment (START) study, the incidence rate of serious bacterial infections overall was 0.87 per 100 person-years, and approximately 40% of these infections were due to bacterial pneumonia.4 Recurrent bacterial pneumonia as an AIDS-defining illness is also less frequently encountered in individuals on ART; however, its exact incidence is hard to evaluate because surveillance data for it are not collected systematically as for other opportunistic infections (OIs).8 Risk Factors Yet despite ART, bacterial pneumonia remains more common in people with HIV than in those who do not have HIV.9-11 Bacterial pneumonia may be the first manifestation of underlying HIV infection and can occur at any stage of HIV disease and at any CD4 count. Bacterial pneumonia in individuals with HIV results from multiple risk factors, particularly immune defects. A CD4 count decrease, especially when below 100 cells/mm3, continues to be a major risk factor for pneumonia due to routine bacterial pathogens. Other immune defects include quantitative and qualitative B-cell abnormalities that result in impaired pathogen-specific antibody production, abnormalities in neutrophil function or numbers, and abnormalities in alveolar macrophage function.12,13 Lack of ART or intermittent use of ART increases the risk for pneumonia, likely due to uncontrolled HIV viremia.14 Additional risk factors that contribute to the continued risk for bacterial pneumonia in individuals with HIV include chronic viral hepatitis, tobacco, alcohol, injection drug use and prescribed opioid Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-2 use, particularly higher doses and opioids with immunosuppressive properties.3,10,15,16,17 Chronic obstructive pulmonary disease (COPD), malignancy, renal insufficiency, and congestive heart failure (CHF) are emerging as risk factors for pneumonia, particularly in the population of older adults with HIV.18 Risk for CAP can also increase with obesity4, an emerging health problem in people living with HIV. Microbiology In individuals with HIV, Streptococcus pneumoniae (S. pneumoniae) and Haemophilus species are the most frequently identified causes of community-acquired bacterial pneumonia, the same as in individuals without HIV.19-25 Staphylococcus aureus (S. aureus) and S. pneumoniae are among the most common etiologies of pneumonia in association with influenza infection.26,27 Atypical bacterial pathogens such as Legionella pneumophila, Mycoplasma pneumoniae, and Chlamydophila species have been reported as infrequent causes of CAP in individuals with HIV.22,28 However, when more extensive testing such as serology to detect IgM antibodies (IgM) antibodies and/or positive polymerase chain reaction (PCR) of respiratory secretions was performed, additional infections due to Mycoplasma and Chlamydia were detected.29 Additional microbial etiologies of CAP that should be considered in people with HIV include Mycobacterium tuberculosis, Pneumocystis, other opportunistic infections, and respiratory viruses. The incidence of these different organisms will vary depending on geographic region and patient risk factors including degree of immunocompromise when considering opportunistic infections. For example, in a recent prospective study from South Africa of 284 patients with HIV and suspected pneumonia, sputum real-time multiplex PCR testing found that tuberculosis was more common than bacterial causes of CAP in this setting; viruses were detected in 203 patients, with the most common being human metapneumovirus, although the pathogenic significance of the viral pathogens was uncertain.30 As noted, respiratory viruses, influenza and SARS-CoV-2 are also common causes of CAP in people with HIV. While influenza and COVID-19 generally present similarly in people with and without HIV, some studies suggest mortality may be increased among people with HIV for these viral infections, particularly in low-and-middle income country settings.31-36 Risk Factors for Pseudomonas aeruginosa and Methicillin-Resistant Staphylococcus aureus The frequency of Pseudomonas aeruginosa (P. aeruginosa) and S. aureus as community-acquired pathogens is higher in individuals with HIV than in those without HIV based on studies in the early combination ART era.23,37 Many of these patients often had poorly controlled HIV or the presence of other concomitant risk factors that contributed to risk for P. aeruginosa or S. aureus. Patients with advanced HIV disease (CD4 count ≤50 cells/mm3) or underlying neutropenia, as well as pre-existing lung disease such as bronchiectasis or severe COPD have an increased risk of infection with P. aeruginosa. Other risk factors for infection include the use of corticosteroids, severe malnutrition, hospitalization within the past 90 days, residence in a health care facility or nursing home, and chronic hemodialysis.38 S. aureus should be considered in patients with recent viral infection (particularly influenza), a history of injection drug use, or severe, bilateral, necrotizing pneumonia. Risk factors for S. aureus pneumonia in patients with HIV include receipt of antibiotics prior to hospital admission, comorbid illnesses, and recent healthcare contact.39 Community outbreaks of methicillin-resistant S. aureus (MRSA) infection have also been seen among men who have sex with men.40 Studies of patients Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-3 without HIV have identified hemodialysis, known prior colonization or infection with MRSA, as well as recurrent skin infections to be risk factors for MRSA pneumonia.38 Notably, nasal carriage and colonization of skin sites with MRSA is more common in individuals with HIV than in those without HIV, and is more likely in patients recently incarcerated and/or hospitalized.41,42 Clinical Manifestations Clinical and Radiographic Presentation The clinical and radiographic presentation of bacterial pneumonia in individuals with HIV, particularly in those with higher CD4 count and HIV viral suppression, is similar to that in individuals without HIV.43 Patients with pneumonia caused by bacteria such as S. pneumoniae or Haemophilus species characteristically have acute onset (3 to 5 days) of symptoms, including fevers, chills, rigors, chest pain or pleurisy, cough productive of purulent sputum, and dyspnea.44 The presence of fever, tachycardia, and/or hypotension can be indicators of sepsis. Tachypnea and decreased arterial oxygen saturation indicate moderate-to-severe pneumonia, and in such cases, clinicians should strongly consider hospitalizing the patient. Patients with bacterial pneumonia typically have signs of focal consolidation, such as egophony, and/or pleural effusion on lung examination. In contrast, lung examination often is normal in those with Pneumocystis pneumonia (PCP), and if abnormal, reveals inspiratory crackles. In patients with bacterial pneumonia, the white blood cell (WBC) count usually is elevated. The elevation may be relative to baseline WBC count in those with advanced HIV. Neutrophilia or a left shift in WBC differential may be present. Individuals with bacterial pneumonia characteristically exhibit unilateral, focal, segmental, or lobar consolidation on chest radiograph. The frequency of these typical radiographic findings, however, may depend on the underlying bacterial pathogen. Those with pneumonia due to S. pneumoniae or Haemophilus typically present with consolidation, whereas cavitation may be a feature more suggestive of P. aeruginosa or S. aureus. Risk Factors for Bacteremia In individuals with HIV the incidence of bacteremia accompanying pneumonia is greater than in individuals without HIV, especially when infection is due to S. pneumoniae.45 In data from the CDC, the incidence of invasive pneumococcal disease, inclusive of bacteremia, was significantly higher in individuals with HIV: rates were 173 cases per 100,000 in those with HIV infection, compared to 3.8 per 100,000 in younger adults aged 18–34 years and 36.4 per 100,000 among those aged ≥65 years in the general population.46 Similarly, in a study from Kenya, the rate of pneumococcal bacteremia was significantly higher in individuals with HIV infection (rate ratio of HIV-infected versus HIV-negative adults, 19.7, 95% CI 12.4-31.1).47 With the introduction of ART and pneumococcal conjugate vaccines for both the general pediatric population and individuals living with HIV, this disparity in incidence rates of bacteremia between people with and without HIV has narrowed but has not been eliminated.48-52 In one recent study of invasive pneumococcal disease (IPD), which includes bacteremia, IPD was more common in people with HIV who had CD4 counts < 500 cells/mm3, but even those with counts > 500 cells/mm3, had a higher incidence than in the general population.53 Risk factors associated with bacteremia include lack of ART, low CD4 count (particularly <100 cells/mm3), as well as alcohol abuse, current smoking, and comorbidities, particularly liver disease.49 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-4 Severity of Illness Disease severity and arterial oxygenation should be assessed in all patients with pneumonia. Noninvasive measurement of arterial oxygen saturation by pulse oximetry is an appropriate screening test. Arterial blood gas analysis is indicated for patients with evidence of hypoxemia suggested by noninvasive assessment and for patients who have tachypnea and/or respiratory distress. Assessment of additional clinical features and the use of severity scoring systems for pneumonia such as the Pneumonia Severity Index (PSI) and CURB-65 and their application to patients with HIV are discussed in the Treating Disease section. Outcomes Although some studies suggest that bacterial pneumonia is associated with increased mortality in individuals with HIV,23,54,55 others do not.43,56-58 Independent predictors of increased mortality in a prospective, multicenter study of individuals with HIV with community-acquired bacterial pneumonia were CD4 count <100 cells/mm3, radiographic progression of disease, and presence of shock.59 In that study, multilobar infiltrates, cavitary infiltrates, and pleural effusion on baseline imaging were all independent predictors of radiographic progression of disease. However, in patients on ART with controlled HIV viremia, and high CD4 counts (>350 cells/mm3), the clinical courses and outcomes of pneumonia appear to be similar to those in patients without HIV.43 As in patients without HIV, pneumonia may have an impact on longer term outcomes of patients with HIV. This includes greater long-term mortality, as hospitalization for pneumonia has been associated with increased mortality up to one year later.60 One factor that may add to this long-term mortality is cardiovascular disease associated with CAP, which occurs at a similar rate in those with HIV infection , as those without, even though in one retrospective cohort study of 4,384 patients, people with HIV were younger, had less severe CAP and fewer traditional cardiovascular risk factors than those without HIV infection.61 Pneumonia has also been associated with impaired lung function and risk of subsequent lung cancer in individuals with HIV.62-64 Diagnosis General Approach Patients with clinical symptoms and signs suggestive of CAP should have posteroanterior and lateral chest radiographs; evidence of pneumonia can also be found on chest computed tomography (CT) scan, but routine use of chest CT scan for this purpose is not recommended. Lung ultrasound can also be used to aid in the diagnosis pneumonia. If previous radiographs are available, they should be reviewed to assess for new findings. The clinical diagnosis of bacterial pneumonia requires a demonstrable infiltrate by chest radiograph or other imaging technique in conjunction with compatible clinical symptoms and signs. The differential diagnosis of pneumonia in individuals with HIV is broad and a confirmed microbiologic diagnosis should be pursued. Microbial identification can allow clinicians to target the specific pathogen(s) and discontinue broad spectrum antibiotic therapy and/or empiric therapy that targets non-bacterial pathogens. Microbiologic testing should include evaluation of the upper respiratory tract for SARS-CoV-2, influenza in the appropriate season, and may include testing other respiratory viruses.65 Given the increased incidence of Mycobacterium tuberculosis (M. tuberculosis) in individuals with HIV, a tuberculosis (TB) diagnosis should always be considered in patients with Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-5 HIV who have pneumonia, particularly in high incidence areas. Those with clinical and radiographic findings suggestive of TB should be managed as potentially having TB (i.e., airborne precautions for hospitalized patients), and two to three sputum specimens should be obtained for acid fast bacilli evaluation (including TB PCR; see Mycobacterium tuberculosis Infection and Disease section). Bronchoscopy with bronchoalveolar lavage should be considered, especially if the differential diagnosis includes opportunistic pathogens such as Pneumocystis jirovecii. Procalcitonin (PCT) testing has been proposed as a tool to distinguish between bacterial and viral respiratory infections. One study from Africa specifically evaluated the usefulness of PCT testing to distinguish CAP due to bacteria (non-TB), M. tuberculosis, and PCP in people with HIV. In general, PCT levels associated with bacterial pneumonia are higher than those associated with viral or fungal pneumonias, but levels can also be elevated in non-bacterial pulmonary infections.66 Specific PCT thresholds have not been established or validated in HIV-associated bacterial pneumonia. Thus, given the lack of data, the use of PCT to guide decisions regarding etiology of pneumonia, initiation of anti-bacterial treatment, or duration of treatment in patients with HIV is not recommended. Recommended Diagnostic Evaluation in CAP American Thoracic Society (ATS) and the Infectious Diseases Society of America (IDSA) guidelines for microbiologic testing for diagnosis of CAP in individuals without HIV generally also apply to people with HIV.67 • In patients with HIV with CAP who are well enough to be treated as outpatients, routine diagnostic tests to identify a bacterial etiologic diagnosis are optional, especially if the microbiologic studies cannot be performed promptly. • In patients with HIV hospitalized for CAP, a Gram stain of expectorated sputum and two blood cultures are recommended, particularly in those with severe pneumonia, in those who are not on ART; or in those who are known to have a CD4 count <350 cells/mm3 (and especially if <100 cells/mm3) prior to hospitalization. Specimens should ideally be obtained before initiation of antibiotics, or within 12 hours to 18 hours of such initiation. • Urinary antigen tests for L. pneumophila and S. pneumoniae are recommended in hospitalized patients, particularly those with severe CAP. In addition, lower respiratory tract secretions should be cultured for Legionella on selective media or undergo Legionella nucleic acid amplification testing in adults with severe CAP. Legionella testing should also be done in people with HIV with non-severe CAP when indicated by epidemiological factors, such as association with a Legionella outbreak or recent travel. • Microbiologic diagnostic testing is indicated whenever epidemiologic, clinical, or radiologic clues prompt suspicion of specific pathogens that could alter standard empirical management decisions. • If available, rapid MRSA nasal testing should be performed, particularly in patients with risk factors for MRSA or in a high prevalence setting, as results can direct empiric antibiotic therapy.68 Gram stain and culture of sputum is recommended in all hospitalized patients meeting the criteria stated above, and is optional in people with HIV with CAP not meeting these criteria. In general, Gram stain and culture of expectorated sputum should be performed only if a good-quality specimen can be obtained prior to—or not more than 12 hours to 18 hours after—initiation of antibiotics, and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-6 quality performance measures for collection, transport, and processing of samples can be met. Sputum cultures in people with HIV have been shown to identify a bacterial etiology in up to 30-40% of good quality specimens55,69 although yield is less in other studies.14,29 Correlation of sputum culture with Gram stain can help in interpretation of sputum culture data. For intubated patients, an endotracheal aspirate sample should be obtained promptly after intubation, or bronchoscopy may be indicated. Blood cultures are more likely to be positive in people with HIV than in those without HIV. Patients with HIV, particularly those with lower CD4 counts, are at increased risk of invasive infection with S. pneumoniae. Given concerns for drug-resistant S. pneumoniae70,71, as well as S. aureus and/or other drug-resistant pathogens, blood cultures are recommended for patients with HIV who meet the criteria as noted above, and are optional for those who do not meet the criteria listed. Diagnostic thoracentesis should be performed in all patients with pleural effusion if concern exists for accompanying empyema, and pleural fluid should be sent for microbiologic studies. Therapeutic thoracentesis should be performed to relieve respiratory distress secondary to a moderate-to-large-sized pleural effusion. Given the increased risk of invasive pneumococcal disease in patients with HIV, clinicians should be vigilant for evidence of extra-pulmonary complications of infection. Preventing Exposure No effective means exist to reduce exposure to S. pneumoniae and Haemophilus influenzae, which are common in the community. General precautions to maintain health, such as adhering to hand hygiene and cough etiquette and refraining from close contact with individuals who have respiratory infections, should be emphasized for patients with HIV as for other patient populations. Preventing Disease Pneumococcal Vaccine Vaccination against S. pneumoniae is an important measure in preventing bacterial pneumonia. Some observational studies have reported benefits of pneumococcal polysaccharide vaccine (PPSV) use in people with HIV against IPD (e.g., bacteremia, meningitis)49,72, and all-cause pneumonia;73-75 however, results have been variable.72,76-78 One randomized placebo-controlled trial of PPSV in Africa paradoxically found that vaccination was associated with an increased risk of pneumonia, and there was no evidence of reduced risk of IPD among vaccinated participants.79 Follow-up of this cohort not only confirmed the increase in pneumonia in vaccinated participants, but also showed a decrease in all-cause mortality, although participants in this study were not treated with ART.80 A recent study81 evaluating the impact of the 13-valent pneumococcal conjugate vaccine (PCV13) vaccination on the rates of IPD in adults with HIV between 2008 and 2018 found that IPD rates remained high despite reductions with the introduction of PCV13. PCV20/non-PCV15 serotypes comprised 16.5% of cases of IPD, suggesting that the use of higher valent conjugate pneumococcal vaccines may reduce IPD. In 2021, two PCVs, 15-valent (PCV15) and 20-valent (PCV20), were licensed by the FDA for use in U.S. adults.82 PCV15 and PCV20 were licensed based on safety and immunogenicity data compared with the 13-valent PCV or 23-valent pneumococcal polysaccharide vaccine (PPSV23). Effectiveness data of these vaccine against pneumococcal disease in adults with HIV infection are currently not available. One phase 3 clinical trial of PCV15 followed by PPSV23 8 weeks later in people with HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-7 demonstrated safety and immunogenicity of this approach.83 No clinical data exist for the use of PCV20 in people with HIV. To date, one randomized, double-blind, placebo-controlled trial has assessed the efficacy of PCV against pneumococcal disease in adults with HIV. This was a trial on 7-valent PCV (PCV7) among adults with HIV in Malawi, which demonstrated 74% efficacy against vaccine-type IPD, with clear evidence of efficacy in those with CD4 counts <200 cells/mm3.84 However, study participants were those who had recovered from IPD, and received two doses of PCV7 four weeks apart. Therefore, findings may not be directly applicable to adults with HIV infection. Patients with CD4 counts ≥200 cells/mm3 should receive a dose of PPSV23 at least 8 weeks later (AI).72-75,85-89 While individuals with HIV with CD4 counts <200 cells/mm3 can also be offered PPSV23 at least 8 weeks after receiving PCV15 (CIII) (such as if there are concerns with retention in care), PPSV23 should preferably be deferred until after an individual’s CD4 count increases to >200 cells/mm3 while on ART (BIII). Clinical evidence supporting use of PPSV23 in persons with CD4 counts <200 cells/mm3 appears strongest in patients who also have HIV RNA <100,000 copies/mL;75,89 evidence also suggests benefit for those who start ART before receiving PPSV vaccination.72,90 People with HIV who have received PCV13 but have not completed their recommended pneumococcal vaccine series with PPSV23, one dose of PCV20 may be used if PPSV23 is not available. If PCV20 is used, their pneumococcal vaccinations are complete (CIII). Influenza Vaccine Influenza vaccination is pertinent to prevention of CAP from influenza or influenza-associated bacterial pneumonia, which can occur as a complication of influenza. Influenza and pneumococcal vaccines can be administered during the same visit. Use of high-dose inactivated influenza vaccine is associated with decreased incidence of influenza and greater antibody response in adults without HIV age ≥65 years compared with standard-dose inactivated vaccine.91,92 One trial found greater immunogenicity in people with HIV age ≥18 years who were given high-dose influenza vaccine compared with standard-dose inactivated vaccine.93 See the “Influenza Vaccine” section in the Immunization section of the Adult and Adolescent Opportunistic Infections Guidelines for a detailed evidence summary. All people with HIV infection during influenza season (AI) should be immunized against influenza with inactivated, standard dose or recombinant influenza vaccine per recommendation of the season (AI). High-dose inactivated influenza vaccine may be given to individuals age >65 years (AIII). For pregnant people with HIV, administer inactivated influenza or recombinant vaccine at any time during pregnancy (AI). Additional Vaccines The incidence of H. influenzae type b infection in adults with HIV is low. Therefore, H. influenzae type vaccine is not usually recommended for adult use (BIII)90 unless a patient also has anatomic or functional asplenia. Recommendations for COVID-19 vaccination are provided in the Immunization section of the Adult and Adolescent Opportunistic Infections Guidelines. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-8 Prophylaxis and Risk Reduction Several factors are associated with a decreased risk of bacterial pneumonia in HIV, including use of ART and trimethoprim-sulfamethoxazole (TMP-SMX) for PCP prophylaxis.55 In many studies, daily administration of TMP-SMX for PCP prophylaxis reduced the frequency of bacterial respiratory infections.9,94,95 This point should be considered when selecting an agent for PCP prophylaxis; however, indiscriminate use of TMP-SMX (when not indicated for PCP prophylaxis or other specific reasons) may promote development of TMP-SMX-resistant organisms. Thus, in the United States, TMP-SMX should not be prescribed solely to prevent bacterial respiratory infection (AIII). Similarly, clarithromycin or azithromycin should not be prescribed solely for preventing bacterial respiratory infection (AIII). A decreased absolute neutrophil count (e.g., <500 cells/mm3) is associated with an increased risk of bacterial infections, including pneumonia, although this risk has been demonstrated primarily in persons with malignant neoplasms. To reduce the risk of such bacterial infections, clinicians should take steps to reverse neutropenia, such as by stopping myelosuppressive drugs (CIII). Studies of granulocyte-colony stimulating factor (G-CSF) in people with HIV have failed to document benefit.96,97 Modifiable factors associated with an increased risk of bacterial pneumonia include smoking cigarettes, using injection drugs, and consuming alcohol.9,74,98-100 Clinicians should encourage cessation of these behaviors, refer patients to appropriate services, and/or prescribe medications to support quitting. Data demonstrate that smoking cessation can decrease the risk of bacterial pneumonia.15 Treating Disease General Approach to Treatment The basic principles of antibiotic treatment of CAP are the same for patients with HIV as for those who do not have HIV.67 As discussed in the Diagnosis section, if specimens are to be collected for diagnosis, they should preferably be collected before antibiotic therapy is initiated or within 12 hours to 18 hours of antibiotic initiation. However, antibiotic therapy should be administered promptly, without waiting for the results of diagnostic testing. Empiric therapy varies based on geographic region and common pathogens in these regions, and should take into account local resistance patterns, results of MRSA rapid swab testing if done, and individual patient risk factors, including severity of immunocompromise (recent CD4 cell count, HIV viral load) and use of ART. In patients with HIV, providers must also consider the risk of opportunistic lung infections, such as PCP, that would alter empiric treatment. In settings where the prevalence of TB is high, initiation of empiric therapy for both bacterial pneumonia and TB may be appropriate for patients in whom both diagnoses are strong considerations and after diagnostic studies are undertaken. Because respiratory fluoroquinolones are also active against M. tuberculosis, they should be used with caution in patients with suspected TB who are not being treated with concurrent standard four-drug TB therapy. Thus, patients with TB who are treated with fluoroquinolones in the absence of standard four-drug TB therapy may have an initial, but misleading response, that could delay diagnosis of TB and initiation of appropriate multidrug TB therapy, increasing the risk of drug-resistant TB and TB transmission. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-9 Assessing Severity of Disease and Treatment Location Whether patients should be treated on an outpatient basis or admitted to the hospital depends on several factors. In addition to considerations regarding ability to take oral medications, adherence, and other confounding factors (housing, comorbid diseases, etc.), severity of illness is a key factor that helps to guide decisions regarding treatment location for CAP—outpatient versus inpatient, including intensive care unit (ICU). Notably, no prospective randomized clinical trials have assessed the performance of the Pneumonia Severity Index (PSI) for CAP or other severity scores (e.g., the ATS/IDSA severity criteria67 or CURB-65 Score for Pneumonia Severity, to guide decisions regarding inpatient or outpatient treatment location for people with HIV. However, the PSI, CURB-65, the ATS/IDSA severity criteria, and other scoring systems appear to be valid for predicting mortality in patients with HIV with CAP, especially when used in combination with CD4 count.59,101,102 Whether the performance of severity indices is improved by including HIV-related variables is uncertain. One study suggested that the site of care decision be dictated by considering the PSI score and CD4 count together.101 Mortality was increased in patients with higher PSI risk class; however, even in those without an increased mortality risk by PSI, a CD4 count <200 cells/mm3 was associated with an increased risk of death.101 This led to the suggestion to hospitalize CAP patients with CD4 counts <200 cells/mm3 and to use the PSI to help guide decision-making in those with higher CD4 counts.103 However, other studies have found the PSI was predictive of outcomes independent of CD4 count.104 Furthermore, CD4 count or HIV RNA level are not clearly associated with short-term outcomes of CAP.105 Other HIV-specific scoring systems such as the Veterans Aging Cohort Study (VACS) Index, although originally designed to predict overall mortality, may also be useful in predicting ICU admission and mortality. In a study of older patients with and without HIV with CAP, a higher VACS Index was associated with greater 30-day mortality, readmission, and length of stay.106 Another possible tool is the SWAT-Bp tool developed in Malawi.107 This tool measures male [S]ex, muscle [W]asting, non-[A]mbulatory, [T]emperature (>38°C or <35°C), and [B]lood [p]ressure (systolic<100 and/or diastolic<60)). In a retrospective study of 216 patients (84% with HIV), demonstrated moderate discriminatory power, while the CURB-65 was less accurate. Thus in general, validated clinical prediction scores for prognosis can be used in patients with HIV in conjunction with clinical judgement to guide treatment location for CAP. Low risk patients for whom there are no other concerns regarding adherence or complicating factors can be treated as outpatients. Patients with severe CAP, including those presenting with shock or respiratory failure, usually require a higher level of care, typically ICU admission. Additionally, severe CAP criteria can include PSI risk class of III or IV or CURB-65 scores ≥3. Patients with ≥3 of the ATS/IDSA minor severity criteria for CAP67 often require ICU or higher level of care, as well. Empiric Antibiotic Therapy by Treatment Setting and Severity of Diseases There is a general paucity of clinical trials evaluating different antibiotic regimens for treating CAP in populations with HIV and a lack of evidence that treatment response to antibiotics is different in individuals with HIV than in those without HIV. Therefore, treatment recommendations for CAP in individuals with HIV are generally consistent with the ATS/IDSA guidelines for people without HIV.67 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-10 Outpatient CAP Treatment Individuals with HIV who are being treated as outpatients should receive an oral beta-lactam plus a macrolide (AI), or a respiratory fluoroquinolone (AI). Preferred beta-lactams are high-dose amoxicillin or amoxicillin-clavulanate; alternatives are cefpodoxime or cefuroxime. Preferred macrolides are azithromycin or clarithromycin. Preferred respiratory fluoroquinolones are moxifloxacin or levofloxacin. A respiratory fluoroquinolone (moxifloxacin or levofloxacin) should be used as an alternative to a beta lactam in patients who are allergic to penicillin. If a patient has contraindications to a macrolide or a fluoroquinolone, then doxycycline should be given as an alternative (BIII) in addition to a beta-lactam. Empirical monotherapy with a macrolide for outpatient CAP is not routinely recommended in patients with HIV for two reasons (BIII). First, increasing rates of pneumococcal resistance have been reported with erythromycin-resistant rates up to 30%,108 prompting concerns for possible treatment failure. In this regard, local drug resistance patterns, if available, can help inform treatment decisions. Additionally, patients who are already receiving a macrolide for MAC prophylaxis may have resistance due to chronic exposure, and should also not receive macrolide monotherapy for empiric treatment of bacterial pneumonia. However, macrolides can be used as part of a combination CAP regimen. Non-Severe CAP Inpatient Treatment Individuals with HIV who are being treated as inpatients should receive an intravenous (IV) beta-lactam plus a macrolide (AI) or a respiratory fluoroquinolone (AI). Monotherapy with a macrolide is not recommended in the inpatient setting. The role for dual therapy with a macrolide is somewhat controversial based on prior observational studies and two prospective clinical trials in patients without HIV with CAP that evaluated outcomes in those treated with beta-lactam monotherapy and those treated with dual-therapy including a macrolide.109,110 In one study, beta-lactam monotherapy was not found to be non-inferior to beta-lactam/macrolide combination therapy. Notably, in the monotherapy arm, patients who had more severe CAP, as indicated by a PSI ≥IV, or who had atypical pathogens were less likely to reach clinical stability. There were also more 30-day readmissions among the patients on monotherapy.109 While there was a trend towards improved outcomes in those on dual therapy, the difference between arms was not statistically significant. In a pragmatic, cluster-randomized, cross-over trial of non-ICU hospitalized patients with CAP, beta-lactam monotherapy was found to be non-inferior to beta-lactam/macrolide combination therapy or fluoroquinolone monotherapy.110 However in this study, the diagnosis of CAP did not require radiographic confirmation, illness was mild, and there were cross-overs between groups. Only one study thus far has compared a cephalosporin (ceftriaxone) to dual therapy with a cephalosporin (ceftriaxone) plus macrolide in 225 people with HIV with CAP, finding no difference between in-hospital or 14-day mortality between the groups; most patients had lower severity of disease, with only 7% of the cohort having a CURB-65 score >2 and 17% with a PSI risk class >III.111 Given the heterogeneity and limitations of recent studies and scarce data in patients with HIV, the recommendation for patients with HIV who are hospitalized with non-severe CAP remains that same as in people without HIV: to administer either beta-lactam/macrolide combination therapy, or a single drug regimen of a respiratory fluoroquinolone (AI). Preferred beta-lactams are ceftriaxone, cefotaxime, or ampicillin-sulbactam. Preferred macrolides are azithromycin and clarithromycin. Preferred respiratory fluoroquinolones are moxifloxacin or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-11 levofloxacin. If a patient has contraindications to a macrolide or a fluoroquinolone, then doxycycline should be given as an alternative (BIII) in addition to a beta-lactam. Clinical and Laboratory Standards Institute and U. S. Food and Drug Administration (FDA) changes in the penicillin breakpoints for treatment of non-meningitis pneumococcal disease imply IV penicillin is an acceptable option for treatment of pneumococcal disease in patients with HIV (BIII).112 In patients who are allergic to penicillin, a respiratory fluoroquinolone (moxifloxacin or levofloxacin [750 mg/day]) alone should be used (AI). As noted, fluoroquinolone monotherapy should be used with caution in patients in whom TB is suspected but who are not being treated with concurrent standard four-drug TB therapy. Severe CAP Treatment Patients with severe CAP should not receive empiric monotherapy, even with a fluoroquinolone, because of the range of potential pathogens and the desirability of prompt and microbiologically active therapy (AI). In one study, the use of dual therapy (usually with a beta-lactam plus a macrolide) was associated with reduced mortality in patients with bacteremic pneumococcal pneumonia, including those admitted to the ICU.113 Patients with severe pneumonia should be treated with an IV beta-lactam plus either azithromycin (AI) or a respiratory fluoroquinolone (moxifloxacin or levofloxacin [750 mg/day]) (AI). Both have a strong recommendation. Weak observational data, in the absence of prospective randomized controlled data, suggest that beta-lactam plus macrolide may be associated with decreased mortality.77,114,115 Preferred beta-lactams are ceftriaxone, cefotaxime, or ampicillin-sulbactam. In patients who are allergic to penicillin, aztreonam plus a respiratory fluoroquinolone (moxifloxacin or levofloxacin [750 mg/day]) should be used (BIII). The majority of CAP pathogens can be treated adequately with recommended empiric regimens. The increased incidence of P. aeruginosa and S. aureus (including community-acquired MRSA) as causes of CAP are exceptions. Both of these pathogens occur in specific epidemiologic patterns with distinct clinical presentations for which empiric antibiotic coverage may be warranted. Diagnostic tests (sputum Gram stain and culture) are likely to be of high yield for these pathogens, allowing early discontinuation of empiric treatment if results are negative. In the most recent ATS/IDSA CAP guidelines, empiric therapy for P. aeruginosa or MRSA is recommended in those with severe CAP, who have had these organisms previously isolated from sputum cultures, with de-escalation if these organisms are not isolated from current cultures.67 The addition of corticosteroids for treating CAP has not been studied in people with HIV. Data from studies in people without HIV with CAP suggest that corticosteroids may decrease a composite outcome of mortality, time to clinical stability, and length of hospital stay.116 Importantly, effects of corticosteroids appear variable according to etiology and severity of pneumonia, however, as corticosteroids may increase mortality in influenza pneumonia,117 but decrease mortality in patients with COVID-19 who require higher levels of respiratory support.118 The optimal regimen including dose, duration, and formulation of corticosteroid, and the patient population with bacterial non-viral related CAP most likely to benefit from the additional use of corticosteroids remain uncertain. Selecting HIV-uninfected patients with severe CAP and increased inflammation as defined by C-reactive protein levels >150 mg/mL is one strategy for treatment of CAP that has been shown to be beneficial.119 ATS/IDSA guidelines recommend not using corticosteroids routinely in non-severe (AI) or severe CAP (BII) but endorse use in CAP with refractory shock67 Similarly, the use of corticosteroids in HIV-infected patients with severe CAP is not routinely recommended (BII) given the lack of data Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-12 specifically in HIV-infected population. If providers administer corticosteroids to HIV-infected patients with severe CAP, they must ensure that no other contraindications to steroids exist; in patients who have no contraindications and have persistent shock despite fluid resuscitation, Surviving Sepsis Guidelines120 provide a weak recommendation for administering hydrocortisone 200 mg IV daily for 5 to 7 days or tapering once vasopressors are no longer needed. Empiric Pseudomonas aeruginosa Treatment If risk factors for Pseudomonas infection are present, an antipneumococcal, antipseudomonal beta-lactam plus either ciprofloxacin or levofloxacin (750-mg dose) should be used (AI). Preferred beta-lactams are piperacillin-tazobactam, cefepime, imipenem, or meropenem. Alternative therapeutic agents that are recommended are an antipneumococcal, antipseudomonal beta-lactam plus an aminoglycoside and azithromycin (BII) or an antipneumococcal, antipseudomonal beta-lactam plus an aminoglycoside and an antipneumococcal fluoroquinolone (BII). In patients who are allergic to penicillin, aztreonam is recommended to be used in place of the beta-lactam (BII). Empiric Staphylococcus aureus Treatment A nasal swab for MRSA can help inform decision-making whether initial empiric coverage should include MRSA. In studies of patients without HIV, negative test results have a high negative predictive value for pneumonia due to MRSA. If the nasal swab is negative for MRSA and the pneumonia is not severe and no other risk factors or features suggestive of MRSA pneumonia are present, empiric coverage for MRSA may be withheld (BII).68 However, in patients who have risk factors for S. aureus infection, vancomycin or linezolid should be added to the antibiotic regimen (AII). Empiric coverage for MRSA should also be added if a rapid nasal swab is positive for MRSA, although the positive predictive value for pneumonia is only moderate, and therapy should be de-escalated if cultures are negative (BIII). Although not routinely recommended, the addition of clindamycin to vancomycin (but not to linezolid) or the use of linezolid alone, is recommended by many experts if severe necrotizing pneumonia is present to minimize bacterial toxin production (CII). Telavancin is an alternative agent that can be used for S. aureus pneumonia (BIII); it is currently FDA-approved for treatment of hospital-acquired and ventilator-associated (rather than community-acquired) pneumonia based on studies in people without HIV infection.121 While ceftaroline has activity against MRSA, and data suggest it can be effective for MRSA pneumonia, it has been FDA approved for treatment of bacterial CAP based on two studies that did not include any MRSA isolates.122 Neither telavancin or ceftaroline have been specifically studied in patients with HIV with bacterial pneumonia. Daptomycin should not be used to treat pneumonia as it is not active in the lung (AI). Pathogen-Directed Therapy When the etiology of the pneumonia has been identified based on reliable microbiological methods, antimicrobial therapy should be modified and directed at the identified pathogen (BIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-13 Switch From Intravenous to Oral Therapy A switch to oral therapy should be considered in patients with CAP on IV antibiotic therapy who have improved clinically, can swallow and tolerate oral medications, and have intact gastrointestinal function.67 A longer duration of IV and overall antibiotic therapy is often necessary in patients who have severe CAP or who have bacteremia, particularly if due to S. pneumoniae or S. aureus and complicated infection is present. Special Considerations Regarding When to Start Antiretroviral Therapy In patients with bacterial pneumonia who are not already on ART, ART should be initiated promptly (i.e., within 2 weeks of initiating therapy for the pneumonia) unless comorbidities make ART unwise (AI). Monitoring of Response to Therapy and Adverse Events (Including IRIS) The clinical response to appropriate antimicrobial therapy for CAP is similar in patients with and without HIV.43,58 A clinical response (i.e., reduction in fever and improvement in respiratory symptoms, physical findings, and laboratory studies) typically is observed within 48 to 72 hours after initiation of appropriate antimicrobial therapy. A review of patients with CAP found that advanced HIV infection and CD4 count <100 cells/mm3 were predictors for longer time to clinical stability (i.e., >7 days) and that patients who received ART tended to become clinically stable sooner and had better outcomes.103,106 The presence of bacteremia is a significant factor that impacts outcomes. Among those with pneumococcal pneumonia, longer time to clinical stability is more often seen in the setting of bacteremia. As in patients without HIV, radiographic improvement usually lags behind clinical improvement. Immune reconstitution inflammatory syndrome (IRIS) has been rarely described in association with bacterial CAP and initiation of treatment with ART in patients with HIV. This could be secondary to a number of reasons: 1) patients with recurrent pneumonia have not been included in the study population; 2) IRIS among participants with bacterial pneumonia has not been specified or 3) this complication has truly not been observed.2,123 Only case reports describe IRIS with pneumonia due to Rhodococcus equii. More commonly IRIS occurs with pneumonia due to Pneumocystis and mycobacterial infections. Managing Treatment Failure Patients who do not respond to appropriate antimicrobial therapy should undergo further evaluation to search for complications secondary to pneumonia (empyema, abscess formation, metastatic infection), other infectious process, the presence of a drug-resistant pathogen, and/or noninfectious causes of pulmonary dysfunction (pulmonary embolus, COPD). Preventing Recurrence Patients with HIV should receive pneumococcal (AI) and influenza vaccines (AI) as recommended. Antibiotic chemoprophylaxis generally is not recommended specifically to prevent recurrences of bacterial respiratory infections because of the potential for development of drug-resistant microorganisms and drug toxicity (AI). Smoking cessation reduces the risk of bacterial pneumonia (by approximately 27%),124 and patients who smoke tobacco should be encouraged to quit and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-14 provided with the appropriate tools and referrals whenever possible (AI). Likewise, patients with substance use disorders (alcohol, injection or non-injection drugs) should be referred for appropriate counseling and services (AI). However, likely the most important intervention for prevention of bacterial pneumonia (first episode or recurrence) is initiation and adherence to ART, which is beneficial even among those with high CD4 count at time of ART initiation.4 Thus prompt initiation or re-initiation of ART is recommended for all patients with HIV with bacterial pneumonia (AI). Special Considerations During Pregnancy The diagnosis of bacterial respiratory tract infections in pregnant women is the same as in those who are not pregnant, with appropriate shielding of the abdomen during radiographic procedures. Bacterial respiratory tract infections should be managed in pregnant women as in women who are not pregnant, with certain exceptions. Among macrolides, clarithromycin is not recommended because of an increased risk of birth defects seen in some animal studies. Two studies, each involving at least 100 women with first-trimester exposure to clarithromycin, did not document a clear increase in or specific pattern of birth defects, although an increased risk of spontaneous abortion was noted in one study.125,126 Azithromycin did not produce birth defects in animal studies, but experience with human use in the first trimester is limited. Azithromycin is recommended when a macrolide is indicated in pregnancy (BIII). Arthropathy has been noted in immature animals with in utero exposure to quinolones. Studies evaluating quinolone use in pregnant women did not find an increased risk of birth defects or musculoskeletal abnormalities.127,128 When indicated, quinolones can be used in pregnancy for serious respiratory infections only when a safer alternative is not available (CIII).129 Doxycycline is not recommended for use during pregnancy because of increased hepatotoxicity and staining of fetal teeth and bones. Beta-lactam antibiotics have not been associated with teratogenicity or increased toxicity in pregnancy. Clindamycin use in pregnancy has not been associated with an increased risk of birth defects or adverse outcomes.130 Aminoglycosides can be used as needed. A theoretical risk of fetal renal or eighth nerve damage exists with aminoglycoside exposure during pregnancy, but this finding has not been documented in humans, except with streptomycin (10% risk) and kanamycin (2% risk). Animal reproductive toxicity studies in rats and rabbits were negative for vancomycin, but data on first trimester exposure in humans are limited.131 A study of neonates after in utero exposure did not find evidence of renal or ototoxicity.132 Reproductive toxicity studies of televancin in animals have shown increased rates of limb malformations in rats, rabbits, and mini pigs at doses similar to human exposure; no human data are available.131 Use of telavancin should be avoided in the first trimester if alternate agents with more experience in use in pregnancy are available. Cases of exposure to telavancin in pregnancy should be reported to the Televancin Pregnancy Registry at 1-855-633-8479. Experience with linezolid in human pregnancy has been limited, but it was not teratogenic in mice, rats, and rabbits. Pneumonia during pregnancy is associated with increased rates of preterm labor and delivery. Pregnant women with pneumonia after 20 weeks’ gestation should be monitored for evidence of contractions (BII). Pneumococcal vaccine can be administered during pregnancy (AIII). A study comparing administration of PCV10, PPSV23, or control (1:1:1) among 347 women during weeks 13–34 of pregnancy found that PCV10 and PPSV23 were equally safe and immunogenic in pregnant women with HIV and conferred similar levels of seroprotection to their infants.133 No adverse consequences have been reported among newborns whose mothers were vaccinated during pregnancy. Women who did not receive vaccines during pregnancy were vaccinated post-partum; these data demonstrated higher antibody responses compared to women vaccinated ante-partum, suggesting that postpartum booster doses may be beneficial and require further study.134 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-15 Inactivated influenza vaccine is recommended for all pregnant women during influenza season (AI). Live attenuated influenza vaccine should not be used in people with HIV (AIII). Because administration of vaccines can be associated with a transient rise in plasma HIV RNA levels, vaccination of pregnant women is recommended after ART has been initiated to minimize increases in plasma HIV RNA levels that might increase the risk of perinatal transmission of HIV. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-16 Recommendations for Preventing and Treating Community-Acquired Pneumonia Preventing Streptococcus pneumoniae Infections Indications for Pneumococcal Vaccination • All people with HIV regardless of CD4 count (AI) Vaccination Recommendations • For all people with HIV without history of pneumococcal vaccination or unknown vaccine history: o Administer either 15-valent pneumococcal conjugate vaccine (PCV15) or 20-valent pneumococcal conjugate vaccine (PCV20) (AII). If PCV20 is used, their pneumococcal vaccination is complete. o If PCV15 is used, a dose of PPSV23 should be administered at least 8 weeks later (AII). No additional pneumococcal vaccine doses are recommended. • For people with HIV who previously started or completed a pneumococcal vaccination series, there is no need to restart the series. o People with HIV who received PCV13 and were 65 or older when they received a dose of PPSV23 do not require further doses of PPSV23; for those who received PPSV23 younger than age 65, additional doses of PPSV23 are recommended as indicated below (BIII).  People with HIV who have received PCV13 and PPSV23 at age <65 should receive a second dose of PPSV23 at least 5 years after the first dose. If they are age 65 or older at the time of their second dose, they do not require additional doses of PPSV23.  If they were <65 at the time of the second dose, they should receive a third and final dose at or after age 65, at least 5 years after the second PPSV23 dose. o People with HIV who have only received PPSV23 may receive a PCV (either PCV20 or PCV15) ≥1 year after their last PPSV23 dose. When PCV15 is used in those with history of PPSV23 receipt, it need not be followed by another dose of PPSV23 at any age (BIII). Footnotes Patients with CD4 counts >200 cells/mm3 should receive a dose of PPSV23 at least 8 weeks later (AI). While individuals with HIV with CD4 counts <200 cells/mm3 can also be offered PPSV23 at least 8 weeks after receiving PCV15 (CIII) (such as if there are concerns with retention in care), PPSV23 should preferably be deferred until after an individual’s CD4 count increases to >200 cells/mm3 while on ART (BIII). Clinical evidence supporting use of PPSV23 in persons with CD4 counts <200 cells/mm3 appears strongest in patients who also have HIV RNA <100,000 copies/mL; evidence also suggests benefit for those who start ART before receiving PPSV vaccination. People with HIV who have received PCV13 but have not completed their recommended pneumococcal vaccine series with PPSV23, one dose of PCV20 may be used if PPSV23 is not available. If PCV20 is used, their pneumococcal vaccinations are complete (CIII). Preventing Influenza and Bacterial Pneumonia as a Complication of Influenza Indication for Influenza Vaccination • All people with HIV infection during influenza season (AI) Vaccination • Adults age ≥65 years are recommended to receive high-dose IIV (Fluzone® High-Dose) or adjuvanted IIV (FLUAD®) over standard-dose unadjuvanted vaccine (AII). • People age ≥18 years also may use RIV (Flublok® Quadrivalent). Recommendations for Preventing and Treating Community-Acquired Pneumonia Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-17 • For people with egg allergy, use IIV or RIV appropriate for age (if the allergic reaction is more severe than hives, give the vaccine in a medical setting appropriate to manage severe allergic reaction). • For pregnant people with HIV, administer inactivated influenza or recombinant vaccine at any time during pregnancy (AI). • Influenza vaccines are quadrivalent, with formulations that change from season to season. Note: Live attenuated influenza vaccine is contraindicated in people with HIV (AIII). Treating Community-Acquired Bacterial Pneumonia Note: Empiric antimicrobial therapy should be initiated promptly for patients presenting with clinical and radiographic evidence consistent with bacterial pneumonia. The recommendations listed below are suggested empiric therapy. The regimen should be modified as needed once microbiologic and drug susceptibility results are available. Providers must also consider the risk of opportunistic lung infections such as PCP or TB, which may alter the empiric therapy as needed. Empiric Outpatient Therapy (Oral) Preferred Therapy • An oral beta-lactam + a macrolide (azithromycin or clarithromycin) (AI) o Preferred beta-lactams: high-dose amoxicillin or amoxicillin/clavulanate o Alternative beta-lactams: cefpodoxime or cefuroxime or • A respiratory fluoroquinolone (levofloxacin or moxifloxacin)a (AI), especially for patients with penicillin allergies. Alternative Therapy • A beta-lactam + doxycycline (BIII) Empiric Therapy for Hospitalized Patients with Non-Severe CAP Preferred Therapy • An IV beta-lactam + a macrolide (azithromycin or clarithromycin) (AI) o Preferred beta-lactams: ceftriaxone, cefotaxime, or ampicillin-sulbactam or • A respiratory fluoroquinolone (levofloxacin or moxifloxacin)a (AI), especially for patients with penicillin allergies. Alternative Therapy • An IV beta-lactam + doxycycline (BIII) • IV penicillin may be used for confirmed pneumococcal pneumonia (BIII) Empiric Therapy for Patients with Severe CAP Preferred Therapy • An IV beta-lactam + azithromycin (AI), or • An IV beta-lactam + a respiratory fluoroquinolone (levofloxacin or moxifloxacin)a (AI) o Preferred beta-lactams: ceftriaxone, cefotaxime, or ampicillin-sulbactam Alternative Therapy For Penicillin-Allergic Patients • Aztreonam (IV) + a respiratory fluoroquinolone (moxifloxacin or levofloxacin)a (BIII) Empiric Therapy for Patients at Risk of Pseudomonas Pneumonia Recommendations for Preventing and Treating Community-Acquired Pneumonia Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-18 Preferred Therapy • An IV antipneumococcal, antipseudomonal beta-lactam + (ciprofloxacin IV or levofloxacin IV 750 mg/day) (AI) o Preferred beta-lactams: piperacillin-tazobactam, cefepime, imipenem, or meropenem Alternative Therapy • An IV antipneumococcal, antipseudomonal beta-lactam + an IV aminoglycoside + IV azithromycin (BII), or • An IV antipneumococcal, antipseudomonal beta-lactam + an IV aminoglycoside + an antipneumococcal fluoroquinolone (moxifloxacin or levofloxacin) (BII) For Penicillin-Allergic Patients • Replace the beta-lactam with aztreonam (BII). Empiric Therapy for Patients at Risk of Methicillin-Resistant Staphylococcus aureus (MRSA) Pneumonia Preferred Therapy • A nasal swab for MRSA can help inform decision of initial coverage for MRSA (see text for discussion) • Vancomycin IV or linezolid (IV or PO) should be added to the baseline regimen (AII). • Although not routinely recommended, the addition of clindamycin to vancomycin (but not to linezolid) may be considered for severe necrotizing pneumonia to minimize bacterial toxin production (CII). Duration of Therapy • For most patients: 5–7 days. The patient should be afebrile for 48–72 hours, and should be clinically stable before discontinuation of therapy. • Longer duration of antibiotics is often required if severe CAP or bacteremia is present, and particularly if due to S. pneumoniae or complicated S. aureus infection. Switch from IV to PO Therapy • A switch should be considered for patients who have improved clinically, can swallow and tolerate oral medications, and have intact gastrointestinal function (BIII). Other Considerations • Empiric therapy with a macrolide alone is not routinely recommended because of increasing pneumococcal resistance (up to 30%) (BIII), and patients receiving a macrolide for MAC prophylaxis may have resistance due to chronic exposure (BIII). • Fluoroquinolones should be used with caution in patients in whom TB is suspected but who are not being treated with concurrent standard four-drug TB therapy (BIII). • Once the pathogen has been identified by reliable microbiologic methods, antibiotic therapy should be modified to target the pathogen (BIII). • If drug-resistant pathogens have not been identified by reliable microbiologic methods, antibiotic therapy can be de-escalated to cover routine causes of CAP (BIII). • Antibiotics chemoprophylaxis is generally not recommended because of the potential for development of drug resistance microorganisms and drug toxicities (AI). a Respiratory fluoroquinolones such as levofloxacin or moxifloxacin are also active against Mycobacterium tuberculosis. 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Mohapi L, Pinedo Y, Osiyemi O, et al. Safety and immunogenicity of V114, a 15-valent pneumococcal conjugate vaccine, in adults living with HIV. AIDS. 2022;36(3):373-382. Available at: 84. French N, Gordon SB, Mwalukomo T, et al. A trial of a 7-valent pneumococcal conjugate vaccine in HIV-infected adults. N Engl J Med. 2010;362(9):812-822. Available at: 85. Advisory Committee on Immunization Practices. Recommended adult immunization schedule: United States, October 2007–September 2008. Ann Intern Med. 2007;147(10):725-729. Available at: 86. Gebo KA, Moore RD, Keruly JC, Chaisson RE. Risk factors for pneumococcal disease in human immunodeficiency virus-infected patients. J Infect Dis. 1996;173(4):857-862. Available at: 87. Breiman RF, Keller DW, Phelan MA, et al. Evaluation of effectiveness of the 23-valent pneumococcal capsular polysaccharide vaccine for HIV-infected patients. Arch Intern Med. 2000;160(17):2633-2638. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-27 88. Dworkin MS, Hanson DL, Navin TR. Survival of patients with AIDS, after diagnosis of Pneumocystis carinii pneumonia, in the United States. J Infect Dis. 2001;183(9):1409-1412. Available at: 89. Penaranda M, Falco V, Payeras A, et al. Effectiveness of polysaccharide pneumococcal vaccine in HIV-infected patients: a case-control study. Clin Infect Dis. 2007;45(7):e82-87. Available at: 90. Rubin LG, Levin MJ, Ljungman P, et al. 2013 IDSA clinical practice guideline for vaccination of the immunocompromised host. Clin Infect Dis. 2014;58(3):309-318. Available at: 91. DiazGranados CA, Dunning AJ, Kimmel M, et al. Efficacy of high-dose versus standard-dose influenza vaccine in older adults. N Engl J Med. 2014;371(7):635-645. Available at: 92. Grohskopf LA. National Center for Immunization and Respiratory Diseases (U.S.) United States. Advisory Committee on Immunization Practices. Influenza Division. Influenza vaccines for older adults: GRADE summary. Presented at: ACIP meeting Influenza; 2022. Atlanta, GA. Available at: 93. McKittrick N, Frank I, Jacobson JM, et al. Improved immunogenicity with high-dose seasonal influenza vaccine in HIV-infected persons: a single-center, parallel, randomized trial. Ann Intern Med. 2013;158(1):19-26. Available at: 94. Anglaret X, Chene G, Attia A, et al. Early chemoprophylaxis with trimethoprim-sulphamethoxazole for HIV-1-infected adults in Abidjan, Cote d’Ivoire: a randomised trial. Cotrimo-CI Study Group. Lancet. 1999;353(9163):1463-1468. Available at: 95. Hardy WD, Feinberg J, Finkelstein DM, et al. A controlled trial of trimethoprim-sulfamethoxazole or aerosolized pentamidine for secondary prophylaxis of Pneumocystis carinii pneumonia in patients with the acquired immunodeficiency syndrome. AIDS Clinical Trials Group Protocol 021. N Engl J Med. 1992;327(26):1842-1848. Available at: 96. Angel JB, High K, Rhame F, et al. Phase III study of granulocyte-macrophage colony-stimulating factor in advanced HIV disease: effect on infections, CD4 cell counts and HIV suppression. Leukine/HIV Study Group. AIDS. 2000;14(4):387-395. Available at: 97. Keiser P, Rademacher S, Smith JW, Skiest D, Vadde V. Granulocyte colony-stimulating factor use is associated with decreased bacteremia and increased survival in neutropenic HIV-infected patients. Am J Med. 1998;104(1):48-55. Available at: 98. Crothers K, Griffith TA, McGinnis KA, et al. The impact of cigarette smoking on mortality, quality of life, and comorbid illness among HIV-positive veterans. J Gen Intern Med. 2005;20(12):1142-1145. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-28 99. Navin TR, Rimland D, Lennox JL, et al. Risk factors for community-acquired pneumonia among persons infected with human immunodeficiency virus. J Infect Dis. 2000;181(1):158-164. Available at: 100. Justice AC, Lasky E, McGinnis KA, et al. Medical disease and alcohol use among veterans with human immunodeficiency infection: a comparison of disease measurement strategies. Med Care. 2006;44(8 Suppl 2):S52-60. Available at: 101. Curran A, Falco V, Crespo M, et al. Bacterial pneumonia in HIV-infected patients: use of the pneumonia severity index and impact of current management on incidence, aetiology and outcome. HIV Med. 2008;9(8):609-615. Available at: 102. Almeida A, Almeida AR, Castelo Branco S, Vesza Z, Pereira R. CURB-65 and other markers of illness severity in community-acquired pneumonia among HIV-positive patients. Int J STD AIDS. 2016;27(11):998-1004. Available at: 103. Madeddu G, Laura Fiori M, Stella Mura M. Bacterial community-acquired pneumonia in HIV-infected patients. Curr Opin Pulm Med. 2010;16(3):201-207. Available at: 104. Chew KW, Yen IH, Li JZ, Winston LG. Predictors of pneumonia severity in HIV-infected adults admitted to an Urban public hospital. AIDS Patient Care STDS. 2011;25(5):273-277. Available at: 105. Bordon J, Kapoor R, Martinez C, et al. CD4+ cell counts and HIV-RNA levels do not predict outcomes of community-acquired pneumonia in hospitalized HIV-infected patients. Int J Infect Dis. 2011;15(12):e822-827. Available at: 106. Barakat LA, Juthani-Mehta M, Allore H, et al. Comparing clinical outcomes in HIV-infected and uninfected older men hospitalized with community-acquired pneumonia. HIV Med. 2015;16(7):421-430. Available at: 107. Buss IM, Birkhamshaw E, Innes MA, Magadoro I, Waitt PI, Rylance J. Validating a novel index (SWAT-Bp) to predict mortality risk of community-acquired pneumonia in Malawi. Malawi Med J. 2018;30(4):230-235. Available at: 108. Centers for Disease Control and Prevention. Streptococcus pneumoniae, 2019. 2019. Available at: 109. Garin N, Genne D, Carballo S, et al. beta-Lactam monotherapy vs beta-lactam-macrolide combination treatment in moderately severe community-acquired pneumonia: a randomized noninferiority trial. JAMA Intern Med. 2014;174(12):1894-1901. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-29 110. Postma DF, van Werkhoven CH, van Elden LJ, et al. Antibiotic treatment strategies for community-acquired pneumonia in adults. N Engl J Med. 2015;372(14):1312-1323. Available at: 111. Figueiredo-Mello C, Naucler P, Negra MD, Levin AS. Ceftriaxone versus ceftriaxone plus a macrolide for community-acquired pneumonia in hospitalized patients with HIV/AIDS: a randomized controlled trial. Clin Microbiol Infect. 2018;24(2):146-151. Available at: 112. Weinstein MP, Klugman KP, Jones RN. Rationale for revised penicillin susceptibility breakpoints versus Streptococcus pneumoniae: coping with antimicrobial susceptibility in an era of resistance. Clin Infect Dis. 2009;48(11):1596-1600. Available at: 113. Baddour LM, Yu VL, Klugman KP, et al. Combination antibiotic therapy lowers mortality among severely ill patients with pneumococcal bacteremia. Am J Respir Crit Care Med. 2004;170(4):440-444. Available at: 114. Sligl WI, Asadi L, Eurich DT, Tjosvold L, Marrie TJ, Majumdar SR. Macrolides and mortality in critically ill patients with community-acquired pneumonia: a systematic review and meta-analysis. Crit Care Med. 2014;42(2):420-432. Available at: 115. Vardakas KZ, Trigkidis KK, Falagas ME. Fluoroquinolones or macrolides in combination with beta-lactams in adult patients hospitalized with community acquired pneumonia: a systematic review and meta-analysis. Clin Microbiol Infect. 2017;23(4):234-241. Available at: 116. Siemieniuk RA, Meade MO, Alonso-Coello P, et al. Corticosteroid therapy for patients hospitalized with community-acquired pneumonia: a systematic review and meta-analysis. Ann Intern Med. 2015;163(7):519-528. Available at: 117. Ni YN, Chen G, Sun J, Liang BM, Liang ZA. The effect of corticosteroids on mortality of patients with influenza pneumonia: a systematic review and meta-analysis. Crit Care. 2019;23(1):99. Available at: 118. RECOVERY Collaborative Group, Horby P, Lim WS, et al. Dexamethasone in hospitalized patients with Covid-19. N Engl J Med. 2021;384(8):693-704. Available at: 119. Torres A, Sibila O, Ferrer M, et al. Effect of corticosteroids on treatment failure among hospitalized patients with severe community-acquired pneumonia and high inflammatory response: a randomized clinical trial. JAMA. 2015;313(7):677-686. Available at: 120. Evans L, Rhodes A, Alhazzani W, et al. Surviving sepsis campaign: international guidelines for management of sepsis and septic shock 2021. Crit Care Med. 2021;49(11):e1063-e1143. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-30 121. Rubinstein E, Lalani T, Corey GR, et al. Telavancin versus vancomycin for hospital-acquired pneumonia due to gram-positive pathogens. Clin Infect Dis. 2011;52(1):31-40. Available at: 122. File TM, Jr., Low DE, Eckburg PB, et al. Integrated analysis of FOCUS 1 and FOCUS 2: randomized, doubled-blinded, multicenter phase 3 trials of the efficacy and safety of ceftaroline fosamil versus ceftriaxone in patients with community-acquired pneumonia. Clin Infect Dis. 2010;51(12):1395-1405. Available at: 123. Novak RM, Richardson JT, Buchacz K, et al. Immune reconstitution inflammatory syndrome: incidence and implications for mortality. AIDS. 2012;26(6):721-730. Available at: 124. De P, Farley A, Lindson N, Aveyard P. Systematic review and meta-analysis: influence of smoking cessation on incidence of pneumonia in HIV. BMC Med. 2013;11:15. Available at: 125. Einarson A, Phillips E, Mawji F, et al. A prospective controlled multicentre study of clarithromycin in pregnancy. Am J Perinatol. 1998;15(9):523-525. Available at: 126. Drinkard CR, Shatin D, Clouse J. Postmarketing surveillance of medications and pregnancy outcomes: clarithromycin and birth malformations. Pharmacoepidemiol Drug Saf. 2000;9(7):549-556. Available at: 127. Schaefer C, Amoura-Elefant E, Vial T, et al. Pregnancy outcome after prenatal quinolone exposure. Evaluation of a case registry of the European Network of Teratology Information Services (ENTIS). Eur J Obstet Gynecol Reprod Biol. 1996;69(2):83-89. Available at: 128. Loebstein R, Addis A, Ho E, et al. Pregnancy outcome following gestational exposure to fluoroquinolones: a multicenter prospective controlled study. Antimicrob Agents Chemother. 1998;42(6):1336-1339. Available at: 129. Nahum GG, Uhl K, Kennedy DL. Antibiotic use in pregnancy and lactation: what is and is not known about teratogenic and toxic risks. Obstet Gynecol. 2006;107(5):1120-1138. Available at: 130. McCormack WM, Rosner B, Lee YH, Munoz A, Charles D, Kass EH. Effect on birth weight of erythromycin treatment of pregnant women. Obstet Gynecol. 1987;69(2):202-207. Available at: 131. Bookstaver PB, Bland CM, Griffin B, Stover KR, Eiland LS, McLaughlin M. A review of antibiotic use in pregnancy. Pharmacotherapy. 2015;35(11):1052-1062. Available at: 132. Reyes MP, Ostrea EM, Jr., Cabinian AE, Schmitt C, Rintelmann W. Vancomycin during pregnancy: does it cause hearing loss or nephrotoxicity in the infant? Am J Obstet Gynecol. 1989;161(4):977-981. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV G-31 133. Weinberg A, Muresan P, Laimon L, et al. Safety, immunogenicity, and transplacental antibody transport of conjugated and polysaccharide pneumococcal vaccines administered to pregnant women with HIV: a multicentre randomised controlled trial. Lancet HIV. 2021;8(7):e408-e419. Available at: 134. Duarte G, Muresan P, Ward S, et al. Immunogenicity of conjugated and polysaccharide pneumococcal vaccines administered during pregnancy or postpartum to women with HIV. J Infect Dis. 2022;225(6):1021-1031. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-1 Cryptococcosis Updated: July 1, 2021 Reviewed: January 10, 2024 Epidemiology Most HIV-associated cryptococcal infections are caused by Cryptococcus neoformans, but occasionally Cryptococcus gattii is the cause. C. neoformans is found worldwide, whereas C. gattii most often is found in Australia and similar subtropical regions and in the Pacific Northwest. Before the era of effective antiretroviral therapy (ART), approximately 5% to 8% of patients with HIV in high-income countries had disseminated cryptococcosis.1 In a surveillance study in the late 1990s, people with HIV who developed cryptococcosis were severely immunosuppressed and had limited access to routine HIV medical care.2 Current estimates indicate that every year, approximately 280,000 cases of cryptococcal infection in people with AIDS occur worldwide, and the disease accounts for 15% of AIDS-related deaths.3 Overall, 90% of cryptococcal cases in people with HIV4 are observed in those who have CD4 T lymphocyte (CD4) cell counts <100 cells/mm3. The incidence of the disease has declined substantially among people treated with ART.4 Clinical Manifestations In people with HIV, cryptococcosis commonly presents as a subacute meningitis or meningoencephalitis with fever, malaise, and headache slowly developing over many weeks, with a median onset of 2 weeks after infection.1 Classic meningeal symptoms and signs—such as neck stiffness and photophobia—occur in only one-quarter to one-third of patients. Some patients experience encephalopathic symptoms—such as lethargy, altered mentation, personality changes, and memory loss—that are usually a result of increased intracranial pressure (ICP). Among people presenting with cryptococcal meningitis shortly after initiating ART, the symptom onset can be more acute, likely related to unmasking immune reconstitution inflammatory syndrome (IRIS).5 Cryptococcosis usually is disseminated when diagnosed in a patient with HIV. In spite of widespread disseminated disease, patients with HIV may manifest few symptoms suggesting a disseminated infection. Any organ can be involved, and skin lesions may show different manifestations, including umbilicated skin lesions that mimic those seen with molluscum contagiosum. Isolated pulmonary infection is also possible; symptoms and signs include cough and dyspnea in association with an abnormal chest radiograph, which typically demonstrates lobar consolidation, although nodular infiltrates have been reported. Pulmonary cryptococcosis may present as acute respiratory distress syndrome and even mimic Pneumocystis pneumonia. Diagnosis Analysis of cerebrospinal fluid (CSF) generally demonstrates mildly elevated protein levels, low-to-normal glucose concentrations, and a variable presence of pleocytosis consisting mostly of lymphocytes. Some patients with HIV have very few CSF inflammatory cells. A Gram stain or an India ink preparation, if available, may demonstrate numerous yeast forms. In patients with HIV and cryptococcal meningitis, the opening pressure in the CSF may be elevated, with pressures ≥25 cm H2O occurring in 60% to 80% of patients.6,7 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-2 Cryptococcal disease can be diagnosed by culture, CSF microscopy, cryptococcal antigen (CrAg) detection, or CSF polymerase chain reaction (PCR). In patients with HIV-related cryptococcal meningitis, approximately 50% of blood cultures will be positive, and approximately 80% of CSF cultures will be positive. Visible Cryptococcus colonies on a Sabouraud dextrose agar plate generally can be detected within 7 days. Cryptococcus may be identified occasionally on a routine Gram stain preparation of CSF as poorly staining Gram-positive yeasts. India ink staining of CSF demonstrates encapsulated yeasts in 60% to 80% of cases, but many laboratories in the United States no longer perform this test. India ink is relatively insensitive early in disease when <1,000 Cryptococcus colony-forming units (CFU)/mL are present.8 CSF CrAg is usually positive in patients with cryptococcal meningoencephalitis; however, early meningitis can present with negative CSF studies and positive CrAg in blood only.9 Thus, serum CrAg testing always should be performed in an immunocompromised individual with an unknown central nervous system (CNS) disorder.9 Serum CrAg is positive in both meningeal and non-meningeal cryptococcal infections and may be present weeks to months before symptom onset.10 Three methods exist for antigen detection: latex agglutination, enzyme immunoassay (EIA), and lateral flow assay (LFA). The IMMY CrAg LFA (IMMY, Norman, Oklahoma) is the only LFA test for CrAg approved by the Food and Drug Administration (FDA). It is a useful initial screening tool to diagnose cryptococcosis in patients with HIV when applied to serum or plasma,8,11 and it also can be used with whole blood or CSF. CrAg testing of serum or plasma may be particularly useful when a lumbar puncture is delayed or refused. In a patient with HIV, when serum CrAg LFA titers are >1:160, disseminated disease becomes increasingly more likely, and when CrAg LFA titers are >1:640, disseminated and/or CNS involvement should be assumed, regardless of CSF test results.12,13 Antigen titers by the LFA are approximately fourfold higher than those with latex agglutination or EIA testing, thus a titer of 1:640 by LFA is approximately equal to a titer of 1:160 by EIA or latex agglutination. In 2016, the BioFire FilmArray Meningitis/Encephalitis Panel PCR assay (Biofire Diagnostics, Salt Lake City, UT) was approved by the FDA. This multiplex PCR tests for 14 targets, including C. neoformans and C. gattii, and performs well in infections with a moderate to high fungal burden.14-16 False negative results have been noted to occur when there is a low burden of organisms; in one study, when there were <100 CFU/mL, the sensitivity of the PCR test fell to 50%.14 In one well-described case, a woman who had two negative results with this PCR assay later had a positive result on a CrAg test done by IMMY LFA.17 Thus, a negative CSF PCR does not completely exclude cryptococcal meningitis, and CrAg testing of CSF and blood should always be performed simultaneously. The PCR assay appears to have diagnostic utility when a second episode of cryptococcal meningitis is suspected; the test has been noted to differentiate a relapse (PCR positive) from IRIS (PCR negative).14 Preventing Exposure Cryptococcus is ubiquitous in the environment. People with HIV cannot completely avoid exposure to C. neoformans or C. gattii. Limited epidemiological evidence suggests that exposure to dried bird droppings, including those from chickens and pet birds, may increase the risk of infection. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-3 Preventing Disease The incidence of cryptococcal disease is low among people with HIV in the United States. However, one report indicates that among study participants with HIV in the United States with peripheral blood CD4 counts ≤100 cells/mm3, the prevalence of cryptococcal antigenemia—a harbinger of disease—was 2.9%, and for those with CD4 counts ≤50 cells/ mm3, the prevalence was 4.3%.18 Routine surveillance testing for serum CrAg in people with newly diagnosed HIV who have no overt clinical signs of meningitis is recommended for patients whose CD4 counts are ≤100 cells/mm3 and particularly in those with CD4 counts ≤50 cells/mm3 (AII). A positive test generally should prompt CSF evaluation for CNS infection (BIII), particularly when the serum LFA titer is ≥1:160 (AII).13 Prospective, controlled trials indicate that prophylactic fluconazole or itraconazole can reduce the frequency of primary cryptococcal disease in patients with HIV19,20 who have CD4 counts <100 cells/mm3.19,21 However, in the United States, primary prophylaxis in the absence of a positive serum CrAg test is not recommended because of the relative infrequency of cryptococcal disease, lack of survival benefit associated with prophylaxis, possibility of drug–drug interactions, potential development of antifungal drug resistance, and costs (BII). Treating Disease Treatment consists of three phases: induction, consolidation, and maintenance. Induction Treatment For induction treatment of cryptococcal meningitis and other forms of extrapulmonary cryptococcosis, an amphotericin B formulation given intravenously, in combination with oral flucytosine, is recommended (AI). Historically, amphotericin B deoxycholate at a dose of 0.7 to 1.0 mg/kg daily has been the preferred formulation of the drug. However, evidence that lipid formulations of amphotericin B are effective for cryptococcosis is growing, particularly in patients who experience clinically significant kidney dysfunction during therapy or who are likely to develop acute kidney injury. A study that compared amphotericin B deoxycholate (0.7 mg/kg daily) and liposomal amphotericin B (AmBisome®) at two doses (3 mg/kg daily and 6 mg/kg daily) showed similar efficacy for all three regimens; however, less nephrotoxicity was observed among those receiving the 3 mg/kg daily liposomal amphotericin B regimen.20 Additional data from animal models and a phase 2 trial in humans, show that single-dose liposomal amphotericin B at a dose of 10 mg/kg has similar rates of CSF yeast clearance and less toxicity than 14 days of amphotericin B deoxycholate.22 The preferred regimen for primary induction therapy for patients with normal renal function is 2 weeks of an amphotericin B formulation once daily plus flucytosine 25 mg/kg four times daily (AI).23,24 Based on available clinical trial data and clinical experience, liposomal amphotericin B, at a dose of 3 to 4 mg/kg daily, is the favored formulation (AI). Amphotericin B deoxycholate at a dose of 0.7 to 1.0 mg/kg daily is equally effective and can be used if the costs of lipid formulations are prohibitive and/or interruption of induction therapy because of kidney damage is unlikely (AI). The noncomparative CLEAR study demonstrated a 58% response rate in patients with HIV who were treated with amphotericin B lipid complex at a mean dose of 4.4 mg/kg daily.25 Thus, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-4 amphotericin B lipid complex at a dose of 5 mg/kg daily can be used as an alternative amphotericin B formulation although fewer data are available to support its use (BII). When using flucytosine, therapeutic drug monitoring should be performed, if available, particularly in patients who have renal impairment. Serum peak concentrations of flucytosine, should be obtained 2 hours postdose after three to five doses have been administered. Peak serum concentrations should be between 25 mg/L and 100 mg/L.16 Renal function should be monitored closely and the flucytosine dose adjusted accordingly for patients with renal impairment. The dose of flucytosine should be reduced by 50% for every 50% decline in creatinine clearance. The addition of flucytosine to the amphotericin B regimen during acute treatment is associated with more rapid sterilization of CSF and survival benefit.23,26-28 A randomized clinical trial also showed that the combination of amphotericin B deoxycholate at a dose of 1 mg/kg daily plus flucytosine was associated with improved survival compared to the same dose of amphotericin B without adjunctive flucytosine.29 Adjunctive fluconazole 800 to 1,200 mg per day plus amphotericin B has been used in the absence of flucytosine, but adjunctive flucytosine has a survival advantage over adjunctive fluconazole and is preferred (AI).24 Amphotericin B deoxycholate alone or with fluconazole at a dose of 800 to 1,200 mg daily (BI) or lipid-formulation amphotericin B alone (BI) or with fluconazole at a dose of 800 to 1,200 mg daily (BIII) may be viable options in some circumstances, but they are less preferable alternatives than lipid-formulation amphotericin B plus flucytosine.24 Fluconazole (1,200 mg daily) plus flucytosine is also a potential alternative to amphotericin B regimens (BII). Some experts would use 800 mg fluconazole daily with flucytosine (BIII).24,30 Fluconazole alone, based on studies assessing early fungicidal activity, is inferior to amphotericin B for induction therapy31,32 and is recommended only for patients who cannot tolerate or who do not respond to standard treatment. If fluconazole alone is used for primary induction therapy, the starting daily dose should be 1,200 mg (CI).33 The duration of induction therapy historically has been 2 weeks. In a multicenter clinical trial that evaluated 10-week outcomes of treatment of cryptococcal meningitis in 721 African adults with HIV, 1 week of amphotericin B deoxycholate therapy was shown to be noninferior to 2 weeks,24 and at 1 year, follow-up of 236 patients from this treatment trial showed continued noninferiority of the 1-week regimen compared with the 2-week regimen.34 Thus, in resource-limited settings, 1 week of amphotericin B deoxycholate with flucytosine followed by high-dose fluconazole is now preferred (BIII).35 However, in high-resource settings where the less toxic liposomal or other lipid amphotericin B formulations is used and a greater capacity to provide supportive care to mitigate amphotericin B toxicities exists, 2 weeks of induction amphotericin B combination therapy is recommended (AI). Consolidation Treatment A lumbar puncture and repeat CSF culture should be performed after 2 weeks of induction therapy. At that point, clinically stable patients may be switched to consolidation therapy while awaiting CSF culture results. Successful induction therapy is defined as substantial clinical improvement and a negative CSF culture from the end-of-induction lumbar puncture. India ink and CSF CrAg frequently remain positive at Week 2 of therapy and are not indicative of failure. Monitoring serum or CSF CrAg titers is of no value in determining initial response to therapy and is not recommended (AII).36,37 If new symptoms or clinical findings occur later, a repeat lumbar puncture, with measurement of lumbar opening pressure and CSF culture, should be performed. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-5 Consolidation therapy should be initiated with fluconazole 800 mg daily (AI). The recommendation to use 800 mg rather than 400 mg fluconazole for consolidation therapy is based on several findings. Early clinical trials that used 400 mg fluconazole for consolidation noted breakthrough infection during consolidation.23 Fluconazole 400 mg per day provides concentrations in the CSF that are only fungistatic, and other studies showed that the early antifungal activity of fluconazole in CSF of patients with cryptococcal meningitis increases linearly with increasing doses of the drug.29,31 A phase 2 trial of treatment with either 400 mg or 800 mg fluconazole found that relapses were more frequent in patients receiving 400 mg fluconazole.38 In clinically stable patients, the dose of fluconazole for consolidation therapy should be 800 mg per day until CSF cultures are known to be sterile and ART is initiated, at which point the dose can be decreased to 400 mg per day (AII).39 For patients who have completed 2 weeks of induction therapy, but have not improved clinically or remain clinically unstable, continuation of amphotericin B plus flucytosine is recommended until the CSF cultures are confirmed to be negative (BIII). For patients who have improved clinically, but whose CSF remains culture positive after 2 weeks of induction therapy, the fluconazole dose should be increased to 1,200 mg per day and another lumbar puncture should be performed 2 weeks later (BIII). For all patients with CSF cultures positive at Week 2, the duration of consolidation therapy should be 8 weeks from the time the CSF cultures are negative (AI).23,26,40 An alternative approach for outpatients who are not ill enough to be hospitalized but still have positive CSF cultures after completing 2 weeks of induction therapy is to continue flucytosine for an additional 2 weeks together with fluconazole at a dose of 1,200 mg per day before starting single-drug consolidation therapy. Itraconazole can be used as an alternative therapy for consolidation (CI), but it is clearly inferior to fluconazole.40 Limited data are available for use of the newer triazoles—voriconazole, posaconazole, and isavuconazole—for either consolidation or maintenance therapy for patients with cryptococcosis. Most of the reported data have been on use of these extended-spectrum triazole antifungals for treatment of refractory cases, with success rates of approximately 50%.41-43 Currently, the role of posaconazole, voriconazole, and isavuconazole in the initial management of cryptococcosis has not been established in randomized clinical trials, and these agents are not recommended for consolidation or maintenance therapy (AIII). Echinocandins have no activity against Cryptococcus spp. and are not recommended for clinical management of cryptococcosis (AII). Maintenance Treatment Fluconazole 200 mg per day is used for maintenance treatment and continue until at least one year from initiation of antifungal therapy (AI) (see the Preventing Recurrence section below).44 Treatment of Non-CNS Cryptococcosis and Asymptomatic Antigenemia Non-CNS, extrapulmonary cryptococcosis and diffuse pulmonary disease should be treated the same as CNS disease (BIII). For those with mild to moderate symptoms and only focal pulmonary infiltrates, treatment with fluconazole 400 to 800 mg per day for 10 weeks followed by 200 mg daily for a total of 6 months combined with effective ART is recommended (BIII).26 Patients with isolated or asymptomatic cryptococcal antigenemia without meningitis and low serum CrAg titers (i.e., <1:320 using LFA) can be treated in a similar fashion as patients with mild to moderate symptoms and only focal pulmonary cryptococcosis with fluconazole 400 to 800 mg per Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-6 day (BIII). If the serum CrAg titer by LFA is ≥1:640 (or >1:160 by EIA or latex agglutination), even in the absence of meningitis, the risk for mortality and/or progression to meningitis increases with fluconazole monotherapy alone, and patients should be treated the same as patients with cryptococcal meningitis (BIII).13 All patients with asymptomatic cryptococcal antigenemia should have their CSF sampled to rule out CNS disease. If serum CrAg titers are >1:640 with the LFA test and a CSF sample is not available, CNS involvement should be assumed regardless of CSF culture results or clinical signs or symptoms, and the patient should be treated as detailed above for CNS disease (AII).12,13,45 Special Considerations with Regard to Starting ART Unlike with other opportunistic infections, ART initiation generally is deferred for 4 to 6 weeks after antifungal agents are started (AI). A randomized clinical trial conducted at three sites in Africa compared patients with cryptococcal meningitis who started ART within 1 to 2 weeks (median 8 days) after the diagnosis of meningitis with patients for whom ART was delayed for 4 to 6 weeks (median 35 days) after diagnosis.46 This clinical trial used amphotericin B deoxycholate 0.7 to 1.0 mg/kg once daily plus fluconazole 800 mg once daily during the induction phase of antifungal treatment. A significantly greater increase in 6-month mortality occurred in the early ART group than in the delayed ART group (45% versus 30%, P = 0.03). This increase was most pronounced during the first 8 to 30 days of study (P = 0.007). The difference in mortality between the early ART group and the delayed ART group was even greater among individuals with CSF white cell count <5 cells/µL (P = 0.008). The excess of deaths in the early ART group was likely attributable to paradoxical IRIS.47 Most experts aim to start ART after 4 to 6 weeks of antifungal therapy; however, individual patient factors may alter this timing. In general, ensuring that the patient’s CSF cultures are sterile before starting ART will reduce the risk of IRIS.48 If ART must be started sooner, the patient should be monitored closely for paradoxical IRIS with a low threshold to intervene (see “Monitoring of Response to Therapy and Adverse Events,” below). For non-CNS cryptococcosis, for which the risk of IRIS appears to be lower, the optimal time to begin ART and antifungal therapy is less clear. However, in patients with non-CNS cryptococcosis, it is prudent to delay initiation of ART for 2 weeks after starting antifungal therapy (BIII). All of the triazole antifungals have the potential for complex and possibly bidirectional interactions with certain antiretroviral agents. These interactions and recommendations for dosage adjustments, where feasible, are listed in the drug–drug interaction tables in the Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents with HIV. Monitoring of Response to Therapy and Adverse Events Elevation of ICP can cause clinical deterioration despite a microbiologic response; complications are more likely to occur if the CSF lumbar opening pressure is ≥25 cm H2O in the lateral decubitus position.6,23 In a large clinical trial in patients with AIDS and cryptococcal meningitis, increased ICP was associated with 93% of deaths during the first 2 weeks of antifungal therapy and 40% of deaths during weeks 3 to 10.6 In another clinical trial, patients with HIV-associated cryptococcal meningitis who received at least one therapeutic lumbar puncture within 7 days after diagnosis (median time of 3 days) had a 69% relative reduction in the risk of death through 11 days, regardless of initial opening pressure.49 Although it is uncertain which patients with high lumbar opening pressures will Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-7 experience clinical deterioration, those with symptoms and signs of increased ICP require immediate clinical intervention to reduce ICP. Control of elevated ICP is critical to reducing acute mortality. Lumbar opening pressure should be measured in all patients with cryptococcal meningitis at the time of diagnosis. However, in routine practice, CSF opening pressure frequently is not measured. Among patients in whom CSF opening pressure was not measured initially, a repeat lumbar puncture should be performed with measurement of opening pressure. For patients with ongoing headaches, a repeat lumbar puncture should be performed with urgency, and among those without headaches, a repeat lumber puncture should be considered strongly within 48 hours of the initial procedure.49 Measures to decrease ICP should be used for all patients with confusion, blurred vision, papilledema, lower extremity clonus, or other neurologic signs indicative of increased ICP. Drainage of CSF via lumbar puncture is recommended for initial management (AII). One approach is to remove a volume of CSF that at least halves the opening pressure or normalizes the pressure to <20 cm H2O.49,50 In the absence of a manometer, removal of 20 to 25 mL of CSF is recommended (AIII). Among patients with ongoing symptoms, therapeutic lumbar punctures should be repeated daily until symptoms and signs consistently improve and opening pressure normalizes to <20 cm H2O (AII). Because a survival benefit is associated with therapeutic lumbar puncture regardless of baseline CSF opening pressure, strong consideration should be given to repeating a therapeutic lumbar puncture within 72 hours of the initial procedure in those patients who are relatively asymptomatic or who had a baseline CSF opening pressure of <20 cm H2O, (BII).49 This second lumbar puncture can be especially useful if the initial opening pressure was not measured (AII). ICP can be a dynamic process that changes over time. CSF shunting through a lumbar drain or ventriculostomy should be considered for patients who cannot tolerate repeated lumbar punctures or for those in whom signs and symptoms of increased ICP persist after multiple lumbar punctures (BIII). Corticosteroids and mannitol have been shown to be ineffective in managing ICP and are not recommended (AIII). Acetazolamide should not be used as therapy for increased ICP management because it may exacerbate hyperchloremic acidosis from amphotericin B and does not result in a decrease in ICP (AI).51 A randomized study that compared a 6-week course of a tapering dose of dexamethasone with placebo among 451 Asian and African patients with cryptococcal meningitis found that dexamethasone did not improve survival through 10 weeks, was noted to decrease killing of Cryptococcus, and was associated with more adverse events.52 These data support the recommendation that corticosteroids should not be used during induction therapy for ICP control for HIV-associated cryptococcal meningitis unless they are being used for treatment of IRIS (AI). Patients treated with amphotericin B formulations should be monitored for nephrotoxicity and electrolyte disturbances. Pre-infusion administration of 1,000 mL of normal saline reduces the risk of nephrotoxicity during amphotericin B treatment. For people with severe infusion-related adverse reactions, acetaminophen (650 mg) and diphenhydramine (25–50 mg) or hydrocortisone (50–100 mg) typically are administered 30 minutes before the infusion to reduce the severity of amphotericin infusion reactions (CIII), but scant data exist to support these practices. Meperidine (25–50 mg titrated during infusion) is effective for preventing and treating amphotericin B–associated rigors (BII). Routine use of potassium chloride, 40 mEq per day and magnesium 8 mEq per day, supplementation should be considered because the risk of hypokalemia and hypomagnesemia becomes near universal after 1 week of therapy, regardless of amphotericin B formulation (AII).53 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-8 In patients receiving flucytosine, dosage should be adjusted based on changes in creatinine clearance and can be guided by flucytosine levels. Peak serum flucytosine levels should be obtained 2 hours after an oral dose; the therapeutic range is between 25 and 100 mg/L. If therapeutic drug monitoring is not possible or kidney dysfunction is not present, frequent complete blood counts with differential (i.e., at least biweekly) can be used to detect cytopenias (BII).24 Flucytosine is associated with concentration-dependent bone marrow toxicity. Patients treated with flucytosine also should be monitored for hepatotoxicity and gastrointestinal toxicities. Common side effects of higher dose fluconazole therapy can include dry skin (17% of patients) and alopecia (16% of patients).54 Increased liver transaminases or alkaline phosphatase are relatively rare with fluconazole 400 to 800 mg use, with only 1 to 2% having values >5 times the upper limit of normal.46 For people who have difficulty tolerating higher fluconazole doses, it appears safe to reduce the consolidation therapy fluconazole dose to 400 mg per day after initiation of ART (BII).39 Immune Reconstitution Inflammatory Syndrome An estimated 10 to 30% of people with HIV who have cryptococcal meningitis experience IRIS after initiation or re-initiation of effective ART.55,56 Patients with HIV who have cryptococcal IRIS are more likely to be ART naive and have less CSF inflammation on initial presentation.57 The risk of IRIS can be minimized by achieving CSF culture sterility before starting ART, using fluconazole 800 mg per day as consolidation therapy, and deferring ART initiation for 4 to 6 weeks from the start of antifungal therapy (AII).46,58 Distinguishing paradoxical IRIS from treatment failure with culture-positive relapse is difficult. In general, cryptococcal IRIS presents with worsening clinical disease despite microbiological evidence of effective antifungal therapy with sterile CSF cultures,57,59 whereas treatment failure is associated with continued positive cultures. The primary microbiological criterion for treatment failure is a CSF culture that yields Cryptococcus; the culture may take days to weeks to become positive. A negative PCR test (e.g., Biofire FilmArray Meningitis/Encephalitis Panel) has a high predictive value for predicting sterile CSF cultures and can be diagnostically useful to distinguish paradoxical IRIS with a negative CSF PCR from culture-positive relapse with a positive CSF PCR.14 The appropriate management strategy for IRIS is to continue both ART and antifungal therapy and reduce elevated ICP if present (AII). While diagnostic tests are pending, escalating antifungal therapy is appropriate, such as restarting amphotericin B therapy or increasing the fluconazole dose to 1,200 mg per day (BIII). In patients with severe symptoms of IRIS, some experts recommend a brief course of tapering doses of corticosteroids. Dosages have varied, but commonly start at 1.0 mg/kg per day of prednisone (BIII); precise data-driven management strategies have not been developed. Serum C–reactive protein (CRP) is generally elevated at the time IRIS develops;60 CRP will decrease with corticosteroid therapy if IRIS is present and can be used to monitor IRIS resolution. At hospital discharge, restarting fluconazole therapy at consolidation therapy doses to be continued for 8 weeks is recommended (BIII). The risk of IRIS appears to be much lower and the syndrome seems to be less severe with other forms of cryptococcosis—such as lymphadenitis, cutaneous abscesses, and bony lesions—than with cryptococcal meningitis.61 Management of IRIS with other forms of cryptococcosis is similar to that for IRIS associated with cryptococcal meningitis, including continuing ART, initiating or continuing antifungal therapy (AIII), and considering the use of corticosteroids if clinical symptoms are severe (CIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-9 Managing Treatment Failure Treatment failure is defined as: (1) a lack of clinical improvement and continued positive cultures after 2 weeks of appropriate therapy that has included management of increased ICP, or (2) relapse after an initial clinical response, defined as recurrence of symptoms with a positive CSF culture after ≥4 weeks of treatment. Primary fluconazole resistance in Cryptococcus isolates has been reported in the United States but is uncommon.62 Therefore, susceptibility testing is not recommended routinely for initial management of cryptococcosis. However, if treatment failure or relapse occurs, Cryptococcus isolates should undergo antifungal susceptibility testing. Robust clinical data are lacking, but strains of Cryptococcus with fluconazole minimum inhibitory concentrations (MIC) ≥16 µg/mL are considered not fully susceptible.63,64 Optimal therapy for patients with treatment failure has not been established. Patients who do not respond to induction with fluconazole monotherapy should be switched to amphotericin B, with or without flucytosine. Those initially treated with an amphotericin B formulation should remain on this agent until clinical response occurs. In this setting, liposomal amphotericin B (4–6 mg/kg daily) or amphotericin B lipid complex (5 mg/kg daily) is better tolerated and has greater efficacy than the deoxycholate formulation20,65,66 and should be considered when initial treatment with other regimens fails (AII). In the setting of treatment failure or relapse, verifying CSF culture sterility at the completion of re-induction therapy is critical (AIII). After CSF sterility is achieved, outpatient consolidation therapy should consist of fluconazole at a higher dose of 1,200 mg per day and optimization of ART. For Cryptococcus with decreased azole-susceptibility (i.e., >16 µg/mL MIC for fluconazole) some experts would recommend adjunctive weekly amphotericin B administration during consolidation therapy (BIII).64 Higher doses of fluconazole (i.e., 1,200 mg per day) in combination with flucytosine 25 mg/kg 4 times per day also may be considered (BI). The newer triazoles— posaconazole, voriconazole, and isavuconazole—have activity against Cryptococcus spp. in vitro and may have a role in salvage therapy, but they offer no specific advantages over fluconazole unless in vitro susceptibility testing indicates high-level fluconazole resistance. Most clinical failures are not due to antifungal drug resistance, but rather result from inadequate induction therapy, nonadherence, drug interactions that decrease the serum concentrations of fluconazole (e.g., with rifampin), or the development of paradoxical IRIS. Preventing Recurrence When to Start Maintenance Therapy Patients who have completed 10 weeks of induction and consolidation therapy for cryptococcal meningitis or disseminated cryptococcosis should be treated with chronic maintenance or suppressive therapy with fluconazole 200 mg per day for at least 1 year (AI). Itraconazole is inferior to fluconazole for preventing relapse of cryptococcal disease (CI).40 One study demonstrated that only 70% of patients receiving fluconazole 200 mg per day achieved therapeutic concentrations of fluconazole in plasma when the fluconazole MIC was >8 µg/mL, and only 30% when the MIC was 16 µg/mL.64 For patients in whom susceptibility studies have been performed and the fluconazole MIC is >8 µg/mL, some experts recommend that the fluconazole dose be increased to 400 mg per day (BIII). Failure to administer secondary prophylaxis for an entire year is the most common reason for subsequent relapse of cryptococcal disease.67 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-10 When to Stop Maintenance Therapy Only a few patients have been evaluated for relapse after successful antifungal therapy for cryptococcosis and discontinuation of maintenance therapy while on ART. In a European study, recurrences of cryptococcosis were not found among 39 participants on potent ART whose antifungal therapy was discontinued. In this cohort, when maintenance therapy was stopped, the median CD4 count was 297 cells/mm3, the median HIV RNA concentration was <500 copies/mL, and the median time on potent ART was 25 months.68 A prospective, randomized study of 60 patients in Thailand documented no recurrences of cryptococcosis during 48 weeks of follow-up among 22 patients whose antifungal therapy was discontinued after reaching a CD4 count >100 cells/mm3 with a sustained undetectable HIV RNA level for 3 months on potent ART.69 Given these data and inference from data on discontinuation of secondary prophylaxis for other HIV-associated opportunistic infections, it is reasonable to discontinue maintenance therapy after at least 1 year from initiation of antifungal therapy, in patients whose CD4 counts are >100 cells/mm3 with undetectable viral loads on ART (BII).70 Maintenance therapy should be reinitiated if the CD4 count decreases to <100 cells/mm3 (AIII). Special Considerations During Pregnancy The diagnosis of cryptococcal infections in individuals who are pregnant is similar to that in individuals who are not pregnant. Treatment should be initiated promptly after a diagnosis is confirmed. It should be emphasized that initiating antifungal therapy during the postpartum period is associated with an increased risk of IRIS.71 Lipid formulations of amphotericin B are preferred for the initial regimen for the treatment of cryptococcal meningoencephalitis, disseminated disease, or severe pulmonary cryptococcosis in patients who are pregnant. Extensive clinical experience with amphotericin B has not documented teratogenicity. Neonates born to women on chronic amphotericin B at delivery should be evaluated for renal dysfunction and hypokalemia. In animal studies, flucytosine is teratogenic; experience in humans is limited to case reports and small series. Therefore, flucytosine use should be considered only when the benefits outweigh the risks to the fetus and only in the third trimester (AIII). Fluconazole is teratogenic in the first trimester. Congenital malformations similar to those observed in animals exposed to the drug—including craniofacial and limb abnormalities—have been reported in infants born to mothers who received fluconazole at doses of ≥400 mg per day through or beyond the first trimester of pregnancy.72 A recent systematic review and meta-analysis of cohort or case-control studies reporting fetal outcomes after exposure to fluconazole in the first trimester of pregnancy analyzed more than 16,000 exposures and found an association with increased risk of heart defects and spontaneous abortion; exposure to a fluconazole dose ≥150 mg was associated with an increase in overall congenital malformations.73 One registry-based cohort study included in the systematic review74 and a more recent large population-based case-control study75 specifically noted an increase in conotruncal heart defects. The latter study also suggested an increase in cleft lip with cleft palate. A nationwide cohort study in Denmark also found that exposure to oral fluconazole during pregnancy was associated with an increased risk of spontaneous abortion compared with unexposed pregnancies or those with topical azole exposure only.76 A cohort study using Swedish and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-11 Norwegian registry data (n = 1,485,316 pregnancies) found no association between fluconazole use during pregnancy and risk of stillbirth or neonatal death.77 Most of the studies regarding effects of fluconazole during pregnancy have involved low doses of the drug and short-term exposure. On the basis of reported birth defects, the FDA classified fluconazole as pregnancy category D for any use other than a single dose of fluconazole 150 mg to treat vaginal candidiasis. Use of fluconazole in the first trimester should be considered only if the benefits clearly outweigh the risks. For pregnant women, amphotericin B should be continued throughout the first trimester. After induction therapy, weekly amphotericin B has been used for consolidation therapy for women who are pregnant throughout the first trimester.71 After the first trimester, switching to oral fluconazole 200 mg per day may be considered if appropriate clinically. In a case series of 12 pregnant Ugandan women with cryptococcal meningitis who received amphotericin B deoxycholate 0.7 to 1 mg/kg induction therapy, maternal mortality was 25%.71 Stillbirths and miscarriages were common during the initial maternal hospitalization with only 33% (4 live births out of 12 pregnancies) fetal survival.71 Consolidation therapy comprised weekly amphotericin during the first trimester and fluconazole thereafter. With life-threatening cryptococcal disease, fetal demise is common even without fluconazole exposure.71 Although case reports of birth defects in infants exposed to itraconazole exist, prospective cohort studies of >300 women with first-trimester exposure did not show an increased risk of fetal malformation.78,79 However, in general, azole antifungals should be avoided during the first trimester of pregnancy (BIII). Voriconazole (at doses lower than recommended human doses), posaconazole, and isavuconazole are teratogenic and embryotoxic in animals; no adequately controlled studies have assessed their teratogenicity and embryotoxicity in humans. Voriconazole, posaconazole, and isavuconazole are not recommended for use during pregnancy, especially in the first trimester (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-12 Recommendations for Treating Cryptococcosis Treating Cryptococcal Meningitis Treatment consists of three phases: induction, consolidation, and maintenance therapy. Induction Therapy (Duration of Therapy: 2 Weeks, Followed by Consolidation Therapy) Preferred Regimens • Liposomal amphotericin B 3–4 mg/kg IV once daily plus flucytosine 25 mg/kg PO four times a day (AI), or • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV once daily plus flucytosine 25 mg/kg PO four times a day (AI)—if cost is an issue and the risk of renal dysfunction is low. Note: Flucytosine dose should be adjusted in renal impairment (see Table 6). Alternative Regimens • Amphotericin B lipid complex 5 mg/kg IV once daily plus flucytosine 25 mg/kg PO four times a day (BII); or • Liposomal amphotericin B 3–4 mg/kg IV once daily plus fluconazole 800–1,200 mg PO or IV once daily (BIII); or • Fluconazole 1,200 mg PO or IV once daily plus flucytosine 25 mg/kg PO four times a day (BII); or • Fluconazole 800 mg PO or IV once daily plus flucytosine 25 mg/kg PO four times a day (BIII); or • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV once daily plus fluconazole 800–1,200 mg PO or IV once daily (BI); or • Liposomal amphotericin B 3–4 mg/kg IV once daily alone (BI); or • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV once daily alone (BI); or • Liposomal amphotericin B 3–4 mg/kg IV once daily plus flucytosine 25 mg/kg PO four times a day for 1 week followed by fluconazole 1,200 mg PO once daily (BIII); or • Fluconazole 1,200 mg PO or IV once daily alone (CI) If not improved clinically or remain clinically unstable, continue induction therapy until the CSF culture is confirmed to be negative (BIII). Consolidation Therapy (Duration of Therapy: ≥8 Weeks, Followed by Maintenance Therapy) Preferred Regimen • Fluconazole 800 mg PO once daily (AI) • For clinically stable patients with negative CSF cultures, dose can be reduced to 400 mg PO once daily (AII) • If CSF remains positive (but clinically stable) after 2 weeks of induction therapy, increase fluconazole dose to 1,200mg and perform LP 2 weeks later (BIII); duration of consolidation therapy should be 8 weeks from the time of negative CSF culture (AI). Maintenance Therapy Preferred Regimen • Fluconazole 200 mg PO once daily for ≥1 year from initiation of antifungal therapy (AI)—see below for recommendation on when to stop maintenance therapy Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-13 Stopping Maintenance Therapy If the Following Criteria Are Fulfilled (BII) • At least 1 year from initiation of antifungal therapy, and • Patient remains asymptomatic from cryptococcal infection, and • CD4 count ≥100 cells/mm3 and suppressed HIV RNA in response to effective ART Restarting Maintenance Therapy • If CD4 count declines to ≤100 cells/mm3 (AIII) Treating Non-CNS Extrapulmonary, Diffuse Pulmonary Disease, or Asymptomatic Patients with Isolated Cryptococcal Antigenemia (Serum LFA Titer ≥1:640) • Same treatment as for CNS disease (BIII) Treating Non-CNS Focal Pulmonary Disease or Asymptomatic Patients with Isolated Cryptococcal Antigenemia (Serum LFA Titer ≤1:320) • Fluconazole 400 to 800 mg PO daily for 10 weeks followed by fluconazole 200 mg daily for a total of 6 months (BIII) Other Considerations • Addition of flucytosine to an amphotericin B-based regimen has been associated with more rapid sterilization of CSF, decreased risk for subsequent relapse, and improved survival. • When flucytosine is used, serum concentrations (if TDM available) should be monitored 2 hours postdose, after 3–5 doses have been administered, and drug concentration should be between 25 and 100 mg/L. Alternatively, if flucytosine levels cannot be measured, at least twice weekly complete blood counts may be used to monitor for cytopenias. • CSF opening pressure should always be measured when an LP is performed. Repeated therapeutic LPs are essential to manage symptomatic increased ICP and have a survival benefit (AII). • Typical duration of induction therapy is 2 weeks. In the setting of severe amphotericin B–induced toxicity, at least 1 week of amphotericin B deoxycholate was noninferior to 2 weeks of amphotericin B deoxycholate (BIII).24 • Corticosteroids should not be used routinely during induction therapy unless used for management of IRIS (AI). • Corticosteroids and mannitol are ineffective in reducing ICP and are not recommended (AIII). • All the triazole antifungals have the potential to interact with certain antiretroviral agents and other anti-infective agents. These interactions are complex and can be bidirectional. Table 4 lists these interactions and recommends dosage adjustments where feasible. Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte cell; CNS = central nervous system; CSF = cerebrospinal fluid; ICP = intracranial pressure; IRIS = immune reconstitution inflammatory syndrome; IV = intravenous; LFA = lateral flow assay; LP = lumbar puncture; PO = orally; TDM = therapeutic drug monitoring Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-14 References 1. Aberg J, WG. P. Cryptococcosis. In: Secondary Aberg J, WG. P, ed^eds. Subsidiary Aberg J, WG. P, trans. Secondary Cryptococcosis. Vol. ed. New York, NY: Churcill Livingstone; 2002:498-510. 2. Mirza SA, Phelan M, Rimland D, et al. The changing epidemiology of cryptococcosis: an update from population-based active surveillance in 2 large metropolitan areas, 1992-2000. Clin Infect Dis. 2003;36(6):789-794. Available at: &list_uids=12627365 3. Rajasingham R, Smith RM, Park BJ, et al. Global burden of disease of HIV-associated cryptococcal meningitis: an updated analysis. Lancet Infect Dis. 2017;17(8):873-881. Available at: 4. Pyrgos V, Seitz AE, Steiner CA, Prevots DR, Williamson PR. Epidemiology of Cryptococcal Meningitis in the US: 1997-2009. PLoS One. 2013;8(2):e56269. Available at: 5. Rhein J, Hullsiek KH, Evans EE, et al. Detrimental outcomes of unmasking cryptococcal meningitis with recent ART initiation. Open Forum Infect Dis. 2018;5(8):ofy122. Available at: 6. Graybill JR, Sobel J, Saag M, et al. Diagnosis and management of increased intracranial pressure in patients with AIDS and cryptococcal meningitis. The NIAID Mycoses Study Group and AIDS Cooperative Treatment Groups. Clin Infect Dis. 2000;30(1):47-54. Available at: 7. Bicanic T, Brouwer AE, Meintjes G, et al. Relationship of cerebrospinal fluid pressure, fungal burden and outcome in patients with cryptococcal meningitis undergoing serial lumbar punctures. 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Dromer F, Mathoulin-Pelissier S, Launay O, Lortholary O, French Cryptococcosis Study G. Determinants of disease presentation and outcome during cryptococcosis: the CryptoA/D study. PLoS Med. 2007;4(2):e21. Available at: 28. Dromer F, Bernede-Bauduin C, Guillemot D, Lortholary O, French Cryptococcosis Study G. Major role for amphotericin B-flucytosine combination in severe cryptococcosis. PLoS One. 2008;3(8):e2870. Available at: 29. Day JN, Chau TT, Wolbers M, et al. Combination antifungal therapy for cryptococcal meningitis. N Engl J Med. 2013;368(14):1291-1302. Available at: 30. Larsen RA, Bozzette SA, Jones BE, et al. Fluconazole combined with flucytosine for treatment of cryptococcal meningitis in patients with AIDS. Clin Infect Dis. 1994;19(4):741-745. Available at: 31. Bicanic T, Meintjes G, Wood R, et al. Fungal burden, early fungicidal activity, and outcome in cryptococcal meningitis in antiretroviral-naive or antiretroviral-experienced patients treated with amphotericin B or fluconazole. Clin Infect Dis. 2007;45(1):76-80. Available at: &list_uids=17554704. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-17 32. Longley N, Muzoora C, Taseera K, et al. Dose response effect of high-dose fluconazole for HIV-associated cryptococcal meningitis in southwestern Uganda. Clin Infect Dis. 2008;47(12):1556-1561. Available at: &list_uids=18990067. 33. Nussbaum JC, Jackson A, Namarika D, et al. Combination flucytosine and high-dose fluconazole compared with fluconazole monotherapy for the treatment of cryptococcal meningitis: a randomized trial in Malawi. Clin Infect Dis. 2010;50(3):338-344. Available at: 34. Kanyama C, Molloy SF, Chan AK, et al. One-year Mortality Outcomes From the Advancing Cryptococcal Meningitis Treatment for Africa Trial of Cryptococcal Meningitis Treatment in Malawi. Clin Infect Dis. 2020;70(3):521-524. Available at: 35. World Health Organization. Guidelines for the diagnosis, prevention and management of cryptococcal disease in HIV-infected adults, adolescents and children. 2018. Available at: 36. Kabanda T, Siedner MJ, Klausner JD, Muzoora C, Boulware DR. Point-of-care diagnosis and prognostication of cryptococcal meningitis with the cryptococcal antigen lateral flow assay on cerebrospinal fluid. Clin Infect Dis. 2014;58(1):113-116. Available at: 37. Aberg JA, Watson J, Segal M, Chang LW. Clinical utility of monitoring serum cryptococcal antigen (sCRAG) titers in patients with AIDS-related cryptococcal disease. HIV Clin Trials. 2000;1(1):1-6. Available at: 38. Pappas PG, Chetchotisakd P, Larsen RA, et al. A phase II randomized trial of amphotericin B alone or combined with fluconazole in the treatment of HIV-associated cryptococcal meningitis. Clin Infect Dis. 2009;48(12):1775-1783. Available at: 39. Rolfes MA, Rhein J, Schutz C, et al. Cerebrospinal fluid culture positivity and clinical outcomes after amphotericin-based induction therapy for cryptococcal meningitis. Open Forum Infect Dis. 2015;2(4):ofv157. Available at: 40. Saag MS, Cloud GA, Graybill JR, et al. A comparison of itraconazole versus fluconazole as maintenance therapy for AIDS-associated cryptococcal meningitis. National Institute of Allergy and Infectious Diseases Mycoses Study Group. Clin Infect Dis. 1999;28(2):291-296. Available at: &list_uids=10064246. 41. Perfect JR, Marr KA, Walsh TJ, et al. Voriconazole treatment for less-common, emerging, or refractory fungal infections. Clin Infect Dis. 2003;36(9):1122-1131. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-18 42. Pitisuttithum P, Negroni R, Graybill JR, et al. Activity of posaconazole in the treatment of central nervous system fungal infections. J Antimicrob Chemother. 2005;56(4):745-755. Available at: 43. Thompson GR, 3rd, Rendon A, Ribeiro Dos Santos R, et al. Isavuconazole Treatment of Cryptococcosis and Dimorphic Mycoses. Clin Infect Dis. 2016;63(3):356-362. Available at: 44. Powderly WG, Saag MS, Cloud GA, et al. A controlled trial of fluconazole or amphotericin B to prevent relapse of cryptococcal meningitis in patients with the acquired immunodeficiency syndrome. The NIAID AIDS Clinical Trials Group and Mycoses Study Group. N Engl J Med. 1992;326(12):793-798. Available at: &list_uids=1538722. 45. Faini D, Kalinjuma AV, Katende A, et al. Laboratory-Reflex Cryptococcal Antigen Screening Is Associated With a Survival Benefit in Tanzania. J Acquir Immune Defic Syndr. 2019;80(2):205-213. Available at: 46. Boulware DR, Meya DB, Muzoora C, et al. Timing of antiretroviral therapy after diagnosis of cryptococcal meningitis. N Engl J Med. 2014;370(26):2487-2498. Available at: 47. Scriven JE, Rhein J, Hullsiek KH, et al. Early ART after cryptococcal meningitis is associated with cerebrospinal fluid pleocytosis and macrophage activation in a multisite randomized trial. J Infect Dis. 2015;212(5):769-778. Available at: 48. Chang CC, Dorasamy AA, Gosnell BI, et al. Clinical and mycological predictors of cryptococcosis-associated Immune reconstitution inflammatory syndrome (C-IRIS). AIDS. 2013. Available at: 49. Rolfes MA, Hullsiek KH, Rhein J, et al. The effect of therapeutic lumbar punctures on acute mortality from cryptococcal meningitis. Clin Infect Dis. 2014;59(11):1607-1614. Available at: 50. Fessler RD, Sobel J, Guyot L, et al. Management of elevated intracranial pressure in patients with Cryptococcal meningitis. J Acquir Immune Defic Syndr Hum Retrovirol. 1998;17(2):137-142. Available at: 51. Newton PN, Thai le H, Tip NQ, et al. A randomized, double-blind, placebo-controlled trial of acetazolamide for the treatment of elevated intracranial pressure in cryptococcal meningitis. Clin Infect Dis. 2002;35(6):769-772. Available at: 52. Beardsley J, Wolbers M, Kibengo FM, et al. Adjunctive Dexamethasone in HIV-Associated Cryptococcal Meningitis. N Engl J Med. 2016;374(6):542-554. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-19 53. Bahr NC, Rolfes MA, Musubire A, et al. Standardized electrolyte supplementation and fluid management improves survival during amphotericin therapy for cryptococcal meningitis in resource-limited settings. Open Forum Infect Dis. 2014;1(2):ofu070. Available at: 54. Davis MR, Nguyen MH, Donnelley MA, Thompson 3rd GR. Tolerability of long-term fluconazole therapy. J Antimicrob Chemother. 2019;74(3):768-771. Available at: 55. Shelburne SA, 3rd, Darcourt J, White AC, Jr., et al. The role of immune reconstitution inflammatory syndrome in AIDS-related Cryptococcus neoformans disease in the era of highly active antiretroviral therapy. Clin Infect Dis. 2005;40(7):1049-1052. Available at: &list_uids=15825000. 56. Muller M, Wandel S, Colebunders R, et al. Immune reconstitution inflammatory syndrome in patients starting antiretroviral therapy for HIV infection: a systematic review and meta-analysis. Lancet Infect Dis. 2010;10(4):251-261. Available at: 57. Boulware DR, Bonham SC, Meya DB, et al. Paucity of initial cerebrospinal fluid inflammation in cryptococcal meningitis is associated with subsequent immune reconstitution inflammatory syndrome. J Infect Dis. 2010;202(6):962-970. Available at: 58. Chang CC, Dorasamy AA, Gosnell BI, et al. Clinical and mycological predictors of cryptococcosis-associated immune reconstitution inflammatory syndrome. AIDS. 2013;27(13):2089-2099. Available at: 59. Haddow LJ, Colebunders R, Meintjes G, et al. Cryptococcal immune reconstitution inflammatory syndrome in HIV-1-infected individuals: proposed clinical case definitions. Lancet Infect Dis. 2010;10(11):791-802. Available at: 60. Boulware DR, Meya DB, Bergemann TL, et al. Clinical features and serum biomarkers in HIV immune reconstitution inflammatory syndrome after cryptococcal meningitis: a prospective cohort study. PLoS Med. 2010;7(12):e1000384. Available at: 61. Kuttiatt V, Sreenivasa P, Garg I, Shet A. Cryptococcal lymphadenitis and immune reconstitution inflammatory syndrome: current considerations. Scand J Infect Dis. 2011;43(8):664-668. Available at: 62. Brandt ME, Pfaller MA, Hajjeh RA, et al. Trends in antifungal drug susceptibility of Cryptococcus neoformans isolates in the United States: 1992 to 1994 and 1996 to 1998. Antimicrob Agents Chemother. 2001;45(11):3065-3069. Available at: 63. Witt MD, Lewis RJ, Larsen RA, et al. Identification of patients with acute AIDS-associated cryptococcal meningitis who can be effectively treated with fluconazole: the role of Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-20 antifungal susceptibility testing. Clin Infect Dis. 1996;22(2):322-328. Available at: 64. Chesdachai S, Rajasingham R, Nicol MR, et al. Minimum Inhibitory Concentration Distribution of Fluconazole against Cryptococcus Species and the Fluconazole Exposure Prediction Model. Open Forum Infect Dis. 2019;6(10). Available at: 65. Leenders AC, Reiss P, Portegies P, et al. Liposomal amphotericin B (AmBisome) compared with amphotericin B both followed by oral fluconazole in the treatment of AIDS-associated cryptococcal meningitis. AIDS. 1997;11(12):1463-1471. Available at: 66. Chen SC, Australasian Society for Infectious Diseases Mycoses Iterest G. Cryptococcosis in Australasia and the treatment of cryptococcal and other fungal infections with liposomal amphotericin B. J Antimicrob Chemother. 2002;49 Suppl 1(Suppl 1):57-61. Available at: 67. Jarvis JN, Meintjes G, Williams Z, Rebe K, Harrison TS. Symptomatic relapse of HIV-associated cryptococcal meningitis in South Africa: the role of inadequate secondary prophylaxis. S Afr Med J. 2010;100(6):378-382. Available at: 68. Kirk O, Reiss P, Uberti-Foppa C, et al. Safe interruption of maintenance therapy against previous infection with four common HIV-associated opportunistic pathogens during potent antiretroviral therapy. Ann Intern Med. 2002;137(4):239-250. Available at: 69. Vibhagool A, Sungkanuparph S, Mootsikapun P, et al. Discontinuation of secondary prophylaxis for cryptococcal meningitis in human immunodeficiency virus-infected patients treated with highly active antiretroviral therapy: a prospective, multicenter, randomized study. Clin Infect Dis. 2003;36(10):1329-1331. Available at: 70. Mussini C, Pezzotti P, Miro JM, et al. Discontinuation of maintenance therapy for cryptococcal meningitis in patients with AIDS treated with highly active antiretroviral therapy: an international observational study. Clin Infect Dis. 2004;38(4):565-571. Available at: 71. Pastick KA, Nalintya E, Tugume L, et al. Cryptococcosis in pregnancy and the postpartum period: Case series and systematic review with recommendations for management. Med Mycol. 2020;58(3):282-292. Available at: 72. Pursley TJ, Blomquist IK, Abraham J, Andersen HF, Bartley JA. Fluconazole-induced congenital anomalies in three infants. Clin Infect Dis. 1996;22(2):336-340. Available at: 73. Zhang Z, Zhang X, Zhou YY, Jiang CM, Jiang HY. The safety of oral fluconazole during the first trimester of pregnancy: a systematic review and meta-analysis. BJOG. 2019;126(13):1546-1552. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV H-21 74. Molgaard-Nielsen D, Pasternak B, Hviid A. Use of oral fluconazole during pregnancy and the risk of birth defects. N Engl J Med. 2013;369(9):830-839. Available at: 75. Howley MM, Carter TC, Browne ML, Romitti PA, Cunniff CM, Druschel CM. Fluconazole use and birth defects in the National Birth Defects Prevention Study. Am J Obstet Gynecol. 2016;214(5):657 e651-659. Available at: 76. Mølgaard-Nielsen D, Svanstrom H, Melbye M, Hviid A, Pasternak B. Association between use of oral fluconazole during pregnancy and risk of spontaneous abortion and stillbirth. JAMA. 2016;315(1):58-67. Available at: 77. Pasternak B, Wintzell V, Furu K, Engeland A, Neovius M, Stephansson O. Oral Fluconazole in Pregnancy and Risk of Stillbirth and Neonatal Death. JAMA. 2018;319(22):2333-2335. Available at: 78. De Santis M, Di Gianantonio E, Cesari E, Ambrosini G, Straface G, Clementi M. First-trimester itraconazole exposure and pregnancy outcome: a prospective cohort study of women contacting teratology information services in Italy. Drug Saf. 2009;32(3):239-244. Available at: 79. Bar-Oz B, Moretti ME, Bishai R, et al. Pregnancy outcome after in utero exposure to itraconazole: a prospective cohort study. Am J Obstet Gynecol. 2000;183(3):617-620. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-1 Cryptosporidiosis Updated: January 18, 2023 Reviewed: January 10, 2024 Epidemiology Cryptosporidiosis is caused by various species of the protozoan parasite Cryptosporidium, which infects the small bowel mucosa, and, if symptomatic, the infection typically causes diarrhea. Cryptosporidium can also infect other gastrointestinal and extraintestinal sites, especially in individuals whose immune systems are suppressed. Advanced immunosuppression—typically CD4 T lymphocyte (CD4) cell counts <100 cells/mm3—is associated with the greatest risk for prolonged, severe, or extraintestinal cryptosporidiosis.1 The three species that most commonly infect humans are C. hominis, C. parvum, and C. meleagridis. Infections are usually caused by one species, but a mixed infection is possible.2,3 Cryptosporidiosis remains a common cause of chronic diarrhea in people with HIV and AIDS in low- and middle-income countries.4 In high-income countries with low rates of environmental contamination and widespread availability of potent antiretroviral therapy (ART), the incidence of cryptosporidiosis in people with HIV has decreased. In the United States, the incidence of cryptosporidiosis in people with HIV is now <1 case per 1,000 person-years.5 Infection occurs through ingestion of Cryptosporidium oocysts. Viable oocysts in feces can be transmitted directly through contact with humans or animals infected with Cryptosporidium, particularly those with diarrhea. Cryptosporidium oocysts can contaminate public water supplies and recreational water sources—such as swimming pools and lakes—and may persist despite standard chlorination. Person-to-person transmission of Cryptosporidium is common, especially among sexually active men who have sex with men. Clinical Manifestations Patients with cryptosporidiosis most commonly present with acute or subacute onset of watery diarrhea, which may be accompanied by nausea, vomiting, and lower abdominal cramping. Disease severity can range from asymptomatic to profuse, watery, voluminous diarrhea.6 More severe symptoms tend to occur in immunosuppressed people, whereas transient diarrhea alone is typical in people with competent immune systems. Fever is present in approximately one-third of patients, and malabsorption is common. The epithelium of the biliary tract and the pancreatic duct can be infected with Cryptosporidium, leading to sclerosing cholangitis and to pancreatitis secondary to papillary stenosis, particularly among people with prolonged disease and low CD4 counts.7 Pulmonary Cryptosporidium infections also have been reported and may be under-recognized.8,9 Diagnosis Diagnosis of cryptosporidiosis was traditionally made by microscopic identification of the oocysts in stool with acid-fast staining or direct immunofluorescence, which offers higher sensitivity.10 Concentration methods (e.g., formalin-ethyl acetate) may facilitate diagnosis of cryptosporidiosis. However, these methods are insensitive, and other diagnostic methods are being increasingly used. Antigen detection by enzyme-linked immunosorbent assay or immunochromatographic tests also is Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-2 useful; depending on the specific test, sensitivities reportedly range from 66% to 100%. However, some immunochromatographic tests produce frequent false-positive results.11 Polymerase chain reaction and multiplex molecular methods are increasingly used for diagnosis and can identify a greater number of cases than microscopic methods.10,12 Cryptosporidial enteritis also can be diagnosed from small sections of tissue from intestinal biopsy. A single stool specimen is usually adequate to diagnose cryptosporidiosis in individuals with profuse diarrheal illness, whereas repeat stool sampling is recommended for those with milder disease. Preventing Exposure People with HIV should be educated and counseled about how Cryptosporidium can be transmitted (BIII). Modes of transmission include direct contact with animals and people, including diapered children, infected with Cryptosporidium; swallowing contaminated water during recreational activities; drinking contaminated water; and eating contaminated food. Scrupulous handwashing can reduce the risk of diarrhea, including diarrhea caused by Cryptosporidium, in individuals with HIV.13 People with HIV should be advised to wash their hands after potential contact with human feces (including after diapering small children). Handwashing also should be recommended in association with the following activities: after handling pets or other animals, after gardening or any other contact with soil, before preparing food or eating, and before and after sex (BIII). Individuals with HIV should avoid unprotected sex, especially practices that could lead to direct (e.g., oral-anal sex) or indirect (e.g., penile-anal sex) contact with feces. They should be advised to use prophylactic barrier methods—such as condoms and dental dams—during sex to reduce such exposures (BIII). People with HIV—particularly those with CD4 counts <200 cells/mm3—should avoid direct contact with diarrhea or stool from pets (BIII). They should wear gloves when handling feces or cleaning areas that might have been contaminated by feces from pets (BIII). People with HIV should also limit or avoid direct exposure to calves and lambs (BII). Paying attention to hygiene and avoiding direct contact with stool are important when visiting farms or petting zoos or other premises where animals are housed or exhibited. People with HIV should not drink water directly from lakes or rivers (AIII). Waterborne infection also can result from swallowing water during recreational activities. Individuals with HIV should be cautioned that lakes, rivers, saltwater beaches, some swimming pools, recreational water parks, and ornamental water fountains may be contaminated with human or animal waste that contains Cryptosporidium. Cryptosporidium oocysts are extremely chlorine resistant and thus may persist even in chlorinated recreational water.14,15 They should avoid swimming in water that is likely contaminated and should avoid swallowing water while swimming or playing in recreational water (BIII). Outbreaks of cryptosporidiosis have been linked to drinking water from municipal water supplies. During outbreaks or in other situations in which a community boil water advisory is issued, boiling water for at least 1 minute will eliminate the risk for cryptosporidiosis (AIII). Using submicron personal-use water filters (home or office types) or bottled water also may reduce the risk of infection from water from a municipal source or a well (BII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-3 For people with low CD4 counts, the magnitude of the risk of acquiring cryptosporidiosis from drinking water in a non-outbreak setting is uncertain but is likely small. Available data are inadequate to recommend that all people with HIV boil water or avoid drinking tap water in non-outbreak settings. However, people with HIV may consider drinking only filtered water (CIII), despite the complexities involved in selecting appropriate water filters, the lack of enforceable standards for removal of Cryptosporidium oocysts, the costs of the products, and the difficulty of using the products consistently. Note that ice made from contaminated tap water also can be a source of infection. People with HIV with low CD4 counts should be cautious about eating raw oysters because cryptosporidial oocysts can survive in oysters for >2 months and have been found in oysters harvested from certain commercial oyster beds (CIII). In the hospital setting, standard precautions for use of gloves and for handwashing after removal of gloves should be sufficient to prevent transmission of cryptosporidiosis from an infected patient to a susceptible individual with HIV (BIII). Because of the potential for fomite transmission, some specialists recommend that people with HIV, especially individuals who are severely immunocompromised, not share a room with a patient with cryptosporidiosis (CIII). People with HIV who travel to low- and middle-income countries should be warned to avoid drinking tap water or using tap water to brush their teeth (BIII). They should also avoid using ice that is not made from bottled water and consuming raw fruits or vegetables that may have been washed in tap water (BIII). People with HIV also should avoid other sources of Cryptosporidium oocysts as much as possible (BIII). This includes avoiding directly working with people with diarrhea; with farm animals, such as cattle and sheep; and with domestic pets that are very young or have diarrhea. If exposure is unavoidable, gloves should be worn and good hand hygiene observed. Preventing Disease Recommendations for Preventing Cryptosporidiosis Preventing Chronic Cryptosporidiosis • Because chronic cryptosporidiosis occurs primarily in people with advanced immunodeficiency, initiation of ART before the patient becomes severely immunosuppressed should prevent the disease (AII). Key: ART = antiretroviral therapy Because chronic cryptosporidiosis occurs primarily in people with HIV with advanced immunodeficiency, initiation of ART before they become severely immunosuppressed should prevent the disease (AII). Rifabutin and possibly clarithromycin taken for Mycobacterium avium complex prophylaxis have been found to protect against cryptosporidiosis.16,17 Rifaximin, which is used for prevention of traveler’s diarrhea, also has been used to treat cryptosporidial diarrhea. However, it is unclear whether rifaximin can protect against cryptosporidiosis.18 Data are insufficient, however, to warrant a recommendation to use rifaximin, rifabutin, or clarithromycin as chemoprophylaxis for cryptosporidiosis. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-4 Treating Disease Recommendations for Treating Cryptosporidiosis Managing Cryptosporidiosis • Preferred Management Strategies o Aggressive oral and/or IV rehydration and replacement of electrolyte loss (AIII), and o Symptomatic treatment of diarrhea with antimotility agents (AIII); tincture of opium may be more effective than loperamide (CIII). o People with HIV not taking ART should initiate ART to achieve immune restoration to CD4 count >100 cells/mm3 (AII). • General Considerations o Nitazoxanide 500 mg to 1,000 mg PO twice daily with food for at least 14 days (CIII) plus optimized ART, symptomatic treatment, and rehydration and electrolyte replacement, or o Paromomycin 500 mg PO four times a day for at least 14 days to 21 days (CIII) plus optimized ART, symptomatic treatment, and rehydration and electrolyte replacement Pregnancy Considerations • Rehydration and initiation of ART are the mainstays of initial treatment of cryptosporidiosis during pregnancy, as they are in nonpregnant people (AII). • Opiate exposure in late pregnancy has been associated with neonatal respiratory depression, and chronic exposure may result in neonatal withdrawal; therefore, tincture of opium is not recommended in late pregnancy (AIII). • Loperamide is the preferred antimotility agent in late pregnancy (CIII). Loperamide should be avoided in the first trimester unless benefits are felt to outweigh potential risks (CIII). • Nitazoxanide (CIII) and paromomycin (CIII) can be used in pregnancy after the first trimester. Other Considerations • Because diarrhea can cause lactase deficiency, people with cryptosporidiosis should avoid milk products (CIII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte cell; IV = intravenous; PO = orally In the setting of severe immune suppression, ART with immune restoration to a CD4 count >100 cells/mm3 usually leads to resolution of clinical cryptosporidiosis19-22 and is the mainstay of treatment. People with HIV not already taking antiretrovirals who develop cryptosporidiosis should be started on ART as part of the initial management of cryptosporidiosis (AII). Management should also include symptomatic treatment of diarrhea with antimotility agents (AIII). Tincture of opium may be more effective than loperamide (CIII). Octreotide, a synthetic octapeptide analog of naturally occurring somatostatin that is approved to treat secreting tumor–induced diarrhea, is no more effective than other oral antidiarrheal agents and is usually not recommended (CII).23 Because diarrhea can cause lactase deficiency, people with HIV and cryptosporidiosis should avoid milk products (CIII). Rehydration and repletion of electrolyte losses by either oral or intravenous route are important. Stool volume in patients with HIV and AIDS with severe diarrhea can exceed 10 L/day; managing the diarrhea often requires intensive support. Oral rehydration should be pursued aggressively with Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-5 oral rehydration solutions (AIII). Most patients can be treated with enteral nutrition; total parenteral nutrition is rarely indicated (CIII). Patients with biliary tract involvement may require endoscopic retrograde cholangiopancreatography for diagnosis. They may also benefit from sphincterotomy, stenting, or both.7,24 Several agents—including nitazoxanide, paromomycin, clofazimine, and spiramycin—have been investigated in small, randomized controlled clinical trials of adults with HIV.25 No pharmacologic or immunologic therapy directed specifically against Cryptosporidium has been shown to be consistently effective when used without ART.26 Nitazoxanide is an orally administered nitrothiazole benzamide with in vivo activity against a broad range of helminths, bacteria, and protozoa. Nitazoxanide is approved by the U.S. Food and Drug Administration for treatment of cryptosporidiosis in children over 1 year of age and adults. Nitazoxanide 500 mg administered twice daily for 3 days to adults without HIV but with cryptosporidiosis resulted in higher rates of diarrhea resolution and oocyst-free stools than placebo.27,28 In one study, adults with HIV with cryptosporidiosis and CD4 counts >50 cells/mm3 were treated with nitazoxanide 500 mg to 1,000 mg twice daily for 14 days; the nitazoxanide treatment group had substantially higher rates of parasitological cure and resolution of diarrhea than the placebo group.29 Efficacy of nitazoxanide for the treatment of cryptosporidial diarrhea in children with HIV, however, was not confirmed in two randomized trials in children.30,31 Data from a compassionate use program before the advent of potent ART, which included primarily white male adults with median CD4 counts <50 cells/mm3, reported that a majority of patients experienced some degree of clinical response (reduction in frequency of total stool and of liquid stools), usually within the first week of treatment.32 Adverse events associated with nitazoxanide are typically mild, and no important drug–drug interactions have been reported. Because of the clinical significance of cryptosporidiosis, many experts will institute a trial of nitazoxanide or paromomycin in conjunction with ART but never instead of ART (CIII). Paromomycin is a nonabsorbable aminoglycoside indicated for the treatment of intestinal amebiasis but not specifically approved for cryptosporidiosis. Paromomycin in high doses is effective for the treatment of cryptosporidiosis in animal models. A meta-analysis of 11 published studies of paromomycin in humans reported a response rate of 67%; however, there were few cures, relapses were common, and long-term success rates were only 33%.24 Two randomized trials comparing paromomycin with placebo demonstrated limited effectiveness of the drug among patients with AIDS and cryptosporidiosis.33,34 One case series suggested a better response rate in patients receiving paromomycin along with ART.35 Paromomycin may be used instead of nitazoxanide in conjunction with ART but never instead of ART (CIII). Special Considerations with Regard to Starting ART As noted above, patients with cryptosporidiosis should be offered ART as part of the initial management of cryptosporidiosis (AII). In animal and in vitro models, HIV protease inhibitors (PI) can inhibit Cryptosporidium, but there is no clinical evidence that PI-based ART is preferable in patients with documented cryptosporidiosis (CIII).36,37 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-6 Monitoring of Response to Therapy and Adverse Events (Including IRIS) Patients should be monitored closely for signs and symptoms of volume depletion, electrolyte imbalance, weight loss, and malnutrition. Immune reconstitution inflammatory syndrome (IRIS) has been described in association with three cases of extraintestinal cryptosporidiosis.38 Managing Treatment Failure Supportive treatment and optimization of ART to achieve full virologic suppression are the main approaches to managing treatment failure (AIII). The clinical response rather than results of stool tests should be used to guide the response to therapy. Some authorities advocate adding antiparasitic drugs (CIII), such as nitazoxanide or paromomycin alone or in combination with azithromycin, as well as optimizing ART in patients with treatment failure and cryptosporidiosis.39,40 Preventing Recurrence No pharmacologic interventions are known to be effective in preventing the recurrence of cryptosporidiosis. Special Considerations During Pregnancy Rehydration and initiation of ART are the mainstays of initial treatment of cryptosporidiosis during pregnancy, as they are in nonpregnant people (AII). Pregnancy should not preclude the use of ART and, in fact, is always an indication for ART. Nitazoxanide is not teratogenic in animals, but no data on use in human pregnancy are available. Nitazoxanide can be used in pregnancy after the first trimester in people with severe symptoms (CIII). Limited information is available about the teratogenic potential of paromomycin, but oral administration is associated with minimal systemic absorption, which may minimize potential risk. Paromomycin can be used in pregnancy after the first trimester in people with severe symptoms (CIII). Loperamide is poorly absorbed and has not been associated with birth defects in animal studies. However, one study identified an increased risk of congenital malformations, and specifically hypospadias, among 683 women with exposure to loperamide early in pregnancy.41 Therefore, loperamide should be avoided in the first trimester, unless benefits are felt to outweigh potential risks (CIII). Loperamide is the preferred antimotility agent in late pregnancy (CIII). Opiate exposure in late pregnancy has been associated with neonatal respiratory depression, and chronic exposure may result in neonatal withdrawal; therefore, tincture of opium is not recommended in late pregnancy (AIII).42 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-7 References 1. Flanigan T, Whalen C, Turner J, et al. Cryptosporidium infection and CD4 counts. Ann Intern Med. 1992;116(10):840-842. Available at: 2. Cama VA, Ross JM, Crawford S, et al. Differences in clinical manifestations among Cryptosporidium species and subtypes in HIV-infected persons. J Infect Dis. 2007;196(5):684-691. Available at: 3. Wanyiri JW, Kanyi H, Maina S, et al. Cryptosporidiosis in HIV/AIDS patients in Kenya: clinical features, epidemiology, molecular characterization and antibody responses. Am J Trop Med Hyg. 2014;91(2):319-328. Available at: 4. Wang RJ, Li JQ, Chen YC, Zhang LX, Xiao LH. Widespread occurrence of Cryptosporidium infections in patients with HIV/AIDS: Epidemiology, clinical feature, diagnosis, and therapy. Acta Trop. 2018;187:257-263. Available at: 5. Buchacz K, Lau B, Jing Y, et al. Incidence of AIDS-defining opportunistic infections in a multicohort analysis of HIV-infected persons in the United States and Canada, 2000– 2010. J Infect Dis. 2016;214(6):862-872. Available at: 6. Checkley W, White AC, Jr., Jaganath D, et al. A review of the global burden, novel diagnostics, therapeutics, and vaccine targets for cryptosporidium. Lancet Infect Dis. 2015;15(1):85-94. Available at: 7. Naseer M, Dailey FE, Juboori AA, Samiullah S, Tahan V. Epidemiology, determinants, and management of AIDS cholangiopathy: A review. World J Gastroenterol. 2018;24(7):767-774. Available at: 8. Sponseller JK, Griffiths JK, Tzipori S. The evolution of respiratory Cryptosporidiosis: evidence for transmission by inhalation. Clin Microbiol Rev. 2014;27(3):575-586. Available at: 9. Mor SM, Ascolillo LR, Nakato R, et al. Expectoration of Cryptosporidium Parasites in Sputum of Human Immunodeficiency Virus-Positive and -Negative Adults. Am J Trop Med Hyg. 2018;98(4):1086-1090. Available at: 10. Garcia LS, Arrowood M, Kokoskin E, et al. Practical guidance for clinical microbiology laboratories: laboratory diagnosis of parasites from the gastrointestinal tract. Clin Microbiol Rev. 2018;31(1). Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-8 11. Roellig DM, Yoder JS, Madison-Antenucci S, et al. Community laboratory testing for Cryptosporidium: multicenter study retesting public health surveillance stool samples positive for Cryptosporidium by rapid cartridge assay with direct fluorescent antibody testing. PLoS One. 2017;12(1):e0169915. Available at: 12. Ryan U, Paparini A, Oskam C. New technologies for detection of enteric parasites. Trends Parasitol. 2017;33(7):532-546. Available at: 13. Huang DB, Zhou J. Effect of intensive handwashing in the prevention of diarrhoeal illness among patients with AIDS: a randomized controlled study. J Med Microbiol. 2007;56(Pt 5):659-663. Available at: 14. King BJ, Monis PT. Critical processes affecting Cryptosporidium oocyst survival in the environment. Parasitology. 2007;134(Pt 3):309-323. Available at: 15. Gharpure R, Perez A, Miller AD, Wikswo ME, Silver R, Hlavsa MC. Cryptosporidiosis outbreaks—United States, 2009–2017. MMWR Morb Mortal Wkly Rep. 2019;68(25):568-572. Available at: 16. Holmberg SD, Moorman AC, Von Bargen JC, et al. Possible effectiveness of clarithromycin and rifabutin for cryptosporidiosis chemoprophylaxis in HIV disease. HIV Outpatient Study (HOPS) Investigators. JAMA. 1998;279(5):384-386. Available at: 17. Fichtenbaum CJ, Zackin R, Feinberg J, Benson C, Griffiths JK, AIDS Clinical Trials Group New Works Concept Sheet Team 064. Rifabutin but not clarithromycin prevents cryptosporidiosis in persons with advanced HIV infection. AIDS. 2000;14(18):2889-2893. Available at: 18. Gathe JC, Jr., Mayberry C, Clemmons J, Nemecek J. Resolution of severe cryptosporidial diarrhea with rifaximin in patients with AIDS. J Acquir Immune Defic Syndr. 2008;48(3):363-364. Available at: 19. Maggi P, Larocca AM, Quarto M, et al. Effect of antiretroviral therapy on cryptosporidiosis and microsporidiosis in patients infected with human immunodeficiency virus type 1. Eur J Clin Microbiol Infect Dis. 2000;19(3):213-217. Available at: 20. Miao YM, Awad-El-Kariem FM, Franzen C, et al. Eradication of cryptosporidia and microsporidia following successful antiretroviral therapy. J Acquir Immune Defic Syndr. 2000;25(2):124-129. Available at: 21. Schmidt W, Wahnschaffe U, Schafer M, et al. Rapid increase of mucosal CD4 T cells followed by clearance of intestinal cryptosporidiosis in an AIDS patient receiving highly Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-9 active antiretroviral therapy. Gastroenterology. 2001;120(4):984-987. Available at: 22. Dillingham RA, Pinkerton R, Leger P, et al. High early mortality in patients with chronic acquired immunodeficiency syndrome diarrhea initiating antiretroviral therapy in Haiti: a case-control study. Am J Trop Med Hyg. 2009;80(6):1060-1064. Available at: 23. Simon DM, Cello JP, Valenzuela J, et al. Multicenter trial of octreotide in patients with refractory acquired immunodeficiency syndrome-associated diarrhea. Gastroenterology. 1995;108(6):1753-1760. Available at: 24. Hashmey R, Smith NH, Cron S, Graviss EA, Chappell CL, White AC, Jr. Cryptosporidiosis in Houston, Texas. A report of 95 cases. Medicine (Baltimore). 1997;76(2):118-139. Available at: 25. Diptyanusa A, Sari IP. Treatment of human intestinal cryptosporidiosis: a review of published clinical trials. Int J Parasitol Drugs Drug Resist. 2021;17:128-138. Available at: 26. White AC, Jr. Cryptosporidiosis (Cryptosporidium Species). In: Secondary White AC, Jr., ed^eds. Subsidiary White AC, Jr., trans. Secondary Cryptosporidiosis (Cryptosporidium Species). Vol. 9th ed. Philadelphia: Elsevier Saunders; 2020:3410-3420. 27. Rossignol JF, Ayoub A, Ayers MS. Treatment of diarrhea caused by Cryptosporidium parvum: a prospective randomized, double-blind, placebo-controlled study of Nitazoxanide. J Infect Dis. 2001;184(1):103-106. Available at: 28. Rossignol JF, Kabil SM, el-Gohary Y, Younis AM. Effect of nitazoxanide in diarrhea and enteritis caused by Cryptosporidium species. Clin Gastroenterol Hepatol. 2006;4(3):320-324. Available at: 29. Rossignol JF, Hidalgo H, Feregrino M, et al. A double-'blind' placebo-controlled study of nitazoxanide in the treatment of cryptosporidial diarrhoea in AIDS patients in Mexico. Trans R Soc Trop Med Hyg. 1998;92(6):663-666. Available at: 30. Amadi B, Mwiya M, Sianongo S, et al. High dose prolonged treatment with nitazoxanide is not effective for cryptosporidiosis in HIV positive Zambian children: a randomised controlled trial. BMC Infect Dis. 2009;9:195. Available at: 31. Amadi B, Mwiya M, Musuku J, et al. Effect of nitazoxanide on morbidity and mortality in Zambian children with cryptosporidiosis: a randomised controlled trial. Lancet. 2002;360(9343):1375-1380. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-10 32. Rossignol JF. Nitazoxanide in the treatment of acquired immune deficiency syndrome-related cryptosporidiosis: results of the United States compassionate use program in 365 patients. Aliment Pharmacol Ther. 2006;24(5):887-894. Available at: 33. White AC, Jr., Chappell CL, Hayat CS, Kimball KT, Flanigan TP, Goodgame RW. Paromomycin for cryptosporidiosis in AIDS: a prospective, double-blind trial. J Infect Dis. 1994;170(2):419-424. Available at: 34. Hewitt RG, Yiannoutsos CT, Higgs ES, et al. Paromomycin: no more effective than placebo for treatment of cryptosporidiosis in patients with advanced human immunodeficiency virus infection. AIDS Clinical Trial Group. Clin Infect Dis. 2000;31(4):1084-1092. Available at: 35. Maggi P, Larocca AM, Ladisa N, et al. Opportunistic parasitic infections of the intestinal tract in the era of highly active antiretroviral therapy: is the CD4(+) count so important? Clin Infect Dis. 2001;33(9):1609-1611. Available at: 36. Hommer V, Eichholz J, Petry F. Effect of antiretroviral protease inhibitors alone, and in combination with paromomycin, on the excystation, invasion and in vitro development of Cryptosporidium parvum. J Antimicrob Chemother. 2003;52(3):359-364. Available at: 37. Mele R, Gomez Morales MA, Tosini F, Pozio E. Indinavir reduces Cryptosporidium parvum infection in both in vitro and in vivo models. Int J Parasitol. 2003;33(7):757-764. Available at: 38. Sullivan T, Reese L, Huprikar S, Lee M. Pulmonary cryptosporidiosis and immune reconstitution inflammatory syndrome: a case report and review. Int J STD AIDS. 2013;24(4):333-334. Available at: 39. Smith NH, Cron S, Valdez LM, Chappell CL, White AC, Jr. Combination drug therapy for cryptosporidiosis in AIDS. J Infect Dis. 1998;178(3):900-903. Available at: 40. Tomczak E, McDougal AN, White AC, Jr. Resolution of cryptosporidiosis in transplant recipients: review of the literature and presentation of a renal transplant patient treated with nitazoxanide, azithromycin, and rifaximin. Open Forum Infect Dis. 2022;9(1):ofab610. Available at: 41. Kallen B, Nilsson E, Otterblad Olausson P. Maternal use of loperamide in early pregnancy and delivery outcome. Acta Paediatr. 2008;97(5):541-545. Available at: 42. Esposito DB, Huybrechts KF, Werler MM, et al. Characteristics of prescription opioid analgesics in pregnancy and risk of neonatal opioid withdrawal syndrome in newborns. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV I-11 JAMA Netw Open. 2022;5(8):e2228588. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV J-1 Cystoisosporiasis (Formerly Isosporiasis) (Last updated September 10, 2015; last reviewed January 10, 2024) Epidemiology Isosporiasis, also known as cystoisosporiasis, occurs worldwide but predominantly in tropical and subtropical regions. Immunocompromised patients, including those who are HIV-infected, are at increased risk for chronic, debilitating illness.1-7 Although Isospora (Cystoisospora) belli completes its life cycle in humans, the oocysts shed in the feces of infected individuals must mature (sporulate) outside the host, in the environment, to become infective. On the basis of limited data, the maturation process is completed in approximately 1 to 2 days but might occur more rapidly in some settings.2 Infection results from ingestion of sporulated oocysts, such as from contaminated food or water. After ingestion, the parasite invades enterocytes in the small intestine. Ultimately, immature oocysts are produced and shed in stool. Clinical Manifestations The most common manifestation is watery, non-bloody diarrhea, which may be associated with abdominal pain, cramping, anorexia, nausea, vomiting, and low-grade fever. The diarrhea can be profuse and prolonged, particularly in immunocompromised patients, resulting in severe dehydration, electrolyte abnormalities such as hypokalemia, weight loss, and malabsorption.6-12 Acalculous cholecystitis/cholangiopathy2,13-15 and reactive arthritis16 also have been reported. Diagnosis Typically, infection is diagnosed by detecting Isospora oocysts (dimensions, 23–36 µm by 12–17 µm) in fecal specimens.2 Oocysts may be shed intermittently and at low levels, even by patients with profuse diarrhea. Diagnosis can be facilitated by repeated stool examinations with sensitive methods, such as modified acid-fast techniques, on which oocysts stain bright red, and UV fluorescence microscopy, under which they autofluoresce.2,17 Infection also can be diagnosed by detecting oocysts in duodenal aspirates/ mucus or developmental stages of the parasite in intestinal biopsy specimens.2,10 Extraintestinal infection, such as in the biliary tract, lymph nodes, spleen, and liver, has been documented in postmortem examinations of HIV-infected patients.2,18-20 Preventing Exposure Because I. belli is acquired by ingesting infected water or food, avoiding potentially contaminated food or water in isosporiasis-endemic areas may help prevent infection. Preventing Disease In some settings, chemoprophylaxis with trimethoprim-sulfamethoxazole (TMP-SMX) has been associated with a lower incidence or prevalence of isosporiasis.1,3,4,21 In a randomized, placebo-controlled trial, daily TMP-SMX (160/800 mg) was protective against isosporiasis in persons with early-stage HIV infection (World Health Organization clinical stage 2 or 3 at enrollment).1 In an observational study, incidence of isosporiasis decreased after widespread introduction of antiretroviral therapy (ART), except in patients with CD4 counts <50 cells/mm3.3 After adjustment for the CD4 T lymphocyte (CD4) cell count, the risk of isosporiasis was substantially lower in those receiving prophylaxis with TMP-SMX, sulfadiazine, or pyrimethamine (unspecified regimens). In analyses of data from a Los Angeles county AIDS surveillance registry during the pre-ART era, the prevalence of isosporiasis was lower in patients with versus without a history of Pneumocystis pneumonia—indirect evidence of a protective effect from use of TMP-SMX for Pneumocystis pneumonia.4 Insufficient evidence is available, however, to support a general recommendation for primary prophylaxis for isosporiasis per se, especially for U.S. travelers in isoporiasis-endemic areas. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV J-2 Treating Disease Clinical management includes fluid and electrolyte support for dehydrated patients and nutritional supplementation for malnourished patients (AIII). TMP-SMX is the antimicrobial agent of choice for treatment of isosporiasis (AI). It is the only agent whose use is supported by substantial published data and clinical experience. Therefore, potential alternative therapies should be reserved for patients with documented sulfa intolerance or in whom treatment fails (AIII). Three studies in HIV-infected patients in Haiti have demonstrated the effectiveness of various treatment regimens of TMP-SMX.6,7,22 The patients were not receiving ART, and laboratory indicators of immunodeficiency (such as CD4 cell counts) were not specified. On the basis of the initial studies,6,7 the traditional treatment regimen has been a 10-day course of TMP-SMX (160/800 mg) administered orally four times daily (AII).23 In another study, TMP-SMX (160/800 mg) administered twice daily was also effective (BI).22 Although published experience using two daily doses of TMP-SMX (160/800 mg) is limited, one approach would be to start with this regimen but to increase the daily dose and the duration of therapy (up to 3–4 weeks)6,10 if symptoms worsen or persist (BIII). Intravenous administration of TMP-SMX should be considered for patients with potential or documented malabsorption. Limited data suggest that therapy with pyrimethamine–sulfadiazine and pyrimethamine–sulfadoxine may be effective.2,9,10,24-26 However, the combination of pyrimethamine plus sulfadoxine is not typically recommended for use in the United States (CIII); it has been associated with an increased risk of severe cutaneous reactions, including Stevens-Johnson syndrome,27 and pyrimethamine and sulfadoxine clear slowly from the body after therapy is discontinued. Single-agent therapy with pyrimethamine has been used, with anecdotal success for treatment and prevention of isosporiasis.3,28,29 Pyrimethamine (50–75 mg/day) plus leucovorin (10–25 mg/day) to prevent myelosuppression may be an effective treatment alternative; it is the option for sulfa-intolerant patients (BIII). The author panel has issued a statement on the availability of pyrimethamine. For more information, please visit Special Considerations with Regard to Starting ART Only limited data address the utility of ART in the setting of Isospora and HIV co-infection.3,14,21 Immune reconstitution with ART may result in fewer relapses of isosporiasis, and no cases of immune reconstitution inflammatory syndrome (IRIS) have been reported. Therefore, the potential benefits of ART likely outweigh the risks. For patients with isosporiasis who otherwise fulfill criteria for ART, TMP-SMX therapy and ART can be started simultaneously; there is no known reason to defer initiation of ART other than the potential for poor ART absorption (AIII). Monitoring of Response to Therapy and Adverse Events (Including IRIS) Patients should be monitored for clinical response and adverse events. In HIV-infected patients, TMP-SMX therapy is commonly associated with side effects, such as rash, fever, leukopenia, thrombocytopenia, and elevated transaminase levels. IRIS has not been described. Managing Treatment Failure If symptoms worsen or persist despite approximately 5 to 7 days of TMP-SMX therapy, the possibilities of noncompliance, malabsorption, and concurrent infections/enteropathies should be considered; the TMP-SMX regimen (daily dose, duration, and mode of administration) also should be reevaluated. For patients with documented sulfa intolerance or in whom treatment fails, use of a potential alternative agent (typically pyrimethamine) should be considered. Ciprofloxacin is a second-line agent (CI). On the basis of limited data from a randomized, controlled trial in Haiti, ciprofloxacin (500 mg twice daily for 7 days) is less effective than TMP-SMX but may have modest activity against I. belli.22 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV J-3 Unsubstantiated or mixed data are available for albendazole,29-31 nitazoxanide,32,33 doxycycline,34 the macrolides roxithromycin and spiramycin,25,35,36 and the veterinary anticoccidial agent diclazuril (CIII).37,38 Limited data suggest that drugs such as metronidazole, quinacrine, iodoquinol, paromomycin, and furazolidone are ineffective.8,25,26,28,35,37 Apparent or partial responses, if noted, may be attributable to treatment of concomitant infections or to nonspecific effects. Preventing Recurrence Patients with CD4 cell counts <200 cells/mm3 should receive secondary prophylaxis (chronic maintenance therapy) with TMP-SMX, which is also protective against Pneumocystis jirovecii and Toxoplasma gondii infections (AI). In studies in Haiti, approximately 50% of patients who did not receive secondary prophylaxis had symptomatic recurrences approximately 2 months after completing a course of TMP-SMX therapy, relapses rapidly responded to retreatment, and secondary prophylaxis decreased the risk of relapse.6,7,22 In a randomized, placebo-controlled trial, no symptomatic recurrences were noted in patients who received maintenance therapy with thrice-weekly TMP-SMX (160/800 mg) (AI).7 Daily TMP-SMX (160/800 mg) and thrice-weekly TMP-SMX (320/1600 mg) have been effective (BIII);5,10 however, clinical and parasitologic relapses despite maintenance TMP-SMX therapy and ART have been reported.14 In sulfa-intolerant patients, pyrimethamine (25 mg/day) with leucovorin (5–10 mg/day) has been used (BIII).28 On the basis of limited data, ciprofloxacin (500 mg thrice weekly) is considered a second-line alternative (CI).22 When To Stop Secondary Prophylaxis The issue of discontinuing prophylaxis has not been evaluated in a clinical trial. Chemoprophylaxis probably can be safely discontinued in patients without evidence of active I. belli infection who have a sustained increase in the CD4 cell count to levels >200 cells/mm3 for >6 months after initiation of ART (BIII). Special Considerations During Pregnancy TMP-SMX is the agent of choice for primary treatment and secondary prophylaxis in pregnant women, as it is in persons who are not pregnant. Although first-trimester exposure to trimethoprim has been associated with a small increased risk of birth defects,39-42 TMP-SMX therapy should be provided in the setting of maternal symptomatic I. belli infection. Because of concerns about possible teratogenicity associated with first-trimester drug exposure, clinicians may withhold secondary prophylaxis during the first trimester and treat only symptomatic infection (CIII). Although pyrimethamine has been associated with birth defects in animals, limited human data have not suggested an increased risk of defects.43 Human data about the use of ciprofloxacin during several hundred pregnancies have not suggested an increased risk of birth defects or cartilage abnormalities.44 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV J-4 Treating Isospora belli Infection General Management Considerations: • Fluid and electrolyte support in patients with dehydration (AIII) • Nutritional supplementation for malnourished patients (AIII) Preferred Therapy for Acute Infection: • TMP-SMX (160 mg/800 mg) PO (or IV) QID for 10 days (AII), or • TMP-SMX (160 mg/800 mg) PO (or IV) BID for 7–10 days (BI) •  One approach is to start with TMP-SMX (160 mg/800 mg) BID regimen first, and increase daily dose and/or duration (up to 3–4 weeks) if symptoms worsen or persist (BIII) • IV therapy for patients with potential or documented malabsorption Alternative Therapy For Acute Infection (For Patients with Sulfa Intolerance): • Pyrimethamine 50–75 mg PO daily + leucovorin 10–25 mg PO daily (BIII), or • Ciprofloxacin 500 mg PO BID for 7 days (CI) Chronic Maintenance Therapy (Secondary Prophylaxis) (In Patients with CD4 Count <200/mm3) Preferred Therapy: • TMP-SMX (160 mg/800 mg) PO 3 times weekly (AI) Alternative Therapy: • TMP-SMX (160 mg/800 mg) PO daily (BIII), or • TMP-SMX (320 mg/1600 mg) PO 3 times weekly (BIII), or • Pyrimethamine 25 mg PO daily + leucovorin 5–10 mg PO daily (BIII) • Ciprofloxacin 500 mg PO 3 times weekly (CI) as a second line alternative Criteria for Discontinuation of Chronic Maintenance Therapy •  Sustained increase in CD4 count >200 cells/mm3 for >6 months in response to ART and without evidence of active I. belli infection (BIII) Recommendations for Treating Isospora belli Infection Key to Acronyms: ART = antiretroviral therapy; BID = twice daily; IV = intravenous; PO = orally; QID = four times a day; TMP-SMX = trimethoprim-sulfamethoxazole References 1.  Anglaret X, Chene G, Attia A, et al. Early chemoprophylaxis with trimethoprim-sulphamethoxazole for HIV-1-infected adults in Abidjan, Cote d’Ivoire: a randomised trial. Cotrimo-CI Study Group. Lancet. May 1 1999;353(9163):1463-1468. Available at 2.  Lindsay DS, Dubey JP, Blagburn BL. Biology of Isospora spp. from humans, nonhuman primates, and domestic animals. Clin Microbiol Rev. Jan 1997;10(1):19-34. Available at 3.  Guiguet M, Furco A, Tattevin P, Costagliola D, Molina JM, French Hospital Database on HIVCEG. HIV-associated Isospora belli infection: incidence and risk factors in the French Hospital Database on HIV. HIV Med. Mar 2007;8(2):124-130. Available at 4.  Sorvillo FJ, Lieb LE, Seidel J, Kerndt P, Turner J, Ash LR. Epidemiology of isosporiasis among persons with acquired immunodeficiency syndrome in Los Angeles County. Am J Trop Med Hyg. Dec 1995;53(6):656-659. Available at http:// www.ncbi.nlm.nih.gov/pubmed/8561272. 5.  Certad G, Arenas-Pinto A, Pocaterra L, et al. Isosporiasis in Venezuelan adults infected with human immunodeficiency virus: clinical characterization. Am J Trop Med Hyg. Aug 2003;69(2):217-222. Available at gov/pubmed/13677379. 6.  DeHovitz JA, Pape JW, Boncy M, Johnson WD, Jr. Clinical manifestations and therapy of Isospora belli infection in patients with the acquired immunodeficiency syndrome. N Engl J Med. Jul 10 1986;315(2):87-90. Available at http:// Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV J-5 www.ncbi.nlm.nih.gov/pubmed/3487730. 7.  Pape JW, Verdier RI, Johnson WD, Jr. Treatment and prophylaxis of Isospora belli infection in patients with the acquired immunodeficiency syndrome. N Engl J Med. Apr 20 1989;320(16):1044-1047. Available at nlm.nih.gov/pubmed/2927483. 8.  Forthal DN, Guest SS. Isospora belli enteritis in three homosexual men. Am J Trop Med Hyg. Nov 1984;33(6):1060-1064. Available at 9.  Modigliani R, Bories C, Le Charpentier Y, et al. 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Isospora belli infection: observation of unicellular cysts in mesenteric lymphoid tissues of a Brazilian patient with AIDS and animal inoculation. The Journal of eukaryotic microbiology. 2003;50 Suppl:682-684. Available at 19.  Restrepo C, Macher AM, Radany EH. Disseminated extraintestinal isosporiasis in a patient with acquired immune deficiency syndrome. Am J Clin Pathol. Apr 1987;87(4):536-542. Available at pubmed/3826017. 20.  Bernard E, Delgiudice P, Carles M, et al. Disseminated isosporiasis in an AIDS patient. Eur J Clin Microbiol Infect Dis. Sep 1997;16(9):699-701. Available at 21.  Dillingham RA, Pinkerton R, Leger P, et al. High early mortality in patients with chronic acquired immunodeficiency syndrome diarrhea initiating antiretroviral therapy in Haiti: a case-control study. Am J Trop Med Hyg. Jun 2009;80(6):1060-1064. Available at 22.  Verdier RI, Fitzgerald DW, Johnson WD, Jr., Pape JW. 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Chronic intestinal coccidiosis in man: intestinal morphology and response to treatment. Gastroenterology. May 1974;66(5):923-935. Available at 27.  Navin TR, Miller KD, Satriale RF, Lobel HO. Adverse reactions associated with pyrimethamine-sulfadoxine prophylaxis for Pneumocystis carinii infections in AIDS. Lancet. Jun 8 1985;1(8441):1332. Available at pubmed/2860516. 28.  Weiss LM, Perlman DC, Sherman J, Tanowitz H, Wittner M. Isospora belli infection: treatment with pyrimethamine. Ann Intern Med. Sep 15 1988;109(6):474-475. Available at 29.  Jongwutiwes S, Sampatanukul P, Putaporntip C. Recurrent isosporiasis over a decade in an immunocompetent host successfully treated with pyrimethamine. Scandinavian journal of infectious diseases. 2002;34(11):859-862. Available at 30.  Dionisio D, Sterrantino G, Meli M, Leoncini F, Orsi A, Nicoletti P. Treatment of isosporiasis with combined albendazole and ornidazole in patients with AIDS. AIDS. Sep 1996;10(11):1301-1302. Available at pubmed/8883600. 31.  Zulu I, Veitch A, Sianongo S, et al. Albendazole chemotherapy for AIDS-related diarrhoea in Zambia--clinical, parasitological and mucosal responses. Alimentary pharmacology & therapeutics. 2002; 16(3):595-601. Available at http:// www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=11876715. 32.  Romero Cabello R, Guerrero LR, Munoz Garcia MR, Geyne Cruz A. Nitazoxanide for the treatment of intestinal protozoan and helminthic infections in Mexico. Trans R Soc Trop Med Hyg. Nov-Dec 1997;91(6):701-703. Available at ncbi.nlm.nih.gov/pubmed/9580117. 33.  Doumbo O, Rossignol JF, Pichard E, et al. Nitazoxanide in the treatment of cryptosporidial diarrhea and other intestinal parasitic infections associated with acquired immunodeficiency syndrome in tropical Africa. Am J Trop Med Hyg. Jun 1997;56(6):637-639. Available at 34.  Meyohas MC, Capella F, Poirot JL, et al. [Treatment with doxycycline and nifuroxazide of Isospora belli infection in AIDS]. Pathologie-biologie. Jun 1990;38(5 ( Pt 2)):589-591. Available at 35.  Gaska JA, Tietze KJ, Cosgrove EM. Unsuccessful treatment of enteritis due to Isospora belli with spiramycin: a case report. J Infect Dis. Dec 1985;152(6):1336-1338. Available at 36.  Musey KL, Chidiac C, Beaucaire G, Houriez S, Fourrier A. Effectiveness of roxithromycin for treating Isospora belli infection. J Infect Dis. Sep 1988;158(3):646. Available at 37.  Limson-Pobre RN, Merrick S, Gruen D, Soave R. Use of diclazuril for the treatment of isosporiasis in patients with AIDS. Clin Infect Dis. Jan 1995;20(1):201-202. Available at 38.  Kayembe K, Desmet P, Henry MC, Stoffels P. Diclazuril for Isospora belli infection in AIDS. Lancet. Jun 17 1989;1(8651):1397-1398. Available at 39.  Czeizel AE, Rockenbauer M, Sorensen HT, Olsen J. The teratogenic risk of trimethoprim-sulfonamides: a population based case-control study. Reprod Toxicol. Nov-Dec 2001;15(6):637-646. Available at 40.  Hernandez-Diaz S, Werler MM, Walker AM, Mitchell AA. Folic acid antagonists during pregnancy and the risk of birth defects. N Engl J Med. Nov 30 2000;343(22):1608-1614. Available at 41.  Hernandez-Diaz S, Werler MM, Walker AM, Mitchell AA. Neural tube defects in relation to use of folic acid antagonists during pregnancy. American journal of epidemiology. May 15 2001;153(10):961-968. Available at nih.gov/pubmed/11384952. 42.  Jungmann EM, Mercey D, DeRuiter A, et al. Is first trimester exposure to the combination of antiretroviral therapy and folate antagonists a risk factor for congenital abnormalities? Sexually transmitted infections. Dec 2001;77(6):441-443. Available at 43.  Deen JL, von Seidlein L, Pinder M, Walraven GE, Greenwood BM. The safety of the combination artesunate and pyrimethamine-sulfadoxine given during pregnancy. Trans R Soc Trop Med Hyg. Jul-Aug 2001;95(4):424-428. Available at 44.  Nahum GG, Uhl K, Kennedy DL. Antibiotic use in pregnancy and lactation: what is and is not known about teratogenic and toxic risks. Obstet Gynecol. May 2006;107(5):1120-1138. Available at Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-1 Cytomegalovirus Disease (Last updated July 1, 2021; last reviewed January 10, 2024) Epidemiology Cytomegalovirus (CMV) is a double-stranded DNA virus in the herpesvirus family that can cause disseminated or localized end-organ disease in people with HIV with advanced immunosuppres­ sion. Most clinical disease occurs in individuals previously infected with CMV experiencing reactivation of latent infection. Infection with a novel strain also may occur. End-organ disease caused by CMV occurs in patients with HIV and advanced immunosuppres­ sion, typically those with CD4+ T lymphocyte cell (CD4) counts <50 cells/mm3 who are not receiving, adherent to, or responding to antiretroviral therapy (ART).1–3 Among those treated with ART who have achieved virologic control, a new diagnosis of CMV end-organ disease is exceedingly rare. Before potent ART, an estimated 30% of patients with AIDS experienced CMV retinitis, the most common CMV end-organ disease in such patients.1–3 The incidence of new cases of CMV end-or­ gan disease has declined by ≥95% with the advent of potent ART.4,5 For those with established CMV retinitis, recurrence of active lesions occurs at a rate substantially lower than that seen in the era before potent ART. Nevertheless, even for those with immune recovery sufficient to warrant discontinuation of anti-CMV therapy (i.e., CD4+ counts >100 cells/mm3) relapse of the retinitis occurs at a rate of 0.03/ person-year and has been documented6 at CD4 counts as high as 1,250 cells/mm3. Therefore, regardless of whether or not anti-CMV therapy is continued, regular ophthalmologic follow-up is needed. Clinical Manifestations Retinitis is the most common clinical manifestation of CMV end-organ disease in people with HIV. It occurs as unilateral disease in two-thirds of patients at presentation, but disease ultimately progresses to bilateral in most patients in the absence of therapy or immune recovery.6 In patients with unilateral CMV retinitis and CD4 count <50 cells/mm3, rates of contralateral disease approach those of the prepotent ART era.6 Peripheral retinitis (i.e., outside the major vascular arcades, not involving the macula or optic disc) may be asymptomatic or present with floaters, scotomata, or peripheral visual field defects. Posterior retinal lesions, especially those impinging on the macula or optic disc, are associated with decreased visual acuity or central visual field defects. CMV retinitis is a full-thickness necrotizing retinal infection. The characteristic ophthalmologic appearance is that of fluffy, yellow-white retinal lesions, with or without intraretinal hemorrhage. The most typical feature is the lesion border, which has tiny dry-appearing, granular, dot-like “satellites” at the interface between infected and normal retina. There will be little inflammation of the vitreous humor unless immune recovery with ART occurs.1 Blood vessels near the lesions may appear to be sheathed. Occasionally, CMV retinitis lesions, particularly peripheral lesions, may have only a granular appearance throughout the lesion. In the absence of effective ART or specific anti-CMV therapy, retinitis lesions invariably enlarge. Untreated lesions in severely immunodeficient individuals will involve the entire retina over a period of no longer than 6 months. Movement of lesion borders occurs at variable rates in different directions,7 causing a characteristic “brushfire” pattern, with their granular, leading edges advancing before an atrophic gliotic scar.8 Colitis occurs in 5% to 10% of patients with AIDS and CMV end-organ disease.2 The most frequent clinical manifestations are weight loss, fever, anorexia, abdominal pain, diarrhea, and malaise. In the colon, and especially in the cecum, CMV can cause perforation and present as an acute abdomen. Computed tomography may show colonic thickening or a colonic mass that may be mistaken for malignancy or other opportunistic infections (OI). Hemorrhage and perforation can be life-threatening complications. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-2 Esophagitis occurs in a small percentage of patients with AIDS who experience CMV end-organ disease and causes odynophagia, nausea, and occasionally midepigastric or retrosternal discomfort as well as fever. CMV pneumonitis is uncommon in people with HIV, which is in contrast to other conditions with severe immunosuppression, such as solid organ and stem-cell transplant patients. CMV is detected frequently in the bronchoalveolar lavage (BAL) using DNA–specific polymerase chain reaction (PCR), but is a bystander most of the time and should trigger a search for a more likely causative pathogen. CMV PCR from the BAL has not been shown to have diagnostic value in people with HIV. CMV neurologic disease includes dementia, ventriculoencephalitis, and polyradiculomyelopathies.9 Patients with dementia caused by CMV encephalitis typically have lethargy or confusion in the presence or absence of fever. Cerebrospinal fluid (CSF) typically demonstrates lymphocytic pleocytosis, low-to-normal glucose levels, and normal-to-elevated protein levels, although normal CSF findings do not rule out the diagnosis of CMV encephalitis. Patients with ventriculoencephalitis have a more acute course, with focal neurologic signs, often including cranial nerve palsies or nystagmus, and rapid progression to death. Periventricular enhancement of computed tomography or magnetic resonance images is highly suggestive of CMV ventriculoencephalitis, rather than HIV-associated neurocognitive disorder. CMV polyradiculomyelopathy or transverse myelitis causes a Guillain-Barre-like syndrome characterized by radicular back pain, urinary retention, and progressive bilateral leg weakness. Clinical symptoms usually progress over several weeks to include loss of bowel and bladder control and flaccid paraplegia. A spastic myelopathy has been reported, and sacral paresthesia can occur. The CSF in CMV polyradiculopathy usually demonstrates neutrophilic pleocytosis (usually 100 to 200 neutrophils/µL and some erythrocytes) accompanied by hypoglycorrhachia and elevated protein levels. Diagnosis The diagnosis of CMV end-organ disease is typically made on the basis of the clinical presentation and, when possible, evidence of the virus in tissue. CMV retinitis usually is diagnosed based on recognition of characteristic retinal changes observed through a dilated pupil during an ophthalmoscopic examination performed by an experienced ophthalmologist. Diagnosis in that setting has a 95% positive predictive value. In rare cases, the diagnosis may be unclear, and PCR of aqueous or vitreous humor specimens for CMV and other pathogens—especially herpes simplex virus, varicella zoster virus, and Toxoplasma gondii—can be useful for establishing the diagnosis. Detection of CMV DNA in CSF or vitreous or aqueous humor specimens is highly suggestive that CMV is the cause of ocular disease. In one study, CMV DNA was detected in 82% of vitreous specimens collected at diagnosis of CMV retinitis, in 77% of relapsed retinitis, and in 23% of quiescent retinitis.10 Therefore, failure to detect CMV DNA in vitreous specimens does not rule out the presence of CMV retinitis. A response to empiric anti-CMV therapy also can be an important diagnostic indicator. CMV colitis usually is diagnosed based on demonstration of mucosal ulcerations on endoscopic examination, combined with histopathologic demonstration of characteristic intranuclear and intracytoplasmic inclusions on hematoxylin and eosin stains.2,11 Similarly, CMV esophagitis is diagnosed by presence of ulcers of the distal esophagus together with biopsy evidence of intranuclear inclusion bodies in the endothelial cells with an inflammatory reaction at the edge of the ulcer.2 The number of inclusion bodies in specimens varies from many inclusion bodies to rare or isolated inclusion bodies. Immunohistochemistry also may be used to detect CMV in tissue. Culturing CMV, or detection of CMV DNA by PCR, from a biopsy or cells brushed from the colon or the esophagus is insufficient to establish the diagnosis of CMV colitis or esophagitis in the absence of histopathologic changes, because a substantial number of patients with low CD4 cell counts may shed CMV and have positive cultures in the absence of clinical disease.12 The diagnosis of CMV pneumonitis requires consistent clinical and radiological findings (i.e., Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-3 diffuse pulmonary interstitial infiltrates, fever, and cough or dyspnea), identification of multiple CMV inclusion bodies in lung tissue or cytology, and the absence of any other pathogens that are more commonly associated with pneumonitis.13 Detection of CMV in the lungs in the absence of these criteria typically represents shedding, rather than clinical disease. CMV neurologic disease is diagnosed on the basis of a compatible clinical syndrome and the presence of CMV in CSF or brain tissue, most often evaluated with PCR.3,14,15 Blood tests to detect CMV by antigen detection, culture, or PCR are not recommended for diagnosis of CMV end-organ disease because of their poor positive predictive value in people with advanced AIDS.16 CMV viremia can be detected by PCR, antigen assays, or culture and is often present in endorgan disease. A negative serum or plasma PCR assay does not rule out CMV end-organ disease. CMV viremia may be present in the absence of end-organ disease in people with HIV with low CD4 cell counts.9,12–15,17 Monitoring for CMV viremia is not recommended. The presence of serum antibodies to CMV, in and of itself, does not establish the presence of CMV disease, because a large proportion of the general population has been exposed to CMV and is seropositive. However, a negative immunoglobulin G (IgG) antibody level indicates that CMV is unlikely to be the cause of the disease process. Preventing Exposure Although CMV infection is common in the general population, geographic, socioeconomic, and racial and ethnic differences exist in CMV prevalence.10 In the National Health and Nutrition Exam­ ination Survey (NHANES) 1999–2004, CMV seropositivity was associated with older age, female sex, foreign birthplace, and markers of socioeconomic status, such as low household income and education and high household crowding. Some people with HIV may belong to groups with relatively low sero­ prevalence rates for CMV and, therefore, cannot be presumed to be seropositive. Adolescents and adults with HIV should be advised that CMV is shed in semen, cervical secretions, and saliva and that latex condoms used during sexual contact reduce the risk of exposure to CMV, as well as other sexually trans­ mitted pathogens (AII). Preventing Disease CMV end-organ disease is best prevented using ART to maintain the CD4 count >100 cells/mm3 (BI). A randomized, placebo-controlled trial addressed whether valganciclovir (the current standard oral agent for treatment of CMV disease) in addition to ART might reduce CMV end-organ disease in AIDS patients at high risk (CD4 count <100 cells/mm3 and CMV viremia detected by plasma CMV DNA PCR assay).18 This study failed to show a benefit for such preventive therapy; therefore, valganciclovir primary prophylaxis is not recommended to prevent CMV end-organ disease in people with HIV, even among patients who have CMV viremia (AI). The primary method for preventing severe CMV disease is recognizing the early manifestations of the disease and instituting proper therapy. Patients who have a low CD4 cell count (<100 cells/ mm3) and are not on ART should be made aware of the implications of increased floaters in the eye and be advised to assess their visual acuity regularly using simple techniques, such as reading newsprint. Development of floaters or changes in visual acuity should prompt an urgent referral to ophthalmology (AIII). In the premodern ART era, some specialists recommended ophthalmologic examinations every 3 to 4 months for patients with CD4+ cells <50 cells/mm3, because up to one-half of early CMV retinitis was asymptomatic (CIII). However, with the decline in CMV incidence in the modern ART era, the value of this recommendation is unknown. Some clinicians do recommend a baseline ophthalmologic exam for people with HIV with CD4 <100 cells/mm3 (CIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-4 The therapeutic approach to CMV retinitis should be individualized based on tolerance of sys­ temic medications, prior exposure to anti-CMV drugs, and possibly the location of lesions (AIII). CMV retinitis should ideally be treated with the active participation of an ophthalmologist who is familiar with the diagnosis and management of this retinal disease (AIII). Oral valganciclovir (AI), intravenous (IV) ganciclovir (AI), or IV ganciclovir induction followed by oral valganciclovir maintenance (AI) are first-line therapies for treating CMV retinitis. Although IV foscarnet (BI), and IV cidofovir (CI) are also effective treatments for CMV retinitis, substantial toxici­ ties, including nephrotoxicity, make these less-preferred options.8,19–26 Systemic therapy has been docu­ mented to reduce CMV involvement of the contralateral eye,19 to reduce CMV visceral disease, and to improve survival.20,27 Given the evident benefits of systemic anti-CMV therapy, treatment regimens for CMV retinitis should include a systemic component. Few trials have compared regimen efficacy during the past 15 years. None of the listed regimens has been proven in a clinical trial to have superior efficacy related to protecting vision. Therefore, clinical judgment must be used when choosing a regimen.21–25 When systemic therapy is indicated, most clinicians will prescribe IV ganciclovir (AI) or oral valganciclovir (AI) for an induction period lasting a minimum of 14 to 21 days, with the duration deter­ mined by clinical response based on retinal examination. Many prefer the IV formulation when retinitis is more central and sight-threatening or when adequate gastrointestinal (GI) absorption is a concern. In such cases, the patient’s transition to oral valganciclovir can be considered when there is evidence of clinical response. In cases where toxicity of ganciclovir and valganciclovir (i.e., severe cytopenias) is a concern and there is not renal insufficiency, or when ganciclovir-resistant CMV is a concern, IV foscar­ net may be used (BI). IV cidofovir is rarely used, unless there is the need to avoid both ganciclovir and foscarnet (CI). Cidofovir administration is complicated by the need to co-administer IV fluid hydration and probenecid to counter the nephrotoxicity of the drug. In addition, IV cidofovir is associated with in­ creased risk of immune recovery uveitis, hypotony, and neutropenia.28 In the presence of immediately sight-threatening lesions (those within 1,500 microns of the fovea or optic disc) at presentation (AIII), some clinicians will supplement systemic therapy with intravitreous injections of ganciclovir or foscarnet, at least initially, to provide immediate, high intraocular levels of the drug and presumably faster control of the retinitis (AIII). Injections are continued on a weekly basis until lesion inactivity is achieved, at which time systemic treatment alone is considered to be adequate for maintenance therapy. The recommendation to supplement systemic therapy with intravitreous injec­ tions is based on pharmacokinetic considerations, but the clinical benefit of such supplementation has not been confirmed in clinical trials. Although intravitreous injections deliver high concentrations of the drug to the target organ immediately while steady-state concentrations in the eye are being achieved over time with systemically delivered medications,19 such injections can be complicated by bacterial or fungal infections, hemorrhage, or retinal detachment. Repeated intravitreous injections of ganciclovir or of foscarnet alone have appeared to be effective for maintenance therapy of CMV retinitis in uncon­ trolled case series,29 but this strategy should be reserved for those individuals who cannot be treated sys­ temically. Intravitreous cidofovir is associated with hypotony and uveitis—and a substantially increased risk of immune recovery uveitis—and should be avoided (AIII).30 For patients without sight-threatening lesions, oral valganciclovir alone often is adequate (AI). The ganciclovir implant, a surgically implanted reservoir of ganciclovir that lasts for approximately 6 months, is no longer manufactured. Treatment with systemic anti-CMV therapy, such as oral valganciclovir for the first 3 to 6 months until ART has induced immune recovery, is beneficial (AII). Ocular complications, such as immune recovery uveitis (IRU) and retinal detachment, are related to lesion size, so minimizing lesion size with anti-CMV therapy until immune recovery is sufficient to control the retinitis is logical. Fur­ thermore, evidence from both the pre-ART and ART eras demonstrate that specific anti-CMV therapy decreases mortality among immune-compromised patients with CMV retinitis.12,20,26,31 Treating Disease Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-5 For patients who have colitis or esophagitis, many HIV specialists recommend anti-CMV ther­ apy for 21 to 42 days (CII) or until signs and symptoms have resolved. IV ganciclovir generally is the therapy of choice and can be switched to oral valganciclovir once the patient can tolerate and absorb oral medications (BI). Foscarnet can be used as an alternative if ganciclovir-related toxicity is treatment-lim­ iting or in cases of ganciclovir-resistant virus (BIII). Oral valganciclovir can be used in patients with mild disease (BIII). Experience treating well-documented CMV pneumonia in patients with HIV infection is limited and anecdotal. Treatment with IV ganciclovir or, alternatively, with foscarnet, is logical (CIII). The opti­ mal duration of therapy and the role of oral valganciclovir have not been established. Therapy for well-documented neurologic disease also has not been extensively studied. Given the poor outcomes in many patients with CMV-related neurologic disease, some experts would initiate therapy with both IV ganciclovir and IV foscarnet, despite the substantial toxicities associated with such an approach (CIII). The optimal duration of therapy and the role of oral valganciclovir have not been established. Special Considerations with Regard to Starting Antiretroviral Therapy Immune reconstitution inflammatory syndrome (IRIS) from CMV may occur in patients who have active retinitis and those who have had CMV retinitis in the recent or distant past. One study demonstrated a substantial increase in immune reconstitution uveitis (IRU) in association with imme­ diate, as opposed to deferred initiation of ART (71% vs. 31%).32 However, in the current era, the rate of clinically significant IRU following initiation of ART appears to be low (approximately 0.02 per person-year). Delaying ART until retinitis is controlled may reduce the likelihood or severity of IRU; however, this strategy must be weighed against the potential for a worsened immunocompromised state and the occurrence of other OIs. Several trials have demonstrated benefits of early versus delayed ART, including reduced risk of mortality, reduced AIDS progression, and shorter time to viral suppression.33–36 Only one study has evaluated the benefits of early ART during treatment of an active OI, and it included few participants with CMV disease.34 As CMV replication usually declines within 1 to 2 weeks after anti-CMV therapy is initiated, most experts would initiate ART no later than 1 to 2 weeks after starting anti-CMV therapy for retinitis, esophagitis, colitis, or other end-organ diseases caused by CMV (CIII). IRIS is a particular concern with any neurologic disease, including CMV encephalitis, ventriculitis, and radiculitis. In these cases, how­ ever, most experts would not defer initiation of ART for more than 2 weeks, although clinical judgment based on individual cases is needed (CIII). Monitoring of Response to Therapy and Adverse Events (Including IRIS) Indirect ophthalmoscopy of both eyes through dilated pupils should be performed at the time of diagnosis of CMV retinitis, 2 weeks after initiating therapy, and monthly thereafter while the patient is on anti-CMV treatment (CIII). The purpose of such examinations is to evaluate efficacy of treatment, identify second eye involvement in cases of unilateral disease, and detect IRU or such complications as retinal detachment. Monthly fundus photographs, using a standardized technique that documents the appearance of the retina, provide the optimum method for following patients and detecting early lesion reactivation. For patients who have experienced immune recovery (CD4+ count >100 cells/mm3 for ≥3 months), the frequency of ophthalmologic follow-up can be decreased to every 3 months, but clinicians should be aware that lesion reactivation and retinal complications still occasionally occur in patients with immune reconstitution. Adverse effects of ganciclovir/valganciclovir include anemia, neutropenia, thrombocytopenia, nausea, diarrhea, and renal dysfunction. Ganciclovir-related neutropenia often can be reversed with granulocyte colony stimulating factor (G-CSF).33,34 In patients receiving ganciclovir or valganciclovir, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-6 complete blood counts and renal function should be monitored twice weekly during induction and at least once weekly during maintenance therapy (AIII). Adverse effects of foscarnet include nephrotox­ icity and electrolyte abnormalities; seizures that occur characteristically in the context of renal insuf­ ficiency; and anemia. Genital ulcers also can occur during foscarnet administration in those who are incontinent to urine due to the toxic effects of excreted drug on exposed skin. Foscarnet often is given in the inpatient setting because of the intensity of monitoring and need for hydration. For patients receiving foscarnet in the outpatient setting, serum electrolytes (including potassium, magnesium, calcium, and phosphorus) and renal function should be measured at least twice weekly during induction and at least weekly during maintenance therapy. Complete blood counts should be monitored weekly (AIII). Adverse effects of cidofovir include dose-related nephrotoxicity, neutropenia, uveitis, and hy­ potony (low intraocular pressure). The risk of severe renal injury from IV cidofovir can be reduced by prehydration and oral probenecid before cidofovir administration. In patients receiving IV cidofovir, analysis of blood urea nitrogen and creatinine levels and urinalysis should be performed before each in­ fusion. Drug administration is contraindicated if renal dysfunction or substantial proteinuria is detected. Particular attention is needed for patients receiving other potentially nephrotoxic medications, including tenofovir disoproxil fumarate. Periodic ophthalmologic examinations are needed to monitor for cidofo­ vir-associated uveitis or hypotony, even when CMV disease does not include retinitis. As noted previously, patients with CMV retinitis must have careful ophthalmologic monitoring to detect and manage the wide range of complications related to CMV, the drugs used to treat CMV, and IRIS. IRU, an ocular form of IRIS presumed to be an adverse immunologic reaction to CMV, is charac­ terized by inflammation in the anterior chamber or vitreous body in the setting of immune recovery after initiation of ART. IRU usually is observed in patients with a substantial rise in CD4 cell count in the first 4 to 12 weeks after initiation of ART.28,35–38 The estimated incidence of IRU is 0.02/person-year after immune recovery.39 Ocular complications of IRU include macular edema and development of epiretinal membranes, which can cause loss of vision. Although the inflammatory reactions seen at the onset of IRU can be transient as immune reconstitution occurs, the complications may persist, permanently com­ promising vision. Treatment of IRU usually consists of some type of corticosteroid therapy. The benefit of an­ ti-CMV therapy is unclear.35,40 Many experts would use both corticosteroids and anti-CMV therapy (CIII). Data are insufficient on which to base a recommendation regarding the preferred route of cor­ ticosteroid administration; periocular, intravitreous, and oral administration all have been reported to be potentially successful. When oral corticosteroids are used, a short course rather than chronic therapy usually is recommended (BIII).41 IRU can occur months or years after successful treatment of CMV ret­ initis in patients with a history of CMV retinitis who subsequently start taking ART or have such therapy optimized. People with advanced HIV remain at risk for development of CMV retinitis prior to immune re­ constitution, even after initiation of ART.42,43 Development of CMV retinitis in the setting of recent ART initiation should be treated with systemic anti-CMV therapy, similar to any patient with CMV retinitis, and the same ART regimen should be continued (AI). Corticosteroids are not recommended (AIII). In addition, in the absence of uveitis, corticosteroids should not be used in patients undergoing treatment for CMV retinitis who have worsening of retinitis upon ART initiation. In this situation, anti-CMV ther­ apy and ART regimens should be continued (AIII). Managing Treatment Failure Failure of therapy for CMV retinitis or reactivation of lesions is most likely in patients who do not have substantial immune reconstitution after initiation or optimization of ART.44 Treatment failure Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-7 also may be a result of inadequate anti-CMV drug levels in the eye, CMV drug resistance, or nonadher­ ence. Many experts believe that early progression of disease (enlargement of lesions or new lesions) is most often caused by the limited intraocular penetration of systemically administered drugs.40,45,46 When reactivation of lesions occurs in patients receiving maintenance therapy, retinitis usually can be controlled with re-induction of the same drug used for maintenance followed by re-institution of maintenance therapy (BIII).47 Ganciclovir and foscarnet in combination appear to be superior in efficacy to either agent alone and should be considered for patients whose disease does not respond to single-drug therapy and for patients with continued progression or multiple reactivations of retinitis (CIII).47 This drug combination, however, is associated with substantial toxicity. Drug resistance can occur in patients receiving long-term anti-CMV therapy.48–51 Drug resistance rates of approximately 25% per person-year were reported in the pre-ART era48,52,53 for ganciclovir, foscarnet, and cidofovir.48,49 In the ART era, the rate of resistance appears to be lower (approximately 5% per person-year).54 Low-level resistance to ganciclovir occurs through mutations in the CMV UL97 (phosphotransferase) gene, and high-level resistance to ganciclovir typically occurs because of mu­ tations in both the CMV UL97 and UL54 (DNA polymerase) genes.50,55–59 Resistance to foscarnet or cidofovir occurs because of mutations in the CMV UL54 gene. High-level resistance to ganciclovir often is associated with cross-resistance to cidofovir57 and occasionally to foscarnet.58 Although early CMV disease progression typically is not a result of drug resistance, late CMV reactivation may be. By them­ selves, peripheral blood CMV viral load measurements have poor positive predictive value for treatment failure. Ganciclovir resistance in patients who fail therapy can be detected by CMV DNA PCR of blood specimens followed by detection of UL97 mutations by DNA sequencing or by a point mutation assay60 –62 Sequencing the UL97 gene from PCR-amplified specimens from blood can be accomplished in less than 48 hours and correlates well with conventional drug susceptibility testing and clinical outcomes.62 Circulating CMV in blood and vitreous fluid have identical UL97 sequences in more than 90% of cases;63 therefore, evaluating the blood for resistance is reasonable, and detection of resistance in the blood or urine correlates with clinical behavior of the retinitis in most cases.64 Viral culture and suscep­ tibility testing and viral DNA sequencing often are not available in clinical laboratories because they are too time consuming or costly. UL97 mutants usually respond to foscarnet, as do some UL54 mutants.65 Many clinicians will treat ganciclovir-resistant CMV with a series of intravitreous injections of foscarnet and/or IV foscarnet or cidofovir (CIII). Preventing Recurrence When to Start Maintenance Therapy After induction therapy for CMV retinitis, chronic maintenance therapy should be contin­ ued,9,14,19,22,66 until immune reconstitution occurs as a result of ART (AI). Maintenance therapy is started after induction has achieved control of retinitis, as evidenced by resolved or markedly reduced retinal lesion opacity, indicating virus inactivity. Although several regimens are effective for chronic suppres­ sion—including parenteral ganciclovir, parenteral foscarnet, and parenteral cidofovir—oral valganci­ clovir may be the easiest and least toxic to administer to an outpatient population, provided that GI absorption is adequate. Systemic therapy must be administered to prevent disease in the contralateral eye until immune reconstitution has occurred. The choice of regimen (i.e., which drug[s] and whether given intravitreously, orally, or intra­ venously) should be made in consultation with an ophthalmologist. Considerations should include the anatomic location of the retinal lesion; vision in the contralateral eye; and a patient’s immunologic and virologic status, comorbidities, concomitant medications, and response to ART. After resolution of the acute CMV syndrome and initiation of effective ART, chronic mainte­ Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-8 nance therapy is not routinely recommended for CMV GI disease, pneumonitis, and central nervous system disease unless there is concurrent retinitis, there have already been recurrent infections, or severe disease was present initially (BII). When to Stop Maintenance Therapy Maintenance therapy can be discontinued safely in adults and adolescents with CMV retinitis whose lesions have been treated for at least 3 to 6 months and are inactive and who have had sustained (i.e., 3–6 months) increases in CD4 cell counts to >100 cells/mm3 in response to ART (AII).4,67–73 Such decisions should be made in consultation with an ophthalmologist. A 3% reactivation rate is reported in patients whose anti-CMV therapy has been discontinued for immune recovery, and no level of CD4 cell count is absolutely safe (reactivations have been reported at CD4 cell counts of 1,250 cells/mm3). Therefore, in all patients for whom anti-CMV maintenance therapy has been discontinued, ophthalmologic monitoring for early detection of CMV relapse and for IRU should be performed at least every 3 months and periodically after immune reconstitution (AIII). Monitoring CMV viral load in blood has poor positive predictive value for relapse of retinitis and, therefore, is not recommended (AII).16 Reactivation of CMV retinitis occurs frequently in patients whose CD4 cell counts have de­ creased to <50 cells/mm3 and whose anti-CMV maintenance therapies have been discontinued.74 There­ fore, reinstitution of maintenance therapy should occur when the CD4 cell count has decreased to <100 cells/mm3 (AIII). Special Considerations During Pregnancy The diagnostic considerations among pregnant women are the same as for nonpregnant women. Indications for treatment of CMV infection during pregnancy are the same as for nonpregnant people with HIV (AIII). For retinal disease, use of intravitreous injections for local therapy should be consid­ ered in the first trimester, if possible, to limit fetal exposure to systemically administered antiviral drugs (BIII). Systemic antiviral therapy should then be started after the first trimester. For life-threatening in­ dications, treatment with systemic antiviral therapy during the first trimester may be necessary. Ganciclovir is embryotoxic among rabbits and mice and teratogenic (i.e., cleft palate, anophthal­ mia, aplastic kidney and pancreas, and hydrocephalus) in rabbits.75–77 However, safe use in all trimesters of human pregnancy after organ transplantation and in other patient populations has been reported.75–79 Foscarnet is associated with an increase in skeletal anomalies or variants in rats and rabbits. No experience with use early in human pregnancy has been reported. A single case report of use in the third trimester described normal infant outcome.80 Because toxicity of foscarnet is primarily renal, weekly monitoring of amniotic fluid volumes by ultrasound is recommended after 20 weeks of gestation to de­ tect oligohydramnios if foscarnet is used. Cidofovir is embryotoxic and teratogenic (i.e., meningomyelocele and skeletal abnormalities) among rats and rabbits. No experience with use of cidofovir in human pregnancy has been reported; use in pregnancy is not recommended (AIII). On the basis of limited data, toxicity reports, and ease of use of the various drugs, valganciclo­ vir is recognized as the treatment of choice during pregnancy (BIII). The fetus should be monitored by fetal-movement counting in the third trimester and by periodic ultrasound monitoring after 20 weeks of gestation to look for evidence of hydrops fetalis indicating substantial anemia. No data exist to support use of pooled or CMV-specific intravenous immunoglobulin in this clinical situation. Primary infection, reactivation, and reinfection with a different strain of CMV during pregnancy (non-primary infection)81 all can lead to in utero transmission and congenital CMV. Maternal ART in pregnancy has been associated with decreased rates of perinatal/early postnatal CMV and decreased Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-9 CMV-related clinical symptoms among infants exposed to or infected with HIV.82 Recent studies indi­ cate the prevalence of congenital CMV among infants in the United States who are exposed to HIV is 1.2% to 1.3%.83 Risk factors for congenital CMV include mothers with CD4+ <200 cells/mm3, mothers with urinary CMV shedding,84 and HIV transmission to infants. Maternal CMV and infant congenital CMV also have been associated with increased risk of HIV perinatal transmission in pregnant women with HIV who have not received antenatal ART.85 In women diagnosed with primary CMV infection in pregnancy, the fetus should be monitored by periodic ultrasound after 20 weeks gestation (CIII). In studies in HIV-uninfected populations, about 5% to 25% of newborns infected with CMV had ultrasound evidence of congenital infection (e.g., cere­ bral calcifications, abdominal and liver calcifications, hydrops, microcephaly, ventriculomegaly, ascites, and echogenic fetal bowel).86 Any ultrasound findings suspicious for congenital CMV infection should prompt consideration of invasive testing (i.e., amniocentesis) for definitive diagnosis. Referral to a ma­ ternal–fetal medicine specialist for evaluation, counseling, and potential further testing is recommended. Potential noninvasive biomarkers for predicting congenital CMV infection are under study.87 If fetal CMV infection is confirmed, no standard therapy exists for in utero treatment. Available clinical studies support the possible effectiveness and safety of CMV hyperimmune globulin in preg­ nancy for prevention or treatment of congenital CMV.88,89 A nonrandomized trial of CMV hyperimmune globulin in women not infected with HIV with primary CMV infection in pregnancy found decreased incidence of having a symptomatic newborn at birth90 and regression of fetal cerebral abnormalities;91 however, a well-designed, prospective, randomized, placebo-controlled study with relatively large sam­ ple size subsequently found no benefit of CMV hyperimmune globulin in pregnant women.88,92,93 A second randomized clinical trial that planned to enroll 800 patients with primary CMV infection at <24 weeks gestation was stopped for futility after enrollment of 399 participants when a planned interim analysis suggested that complete enrollment would not provide a significant outcome.93 Routine screening for CMV infection in pregnancy is not recommended in the absence of effec­ tive in utero therapy. Treatment of asymptomatic maternal CMV infection during pregnancy solely to prevent infant infection is not indicated (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-10 Recommendations for Treating Cytomegalovirus Infections Preventing CMV Disease • CMV end-organ disease is best prevented by using ART to maintain CD4+ count >100 cells/mm3. Managing CMV Retinitis • The choice of therapy for CMV retinitis should be individualized, based on tolerance of systemic medications; prior exposure to anti-CMV drugs; and on the location of lesions (AIII). • Given the evident benefits of systemic therapy in preventing contralateral eye involvement, reducing CMV visceral disease, and improving survival, treatment should include systemic therapy whenever feasible. Initial Therapy Followed by Chronic Maintenance Therapy—For Immediate Sight-Threatening Lesions (within 1,500 microns of the fovea) Preferred Therapy • Ganciclovir 5 mg/kg IV q12h for 14–21 days, then 5 mg/kg IV daily (AI), or • Ganciclovir 5 mg/kg IV q12h for 14–21 days, then valganciclovir 900 mg PO daily (AI), or • Valganciclovir 900 mg PO q12h for 14–21 days, then 900 mg once daily (AI); or with or without • Intravitreous injections of ganciclovir (2 mg/injection) or foscarnet (2.4 mg/injection) repeat weekly until lesion inactivity is achieved. This is to provide higher intraocular levels of drug and faster control of the infection until steady-state intraocular ganciclovir concentrations are achieved. (AIII) • Note: IV ganciclovir can be switched to oral valganciclovir if the patient is clinically improving and there are no concerns about gastrointestinal absorption. Alternative Therapy • Intravitreous injections as listed above (AIII); plus one of the following systemic therapies: • Foscarnet 60 mg/kg IV q8h or 90 mg/kg IV q12h for 14–21 days, then 90–120 mg/kg IV q24h (BI), or • Cidofovir 5 mg/kg/week IV for 2 weeks, then 5 mg/kg every other week with saline hydration before and after therapy and probenecid 2 g PO 3 hours before the dose followed by 1 g PO 2 hours after the dose, and 1 g PO 8 hours after the dose (total of 4 g) (CI). Cidofovir is contraindicated in patients with a serum creatinine >1.5 mg/dL, a calculated creatinine clearance ≤55 mL/min or a urine protein ≥100 mg/dL (equivalent to ≥2+ proteinuria). Given the nephrotoxic potential of cidofovir, cautious use of cidofovir with tenofovir is advised • Note: This regimen should be avoided in patients with sulfa allergy because of cross-hypersensitivity with probenecid. For Peripheral Lesions • Valganciclovir 900 mg PO q12h for 14–21 days, then 900 mg once daily (AI) for the first 3–6 months until ART-induced immune recovery (AII). IRU • Minimizing lesion size by treating all CMV retinitis lesions until there is immune recovery may reduce the incidence of IRU (BII). • IRU might develop in the setting of immune reconstitution. Treatment of IRU • Periocular or intravitreal corticosteroid or a short course of systemic steroid (BIII). Stopping Chronic Maintenance Therapy for CMV Retinitis • CMV treatment for at least 3–6 months, and lesions are inactive, and with CD4+ count >100 cells/mm3 for 3–6 months in response to ART (AII). • Therapy should be discontinued only after consultation with an ophthalmologist, taking into account magnitude and duration of CD4 cell count increase, anatomic location of the lesions, vision in the contralateral eye, and the feasibility of regular ophthalmologic monitoring. • Routine (i.e., every 3 months) ophthalmologic follow-up is recommended after stopping chronic maintenance therapy for early detection of relapse or IRU, and then periodically after sustained immune reconstitution (AIII). Reinstituting Chronic Maintenance for CMV Retinitis • CD4 count <100 cells/mm3 (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-11 Managing CMV Esophagitis or Colitis • Doses are the same as for CMV retinitis. Preferred Therapy • Ganciclovir 5 mg/kg IV q12h; may switch to valganciclovir 900 mg PO q12h once the patient can absorb and tolerate PO therapy (BI). Alternative Therapy • Foscarnet 60 mg/kg IV q8h or 90 mg/kg IV q12h (BIII)—for patients with treatment-limiting toxicities to ganciclovir or with ganciclovir resistance; or • Oral valganciclovir may be used if symptoms are not severe enough to interfere with oral absorption (BIII); or Duration of Anti-CMV Therapy • 21–42 days or until signs and symptoms have resolved (CII). Note: Maintenance therapy is usually not necessary, but should be considered after relapses (BII). Managing Well-Documented CMV Pneumonitis • Doses are the same as for CMV retinitis. • Treatment experience for CMV pneumonitis in HIV patients is limited. Use of IV ganciclovir or IV foscarnet is reasonable (CIII). • The role of oral valganciclovir has not been established. • The optimal duration of therapy has not been established. Managing CMV Neurological Disease • Doses are the same as for CMV retinitis. • Treatment should be initiated promptly. • Combination of ganciclovir IV plus foscarnet IV to stabilize disease and maximize response (CIII). • Optimal duration of therapy has not been established. • The role of oral valganciclovir has not been established. • Optimize ART to achieve viral suppression and immune reconstitution (BIII). Key to Acronyms: ART = antiretroviral therapy; BID = twice a day; CMV = cytomegalovirus; IRU = immune recovery uveitis; PO = orally; IV = intravenously; q(n)h = every “n” hours References 1. Jabs DA, Van Natta ML, Kempen JH, et al. Characteristics of patients with cytomegalovirus retinitis in the era of highly active antiretroviral therapy. Am J Ophthalmol. 2002;133(1):48-61. Available at: http:// www.ncbi.nlm.nih.gov/pubmed/11755839. 2. Dieterich DT, Rahmin M. Cytomegalovirus colitis in AIDS: presentation in 44 patients and a review of the literature. 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Control Clin Trials. 1992;13(1):22-39. Available at: 67. Tural C, Romeu J, Sirera G, et al. Long-lasting remission of cytomegalovirus retinitis without maintenance therapy in human immunodeficiency virus-infected patients. J Infect Dis. 1998;177(4):1080-1083. Available at: 68. Vrabec TR, Baldassano VF, Whitcup SM. Discontinuation of maintenance therapy in patients with quiescent cytomegalovirus retinitis and elevated CD4+ counts. Ophthalmology. 1998;105(7):1259-1264. Available at: 69. Macdonald JC, Torriani FJ, Morse LS, Karavellas MP, Reed JB, Freeman WR. Lack of reactivation of cytomegalovirus (CMV) retinitis after stopping CMV maintenance therapy in AIDS patients with sustained elevations in CD4 T cells in response to highly active antiretroviral therapy. J Infect Dis. 1998;177(5):1182-1187. Available at: 70. Whitcup SM, Fortin E, Lindblad AS, et al. Discontinuation of anticytomegalovirus therapy in patients with HIV infection and cytomegalovirus retinitis. JAMA. 1999;282(17):1633-1637. Available at: http:// www.ncbi.nlm.nih.gov/pubmed/10553789. 71. Jabs DA, Bolton SG, Dunn JP, Palestine AG. Discontinuing anticytomegalovirus therapy in patients with immune reconstitution after combination antiretroviral therapy. Am J Ophthalmol. 1998;126(6):817-822. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-17 72. Jouan M, Saves M, Tubiana R, et al. Discontinuation of maintenance therapy for cytomegalovirus retinitis in HIV-infected patients receiving highly active antiretroviral therapy. AIDS. 2001;15(1):23-31. Available at: 73. Walmsley SL, Raboud J, Angel JB, et al. Long-term follow-up of a cohort of HIV-infected patients who discontinued maintenance therapy for cytomegalovirus retinitis. HIV Clin Trials. 2006;7(1):1-9. Available at: 74. Torriani FJ, Freeman WR, Macdonald JC, et al. CMV retinitis recurs after stopping treatment in virological and immunological failures of potent antiretroviral therapy. AIDS. 2000;14(2):173-180. Available at: 75. Faqi AS, Klug A, Merker HJ, Chahoud I. Ganciclovir induces reproductive hazards in male rats after short-term exposure. Hum Exp Toxicol. 1997;16(9):505-511. Available at: pubmed/9306137. 76. Miller BW, Howard TK, Goss JA, Mostello DJ, Holcomb WL, Jr., Brennan DC. Renal transplantation one week after conception. Transplantation. 1995;60(11):1353-1354. Available at: gov/pubmed/8525535. 77. Pescovitz MD. Absence of teratogenicity of oral ganciclovir used during early pregnancy in a liver transplant recipient. Transplantation. 1999;67(5):758-759. Available at: pubmed/10096536. 78. Adler SP, Nigro G, Pereira L. Recent advances in the prevention and treatment of congenital cytomegalovirus infections. Semin Perinatol. 2007;31(1):10-18. Available at: gov/pubmed/17317422. 79. Seidel V, Feiterna-Sperling C, Siedentopf JP, et al. Intrauterine therapy of cytomegalovirus infection with valganciclovir: review of the literature. Med Microbiol Immunol. 2017;206(5):347-354. Available at: 80. Alvarez-McLeod A, Havlik J, Drew KE. Foscarnet treatment of genital infection due to acyclovir-resistant herpes simplex virus type 2 in a pregnant patient with AIDS: case report. Clin Infect Dis. 1999;29(4):937-938. Available at: 81. Yamamoto AY, Mussi-Pinhata MM, Boppana SB, et al. Human cytomegalovirus reinfection is associated with intrauterine transmission in a highly cytomegalovirus-immune maternal population. Am J Obstet Gynecol. 2010;202(3):297 e291-298. Available at: 82. Frederick T, Homans J, Spencer L, et al. The effect of prenatal highly active antiretroviral therapy on the transmission of congenital and perinatal/early postnatal cytomegalovirus among HIV-infected and HIV-exposed infants. Clin Infect Dis. 2012;55(6):877-884. Available at: pubmed/22675157. 83. Purswani MU, Russell JS, Dietrich M, et al. Birth prevalence of congenital cytomegalovirus infection in HIV-exposed uninfected children in the era of combination antiretroviral therapy. J Pediatr. 2020;216:82-87.e82. Available at: S0022347619311618?via%3Dihub. 84. Adachi K, Xu J, Ank B, et al. Cytomegalovirus urinary shedding in HIV-infected pregnant women and congenital cytomegalovirus infection. Clin Infect Dis. 2017;65(3):405-413. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV K-18 ncbi.nlm.nih.gov/28369278/. 85. Adachi K, Xu J, Ank B, et al. Congenital cytomegalovirus and HIV perinatal transmission. Pediatr Infect Dis J. 2018;37(10):1016-1021. Available at: 86. Society for Maternal-Fetal M, Hughes BL, Gyamfi-Bannerman C. Diagnosis and antenatal management of congenital cytomegalovirus infection. Am J Obstet Gynecol. 2016;214(6):B5-B11. Available at: https:// www.ncbi.nlm.nih.gov/pubmed/26902990. 87. Tanimura K, Yamada H. Potential biomarker for predicting congenital cytomegalovirus infection. Int J Mol Sci. 2018;19(12):3760. Available at: 88. Kagan KO, Enders M, Schampera MS, et al. Prevention of maternal-fetal transmission of cytomegalovirus after primary maternal infection in the first trimester by biweekly hyperimmunoglobulin administration. Ultrasound Obstet Gynecol. 2019;53(3):383-389. Available at: nih.gov/29947159/. 89. Nigro G, Adler SP. High-dose cytomegalovirus (CMV) hyperimmune globulin and maternal CMV DNAemia independently predict infant outcome in pregnant women with a primary CMV infection. Clin Infect Dis. 2020;71(6):1491-1498. Available at: 90. Nigro G, Adler SP, La Torre R, Best AM, Congenital Cytomegalovirus Collaborating Group. Passive immunization during pregnancy for congenital cytomegalovirus infection. N Engl J Med. 2005;353(13):1350-1362. Available at: 91. Nigro G, Torre RL, Pentimalli H, et al. Regression of fetal cerebral abnormalities by primary cytomegalovirus infection following hyperimmunoglobulin therapy. Prenat Diagn. 2008;28(6):512-517. Available at: 92. Revello MG, Lazzarotto T, Guerra B, et al. A randomized trial of hyperimmune globulin to prevent congenital cytomegalovirus. N Engl J Med. 2014;370(14):1316-1326. Available at: nih.gov/pubmed/24693891. 93. Hughes B. LB17. Randomized trial to prevent congenital cytomegalovirus (CMV). Open Forum Infect Dis. 2019;6:S1000-S1001. Available at: S1000/5603805. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-1 Hepatitis B Virus Infection Updated: November 14, 2023 Reviewed: January 10, 2024 Epidemiology Hepatitis B virus (HBV) is the leading cause of chronic liver disease worldwide.1-5 Globally and in North America, approximately 10% of people with HIV have evidence of chronic HBV infection.6-8 Transmission routes vary geographically, with perinatal and early-childhood exposures responsible for most HBV transmission in higher-prevalence regions.9 In low-prevalence regions—such as Europe and North America—a large proportion of transmission is through sexual contact and injection drug use, but perinatal transmission is becoming prevalent due to the increasing foreign-born population.10 Although the general modes of transmission are similar to those of HIV, HBV is transmitted more efficiently than HIV.1,2 The risk of progression to chronic HBV infection decreases with age and is 90% among those with HBV infection before 1 year of age, 25% to 50% among those with HBV infection between 1 year and 5 years of age, and <5% among those infected with HBV as adults.10,11 People with HIV are at increased risk for developing chronic HBV infection.12 Genotypes of HBV (A–J) have been identified, and their geographic distributions differ.13 Genotype A is most common among people with HBV infection in North America and Western Europe and genotypes B and C among people with HBV infection in Asia.14 Clinical Manifestations Acute HBV infection is asymptomatic in approximately 70% of people infected; <1% of people with HBV infection develop fulminant hepatic failure.3,15 When symptoms manifest, they may include right upper quadrant abdominal pain, nausea, vomiting, fever, and arthralgias with or without jaundice. HBV has an average incubation period of 90 days (range 60–150 days) from exposure to onset of jaundice and 60 days (range 40–90 days) from exposure to onset of abnormal liver enzymes. Most people with chronic HBV infection are asymptomatic or have nonspecific symptoms, such as fatigue. Between 15% and 40% of people with chronic HBV infection will develop cirrhosis, hepatocellular carcinoma (HCC), or liver failure, and up to 25% of people will die prematurely from complications of chronic HBV infection.16 Diagnosis The Centers for Disease Control and Prevention, the United States Preventive Services Taskforce, and the American Association for the Study of Liver Disease (AASLD) recommend testing people with HIV for chronic HBV infection.17-19 Initial testing should include serologic testing for HBV surface antigen (HBsAg), hepatitis B core antibody (anti-HBc total), and hepatitis B surface antibody (anti-HBs) (AI). In acute infection, HBsAg can be detected 4 weeks (range 1–9 weeks) after exposure, and anti-HBc immunoglobulin M is usually detectable at the onset of symptoms. Chronic HBV infection is defined as persistent HBsAg detected on two occasions at least 6 months apart.19 People with chronic HBV infection should be tested further for HBV e antigen (HBeAg), antibody to HBeAg (anti-HBe), and HBV DNA. Active disease, which can be HBeAg negative or HBeAg positive, can be distinguished from inactive disease by the presence of serum HBV DNA and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-2 persistent or fluctuating alanine transaminase (ALT) elevations.19 People whose past infection has resolved are HBsAg negative with positive anti-HBs and/or anti-HBc, although covalently closed circular DNA (cccDNA) may remain in hepatocyte nuclei.3,20 With cccDNA in hepatocyte nuclei, a person with severe immune suppression—such as seen with anti-CD20 therapy or after stem cell transplant—may become serum HBsAg positive again with HBV viremia.21,22 The presence of an isolated anti-HBc test result usually signifies infection with HBV in the past with subsequent loss of anti-HBs and occurs in 7% to 19% of people with HIV.23-27 Incidence of HBV viremia among people with HIV and isolated anti-HBc ranges from 1% to 36%.23,25,28-30 The clinical significance of isolated anti-HBc is unknown,23,27,30-32 but in people with HIV, it may indicate chronic or, more likely, resolved HBV infection.26,33,34 In a low-prevalence country—such as the United States—isolated anti-HBc also may represent a false-positive result.26,33,35,36 People with HIV—particularly those with underlying hepatitis C virus (HCV) coinfection—have a higher frequency of isolated anti-HBc.26,37,38 Diagnosing HBV Disease Progression and the Role of Assessment of Liver Fibrosis Compared with people with HBV mono-infection, those with HIV/HBV coinfection have higher levels of HBV viremia and lower likelihood of resolved infection following acute HBV infection.39 Among people with HBV mono-infection, HBV DNA suppression, anti-HBe seroconversion (to anti-HBe-seronegativity), HBsAg loss, and acquisition of anti-HBs are all associated with a decreased incidence of cirrhosis and HCC40-42 and improved survival.43-46 In comparison, people with HIV/HBV coinfection are usually more likely to have detectable HBeAg,39,47 lower rates of seroconversion to anti-HBe, and increased risk of HCC and liver-related mortality and morbidity.48,49 Chronic HBV infection is a dynamic disease with a number of phases that are associated with either active or inactive chronic hepatitis and include the following: the immune-tolerant phase (normal ALT [upper limits of normal 19–25 U/L for women and 29–33 U/L for men], HBeAg positive, high HBV DNA); the immune active phase (HBeAg positive or negative, detectable HBV DNA, elevated ALT); and the inactive hepatitis B phase (HBeAg negative, anti-HBe positive, low or undetectable HBV DNA, normal ALT).19 Duration of disease phases is different in those who acquire infection as neonates or young children than in those who acquire infection as adults. The immune-tolerant phase occurs primarily among people who acquired HIV perinatally. Clinicians should be knowledgeable about these phases among people with HBV mono-infection to determine who needs treatment and who should be monitored (see the AASLD 2018 Hepatitis B Guidance). In HIV/HBV coinfection, monitoring and treatment also are focused on the simultaneous treatment of both viruses. People with anti-HBe seroconversion and HBeAg loss usually transition into the inactive hepatitis B phase.16 This transition can be spontaneous or associated with effective HBV treatment. In some instances, increased levels of ALT may precede a decline in HBV DNA that is accompanied by anti-HBe seroconversion—that is, loss of HBeAg and development of anti-HBe.50 However, such spontaneous HBeAg conversion rates appear to be lower among people with HIV/HBV coinfection than among people with HBV mono-infection. People in the inactive state remain at risk of reactivation of HBV infection and development of HCC, but the risk is lower than for people with active HBV replication. In any person, the reemergence of abnormal liver enzyme tests may reflect HBeAg-negative chronic HBV disease, a result of mutations in the basal core and precore promoter regions of the virus.16 Although people who are HBeAg negative usually have lower levels of HBV DNA, they experience unrelenting but fluctuating disease progression, with changing HBV DNA Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-3 levels.51 People in the inactive phase still require HBeAg, ALT, and HBV DNA monitoring. Persistent low-level serum ALT abnormalities may be associated with significant liver disease, although normal ALT levels also may be seen in the setting of cirrhosis.51 When chronic HBV infection is diagnosed, a patient should be linked to care and have a complete history and physical examination for signs of cirrhosis or HCC. In addition, clinicians should perform HBV serologic testing (HBeAg/anti-HBe and HBV DNA) and other laboratory testing— complete blood count, ALT, aspartate aminotransferase (AST), albumin, total bilirubin, alkaline phosphatase, international normalized ratio (INR), and anti-hepatitis A virus—to determine the need for vaccination, abdominal ultrasound, and liver fibrosis assessments at the initial visit and monitor these every 6 to 12 months.3 People with chronic HBV infection are at increased risk of HCC; therefore, HCC surveillance every 6 months is required for people who are cirrhotic and for people in the following groups who are at increased risk of disease progression: Asian males older than age 40, Asian females older than age 50, and males older than age 20 who are from sub-Saharan Africa.52 People with HIV/HBV coinfection are at increased risk of HCC,53 and some experts recommend screening people who have HIV/HBV coinfection and who are older than 40 years of age for HCC. Assessment of the patient’s liver fibrosis stage is important. Increasing evidence indicates that noninvasive methods (i.e., elastography and serum markers) to evaluate liver fibrosis can be used to determine fibrosis in HBV infection.54 The decision to perform a liver biopsy should be individualized, but the procedure is rarely necessary.3 Preventing Exposure HBV infection is transmitted primarily through percutaneous or mucosal exposure to infectious blood or body fluids. Therefore, people with HIV should be counseled about transmission risks for HBV infection and encouraged to avoid behaviors associated with such transmission (AIII). Such counseling should emphasize sexual transmission and the risks associated with sharing needles and syringes, unregulated tattooing, or body piercing. Preventing Disease Recommendations for Preventing Hepatitis B Virus Infection Indications for HepB Vaccination • People without chronic HBV infection and without immunity to HBV infection (anti-HBs <10 mIU/mL) (AII). • People with isolated anti-HBc (BII). Recommend one standard dose of HepB vaccine followed by anti-HBs at 1–2 months. If the titer is >100 mIU/mL, no further vaccination is needed, but if the titer is <100 mIU/mL, a complete series of HepB vaccine should be completed (see below for Vaccination Schedule), followed by anti-HBs testing (BII). If anti-HBs quantitative titer is not available, then recommend a complete HepB vaccine series followed by qualitative anti-HBs testing (BII). • Although vaccine response is better in people with CD4 >350 cells/mm3, vaccination should not be deferred in people with a lower CD4 count because some people with CD4 <350 cells/mm3 do respond to vaccination (AII). Vaccination Schedule • HepB vaccine IM (Engerix-B 40 mcg [2 injections of 20 mcg each] or Recombivax HB 20 mcg [2 injections of 10 mcg each]) at 0, 1, and 6 months (these doses are considered a “double-dose,” three-dose series) (AII); or • Combined HepA and HepB vaccine (Twinrix) 1 mL IM as a three-dose series (at 0, 1, and 6 months) (AII); or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-4 • Vaccine conjugated to CpG (Heplisav-B) IM at 0 and 1 months for vaccine-naive patients (AII) • Anti-HBs should be obtained 1 to 2 months after completion of the vaccine series. For Vaccine Nonresponders • Response to HepB vaccination, defined as anti-HBs ≥10 mIU/ml, should be documented 4 weeks after the last dose of vaccine (AII). • Revaccinate with a second double-dose, three-dose series of recombinant HBV vaccine (Engerix-B 40 mcg [2 injections of 20 mcg each] or Recombivax HB 20 mcg [2 injections of 10 mcg each]) (BIII); or • Revaccinate with two-dose series of HepBCpG (Heplisav-B) (BIII). • For people with low CD4 count at the time of first vaccination series, some experts might delay revaccination until after a CD4 count ≥200 is achieved and sustained with ART (CIII). Some experts consider that a double-dose, four-dose series of recombinant HepB vaccine (Engerix-B 40 mcg or Recombivax 20 mcg at 0, 1, 2, and 6 months) may produce a better immunologic response, but this approach has not been demonstrated to be superior to a double-dose, three-dose series. Other Considerations • HepA vaccination is recommended for all people who are total HAV antibody negative and have chronic liver disease, are men who have sex with men, or are injection drug users (AIII). • Antibody response to HepA vaccine should be assessed 1 month after completion of vaccination series. If total anti-HAV (IgG and IgM) is negative, people should be revaccinated when the CD4 count is >200 cells/mm3 (BIII). • Pregnant people with chronic HBV infection who have not already received the HepA vaccine series should be screened for immunity to HAV infection. If they screen negative for total anti-HAV, they should receive the HepA vaccine series (AIII). Key: anti-HBc = hepatitis B core antibody; anti-HBs = hepatitis B surface antibody; ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CpG = cytosine phosphoguanine; HAV = hepatitis A virus; HBV = hepatitis B virus; HepA = hepatitis A; HepB = hepatitis B; IgG = immunoglobulin G; IgM = immunoglobulin M; IM = intramuscular; mIU/mL = milli-international units per milliliter All family members and sexual contacts of people with HBV infection should be tested, and all susceptible contacts should receive hepatitis B (HepB) vaccine regardless of whether they have HIV (AII). HepB vaccination is the most effective way to prevent HBV infection and its consequences. All people with HIV who are susceptible to HBV infection should receive HepB vaccination with one of the available vaccines (see below) (AII) or with the combined hepatitis A (HepA) and HepB vaccine (Twinrix) (AII). All people with HIV should be screened for HBV infection, and screening should include HBsAg, anti-HBs, and anti-HBc.17,18,51 A person who is seropositive for anti-HBc and anti-HBs has resolved infection and does not need vaccination. Similarly, the presence of anti-HBs alone at levels ≥10 mIU/mL after completion of the vaccine series is consistent with seroprotection,55 and no further vaccinations are required.56 The interpretation is less clear among people with the isolated anti-HBc pattern (HBsAg negative, anti-HBc positive, anti-HBs negative). Aside from false-positive results, this pattern may signify infection in the distant past with subsequent loss of anti-HBs.57 Most people with HIV with isolated anti-HBc are HBV DNA negative and not immune to HBV infection38; therefore, routinely checking HBV DNA is not recommended. However, such people should be vaccinated with one standard dose of HepB vaccine (Engerix-B or Recombivax HB) or one dose of Heplisav-B, and anti-HBs titers should be checked 1 to 2 months after vaccination (BII). If the anti-HBs titer is >100 mIU/mL, no further vaccination is needed, but if the titer is <100 mIU/mL, a Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-5 complete series of the same HepB vaccine should be completed and followed by anti-HBs testing (BII).58 The cutoff of 100 mIU/mL is used in this situation because one study demonstrated that 100% of people with isolated anti-HBc who achieved a titer of 100 mIU/mL after a booster dose maintained an anti-HBs response for >18 months compared with only 23% of those who achieved a titer of 10 to 100 mIU/mL.58 If anti-HBs quantitative titers are not available, then the complete series of HepB vaccine should be completed followed by qualitative anti-HBs testing (BII). Available adult single-antigen HepB vaccines include two recombinant HBsAg vaccines (Engerix-B and Recombivax HB) and a recombinant HBsAg vaccine conjugated to a cytosine phosphoguanine oligonucleotide (CpG 1018) adjuvant, which is a toll-like receptor 9 agonist (Heplisav-B). The magnitude and duration of immunogenicity to HepB vaccination with the recombinant vaccines in adults with HIV are significantly lower than in healthy adults who are HIV seronegative.56,59-61 Factors associated with poor response to recombinant vaccines include low CD4 T lymphocyte (CD4) cell counts,59,62-67 presence of detectable HIV RNA,63,67,68 coinfection with HCV, occult HBV infection, and the general health status of the host.25,38,69-73 Although vaccine response is better when CD4 counts are >350 cells/mm3, vaccination should not be deferred until CD4 counts increase to >350 cells/mm3 because some people with HIV with CD4 counts <350 cells/mm3 do respond to vaccination (AII). The Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV (the Panel) recommends hepatitis B vaccination for all non-immune patients either with double-dose vaccine Engerix-B or Recombivax HB as the primary series (AII), combined HepA and HepB as a three-dose series (AII), or, for vaccine-naive patients, Heplisav-B as a two-dose series (AII). A meta-analysis of 10 studies of people with HIV demonstrated that compared to a single dose, a double dose of Engerix-B or Recombivax HB had better response rates at 4 to 6 weeks (odds ratio [OR] 1.76; 95% confidence interval [CI], 1.36–2.29) and at >12 months (OR 2.28; 95% CI, 1.73–3.01) after vaccine completion.74 A double dose of Engerix-B is 40 mcg (two injections of the 20-mcg dose). A double dose of Recombivax HB is 20 mcg (two injections of the 10-mcg dose). In four randomized controlled trials, a regimen of two doses of Heplisav-B was superior to three doses of Engerix-B in people without HIV.75-77 In the largest trial, the protection rate was 95% for Heplisav-B and 81% for Engerix-B.77 An increase in the number of cardiovascular events that was not statistically significant was observed in the Heplisav-B group. In a multicenter trial of the safety and efficacy of Heplisav-B in people with HIV naive to vaccine, the vaccine achieved a 98.5% seroprotective response rate after two doses (administered at 0 and 1 months) and evaluated 6 months after the first dose. The study found a 100% seroprotective rate 4 weeks after a third dose.78 If Heplisav-B is used, the vaccine should not be interchanged with either of the other recombinant vaccines for the second dose. Recommendations provided by the Advisory Committee on Immunization Practices state that the two-dose vaccine series is appropriate only when both doses are Heplisav-B. In other situations, three total doses of vaccine should be given. Response to HepB vaccination, defined as anti-HBs ≥10 mIU/ml, should be documented 4 weeks after the last dose of vaccine (AII). In an observational study of 409 people with HIV who received the HepB vaccine, those with anti-HBs ≥10 mIU/mL were less likely to develop acute HBV infection compared to those who did not achieve that level (5% vs. 11%, hazard ratio 0.51; 95% CI 0.3–1.0).79 In addition, among those who were acutely HBV infected, 0% of those with anti-HBs ≥10 mIU/mL developed chronic infection compared to 35% of those with anti-HBs <10 mIU/mL (P = 0.02). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-6 Because of waning immunity, some experts would check anti-HBs annually and a booster dose would be given if levels fall below 10 mIU/mL, particularly if a person has ongoing risk factors for acquiring HBV and is not receiving tenofovir. Among people with HIV who did not respond (anti-HBs titers <10 mIU/mL) to a primary three-dose vaccine series with a single-dose recombinant vaccine, 25% to 50% responded to an additional vaccine dose, and 44% to 100% responded to a three-dose revaccination series.80-83 As a result, people with HIV who do not respond to a complete HepB vaccination series with one of the recombinant vaccines should be revaccinated with three double doses of a recombinant HBV vaccine (BIII) or with Heplisav-B (BIII),56 although some specialists might delay revaccination until antiretroviral therapy (ART) results in a sustained increase in CD4 count (CD4 ≥200 cells/mm3) (CIII). Two randomized controlled trials have shown that giving four double doses of the recombinant vaccine produces higher anti-HBs titers than three doses of single-dose vaccine,84,85 and one study also showed a higher overall response rate.85 Some specialists consider that this approach—four doses—improves immunologic response in people with HIV either as an initial vaccination schedule or among people who are nonresponders. However, whether vaccination with a schedule of four double doses is superior to four single doses or three double doses is still unclear. Preventing Other Liver Diseases HepA vaccination is recommended for all people with HIV who are hepatitis A virus (HAV) antibody negative, particularly those who have chronic liver disease,3 are injection and non-injection drug users, and men who have sex with men (AIII). Among people with HIV with CD4 counts <200 cells/mm3, responses to the HepA vaccine are reduced.86,87 Antibody response should be assessed 1 month after vaccination is complete. If total anti-HAV immunoglobulin (immunoglobulin G and immunoglobulin M) is negative, people should be revaccinated when their CD4 count is >200 cells/mm3 (BIII). People with chronic HBV infection should be advised to avoid alcohol consumption (AIII). Treating Disease Recommendations for Treating Hepatitis B Virus Infection Indication for Therapy • For all people with HIV/HBV coinfection, including pregnant people, regardless of CD4 count and HBV DNA level (AIII), therapy should be selected that includes drugs active against both HIV and HBV infections (AIII). Preferred Therapy (CrCl ≥60 mL/min) • The ART regimen must include two drugs active against HBV, preferably with (TDF 300 mg plus [FTC 200 mg or 3TC 300 mg]) or (TAF [10 or 25 mg]a plus FTC 200 mg) PO once daily (AII). Preferred Therapy (CrCl 30–59 mL/min) • The ART regimen must include two drugs active against HBV, preferably with TAF (10 or 25 mg)a plus FTC 200 mg PO once daily (AII). Preferred Therapy (CrCl <30 mL/min, Not Receiving HD) • Renally dosed entecavir (in place of TDF or TAF), or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-7 • ART with renally dose-adjusted TDF and FTC (BIII) when recovery of renal function is unlikely (see Table 6 for dosing recommendation for TDF and FTC or 3TC for people with renal impairment). Guidance for TAF use in people with CrCl <30 is not yet established. Preferred Therapy (Receiving HD) • (TDF or TAF) plus (FTC or 3TC) can be used. Refer to Table 6 for dosing recommendation. Duration of Therapy • People on treatment for HBV and HIV should receive therapy indefinitely (BIII). Alternative Therapy For People Not on ART • Anti-HBV therapy is indicated for all those who meet criteria for treatment according to the AASLD 2018 Hepatitis B Guidance. • Peg-IFN-alfa 2a 180 mcg SQ once weekly for 48 weeks (CIII), or • Peg-IFN-alfa 2b 1.5 mcg/kg SQ once weekly for 48 weeks (CIII) • Anti-HBV drugs—such as 3TC, FTC, TAF, TDF, entecavir, adefovir, and telbivudine—must not be given in the absence of a fully suppressive ART regimen to avoid selection of drug-resistant HIV (AII). Other Considerations • Because people with HBV/HCV/HIV coinfection appear to have accelerated liver fibrosis progression, high risk of HCC, and increased mortality, treatment for both HBV and HCV infection should be initiated, if feasible. • Because HBV reactivation can occur during treatment for HCV with direct-acting antivirals in the absence of anti-HBV therapy, all people with HIV/HBV coinfection who will be treated for HCV infection should be on HBV-active ART at the time of HCV treatment initiation (AIII). • When changing ART regimens, it is crucial to continue agents with anti-HBV activity (AIII). • If anti-HBV therapy must be discontinued, serum transaminase levels should be monitored every 6 weeks for 3 months, then every 3 to 6 months thereafter. • If a hepatic flare occurs after drug discontinuation, HBV therapy should be reinstituted because it can be potentially lifesaving (AIII). • If immunosuppressive therapy is given, HBV reactivation can occur. For people who are HBsAg positive, treatment for HBV infection should be administered (AII). People with isolated anti-HBc can either be monitored or be given prophylaxis to prevent reactivation depending on the degree of immunosuppression and whether HBV DNA is detectable (AII). Pregnancy Considerations • TAF or TDF given in combination with 3TC or FTC is the preferred dual-NRTI backbone for pregnant people with chronic HBV infection (AIII). • A person with HBV/HIV coinfection who becomes pregnant while virally suppressed on an ARV regimen that includes TAF can be offered the choice of continuing TAF or switching from TAF to TDF (BIII). • 3TC has been well tolerated by pregnant people and is a recommended NRTI for use in pregnancy (AII). • FTC is a recommended NRTI and is used commonly in pregnancy (BII). • IFN-alfa formulations are not recommended for use in pregnancy. Although these agents are not teratogenic, they are abortifacient at high doses in monkeys and should not be used in pregnant people because of their direct antigrowth and antiproliferative effects (AII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-8 • Infants born to people who are HBsAg positive should receive HBIG and HepB vaccine (first dose of three) within 12 hours of delivery (AI). The second and third doses of vaccine should be administered at 1 month and 6 months of age, respectively (AI). a TAF 10 mg dose is in the fixed-dose combination tablets of elvitegravir/cobicistat/TAF/FTC and darunavir/cobicistat/TAF/FTC; when TAF is used with other antiretrovirals, the dose is 25 mg. Key: 3TC = lamivudine; AASLD = American Association for the Study of Liver Disease; anti-HBc = HBV core antibody; ARV = antiretroviral; ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CrCl = creatinine clearance; FTC = emtricitabine; HBsAg = HBV surface antigen; HBV = hepatitis B virus; HBIG = hepatitis B immune globulin G; HCC = hepatocellular carcinoma; HCV = hepatitis C virus; HD = hemodialysis; HepB = hepatitis B; IFN = interferon; NRTI = nucleoside reverse transcriptase inhibitor; PO = orally; SQ = subcutaneous; TAF = tenofovir alafenamide; TDF = tenofovir disoproxil fumarate The ultimate treatment goals in HIV/HBV coinfection are the same as for HBV mono-infection: to prevent disease progression and to reduce HBV-related morbidity and mortality. People with HIV/HBV coinfection should receive tenofovir disoproxil fumarate (TDF)- or tenofovir alafenamide (TAF)-based ART. Special Considerations with Regard to Starting ART Preferred Regimen The U.S. Department of Health and Human Services Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents with HIV (Adult and Adolescent Antiretroviral Guidelines) recommend the fixed-dose coformulations of TDF/(emtricitabine [FTC] or lamivudine [3TC]), TAF/FTC, or abacavir/3TC as nucleoside reverse transcriptase inhibitor (NRTI) regimen backbones for most ART-naive people regardless of CD4 count.88 Because both components of these tenofovir combinations (tenofovir and either FTC or 3TC) have anti-HBV activity, they are also the treatment of choice for people with HIV/HBV coinfection (AIII) regardless of CD4 count (AI) and HBV DNA level (AIII) (see Hepatitis B Virus/HIV Coinfection in the Adult and Adolescent Antiretroviral Guidelines). TDF and TAF are both active against wild-type and 3TC-resistant HBV strains. Studies among people with HIV/HBV coinfection (most of them carrying 3TC-resistant HBV) have shown, on average, 4 log10 declines in HBV DNA levels.89-94 TDF and TAF have a high genetic barrier for development of resistance mutations (AI).3,95 The decision to use TAF/FTC versus TDF/FTC should be based upon creatinine clearance (CrCl) and an assessment of risk for nephrotoxicity and risk for acceleration of bone loss. Among people with CrCl ≥60 mL/min, either TAF/FTC or TDF/FTC can be considered. Among people with a CrCl 30 to 59 mL/min, a TAF/FTC regimen is preferred. Currently approved TAF/FTC-containing regimens for the treatment of HIV are not recommended for use among people with CrCl <30 mL/min who are not on hemodialysis. For these people, renally dosed entecavir with a fully suppressive ART regimen is recommended (BIII). Renally dosed TDF also can be used if recovery of renal function is unlikely (BIII). If renally dosed TDF is used, then the CrCl needs to be monitored carefully. Among people with HIV/HBV coinfection, switching from a primarily TDF-based ART regimen to single-tablet TAF/FTC/elvitegravir/cobicistat maintained or achieved HBV suppression, with improved estimated glomerular filtration rate (eGFR) and bone turnover markers.96 Among people with HBV mono-infection, TAF 25 mg was non-inferior to TDF 300 mg based on the percentage of people with HBV DNA levels <29 IU/mL at 48 weeks of therapy (94% for TAF vs. 93% for TDF; P = 0.47). People on TAF also experienced significantly smaller mean percentage decreases from baseline in hip and spine bone mineral density at 48 weeks than people receiving Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-9 TDF (P < 0.0001). Furthermore, the median change in eGFR from baseline to 48 weeks also favored TAF (P = 0.004).97,98 Chronic administration of 3TC or FTC as the only active drug against HBV should be avoided because of the high rate of selection of HBV drug-resistance mutations (AI). People receiving ART should continue HBV therapy indefinitely (BIII) because relapses after response can occur, particularly in those with lower CD4 counts.3 Additionally, discontinuation of nucleos(t)ide analog therapy is associated with an HBV flare in approximately 30% of cases,99,100 with loss of the benefit accrued from previous anti-HBV treatment and possible decompensation of liver disease.59,101-103 In addition, switching to the one-pill regimen of dolutegravir/3TC should be avoided because 3TC is then the only active drug against HBV. If anti-HBV therapy and ART must be discontinued, transaminase levels should be monitored every 6 weeks for 3 months and every 3 to 6 months thereafter. If a flare occurs, anti-HBV therapy and ART should be reinstituted and can be potentially lifesaving (AIII). Some people with HIV/HBV coinfection also have chronic HCV infection. Scant information is available on the treatment of HBV/HCV/HIV coinfection. Because people with HBV/HCV/HIV coinfection appear to have accelerated progression of liver fibrosis, higher risk of HCC, and increased mortality,104-106 attempts should be made to treat both hepatitis viruses, if feasible. If ART is administered, then anti-HBV therapy must be included as part of the regimen (as above) and anti-HCV therapy can be introduced as needed (see Hepatitis C Virus) (CIII). Because HBV reactivation can occur during treatment for HCV infection with direct-acting antivirals in the absence of anti-HBV therapy, all people with HIV/HBV coinfection who will be treated for HCV infection should be on HBV-active ART at the time of HCV treatment initiation (AIII).107-110 Alternative Treatment of HBV Infection Among People with HIV Who Are Not Receiving HBV-Active ART All people with HIV should receive ART. Among people with HBV infection and HIV, co-treatment is essential and recommended.88 Few options exist that can be used for treatment of HBV alone in a person with HIV/HBV coinfection. Anti-HBV therapy must not be given in the absence of a fully suppressive ART regimen (AII). Only pegylated interferon (IFN)-alfa-2a monotherapy may be considered for people with HIV/HBV coinfection who are not receiving ART and who meet criteria for anti-HBV therapy as described in the AASLD 2018 Hepatitis B Guidance (CIII).19 Regimens That Are Not Recommended Tenofovir (TDF and TAF), entecavir, 3TC, FTC, and telbivudine should not be used alone in the absence of a fully suppressive ART regimen because of the potential for development of HIV drug-resistance mutations (AI).111,112 Other anti-HBV treatment regimens include adefovir in combination with 3TC or FTC in addition to a fully suppressive ART regimen94,113,114; however, data on this regimen among people with HIV/HBV coinfection are limited. In addition, compared with TDF or TAF or entecavir, adefovir is associated with higher incidence of toxicity, including renal disease, as well as higher rates of HBV treatment failure. Therefore, the Panel does not recommend adefovir-containing regimen for people with HIV/HBV coinfection (AI). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-10 Monitoring of Response to Therapy and Adverse Events To prevent emergence of drug-resistant variants and evaluate response for people on nucleos(t)ide analogs, treatment response should be monitored by testing for HBV DNA at 3- to 6-month intervals (AI). Treatment responses are defined as the following: • Primary non-response: HBV DNA <1 log10 decline at 12 weeks.115 • Complete virologic response: undetectable HBV DNA by real-time polymerase chain reaction at 24 to 48 weeks.116 • Partial virologic response: ≥1 log10 decline, but still detectable HBV DNA at 24 weeks.116 • Maintained virologic response: response that continues while on therapy.116 • Sustained virologic response: one that is still present 6 months after stopping therapy.116 For people who are HBeAg positive, loss of HBeAg is also a measure of virologic response. Other markers that indicate treatment success include improvement in liver histology based on biopsy; transient elastography or noninvasive markers; normalization of serum aminotransferases; and, in those with loss of HBeAg, the development of anti-HBe. Sustained loss of HBsAg is considered by some to be a complete response; however, this desirable serologic response is uncommon (<1% of HBsAg-positive people per year).3 Adverse Events Renal toxicity with TDF, including increased serum creatinine or renal tubular dysfunction, has been observed; both increased serum creatinine and renal tubular dysfunction are more frequent among people with HIV who have underlying renal insufficiency, are older, or have been treated with TDF for prolonged periods.117 These biochemical changes are usually reversible when TDF is discontinued or changed to TAF.118 Electrolytes and serum creatinine levels should be evaluated at baseline and every 3 to 6 months, with urinalysis every 6 months. Because renal toxicity may be reversible, alternative anti-HBV therapy should be used if renal toxicity occurs (AI). If TDF is used among people with baseline renal insufficiency, either a dose adjustment as noted in the package insert or a change to TAF with appropriate dose adjustment is required.118 All nucleos(t)ides must be dose adjusted for renal dysfunction (see package insert), and TAF with FTC or 3TC is not recommended for people with CrCl <30 mL/min unless they are on hemodialysis (AI). TDF has been associated with a decrease in bone mineral density (BMD). TAF is associated with less of a decrease in BMD than TDF. TAF also has been associated with weight gain among people with HIV but has not been studied in HBV mono-infection. See the Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents with HIV for more information on adverse events related to TAF and TDF in Considerations for Antiretroviral Use in Patients with Coinfection: Hepatitis B Virus/HIV Coinfection. Entecavir-associated lactic acidosis is uncommon but has been reported among people with HBV mono-infection with advanced cirrhosis.119 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-11 Major toxicities of IFN-alfa (pegylated or standard) are flu-like symptoms—such as fatigue, pyrexia, myalgia, and headache—and psychiatric reactions, including depression, insomnia, irritability, and anxiety. Other common reactions are anorexia, nausea and vomiting, diarrhea, arthralgias, injection site reactions, alopecia, and pruritus. Immune Reconstitution Inflammatory Syndrome (IRIS) Return of immune competence after ART (or after steroid withdrawal or chemotherapy) can lead to reactivation of HBV-associated liver disease. Any immune reconstitution can lead to a rise in serum aminotransferases, so-called “hepatitis flare,”120 which constitutes IRIS among people with HIV/HBV coinfection. IRIS may manifest when serum aminotransferase levels dramatically increase as CD4 counts rise within the first 6 to 12 weeks after ART is started, with signs and symptoms characteristic of acute hepatitis and without another cause for the flare.121,122 After introduction of ART, serum ALT levels should be monitored closely; some experts recommend ALT testing at 6 and 12 weeks, then every 3 to 6 months thereafter. Any association between abnormal aminotransferases and clinical jaundice or synthetic dysfunction (elevated INR and low serum albumin) should prompt consultation with a hepatologist (CI).118 Flares are worse among people with more severe liver disease, especially those with cirrhosis.123 Distinguishing between drug-induced liver injury or other causes of hepatitis (acute hepatitis caused by HAV, HCV, hepatitis D virus [HDV], hepatitis E virus [HEV], Epstein-Barr virus, herpes simplex virus, or cytomegalovirus infection) and IRIS may be difficult. ART-associated hepatotoxicity may be dose dependent or idiosyncratic. Among people with HIV, the risk of ART-associated hepatotoxicity has been associated consistently with elevated pre-ART aminotransferases (ALT, AST) and the presence of HBV or HCV coinfection before initiation of ART. In HIV/HBV coinfection, baseline elevated HBV DNA levels are predictive of hepatotoxicity.124-127 However, despite this increased risk of hepatotoxicity in the setting of HCV or HBV coinfection, most (80% to 90%) people with HIV/HBV coinfection do not have ART-associated hepatotoxicity,128 and clinically significant hepatotoxicity (elevated direct bilirubin and INR) is rare; aminotransferase levels return to baseline in most cases, even if the offending medication is continued.129,130 Therefore, discontinuing ART usually is not necessary in the presence of hepatotoxicity unless the following symptoms are observed: hypersensitivity (e.g., fever, lymphadenopathy, rash), symptomatic hepatitis (i.e., nausea, vomiting, abdominal pain, or jaundice), or elevations in serum aminotransferase levels >10 times the upper limit of normal. However, the development of jaundice is associated with severe morbidity and mortality, and the offending drug(s) should be discontinued (AIII).131 The major problem in managing ALT flares is distinguishing between drug-induced liver injury and HBV reactivation, IRIS, emergence of HBV drug resistance, and HBeAg seroconversion. In drug-induced liver injury, determining the offending medication also can be challenging. A review of the medication history and testing for serum HBV DNA, HBeAg, HIV RNA, and CD4 count can help distinguish between these possibilities. Liver histology also may help to differentiate drug toxicity (e.g., increased eosinophils) from viral hepatitis (e.g., portal inflammation). If the flare is severe or HBV drug resistance is suspected, then consultation with a hepatologist is recommended. Other causes of abnormal liver tests should be considered, including use of drugs or alcohol, other viral hepatitis infections (HAV, HCV, HDV, and HEV), and nonalcoholic fatty liver disease. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-12 Managing Treatment Failure HBV treatment failure on nucleos(t)ide analogs is defined as primary non-response (HBV DNA <1 log10 decline) after 12 weeks of therapy among people who consistently adhere to HBV therapy or an increase in HBV DNA levels >1 log10 above nadir. In either situation, treatment failure generally is due to either drug-resistant HBV if the person is on 3TC/FTC monotherapy or to non-adherence to therapy.3 If drug-resistant HBV is present, a change in treatment is needed (AII). Distinct resistance patterns exist with the different groups of anti-HBV drugs: the L-nucleosides (telbivudine, 3TC/FTC); acyclic phosphonates/nucleotides (adefovir and tenofovir); and D-cyclopentane (entecavir), which shares some resistance mutations with the L-nucleosides. Many experts will obtain HBV-resistance testing because it has value in distinguishing between non-adherence and drug resistance, evaluating people with unclear prior drug history, assessing different adefovir-resistance pathways, and predicting the level of resistance to entecavir.132 However, TDF is associated infrequently with clinical resistance, although slow response has been noted, as discussed above. Addition of entecavir has led to suppression of HBV DNA among people whose response to TDF is slow.133 3TC (or FTC) monotherapy for HBV infection leads to emergence of drug-resistant HBV, which increases with time on treatment; therefore, it should not be used as the sole anti-HBV drug in an ART regimen (AII). The rate of development of 3TC-resistance is approximately 20% per year among people with HIV/HBV coinfection treated with 3TC alone.134 If 3TC resistance is suspected or documented, TDF or TAF should be added to the ART regimen (BIII).135-137 Because people with 3TC-resistant HBV will have cross-resistance to the other L-nucleosides (telbivudine, FTC), and partial resistance to entecavir, those agents should not be used among people found to have 3TC-resistant HBV (AI).138 All nucleoside analogs must be dose adjusted for renal insufficiency per package insert guidelines and Table 6. If treatment failure occurs on entecavir, the only rational choice is replacement with TDF or TAF (with or without FTC) because of the cross-resistance that occurs with L-nucleosides (telbivudine, 3TC, FTC) (AI). People whose HBV infection initially fails to respond to pegylated IFN-alfa can be given nucleos(t)ide analog therapy following the recommendations previously described (CIII). If treatment failure with TDF or TAF occurs, particularly in 3TC- or FTC-experienced people, entecavir may be an active alternative, especially if higher doses of entecavir can be used (CIII). Declines in HBV DNA levels can be slow, especially when pretherapy HBV DNA levels are very high. HBV DNA levels usually drop quickly among people who are receiving an HBV drug with high potency and a high genetic barrier to resistance—such as tenofovir—but HBV DNA levels may still be detectable for some years.3 Thus, in a person who is adherent to therapy with a partial virologic response to tenofovir, the drug should be continued with monitoring of HBV DNA levels (BII). Improved virologic response has been reported with the addition of entecavir to TDF; however, whether such “intensification therapy” is required is unclear.139 Nonetheless, people on drugs that are less potent or that have a lower barrier to resistance—such as adefovir or L-nucleosides—who have partial virologic responses (<2 log10 drop in HBV DNA levels from baseline at 24 weeks) should be switched to a more potent regimen—such as tenofovir with FTC or entecavir (if on adefovir)—because of the risk of development of drug resistance to the initial therapy (BII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-13 Special Considerations for Treating End-Stage Liver Disease People with HIV/HBV coinfection who have end-stage liver disease should be managed as a person with HBV mono-infection with end-stage liver disease, including referral to a hepatologist (AIII). Among people with HIV/HBV coinfection in end-stage liver disease, IFN-alfa is contraindicated (AI), but nucleoside analogs are safe and efficacious (AI).134,140,141 All people with ascites should undergo paracentesis to exclude spontaneous bacterial peritonitis (SBP).142,143 Management of ascites includes sodium restriction (<2 g/day) and the recommended diuretic regimen is spironolactone combined with furosemide (ratio of 40 mg furosemide: 100 mg spironolactone) (AI). All people who have had SBP and those with ascites total protein <1 g/dL should receive prophylaxis against SBP with administration of oral antibiotics, such as norfloxacin (400 mg/day), ciprofloxacin (750 mg/week), or trimethoprim-sulfamethoxazole (one double-strength tablet/day) (AI).144 Esophagogastroduodenoscopy (EGD or upper endoscopy) should be performed on all people with cirrhosis at the time of diagnosis and then every 1 year to 2 years to identify substantial gastroesophageal varices (see the AASLD 2018 Hepatitis B Guidance). People with varices require nonselective beta blockers—such as nadolol or propranolol—that are the mainstay of both primary and secondary prevention of variceal hemorrhage. Esophageal variceal banding is another preventive option, particularly for those who cannot tolerate beta blockers. Hepatic encephalopathy is treated with a 40-g protein diet and the use of non-absorbable disaccharides—such as lactulose—and/or non-absorbable antibiotics, such as rifaximin.3 People with HBV-related cirrhosis are at increased risk of HCC145 and should have imaging studies performed every 6 months, as recommended in HBV mono-infection (AI).3 Choice of imaging (ultrasound, computed tomography, or magnetic resonance imaging) depends upon the expertise of the imaging center and whether the person has cirrhosis. Usually, ultrasound is the initial preferred imaging modality.3 HCC can occur without cirrhosis in HBV infection, and HIV/HBV coinfection appears to increase the risk of HBV-associated HCC,146 but more frequent surveillance in HIV/HBV coinfection has not been studied, and so cannot be recommended given insufficient evidence. People with HIV/HBV coinfection with decompensated liver disease and/or early HCC are candidates for liver transplantation. HIV infection is not a contraindication to organ transplantation among people on suppressive ART.147 Because transplantation does not cure HBV infection, post-transplant hepatitis B immune globulin (HBIG) and HBV treatment is required (AII). Preventing Recurrence As previously indicated, most people should continue HBV therapy (with the exception of pegylated IFN-alfa) indefinitely (AIII) because relapses after response can occur, particularly in those with lower CD4 counts, and because reports of hepatitis flares after discontinuation of 3TC in those who have not reached treatment endpoints can be extrapolated to other HBV-active drugs.101-103 Special Considerations During Immunosuppressive Therapy With immunosuppressive therapy, both in the context of malignancy and rheumatologic/autoimmune diseases, reactivation of HBV infection can occur. HBV reactivation in HIV-negative people with HBsAg-positive/anti-HBc-positive disease receiving immunomodulatory therapy is well described.148,149 Even among people with HBsAg-negative/anti-HBc-positive disease, HBV reactivation occurs in 8% to 18% of people receiving anti-cancer drugs150 and 1.7% of people receiving rheumatologic disease drugs.151 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-14 If not already performed, people with HIV undergoing immunosuppressive therapy should have HBsAg, anti-HBc, and anti-HBs testing. People who are HBsAg positive should receive treatment with TDF or TAF plus 3TC or an FTC-based ART regimen (see Special Considerations with Regard to Starting ART above). The optimal approach for those people with HBsAg-negative/anti-HBc-positive disease is unknown. However, because TDF or TAF plus FTC is a preferred backbone for ART, it is prudent to start or modify ART to include these drugs before initiating immunosuppressive, cytotoxic, or immunomodulatory therapy among people with HBsAg-negative/anti-HBc-positive disease (BIII). If TDF or TAF/FTC cannot be used as part of their HIV regimen, these people either could receive entecavir for anti-HBV prophylaxis or could be monitored and given entecavir if signs of HBV reactivation occur (increase in HBV DNA or HBsAg seroreversion) (BIII). The option to give pre-emptive entecavir prophylaxis is preferred if HBV DNA is detectable or if immunosuppression is more severe, such as with anti-CD20 antibodies (AII).152 No studies have been performed on the appropriate length of therapy, but the Panel agrees with the AASLD 2018 Hepatitis B Guidance recommendation to continue treatment for 6 months after cessation of immunosuppressive therapy and for 12 months in the setting of anti-CD20 antibodies (BIII).19 Special Considerations During Pregnancy Pregnant people with HIV should be screened for HBV infection, and coinfection with HBV may be first diagnosed at this time (AI).153 People with HIV should be tested for HBsAg during each pregnancy, preferably in the first trimester, even if vaccinated or tested previously.153 Those who are both HBsAg negative and anti-HBs negative should be offered vaccination against HBV. Pregnant people with chronic HBV infection who have not already received the HepA vaccine series should be screened for immunity to HAV infection. Those who screen negative for total anti-HAV should receive the HepA vaccine series (AIII).154 Treatment of symptomatic acute HBV infection during pregnancy should be supportive, with special attention given to maintaining blood glucose levels and normal clotting status. Risk of preterm labor and delivery may increase with acute HBV infection. High maternal HBV DNA levels correlate strongly with perinatal HBV transmission, including failures of HBV passive-active immunoprophylaxis.155-158 See Hepatitis B Virus/HIV Coinfection in the Recommendations for the Use of Antiretroviral Drugs During Pregnancy and Interventions to Reduce Perinatal HIV Transmission in the United States. ART—including drugs active against both HIV and HBV—is recommended for all people with HIV/HBV coinfection, including pregnant people (AIII). TAF or TDF given in combination with 3TC or FTC is the preferred dual-NRTI backbone for pregnant people with chronic HBV infection (AIII).154 A person with HBV/HIV coinfection who becomes pregnant while virally suppressed on an antiretroviral regimen that includes TAF can be offered the choice of continuing TAF or switching from TAF to TDF (BIII).159 Several other antiviral agents have activity against HBV, including entecavir, adefovir, and telbivudine. However, these drugs have not been well evaluated in pregnancy, with too few exposures to assess overall risk. They are currently not recommended for pregnant people with HBV/HIV coinfection.159 Once HBV therapy with nucleos(t)ide analogs and ART is initiated in people with HIV/HBV coinfection, treatment should be continued indefinitely. Cases of adverse events during pregnancy related to any of the antiretroviral or anti-HBV drugs listed should be reported to the Antiretroviral Pregnancy Registry (800-258-4263). As of January 2018, 5,008 cases of pregnancy outcomes after first-trimester exposures to 3TC have been reported to the Antiretroviral Pregnancy Registry, with no indication of an increased risk of birth defects after exposure (see The Antiretroviral Pregnancy Registry Interim Report). 3TC has been well tolerated by Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-15 pregnant people and is a recommended NRTI for use in pregnancy (AII).154 Similarly, no increase in birth defects has been noted in 2,785 cases of first-trimester exposure to FTC. FTC is a recommended NRTI and is used commonly in pregnancy (BII).160 A total of 3,535 cases of first-trimester exposure to tenofovir have been reported to the Antiretroviral Pregnancy Registry with no increase in birth defects noted.160 Several large studies have been conducted to evaluate the effect of tenofovir use in pregnancy. No evidence exists that the use of TDF increases the risk of birth defects. Overall, the available evidence does not indicate a link between maternal TDF use and infants who are low birth weight or small for gestational age. Some concern remains regarding a link between maternal TDF use and preterm birth, but the evidence is mixed; the role of concomitant medications and other cofactors and/or confounders requires further investigation.154 Several other ART agents with activity against HBV—including adefovir and telbivudine—have been evaluated and found not to be teratogenic in animals, but experience with these agents in the first trimester of human pregnancy is limited. These drugs could be included in a regimen during pregnancy if other options are inappropriate and if the benefits are thought to outweigh the risks. Each of these agents should be administered only in combination with a fully suppressive ART regimen because of the risk of development of ART drug resistance. Entecavir was associated with skeletal anomalies in rats and rabbits, but only at high, maternally toxic doses (see package insert). Data on the use of entecavir and adefovir in human pregnancy are not available. Telbivudine given to pregnant people who were HBV seropositive/HIV seronegative during the second and third trimester was well tolerated, with no birth defects observed.161 IFN-alfa formulations are not recommended for use in pregnancy. Although these agents are not teratogenic, they are abortifacient at high doses in monkeys and should not be used in pregnant people because of their direct antigrowth and antiproliferative effects (AII).162 Infants born to people who are HBsAg positive should receive HBIG and HepB vaccine (first dose of three) within 12 hours of delivery (AI). The second and third doses of vaccine should be administered at 1 month and 6 months of age, respectively (AI). Infants who weigh <2,000 g at birth should receive four doses of HepB vaccine; administer one dose of HepB vaccine within 12 hours of delivery and initiate the three-dose HepB vaccine series beginning at age 1 month (four doses total: birth, 1 month, 2–3 months, and 6 months). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-16 References 1. Lee WM. Hepatitis B virus infection. N Engl J Med. 1997;337(24):1733-1745. Available at: 2. Levine OS, Vlahov D, Koehler J, Cohn S, Spronk AM, Nelson KE. Seroepidemiology of hepatitis B virus in a population of injecting drug users: association with drug injection patterns. Am J Epidemiol. 1995;142(3):331-341. Available at: 3. Terrault NA, Bzowej NH, Chang KM, et al. AASLD guidelines for treatment of chronic hepatitis B. Hepatology. 2016;63(1):261-283. Available at: 4. Schweitzer A, Horn J, Mikolajczyk RT, Krause G, Ott JJ. 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Available at: 145. Di Bisceglie AM. Hepatitis C and hepatocellular carcinoma. Hepatology. 1997;26(3 Suppl 1):34S-38S. Available at: 146. Salmon-Ceron D, Rosenthal E, Lewden C, et al. Emerging role of hepatocellular carcinoma among liver-related causes of deaths in HIV-infected patients: The French national Mortalité 2005 study. J Hepatol. 2009;50(4):736-745. Available at: 147. Miro JM, Laguno M, Moreno A, Rimola A, Hospital Clinic Olt in HIV Working Group. Management of end stage liver disease (ESLD): what is the current role of orthotopic liver transplantation (OLT)? J Hepatol. 2006;44(1 Suppl):S140-145. Available at: 148. Lau GK, Yiu HH, Fong DY, et al. Early is superior to deferred preemptive lamivudine therapy for hepatitis B patients undergoing chemotherapy. Gastroenterology. 2003;125(6):1742-1749. Available at: 149. Lee YH, Bae SC, Song GG. Hepatitis B virus reactivation in HBsAg-positive patients with rheumatic diseases undergoing anti-tumor necrosis factor therapy or DMARDs. Int J Rheum Dis. 2013;16(5):527-531. Available at: 150. Huang YH, Hsiao LT, Hong YC, et al. Randomized controlled trial of entecavir prophylaxis for rituximab-associated hepatitis B virus reactivation in patients with lymphoma and resolved hepatitis B. J Clin Oncol. 2013;31(22):2765-2772. Available at: 151. Mori S, Fujiyama S. Hepatitis B virus reactivation associated with antirheumatic therapy: risk and prophylaxis recommendations. World J Gastroenterol. 2015;21(36):10274-10289. Available at: 152. Reddy KR, Beavers KL, Hammond SP, Lim JK, Falck-Ytter YT, American Gastroenterological Association Institute. American Gastroenterological Association Institute guideline on the prevention and treatment of hepatitis B virus reactivation during immunosuppressive drug therapy. Gastroenterology. 2015;148(1):215-219; quiz e216-217. Available at: 153. Schillie S, Vellozzi C, Reingold A, et al. Prevention of hepatitis B virus infection in the United States: recommendations of the Advisory Committee on Immunization Practices. MMWR Recomm Rep. 2018;67(1):1-31. Available at: 154. Panel on Treatment of HIV During Pregnancy and Prevention of Perinatal Transmission. Recommendations for use of antiretroviral drugs during pregnancy and interventions to reduce Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV L-29 perinatal HIV transmission in the United States. 2023. Available at: 155. del Canho R, Grosheide PM, Schalm SW, de Vries RR, Heijtink RA. Failure of neonatal hepatitis B vaccination: the role of HBV-DNA levels in hepatitis B carrier mothers and HLA antigens in neonates. J Hepatol. 1994;20(4):483-486. Available at: 156. Ngui SL, Andrews NJ, Underhill GS, Heptonstall J, Teo CG. Failed postnatal immunoprophylaxis for hepatitis B: characteristics of maternal hepatitis B virus as risk factors. Clin Infect Dis. 1998;27(1):100-106. Available at: 157. Wiseman E, Fraser MA, Holden S, et al. Perinatal transmission of hepatitis B virus: an Australian experience. Med J Aust. 2009;190(9):489-492. Available at: 158. Kubo A, Shlager L, Marks AR, et al. Prevention of vertical transmission of hepatitis B: an observational study. Ann Intern Med. 2014;160(12):828-835. Available at: 159. Panel on Treatment of HIV During Pregnancy and Prevention of Perinatal Transmission. Hepatitis B virus/HIV coinfection. 2023. Available at: 160. Antiretroviral Pregnancy Registry Steering Committee. Antiretroviral Pregnancy Registry international interim report for 1 January 1989–31 January 2019. Wilmington, NC: Registry Coordinating Center; 2019. Available at: 161. Han GR, Jiang HX, Wang CM, et al. Long-term safety and efficacy of telbivudine in infants born to mothers treated during the second or third trimesters of pregnancy. J Viral Hepat. 2017;24(6):514-521. Available at: 162. Boskovic R, Wide R, Wolpin J, Bauer DJ, Koren G. The reproductive effects of beta interferon therapy in pregnancy: a longitudinal cohort. Neurology. 2005;65(6):807-811. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-1 Hepatitis C Virus Infection Updated: January 18, 2023 Reviewed: January 10, 2024 Epidemiology Prevalence and Incidence Estimates Hepatitis C virus (HCV) is an enveloped, single-stranded RNA virus of the Flaviviridae family with seven known genotypes and 84 subtypes, with genotypes 1 and 3 being most common worldwide.1-3 It is the most commonly reported bloodborne infection in the United States and is a leading cause of liver-related morbidity and mortality, particularly among people with HIV. In 2019, the estimated global prevalence of chronic HCV infection was 58 million (0.8% of general population), a decline from previous estimates of 71 million in 2015.4 In the United States, updated estimates for 2013 to 2016 are that approximately 4.1 million people were HCV antibody positive (past or current infection; 1.7% of all adults); 2.4 million were HCV RNA positive (current infection; 1% of all adults).5 Comparable data from 2003 to 2010 showed that 4.6 million people were antibody positive and 3.5 million were living with current HCV infection.6 These updated lower prevalence estimates reflect interval trends, including increased cures with new treatment options and increasing death rates due to aging. However, these may be offset by increases in incident cases due to the opioid crisis in vulnerable counties.7,8 Despite variable state-level surveillance practices,9 Centers for Disease Control and Prevention (CDC) surveillance data from 2019 show regional differences in incidence and prevalence, increasing rates in rural areas, ongoing racial/ethnic disparities, and changing demographics, including a bimodal distribution of infections with peaks at 29 years and at 59 years of age.10 Attributable mortality is highly variable among states and counties.11 Given the shared transmission routes between HIV and HCV, estimates of the burden of HCV infection in people with HIV (HIV/HCV coinfection) have been highly variable depending on the comprehensiveness of databases analyzed. A global systematic review and meta-analysis of studies published between 2002 and 2015 estimated that there were 2.3 million cases of coinfection worldwide, with 1.3 million (58%) attributed to persons who inject drugs; this translates to HCV coinfection prevalence of 6.2% among people with HIV.12 Compared with people without HIV, the odds of HCV infection in people with HIV are six times higher. The prevalence of HCV infection among people with HIV is distributed in the following subgroups: people who inject drugs (82.4%), men who have sex with men (MSM, 6.4%), and those who are pregnant or heterosexually exposed (2.4%).12 Estimates of HCV coinfection in the United States10 have been cited as 21% but have ranged from 6% to 30% with high variability based on the distribution of HIV transmission risk factors.13,14 In the United States, it is estimated that 62% to 80% of people who inject drugs who have HIV also have HCV infection.10 The availability of highly effective treatments for HCV infection has led to national and global initiatives aimed at HCV elimination in general and in high-risk persons, such as those with HIV coinfection. The World Health Organization has developed targets for countries to achieve HCV elimination by 2030: diagnosing 90% of those with chronic infection and curing 80% of those diagnosed.4 The CDC Division of Viral Hepatitis 2025 Strategic Plan aims to increase HCV cure to >85% by 2030.15 The use of an HCV cascade of care has shown that there are ongoing gaps to attaining cure encompassing screening, initiating and completing treatment, and preventing Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-2 reinfection.16,17 Worldwide, 15.2 million (26.2%) out of an estimated 58 million people knew their HCV status by the end of 2019.18 With progress in direct antiviral treatments, 9.4 million people received HCV treatment, with the vast majority cured, between 2015 and 2019.18 Micro-elimination efforts to scale-up treatment as prevention among people with HIV have successfully demonstrated that such efforts can decrease hepatitis C incidence.19-24 Transmission Routes Both HIV and HCV can be transmitted by percutaneous exposure to blood or blood products, sexual intercourse, and perinatal transmission; however, the relative efficiency of transmission by these routes varies substantially.25 HCV is approximately 10 times more infectious than HIV through percutaneous blood exposures and has been shown to survive for weeks in syringes.26,27 Transmission via injection drug use remains the most common mode of acquisition in the United States, while transmission through contaminated blood products is now rare. Health care–associated transmission of HCV also can occur because of improper reuse of parenteral medications and equipment.28 Other factors that have been associated with HCV infection include accidental occupation-related needlestick injuries, intranasal cocaine use, chronic hemodialysis, and tattoo placement. Multiple outbreaks of acute HCV infection in MSM demonstrate that sexual transmission is an important mode of acquisition in this population. Risk factors include unprotected receptive anal intercourse, use of sex toys, non-injection recreational drug use, and concurrent sexually transmitted infections (STIs).29-32 Evidence for increasing HCV incidence and prevalence in HIV-negative men seen in HIV pre-exposure prophylaxis (PrEP) clinics has led to current recommendations to monitor for acute HCV infection and routinely test for HCV as part of PrEP care.33-35 Heterosexual transmission of HCV is uncommon but more likely in those whose partners have HIV/HCV coinfection.16,36-38 Perinatal transmission of HCV infection occurs in approximately 7% and 12% of infants born to HCV-seropositive and RNA-positive mothers without and with HIV,39-41 respectively, with possible decreased transmission risk for women with HIV receiving antiretroviral treatment.42 Clinical Manifestations Both acute and chronic HCV infections are usually minimally symptomatic or asymptomatic. Fewer than 20% of patients with acute infection have characteristic symptoms, including low-grade fever, mild right-upper-quadrant pain, nausea, vomiting, anorexia, dark urine, and jaundice. Unexplained elevations in serum alanine aminotransferase (ALT) or aspartate aminotransferase (AST) levels may be the only laboratory finding during acute and chronic infection. Recognition of acute HCV infection in patients with new-onset liver enzyme elevations is clinically important; early initiation of HCV treatment can lower the likelihood of poorer outcomes and prevent transmission to others (treatment as prevention).43-45 Cirrhosis develops in 20 to 40% of patients with chronic HCV infection within 20 years after infection, although the risk for an individual is highly variable.46-48 Risk factors for development of significant liver disease include older age at the time of infection, male sex, obesity, and concomitant alcohol use.47,49 HIV coinfection adversely affects the course of HCV infection, resulting in significantly accelerated progression of liver disease to cirrhosis, particularly in those with advanced immunodeficiency50,51 (CD4 T lymphocyte [CD4] count <200 cells/mm3). Further, coinfected patients with cirrhosis progress more rapidly to life-limiting outcomes—such as end-stage liver Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-3 disease and hepatocellular carcinoma (HCC)—than those who are HCV mono-infected,52,53 even if they are virally suppressed.54 Because of its high prevalence and accelerated progression, HCV infection was a leading non-AIDS cause of death in people with HIV before the advent of highly effective direct-acting antivirals.55-57 In addition to liver disease, HCV may be associated with symptomatic vasculitis due to cryoglobulinemia (largely affecting the skin or joints), renal disease (membranoproliferative glomerulonephritis), and porphyria cutanea tarda. Diagnosis On entry into HIV care, all patients should undergo routine HCV screening (AII). Initial testing for HCV should be performed using a U.S. Food and Drug Administration (FDA)-approved immunoassay licensed for detection of antibody to HCV (anti-HCV) in blood.58,59 For at-risk HCV-seronegative individuals, specifically MSM or persons who inject drugs, HCV antibody testing, using an FDA-approved immunoassay, is recommended annually or as indicated by clinical presentation, risk activities, or exposure (AII). Concordantly, both the American Association for the Study of Liver Diseases (AASLD)/Infectious Diseases Society of America (IDSA) HCV guidance and CDC PrEP guidelines also recommend HCV serologic testing at baseline and every 12 months for MSM, transgender women, and people who inject drugs.59,60 Nucleic acid testing for HCV RNA is recommended in settings where acute infection is suspected or in persons with known prior infection cleared spontaneously or after treatment (AIII). False-negative anti-HCV antibody results are possible among people with HIV but uncommon (2% to 4%), and more likely to be seen in patients with advanced immunosuppression61 (CD4 cell count <200 cells/ mm3). HCV RNA testing should be performed in those patients with risk factors or unexplained ALT elevation. In addition, negative anti-HCV antibody results can occur during acute infection. Following acute HCV infection, the duration of the window period prior to seroconversion is highly variable, ranging from 2 weeks to more than 24 weeks,62,63 with antibody response in most persons detectable at 8 to 12 weeks. Serum ALT levels are frequently elevated early in the course of HCV infection, and high ALT levels should prompt testing for HCV RNA if serologic test results are negative or indeterminate in individuals at risk of HCV infection.64 Individuals who test positive for HCV antibody should undergo additional diagnostic testing by using a sensitive quantitative assay to measure plasma HCV RNA level and confirm current infection (AI). This should preferentially be done as an automatic reflex to HCV RNA testing of the leftover serum from the blood draw for antibody testing to facilitate diagnosis.65 Reinfection can occur in both seropositive individuals who spontaneously clear their infection or those who achieve a sustained virologic response to treatment. Diagnosing a new active infection will require HCV RNA testing in such individuals (AII). Preventing Exposure The primary route of HCV transmission is blood-to-blood contact, most commonly from sharing drug-injection equipment or paraphernalia (i.e., “cookers,” filters, or water) previously used by an infected person with HCV. Prevention approaches for persons who inject drugs include harm-reduction encompassing opioid agonist therapy and syringe services programs to avoid the reuse or sharing of syringes, needles, water, cotton, and other drug preparation equipment.66,67 Both needle and syringe exchange programs and opioid substitution therapy have been shown to reduce the risk of HCV acquisition in people who inject drugs.67,68 HCV also can be transmitted sexually, especially among MSM with HIV.69 Risk factors for sexual HCV acquisition include unprotected anal receptive Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-4 intercourse, fisting, sharing of sex toys, ulcerative STIs, and use of methamphetamine or other sex-enhancing drugs (injection or otherwise).70,71 Patients should be counseled regarding the risk of sexual HCV acquisition (AII). Those with multiple sex partners or STIs should be advised to use barrier protection to reduce their risk of STIs including hepatitis C infection (AII). Preventing Disease There is no available vaccine or recommended post-exposure prophylaxis to prevent HCV infection.72,73 Following acute HCV infection, chronic infection can be prevented within the first 6 to 12 months after infection through antiviral treatment; high rates of viral clearance have been observed with HCV treatment during the acute phase of infection.74,75 Because most patients with acute HCV infection may transmit to others and are at risk for loss to follow-up, immediate treatment with the same regimens recommended for chronic HCV should be offered (AIII).44,76 Specific treatment regimens in acute infection are the same as those recommended for chronic HCV infection and are detailed in the Treating HCV section. People with HCV infection should be tested for previous or concurrent hepatitis B virus (HBV) infection because coinfection with HBV is associated with increased morbidity (AII). Those without evidence of immunity to HBV infection should be vaccinated (see the Hepatitis B Virus Infection section) (AII). Likewise, because acute hepatitis A virus (HAV) infection is more likely to be fulminant in persons with HCV infection,77 these patients should be screened for immunity (HAV immunoglobulin G or antibody total) and non-immune persons should be vaccinated (AII). People with HCV infection should be counseled about methods to prevent liver damage by avoiding any alcohol consumption (because alcohol accelerates progression of liver disease), limiting ingestion of potentially hepatotoxic medications (e.g., acetaminophen should be limited to <2 g/day for those with acute infection or bridging fibrosis/cirrhosis), and avoiding iron supplementation in the absence of documented iron deficiency.78 People with HIV/HCV coinfection with cirrhosis are at risk of life-threatening complications and should be managed in consultation with a gastroenterologist or hepatologist. In particular, individuals with cirrhosis should undergo serial screening for HCC; current guidelines recommend performing ultrasonography at 6-month intervals, although the optimal screening strategy is unknown (AIII).79 Because of its relatively poor specificity and sensitivity, serum alfa-fetoprotein is an adjunct to ultrasonography but should not be the sole screening method.79 HIV infection is not a contraindication to liver transplantation; accordingly, coinfected patients with decompensated liver disease and/or early HCC may be considered for transplantation at specialized transplant centers. Although earlier studies focused on the potential for antiretroviral (ARV)-associated liver injury with certain agents, more recent studies have found that effective HIV treatment is associated with reduced risk of liver disease progression, though not to levels of persons with HCV infection without HIV.54,80 Coinfected patients should be treated in accordance with the Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents with HIV. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-5 Treating HCV Infection Introduction Direct-acting antiviral (DAA) regimens for HCV infection have become standardized with one of two pangenotypic, highly efficacious and well-tolerated antiviral treatment regimens, which are the preferred therapy for HCV infection for almost all persons with HIV and HCV. Clinicians can refer to the most recent AASLD/IDSA HCV treatment guidance. The goals of therapy, treatment regimen, and monitoring parameters for patients with HIV/HCV coinfection are similar to those recommended for patients with HCV mono-infection. However, people with HIV were historically considered a “special population” with regard to HCV treatment. This designation was rooted in inferior responses to interferon-based treatment for those with HIV.81,82 The arrival of initial DAA regimens narrowed the gap in response to treatment but continued to present significant drug–drug interaction considerations and, in some circumstances, warrant extended treatment durations. Simplified approaches to HCV treatment have emerged as a means to facilitate treatment by non-specialist providers and increase treatment uptake for the majority of persons with HCV infection. In general, simplified approaches to HCV treatment apply to treatment-naive persons without cirrhosis and encompass minimal baseline testing (with omission of genotype), standardized treatment approaches using pangenotypic regimens, no on-treatment testing or in-person follow-up, and limited follow-up to confirm sustained virologic response (SVR). Several factors now allow the inclusion of people with HIV in simplified HCV treatment recommendations. The emergence of unboosted integrase strand transfer inhibitor (INSTI)-based ARV regimens has eliminated clinically significant drug interactions with current first-line DAA regimens. Additionally, the improved safety profile of tenofovir alafenamide (TAF) combined with safety data in the setting of boosted ARV regimens during coadministration with DAAs obviate the need for enhanced toxicity monitoring for people with HIV in most instances. Finally, accumulation of clinical efficacy data and the necessity of expanding treatment access support the use of simpler standardized treatment approaches initially validated in HCV mono-infected populations for those with HIV. Based on these developments and the emergence of pangenotypic DAA regimens, treatment of HCV can be approached using simplified protocols for the majority of people with HIV. Published clinical trial data directly support a simplified approach to HCV treatment, including for people with HIV. The AIDS Clinical Trial Groups (ACTG) A5360 study (MINMON) evaluated an approach consisting of limited baseline testing and supply of the entire 84-tablet (12-week) sofosbuvir/velpatasvir treatment regimen in 399 participants, including 166 with HIV.83 All participants were HCV treatment-naive, compensated cirrhosis was allowed, and no pre-treatment HCV genotyping was performed. No on-study laboratory monitoring or in-person follow-up was conducted. The SVR after 12 weeks post-treatment (SVR12) was 95% overall (95% CI, 92.4% to 96.7%) and 95% in the subset of people with HIV (157/166). The SMART-C study randomized participants to either a standard 8-week treatment with glecaprevir/pibrentasvir (n = 127), which included in-person follow-up at weeks 4 and 8 with medication refill required at week 4, or to a simplified approach (n = 253) that omitted the on-treatment visits with all medication dispensed at initiation.84 Persons with previous HCV treatment or cirrhosis were excluded and only a small number of people with HIV (n = 27) were included. A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-6 modified intention-to-treat analysis (excluding lost to follow-up and missing SVR12 results) established non-inferiority of the simplified approach with SVR12 of 97% (233/241) compared with 98% (121/123) in the standard-approach arm. No difference in response was seen by HIV status. Staging and Monitoring While a pre-HCV treatment assessment of patient readiness for therapy should be completed, with an indication that reasonable adherence can be expected, HCV DAA therapy should not be withheld solely due to perceived lack of adherence with HIV therapy or untreated HIV infection (BIII). Evidence suggests the level of adherence needed for HCV cure is more modest than that required to maintain HIV viral suppression.85-87 In addition, despite a lack of HIV control, patients may be uniquely motivated by the potential for HCV cure, thereby increasing the likelihood of successful treatment. Additional fibrosis stage assessment may be indicated in people with HIV with an indeterminate FIB-4 (1.45–3.25) score, particularly if cirrhosis is suspected (BIII). Additional blood- or serum-based assays for fibrosis staging are not recommended because they provide little benefit over FIB-4 (BII).88,89 Non-invasive ultrasound-based (e.g., shear wave elastography or vibration controlled transient elastography) or imaging-based (e.g., magnetic resonance elastography) modalities are recommended if available (BII). Liver biopsy is no longer recommended for liver fibrosis staging related to HCV infection unless there is another indication to obtain one (AII). Treatment should not be withheld if access to additional staging modalities is not readily available (AIII). Simplified Approach to HCV Treatment The current AASLD/IDSA HCV guidance for simplified HCV treatment of treatment-naive adults (without cirrhosis or with compensated cirrhosis) excludes persons with HIV. The Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV recommends an approach that allows most people with HIV to qualify for simplified HCV treatment. This simplified approach is appropriate except in certain people with HIV with conditions noted in Box 1. Such exclusions highlight the importance of particular ARV regimens with significant drug–drug interactions with ARVs (see below). Box 1. Characteristics of People with HIV for Whom Simplified Hepatitis C Virus Treatment Is Not Recommendeda 1. Prior HCV treatment (Reinfection after prior successful therapy is not an exclusion.) 2. Decompensated cirrhosisb 3. TDF-containing regimen with an eGFR <60mL/min 4. On efavirenz, etravirine, nevirapine, or boosted HIV-1 protease inhibitorsc 5. Untreated chronic HBV infection 6. Pregnancy a People with HIV and HCV infection who meet these exclusion criteria should be treated for HCV following standard approaches (see the AASLD/IDSA HCV Guidance). b Including, but not limited to, current or prior variceal bleeding, ascites, or hepatic encephalopathy Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-7 c People with HIV on boosted protease inhibitors are not eligible for treatment with glecaprevir/pibrentasvir and may require on-treatment monitoring. Key: eGFR = estimated glomerular filtration rate; HBV = hepatitis B virus; HCV = hepatitis C virus; TDF = tenofovir disoproxil fumarate A limited pre-treatment assessment for people with HIV is essentially the same as for people without HIV who qualify for a simplified approach (Box 2) (AIII). Key components are documentation of active HCV infection and initial assessment of liver fibrosis stage. Determination of HCV genotype prior to treatment is not necessary in treatment-naive patients, with the exception of persons with compensated cirrhosis who are planned for treatment with sofosbuvir/velpatasvir. In this case, if genotype 3 HCV infection is identified, additional testing for resistance-associated substitution (RASs) is required before treatment with sofosbuvir/velpatasvir. Notably, HIV parameters (i.e., HIV RNA or CD4 count) are not required to determine eligibility for a simplified approach. The efficacy of HCV DAA treatment for people does not appear to be compromised at lower CD4 counts.90-92 Box 2. Pre-treatment Assessment Under Simplified Approach 1. Creatinine, liver function tests, and complete blood count 2. HCV RNA 3. Hepatitis B surface antigen 4. Initial fibrosis staging with FIB-4 (FIB-4 calculator)a 5. Medication and drug interaction review 6. HCV genotype required if cirrhosis is present a Additional testing may be required if results are indeterminate (see text). Key: HCV = hepatitis C virus Drug–Drug Interactions Drug interactions with ARVs pose less of a constraint on DAA use to treat HCV infection in people with HIV given the prominence of unboosted INSTI and TAF among first-line ARV regimens.93 A comprehensive review of drug interactions between ARVs and antivirals for hepatitis C can be found within the Hepatitis C Virus/HIV Coinfection section of the Guidelines for the Use of Antiretroviral Agents in Adults and Adolescents with HIV. Interactions of clinical significance pertaining to the recommended DAA regimens are highlighted here and in Table 4. Efavirenz coadministration results in a significant decrease in glecaprevir, pibrentasvir, and velpatasvir exposures.94,95 People with HIV on an efavirenz-containing regimen are not eligible for simplified DAA treatment approaches (Box 1) and generally require an ARV switch prior to DAA treatment (AII). Given similar pharmacologic profiles, including cytochrome P450 (CYP) enzyme induction, nevirapine and etravirine are also not recommended for coadministration with HCV DAAs, including glecaprevir/pibrentasvir and sofosbuvir/velpatasvir (AII). Ritonavir- or cobicistat-boosted protease inhibitors significantly increase glecaprevir and pibrentasvir exposure94; people with HIV on boosted protease inhibitor (PI)–based ARV regimens were not included in registrational trials of glecaprevir/pibrentasvir and coadministration is not Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-8 recommended (BII).96 Boosted protease inhibitors also increase velpatasvir exposure, which in turn increases tenofovir plasma exposure particularly when administered as TDF.95 People with HIV on boosted ARV regimens were included in sofosbuvir/velpatasvir registrational trials, and the combination was not associated with increased adverse events.97 Given these considerations, sofosbuvir/velpatasvir can be co-administered with boosted ARV regimens (AII); TAF-based regimens are preferred. People on TDF-containing boosted ARV regimens are not eligible for simplified HCV treatment if their estimated glomerular filtration rate is <60 mL/min because monitoring on treatment is recommended (AII). Summary of Major Drug Interactions Between HIV and HCV Antivirals HIV Antivirals Glecaprevir/Pibrentasvir Sofosbuvir/Velpatasvir EFV, ETR, NVP, and other strong CYP 3A4 and P-gp inducers Significant decrease in glecaprevir and pibrentasvir concentrations (avoid) Significant decrease in velpatasvir concentrations (avoid) PI/r, PI/c, unboosted ATV Significant increase in glecaprevir and pibrentasvir concentrations (avoid) Boosted PIs may increase velpatasvir concentrations, but no significant adverse events in clinical trial Coadministration allowed TDF, TAF Coadministration allowed TAF preferred If TDF is used with boosted PIs if GFR <60 mL/min, monitoring is recommended. RPV, DOR, EVG/c, RAL, BIC, DTG, ABC, FTC, 3TC, MVC Coadministration allowed Coadministration allowed Key: 3TC = lamivudine; ABC = abacavir; ATV = atazanavir; BIC = bictegravir; CYP = cytochrome P450; DOR = doravirine; DTG = dolutegravir; EFV = efavirenz; ETR = etravirine; EVG/c = elvitegravir/cobicistat; GFR = glomerular filtration rate; FTC = emtricitabine; MVC = maraviroc; NVP = nevirapine; PI = protease inhibitor; PI/c = protease inhibitor/cobicistat; PI/r = protease inhibitor/ritonavir; P-gp = p-glycoprotein; RAL = raltegravir; RPV = rilpivirine; TAF = tenofovir alafenamide; TDF = tenofovir disoproxil fumarate HCV Treatment Regimens In HCV treatment-naive persons without cirrhosis, the recommended DAA regimens are either— • Glecaprevir/pibrentasvir fixed dose combination (FDC) (100-mg/40-mg tablet), three tablets daily for 8 weeks (AI) OR • Sofosbuvir/velpatasvir FDC (400-mg/100-mg tablet), one tablet daily for 12 weeks (AI) As noted in Box 1, these recommendations do not apply to HCV treatment–experienced patients because some of these individuals may require other DAA combinations and/or consultation with an expert. Persons meeting other criteria listed in Box 1 should be treated according to standard approaches. Clinicians can refer to the most recent HCV treatment guidance for recommendations. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-9 Primary data supporting the efficacy and safety of the two recommended treatment regimens in people with HIV come from registrational trials. In the ASTRAL-5 study, 12 weeks of sofosbuvir/velpatasvir without ribavirin was given to 106 people with HIV, including 19 with cirrhosis.97 The SVR12 was 95% by intention-to-treat analysis with only two of five failures due to confirmed viral relapse. All participants with cirrhosis were cured. The EXPEDITION-2 study evaluated glecaprevir/pibrentasvir 300 mg/120 mg in 153 people with HIV with duration determined by cirrhosis status, with 137 non-cirrhotic participants treated for 8 weeks and 16 with cirrhosis treated for 12 weeks.96 By intention-to-treat analysis, SVR12 was 98%, including 135 out of 137 participants without cirrhosis and 15 out of 16 participants with cirrhosis. The only confirmed virologic failure was virologic breakthrough at week 8 in a participant with genotype 3 and cirrhosis. Both regimens were well tolerated with low rates of discontinuation and no severe treatment-associated adverse events. If compensated cirrhosis is present and sofosbuvir/velpatasvir is the planned regimen, then pre-treatment HCV genotyping is recommended (AII). If HCV genotype 3 is identified, NS5A resistance testing and modification of the sofosbuvir/velpatasvir regimen or selection of an alternative therapy may be necessary (for a full discussion, see the HCV treatment guidance). For all other genotypes or if glecaprevir/pibrentasvir is being used (regardless of genotype), no modification to the treatment regimen is required in the setting of compensated cirrhosis (AIII). The lower-strength recommendation for use of 8 weeks of glecaprevir/pibrentasvir in the setting of cirrhosis stems from a lack of prospective trials evaluating this duration in people with HIV and cirrhosis; 12 weeks of glecaprevir/pibrentasvir may be used in this setting (CI). The EXPEDITION-8 trial evaluated 8 weeks of glecaprevir/pibrentasvir in 343 participants with compensated cirrhosis and without HIV.98 The intention-to-treat SVR12 was 98% and >99% in a per protocol analysis. The lone virologic failure was in genotype 3 infection yielding a per protocol SVR12 in this group of 98% (60/61). Data from real-world experience of use of 8 weeks of glecaprevir/pibrentasvir in the setting of cirrhosis were recently presented and included a small number of people with HIV.99 Of the 20 people with HIV treated for 8 weeks, 19 out of 20 achieved SVR with no confirmed virologic failures. Specific Treatment Situations Acute HCV Infection Treatment People with HIV are at risk for acute HCV infection. Given the public health implications in reducing onward transmission, in addition to benefit for the individual, HCV treatment should be started as soon as possible in this population (AIII).21,44,100 The simplified treatment regimens outlined above are recommended in acute HCV infection (AII); shorter durations of therapy are currently being investigated. Patients who achieve viral clearance either spontaneously or after treatment should be counseled about the potential for reinfection. Prior DAA Failure Retreatment Despite the high cure rates associated with current DAA regimens, the large number of DAA treatments will inevitably result in an appreciable number of DAA failures. Persons with HIV were not included in the registrational trial of sofosbuvir/velpatasvir/voxilaprevir for retreatment of HCV infection101; nor were they included in initial prospective trials of either glecaprevir/pibrentasvir or sofosbuvir plus glecaprevir/pibrentasvir for HCV treatment of prior NS5A inhibitor containing DAA failures.102,103 A follow-up prospective study comparing 12 weeks versus 16 weeks of Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-10 glecaprevir/pibrentasvir for genotype 1 sofosbuvir plus NS5A inhibitor failures did include a small number of people with HIV (~5%).104 Similarly, published real-world experiences with retreatment of prior DAA failures are underrepresented with respect to people with HIV (all <5% except one with 15%).105-108 Drawing on the experience with initial DAA therapy of HCV infection, where people with HIV have nearly identical outcomes to persons with HCV infection alone, treatment approaches for DAA failures should be the same as those for persons with HCV mono-infection (AIII). Clinicians should refer to the most recent HCV treatment guidance for up-to-date recommendations. Laboratory Monitoring and Post-Treatment Follow-Up Laboratory monitoring while on treatment is not required for patients qualifying for the simplified treatment approach. However, documentation of HCV RNA levels at week 4 of therapy may be required by some payors prior to providing additional refills needed to complete therapy. Effort should be made to document SVR (HCV RNA less than lower limits of quantification) at least 12 weeks after completion of therapy (AI). Patients without cirrhosis who achieve SVR do not require continued liver disease monitoring. Periodic assessment for HCV reinfection should be done via HCV RNA testing on an at least yearly basis for those with ongoing risk behaviors or more frequently as dictated by clinical circumstances (e.g., new STI diagnosis or elevated liver enzymes) (AII). In the setting of cirrhosis, hepatocellular carcinoma screening with liver ultrasound every 6 months should continue indefinitely (BII). Special Considerations During Pregnancy Pregnant individuals, including those with HIV, should be tested for HCV infection to allow appropriate management for the mothers during pregnancy and after delivery and also to ensure their infants are identified as at risk for transmission and monitored (AIII).109 The rate of perinatal transmission has been reported at approximately 7% for infants born to mothers without HIV and 12% for infants born to mothers with HIV.35,39,110 Due in large part to the opioid epidemic, more infants are born today to pregnant people with HCV infection than ever before111,112; thus, universal screening for pregnant people during each pregnancy, regardless of HIV status, is now the standard of care.113 For the care of the infant, knowledge of exposure risk allows for screening for perinatal transmission.114 For the pregnant person, harm-reduction counseling and linkage to HCV care and treatment are important.115 Assessments for liver disease stage can be delayed until pregnancy related and postpartum changes have resolved. Individuals with known cirrhosis are at higher risks of complications during pregnancy, both for the individual and their infant. Hepatitis A and hepatitis B vaccines can be administered during pregnancy, and individuals who have not previously been vaccinated should receive them (AII). Data are limited regarding the role of medical or surgical interventions to reduce the risk of perinatal HCV transmission. Nearly all studies, including those in individuals with and without HIV, have found that elective cesarean delivery does not reduce the risk of perinatal HCV transmission.116-119 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-11 Moreover, there is an increased risk of maternal morbidity associated with cesarean compared with vaginal delivery, particularly in the setting of maternal HIV infection.120-123 Thus, while elective cesarean delivery in individuals with HIV/HCV coinfection can be considered based on HIV-related indications, data do not support its routine use for the prevention of HCV transmission. The current standard of care for treatment of HCV infection, regardless of duration, is DAA combination therapy. In real-world studies, SVR rates are similar to those from registration trials,124,125 and are consistently >90%. DAAs have not been sufficiently studied in pregnant women with HCV infection. In a pilot study of ledipasvir/sofosbuvir in pregnant women (without HIV), treatment was started in the end of the second/beginning of the third trimester and found to be safe and resulted in cure in nine women.126 Pharmacokinetic measurements did not identify clinically significant changes. Historically, while not studied in this population, DAA drugs have not demonstrated significant fetal toxicity concerns in animal studies, in contrast to when interferon and ribavirin were the standard of care. Interferon is no longer used for the treatment of HCV infection and ribavirin is used infrequently and usually in complex treatment or retreatment scenarios. Ribavirin is an FDA category X drug because of its teratogenicity at low doses in multiple animal species. Defects noted in animals include limb abnormalities, craniofacial defects, exencephaly, and anophthalmia. Ribavirin should not be used during pregnancy (AII). Women of childbearing potential and men receiving ribavirin should be counseled about the risks and need for consistent contraceptive use during and for 6 months after completion of ribavirin therapy (AIII). Inadvertent pregnancy during paternal exposure was not associated with adverse events in two newborns.127 For now, treatment with DAA during pregnancy is not recommended (CIII); more safety data are needed. Recommendations for Treatment of Hepatitis C Virus Infections For Treatment-Naive Patients Without Cirrhosis (Any Genotype or No Pre-Treatment Genotype) • Three (glecaprevir 100 mg/pibrentasvir 40 mg per tablet) tablets daily for 8 weeks (AI) or • One (sofosbuvir 400 mg/velpatasvir 100 mg per tablet) tablet daily for 12 weeks (AI) Note: Characteristics that exclude people with HIV from receiving simplified therapy are outlined in Box 1. For Treatment-Naive Patients with Compensated Cirrhosis (Recommendations Based on Genotypes) Genotypes 1, 2, 4–6 Preferred Therapy • Three (glecaprevir 100 mg/pibrentasvir 40 mg per tablet) tablets daily for 8 weeks (AIII) or • One (sofosbuvir 400 mg/velpatasvir 100 mg per tablet) tablet daily for 12 weeks (AI) Alternative Therapy • Three (glecaprevir 100 mg/pibrentasvir 40 mg per tablet) tablets daily for 12 weeks (CI) Genotype 3 Preferred Therapy • Three (glecaprevir 100 mg/pibrentasvir 40 mg per tablet) tablets daily for 8 weeks (AIII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-12 Alternative Therapy • Three (glecaprevir 100 mg/pibrentasvir 40 mg per tablet) tablets daily for 12 weeks (CI) or • One (sofosbuvir 400 mg/velpatasvir 100 mg per tablet) tablet daily, with or without ribavirin for 12 weeks pending results of NS5A RAS testing (CI) For Treatment of Acute HCV Infection • Three (glecaprevir 100 mg/pibrentasvir 40 mg per tablet) tablets daily for 8 weeks (AII) or • One (sofosbuvir 400 mg/velpatasvir 100 mg per tablet) tablet daily for 12 weeks (AII) Recommendations for treatment after DAA failure are not provided; see the corresponding section in the AASLD/IDSA HCV treatment guidance. 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Sofosbuvir and velpatasvir for the treatment of hepatitis C virus in patients coinfected with human immunodeficiency virus type 1: an open-label, Phase 3 study. Clin Infect Dis. 2017;65(1):6-12. Available at: 98. Brown RS, Jr., Buti M, Rodrigues L, et al. Glecaprevir/pibrentasvir for 8 weeks in treatment-naïve patients with chronic HCV genotypes 1-6 and compensated cirrhosis: the EXPEDITION-8 trial. J Hepatol. 2020;72(3):441-449. Available at: 99. Cornberg M, Jimenez AMA, Aghemo A, et al. Safety and effectiveness using 8 weeks of glecaprevir/pibrentasvir in HCV-infected treatment-naive patients with compensated cirrhosis: the CREST study. Hepatology. 2021;74:575A-576A. Available at: 100. Popping S, Hullegie SJ, Boerekamps A, et al. Early treatment of acute hepatitis C infection is cost-effective in HIV-infected men-who-have-sex-with-men. PLoS One. 2019;14(1):e0210179. Available at: 101. Bourlière M, Gordon SC, Flamm SL, et al. Sofosbuvir, velpatasvir, and voxilaprevir for previously treated HCV infection. N Engl J Med. 2017;376(22):2134-2146. Available at: 102. Poordad F, Felizarta F, Asatryan A, et al. Glecaprevir and pibrentasvir for 12 weeks for hepatitis C virus genotype 1 infection and prior direct-acting antiviral treatment. Hepatology. 2017;66(2):389-397. Available at: 103. Wyles D, Weiland O, Yao B, et al. Retreatment of patients who failed glecaprevir/pibrentasvir treatment for hepatitis C virus infection. J Hepatol. 2019;70(5):1019-1023. Available at: 104. Lok AS, Sulkowski MS, Kort JJ, et al. Efficacy of glecaprevir and pibrentasvir in patients with genotype 1 hepatitis C virus infection with treatment failure after NS5A inhibitor plus sofosbuvir therapy. Gastroenterology. 2019;157(6):1506-1517.e1501. Available at: 105. Belperio PS, Shahoumian TA, Loomis TP, Backus LI. Real-world effectiveness of sofosbuvir/velpatasvir/voxilaprevir in 573 direct-acting antiviral experienced hepatitis C patients. J Viral Hepat. 2019;26(8):980-990. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-22 106. Llaneras J, Riveiro-Barciela M, Lens S, et al. Effectiveness and safety of sofosbuvir/velpatasvir/voxilaprevir in patients with chronic hepatitis C previously treated with DAAs. J Hepatol. 2019;71(4):666-672. Available at: 107. Degasperi E, Spinetti A, Lombardi A, et al. Real-life effectiveness and safety of sofosbuvir/velpatasvir/voxilaprevir in hepatitis C patients with previous DAA failure. J Hepatol. 2019;71(6):1106-1115. Available at: 108. Papaluca T, Roberts SK, Strasser SI, et al. Efficacy and safety of sofosbuvir/velpatasvir/voxilaprevir for hepatitis C virus (HCV) NS5A-inhibitor experienced patients with difficult to cure characteristics. Clin Infect Dis. 2021;73(9):e3288-e3295. Available at: 109. The American College of Obstetricians and Gynecologists. Viral hepatitis in pregnancy. 2022. Available at: 110. Prasad M. Risk factors for mother to child transmission of hepatitis C (HCV): a prospective observational study. American Journal of Obstetrics & Gynecology. 2022;226(S5). Available at: 111. Rossi RM, Wolfe C, Brokamp R, et al. Reported prevalence of maternal hepatitis C virus infection in the United States. Obstet Gynecol. 2020;135(2):387-395. Available at: 112. Patrick SW, Bauer AM, Warren MD, Jones TF, Wester C. Hepatitis C virus infection among women giving birth - Tennessee and United States, 2009–2014. MMWR Morb Mortal Wkly Rep. 2017;66(18):470-473. Available at: 113. The American College of Obstetricians and Gynecologists. Routine hepatitis C virus screening in pregnant individuals. 2021. Available at: 114. Jhaveri R, Broder T, Bhattacharya D, Peters MG, Kim AY, Jonas MM. Universal screening of pregnant women for hepatitis C: the time is now. Clin Infect Dis. 2018;67(10):1493-1497. Available at: 115. Chaillon A, Rand EB, Reau N, Martin NK. Cost-effectiveness of universal hepatitis C virus screening of pregnant women in the United States. Clin Infect Dis. 2019;69(11):1888-1895. Available at: 116. McMenamin MB, Jackson AD, Lambert J, et al. Obstetric management of hepatitis C-positive mothers: analysis of vertical transmission in 559 mother-infant pairs. Am J Obstet Gynecol. 2008;199(3):315.e311-315. Available at: 117. Ghamar Chehreh ME, Tabatabaei SV, Khazanehdari S, Alavian SM. Effect of cesarean section on the risk of perinatal transmission of hepatitis C virus from HCV-RNA+/HIV- Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV M-23 mothers: a meta-analysis. Arch Gynecol Obstet. 2011;283(2):255-260. Available at: 118. Mariné-Barjoan E, Berrébi A, Giordanengo V, et al. HCV/HIV co-infection, HCV viral load and mode of delivery: risk factors for mother-to-child transmission of hepatitis C virus? AIDS. 2007;21(13):1811-1815. Available at: 119. European Paediatric Hepatitis C Virus Network. A significant sex--but not elective cesarean section--effect on mother-to-child transmission of hepatitis C virus infection. J Infect Dis. 2005;192(11):1872-1879. Available at: 120. Read JS, Tuomala R, Kpamegan E, et al. Mode of delivery and postpartum morbidity among HIV-infected women: the women and infants transmission study. J Acquir Immune Defic Syndr. 2001;26(3):236-245. Available at: 121. Grubert TA, Reindell D, Kästner R, et al. Rates of postoperative complications among human immunodeficiency virus-infected women who have undergone obstetric and gynecologic surgical procedures. Clin Infect Dis. 2002;34(6):822-830. Available at: 122. Grubert TA, Reindell D, Kästner R, Lutz-Friedrich R, Belohradsky BH, Dathe O. Complications after caesarean section in HIV-1-infected women not taking antiretroviral treatment. Lancet. 1999;354(9190):1612-1613. Available at: 123. Fiore S, Newell ML, Thorne C. Higher rates of post-partum complications in HIV-infected than in uninfected women irrespective of mode of delivery. AIDS. 2004;18(6):933-938. Available at: 124. D'Ambrosio R, Pasulo L, Puoti M, et al. Real-world effectiveness and safety of glecaprevir/pibrentasvir in 723 patients with chronic hepatitis C. J Hepatol. 2019;70(3):379-387. Available at: 125. Mangia A, Milligan S, Khalili M, et al. Global real-world evidence of sofosbuvir/velpatasvir as simple, effective HCV treatment: Analysis of 5,552 patients from 12 cohorts. Liver Int. 2020;40(8):1841-1852. Available at: 126. Chappell CA, Scarsi KK, Kirby BJ, et al. Ledipasvir plus sofosbuvir in pregnant women with hepatitis C virus infection: a phase 1 pharmacokinetic study. Lancet Microbe. 2020;1(5):e200-e208. Available at: 127. Hegenbarth K, Maurer U, Kroisel PM, Fickert P, Trauner M, Stauber RE. No evidence for mutagenic effects of ribavirin: report of two normal pregnancies. Am J Gastroenterol. 2001;96(7):2286-2287. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-1 Herpes Simplex Virus Disease (Last updated May 26, 2020; last reviewed January 10, 2024) Epidemiology Infections with human herpes simplex virus type 1 (HSV-1) and type 2 (HSV-2) are common. Among persons aged 14 to 49 years in the United States, the HSV-1 seroprevalence is 47.8%, and the HSV-2 seroprevalence is 11.9%.1 While most cases of recurrent genital herpes are due to HSV-2, over the past decade, HSV-1 has become an increasing cause of first-episode genital herpes, causing up to 70% of infections in some populations, such as young adult women and men who have sex with men.2 Approximately 70% of persons with HIV are HSV-2 seropositive, and 95% are seropositive for either HSV-1 or HSV-2.3 HSV-2 infection increases the risk of HIV acquisition two- to three-fold,4,5 and in coinfected patients, HSV-2 reactivation results in increases in HIV RNA levels in blood and genital secretions.6 Clinical Manifestations Orolabial herpes (commonly known as cold sores or fever blisters) is the most common manifestation of HSV-1 infection. Classic manifestations of oral HSV-1 include a sensory prodrome in the affected area, rapidly followed by lesions on lips and oral mucosa that evolve in stages from papule to vesicle, ulcer, and crust. The course of illness in untreated patients is 5 days to 10 days. Lesions recur 1 to 12 times per year and can be triggered by sunlight or physiologic stress. Genital herpes is typically caused by HSV-2 and is the most common manifestation of HSV-2 infection. Increasingly, first-episode genital herpes is caused by HSV-1 and is indistinguishable from HSV-2 infection, although recurrences and viral shedding occur less often with genital HSV-1 infection. Typical genital mucosal or skin lesions evolve through stages of papule, vesicle, ulcer, and crust. Ulcerative lesions are usually the only stage observed on mucosal surfaces, but vesicles are commonly seen on skin on or around the genitals (e.g., the penile shaft, mon pubis, thighs). Local symptoms might include a sensory prodrome consisting of pain and pruritus. Mucosal disease is occasionally accompanied by dysuria or vaginal or urethral discharge. Inguinal lymphadenopathy is common with genital herpes, particularly in primary infection.7 These classic manifestations occur in some patients, but most individuals with genital herpes have mild and atypical lesions that are often unrecognized. Regardless of the clinical severity of infection, viral shedding on mucosal surfaces occurs frequently and can result in transmission. HSV shedding occurs more frequently in persons with CD4 T lymphocyte (CD4) cell counts <200 cells/mm3 than in those with higher CD4 counts.8,9 An episode of genital HSV-1 disease is indistinguishable from genital HSV-2 disease, but recurrences and viral shedding occur less often with genital HSV-1 infection. HSV is a significant cause of proctitis in men with HIV infection who have sex with men and may not be associated with external anal ulcers.10 In profoundly immunocompromised patients, extensive, deep, nonhealing ulcerations can occur. These lesions have been reported most often in those with CD4 counts <100 cells/mm3 and also may be associated with acyclovir-resistant HSV.11 In addition, atypical presentations such as hypertrophic genital HSV,12,13 which mimics neoplasia and requires biopsy for diagnosis, may be seen in persons with HIV infection. The manifestations of non-mucosal HSV infections (e.g., HSV keratitis, HSV encephalitis, HSV hepatitis, herpetic whitlow) are similar to those observed in HIV-seronegative individuals. Disseminated HSV infection is rare, even in profoundly immunosuppressed patients. HSV retinitis manifests as acute retinal necrosis, which can lead rapidly to loss of vision. Diagnosis Because mucosal HSV infections cannot be diagnosed accurately by clinical examination, a laboratory diagnosis of all suspected HSV mucosal infections should be pursued.14 HSV DNA polymerase chain Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-2 reaction (PCR), and viral culture are preferred methods for diagnosis of mucocutaneous lesions potentially caused by HSV. PCR is the most sensitive method of diagnosis. HSV detected in genital lesions should be typed as HSV-1 or HSV-2. The frequency of recurrences is greater for HSV-2 than for HSV-1, and therefore knowledge of viral type is helpful for counseling purposes. Type-specific serologic assays are commercially available and can be used for diagnosis of HSV-2 infection in asymptomatic individuals or those with atypical lesions. Type-specific serologic screening for HSV-2 for persons with HIV infection can be considered. However, providers should be aware that there are some important limitations of currently available serologic tests. In particular, false positive HSV-2 serologic test results occur with the enzyme immunoassay antibody tests, particularly at low index values (1.1–3.5).15-17 In such situations, confirmatory testing with a second serologic test is recommended in the 2015 Centers for Disease Control and Prevention (CDC) Sexually Transmitted Disease Treatment Guidelines.18 A diagnosis of HSV-2 should be accompanied by counseling that includes discussion of the risk of transmitting infection to sex partners. Guidelines for counseling are provided in the 2015 CDC Sexually Transmitted Disease Treatment Guidelines.18 Serologic screening for HSV-1 infection is not recommended. Preventing Exposure Although most people with HIV also have HSV-1 and HSV-2 infections, it is important to prevent HSV-2 acquisition in those who do not have HSV-2. Persons with HIV who are HSV-2 seronegative should consider asking their partners to be tested using HSV type-specific serology before initiating sexual activity because disclosure of HSV-2 in heterosexual HIV-negative, HSV-2-discordant couples was associated with reduced risk of transmission of HSV-2 (BII).19 Consistent use of latex condoms reduced HSV-2 acquisition among heterosexual couples, and their use should be encouraged to prevent transmission of HSV-2 and other sexually transmitted pathogens (AII).20,21 Sexual transmission of HSV most often occurs during episodes of asymptomatic viral shedding. However, persons with HIV should specifically avoid sexual contact with partners who have overt genital or orolabial herpetic lesions (AII). In HSV-2 seropositive persons who have symptomatic genital herpes but not HIV, suppressive antiviral therapy (e.g., valacyclovir 500 mg once daily) reduced HSV-2 transmission to susceptible heterosexual partners by 48%.22 However, in HIV-1/HSV-2-seropositive persons not on antiretroviral therapy (ART), suppressive acyclovir (400 mg twice daily) did not prevent HSV-2 transmission to HSV-2 seronegative partners.23 Suppressive anti-HSV therapy to prevent HSV-2 transmission to susceptible partners is not recommended for persons with HIV/HSV-2 coinfection who are not on ART (AI). There are no data available regarding use of suppressive therapy to prevent genital HSV-1 transmission. Preventing Disease Prophylaxis with antiviral drugs to prevent primary HSV infection is not recommended (AIII). In clinical trials, pre-exposure prophylaxis with vaginal tenofovir gel and oral tenofovir disoproxil fumarate (TDF) or with TDF/emtricitabine has been associated with reduced risk of HSV-2 acquisition in persons without HIV.24-26 However, HSV-2 seronegative persons with HIV on TDF-containing ART regimens are at similar risk of acquiring HSV-2 as those on non-TDF containing ART regimens, suggesting that TDF is not effective in preventing HSV-2 acquisition in persons with HIV infection.27 The dose, duration, timing, and efficacy of anti-HSV prophylaxis after known or suspected exposure to HSV has not been evaluated. No vaccine for prevention of HSV infection is available. Some studies have shown that medical male circumcision (MMC) decreased the risk of HSV-2 acquisition in African men without HIV,28,29 and may be associated with decreased risk of HSV-2 transmission to female partners.30 However, MMC to decrease risk of HSV-2 acquisition and transmission has not been studied among men with HIV and therefore is not recommended for the sole purpose of preventing HSV acquisition (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-3 Treating Disease Patients with HSV infections can be treated with episodic antiviral therapy when symptomatic lesions occur or with daily suppressive therapy to prevent recurrences. Acyclovir, valacyclovir, and famciclovir are effective for suppressive and episodic therapy. Valacyclovir is the prodrug of acyclovir, and has improved oral bioavailability, with decreased dosing frequency, compared to acyclovir. When deciding on suppressive therapy for genital HSV-2 infection in persons with HIV and HSV-2 coinfection, factors to consider include the frequency and severity of HSV recurrences and risk for genital ulcer disease (GUD) when initiating ART.31 Episodic treatment for individual recurrences of GUD does not influence the natural history of genital HSV-2 infection. Patients with orolabial HSV lesions can be treated with oral acyclovir, valacyclovir, or famciclovir for 5 days to 10 days (AIII). First episodes of genital HSV should be treated with oral acyclovir, valacyclovir, or famciclovir for 7 days to 10 days; recurrences can be treated for 5 to 10 days (AI). Severe mucocutaneous HSV lesions respond best to initial treatment with intravenous (IV) acyclovir (AIII).11,32 Once the lesions begin to regress, patients can be switched to oral antiviral therapy. Therapy should be continued until the lesions have completely healed. Although disseminated disease due to HSV is rare in persons with HIV, HSV necrotizing retinitis can occur, which may be difficult to distinguish clinically from retinitis caused by varicella-zoster virus. Special Considerations with Regard to Starting Antiretroviral Therapy Orolabial and genital HSV should not influence the decision on when to start ART in persons with HIV. Transient increases in HSV-2–associated genital ulcers have been observed during the first 6 months after initiation of ART in HIV/HSV-2 coinfected persons. In such cases, suppressive anti-HSV therapy can be considered. The frequency and severity of clinical episodes of genital herpes is often reduced in individuals after immune reconstitution on ART. However, immune reconstitution does not reduce the frequency of genital HSV shedding.33 Monitoring of Response to Therapy and Adverse Events (Including IRIS) Acyclovir, valacyclovir, and famciclovir are occasionally associated with nausea or headache. No laboratory monitoring is needed for patients receiving episodic or suppressive HSV therapy unless they have advanced renal impairment. However, for patients receiving high-dose IV acyclovir, monitoring of renal function, and dose adjustment as necessary, are recommended at initiation of treatment and once or twice weekly for the duration of treatment. HSV-2 shedding and GUD can increase in the first 6 months after initiation of ART, particularly in those with low CD4 counts.34,35 Mucocutaneous lesions that are atypical and occasionally recalcitrant to therapy have been reported in individuals initiating ART and have been attributed to immune reconstitution inflammatory syndrome (IRIS).36 Managing Treatment Failure Treatment failure due to acyclovir resistance should be suspected if herpes-related lesions do not begin to resolve within 7 days to 10 days after initiation of anti-HSV therapy. In persons with suspected acyclovir-resistant HSV, viral culture of the lesion should be performed, and if virus is isolated, susceptibility testing done to confirm drug resistance (AII).37 Phenotypic testing of viral isolates has been the gold standard method for assessing HSV resistance; genotypic testing is not yet available. The treatment of choice for acyclovir-resistant HSV is IV foscarnet (AI).38,39 IV cidofovir is a potential alternative (CIII). A novel agent, the helicase-primase inhibitor pritelivir, is currently being testing in clinical trials for treatment of acyclovir-resistant herpes in immunocompromised persons (ClinicalTrials. gov Identifier: NCT03073967). There is an Expanded Access Program available for oral pritelivir in these populations; for more information see AiCuris Pritelivir Early Access website. Topical trifluridine, foscarnet, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-4 cidofovir, and imiquimod also have been used successfully to treat external lesions, although prolonged application for 21 days to 28 days or longer may be required (CIII).40-44 Preventing Recurrence Suppressive therapy with oral acyclovir, valacyclovir, or famciclovir is effective in preventing recurrences of HSV lesions and is preferred for patients who have severe or frequent HSV recurrences or who want to minimize the frequency of recurrences (AI).14,45 Suppressive therapy for HSV may be continued indefinitely, without regard to improved CD4 count, although the need for continued therapy should be addressed on an annual basis, particularly if immune reconstitution has occurred (BIII). Persons starting ART with CD4 counts <250 cells/mm3 have an increased risk of HSV-2 shedding and GUD in the first 6 months on ART. Suppressive acyclovir decreases the risk of GUD nearly 60%, and may be recommended for persons with CD4 counts <250 cells/mm3 starting ART (BI). In persons with HIV not on ART, suppressive anti-HSV therapy also results in a decrease in HIV RNA levels in plasma, anal, and genital secretions, and in a lower risk of HIV progression.46 However, antiviral regimens for herpes do not decrease the risk of HIV transmission to sexual partners, and should not be used in place of ART to delay HIV progression.47 In persons who are taking ART, suppressive HSV antivirals do not delay HIV progression, improve CD4 recovery, or decrease markers of systemic inflammation48,49 and are not useful for these ends (AI). Although there is no data specific to persons with HIV, in hematopoietic stem cell recipients, the risk of developing acyclovir-resistant HSV was lower with daily suppressive acyclovir therapy than with episodic therapy.50 Special Considerations During Pregnancy Laboratory testing to diagnose mucocutaneous HSV infections is the same for pregnant women as for non-pregnant women. Episodic therapy for first-episode HSV disease and for recurrences can be offered during pregnancy. Visceral disease following HSV acquisition is more likely to occur during pregnancy and can be fatal. Acyclovir is the antiviral drug with the most reported experience in pregnancy and appears to be safe, particularly during the second and third trimesters (AIII).51 One recent case–control study suggested a higher risk of gastroschisis associated with both genital herpes and acyclovir use during the first trimester of pregnancy.52 The use of valacyclovir and famciclovir during pregnancy has been described, and the antiviral drugs also appear to be safe and well tolerated during the third trimester.53 Given its simplified dosing schedule valacyclovir is an option for treatment and suppressive therapy during pregnancy (CIII). An additional concern with HSV during pregnancy is the potential for HSV transmission to the fetus or neonate. The rate of neonatal HSV transmission in HSV-2-seropositive pregnant women is low, except in those who acquire genital HSV infection late in pregnancy. However, when HSV transmission does occur, the adverse sequelae for the neonate can be very significant. The predominant risk for neonatal HSV transmission is maternal genital shedding of HSV at delivery. Cesarean delivery is recommended for women with a genital herpes prodrome or visible HSV genital lesions at the onset of labor (BII).14 Use of acyclovir or valacyclovir in late pregnancy suppresses genital herpes outbreaks and reduces the need for cesarean delivery for recurrent HSV in HIV-seronegative women54 and is likely to have similar efficacy in women with HIV infection. However, neonatal HSV disease has been reported in infants born to women treated with antenatal suppressive antiviral therapy.55 Suppressive therapy with either valacyclovir or acyclovir is recommended starting at 36 weeks’ gestation for pregnant women with recurrences of genital herpes during pregnancy (BII).56 Suppressive therapy for women who are seropositive for HSV-2 but no history of genital lesions is not recommended. Maternal genital herpes was a risk factor for perinatal HIV transmission in the era preceding availability of ART.57 Whether HSV facilitates HIV transmission in pregnant women on ART is unknown. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-5 Recommendations for Treating Herpes Simplex Virus Infections Note: Compared to acyclovir, valacyclovir has improved bioavailability and requires less frequent dosing. Treating Orolabial Lesions (Duration: 5–10 Days) •  Valacyclovir 1 g PO twice a day (AIII), or •  Famciclovir 500 mg PO twice a day (AIII), or •  Acyclovir 400 mg PO three times a day (AIII) Treating Initial Genital Lesions (Duration: 7–10 Days) or Recurrent Genital Lesions (Duration: 5–10 Days) •  Valacyclovir 1 g PO twice a day (AI), or •  Famciclovir 500 mg PO twice a day (AI), or •  Acyclovir 400 mg PO three times a day (AI) Treating Severe Mucocutaneous HSV Infections (AIII) •  For initial therapy, acyclovir 5 mg/kg IV every 8 hours •  After lesions begin to regress, change to oral therapy as above. •  Continue treatment until lesions have completely healed. Chronic Suppressive Therapy Indications: •  For patients with severe recurrences (AI), or •  Patients who want to minimize the frequency of recurrences (AI), including pregnant women, or •  To reduce the risk of genital ulcer disease in patients with CD4 counts <250 cells/mm3 who are starting ART (BI) Treatment: •  Valacyclovir 500 mg PO twice a day (AI), or •  Famciclovir 500 mg PO twice a day (AI), or •  Acyclovir 400 mg PO twice a day (AI) •  Evaluate ongoing need for suppressive therapy annually. For Acyclovir-Resistant Mucocutaneous HSV Infections Preferred Therapy: •  IV Foscarnet 80–120 mg/kg/day in 2–3 divided doses until clinical response (AI) Alternative Therapy (Duration: ≥21–28 Days, Based on Clinical Response) (CIII): •  IV cidofovir 5 mg/kg once weekly, or •  Topical trifluridine 1% three times a day, or •  Topical cidofovir 1% gel once daily, or •  Topical imiquimod 5% cream three times a week, or •  Topical foscarnet 1% five times a day Notes: •  Topical formulations of trifluridine, cidofovir, and foscarnet are not commercially available. •  Extemporaneous compounding of topical products can be prepared using trifluridine ophthalmic solution and the IV formulation of cidofovir and foscarnet. •  An expanded access program of oral pritelivir is now available for immunocompromised patients with acyclovir-resistant HSV infection; for more information see AiCuris Pritelivir Early Access website. Key: ART = antiretroviral therapy; HSV = herpes simplex virus; IV = intravenously; PO = orally Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-6 References 1.  McQuillan G, Kruszon-Moran D, Flagg EW, Paulose-Ram R. Prevalence of herpes simplex virus type 1 and type 2 in persons Aged 14–49: United States, 2015-2016. NCHS Data Brief. 2018(304):1-8. Available at: nih.gov/pubmed/29442994. 2.  Ryder N, Jin F, McNulty AM, Grulich AE, Donovan B. Increasing role of herpes simplex virus type 1 in first-episode anogenital herpes in heterosexual women and younger men who have sex with men, 1992-2006. Sex Transm Infect. 2009;85(6):416-419. Available at: 3.  Xu F, Sternberg MR, Kottiri BJ, et al. Trends in herpes simplex virus type 1 and type 2 seroprevalence in the United States. JAMA. 2006;296(8):964-973. Available at: 4.  Wald A, Link K. Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: a meta-analysis. J Infect Dis. 2002;185(1):45-52. Available at: 5.  Looker KJ, Elmes JAR, Gottlieb SL, et al. Effect of HSV-2 infection on subsequent HIV acquisition: an updated systematic review and meta-analysis. Lancet Infect Dis. 2017;17(12):1303-1316. Available at: gov/pubmed/28843576. 6.  Nagot N, Ouedraogo A, Konate I, et al. Roles of clinical and subclinical reactivated herpes simplex virus type 2 infection and human immunodeficiency virus type 1 (HIV-1)-induced immunosuppression on genital and plasma HIV-1 levels. J Infect Dis. 2008;198(2):241-249. Available at: 7.  Corey L, Adams HG, Brown ZA, Holmes KK. Genital herpes simplex virus infections: clinical manifestations, course, and complications. Ann Intern Med. 1983;98(6):958-972. Available at: 8.  Schiffer JT, Swan DA, Magaret A, Schacker TW, Wald A, Corey L. 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Yudin MH, Kaul R. Progressive hypertrophic genital herpes in an HIV-infected woman despite immune recovery on antiretroviral therapy. Infect Dis Obstet Gynecol. 2008;2008:592532. Available at: pubmed/18784844. 13.  Sbidian E, Battistella M, Legoff J, et al. Recalcitrant pseudotumoral anogenital herpes simplex virus type 2 in HIV-infected patients: evidence for predominant B-lymphoplasmocytic infiltration and immunomodulators as effective therapeutic strategy. Clin Infect Dis. 2013;57(11):1648-1655. Available at: 14.  Workowski KA, Berman S, Centers for Disease Control and Prevention. Sexually transmitted diseases treatment guidelines, 2010. MMWR Recomm Rep. 2010;59(RR-12):1-110. Available at: 15.  Agyemang E, Le QA, Warren T, et al. Performance of commercial enzyme-linked immunoassays for diagnosis of herpes simplex virus-1 and herpes simplex virus-2 infection in a clinical setting. Sex Transm Dis. 2017;44(12):763-767. Available at: 16.  Golden MR, Ashley-Morrow R, Swenson P, Hogrefe WR, Handsfield HH, Wald A. Herpes simplex virus type 2 (HSV-2) Western blot confirmatory testing among men testing positive for HSV-2 using the focus enzyme-linked immunosorbent assay in a sexually transmitted disease clinic. Sex Transm Dis. 2005;32(12):771-777. Available at: nih.gov/pubmed/16314775. 17.  Morrow RA, Friedrich D, Meier A, Corey L. Use of “biokit HSV-2 Rapid Assay” to improve the positive predictive value of Focus HerpeSelect HSV-2 ELISA. BMC Infect Dis. 2005;5:84. Available at: pubmed/16225691. 18.  Workowski KA, Bolan GA, Centers for Disease Control and Prevention. Sexually transmitted diseases treatment guidelines, 2015. MMWR Recomm Rep. 2015;64(RR-03):1-137. Available at: 19.  Wald A, Krantz E, Selke S, Lairson E, Morrow RA, Zeh J. Knowledge of partners’ genital herpes protects against Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-7 herpes simplex virus type 2 acquisition. J Infect Dis. 2006;194(1):42-52. Available at: pubmed/16741881. 20.  Wald A, Langenberg AG, Krantz E, et al. The relationship between condom use and herpes simplex virus acquisition. Ann Intern Med. 2005;143(10):707-713. Available at: 21.  Martin ET, Krantz E, Gottlieb SL, et al. A pooled analysis of the effect of condoms in preventing HSV-2 acquisition. Arch Intern Med. 2009;169(13):1233-1240. Available at: 22.  Corey L, Wald A, Patel R, et al. Once-daily valacyclovir to reduce the risk of transmission of genital herpes. N Engl J Med. 2004;350(1):11-20. Available at: 23.  Mujugira A, Magaret AS, Celum C, et al. Daily acyclovir to decrease herpes simplex virus type 2 (HSV-2) transmission from HSV-2/HIV-1 coinfected persons: a randomized controlled trial. J Infect Dis. 2013;208(9):1366-1374. Available at: 24.  Abdool Karim Q, Abdool Karim SS, Frohlich JA, et al. Effectiveness and safety of tenofovir gel, an antiretroviral microbicide, for the prevention of HIV infection in women. Science. 2010;329(5996):1168-1174. Available at: ncbi.nlm.nih.gov/pubmed/20643915. 25.  Celum C, Morrow RA, Donnell D, et al. Daily oral tenofovir and emtricitabine-tenofovir preexposure prophylaxis reduces herpes simplex virus type 2 acquisition among heterosexual HIV-1-uninfected men and women: a subgroup analysis of a randomized trial. Ann Intern Med. 2014;161(1):11-19. Available at: 26.  Marrazzo JM, Rabe L, Kelly C, et al. Tenofovir gel for prevention of herpes simplex virus type 2 acquisition: findings from the VOICE trial. J Infect Dis. 2019;219(12):1940-1947. Available at: 27.  Celum C, Hong T, Cent A, et al. Herpes simplex virus type 2 acquisition among HIV-1-infected adults treated with tenofovir disoproxyl fumarate as part of combination antiretroviral therapy: results from the ACTG A5175 PEARLS Study. J Infect Dis. 2017;215(6):907-910. Available at: 28.  Tobian AA, Serwadda D, Quinn TC, et al. Male circumcision for the prevention of HSV-2 and HPV infections and syphilis. N Engl J Med. 2009;360(13):1298-1309. Available at: 29.  Sobngwi-Tambekou J, Taljaard D, Lissouba P, et al. Effect of HSV-2 serostatus on acquisition of HIV by young men: results of a longitudinal study in Orange Farm, South Africa. J Infect Dis. 2009;199(7):958-964. Available at: nlm.nih.gov/pubmed/19220143. 30.  Grund JM, Bryant TS, Jackson I, et al. Association between male circumcision and women’s biomedical health outcomes: a systematic review. Lancet Glob Health. 2017;5(11):e1113-e1122. Available at: pubmed/29025633. 31.  Keating TM, Kurth AE, Wald A, Kahle EM, Barash EA, Buskin SE. Clinical burden of herpes simplex virus disease in people with human immunodeficiency virus. Sex Transm Dis. 2012;39(5):372-376. Available at: gov/pubmed/22504602. 32.  Meyers JD, Wade JC, Mitchell CD, et al. Multicenter collaborative trial of intravenous acyclovir for treatment of mucocutaneous herpes simplex virus infection in the immunocompromised host. Am J Med. 1982;73(1A):229-235. Available at: 33.  Posavad CM, Wald A, Kuntz S, et al. Frequent reactivation of herpes simplex virus among HIV-1-infected patients treated with highly active antiretroviral therapy. J Infect Dis. 2004;190(4):693-696. Available at: pubmed/15272395. 34.  Graham SM, Masese L, Gitau R, et al. Increased risk of genital ulcer disease in women during the first month after initiating antiretroviral therapy. J Acquir Immune Defic Syndr. 2009;52(5):600-603. Available at: pubmed/19648822. 35.  Tobian AA, Grabowski MK, Serwadda D, et al. Reactivation of herpes simplex virus type 2 after initiation of antiretroviral therapy. J Infect Dis. 2013;208(5):839-846. Available at: 36.  Couppie P, Sarazin F, Clyti E, et al. Increased incidence of genital herpes after HAART initiation: a frequent presentation of immune reconstitution inflammatory syndrome (IRIS) in HIV-infected patients. AIDS Patient Care STDS. 2006;20(3):143-145. Available at: 37.  Balfour HH Jr. Antiviral drugs. N Engl J Med. 1999;340(16):1255-1268. Available at: pubmed/10210711. 38.  Safrin S, Crumpacker C, Chatis P, et al. A controlled trial comparing foscarnet with vidarabine for acyclovir-resistant mucocutaneous herpes simplex in the acquired immunodeficiency syndrome. The AIDS Clinical Trials Group. N Engl J Med. 1991;325(8):551-555. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV N-8 39.  Levin MJ, Bacon TH, Leary JJ. Resistance of herpes simplex virus infections to nucleoside analogues in HIV-infected patients. Clin Infect Dis. 2004;39 Suppl 5:S248-257. Available at: 40.  Lascaux AS, Caumes E, Deback C, et al. Successful treatment of aciclovir and foscarnet resistant Herpes simplex virus lesions with topical imiquimod in patients infected with human immunodeficiency virus type 1. J Med Virol. 2012;84(2):194-197. Available at: 41.  Perkins N, Nisbet M, Thomas M. Topical imiquimod treatment of aciclovir-resistant herpes simplex disease: case series and literature review. Sex Transm Infect. 2011;87(4):292-295. Available at: 42.  Lateef F, Don PC, Kaufmann M, White SM, Weinberg JM. Treatment of acyclovir-resistant, foscarnet-unresponsive HSV infection with topical cidofovir in a child with AIDS. Arch Dermatol. 1998;134(9):1169-1170. Available at: ncbi.nlm.nih.gov/pubmed/9762047. 43.  Kessler HA, Hurwitz S, Farthing C, et al. Pilot study of topical trifluridine for the treatment of acyclovir-resistant mucocutaneous herpes simplex disease in patients with AIDS (ACTG 172). AIDS Clinical Trials Group. J Acquir Immune Defic Syndr Hum Retrovirol. 1996;12(2):147-152. Available at: 44.  Javaly K, Wohlfeiler M, Kalayjian R, et al. Treatment of mucocutaneous herpes simplex virus infections unresponsive to acyclovir with topical foscarnet cream in AIDS patients: a phase I/II study. J Acquir Immune Defic Syndr. 1999;21(4):301-306. Available at: 45.  DeJesus E, Wald A, Warren T, et al. Valacyclovir for the suppression of recurrent genital herpes in human immunodeficiency virus-infected subjects. J Infect Dis. 2003;188(7):1009-1016. Available at: 46.  Lingappa JR, Baeten JM, Wald A, et al. Daily acyclovir for HIV-1 disease progression in people dually infected with HIV-1 and herpes simplex virus type 2: a randomised placebo-controlled trial. Lancet. 2010;375(9717):824-833. Available at: 47.  Celum C, Wald A, Lingappa JR, et al. Acyclovir and transmission of HIV-1 from persons infected with HIV-1 and HSV-2. N Engl J Med. 2010;362(5):427-439. Available at: 48.  Yi TJ, Walmsley S, Szadkowski L, et al. A randomized controlled pilot trial of valacyclovir for attenuating inflammation and immune activation in HIV/herpes simplex virus 2-coinfected adults on suppressive antiretroviral therapy. Clin Infect Dis. 2013;57(9):1331-1338. Available at: 49.  Van Wagoner N, Geisler WM, Bachmann LH, Hook EW. The effect of valacyclovir on HIV and HSV-2 in HIV-infected persons on antiretroviral therapy with previously unrecognised HSV-2. Int J STD AIDS. 2015;26(8):574-581. Available at: 50.  Erard V, Wald A, Corey L, Leisenring WM, Boeckh M. Use of long-term suppressive acyclovir after hematopoietic stem-cell transplantation: impact on herpes simplex virus (HSV) disease and drug-resistant HSV disease. J Infect Dis. 2007;196(2):266-270. Available at: 51.  Stone KM, Reiff-Eldridge R, White AD, et al. Pregnancy outcomes following systemic prenatal acyclovir exposure: Conclusions from the international acyclovir pregnancy registry, 1984-1999. Birth Defects Res A Clin Mol Teratol. 2004;70(4):201-207. Available at: 52.  Ahrens KA, Anderka MT, Feldkamp ML, et al. Antiherpetic medication use and the risk of gastroschisis: findings from the National Birth Defects Prevention Study, 1997-2007. Paediatr Perinat Epidemiol. 2013;27(4):340-345. Available at: https:// www.ncbi.nlm.nih.gov/pubmed/23772935. 53.  Pasternak B, Hviid A. Use of acyclovir, valacyclovir, and famciclovir in the first trimester of pregnancy and the risk of birth defects. JAMA. 2010;304(8):859-866. Available at: 54.  Sheffield JS, Hollier LM, Hill JB, Stuart GS, Wendel GD. Acyclovir prophylaxis to prevent herpes simplex virus recurrence at delivery: a systematic review. Obstet Gynecol. 2003;102(6):1396-1403. Available at: pubmed/14662233. 55.  Pinninti SG, Angara R, Feja KN, et al. Neonatal herpes disease following maternal antenatal antiviral suppressive therapy: a multicenter case series. J Pediatr. 2012;161(1):134-138 e131-133. Available at: pubmed/22336576. 56.  ACOG Committee on Practice Bulleting—Gynecology. ACOG Practice Bulletin No. 117: Gynecologic care for women with human immunodeficiency virus. Obstet Gynecol. 2010;116(6):1492-1509. Available at: gov/pubmed/21099636. 57.  Chen KT, Segu M, Lumey LH, et al. Genital herpes simplex virus infection and perinatal transmission of human immunodeficiency virus. Obstet Gynecol. 2005;106(6):1341-1348. Available at: pubmed/16319261. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-1 Histoplasmosis Updated: September 13, 2019 Reviewed: January 10, 2024 Epidemiology Histoplasmosis is caused by the dimorphic fungus Histoplasma capsulatum. The fungal infection is endemic to the central and south-central United States, where it is especially common in the Ohio and Mississippi River valleys. Histoplasmosis is also found in Latin America and the Caribbean and less commonly in other parts of the world. In endemic areas, the annual incidence rate may approach 5% among individuals with HIV. A CD4 T lymphocyte (CD4) count <150 cells/mm3 is associated with an increased risk of symptomatic illness in people with HIV.1,2 Histoplasmosis is acquired by inhalation of microconidia that form in the mycelial phase of the fungus in the environment. Asymptomatic dissemination of infection beyond the lungs is common, and cellular immunity is critical in controlling infection. Diminished cellular immunity can lead to reactivation of a quiescent focal infection acquired years early; this is the presumed mechanism for disease occurrence in nonendemic areas. Clinical Manifestations In patients with HIV, common clinical manifestations of progressive disseminated histoplasmosis include fever, fatigue, weight loss, and hepatosplenomegaly. Cough, chest pain, and dyspnea occur in approximately 50% of patients.1,3 Central nervous system (CNS), gastrointestinal (GI), and cutaneous manifestations occur in a smaller percentage of patients. Approximately 10% of patients experience shock and multi-organ failure. Patients with CNS histoplasmosis typically experience fever and headache, and if brain involvement is present, seizures, focal neurological deficits, and changes in mental status.4 GI disease usually manifests as diarrhea, fever, abdominal pain, and weight loss.5 In a case series of patients with AIDS in Panama, diarrhea was seen in 50% of the patients with histoplasmosis.6 For patients with CD4 counts >300 cells/mm3, histoplasmosis is often limited to the respiratory tract and usually presents with cough, pleuritic chest pain, and fever. Diagnosis Detection of Histoplasma antigen in blood or urine is a sensitive method for rapid diagnosis of disseminated and acute pulmonary histoplasmosis7 but is insensitive for chronic forms of pulmonary infection. In a study using a newer quantitative assay, Histoplasma antigen was detected in 100% of urine samples and 92% of serum samples from people with AIDS and disseminated histoplasmosis.8 Antigen detection in bronchoalveolar lavage fluid may also be useful method for diagnosis of pulmonary histoplasmosis.9 In patients with severe disseminated histoplasmosis, peripheral blood smears can show the organisms engulfed by white blood cells, and histopathological examination of biopsy material from involved tissues often demonstrate the characteristic 2 to 4 µm in diameter budding yeast cells. H. capsulatum can be cultured from blood (using the lysis-centrifugation technique), bone marrow, respiratory secretions, or from samples from other involved sites in >85% of patients with AIDS and disseminated histoplasmosis, but the organism requires several weeks to grow.10 Serologic tests are Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-2 less useful than antigen assays in patients with AIDS and disseminated histoplasmosis but may be helpful in patients with pulmonary disease who have reasonably intact immune responses.10,11 The diagnosis of Histoplasma meningitis is often difficult. The usual cerebrospinal fluid (CSF) findings are lymphocytic pleocytosis, elevated protein, and low glucose. Fungal stains are usually negative, and CSF cultures are positive in a minority of cases.4 In a recent review of CNS histoplasmosis that included patients with HIV infection, cultures were positive in 38% of patients.12 Histoplasma antigen can be detected in CSF in a far greater number of cases, and antibodies against H. capsulatum are seen in approximately one-half of cases.12 A positive antigen or antibody test result from CSF is diagnostic for histoplasmosis. In cases in which none of these specific tests is positive, a presumptive diagnosis of Histoplasma meningitis is appropriate if the patient has disseminated histoplasmosis and findings of CNS infection not attributable to another cause. Preventing Exposure Individuals with HIV who live in or visit areas in which histoplasmosis is endemic cannot completely avoid exposure to H. capsulatum, but those with CD4 counts <150 cells/mm3 should avoid activities associated with an increased risk for histoplasmosis (BIII). These activities include creating dust when working with surface soil; cleaning chicken coops; disturbing areas contaminated with bird or bat droppings; cleaning, remodeling, or demolishing old buildings; and exploring caves. Preventing Disease Data from a prospective, randomized, controlled trial indicate that itraconazole can reduce the frequency of histoplasmosis, although not mortality, in patients who have advanced HIV and who live in areas in which histoplasmosis is highly endemic.13 Some experts would give prophylaxis with itraconazole at a dose of 200 mg daily to patients with CD4 counts <150 cells/mm3 who are at high risk because of occupational exposure or who live in a community with a hyperendemic rate of histoplasmosis (>10 cases/100 patient-years) (BI). If used, primary prophylaxis can be discontinued in patients on antiretroviral therapy (ART) once CD4 counts are ≥150 cells/mm3 for 6 months and HIV-1 viral load is undetectable (BIII). Prophylaxis should be restarted if the patient’s CD4 count falls to <150 cells/mm3 (BIII). Treating Disease In a randomized clinical trial, intravenous (IV) liposomal amphotericin B (3 mg/kg daily) was more effective than standard IV amphotericin B deoxycholate (0.7 mg/kg daily); the liposomal formulation induced a more rapid and complete response, lowered mortality rates, and reduced toxicity.14 Based on these findings, patients with moderately severe to severe disseminated histoplasmosis should be treated with IV liposomal amphotericin B (3 mg/kg daily) for ≥2 weeks or until they clinically improve (AI). Amphotericin B lipid complex (5 mg/kg daily) can be used if cost is a concern or patient cannot tolerate liposomal amphotericin B (AIII). Step-down therapy to oral itraconazole, 200 mg three times a day for 3 days, and then 200 mg two times a day, should be given for ≥12 months (AII).15 Because absorption of itraconazole can be erratic and because of potential drug interactions between itraconazole and protease inhibitors, efavirenz, rilpivirine, etravirine, and many other drugs, random serum levels of itraconazole should Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-3 be measured 2 weeks after the start of therapy. A serum level of 1 to 2 μg/mL is recommended, and the number and severity of adverse events increase when levels are ≥4 µg/mL.16 In patients with less severe disseminated histoplasmosis, oral itraconazole, 200 mg three times daily for 3 days followed by 200 mg twice daily, is appropriate initial therapy (All).15,17 The liquid formulation of itraconazole, which should be given on an empty stomach, is preferable because it is better absorbed and does not require gastric acid for absorption, but it is less well tolerated than the capsule formulation. The capsule formulation should be given with food and cannot be used when the patient requires gastric acid inhibiting drugs. A new formulation of itraconazole, SUBA-itraconazole, has improved absorption and may prove useful in treating histoplasmosis; however, this agent cannot be recommended, pending further data on its use for this purpose. The management of acute pulmonary histoplasmosis in a patient with HIV who has a CD4 count >300 cells/mm3 is the same as for an immunocompetent patient (AIII).15 In patients with confirmed meningitis, liposomal amphotericin B should be administered as initial therapy at a dosage of 5 mg/kg IV daily for 4 to 6 weeks (AIII). This initial IV therapy should be followed by maintenance therapy with oral itraconazole at a dose of 200 mg two or three times daily for ≥12 months and until resolution of abnormal CSF findings (AIII).15 Oral posaconazole and voriconazole have been reported to be effective in treating histoplasmosis in a small number of patients with AIDS or other immunosuppressive conditions18-21 and may be reasonable alternatives for patients who are only moderately ill and intolerant of itraconazole and for those who have Histoplasma meningitis and require long-term antifungal therapy (BIII). If voriconazole is used, trough serum levels should be measured after 5 days of therapy with a goal of achieving a concentration of 2 to 5 ug/mL. Concentrations are highly variable among different patients and over time, within a given patient. Concentrations can vary because of absorption issues and drug-drug interactions. Neurotoxicity and hepatotoxicity are associated with serum levels >5 ug/mL, but individual patients can experience adverse effects with lower serum levels. Posaconazole serum levels should be measured after 5 days of therapy to ensure adequate absorption, with a goal of achieving a concentration >1 ug/mL. Fluconazole is less effective than itraconazole for treatment of histoplasmosis, but has been shown to be moderately effective at a dose of fluconazole 800 mg daily. At this dose, fluconazole may be a reasonable alternative for those intolerant of itraconazole and for long-term therapy for Histoplasma meningitis (CII).22 Isavuconazole has been used in too few patients with histoplasmosis to be recommended at this time. The echinocandins do not have activity against H. capsulatum and should not be used to treat patients with histoplasmosis (AIII). Monitoring of Response to Therapy and Adverse Events (including IRIS) Serial monitoring of serum or urine for Histoplasma antigen is useful for determining response to therapy. A rise in antigen level suggests relapse. Individuals with HIV diagnosed with histoplasmosis should be started on ART as soon as possible after initiating antifungal therapy (AIII). Immune reconstitution inflammatory syndrome (IRIS) has been uncommonly reportedly in patients with HIV who have histoplasmosis.23,24 ART should, therefore, not be withheld because of concern for the possible development of IRIS (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-4 All triazole antifungals have the potential for complex, and possibly bidirectional, interactions with certain antiretroviral agents and other anti-infective agents. Table 4 lists these interactions and recommendations for dosage adjustments, where feasible. Managing Treatment Failure Liposomal amphotericin B should be used in patients who are severely ill or who have failed to respond to initial azole antifungal therapy (AIII). Oral posaconazole and oral voriconazole are reasonable alternatives for patients intolerant of itraconazole who are only moderately ill (BIII);18-21 fluconazole at a dose of 800 mg daily also can be used (CII).22 Drug interactions may limit the use of voriconazole in patients who are taking non-nucleoside reverse transcriptase inhibitors or protease inhibitors. Posaconazole has fewer known drug interactions with ART medications than voriconazole. Prevention of Relapse Long-term suppressive therapy with itraconazole (200 mg daily) should be administered to patients with severe disseminated infection or CNS infection (AIII) and after re-induction therapy to those whose disease relapsed despite initial receipt of appropriate therapy (BIII). Fluconazole is less effective than itraconazole for this purpose but has some efficacy at 400 mg daily.25,26 The role of voriconazole or posaconazole has not been evaluated in sufficiently powered studies. An AIDS Clinical Treatment Group (ACTG)-sponsored study reported that it was safe to discontinue itraconazole treatment for histoplasmosis in patients who had received >1 year of itraconazole therapy; had negative fungal blood cultures, a Histoplasma serum or urine antigen <4.1 units, and CD4 counts ≥150 cells/mm3; and had been on ART for 6 months.25 No relapses were evident among 32 study participants who were followed for a median of 24 months. Thus, it appears safe to discontinue suppressive azole antifungal therapy in patients who meet the criteria described above, have a serum or urine antigen below the limit of quantification in ng/mL (current terminology that replaces the term “units”), and have an undetectable viral load (AI). Suppressive therapy should be resumed if the CD4 count decreases to <150 cells/mm3 (BIII).25 Special Considerations During Pregnancy Amphotericin B or its lipid formulations are the preferred initial regimen for the treatment of histoplasmosis in pregnant patients. Extensive clinical experience with amphotericin B has not documented teratogenicity. At delivery, infants born to women treated with amphotericin B should be evaluated for renal dysfunction and hypokalemia. Although there are case reports of birth defects in infants exposed to itraconazole, prospective cohort studies of >300 women with first trimester exposure did not show an increased risk of congenital malformation.27,28 However, in general, azole antifungals should be avoided during the first trimester of pregnancy (BIII). Congenital malformations similar to those observed in animals, including craniofacial and limb abnormalities, have been reported in infants born to mothers who received fluconazole at doses ≥400 mg/day throughout or beyond the first trimester of pregnancy.29 Although several cohort studies have shown no increased risk of birth defects with early pregnancy exposure, most of these studies involved low doses and short-term exposure to fluconazole.30,31 On the basis of the reported birth defects, the Food and Drug Administration has changed the pregnancy category for fluconazole for any use other than a single, low dose for treatment of vaginal candidiasis from category C to category D (see the FDA Drug Safety Communication). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-5 In animals, voriconazole (at doses lower than recommended human doses) and posaconazole are teratogenic and embryotoxic. There are no adequately controlled studies of these drugs in humans. Use of voriconazole and posaconazole should be avoided in pregnancy, especially in the first trimester (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-6 Recommendations for Preventing and Treating Histoplasma capsulatum Infections Preventing First Episode of Histoplasma capsulatum Infection (Primary Prophylaxis) Indications for Initiating Primary Prophylaxis • CD4 count <150 cells/mm3 and at high risk because of occupational exposure or residence in a community with a hyperendemic rate of histoplasmosis (>10 cases/100 patient-years) (BI) Preferred Therapy • Itraconazole 200 mg PO once daily (BI) Criteria for Discontinuing Primary Prophylaxis (BIII) • Patient on ART, and • CD4 count ≥150 cells/mm3, and • Undetectable HIV-1 viral load for 6 months Indication for Restarting Primary Prophylaxis • CD4 count <150 cells/mm3 (BIII) Treating Moderately Severe to Severe Disseminated Disease Induction Therapy Preferred Therapy • Liposomal amphotericin B at 3 mg/kg IV daily (AI) Alternative Therapy • Amphotericin B lipid complex at 5 mg/kg IV daily (AIII) Duration • For ≥2 weeks or until clinically improved Maintenance Therapy Preferred Therapy • Itraconazole 200 mg PO three times a day for 3 days, then two times a day for ≥12 months (AII), with dosage adjustment based on interactions with ART and itraconazole serum concentration Treating Less Severe Disseminated Disease Induction and Maintenance Therapy Preferred Therapy • Itraconazole 200 mg PO three times a day for 3 days, then 200 mg PO two times a day for ≥12 months (AII), with dose adjustment based on interactions with ART and itraconazole serum concentration Alternative Therapy • Note: These recommendations are based on limited clinical data for patients who are intolerant to itraconazole and who are only moderately ill. • Posaconazole, extended release tablet 300 mg PO twice daily for 1 day, then 300 mg PO once daily (BIII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-7 • Voriconazole 400 mg PO twice daily for 1 day, then 200 mg PO twice daily (BIII) • Fluconazole 800 mg PO once daily (CII) Treating Histoplasma Meningitis Induction Therapy (4–6 Weeks) • Liposomal amphotericin B 5 mg/kg IV daily (AIII) Maintenance Therapy • Itraconazole 200 mg PO two or three times a day for ≥12 months and until resolution of abnormal CSF findings with dosage adjustment based on interactions with ART and itraconazole serum concentration (AIII) Alternative Therapy • Note: These recommendations are based on limited clinical data for patients intolerant to itraconazole. • Voriconazole 400 mg PO two times a day for 1 day, then 200 mg PO two times a day (BIII) • Posaconazole 300 mg extended release tablet PO twice daily for 1 day, then 300 mg PO once daily (BIII) • Fluconazole 800 mg PO once daily (CII) Long Term Suppressive Therapy Indications • Severe disseminated or CNS infection after completing ≥12 months of treatment (AIII), and • Relapse despite appropriate initial therapy (BIII) Preferred Therapy • Itraconazole 200 mg PO once daily (AIII) Alternative Therapy • Posaconazole 300 mg extended release tablet PO once daily (BIII) • Voriconazole 200 mg PO twice daily (BIII) • Fluconazole 400 mg PO once daily (CII) Criteria for Discontinuing Long Term Suppressive Therapy (AI) • Received azole treatment for >1 year, and • Negative fungal blood cultures, and • Serum or urine Histoplasma antigen below the level of quantification, and • Have an undetectable HIV viral load, and • CD4 count >150 cells/mm3 for ≥6 months in response to ART Indication for Restarting Secondary Prophylaxis • CD4 count <150 cells/mm3 (BII) Other Considerations • Itraconazole serum concentrations should be measured in all patients after 2 weeks of therapy (time it usually takes to reach steady state) to ensure adequate absorption and to assess changes in hepatic metabolism due to drug interactions Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-8 (AIII). Random serum concentrations (itraconazole plus hydroxyitraconazole) should be between 1 to 2 µg/mL. Concentrations >4 µg/mL are associated with increased frequency and severity of adverse effects. • Itraconazole oral solution is preferred over the capsule formulation because of improved absorption but is less well tolerated. However, it is not necessary to use the oral solution if itraconazole concentration is >1.0 µg/mL with the capsule formulation. • Voriconazole trough serum levels should be measured after 5 days of therapy (time it usually takes to reach steady state) with a goal of achieving a concentration of 2 to 5 ug/mL. Levels are highly variable among patients, and for individual patients, levels can vary because of drug-drug interactions. Neurotoxicity and hepatotoxicity are associated with serum levels >5 ug/mL, but individual patients can experience adverse effects with lower serum levels. • Trough posaconazole serum levels should be measured after 5 days of therapy (time it usually takes to reach steady state) to ensure adequate absorption, with a goal of achieving a concentration >1 ug/mL. • Acute pulmonary histoplasmosis in patients with HIV with CD4 count >300 cells/mm3 should be managed the same as in immunocompetent patients (AIII). • All triazole antifungals have the potential to interact with certain ART agents and other anti-infective agents. These interactions are complex and can be bidirectional. Drug-Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines lists these interactions and recommends dosage adjustments where feasible. Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte cell; CNS = central nervous system, CSF = cerebrospinal fluid; CYP = cytochrome P450; IV = intravenous; PI = protease inhibitor; PO = orally Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-9 References 1. Wheat LJ, Connolly-Stringfield PA, Baker RL, et al. Disseminated histoplasmosis in the acquired immune deficiency syndrome: clinical findings, diagnosis and treatment, and review of the literature. Medicine (Baltimore). 1990;69(6):361-374. Available at: 2. McKinsey DS, Spiegel RA, Hutwagner L, et al. Prospective study of histoplasmosis in patients infected with human immunodeficiency virus: incidence, risk factors, and pathophysiology. Clin Infect Dis. 1997;24(6):1195-1203. Available at: 3. Baddley JW, Sankara IR, Rodriquez JM, Pappas PG, Many WJ, Jr. Histoplasmosis in HIV-infected patients in a southern regional medical center: poor prognosis in the era of highly active antiretroviral therapy. Diagn Microbiol Infect Dis. 2008;62(2):151-156. Available at: 4. Wheat LJ, Musial CE, Jenny-Avital E. Diagnosis and management of central nervous system histoplasmosis. Clin Infect Dis. 2005;40(6):844-852. Available at: 5. Assi M, McKinsey DS, Driks MR, et al. Gastrointestinal histoplasmosis in the acquired immunodeficiency syndrome: report of 18 cases and literature review. Diagn Microbiol Infect Dis. 2006;55(3):195-201. Available at: 6. Gutierrez ME, Canton A, Sosa N, Puga E, Talavera L. Disseminated histoplasmosis in patients with AIDS in Panama: a review of 104 cases. Clin Infect Dis. 2005;40(8):1199-1202. Available at: 7. Swartzentruber S, Rhodes L, Kurkjian K, et al. Diagnosis of acute pulmonary histoplasmosis by antigen detection. Clin Infect Dis. 2009;49(12):1878-1882. Available at: 8. Connolly PA, Durkin MM, Lemonte AM, Hackett EJ, Wheat LJ. Detection of histoplasma antigen by a quantitative enzyme immunoassay. Clin Vaccine Immunol. 2007;14(12):1587-1591. Available at: 9. Hage CA, Davis TE, Fuller D, et al. Diagnosis of histoplasmosis by antigen detection in BAL fluid. Chest. 2010;137(3):623-628. Available at: 10. Wheat LJ. Approach to the diagnosis of the endemic mycoses. Clin Chest Med. 2009;30(2):379-389, viii. Available at: 11. Tobon AM, Agudelo CA, Rosero DS, et al. Disseminated histoplasmosis: a comparative study between patients with acquired immunodeficiency syndrome and non-human immunodeficiency virus-infected individuals. Am J Trop Med Hyg. 2005;73(3):576-582. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-10 12. Wheat J, Myint T, Guo Y, et al. Central nervous system histoplasmosis: Multicenter retrospective study on clinical features, diagnostic approach and outcome of treatment. Medicine (Baltimore). 2018;97(13):e0245. Available at: 13. McKinsey DS, Wheat LJ, Cloud GA, et al. Itraconazole prophylaxis for fungal infections in patients with advanced human immunodeficiency virus infection: randomized, placebo-controlled, double-blind study. National Institute of Allergy and Infectious Diseases Mycoses Study Group. Clin Infect Dis. 1999;28(5):1049-1056. Available at: 14. Johnson PC, Wheat LJ, Cloud GA, et al. Safety and efficacy of liposomal amphotericin B compared with conventional amphotericin B for induction therapy of histoplasmosis in patients with AIDS. Ann Intern Med. 2002;137(2):105-109. Available at: 15. Wheat LJ, Freifeld AG, Kleiman MB, et al. Clinical practice guidelines for the management of patients with histoplasmosis: 2007 update by the Infectious Diseases Society of America. Clin Infect Dis. 2007;45(7):807-825. Available at: 16. Lestner JM, Roberts SA, Moore CB, Howard SJ, Denning DW, Hope WW. Toxicodynamics of itraconazole: implications for therapeutic drug monitoring. Clin Infect Dis. 2009;49(6):928-930. Available at: 17. Wheat J, Hafner R, Korzun AH, et al. Itraconazole treatment of disseminated histoplasmosis in patients with the acquired immunodeficiency syndrome. AIDS Clinical Trial Group. Am J Med. 1995;98(4):336-342. Available at: 18. Freifeld A, Proia L, Andes D, et al. Voriconazole use for endemic fungal infections. Antimicrob Agents Chemother. 2009;53(4):1648-1651. Available at: 19. Restrepo A, Tobon A, Clark B, et al. Salvage treatment of histoplasmosis with posaconazole. J Infect. 2007;54(4):319-327. Available at: 20. Freifeld AG, Iwen PC, Lesiak BL, Gilroy RK, Stevens RB, Kalil AC. Histoplasmosis in solid organ transplant recipients at a large Midwestern university transplant center. Transpl Infect Dis. 2005;7(3-4):109-115. Available at: 21. Al-Agha OM, Mooty M, Salarieh A. A 43-year-old woman with acquired immunodeficiency syndrome and fever of undetermined origin. Disseminated histoplasmosis. Arch Pathol Lab Med. 2006;130(1):120-123. Available at: 22. Wheat J, MaWhinney S, Hafner R, et al. Treatment of histoplasmosis with fluconazole in patients with acquired immunodeficiency syndrome. National Institute of Allergy and Infectious Diseases Acquired Immunodeficiency Syndrome Clinical Trials Group and Mycoses Study Group. Am J Med. 1997;103(3):223-232. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV O-11 23. Passos L, Talhari C, Santos M, Ribeiro-Rodrigues R, Ferreira LC, Talhari S. Histoplasmosis-associated immune reconstitution inflammatory syndrome. An Bras Dermatol. 2011;86(4 Suppl 1):S168-172. Available at: 24. Breton G, Adle-Biassette H, Therby A, et al. Immune reconstitution inflammatory syndrome in HIV-infected patients with disseminated histoplasmosis. AIDS. 2006;20(1):119-121. Available at: 25. Goldman M, Zackin R, Fichtenbaum CJ, et al. Safety of discontinuation of maintenance therapy for disseminated histoplasmosis after immunologic response to antiretroviral therapy. Clin Infect Dis. 2004;38(10):1485-1489. Available at: 26. Hecht FM, Wheat J, Korzun AH, et al. Itraconazole maintenance treatment for histoplasmosis in AIDS: a prospective, multicenter trial. Journal of acquired immune deficiency syndromes and human retrovirology : official publication of the International Retrovirology Association. 1997;16(2):100-107. Available at: 27. De Santis M, Di Gianantonio E, Cesari E, Ambrosini G, Straface G, Clementi M. First-trimester itraconazole exposure and pregnancy outcome: a prospective cohort study of women contacting teratology information services in Italy. Drug Saf. 2009;32(3):239-244. Available at: 28. Bar-Oz B, Moretti ME, Bishai R, et al. Pregnancy outcome after in utero exposure to itraconazole: a prospective cohort study. Am J Obstet Gynecol. 2000;183(3):617-620. Available at: 29. Pursley TJ, Blomquist IK, Abraham J, Andersen HF, Bartley JA. Fluconazole-induced congenital anomalies in three infants. Clin Infect Dis. 1996;22(2):336-340. Available at: 30. Norgaard M, Pedersen L, Gislum M, et al. Maternal use of fluconazole and risk of congenital malformations: a Danish population-based cohort study. J Antimicrob Chemother. 2008;62(1):172-176. Available at: 31. Mastroiacovo P, Mazzone T, Botto LD, et al. Prospective assessment of pregnancy outcomes after first-trimester exposure to fluconazole. Am J Obstet Gynecol. 1996;175(6):1645-1650. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-1 Human Herpesvirus-8 Disease Updated: May 29, 2018 Reviewed: January 10, 2024 Epidemiology The seroprevalence of human herpesvirus-8 (HHV-8)—also known as Kaposi sarcoma-associated herpesvirus (KSHV)—varies worldwide and is estimated to be 1% to 5% in the general U.S. population1,2 compared with 10% to 20% in certain Mediterranean countries and 30% to 80% in parts of sub-Saharan Africa.3 In the United States, men who have sex with men (MSM) and persons with HIV infection are at increased risk for HHV-8 infection. Among MSM without HIV infection, the seroprevalence ranges from 13% to 20% and HHV-8 seroprevalence increases to 30% to 35% among MSM with HIV infection.4-6 Injection drug use may also be a risk factor for HHV-8 seropositivity,7 although this association has not been consistently observed.8 HHV-8 is etiologically associated with all forms of Kaposi sarcoma (KS) including classic, endemic, transplant-related, and AIDS-related, as well as rare neoplastic disorders (primary effusion lymphoma [PEL] and solid organ variants) and the lymphoproliferative disorder known as multicentric Castleman’s disease (MCD). Although the precise pathogenesis for these tumors remains unclear, infection with HHV-8 precedes their development.9 Patients who are HHV-8 seropositive and exhibit HHV-8 viremia are at increased risk (approximately nine-fold) for developing KS relative to those without HHV-8 viremia.10 HHV-8 viremia typically accompanies symptomatic episodes of multicentric Castleman’s disease.11 The overall prevalence of KS in the U.S. was as high as 30% among patients with AIDS prior to the advent of effective antiretroviral therapy (ART).12 The incidence of KS rose steeply in the United States between 1981 and 1987 and subsequently gradually declined.13 Reasons for this reduction in KS incidence prior to the widespread availability of ART include the deaths of patients with advanced AIDS who were most susceptible to KS, and the increasing use by individuals with HIV individuals of antiviral drugs that may have had activity against HHV-8 (zidovudine for the treatment of HIV; ganciclovir, foscarnet, and cidofovir use for treatment of CMV disease).14 Supporting the latter hypothesis, observational studies indicate that patients receiving ganciclovir or foscarnet (but not acyclovir) develop KS at a reduced rate.15-18 A more marked reduction in KS incidence occurred beginning in 1996, shortly after the introduction of protease inhibitor-containing ART in the U.S. Despite these declines, KS is among the most common cancers among the AIDS population in the U.S.,19 and HIV infection increases the risk of KS several thousand fold even in the ART era.20 Notably, KS is a common cancer in many countries in sub-Saharan Africa,21 fueled in part by the HIV pandemic, and incidence has not declined in regions of sub-Saharan Africa where ART coverage is increasing but incomplete.22,23 PEL and MCD remain rare relative to KS.24,25 KS and PEL are described most frequently among individuals with HIV exhibiting advanced immunosuppression (CD4 T lymphocyte [CD4] cell counts <200 cells/mm3), although they may occur at any CD4 cell count. Recent reports of KS occurring at higher CD4 cell counts in the United States26,27 suggest that clinicians caring for patients with HIV should be vigilant for the clinical manifestations of KS in patients at risk of HHV-8 infection, regardless of CD4 cell count. MCD may arise at any CD4 cell count. Clinical Manifestations Most individuals latently infected with HHV-8 are asymptomatic.28 Immunocompetent children and organ transplant recipients infected with HHV-8 may develop a primary infection syndrome consisting of fever, rash, lymphadenopathy, bone marrow failure, and occasional rapid progression to KS.29,30 KS manifestations vary Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-2 widely, but most patients have nontender, hyperpigmented, macular or nodular skin lesions. Oral lesions occur in approximately one-third of patients31 and are predictors of pulmonary involvement and less favorable treatment outcomes.32-34 Lymphatic involvement is also common and may lead to debilitating lower extremity edema. Involvement of internal viscera occurs in up to 50% of cases and may be difficult to diagnose. Patients with visceral involvement may be asymptomatic, or manifest with shortness of breath, painless rectal bleeding or melena, and other non-specific pulmonary and gastrointestinal symptoms.35-40 PEL characteristically presents with effusions isolated within the pleural, pericardial, or abdominal cavities,41 but mass lesions and “extracavitary” disease within skin, hematopoietic organs, and the gastrointestinal tract have been described.42-44 MCD routinely manifests with systemic symptoms including fever and night sweats, and findings on examination including generalized adenopathy, fever and hepatosplenomegaly.24,45 MCD may mimic other inflammatory conditions including sepsis, with hypotension, clinical evidence of a systemic inflammatory response, and progression to multi-organ failure.24,46,47 Another HHV-8- associated condition, the KSHV inflammatory cytokine syndrome (KICS), has been more recently described.48-50 Patients with this syndrome display MCD-like inflammatory symptoms, but do not have pathological findings of MCD. Patients with KICS are frequently critically ill and demonstrate marked elevations in IL-6 and IL-10, as well as high plasma HHV-8 viral loads. KICS may contribute to the inflammatory symptoms seen in some patients with severe KS or PEL, and there may be significant clinical overlap between these conditions. Diagnosis The diagnoses of KS, MCD and PEL depend on cytologic and immunologic cell markers, as well as histology. Clinical diagnosis alone is not sufficient for KS, and tissue examination is needed to confirm the diagnosis.51,52 Confirmation of these diagnoses is achieved through immunohistochemical staining of tumors with antibodies recognizing the HHV-8-encoded latency-associated nuclear antigen (LANA).53,54 While not commercially available, diagnoses may also be confirmed utilizing polymerase chain reaction (PCR) to identify HHV-8 DNA within tumor tissue.53,54 Use of serologic testing for HHV-8 antibodies is currently not indicated for either diagnostic testing or routine screening for HHV-8-related illnesses due to lack of standardization and poor sensitivity and specificity of these assays.55 In addition, use of PCR to quantify HHV-8 in the peripheral blood has no established role in the diagnosis of KS, MCD, or PEL.11 HHV-8 Transmission/Preventing Exposure The mode(s) of transmission of HHV-8 remains unclear, but epidemiologic and virologic data suggest that saliva is a source of infectious virus and may be an important route of transmission. Asymptomatic HHV-8 infection is often associated with HHV-8 shedding in the saliva and occasional shedding in genital secretions.4,28,56 In a study of 50 HHV-8-infected MSM in the U.S., HHV-8 was detected by PCR in the saliva of 39% of participants and on more than 35% of days on which samples were obtained.4 HHV-8 shedding is also common among persons in sub-Saharan Africa. Among HHV-8-infected adults without KS in Uganda, 22% had HHV-8 DNA detected in saliva and 3% in genital secretions; HHV-8 was also detected in saliva of 68% of commercial sex workers in Kenya.57,58 Based on these observations, viral shedding may result in HHV-8 transmission to uninfected partners through behaviors associated with exposure to saliva or genital secretions. HHV-8 transmission through blood transfusion has been reported in Uganda, where HHV-8 is endemic;59 however, studies from the U.S. and Western Europe have not found evidence to support HHV-8 transmission through blood transfusion.60,61 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-3 Recommendations to prevent exposure to HHV-8 do not yet exist; screening patients for HHV-8 serostatus or behavioral modifications to limit potential exposures have not been validated and are not currently recommended. Preventing Disease Despite observational evidence supporting a role for anti-HHV-8 therapy in preventing the development of KS, the toxicity of current anti-HHV-8 treatments outweighs the potential use for prophylaxis (AIII). Because strong risk factors for the development of KS in HIV-positive individuals include both low CD4-positive T cell count62 and uncontrolled viremia,63 early initiation of ART is likely to be the most effective measure for the prevention of KS (AII). Although epidemiologic data are somewhat conflicting, there are no antiretroviral agents which have proven clearly superior for the prevention of KS.60-65 Therefore, specific classes of ART for prevention of KS or other HHV-8-associated illnesses are not recommended (AII). Treating Disease KS: Chemotherapy, in combination with ART, should be administered to patients with visceral involvement (AI) and is likely to be a useful adjunctive therapy in individuals with disseminated cutaneous KS (BIII).64-67 Liposomal doxorubicin and paclitaxel exhibit comparable response rates and progression-free survival, although liposomal doxorubicin exhibits less high-grade toxicity relative to paclitaxel and is, therefore, generally preferred as first-line therapy (AI).64 Paclitaxel has proven effective with relapse following treatment failure with liposomal doxorubicin.67 Importantly, concurrent use of corticosteroids in patients with KS should be either avoided or used with caution and under close observation, given the potential for exacerbation of life-threatening disease, as well as an association between the use of corticosteroids and development of KS (AIII).68-70 KS arising in the setting of organ transplantation is related to the use of corticosteroids and other non-targeted immunosuppressives, especially in geographic areas of high HHV-8 seroprevalence.71 Transplant-associated KS may be effectively treated or avoided with use of immunosuppressive regimens which include drugs that inhibit the mammalian target of rapamycin (mTOR) such as rapamycin and sirolimus.71-73 The antiviral agents ganciclovir, foscarnet, and cidofovir exhibit in vitro activity against HHV-8.74,75 Available data indicate that antivirals have limited efficacy for the treatment of KS (ganciclovir and cidofovir)76,77 and HHV-8-associated hemophagocytosis (foscarnet).78,79 Therefore, antiviral agents with activity against HHV-8 are not recommended for KS treatment (AII). PEL: Chemotherapy, in combination with ART, should be administered to patients with PEL (AIII), although, given its rarity, there are limited data available from longitudinal observational series or prospective randomized clinical trials. The combination of cyclophosphamide, doxorubicin, vincristine, and prednisolone (CHOP) in combination with ART has demonstrated some benefit, albeit still limited, for PEL, and the combination of infusional etoposide, prednisone, vincristine, cyclophosphamide, and doxorubicin (EPOCH) demonstrated superior survival relative to CHOP in one pooled analysis (BII).80,81 Rituximab may be considered for rare CD20-positive cases of PEL (CIII), and dose-adjusted EPOCH (DA-EPOCH) may be beneficial for some patients (CIII).82,83 Antiviral agents, including valganciclovir or zidovudine, may also be used as adjunctive therapies, but available data are limited for this approach and additive toxicities may limit their utility (CIII).84-86 MCD: There are no standardized treatments for MCD, but several treatment regimens have been utilized. The use of either IV ganciclovir or oral valganciclovir are options for treatment of MCD (CII). A 3-week course of twice-daily IV ganciclovir or oral valganciclovir was associated with remissions in MCD in one report,87 and a combination of valganciclovir and high-dose zidovudine has led to durable clinical remissions (CII).88 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-4 Rituximab has also emerged as an important adjunctive treatment for MCD (CII),89,90 although up to one-third of patients receiving rituximab may have subsequent exacerbations or emergence of KS.91,92 For patients with concurrent diagnoses of KS and MCD, use of both rituximab and liposomal doxorubicin is recommended (BII).45 Therapeutic monoclonal antibodies targeting either interleukin-6 (IL-6) or the IL-6 receptor have also proven effective for some patients with MCD and may be utilized in some situations (BII).93-95 At this time, there is insufficient evidence to recommend monitoring IL-6 levels for diagnostic or prognostic purposes. Although corticosteroids are potentially effective as an adjunctive therapy for MCD, they should be used with caution or avoided, especially in patients with concurrent KS, given potential for exacerbation of life-threatening KS (AIII).68-70 Detailed recommendations for the treatment of HHV-8 malignancies (including chemotherapy and radiation therapy) are beyond the scope of these guidelines. Treatment should be undertaken in consultation with an experienced specialist with appropriate guidance from both oncology and infectious disease specialists (AIII). Preferred ART to be given concurrently with chemotherapy for HHV-8 malignancies should be chosen to minimize drug-drug interactions and additive toxicities. Special Considerations When Starting Antiretroviral Therapy Early initiation of ART may prevent incident KS and PEL.74,96 ART that suppresses HIV replication should be administered to all patients with HIV and KS (AII), PEL (AIII), or MCD (AIII), although insufficient evidence exists to support using one ART regimen over another. Monitoring of Response to Therapy and Adverse Events (Including IRIS) Immune reconstitution inflammatory syndrome (IRIS) may occur among HHV-8-infected patients initiating ART. KS: KS-IRIS is characterized by either first presentation of KS (“unmasking”), or paradoxical worsening of pre-existing KS following ART initiation, and can be associated with significant morbidity and mortality.97 Studies in the U.S. and Europe reveal that KS is the most commonly reported form of IRIS, occurring in 6% to 34% of KS patients with HIV who are initiating ART.98,99 In sub-Saharan Africa, exacerbations of KS compatible with KS-IRIS have been reported in 18% to 61% of adults initiating ART treatment.100-102 Risk factors for developing KS-IRIS include advanced KS tumor stage (T1), pre-treatment HIV viral load >5 log10 copies/mL, detectable pre-treatment plasma HHV-8, and initiation of ART alone without concurrent chemotherapy.97 Treatment of KS-IRIS includes systemic chemotherapy and supportive measures. Steroids are strongly discouraged for management of KS-IRIS, as corticosteroid therapy has been associated with exacerbation of pre-existing KS in persons with HIV (AIII).70,103 PEL: No data exist on the frequency with which initiation of ART complicates the course of primary effusion lymphoma. MCD: A small number of patients with HIV-associated MCD have experienced clinical decompensation upon initiation of ART.104,105 Although neither the incidence nor predictors of HHV-8-associated IRIS are well-described, suppression of HIV replication and immune reconstitution are key components of therapy, and initiation of ART should not be delayed (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-5 Preventing Recurrence Effective suppression of HIV replication with ART in patients with HIV and KS may prevent KS progression or occurrence of new lesions. Because KS is an AIDS-defining cancer, ART is indicated for all patients with active KS (AII). Suppression of HIV replication to prevent recurrence is also recommended for patients with MCD (AIII) as well as those with malignant lymphoproliferative disorders (AIII). Special Considerations During Pregnancy The seroprevalence of HHV-8 infection among pregnant women with HIV varies by geographic area, ranging from 1.7% among U.S.-born and 3.6% among Haitian-born women in New York City to 11.6% among pregnant women from 4 other U.S. cities.106 Pregnancy does not appear to affect the prevalence of antibodies to HHV-8 or the antibody levels,107 although levels of HHV-8 DNA in the peripheral blood may increase late in pregnancy.108 HHV-8 seropositivity does not appear to influence pregnancy outcome. Routine screening for HHV-8 by PCR or serology is not indicated for pregnant women with HIV (AIII). Antiviral therapy for HHV-8 infection in pregnancy is not recommended (AIII). Given the rarity of KS, PEL, and MCD in pregnancy and the potential toxicity of the drugs used for treatment, when these conditions occur in pregnancy, they should be managed with consultations between the obstetrician, infectious disease specialist, and oncologist. With limited disease, treatment may be deferred until after delivery.109 In vitro models suggest that beta-human chorionic gonadotropin induces regression of KS tumors, but clinical reports on the incidence and natural history of KS in pregnancy are conflicting.110-113 Perinatal transmission of HHV-8 occurs infrequently. Evidence supporting vertical transmission during pregnancy or the intrapartum period includes cases of KS occurring in the infant shortly after birth,114,115 higher risk for transmission with higher maternal antibody titer (and, by inference, higher maternal levels of HHV-8),116 and detection of similar strains of HHV-8 DNA by PCR in specimens drawn at birth from HHV-8-seropositive mothers and their infants.117 Data indicate increased mortality through age 24 months among infants with HIV born to HHV-8-seropositive mothers compared with HHV-8-seronegative mothers,114-116,118-123 but these studies could not completely account for other confounding factors affecting infants with HIV. The majority of studies document a substantially higher rate of HHV-8 seropositivity among children born to HHV-8 antibody-positive compared with HHV-8 antibody-negative women.118-123 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-6 Recommendations for Preventing and Treating HHV-8 Diseases—Kaposi Sarcoma (KS), Primary Effusion Lymphoma (PEL), Multicentric Castleman’s Disease (MCD) Preventing development of KS: • Since low CD4 cell count and uncontrolled HIV viremia are strong risk factors of KS, early initiation of ART is likely to be the most effective measure for the prevention of KS (AII) Mild-to-Moderate KS (localized involvement of skin and/or lymph nodes)1: • Initiation or optimization of ART (AII) Advanced KS (visceral and/or disseminated cutaneous disease)1: • Chemotherapy (in consultation with specialist) + ART [visceral KS (AI) or widely-disseminated cutaneous KS (BIII)]. • Liposomal doxorubicin is preferred first-line chemotherapy (A1) • Avoid use of corticosteroids in patients with KS, including those with KS-IRIS, given the potential for exacerbation of life-threatening disease (AIII) • Antiviral agents with activity against HHV-8 are not recommended for KS treatment (AIII). PEL: • Chemotherapy (in consultation with a specialist) (AIII) + ART (AIII) • Oral valganciclovir or IV ganciclovir can be used as adjunctive therapy (CIII) MCD: All patients with MCD should receive ART (AIII) in conjunction with one of the therapies listed below. Therapy Options (in consultation with a specialist, and depending on HIV/HHV-8 status, presence of organ failure, and refractory nature of disease): • IV ganciclovir (or oral valganciclovir) +/- high dose zidovudine (CII) • Rituximab +/- prednisone (CII) • For patients with concurrent KS and MCD – rituximab + liposomal doxorubicin (BII) • Monoclonal antibody targeting IL-6 or IL-6 receptor (BII) • Corticosteroids are potentially effective as adjunctive therapy, but should be used with caution or avoided, especially in patients with concurrent KS. (AIII) Other Considerations: • Patients who receive rituximab or corticosteroids for treatment of MCD may experience subsequent exacerbation or emergence of KS Key to Acronyms: ART = antiretroviral therapy; BID = twice daily; IV = intraveneously; KS = Kaposi sarcoma; MCD = multicentric Castleman’s disease; PEL = primary effusion lymphoma; PO = orally; q(n)h = every “n” hours 1 The commonly used AIDS Clinical Trials Group (ACTG) KS Staging Classification uses T(Tumor), Immune(I), and Systemic illness (S) criteria to classify patients into “Good Risk” and “Poor Risk” categories (ref Krown, JCO, 1989). “Good Risk” tumor stage criteria are used by some specialists to correspond with mild-to-moderate KS. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-7 References 1. Pellett PE, Wright DJ, Engels EA, et al. Multicenter comparison of serologic assays and estimation of human herpesvirus 8 seroprevalence among US blood donors. Transfusion. 2003;43(9):1260-1268. Available at: 2. Hudnall SD, Chen T, Rady P, Tyring S, Allison P. Human herpesvirus 8 seroprevalence and viral load in healthy adult blood donors. Transfusion. 2003;43(1):85-90. Available at: 3. Dollard SC, Butler LM, Jones AM, et al. Substantial regional differences in human herpesvirus 8 seroprevalence in sub-Saharan Africa: insights on the origin of the "Kaposi's sarcoma belt". Int J Cancer. 2010;127(10):2395-2401. Available at: 4. Pauk J, Huang ML, Brodie SJ, et al. Mucosal shedding of human herpesvirus 8 in men. N Engl J Med. 2000;343(19):1369-1377. Available at: 5. Kedes DH, Operskalski E, Busch M, Kohn R, Flood J, Ganem D. The seroepidemiology of human herpesvirus 8 (Kaposi's sarcoma-associated herpesvirus): distribution of infection in KS risk groups and evidence for sexual transmission. Nat Med. 1996;2(8):918-924. Available at: 6. Gao SJ, Kingsley L, Li M, et al. KSHV antibodies among Americans, Italians and Ugandans with and without Kaposi's sarcoma. Nat Med. 1996;2(8):925-928. Available at: 7. Cannon MJ, Dollard SC, Smith DK, et al. Blood-borne and sexual transmission of human herpesvirus 8 in women with or at risk for human immunodeficiency virus infection. N Engl J Med. 2001;344(9):637-643. Available at: 8. Renwick N, Dukers NH, Weverling GJ, et al. Risk factors for human herpesvirus 8 infection in a cohort of drug users in the Netherlands, 1985-1996. J Infect Dis. 2002;185(12):1808-1812. Available at: 9. Gao SJ, Kingsley L, Hoover DR, et al. Seroconversion to antibodies against Kaposi's sarcoma-associated herpesvirus-related latent nuclear antigens before the development of Kaposi's sarcoma. N Engl J Med. 1996;335(4):233-241. Available at: 10. Lennette ET, Blackbourn DJ, Levy JA. Antibodies to human herpesvirus type 8 in the general population and in Kaposi's sarcoma patients. Lancet. 1996;348(9031):858-861. Available at: 11. Oksenhendler E, Carcelain G, Aoki Y, et al. High levels of human herpesvirus 8 viral load, human interleukin-6, interleukin-10, and C reactive protein correlate with exacerbation of multicentric castleman disease in HIV-infected patients. Blood. 2000;96(6):2069-2073. Available at: 12. Beral V. The epidemiology of cancer in AIDS patients. AIDS. 1991;5 Suppl 2:S99-103. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-8 13. Eltom MA, Jemal A, Mbulaiteye SM, Devesa SS, Biggar RJ. Trends in Kaposi's sarcoma and non-Hodgkin's lymphoma incidence in the United States from 1973 through 1998. J Natl Cancer Inst. 2002;94(16):1204-1210. Available at: 14. Casper C. Defining a role for antiviral drugs in the treatment of persons with HHV-8 infection. Herpes. 2006;13(2):42-47. Available at: 15. Martin DF, Kuppermann BD, Wolitz RA, Palestine AG, Li H, Robinson CA. Oral ganciclovir for patients with cytomegalovirus retinitis treated with a ganciclovir implant. Roche Ganciclovir Study Group. N Engl J Med. 1999;340(14):1063-1070. Available at: 16. Ioannidis JP, Collier AC, Cooper DA, et al. Clinical efficacy of high-dose acyclovir in patients with human immunodeficiency virus infection: a meta-analysis of randomized individual patient data. J Infect Dis. 1998;178(2):349-359. Available at: 17. Mocroft A, Youle M, Gazzard B, Morcinek J, Halai R, Phillips AN. Anti-herpesvirus treatment and risk of Kaposi's sarcoma in HIV infection. Royal Free/Chelsea and Westminster Hospitals Collaborative Group. AIDS. 1996;10(10):1101-1105. Available at: 18. Glesby MJ, Hoover DR, Weng S, et al. Use of antiherpes drugs and the risk of Kaposi's sarcoma: data from the Multicenter AIDS Cohort Study. J Infect Dis. 1996;173(6):1477-1480. Available at: 19. Shiels MS, Pfeiffer RM, Gail MH, et al. Cancer burden in the HIV-infected population in the United States. J Natl Cancer Inst. 2011;103(9):753-762. Available at: 20. Grulich AE, van Leeuwen MT, Falster MO, Vajdic CM. Incidence of cancers in people with HIV/AIDS compared with immunosuppressed transplant recipients: a meta-analysis. Lancet. 2007;370(9581):59-67. Available at: 21. North AB, South CD. Cancer Incidence in Antarctica (2003-2007). In: Secondary North AB, South CD, ed^eds. Subsidiary North AB, South CD, trans. Secondary Cancer Incidence in Antarctica (2003-2007). Vol. ed. Lyon: International Agency for Research on Cancer; 2013. 22. Casper C. The increasing burden of HIV-associated malignancies in resource-limited regions. Annu Rev Med. 2011;62:157-170. Available at: 23. Mutyaba I, Phipps W, Krantz EM, et al. A Population-Level Evaluation of the Effect of Antiretroviral Therapy on Cancer Incidence in Kyadondo County, Uganda, 1999-2008. J Acquir Immune Defic Syndr. 2015;69(4):481-486. Available at: 24. Casper C. The aetiology and management of Castleman disease at 50 years: translating pathophysiology to patient care. Br J Haematol. 2005;129(1):3-17. Available at: 25. Bhutani M, Polizzotto MN, Uldrick TS, Yarchoan R. Kaposi sarcoma-associated herpesvirus-associated malignancies: epidemiology, pathogenesis, and advances in treatment. Semin Oncol. 2015;42(2):223-246. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-9 26. Maurer T, Ponte M, Leslie K. HIV-associated Kaposi's sarcoma with a high CD4 count and a low viral load. N Engl J Med. 2007;357(13):1352-1353. Available at: 27. Mani D, Neil N, Israel R, Aboulafia DM. A retrospective analysis of AIDS-associated Kaposi's sarcoma in patients with undetectable HIV viral loads and CD4 counts greater than 300 cells/mm(3). J Int Assoc Physicians AIDS Care (Chic). 2009;8(5):279-285. Available at: 28. Casper C, Krantz E, Selke S, et al. Frequent and asymptomatic oropharyngeal shedding of human herpesvirus 8 among immunocompetent men. J Infect Dis. 2007;195(1):30-36. Available at: 29. Andreoni M, Sarmati L, Nicastri E, et al. Primary human herpesvirus 8 infection in immunocompetent children. JAMA. 2002;287(10):1295-1300. Available at: 30. Luppi M, Barozzi P, Schulz TF, et al. Bone marrow failure associated with human herpesvirus 8 infection after transplantation. N Engl J Med. 2000;343(19):1378-1385. Available at: 31. Nichols CM, Flaitz CM, Hicks MJ. Treating Kaposi's lesions in the HIV-infected patient. J Am Dent Assoc. 1993;124(11):78-84. Available at: 32. Reichart PA. Oral manifestations in HIV infection: fungal and bacterial infections, Kaposi's sarcoma. Med Microbiol Immunol. 2003;192(3):165-169. Available at: 33. Rohrmus B, Thoma-Greber EM, Bogner JR, Rocken M. Outlook in oral and cutaneous Kaposi's sarcoma. Lancet. 2000;356(9248):2160. Available at: 34. Gorsky M, Epstein JB. 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Diverse clinicopathologic features in human herpesvirus 8-associated lymphomas lead to diagnostic problems. Am J Clin Pathol. 2014;142(6):816-829. Available at: 44. Liao G, Cai J, Yue C, Qing X. Extracavitary/solid variant of primary effusion lymphoma presenting as a gastric mass. Exp Mol Pathol. 2015;99(3):445-448. Available at: 45. Uldrick TS, Polizzotto MN, Aleman K, et al. Rituximab plus liposomal doxorubicin in HIV-infected patients with KSHV-associated multicentric Castleman disease. Blood. 2014;124(24):3544-3552. Available at: 46. Soumerai JD, Sohani AR, Abramson JS. Diagnosis and management of Castleman disease. Cancer Control. 2014;21(4):266-278. Available at: 47. Anderson S, Sasson SC, Lee FJ, Cooper W, Larsen S, Garsia R. Episodic fevers and vasodilatory shock mimicking urosepsis in a patient with HIV-associated multicentric Castleman's Disease: a case report. BMC Infect Dis. 2016;16:53. Available at: 48. Uldrick TS, Wang V, O'Mahony D, et al. An interleukin-6-related systemic inflammatory syndrome in patients co-infected with Kaposi sarcoma-associated herpesvirus and HIV but without Multicentric Castleman disease. Clin Infect Dis. 2010;51(3):350-358. Available at: 49. Polizzotto MN, Uldrick TS, Hu D, Yarchoan R. Clinical Manifestations of Kaposi Sarcoma Herpesvirus Lytic Activation: Multicentric Castleman Disease (KSHV-MCD) and the KSHV Inflammatory Cytokine Syndrome. Front Microbiol. 2012;3:73. Available at: 50. Polizzotto MN, Uldrick TS, Wyvill KM, et al. Clinical Features and Outcomes of Patients With Symptomatic Kaposi Sarcoma Herpesvirus (KSHV)-associated Inflammation: Prospective Characterization of KSHV Inflammatory Cytokine Syndrome (KICS). Clin Infect Dis. 2016;62(6):730-738. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-11 51. Patel RM, Goldblum JR, Hsi ED. 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HIV infection and human herpesvirus-8 oral shedding among men who have sex with men. J Acquir Immune Defic Syndr. 2004;35(3):233-238. Available at: 57. Johnston C, Orem J, Okuku F, et al. Impact of HIV infection and Kaposi sarcoma on human herpesvirus-8 mucosal replication and dissemination in Uganda. PLoS One. 2009;4(1):e4222. Available at: 58. Phipps W, Saracino M, Selke S, et al. Oral HHV-8 replication among women in Mombasa, Kenya. J Med Virol. 2014;86(10):1759-1765. Available at: 59. Hladik W, Dollard SC, Mermin J, et al. Transmission of human herpesvirus 8 by blood transfusion. N Engl J Med. 2006;355(13):1331-1338. Available at: 60. Cannon MJ, Operskalski EA, Mosley JW, Radford K, Dollard SC. Lack of evidence for human herpesvirus-8 transmission via blood transfusion in a historical US cohort. J Infect Dis. 2009;199(11):1592-1598. Available at: 61. Schennach H, Schonitzer D, Wachter H, Fuchs D. Blood donations and viruses. Lancet. 1997;349(9061):1327-1328. Available at: 62. 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A randomized, double-blind study of pegylated liposomal doxorubicin for the treatment of AIDS-related Kaposi's sarcoma. Oncologist. 2007;12(1):114-123. Available at: 66. Cheung TW, Remick SC, Azarnia N, Proper JA, Barrueco JR, Dezube BJ. AIDS-related Kaposi's sarcoma: a phase II study of liposomal doxorubicin. The TLC D-99 Study Group. Clin Cancer Res. 1999;5(11):3432-3437. Available at: 67. Tulpule A, Groopman J, Saville MW, et al. Multicenter trial of low-dose paclitaxel in patients with advanced AIDS-related Kaposi sarcoma. Cancer. 2002;95(1):147-154. Available at: 68. Volkow PF, Cornejo P, Zinser JW, Ormsby CE, Reyes-Teran G. Life-threatening exacerbation of Kaposi's sarcoma after prednisone treatment for immune reconstitution inflammatory syndrome. AIDS. 2008;22(5):663-665. Available at: 69. Jinno S, Goshima C. Progression of Kaposi sarcoma associated with iatrogenic Cushing syndrome in a person with HIV/AIDS. AIDS Read. 2008;18(2):100-104. Available at: 70. Trattner A, Hodak E, David M, Sandbank M. The appearance of Kaposi sarcoma during corticosteroid therapy. Cancer. 1993;72(5):1779-1783. Available at: 71. Hosseini-Moghaddam SM, Soleimanirahbar A, Mazzulli T, Rotstein C, Husain S. Post renal transplantation Kaposi's sarcoma: a review of its epidemiology, pathogenesis, diagnosis, clinical aspects, and therapy. Transpl Infect Dis. 2012;14(4):338-345. Available at: 72. Monaco AP. The role of mTOR inhibitors in the management of posttransplant malignancy. Transplantation. 2009;87(2):157-163. Available at: 73. Stock PG, Barin B, Murphy B, et al. Outcomes of kidney transplantation in HIV-infected recipients. N Engl J Med. 2010;363(21):2004-2014. Available at: 74. Kedes DH, Ganem D. Sensitivity of Kaposi's sarcoma-associated herpesvirus replication to antiviral drugs. Implications for potential therapy. J Clin Invest. 1997;99(9):2082-2086. Available at: 75. Medveczky MM, Horvath E, Lund T, Medveczky PG. In vitro antiviral drug sensitivity of the Kaposi's sarcoma-associated herpesvirus. AIDS. 1997;11(11):1327-1332. Available at: 76. Little RF, Merced-Galindez F, Staskus K, et al. A pilot study of cidofovir in patients with kaposi sarcoma. J Infect Dis. 2003;187(1):149-153. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-13 77. Krown SE, Dittmer DP, Cesarman E. Pilot study of oral valganciclovir therapy in patients with classic Kaposi sarcoma. J Infect Dis. 2011;203(8):1082-1086. Available at: 78. Luppi M, Barozzi P, Rasini V, et al. Severe pancytopenia and hemophagocytosis after HHV-8 primary infection in a renal transplant patient successfully treated with foscarnet. Transplantation. 2002;74(1):131-132. Available at: 79. Low P, Neipel F, Rascu A, et al. Suppression of HHV-8 viremia by foscarnet in an HIV-infected patient with Kaposi's sarcoma and HHV-8 associated hemophagocytic syndrome. Eur J Med Res. 1998;3(10):461-464. Available at: 80. Boulanger E, Gerard L, Gabarre J, et al. Prognostic factors and outcome of human herpesvirus 8-associated primary effusion lymphoma in patients with AIDS. J Clin Oncol. 2005;23(19):4372-4380. Available at: 81. Barta SK, Lee JY, Kaplan LD, Noy A, Sparano JA. Pooled analysis of AIDS malignancy consortium trials evaluating rituximab plus CHOP or infusional EPOCH chemotherapy in HIV-associated non-Hodgkin lymphoma. Cancer. 2012;118(16):3977-3983. Available at: 82. Lim ST, Rubin N, Said J, Levine AM. Primary effusion lymphoma: successful treatment with highly active antiretroviral therapy and rituximab. Ann Hematol. 2005;84(8):551-552. Available at: 83. Jessamy K, Ojevwe FO, Doobay R, Naous R, Yu J, Lemke SM. Primary Effusion Lymphoma: Is Dose-Adjusted-EPOCH Worthwhile Therapy? Case Rep Oncol. 2016;9(1):273-279. Available at: 84. Crum-Cianflone NF, Wallace MR, Looney D. Successful secondary prophylaxis for primary effusion lymphoma with human herpesvirus 8 therapy. AIDS. 2006;20(11):1567-1569. Available at: 85. Pereira R, Carvalho J, Patricio C, Farinha P. Sustained complete remission of primary effusion lymphoma with adjunctive ganciclovir treatment in an HIV-positive patient. BMJ Case Rep. 2014;2014. Available at: 86. Oksenhendler E, Clauvel JP, Jouveshomme S, Davi F, Mansour G. Complete remission of a primary effusion lymphoma with antiretroviral therapy. Am J Hematol. 1998;57(3):266. Available at: 87. Casper C, Nichols WG, Huang ML, Corey L, Wald A. Remission of HHV-8 and HIV-associated multicentric Castleman disease with ganciclovir treatment. Blood. 2004;103(5):1632-1634. Available at: 88. Uldrick TS, Polizzotto MN, Aleman K, et al. High-dose zidovudine plus valganciclovir for Kaposi sarcoma herpesvirus-associated multicentric Castleman disease: a pilot study of virus-activated cytotoxic therapy. Blood. 2011;117(26):6977-6986. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-14 89. Bower M, Newsom-Davis T, Naresh K, et al. Clinical Features and Outcome in HIV-Associated Multicentric Castleman's Disease. J Clin Oncol. 2011;29(18):2481-2486. Available at: 90. Marcelin AG, Aaron L, Mateus C, et al. Rituximab therapy for HIV-associated Castleman disease. Blood. 2003;102(8):2786-2788. Available at: 91. Gerard L, Berezne A, Galicier L, et al. Prospective study of rituximab in chemotherapy-dependent human immunodeficiency virus associated multicentric Castleman's disease: ANRS 117 CastlemaB Trial. J Clin Oncol. 2007;25(22):3350-3356. Available at: 92. Bower M, Powles T, Williams S, et al. Brief communication: rituximab in HIV-associated multicentric Castleman disease. Ann Intern Med. 2007;147(12):836-839. Available at: 93. Nishimoto N, Kanakura Y, Aozasa K, et al. Humanized anti-interleukin-6 receptor antibody treatment of multicentric Castleman disease. Blood. 2005;106(8):2627-2632. Available at: 94. Nagao A, Nakazawa S, Hanabusa H. Short-term efficacy of the IL6 receptor antibody tocilizumab in patients with HIV-associated multicentric Castleman disease: report of two cases. J Hematol Oncol. 2014;7:10. Available at: 95. van Rhee F, Fayad L, Voorhees P, et al. Siltuximab, a novel anti-interleukin-6 monoclonal antibody, for Castleman's disease. J Clin Oncol. 2010;28(23):3701-3708. Available at: 96. From RP, Mehta MP, Pathak D. Serum potassium concentrations following succinylcholine in patients undergoing beta-adrenoceptor blocking therapy. J Clin Anesth. 1989;1(5):350-353. Available at: 97. Letang E, Lewis JJ, Bower M, et al. Immune reconstitution inflammatory syndrome associated with Kaposi sarcoma: higher incidence and mortality in Africa than in the UK. AIDS. 2013;27(10):1603-1613. Available at: 98. Bower M, Nelson M, Young AM, et al. Immune reconstitution inflammatory syndrome associated with Kaposi's sarcoma. J Clin Oncol. 2005;23(22):5224-5228. Available at: 99. Achenbach CJ, Harrington RD, Dhanireddy S, Crane HM, Casper C, Kitahata MM. Paradoxical immune reconstitution inflammatory syndrome in HIV-infected patients treated with combination antiretroviral therapy after AIDS-defining opportunistic infection. Clin Infect Dis. 2012;54(3):424-433. Available at: 100. Mosam A, Shaik F, Uldrick TS, et al. A randomized controlled trial of highly active antiretroviral therapy versus highly active antiretroviral therapy and chemotherapy in therapy-naive patients with HIV-associated Kaposi sarcoma in South Africa. J Acquir Immune Defic Syndr. 2012;60(2):150-157. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-15 101. Borok M, Fiorillo S, Gudza I, et al. Evaluation of plasma human herpesvirus 8 DNA as a marker of clinical outcomes during antiretroviral therapy for AIDS-related Kaposi sarcoma in Zimbabwe. Clin Infect Dis. 2010;51(3):342-349. Available at: 102. Letang E, Almeida JM, Miro JM, et al. Predictors of immune reconstitution inflammatory syndrome-associated with kaposi sarcoma in mozambique: a prospective study. J Acquir Immune Defic Syndr. 2010;53(5):589-597. Available at: 103. Chabria S, Barakat L, Ogbuagu O. Steroid-exacerbated HIV-associated cutaneous Kaposi's sarcoma immune reconstitution inflammatory syndrome: 'Where a good intention turns bad'. Int J STD AIDS. 2016;27(11):1026-1029. Available at: 104. Aaron L, Lidove O, Yousry C, Roudiere L, Dupont B, Viard JP. Human herpesvirus 8-positive Castleman disease in human immunodeficiency virus-infected patients: the impact of highly active antiretroviral therapy. Clin Infect Dis. 2002;35(7):880-882. Available at: 105. Achenbach C, Kitahata MM. Recurrence or Worsening of AIDS-defining Opportunistic Infection (OI) due to Immune Reconstitution Inflammatory Syndrome (IRIS) During Inititial HAART Among a Clinic-Based Population. Presented at: 48th ICAAC/IDSA 46th Annual Meeting; 2008. Washington, DC. Available at. 106. Goedert JJ, Kedes DH, Ganem D. Antibodies to human herpesvirus 8 in women and infants born in Haiti and the USA. Lancet. 1997;349(9062):1368. Available at: 107. Huang LM, Huang SY, Chen MY, et al. Geographical differences in human herpesvirus 8 seroepidemiology: a survey of 1,201 individuals in Asia. J Med Virol. 2000;60(3):290-293. Available at: 108. Lisco A, Barbierato M, Fiore JR, et al. Pregnancy and human herpesvirus 8 reactivation in human immunodeficiency virus type 1-infected women. J Clin Microbiol. 2006;44(11):3863-3871. Available at: 109. Adeyemo A, Wood C, Govind A. Kaposi's sarcoma in pregnancy after initiation of highly active antiretroviral therapy: a manifestation of immune reconstitution syndrome. Int J STD AIDS. 2012;23(12):905-906. Available at: 110. Berger P, Dirnhofer S. Kaposi's sarcoma in pregnant women. Nature. 1995;377(6544):21-22. Available at: 111. Lunardi-Iskandar Y, Bryant JL, Zeman RA, et al. Tumorigenesis and metastasis of neoplastic Kaposi's sarcoma cell line in immunodeficient mice blocked by a human pregnancy hormone. Nature. 1995;375(6526):64-68. Available at: 112. Rabkin CS, Chibwe G, Muyunda K, Musaba E. Kaposi's sarcoma in pregnant women. Nature. 1995;377(6544):21; author reply 22. Available at: 113. Schulz TF, Weiss RA. Kaposi's sarcoma. A finger on the culprit. Nature. 1995;373(6509):17-18. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV P-16 114. Gutierrez-Ortega P, Hierro-Orozco S, Sanchez-Cisneros R, Montano LF. Kaposi's sarcoma in a 6-day-old infant with human immunodeficiency virus. Arch Dermatol. 1989;125(3):432-433. Available at: 115. 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Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-1 Human Papillomavirus Disease Updated: July 9, 2024 Reviewed: July 9, 2024 Recommendations for Cervical Cancer Screening for People With HIV Figure 1. Screening Algorithm for Cervical Cancer in People With HIV Aged 21 to 29 Years Figure 2. Screening Algorithm for Cervical Cancer in People With HIV Aged 30 Years and Older Recommendations for Anal Cancer Screening for People With HIV Figure 3. Screening Algorithm for Anal Cancer in Asymptomatic People With HIV Figure 4. Assessment of Anal Cytology and HPV Results in People With HIV Epidemiology At least 12 human papillomavirus (HPV) types are considered oncogenic, including HPV16, 18, 31, 33, 35, 39, 45, 51, 52, 56, 58, and 59.1-3 HPV68 is considered “probably oncogenic,” and several other HPV types are considered “possibly oncogenic.” HPV16 alone accounts for approximately 53% to 73% of cervical cancers in the general population and HPV18 for another 12% to 21%.4 The other oncogenic HPV types each account for under 5% of cervical cancers.4 Anal cancer and a subset of tumors of the vulva, vagina, penis, and oropharyngeal carcinoma (OPC) are also associated with HPV, and HPV16 and 18 are the most commonly detected in noncervical HPV-positive tumors.2,5-14 While anal cancer and OPC occur in both women and men with HIV, these two tumors disproportionally affect males with HIV, as well as African Americans.15-18 Data also suggest that the distribution of oncogenic HPV types detected in cervical and anal cancers among people with HIV may differ from those in the general population.19,20 HPV infection is the major risk factor for development of cervical cancer,5,21 the fourth most common cancer in women worldwide.22 Nearly all cervical cancers contain oncogenic HPV DNA sequences.23-25 While HPV is a common sexually transmitted cervical infection, most of these infections resolve spontaneously.26-30 Cervical tumorigenesis occurs mostly, if not exclusively, in the presence of persistent oncogenic HPV infection.1,5,31 Women with HIV have high incidence and persistence of HPV relative to women without HIV, as well as high rates of cervical intraepithelial neoplasia (CIN), cervical precancer (CIN 3), and invasive cancer.32-40 Rates of cervical cancer in women with HIV were elevated significantly compared with the general population—3 to 4 times overall (95% confidence interval [CI], 3.13–3.70).41 Most of these relative risks increase with decreasing CD4 T lymphocyte (CD4) cell counts, and cervical cancer is itself associated with advanced HIV.42-54 The percentage with adenocarcinoma histology compared with squamous cell carcinoma is lower in women with HIV than in the general population. Several studies found decreased incident detection, persistence, and progression of HPV and CIN with effective Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-2 antiretroviral therapy (ART) use,55,56 including one study that distinguished between adherent versus nonadherent or effective versus ineffective ART use (based on HIV RNA level). In a report from the HIV/AIDS Cancer Match Study (2002–2016)—which included a population of 164,084 women with HIV—552 cases of invasive cervical cancer (ICC) occurred in 1.16 million person-years of follow-up (rate = 47.7 per 100,000). By age group, the highest incidence rates occurred in the 40- to 44- and 35- to 39-year-old age groups (rate = 66.1 and 64.5 per 100,000, respectively). No cases of ICC were identified in the under 25-year-old age group during 69,900 person-years of follow-up (standardized incidence ratio [SIR] = 0; 95% CI, 0,7.1).41 People with HIV have an increased incidence of anogenital tumors (vulva, vagina, penis) and OPC relative to the general population.23,57-60 Low CD4 counts in people with HIV have been associated with increased risk of anal cancer,61-63 as well as high-grade anal intraepithelial neoplasia (AIN; the likely anal cancer precursor lesion),64-66 anal and genital warts, and vulvar intraepithelial neoplasia (VIN) and vaginal intraepithelial neoplasia (VAIN).67-69 Registry-based data indicate a downward trend in anal cancer incidence relative to the general population (i.e., a reduction in SIR from approximately SIR ~40 in 1996 to SIR ~20 in 2012; P = 0.0001),59 as well as a possible (P = 0.09) decrease in cervical cancer from SIR ~5 in 1996 to SIR ~3 in 2012, and a nonsignificant decrease in OPC.70,71 Other HPV-related tumors are less common, and less is known about trends in their incidence. The elevated risk of HPV-associated cancers in people with HIV continues into older age (>50 years of age).39 Registry-based data show that the 5-year risk (cumulative incidence) of anal cancer was 0.65% and 0.33% in men aged 45 to 59 years with HIV who have sex with men with and without AIDS, respectively, whereas the results were 0.10% and 0.04% for men with HIV who do not have sex with men, and 0.20% and 0.08% for women with HIV.70 Similar results were obtained in a recent meta-analysis of available studies.72 The ANCHOR study estimated the cumulative 4-year progression from high-grade squamous intraepithelial lesion (HSIL) to anal cancer was 1.8%.73 Anogenital warts have very low carcinogenic potential but are an important HPV-associated disease in people with HIV. These lesions are common, and more likely to be persistent in people with HIV than in the general population. Approximately 80% to 90% of anogenital warts are caused by non-oncogenic HPV types 6 or 11.74 HPV types 6 and 11 also have been associated with conjunctival, nasal, oral, and laryngeal warts. In the United States, prior to the introduction of HPV vaccination, the incidence of anogenital warts was 60.2 per 10,000 women (aged 20–24 years) and 53.8 per 10,000 men (aged 20–24 years),75-77 but with several-fold greater rates in people with HIV.67 Low-grade vulvar lesions and genital warts were both found to decrease with ART.67 Clinical Manifestations The principal clinical manifestations of mucosal HPV infection are genital, anal, and oral warts; CIN; VIN; VAIN; AIN; anogenital squamous cell cancers; and cervical adenocarcinomas. A subset of oropharyngeal cancers is also caused by HPV.78 Oral, genital (condyloma acuminata), and anal warts are usually flat, papular, or pedunculated growths on the mucosa or epithelium. The lesions may measure a few millimeters to 1 to 2 centimeters in diameter. Most warts are asymptomatic, but warts can be associated with itching or discomfort. In cases associated with more severe immunosuppression, marked enlargement may cause dyspareunia or dyschezia. Lesions of any size may cause cosmetic concerns. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-3 Low-grade squamous intraepithelial lesions (LSIL) and HSIL in the cervix, vagina, vulva, and anal canal are often asymptomatic but may manifest with bleeding or itching. Related cancers also may be asymptomatic or may manifest with bleeding, pain, odor, or a visible/palpable mass. External lesions may be visible or palpable. Similarly, squamous cell cancers at these sites also can be asymptomatic or may manifest with bleeding, pain, or a visible/palpable mass.79 Preventing HPV Infection Recommendations for Preventing HPV Infection • HPV vaccine is recommended for routine vaccination at age 11 or 12 years. o Administer three doses of 9-valent HPV vaccine (Gardasil 9) at 0, 1 to 2, and 6 months (AIII). Ideally, the series should have been initiated at age 11 or 12 years but may be started as early as age 9 years. The two-dose series is not recommended in people with HIV. • For all people with HIV aged 13 to 26 years who were not vaccinated previously: o Administer three doses of 9-valent HPV vaccine (Gardasil 9) at 0, 1 to 2, and 6 months (AIII). The two-dose series is not recommended in people with HIV. • For people with HIV aged 27 to 45 years who were not adequately vaccinated previously: o HPV vaccine is not routinely recommended; instead, shared clinical decision-making regarding HPV vaccination is recommended for people who may be at risk for a new HPV infection (AIII). • For people who were adequately vaccinated with bivalent or quadrivalent HPV vaccine: o Some experts would consider additional vaccination with 9-valent HPV vaccine, but data are lacking to define the efficacy and cost-effectiveness of this approach (CIII). • HPV vaccination is not recommended during pregnancy (CIII). HPV Vaccine HPV vaccination prevents HPV infection and is ideally administered before sexual exposure to HPV. Although HPV vaccine is most effective in people with few or no sex partners prior to vaccination, HPV vaccination in people with multiple lifetime sex partners can still prevent HPV infection from subtypes they have not been exposed to yet. Three U.S. Food and Drug Administration (FDA)– approved HPV vaccines are licensed: bivalent, quadrivalent, and 9-valent. Currently, only the 9-valent vaccine (9vHPV, protective against HPV types 6, 11, 16, 18, 31, 33, 45, 52, and 58) is available in the United States.14,80 This vaccine has an FDA indication for prevention of cervical, vaginal, vulvar, and anal cancer; genital warts, and oropharyngeal and other head and neck cancers81 based on randomized clinical trial (RCT) data; however, these studies were not conducted in people with HIV.82-88 These RCTs evaluated several endpoints accepted by FDA and established the safety of the vaccine in children as young as 9 years of age and young people aged 16 to 26, as well as older women (aged 27–45 years).89,90 Although no clinical trials have been conducted to demonstrate HPV vaccine efficacy in prevention of oropharyngeal cancers, some evidence exists that the prevalence of oral HPV infections from types contained in the vaccines are reduced with vaccination.91,92 Protection against more subtypes might be more useful in people with HIV because there is more diversity of oncogenic subtypes of HPV.14,80 Routine HPV vaccination with the 9-valent vaccine should be initiated at age 11 or 12 years but may be started as early as age 9 years.93,94 Although the Centers for Disease Control and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-4 Prevention (CDC) Advisory Committee on Immunization Practices recommends a two-dose series,95 the Panel recommends that people with HIV receive a three-dose series (0, 1–2, and 6 months) because their immune response to vaccination might be attenuated (AIII). Because HPV vaccination is safe and immunogenic and has the potential benefit of preventing HPV-associated disease and cancer, catch-up HPV vaccination is recommended for people with HIV aged 13 to 26 years (AIII). Although routine vaccination beyond age 26 is not recommended, shared clinical decision-making regarding HPV vaccination is recommended for adults aged 27 to 45 years who are not adequately vaccinated and are at risk for a new HPV infection (AIII).94 Considerations to help guide shared clinical decision-making are available on the CDC website. For patients who have completed a vaccination series with the recombinant bivalent or quadrivalent vaccine, some experts would give an additional full series (three doses) of vaccination with the 9-valent vaccine (CIII), however no data exist to define who might benefit or how cost-effective this approach might be. Several studies have established the safety and immunogenicity of HPV vaccines in a broad range of people with HIV.95-97 Some studies have demonstrated lower antibody levels in people with HIV than in those who do not have HIV; however, the clinical significance of this observation is unknown.98-100 Studies have shown that HPV vaccination induces an anamnestic response in children and adults with HIV.83,96,101 Immune responses appear stronger among those with higher CD4 counts and suppressed HIV viral loads.97,102 Although HPV vaccine clinical trials in people with HIV reported appropriate immunogenicity and safety,95-104 few, if any, RCTs have utilized clinical endpoints, such as CIN 3 or incident persistent infection with vaccine HPV types. There is also a paucity of prospective epidemiologic studies using these endpoints.105 One randomized, double-blind clinical trial evaluated the efficacy of the quadrivalent HPV vaccine (4vHPV) in a population of people with HIV who were older than 27 years with high rates of prior and current HPV infection. The trial did not show efficacy for prevention of new anal HPV infections or improvement in anal HSIL outcomes.106 Anal cancer endpoints, including anal HSIL and anogenital wart incidence, were studied in another RCT of 4vHPV that involved 129 men who have sex with men (MSM) and who were on ART with a mean age of 38.8 years and who had history of AIDS.107 Although the vaccine and placebo arms did not differ by HSIL or genital wart incidence, vaccine HPV types were less common in the vaccine arm, and in secondary analyses the investigators found that those with the longest time since immunization had significantly reduced risk of HSIL. A one-arm study of 260 MSM with HIV, aged 18 to 26 years, who received 4vHPV and were followed with high-resolution anoscopy at 7, 12, and 24 months found that no participants who were naive at baseline for one or more 4vHPV types developed LSIL or HSIL related to those HPV.108 Conversely, a Phase 3 4vHPV RCT involving older males and females with HIV (aged ≥27 years) ended early due to an insufficient vaccine effect to meet stopping rules.106 This trial did, however, suggest efficacy for short-term prevention of oral HPV infection, which decreased significantly from 88% to 32% after 6 months. A prospective observational cohort study of female youth who received 4vHPV showed unexpectedly high rates of abnormal cervical cytology, occurring in 33 of 56 youth who acquired HIV perinatally and only 1 of 7 of youth who were exposed but uninfected and yielding incidence rates of 100 person-years of 15 (10.9–29.6) and 2.9 (0.4–22.3), respectively. The majority of the diagnoses were LSIL or less, and the genotypes associated with these abnormal cytology results were unknown.103 People with HIV who have been vaccinated should continue routine cervical cancer screening because the vaccine does not prevent all HPV types that may be precursors to cervical cancer, and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-5 because the vaccine may be less effective in people with HIV (especially those with low CD4 counts) than in people without HIV. Condom Use The use of male latex condoms is strongly recommended for preventing transmission or acquisition of HPV infection, as well as for preventing HIV and other sexually transmitted infections (STIs) (AII).109-111 Latex condoms provide a sufficient barrier to prevent passage of particles the size of HPV. Consistent and proper use of latex male condoms has been associated with 70% lower incidence of oncogenic HPV infection among women.111 Similarly, cross-sectional data suggested that among heterosexual men with no steady sex partner, consistent condom use was associated with 50% lower odds of HPV infection of the penis.112 A meta-analysis found that condom use was associated with reduced risk of genital warts and, in women, with lower rates of CIN.109 An RCT of condom use in heterosexual couples found significantly more frequent clearance of CIN and HPV among women randomized to condom use and of penile lesions among their male partners.113,114 Male condoms have benefits in reducing risk of transmission of nearly all STIs (including HIV infection) during heterosexual intercourse and same-sex intercourse between men. In circumstances when a male condom cannot be used properly, a female condom (e.g., an FC1 or FC2 Female Condom) should be considered for heterosexual vaginal intercourse (AII) and for heterosexual or male same-sex anal intercourse (BIII). Data on FC1 and FC2 Female Condoms suggest that the devices are protective against STIs.110 Male Circumcision There is evidence that male circumcision reduces rates of oncogenic HPV infection of the penis, based on data from RCTs and observational studies.115-118 Observational studies in the general population also suggest that circumcision is associated with lower risk of penile cancer and of cervical cancer in sexual partners. Relevant data in men with HIV, however, are limited; findings to date suggest that the effects of circumcision against HPV infection (while protective) may be less in people with HIV than in those without. Furthermore, no clinical trials have assessed whether circumcision of men who have HIV reduces the risk of genital or anal HPV-related cancer or precancer (such as AIN) or oncogenic HPV infection of the anal or oral mucosa for them or their sexual partners. Evidence is insufficient to recommend adult male circumcision solely to reduce the risk of oncogenic HPV infection in men with HIV or their sex partners. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-6 Preventing Disease Cervical Cancer Screening Recommendations Recommendations for Cervical Cancer Screening for People With HIV Figure 1. Screening Algorithm for Cervical Cancer in People With HIV Aged 21 to 29 Years Figure 2. Screening Algorithm for Cervical Cancer in People With HIV Aged 30 Years and Older The same cytology and colposcopic techniques with biopsy are used to detect CIN among people with and without HIV (see section on Preventing Disease). At the time of cytology screening, the genitalia and anal canal should be inspected carefully for visual signs of warts or invasive cancer. Available HPV tests can detect up to 14 oncogenic HPV types in clinical specimens and are sensitive for the detection of cervical cancer precursors. Some commercially available HPV tests will specify whether the oncogenic HPV includes genotypes HPV16 or HPV16/18. The available tests for oncogenic HPV have been incorporated into the screening algorithms. HPV testing is always for oncogenic HPV types only; there is no role for non-oncogenic HPV testing. Observational epidemiologic studies in people with HIV have been instrumental in the decisions to adopt several cervical cancer screening guidelines that had been validated in large clinical trials in the general population. This included studies that supported the incorporation of cervical HPV testing for determining referral to colposcopy versus retesting in 1 year or during routine follow-up. For example, despite the very high prevalence of HPV in women with HIV, normal cytology with negative HPV co-testing had a strong negative predictive value, with low 3- to 5-year incidence of cervical intraepithelial neoplasia grade 2 (CIN 2+) regardless of CD4 count.119,120 Conversely, the risk of precancer was high in women with HIV who tested positive for oncogenic HPV despite normal cervical cytology results and several-fold greater still if HPV16 was specifically detected.121 Additional studies showed that oncogenic HPV testing had high sensitivity and negative predictive value in the triage of borderline cervical cytology results (i.e., atypical squamous cells of uncertain significance [ASC-US]).122,123 Possible cervical cytology results include the following: • Normal (negative for intraepithelial lesion or malignancy) • LSIL or CIN 1 (cervical intraepithelial neoplasia grade 1) • HSIL or CIN 2, 3 • ASC-US • ASC-H (atypical squamous cells, cannot rule out a high-grade lesion) • AGC (atypical glandular cells) For people with HIV, cervical cancer screening and treatment of precancer are, in and of themselves, a major burden. Positive HPV screening tests are several-fold more common in women with HIV than in the general population, and as many as 16% of women with HIV have abnormal cervical Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-7 cytology with ASC-US or worse at each clinical visit.124 This often leads to repeated colposcopy and biopsy, although most of these colposcopies and biopsies in people with HIV find LSIL rather than clinically relevant disease (e.g., HSIL, cancer). A study of “primary oncogenic HPV screening”— which uses HPV testing as the initial screening method and, if positive, often reflex-triage (e.g., HPV16/18-genotyping, cervical cytology)—found that this approach reduced unnecessary colposcopies by almost half relative to currently recommended HPV/cervical cytology co-testing for women with HIV.125 However, these findings require confirmation. There is also a significant need for technical advancement to improve the positive predictive value of the screening tests—especially as many women with HIV exceed the age for routinely recommended HPV vaccination.125 People With HIV Aged 21 to 29 Years Cervical cytology is the primary mode for cervical cancer screening for women with HIV under 30 years of age. People aged 21 to 29 years with HIV should have cervical cytology at the time of initial diagnosis with HIV (AII). See Figure 1. Screening Algorithm for Cervical Cancer in People With HIV Aged 21 to 29 Years for detailed recommendations. The absolute incidence of ICC is exceedingly low among women with HIV under 25 years; therefore, cervical cancer screening is recommended to start at age 21. The rationale for beginning screening at age 21 is to provide a 3- to 5-year window prior to age 25, when the risk of ICC in women with HIV exceeds that of the general population.41 Co-testing (cervical cytology and HPV test) and reflex high-risk HPV (hr-HPV) testing (HPV testing in the presence of abnormal cytology results) is routinely recommended for people without HIV and might be considered for people aged 25 to 29 years with HIV; however, there is a relatively high prevalence of transient HPV before age 30 years, which may lead to unnecessary colposcopy.126 If cytology reveals ASC-US and reflex hr-HPV testing is performed, repeat cytology should be evaluated in 6 to 12 months (AII). If repeat cytology shows ASC-US and reflex hr-HPV is positive, individuals should be referred for colposcopy (CIII). The American Society for Colposcopy and Cervical Pathology (ASCCP) and the American College of Obstetrics and Gynecology (ACOG) recommend screening for cervical cancer using cytology alone for women aged 21 to 29 years. The American Cancer Society (ACS) now recommends initiating cervical cancer screening at age 25 with primary HPV screening (hr-HPV testing alone) every 5 years in the general population. The FDA recently approved self-testing for HPV screening in clinical settings.127 There are ongoing studies to evaluate the use self-testing for HPV screening in people with HIV. The U.S. Preventive Services Task Force (USPSTF) is reviewing its current recommendations and will issue an update soon regarding the use of primary HPV screening for cervical cancer. People With HIV Aged 30 Years and Older Cervical cancer screening in people with HIV should continue throughout their lifetime (and not, as in the general population, end at 65 years of age) (BIII). Either cytology only or cytology and HPV co-testing is acceptable for screening (BIII). See Figure 2. Screening Algorithm for Cervical Cancer in People With HIV Aged 30 Years and Older for detailed recommendations. Current guidelines from both the ACS and the USPSTF allow use of HPV co-testing with cytology. A negative HPV test predicts prolonged low risk of cancer. Cytology/HPV co-testing can allow a prolonged cervical cancer screening interval in women with HIV who are older than 29 years and have normal cervical cytology with concurrent negative HPV testing. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-8 For people aged more than 65 years, it is recommended to continue cervical cancer screening because people with HIV are at higher risk for cervical cancer (BIII). However, clinicians should consider other factors, such as the life expectancy of the patient and the risk for developing cervical cancer at this age.128 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-9 Overview of Cervical Cancer Screening Guidelines <21 Years 21–24 Years 25–29 Years ≥30 Years Comments NIH OAR Adult and Adolescent OI Guidelines (specific to people with HIV) No screening recommended Cytology Only • Cytology yearly o If normal cytology on 3 consecutive annual tests, adjust to every 3 years Cytology Only • Cytology yearly o If normal cytology on 3 consecutive annual tests, adjust to every 3 years Co-testinga • Co-testing yearly o If normal cytology and hr-HPV negative on 3 consecutive years, adjust to every 3 years. Cytology Only • Cytology yearly • If normal cytology on 3 consecutive years, adjust to every 3 years USPSTF (no HIV-specific guidance) No screening recommended • Cytology every 3 years • Cytology every 3 years Cytology Only • Every 3 years hr-HPV Testing Only • Every 5 years Co-testinga • Every 5 years Not specific to people with HIV ASCCP Same as USPSTF ACOG Same as USPSTF ACS (no HIV-specific guidance) No screening recommended No screening recommended Preferred • Primary HPV testb every 5 years Acceptable • Co-testing every 5 years • Cytology alone every 3 years Preferred • Primary HPV testb every 5 years Acceptable • Co-testing every 5 years • Cytology alone every 3 years Updated July 2020 Not specific to people with HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-10 Overview of Cervical Cancer Screening Guidelines WHO (HIV-specific guidance) No screening recommended No screening recommended Preferred • Primary HPV testb (provider-obtained or self-collection) every 3–5 years Preferred • Primary HPV testb (provider-obtained or self-collection every 3–5 years) Updated July 2021 a Co-testing refers to combined cytology and high-risk HPV (hr-HPV) testing. b Primary HPV testing is hr-HPV testing alone. Key: ACOG = American College of Obstetricians and Gynecologists; ACS = American Cancer Society; ASCCP = American Society for Colposcopy and Cervical Pathology; HPV = human papillomavirus; hr-HPV = high-risk HPV; NIH OAR = National Institutes of Health Office of AIDS Research; OI = opportunistic infection; USPSTF = United States Preventive Services Task Force; WHO = World Health Organization Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-11 Preventing Vaginal and Vulvar Cancer VAIN and VIN are recognized through visual inspection, including colposcopy and biopsy as needed. Most patients are asymptomatic, however. Abnormalities are usually detected after colposcopic examination and biopsy in response to abnormal cervical cytology. Following hysterectomy for benign disease, routine screening for vaginal cancer is not recommended for people with HIV (AIII). However, people with a history of high-grade CIN, adenocarcinoma in situ, or ICC are at increased risk and should be followed with annual vaginal cuff cervical cytology (BIII). For patients not known to have had a hysterectomy for a benign indication, continued screening is recommended since studies have shown that CIN is the most common indication for hysterectomy for people with HIV (CIII). Although vaginal cervical cytology results are often abnormal in women with HIV and more common than in women without HIV, VAIN 2+ and vaginal cancers are infrequent.129 Another study in women with HIV with previous hysterectomy and no previous abnormal cervical cytology results, showed that among those with vaginal biopsies, 29% had VAIN 2 or VAIN 3.130 However, this retrospective study was limited due to sample size. For patients with abnormal vaginal cuff cervical cytology results with no visible vaginal colposcopic abnormalities, the use of Lugol’s iodine to stain the vagina is recommended (AIII). Vaginal colposcopy also is indicated in the presence of concomitant cervical and vulvar lesions. Classification of VAIN (i.e., VAIN 1, VAIN 2, and VAIN 3) parallels that of the cervix. No screening procedure is available for vulvar cancer. However, biopsy or referral is indicated when inspection/palpation identifies lesions suspicious for VIN or cancer. Screening for Anal Cancer Recommendations for Anal Cancer Screening for People With HIV Figure 3. Screening Algorithm for Anal Cancer in Asymptomatic People With HIV Figure 4. Assessment of Anal Cytology and HPV Results in People With HIV Based on the high incidence of anal cancer in people with HIV, the high prevalence of anal HSIL in people with HIV, the high progression rate of anal HSIL to anal cancer in the absence of treatment, and efficacy in treating anal HSIL to reduce progression to anal cancer, screening for anal HSIL (AII)73,131 and treatment of anal HSIL (AI) are recommended for people with HIV based on age.73 See Figure 3. Screening Algorithm for Anal Cancer in Asymptomatic People With HIV and Figure 4. Assessment of Anal Cytology and HPV Results in People With HIV for detailed recommendations. People with HIV, regardless of history of anal intercourse, should undergo annual assessment of anal symptoms (e.g., unexplained itching, anal bleeding, or pain; presence of perianal lesions). MSM and transgender women below the age of 35 and others below the age of 45 with anal symptoms should undergo digital anorectal examination (DARE) and standard anoscopy (AIII). See International Anal Neoplasia Society Guidelines for the Practice of Digital Anal Rectal Examination and Performing a Digital Anal Rectal Examination on how to perform a proper DARE. MSM and transgender women aged 35 and above and all others with HIV aged 45 and above with symptoms or abnormal examinations should be referred to high-resolution anoscopy (HRA) if available (BIII). HRA identifies anal HSIL and (following biopsy for histopathologic confirmation) enables treatment of anal HSIL to prevent progression to anal cancer. If HRA is not available, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-12 patients should undergo standard anoscopy (BIII) and be referred for biopsy of identified lesions to determine level of histologic changes and to rule out invasive cancer. Standard anoscopy involves visualization of the anal canal and perianal region through an anoscope without application of 5% acetic acid or Lugol’s iodine to identify lesions. HRA requires specialized training and is performed with 5% acetic acid and Lugol’s iodine to identify lesions under magnification typically provided by a colposcope. HRA allows flat lesions typical of HSIL or cancer to be identified with greater precision than standard anoscopy. When to start screening for anal HSIL in asymptomatic individuals specifically should be based on the overall risk for anal cancer. The risk for anal cancer in people with HIV appears to differ based on age, sex at birth, and HIV exposure group, as evidenced by national estimates from the AIDS/Cancer Match Study, which links HIV/AIDS registries with data from the National Cancer Institute’s Surveillance Epidemiology End Results (SEER), and by findings from a comprehensive meta-analysis of anal cancer screening and treatment studies (see figure on anal cancer incidence from this meta-analysis).70,72 Based on their incidence of anal cancer, and until definitive screening guidelines are available, experts in the field recommend that screening in asymptomatic people with HIV begin at different ages depending on sex and HIV risk group. Initiating screening for anal precancer and cancer is recommended at age 35 for MSM and transgender women who have HIV (AII). Screening for anal cancer should be initiated in cisgender women and all other persons with HIV at age 45 years (AII). MSM and transgender women aged 35 years and older, and other people with HIV aged 45 years and older, should continue to be assessed annually for anal symptoms and undergo DARE regardless of symptoms (BIII). Older age, longer known duration of immune suppression and HIV infection, history of AIDS, smoking, positive HPV16 or 18 status, and higher grade of cytologic abnormality are associated with increased risk of anal cancer.72,132-135 People with HIV who meet any of these criteria should be screened and referred for HRA as soon as feasible (BIII). Screening can be performed using anal cytology alone or with hr-HPV co-testing. Screening individuals with anal cytology to identify those who need HRA with the goal of diagnosing and treating anal HSIL should be performed only when HRA and HRA-based treatment are available. There currently are no FDA-cleared anal HPV tests, but testing is available in many clinical laboratories. It is strongly recommended to use only clinical laboratories that have undergone CLIA certification to conduct anal HPV tests. If cytology will be obtained for screening, defer DARE until after swabbing anal canal to decrease potential for lubricant interfering with cytology results. Until further data on screening algorithms are available, the recommended screening approaches shown in Figure 3. Screening Algorithm for Anal Cancer in Asymptomatic People With HIV can be considered based on testing availability. The International Anal Neoplasia Society (IANS) recently published recommendations for anal cancer screening including but not specific for people with HIV. We concur with the recommendation to screen for anal cancer for MSM and transgender women aged more than 35 years with HIV and all other people aged 45 years or above with HIV. We agree with the use of anal cytology or anal cytology with hr-HPV co-testing as screening modalities. In contrast to the IANS guidelines, we do not recommend HPV screening without cytology at this time due to insufficient supporting evidence in people with HIV (BIII). The prevalence of anal hr-HPV infection is very high among persons with HIV, and the specificity and positive predictive value for anal HSIL are Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-13 expected to be low. Although screening for HPV16 or 18 specifically may improve the specificity and positive predictive value, anal cancer is associated with a broader spectrum of hr-HPV types in people with HIV than in people without HIV; therefore, there may still be insufficient sensitivity for anal HSIL in people with HIV.19 Overview of Anal Cancer Screening Guidelines in People With HIV NIH OAR Adult and Adolescent OI Guidelines IANS Guidelines Primary anal HPV testing alone without cytology as screening option No Yes High-priority patients if HRA availability limited (no priority order specified in either guideline) • Higher grade of cytologic abnormality • HPV16 on HPV testing • Smokers • >60 years of age • Longer known duration of HIV • History of AIDS • Higher grade of cytologic abnormality • HPV16 on HPV testing Key: HPV = human papillomavirus; HRA = high-resolution anoscopy; IANS = International Anal Neoplasia Society; NIH OAR = National Institutes of Health Office of AIDS Research; OI = opportunistic infection If HSIL is identified on biopsy, treatment of the lesion should be performed to reduce the incidence of anal cancer among people with HIV (AI). Further details are presented in the section “Treating AIN and Anal Cancer.” Preventing Oropharyngeal Cancer Although HPV DNA detection might be useful in identifying individuals at high risk of oropharyngeal cancer, no adequate methods currently exist to determine the site of HPV-associated oropharyngeal precancer or cancer to target biopsy or treatment, despite ongoing efforts. It also should be noted that rates of non-HPV-associated oral cancer also are increased in people with HIV,15 and potentially malignant oral disorders can be diagnosed and followed by biopsy in some cases; the effectiveness of this approach has not been tested in RCTs.136 Diagnosis Warts/Condyloma Diagnosis of genital and oral warts is made by visual inspection and can be confirmed by biopsy. However, biopsy is needed only if the diagnosis is uncertain, the lesions do not respond to standard therapy, or the warts are pigmented, indurated, fixed, bleeding, or ulcerated. No data support the use of HPV testing for screening, diagnosis, or management of visible genital/oral warts or oral HPV disease in people with HIV.137 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-14 Cervical Neoplasia The same cytology and colposcopic techniques with biopsy are used to detect CIN among patients without HIV and people with HIV (see section on Preventing Disease). At the time of cytology screening, the genitalia and anal canal should be inspected carefully for visual signs of warts, mucosal abnormalities that may indicate intraepithelial neoplasia, or invasive cancer. Anal and Vulvar/Vaginal Neoplasia AIN, VAIN, and VIN are recognized through visual inspection, including high-resolution anoscopy, colposcopy, and biopsy as needed. A digital examination of the anal canal to feel for masses should be performed as part of routine evaluation.138 Treating Disease Cancer-specific survival following treatment of anal cancer and OPC was reported to be similar in people with HIV and the general population, whereas cervical cancer survival following treatment was reported to be lower in women with HIV.139,140 Another study found that although response to initial therapy for ICC (e.g., radiation treatment) was similar in women with HIV compared with others, HIV was associated with higher risk of relapse (hazard ratio [HR] 3.6; 1.86–6.98) and higher cervical cancer mortality.141 Data from the AIDS Malignancy Consortium showed that women with HIV on ART with locally advanced cervical cancer in sub-Saharan Africa can complete routine cisplatin and radiation therapy. Furthermore, 1-year progression-free overall survival rates observed among women with high-risk advanced tumors were similar to reported studies of women without HIV with generally smaller tumors.142 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-15 Treating Genital and Oral Warts Patient-Applied Treatments Options For Uncomplicated External Warts That Can Be Easily Identified by Patients • Topical imiquimod (5% cream) at bedtime 3 nonconsecutive nights a week, for up to 16 weeks (BII). Each treatment should be washed with soap and water 6 to 10 hours after application. • Topical podofilox (0.5% solution or gel) twice a day for 3 days, followed by 4 days of no therapy. Can be repeated, as necessary, up to four times (BIII). • Topical sinecatechins (15% ointment) three times a day for up to 16 weeks until warts are cleared completely and not visible (BIII) • Topical cidofovir 1% daily for 5 days per week for 8 weeks (CIII). Not commercially available but may be compounded in pharmacies with required equipment. Provider-Applied Treatment Options For Complex or Multicentric Lesions, or Lesions Inaccessible to Patient, or Due to Patient or Provider Preference • Cryotherapy (liquid nitrogen or cryoprobe) applied until each lesion is thoroughly frozen, with treatment repeated every 1 to 2 weeks for up to 4 weeks until lesions are no longer visible (BIII). Some specialists recommend allowing the lesion to thaw and freezing a second time in each session (BIII). • TCA and BCA (80% to 90%) applied to warts only and allowed to dry until a white frosting develops. The treatment can be repeated weekly for up to 6 weeks, until lesions are no longer visible (BIII). • Intralesional cidofovir (15 mg/mL solution) injected directly into the wart (maximum 1 mL per session). May be repeated every 4 weeks for total of three to four treatments (CIII). • Surgical treatments (e.g., tangential scissor excision, tangential shave excision, curettage, electrosurgery, electrocautery, infrared coagulation) can be used for external genital and anal warts (BIII). Laser surgery is an option but is usually more expensive (CIII). Note: Many treatments for anogenital warts cannot be used in the oral mucosa. Surgery is the most common treatment for oral warts that interfere with function or for aesthetic reasons. Considerations in Pregnancy • Topical treatments such as BCA and TCA, as well as ablative therapies (i.e., laser, cryotherapy, and excision) can be used during pregnancy (AIII). • Obstetrical management should not change for people with genital warts unless extensive condylomata might impede vaginal delivery or cause extensive bleeding (AIII). • Pregnant people should undergo cervical and anal cancer screening as recommended for nonpregnant people. • Endocervical curettage is contraindicated in pregnant people (AIII). Key: BCA = bichloroacetic acid, TCA = trichloroacetic acid Treating Genital and Oral Warts People with HIV may have larger or more numerous warts, may not respond as well to therapy for genital warts as individuals who are immunocompetent, and may have more frequent recurrences after treatment. Genital warts are not life-threatening and may regress without therapy, even in people with HIV and especially in those whose immunity is relatively preserved. Treatments are available for genital warts, but none are effective or preferred uniformly. Lacking RCTs specific to people with HIV, guidelines for the treatment of STIs in people without HIV should be followed. More than one treatment option may be required for refractory or recurrent lesions in people with HIV. Histologic diagnosis should be obtained for refractory lesions to confirm the absence of high-Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-16 grade disease. Intra-anal, vaginal, urethral, or cervical warts should be treated and managed by a specialist. Patient-applied treatments are recommended generally for uncomplicated external warts that can be identified easily and treated by the patient. Imiquimod (5% cream) is a topical cytokine inducer that should be applied at bedtime on 3 nonconsecutive nights per week, for up to 16 weeks, until lesions are no longer visible. The treatment area should be washed with soap and water 6 to 10 hours after the application (BII). Podofilox 0.5% solution or gel should be applied to visible anogenital warts twice a day for 3 days, followed by 4 days of no therapy. This cycle can be repeated, as necessary, up to four times (BIII). Another option is sinecatechins (15% ointment), a topical botanical product that contains active catechins from green tea and should be applied three times daily for up to 16 weeks, until warts are cleared completely and not visible (BIII).143 No clinical trials of this latter treatment option have been conducted in people with HIV. Topical application of cidofovir or intralesional cidofovir has reported activity against genital warts (CIII). Topical formulation is not commercially available but may be compounded in pharmacies with required equipment.144-146 Provider-applied treatments—such as cryotherapy, trichloroacetic acid (TCA), bichloroacetic acid (BCA), and surgery—typically are recommended for complex or multicentric lesions, lesions inaccessible to patient-applied therapy, or because of patient or provider preference. Cryotherapy (liquid nitrogen or cryoprobe) destroys lesions by thermal-induced cytolysis and should be applied until each lesion is thoroughly frozen, with treatment repeated every 1 to 2 weeks for up to 4 weeks, until lesions are no longer visible (BIII). Some specialists recommend allowing the lesion to thaw and freezing a second time in each session (BIII). TCA and BCA (80% to 90%) both act as caustic agents to destroy wart tissue and should be applied to warts only and allowed to dry until a white frosting develops. If an excess amount of acid is applied, the treated area should be powdered with talc, sodium bicarbonate, or liquid soap to remove unreacted acid. The treatment can be repeated weekly for up to 6 weeks, until lesions are no longer visible (BIII). Surgical treatments (e.g., tangential scissor excision, tangential shave excision, curettage, electrosurgery, electrocautery, infrared coagulation) can be used for external genital and anal warts (BIII). Laser surgery is an option but is usually more expensive (CIII). Intralesional interferon has been used for the treatment of genital warts, but because of cost, difficulty of administration, and potential for systemic adverse effects—such as fever, fatigue, myalgias, and leukopenia—it is not recommended for first-line treatment (CIII). Podophyllin resin may be an alternative provider-applied treatment, with strict adherence to recommendations on application. It has inconsistent potency in topical preparations and can have toxicity that may limit routine use in clinical practice. No consensus on optimal treatments of oral warts exists. Treatments for anogenital warts cannot be used in the oral mucosa. Given the lack of RCTs, surgical removal is the most common treatment for oral warts that interfere with function or need to be removed for aesthetic reasons. These recommendations align with the CDC STI Treatment Guidelines. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-17 Treating CIN and Cervical Cancer People with HIV with CIN should be managed by a clinician with experience in colposcopy and treatment of cervical cancer precursors. In general, CIN in people with HIV should be managed according to ASCCP guidelines. People with satisfactory colposcopy (transformation is fully visualized) and biopsy-confirmed high-grade CIN (CIN 2/3) can be treated with either ablation (e.g., cryotherapy, laser vaporization, electrocautery, diathermy, cold coagulation) or excisional methods (e.g., loop electrosurgical excision procedure, laser conization, cold knife conization), whereas people with unsatisfactory colposcopy should be treated only with excisional methods (AII). In patients with recurrent high-grade CIN, diagnostic excisional methods are recommended (AII). Hysterectomy is acceptable for treatment of recurrent or persistent biopsy-confirmed high-grade CIN (BII); if invasive disease is suspected, the patient should be managed in consultation with a gynecologic oncologist. The ASCCP guidelines for adolescents and young women aged 21 to 24 years should continue to be followed. In these patients, progression of lesions is more common, and so is recurrence. Therefore, close observation, as outlined in the guidelines, should be considered for management of CIN 1; CIN 2; CIN 2,3 not otherwise specified (when pathology is HSIL but does not specify if CIN 2 or 3); and histologic HSIL in adolescents and adults with HIV who are younger than 25 years (BIII). If concern for loss to follow-up, excisional methods of treatment for CIN 2; CIN 2,3; and HSIL may be preferred (BIII). Management of ICC may follow National Comprehensive Cancer Network (NCCN) guidelines. Although complication and failure rates may be higher in people with HIV, standard treatment appears safe and efficacious.142 Treating VIN, Vulvar Cancer, VAIN, and Vaginal Cancer Low-grade VIN/VAIN (VIN/VAIN1) can be observed or managed the same as vulvovaginal warts. Treatment of high-grade VIN/VAIN should be individualized in consultation with a specialist and is dependent upon the patient’s medical condition and the location and extent of the disease. Various treatment modalities are available for VIN, including local excision, laser vaporization, ablation, and topical therapies (e.g., imiquimod or cidofovir135 therapy). Treatment options for VAIN include topical 5-fluorouracil (5-FU), laser vaporization with CO2 laser, and excisional procedures.147-149 Management of vulvar and vaginal cancer must be individualized in consultation with a specialist, following NCCN guidelines. Treating AIN and Anal Cancer The ANCHOR study was not designed to compare different treatment modalities for efficacy. However, almost all participants were treated with office-based ablation of HSIL, most often hyfrecation. The rate of treatment-associated serious adverse events was very low. Office-based hyfrecation is therefore a reasonable first-line approach to treatment of anal HSIL (AI).73 Those with anal cancer should be referred to Oncology for appropriate treatment. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-18 Treating HPV-Associated Disease at Other Sites, Including the Penis and the Oropharynx Penile and some oropharyngeal cancers are associated with HPV infection. Treatment options do not differ for men and women with and without HIV. Data suggest a more favorable prognosis for HPV-associated oropharyngeal cancers than for non-HPV-associated oropharyngeal cancers.150-152 Surgery, chemotherapy, and radiation are treatment modalities used for oropharyngeal cancers. Special Considerations Regarding Antiretroviral Therapy Initiation Given the strong evidence that early ART initiation is clinically beneficial in reducing risk of AIDS and opportunistic infections (OIs), there is no reason to consider HPV-related oral, anal, or genital disease when deciding whether or when to initiate ART. Monitoring Response to Therapy and Adverse Events (Including IRIS) Monitoring by physical examination is required during and after treatment of genital warts to detect toxicity, persistence, or recurrence, all of which are common with each of the treatments. Because recurrences of CIN and cervical cancer after conventional therapy are more common with HIV, these individuals should be followed after treatment with frequent cytologic screening and colposcopic examination (see Preventing Disease and Treating Disease sections). Treatment of CIN with ablative and excisional modalities can be associated with several adverse events, such as pain and discomfort, intraoperative hemorrhage, postoperative hemorrhage, infection, and cervical stenosis. Individualized treatment of adverse events is required. Each of the treatment modalities for AIN described above is associated with adverse events, primarily pain, bleeding, ulceration, and, in rare cases, development of abscesses, fissures, or fistulas. Patients can be monitored for adverse events using the methods previously described. Treatment for anal cancer with combination radiation and chemotherapy is associated with a high rate of morbidity, even when the treatment is successful. The most important complication is radiation-associated proctitis. During IRIS, HPV may manifest as a paradoxical increase in warts after introduction of ART or by inflammation of existing warts.153,154 A few studies also have shown the development of oral warts while starting ART.155-158 Managing Treatment Failure For persistent or recurrent genital warts, retreatment with any of the modalities previously described should be considered (AIII). Biopsy should be considered to exclude VIN. Genital warts often require more than one course of treatment. Recurrent cytologic and histologic abnormalities after therapy for CIN should be managed according to ASCCP guidelines. No consensus on the treatment of biopsy-proven recurrent VIN exists, and surgical excision can be considered. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-19 Preventing Recurrence Monitoring after therapy for cervical disease should follow ASCCP guidelines. In one study of women with HIV treated for high-grade CIN, low-dose intravaginal 5-FU (2 g twice weekly for 6 months) reduced the short-term risk of recurrence. Clinical experience with this therapy, however, is too limited to provide a recommendation for its use, and no follow-up study to confirm these observations has been reported. No guidelines exist regarding frequency of monitoring after therapy for VIN, but twice-yearly vulvar inspection appears reasonable for people who have been treated for VIN. People who have been treated for high-grade VAIN should be managed like those with CIN 2, that is, with cytology at 6 and 12 months after therapy, and annually thereafter. No indication exists for secondary prophylaxis (chronic maintenance therapy) with any of the conventional modalities to prevent recurrence of genital warts, CIN, or AIN. Special Considerations During Pregnancy Pregnant people with HIV who have genital warts or anogenital HPV-related neoplasia are best managed by an interdisciplinary team of specialists, such as an obstetrician or gynecologist and an infectious disease provider. Pregnancy may be associated with an increased frequency and rate of growth of genital warts. Podofilox should not be used during pregnancy (BIII). At present, the evidence is insufficient to recommend imiquimod use during pregnancy. No anomalies have been observed with the use of imiquimod in animals during pregnancy. Several case series describe the use of imiquimod during pregnancy, also without any significant adverse effects.159,160 Other topical treatments—such as BCA and TCA—and ablative therapies (i.e., laser, cryotherapy, and excision) can be used during pregnancy (AIII). Transmission of genital HPV6 and 11 from vaginal secretions at delivery is the presumed mechanism of juvenile-onset recurrent respiratory papillomatosis in children. This condition is rare but is seen more frequently among children born to women who have genital warts at delivery. Cesarean delivery is not known to prevent this condition in infants and children.161 No change in obstetrical management is indicated for people with genital warts unless extensive condylomata are present that might impede vaginal delivery or cause extensive bleeding (AIII). Pregnant people should undergo cervical and anal cancer screening as recommended above for nonpregnant people. Cytobrush sampling can be done during pregnancy. Pregnant people with abnormal cervical cytology results should undergo colposcopy and cervical biopsy of lesions suspicious for high-grade disease or cancer (BIII). Increased bleeding may occur with cervical biopsy during pregnancy. Endocervical curettage is contraindicated in pregnant people (AIII). Pregnant people with ASC-US or LSIL can be managed the same as nonpregnant people, although deferral of colposcopy until at least 6 weeks postpartum is acceptable (CIII). Treatment of CIN is not recommended during pregnancy unless invasive disease is suspected (AIII). Pregnant people with suspected cervical cancer should be referred to a gynecologic oncologist for definitive diagnosis, treatment, and development of a delivery plan. Vaginal delivery is not recommended for people with ICC (AIII). For people with CIN and without suspicion of invasive disease, re-evaluation with co-testing and colposcopy is recommended after 6 weeks postpartum (AIII). People with CIN can deliver vaginally. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-20 Pregnancy testing is not needed before vaccination. HPV vaccination is not recommended during pregnancy (CIII), as there are limited data for its use in pregnancy; however, no intervention is needed if inadvertently given.162 In a combined analysis of five RCTs of the HPV6/11/16/18 vaccine, administration of the vaccine to women who became pregnant during the course of the trial did not appear to negatively affect pregnancy outcomes.163 Additionally, in a population-based study in Denmark, no increased risk of spontaneous abortion, stillbirth, or infant mortality was observed in more than 5,200 pregnancies exposed to at least one dose of the quadrivalent HPV vaccine. Also in Denmark, an analysis of the Medical Birth Register and National Patient Register found that among 1,665 exposed pregnancies, quadrivalent HPV vaccination was not associated with a significantly increased risk of adverse pregnancy outcomes, including major birth defect, preterm birth, or low birth weight.164 Data on the use of the 9-valent vaccine during pregnancy are more limited, but to date are also reassuring.165-169 The effects of treatment of AIN on pregnancy are unknown. Most experts recommend deferral of diagnosis and treatment of AIN until after delivery unless a strong clinical suspicion of anal cancer exists. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-21 References 1. Schiffman M, Clifford G, Buonaguro FM. Classification of weakly carcinogenic human papillomavirus types: addressing the limits of epidemiology at the borderline. Infect Agent Cancer. 2009;4:8. Available at: 2. 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Safety and immunogenicity of a quadrivalent human papillomavirus (types 6, 11, 16, and 18) vaccine in HIV-infected children 7 to 12 years old. J Acquir Immune Defic Syndr. 2010;55(2):197-204. Available at: 96. Wilkin T, Lee JY, Lensing SY, et al. Safety and immunogenicity of the quadrivalent human papillomavirus vaccine in HIV-1-infected men. J Infect Dis. 2010;202(8):1246-1253. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-29 97. Kojic EM, Kang M, Cespedes MS, et al. Immunogenicity and safety of the quadrivalent human papillomavirus vaccine in HIV-1-infected women. Clin Infect Dis. 2014;59(1):127-135. Available at: 98. Rainone V, Giacomet V, Penagini F, et al. Human papilloma virus vaccination induces strong human papilloma virus specific cell-mediated immune responses in HIV-infected adolescents and young adults. AIDS. 2015;29(6):739-743. Available at: 99. Faust H, Toft L, Sehr P, et al. 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Human papillomavirus antibody levels and quadrivalent vaccine clinical effectiveness in perinatally human immunodeficiency virus-infected and exposed, uninfected youth. Clin Infect Dis. 2019;69(7):1183-1191. Available at: 104. McClymont E, Lee M, Raboud J, et al. The efficacy of the quadrivalent human papillomavirus vaccine in girls and women living with human immunodeficiency virus. Clin Infect Dis. 2019;68(5):788-794. Available at: 105. Staadegaard L, Ronn MM, Soni N, et al. Immunogenicity, safety, and efficacy of the HPV vaccines among people living with HIV: A systematic review and meta-analysis. EClinicalMedicine. 2022;52:101585. Available at: 106. Wilkin TJ, Chen H, Cespedes MS, et al. A randomized, placebo-controlled trial of the quadrivalent HPV vaccine in HIV-infected adults age 27 years or older: AIDS Clinical Trials Group protocol A5298. Clin Infect Dis. 2018. Available at: 107. Hidalgo-Tenorio C, Pasquau J, Omar-Mohamed M, et al. Effectiveness of the quadrivalent HPV vaccine in preventing anal ≥ HSILs in a Spanish population of HIV+ MSM aged > 26 years. Viruses. 2021;13(2). Available at: 108. Palefsky JM, Lensing SY, Belzer M, et al. High prevalence of anal high-grade squamous intraepithelial lesions, and prevention through human papillomavirus vaccination, in young men Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-30 who have sex with men living with human immunodeficiency virus. Clin Infect Dis. 2021;73(8):1388-1396. Available at: 109. Manhart LE, Koutsky LA. Do condoms prevent genital HPV infection, external genital warts, or cervical neoplasia? A meta-analysis. Sex Transm Dis. 2002;29(11):725-735. Available at: 110. Wiyeh AB, Mome RKB, Mahasha PW, Kongnyuy EJ, Wiysonge CS. Effectiveness of the female condom in preventing HIV and sexually transmitted infections: a systematic review and meta-analysis. BMC Public Health. 2020;20(1):319. Available at: 111. Winer RL, Hughes JP, Feng Q, et al. Condom use and the risk of genital human papillomavirus infection in young women. N Engl J Med. 2006;354(25):2645-2654. Available at: 112. Pierce Campbell CM, Lin HY, Fulp W, et al. Consistent condom use reduces the genital human papillomavirus burden among high-risk men: the HPV infection in men study. J Infect Dis. 2013;208(3):373-384. Available at: 113. Bleeker MC, Hogewoning CJ, Voorhorst FJ, et al. Condom use promotes regression of human papillomavirus-associated penile lesions in male sexual partners of women with cervical intraepithelial neoplasia. Int J Cancer. 2003;107(5):804-810. Available at: 114. Hogewoning CJ, Bleeker MC, van den Brule AJ, et al. Condom use promotes regression of cervical intraepithelial neoplasia and clearance of human papillomavirus: a randomized clinical trial. Int J Cancer. 2003;107(5):811-816. Available at: 115. Auvert B, Sobngwi-Tambekou J, Cutler E, et al. Effect of male circumcision on the prevalence of high-risk human papillomavirus in young men: results of a randomized controlled trial conducted in Orange Farm, South Africa. J Infect Dis. 2009;199(1):14-19. Available at: 116. Tobian AA, Serwadda D, Quinn TC, et al. Male circumcision for the prevention of HSV-2 and HPV infections and syphilis. N Engl J Med. 2009;360(13):1298-1309. Available at: 117. Serwadda D, Wawer MJ, Makumbi F, et al. Circumcision of HIV-infected men: effects on high-risk human papillomavirus infections in a randomized trial in Rakai, Uganda. J Infect Dis. 2010;201(10):1463-1469. Available at: 118. Gray RH, Serwadda D, Kong X, et al. Male circumcision decreases acquisition and increases clearance of high-risk human papillomavirus in HIV-negative men: a randomized trial in Rakai, Uganda. J Infect Dis. 2010;201(10):1455-1462. Available at: 119. Keller MJ, Burk RD, Xie X, et al. Risk of cervical precancer and cancer among HIV-infected women with normal cervical cytology and no evidence of oncogenic HPV infection. JAMA. 2012;308(4):362-369. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-31 120. Robbins HA, Strickler HD, Massad LS, et al. Cervical cancer screening intervals and management for women living with HIV: a risk benchmarking approach. AIDS. 2017;31(7):1035-1044. Available at: 121. Keller MJ, Burk RD, Massad LS, et al. Cervical precancer risk in HIV-infected women who test positive for oncogenic human papillomavirus despite a normal pap test. Clin Infect Dis. 2015;61(10):1573-1581. Available at: 122. D'Souza G, Burk RD, Palefsky JM, Massad LS, Strickler HD, Group WHW. Cervical human papillomavirus testing to triage borderline abnormal pap tests in HIV-coinfected women. AIDS. 2014;28(11):1696-1698. Available at: 123. Gilles C, Konopnicki D, Rozenberg S. The recent natural history of human papillomavirus cervical infection in women living with HIV: A scoping review of meta-analyses and systematic reviews and the construction of a hypothetical model. HIV Med. 2023. Available at: 124. Massad LS, Xie X, Minkoff H, et al. Longitudinal assessment of abnormal Papanicolaou test rates among women with HIV. AIDS. 2020;34(1):73-80. Available at: 125. Strickler HD, Keller MJ, Hessol NA, et al. Primary HPV and molecular cervical cancer screening in U.S. women living with human immunodeficiency virus. Clin Infect Dis. 2021;72(9):1529-1537. Available at: 126. McHaro R, Lennemann T, France J, et al. HPV type distribution in HIV positive and negative women with or without cervical dysplasia or cancer in East Africa. Front Oncol. 2021;11:763717. Available at: 127. FDA roundup: May 17, 2024 [press release]. U.S. Food & Drug Administration, May 17 2024. Available at: 128. Massad LS, Xie X, Minkoff HL, et al. Frequency of high-grade squamous cervical lesions among women over age 65 years living with HIV. Am J Obstet Gynecol. 2021;225(4):411.e411-411.e417. Available at: 129. Massad LS, Xie X, Greenblatt RM, et al. Effect of human immunodeficiency virus infection on the prevalence and incidence of vaginal intraepithelial neoplasia. Obstet Gynecol. 2012;119(3):582-589. Available at: 130. Smeltzer S, Yu X, Schmeler KM, Peters Y, Levison J. Abnormal vaginal pap test after hysterectomy in human immunodeficiency virus-infected women. Obstet Gynecol. 2016;127(Suppl 1):4S. Available at: 131. Clarke MA, Wentzensen N. Strategies for screening and early detection of anal cancers: A narrative and systematic review and meta-analysis of cytology, HPV testing, and other biomarkers. Cancer Cytopathol. 2018;126(7):447-460. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Q-32 132. Hoots BE, Palefsky JM, Pimenta JM, Smith JS. Human papillomavirus type distribution in anal cancer and anal intraepithelial lesions. Int J Cancer. 2009;124(10):2375-2383. Available at: 133. Chowdhury S, Darragh TM, Berry-Lawhorn JM, et al. HPV type distribution in benign, high-grade squamous intraepithelial lesions and squamous cell cancers of the anus by HIV status. Cancers (Basel). 2023;15(3). Available at: 134. Daling JR, Madeleine MM, Johnson LG, et al. Human papillomavirus, smoking, and sexual practices in the etiology of anal cancer. Cancer. 2004;101(2):270-280. Available at: 135. Keller K, Ramos-Cartagena JM, Guiot HM, et al. Association of smoking with anal high-risk HPV infection and histologically confirmed anal high-grade squamous intraepithelial lesions among a clinic-based population in Puerto Rico. Cancer Treat Res Commun. 2022;30:100503. Available at: 136. Balasundaram I, Payne KF, Al-Hadad I, Alibhai M, Thomas S, Bhandari R. Is there any benefit in surgery for potentially malignant disorders of the oral cavity? 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Sex Transm Dis. 2001;28(6):343-346. Available at: 145. Orlando G, Fasolo MM, Beretta R, Merli S, Cargnel A. Combined surgery and cidofovir is an effective treatment for genital warts in HIV-infected patients. AIDS. 2002;16(3):447-450. Available at: 146. Burgos J, Campany D, Garcia J, Landolfi S, Falco V, Curran A. Effectiveness of topical cidofovir for treatment of refractory anal high-grade squamous intraepithelial lesion. AIDS. 2023;37(9):1425-1429. Available at: 147. Bradbury M, Cabrera S, García-Jiménez A, et al. Vulvar intraepithelial neoplasia: clinical presentation, management and outcomes in women infected with HIV. AIDS. 2016;30(6):859-868. Available at: 148. Bradbury M, Xercavins N, Garcia-Jimenez A, et al. Vaginal intraepithelial neoplasia: clinical presentation, management, and outcomes in relation to HIV infection status. J Low Genit Tract Dis. 2019;23(1):7-12. Available at: 149. Fiascone S, Vitonis AF, Feldman S. 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Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-1 Immunizations for Preventable Diseases in Adults and Adolescents with HIV Updated: September 7, 2023 Reviewed: January 10, 2024 Overview The Advisory Committee on Immunization Practices (ACIP) recommends immunizing people with HIV similarly to the general population, with a few key exceptions. • The following live virus vaccines are contraindicated in people with HIV: o For any CD4 T lymphocyte (CD4) cell counts  Live attenuated influenza (LAIV) o For CD4 count <200 cells/mm3 or uncontrolled HIV  Measles  Mumps  Rubella  Varicella (VAR)  Live attenuated typhoid Ty21a  Yellow fever • The following vaccines have specific recommendations related to HIV status: o COVID-19 o Hepatitis A (HAV) o Hepatitis B (HBV) o Meningococcus serogroup A, C, W, Y (MenACWY) o Pneumococcal vaccine The National Institutes of Health (NIH)/Infectious Diseases Society of America/Centers for Disease Control and Prevention (CDC) recommendations described here may differ from ACIP recommendations when the committees interpret data differently or when one guideline has been updated more recently than the other. Specific Immunizations COVID-19 Vaccine Whether people with HIV are at greater risk of acquiring SARS-CoV-2 infection is currently unknown. Data are emerging on the clinical outcomes of COVID-19 in people with HIV. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-2 Worse outcomes for patients with HIV and COVID-19, including high COVID-19 mortality rates, have been reported in cohort studies from the United States, the United Kingdom, and South Africa.1-10 HIV was independently associated with an increased risk of severe and critical COVID-19 in a large trial from the World Health Organization’s Global Clinical Platform, which included data from 24 countries.1 In a multicenter cohort study of 286 patients with HIV and COVID-19 in the United States, a lower CD4 count (i.e., <200 cells/mm3) was associated with a higher risk for the composite endpoint of intensive care unit admission, invasive mechanical ventilation, or death. This increased risk was observed even in patients who had achieved virologic suppression of HIV.2 All adults and adolescents should get the COVID-19 vaccine regardless of their CD4 count or HIV viral load.11 Those with severe immunosuppression may have a diminished immune response to the vaccine. Routine serologic testing following vaccination is not recommended.11 For current COVID-19 vaccination recommendations, please visit CDC.gov or the NIH COVID-19 Treatment Guidelines. Note: People with advanced or untreated HIV are considered moderately or severely immunocompromised. Advanced HIV is defined as people with CD4 count <200 cells/mm3, a history of an AIDS-defining illness without immune reconstitution, or clinical manifestations of symptomatic HIV. Further information is available in the NIH COVID-19 Treatment Guidelines. Hepatitis A Vaccine See the “Hepatitis A virus (HAV)” section in the table below for detailed guidance on immunization against HAV. Summary of Recommendations For Vaccination • Administer a two-dose series (dosing interval depends on the vaccine used: at 0 and 6–12 months for Havrix [AII] or 0 and 6–18 months for Vaqta [AIII]) of single-antigen hepatitis A vaccine (HepA) or a three-dose series (0, 1, and 6 months) of the combined hepatitis A and hepatitis B vaccine (HepA-HepB, Twinrix) to any person without evidence of immunity to HAV (and for the combined vaccine, without evidence of immunity to HAV or HBV) (AII). • For travelers, some clinicians recommend a four-dose accelerated regimen (0, 7, 21–30 days, and 12 months) of HepA-HepB (BII). • Assess antibody response 1 to 2 months after completion of the series. If negative, revaccinate when CD4 count is >200 cells/mm3 (BIII). • People with HIV presenting with CD4 count <200 cells/mm3 with ongoing risk for HAV should be immunized and assessed for antibody response 1 to 2 months after completion of the series. For people with HIV without risk factors, waiting for a CD4 count >200 cells/mm3 is an option. Assess antibody response 1 to 2 months after completion of the series. If negative, revaccinate when the CD4 count is >200 cells/mm3 (BIII). For Pre-exposure Prophylaxis (Travel) • For people with HIV who are non-immune and are traveling within 2 weeks to countries with endemic HAV, consider administering immunoglobulin G (IgG) 0.1 mL/kg if duration of travel Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-3 is <1 month. If duration of travel is 1 to 2 months, then administer IgG 0.2 mL/kg. If duration of travel is ≥2 months, IgG 0.2 mL/kg should be repeated every 2 months. For Post-exposure Prophylaxis • For people with HIV who are non-immune, administer HAV vaccine and IgG 0.1 mL/kg simultaneously in different anatomical sites as soon as possible, ideally within 2 weeks of exposure. Hepatitis B Vaccine See the “Preventing Disease” section in Hepatitis B Virus (HBV) Infection for detailed guidance on immunization against HBV, as well as the evidence summary. Summary of Recommendations For Vaccination • HepB vaccine intramuscular (IM) (Engerix-B 40 mcg [two injections of 20 mcg each] or Recombivax HB 20 mcg [two injections of 10 mcg each]) at 0, 1, and 6 months (these doses are considered a “double-dose” three-dose series) (AII); or • Combined HepA and HepB vaccine (Twinrix) 1 mL IM as a three-dose series (at 0, 1, and 6 months) (AII); or • Vaccine conjugated to CpG (Heplisav-B) IM at 0 and 1 months for vaccine-naive patients (AII). • Anti-HBs should be obtained 1 to 2 months after completion of the vaccine series. For Vaccine Nonresponders • Revaccinate with a second double-dose, three-dose series of recombinant HBV vaccine (Engerix-B 40 mcg [two injections of 20 mcg each] or Recombivax HB 20 mcg [two injections of 10 mcg each]) (BIII); or • Revaccinate with two-dose series of HepBCpG (Heplisav-B) (BIII). • For people with low CD4 count at the time of first vaccination series, some experts might delay revaccination until after a CD4 count ≥200 is achieved and sustained with ART (CIII). For Post-exposure Prophylaxis • For exposed people who have been vaccinated previously with a complete HepB vaccine series and have documented antibody response, no additional vaccine is needed. • For exposed people who have received a complete HepB vaccine series without documentation of antibody response, administer a single dose of HepB vaccine. • For exposed people who have not received any HepB vaccine or have not received a complete HepB vaccine series, administer/complete HepB vaccine series and administer one dose of hepatitis B immune globulin (HBIG) at a separate anatomical site as soon as possible after Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-4 exposure (ideally within 24 hours, but up to 7 days after percutaneous exposure and up to 14 days after sexual exposure). • For exposed non-immune people with HIV on tenofovir or lamivudine, HBIG may not be necessary. Human Papillomavirus Vaccine See the “HPV Vaccine” section in Human Papillomavirus (HPV) Disease for detailed guidance on immunization against human papillomavirus (HPV), as well as the evidence summary. Summary of Recommendations • Routine HPV vaccination is recommended for people with HIV. Ideally, the series should be initiated at age 11 or 12 years but may be started as early as age 9 years. For all people with HIV aged 13 to 26 years who were not vaccinated previously, regardless of gender, administer three doses of the recombinant HPV nonavalent vaccine (Gardasil 9) at 0, 1 to 2, and 6 months (AIII). The two-dose series is not recommended in people with HIV. • For people with HIV aged 27 to 45 years not adequately vaccinated previously, the HPV vaccine is not routinely recommended; instead, shared clinical decision-making regarding HPV vaccination is recommended. • At present, vaccination with commercially available HPV vaccine is not recommended during pregnancy (CIII). • For people who have completed a vaccination series with the recombinant HPV bivalent or quadrivalent vaccine, some experts would consider additional vaccination with recombinant HPV nonavalent vaccine, but data are lacking for defining the efficacy and cost-effectiveness of this approach (CIII). Influenza Vaccine Summary of Recommendations • For all adults and adolescents with HIV, administer age-appropriate inactivated influenza vaccine or recombinant influenza vaccine annually (AI). • For pregnant individuals with HIV, administer inactivated influenza or recombinant vaccine at any time during pregnancy (AI). • LAIV administered via nasal spray is contraindicated in people with HIV (AIII). • High-dose and adjuvanted influenza vaccines are recommended for people with HIV aged 65 years or older over standard-dose unadjuvanted vaccines (AII).12 Evidence Summary Influenza is a common respiratory disease in adults and adolescents. Annual epidemics of seasonal influenza typically occur in the United States between October and April. Influenza A and B are most frequently implicated in human epidemics. Influenza A viruses are categorized into subtypes based on characterization of two surface antigens: hemagglutinin (HA) and neuraminidase (NA). Although Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-5 vaccine-induced immunity to the surface antigens HA and NA reduces the likelihood of infection,13,14 the frequent emergence of antigenic variants through antigenic drift15 (i.e., point mutations and recombination events within a subtype) is the virologic basis for seasonal epidemics and necessitates revaccination each season.16 Some studies of influenza have noted higher hospitalization rates17-20 and increased mortality20,21 among people with HIV; however, these findings have not been observed in all settings.22 Increased morbidity may be greatest for people with HIV not on antiretrovirals (ARV) or with advanced disease. People with HIV are at high risk of serious influenza-related complications. For more information, see the CDC’s Flu & People Living with HIV webpage. In general, people with HIV with minimal AIDS-related symptoms and normal or near-normal CD4 counts who receive inactivated influenza vaccine (IIV) develop adequate antibody responses.23-25 Among people with a low CD4 count or who have advanced HIV disease, IIV might not induce protective antibody titers.25-27 In one study, markers of inflammation in older people (≥60 years) with HIV were associated with lower post-vaccination influenza antibody titers.28 In people with HIV, a second dose of vaccine does not improve immune response,26,29 and intradermal influenza vaccine dosing did not improve the immune response compared with intramuscular dosing.30 Two clinical studies have evaluated influenza vaccine efficacy in people with HIV. In an investigation of an influenza A outbreak at a residential facility for people with HIV,17 vaccination was most effective at preventing influenza-like illness among people with a CD4 count >100 cells/mm3 and among those with HIV RNA <30,000 copies/mL. In a randomized placebo-controlled trial conducted in South Africa among 506 individuals with HIV, including 349 people on ARV treatment and 157 who were ARV treatment-naive, efficacy of trivalent IIV for prevention of culture- or RT-PCR–confirmed influenza illness was 75% (95% confidence interval, 9% to 96%).31 Several clinical studies also have evaluated the immunogenicity of influenza vaccine in people with HIV. In a randomized study32 comparing the immunogenicity of high-dose (60 mcg of antigen per strain) versus standard-dose (15 mcg of antigen per strain) trivalent IIV among 195 adults with HIV aged ≥18 years (10% of whom had a CD4 count <200 cells/mm3), seroprotection rates were higher in the high-dose group for influenza A (96% versus 87%; P = 0.029) and influenza B (91% vs. 80%; P = 0.030). However, in a comparative study of 41 children and young adults aged 3 to 21 years with cancer or HIV, high-dose trivalent IIV was no more immunogenic than the standard dose among the recipients with HIV.33 Optimally, influenza vaccination should occur before onset of influenza activity in the community because it takes about 2 weeks after vaccination for protective antibodies to develop.12 Health care providers should offer vaccination by the end of October if possible, and vaccination should continue to be offered as long as influenza viruses are circulating. Although booster doses can make the influenza vaccine more effective, that benefit is limited to specific groups, such as solid-organ transplant recipients.34 One study in people with HIV assessed the effectiveness of a two-dose regimen of IIV and found that the second dose of vaccine did not significantly increase the frequency or magnitude of antibody responses.29 Based on this study, influenza booster immunizations are not recommended for people with HIV. Many licensed injectable influenza vaccine options are available, with no recommendation favoring one product over another.12 Information on currently available influenza vaccines is obtainable Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-6 through the CDC recommendation, “Prevention and Control of Seasonal Influenza with Vaccines.” For adults aged ≥65 years, high-dose IIV,35 adjuvanted IIV,36 or recombinant influenza vaccine37 are preferentially recommended over standard-dose unadjuvanted vaccines based on data suggesting higher efficacy in preventing invasive pneumococcal disease in this age group.38 Influenza vaccines are quadrivalent (two A components and two B components) with formulations that change from season to season. Although a quadrivalent live attenuated influenza vaccine (LAIV4) is available, it is contraindicated for people with HIV because of the paucity of safety data and the availability of alternative vaccines.12 Although unintentional administration of LAIV4 to adults with HIV has been well tolerated,39 it is not recommended for people with HIV. IIVs can be administered to people receiving influenza antiviral drugs for treatment or chemoprophylaxis. Concurrent administration of influenza vaccine does not interfere with the immune response to other inactivated vaccines or to live vaccines. Measles, Mumps, and Rubella Vaccine Summary of Recommendations For Vaccination • Administer two doses of measles, mumps, and rubella vaccine (MMR) at least 1 month apart to people with a CD4 count ≥200 cells/mm3 and who have no evidence of immunity to measles, mumps, and rubella (evidence of immunity is defined as: patient was born before 1957, and/or had documentation of receipt of MMR, and/or has laboratory evidence of immunity or disease) (AIII). • The MMR vaccine is contraindicated during pregnancy. • People of childbearing potential who get the MMR vaccine should wait 4 weeks before getting pregnant. • For pregnant people without immunity to rubella, delay immunization until after pregnancy, and then administer two doses of the MMR vaccine at least 1 month apart if the CD4 count is ≥200 cells/mm3 (AIII). • If no serologic evidence of immunity exists after two doses of MMR vaccine, consider repeating the two-dose MMR series, especially if the person is vaccinated while not virologically suppressed (CIII). • Do not administer MMR vaccine to people with HIV with CD4 count <200 cells/mm3 (AIII). For Post-exposure Prophylaxis • For measles exposure of non-immune individuals with CD4 count >200 cells/mm3, administer the MMR vaccine within 72 hours of exposure or immunoglobulin (IG) within 6 days of exposure. Do not administer the MMR vaccine and IG simultaneously. • For measles exposure of non-immune individuals with CD4 count <200 cells/mm3 or those who are pregnant, administer IG within 6 days of exposure. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-7 Evidence Summary Measles is a highly contagious and potentially life-threatening disease. Measles is particularly virulent in the immunocompromised host, with a reported mortality rate as high as 40% in people with advanced HIV.40 Recently, measles outbreaks have occurred across the United States. From January 1 to October 3, 2019, 1,250 individual cases of measles were confirmed in 31 states, the most cases in 25 years. Current information regarding outbreaks can be found on the CDC website Measles Cases and Outbreaks. With a resurgence of measles both domestically41 and globally,42 people with HIV should be assessed for immunity. Acceptable evidence of immunity includes being born before 1957, documented evidence of two doses of the MMR vaccine, or presence of positive antibody titers. Individuals who do not fulfill any criteria for immunity and have CD4 count ≥200 cells/mm3 should receive two doses of MMR separated by at least 28 days. The combination measles, mumps, rubella, and varicella (MMRV) vaccine has not been studied in immunocompromised hosts and should not be administered to people with HIV. Several studies from the 1990s found that 90% to 95% of adults with HIV were immune to measles.43-45 In these studies, serostatus did not vary by CD4 count, suggesting that people with HIV retained protective immunity even in the context of advanced disease. However, in a more recent study, the measles seroprevalence rate was 70.3%.46 Similarly, people with HIV appear to retain immunity to mumps and rubella even after acquisition of HIV.46 The MMR vaccine is contraindicated for people with HIV with CD4 count <200 cells/mm3 because the MMR vaccine is a live attenuated formulation that has been linked to fatal cases of measles-associated pneumonitis following administration to people with HIV with a low CD4 count.47,48 For people with HIV with CD4 count ≥200 cells/mm3, the vaccine has been shown to be safe, although antibody response may be lower than for patients without HIV.46,49,50 For more detailed information regarding post-exposure prophylaxis, please see Measles (Rubeola). Meningococcal Vaccine Summary of Recommendations • Administer two doses of quadrivalent meningococcal conjugate vaccine at least 8 weeks apart to all people with HIV age ≥18 years (AII). • For people with HIV receiving primary vaccination, administer two doses at least 8 weeks apart. • For individuals with HIV who have been vaccinated previously and are age ≥7 years, repeat vaccination every 5 years throughout life (BIII). • At this time, serogroup B meningococcal vaccination (MenB) is not routinely indicated for adults and adolescents with HIV. Evidence Summary Meningococcal meningitis, caused by Neisseria meningitidis, is the most common cause of bacterial meningitis among children and young adults in the United States. Surveillance data collected from Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-8 1998 to 2007 identified 2,262 cases of meningococcal disease from a sample of 13% of the U.S. population from several states. All available formulations of meningococcal vaccine are inactivated. Two quadrivalent meningococcal conjugate (MenACWY) vaccines are currently licensed and available in the United States: (1) Meningococcal groups A, C, W, and Y oligosaccharide diphtheria CRM197 conjugate vaccine (MenACWY-CRM, Menveo); and (2) Meningococcal groups A, C, W, and Y polysaccharide tetanus toxoid conjugate vaccine (MenACWY-TT, MenQuadfi). Meningococcal groups ACWY polysaccharide diphtheria toxoid conjugate vaccine (MenACWY-D, Menactra) is no longer available. Quadrivalent meningococcal vaccination is recommended for all adolescents aged 11 to 18 years and people aged 2 to 55 years who are at increased risk for disease. A growing body of evidence supports an increased risk of meningococcal disease in people with HIV. Studies have shown a 5- to 24-fold increased risk of meningococcal disease in people with HIV compared with people without HIV; low CD4 count and high HIV viral load are associated with increased risk.51 The average annual incidence rate of invasive meningococcal disease was 0.39 cases per 100,000 people. People with HIV with a lower CD4 count are at higher risk of invasive disease.52 In addition, a cohort study found that uptake of the MenACWY vaccine among people with a new diagnosis of HIV infection was low, and time to receipt of first vaccination was long.53 The safety and immunogenicity of MenACWY-D vaccine have been evaluated only in people with HIV aged 11 to 24 years. Patients with CD4% ≥15% received either one or two doses (at 0 and 24 weeks) of vaccine, and those with CD4% <15% received two doses (at 0 and 24 weeks). Among people with HIV who received one dose of vaccine, 21% to 63% developed an antibody titer of ≥1:128 at 72 weeks after vaccination. Antibody responses at 72 weeks in individuals with CD4% <15% were less robust,54 with only 6% to 28% achieving titers ≥1:128. Local site reactions— such as pain and tenderness at injection site—were uncommon (3.1%), as were grade 3 or greater events (2.2%). No vaccine-related deaths or cases of meningitis were noted. No safety or immunogenicity studies are available for MenACWY-CRM in people with HIV, and clinical outcome data for both vaccines in people with HIV are lacking as well. Menveo and MenQuadfi are recommended for all adults with HIV, regardless of age. At this time, MenB is not routinely indicated for adults and adolescents with HIV. MenB vaccine may be administered to adolescents and young adults with HIV aged 16 to 23 years (preferred range, ages 16–18 years) for short-term protection against most strains of serogroup B meningococcal disease and for patients at increased risk (e.g., those living in dormitories or barracks) and during outbreaks. Those with functional or anatomic asplenia should also be vaccinated. Two MenB vaccines are available: MenB-4C (Bexsero; two-dose series given at 0 and 1 month) and MenB-FHbp (Trumenba; people with HIV should receive the three-dose series given at 0, 1–2, and 6 months, rather than the two-dose option). MenB vaccines are not interchangeable; the same product must be used for all doses in the series. Urban outbreaks of meningococcal meningitis have been reported among men who have sex with men in the United States, in men both with and without HIV. Several outbreaks were associated with clubs and bathhouses. Some public health jurisdictions now recommend meningococcal vaccine for all men who have sex with men, regardless of HIV status; however, ACIP has not adopted this recommendation for men who have sex with men without HIV.55 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-9 Mpox Vaccine See the “Preventing Disease” section in Mpox for detailed guidance on immunization against mpox, as well as the evidence summary. Summary of Recommendations For Vaccination • Mpox vaccination with live nonreplicating vaccinia vaccine, sold as JYNNEOS in the United States, should be offered to all people with HIV who have potential for mpox exposure or anticipate potential exposure to mpox per CDC interim clinical considerations (BII), as well as any other people with HIV who request vaccination (CII). • JYNNEOS is the preferred vaccine before mpox exposure and is safe to use in people with HIV; administer JYNNEOS in two doses (0.1 mL ID or 0.5 mL SQ) 4 weeks (28 days) apart (AII). • If the second dose is not administered during the recommended interval, it should be administered as soon as possible (CIII). There is no need to restart or add doses to the series if there is an extended interval between doses (CIII). • People who had received smallpox vaccination more than 10 years ago should still receive two doses of JYNNEOS (CIII). • Administration of live replicating vaccinia vaccines (i.e., ACAM2000) to pregnant, breastfeeding, or immunocompromised individuals, including people with HIV, is contraindicated (AII). For Post-exposure Prophylaxis • For unvaccinated people with HIV who experience a known or presumed exposure, administer a complete series of JYNNEOS as soon as possible, ideally within 4 to 14 days after exposure (BII). For current information on the state of the outbreak and vaccination recommendation criteria, please visit the CDC’s Mpox webpage. JYNNEOS has been demonstrated to be both safe for people with HIV and equally immunogenic compared with people without HIV.56-58 However, these studies were limited to people who were virologically suppressed and had a CD4 count >100 cells/mm3. Immunogenicity among people with HIV who are not virologically suppressed or have a lower CD4 count remains unknown. Recent studies indicate that JYNNEOS is effective against mpox.59-62 Matched case control study data indicate that vaccine effectiveness against symptomatic infection ranges from 36% to 75% after one dose to 66% to 89% after two doses.62-65 However, all studies to date have had insufficient data to assess effectiveness of JYNNEOS against mpox by HIV status or CD4 count, and immunologic correlates of protection have not yet been established. Pneumococcal Vaccine See the “Preventing Disease” section in Community-Acquired Pneumonia for detailed guidance on immunization against pneumococcal disease, as well as the evidence summary. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-10 Summary of Recommendations For all people with HIV without a history of pneumococcal vaccination or with unknown vaccine history: • Administer either 20-valent pneumococcal conjugate vaccine (PCV20) or PCV15 (AII). • If PCV15 is used, administer a dose of PPSV23 at least 8 weeks later (AII). No additional pneumococcal vaccine doses are recommended. For people with HIV who previously started or completed a pneumococcal vaccination series, there is no need to restart the series. • People with HIV who received PCV13 and were 65 years or older when they received a dose of PPSV23 do not require further doses of PPSV23. Shared clinical decision-making is recommended regarding administration of PCV20 for adults aged ≥65 years who completed their vaccine series with both PCV13 and PPSV23. If a decision to administer PCV20 is made, a dose of PCV20 is recommended at least 5 years after the last pneumococcal vaccine dose (CIII). • For people with HIV who received PCV13 and were younger than 65 when they received a dose of PPSV23, one dose of PCV20 administered at least 5 years after may be used to complete their pneumococcal vaccinations (CIII) or additional doses of PPSV23 are recommended as indicated below (BIII). o People with HIV who have received PCV13 and PPSV23 at age <65 should receive a second dose of PPSV23 at least 5 years after the first dose. If they are age 65 or older at the time of their second dose, they do not require additional doses of PPSV23. o If they were <65 at the time of the second dose, they should receive a third and final dose at or after age 65, at least 5 years after the second PPSV23 dose. • People with HIV who have only received PPSV23 may receive a PCV (either PCV20 or PCV15) ≥1 year after their last PPSV23 dose to complete their pneumococcal vaccination series (BIII). • People with HIV who previously received only the PCV13 should receive one dose of PCV20 at least 1 year later OR receive PPSV23 at least 8 weeks later and then complete the PPSV23 series as recommended above (BIII). Tetanus, Diphtheria, and Pertussis Vaccine Summary of Recommendations • Administer the combination tetanus toxoid, reduced diphtheria toxoid, and acellular pertussis vaccine (Tdap) once if the person with HIV had not been vaccinated at age 11 or older, and then tetanus and diphtheria toxoids vaccine (Td) or Tdap every 10 years thereafter (AII). • For pregnant individuals with HIV, administer one dose of Tdap during each pregnancy, preferably between 27 weeks and 36 weeks gestation (AIII). • For adolescents and adults with HIV who have not received the primary vaccination series for tetanus, diphtheria, or pertussis, administer one dose of Tdap followed by one dose of Td or Tdap at least 4 weeks after Tdap, and another dose of Td or Tdap 6 months to 12 months after the last Td or Tdap. Tdap can be substituted for any Td dose but is preferred as the first dose (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-11 Evidence Summary Antibody response to tetanus and diphtheria vaccination varies by CD4 count. For individuals with advanced HIV and a low CD4 count, immunologic response is attenuated for both tetanus and diphtheria when compared to HIV-uninfected controls.66,67 For people with CD4 count >300 cells/mm3, antibody response to tetanus vaccination is similar to the general population, whereas response to diphtheria remains diminished.66-68 Limited data exist on the efficacy of pertussis vaccination in this population. Two Tdap vaccines for individuals aged ≥10 years are available in the United States (Adacel and Boostrix). Both vaccines are inactivated and considered safe to administer at any CD4 count. People with HIV should receive vaccination for tetanus, diphtheria, and pertussis on the same schedule as individuals without HIV. All adults not previously vaccinated should receive a single dose of Tdap, followed by a Td or Tdap booster every 10 years. Varicella Vaccine See “Vaccination to Prevent Primary Infection (Varicella)” in the Varicella-Zoster Virus Disease section for detailed guidance on immunization against varicella, as well as the evidence summary. Summary of Recommendations • People with HIV with any of the following have presumed immunity to varicella: receipt of two doses of varicella vaccine (VAR or MMRV), diagnosis of varicella or herpes zoster (shingles) by a health care provider, or laboratory evidence of immunity or disease. • For people with HIV who are varicella non-immune with CD4 count ≥200 cells/mm3, administer two doses of VAR 3 months apart (BIII). • VAR is contraindicated for people with HIV with CD4 count <200 cells/mm3 (AIII). Herpes Zoster Vaccine See “Vaccination to Prevent Reactivation Disease (Herpes Zoster)” in the Varicella-Zoster Virus Disease section for detailed guidance on immunization against zoster, as well as the evidence summary. Summary of Recommendations • For people with HIV ≥18 years, administer two doses of recombinant zoster vaccine (RZV) at 0 and 2 to 6 months (AIII). • Consider delaying vaccination until the patient is virologically suppressed on ART (CIII) or until the CD4 count is >200 cells/mm3 to ensure a robust vaccine response (CIII). • People with HIV ≥18 years should receive RZV regardless of previous history of herpes zoster or previous receipt of zoster vaccine live (no longer available). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-12 Recommended Adult Immunization Schedule by Medical Condition and Other Indications Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations COVID-19 All people regardless of CD4 count or viral load (AIII) People with HIV should receive a complete COVID-19 vaccine series regardless of their CD4 count or HIV viral load (AIII). For current COVID-19 vaccination recommendations, please visit CDC.gov. People with advanced or untreated HIV are considered moderately or severely immunocompromised. Advanced HIV is defined as people with CD4 count <200 cells/mm3, a history of an AIDS-defining illness without immune reconstitution, or clinical manifestations of symptomatic HIV. No difference in recommendations Hepatitis A virus (HAV) HAV susceptible with HIV infection (AIII) Two-dose series of either single-antigen vaccine: • Havrix: 1.0 mL IM (0, 6–12 months) (AII); or • Vaqta: 1.0 mL IM (0, 6–18 months) (AIII) Alternative for individuals susceptible to both HAV and HBV: • Twinrix: 1.0 mL IM o Three-dose series (0, 1, 6 months) (AII) Assess antibody response (total or IgG anti-HAV) 1–2 months after completion of the series, and if negative, revaccinate, preferably after the CD4 count is ≥200 cells/mm3 (BIII). For travelers, some clinicians recommend: • Four-dose series (0, 7, 21–30 days, 12 months) of Twinrix (BII) No difference in recommendations Post-exposure prophylaxis Administer HAV vaccine and HepA IgG (0.1 mg/kg) simultaneously in different anatomical sites as soon as possible within 2 weeks of exposure to HAV in people who are non-immune. Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-13 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Hepatitis B virus (HBV) HBV susceptible and never vaccinated (i.e., anti-HBs <10 mIU/mL) Patients may receive any of the following single-antigen vaccines: • Engerix-B (40 mcg) or Recombivax (20 mcg): three-dose series (0, 1, 6 months) (AII); or • Heplisav: two-dose series (0, 1 month) 20 mcg in 0.5 mL IM (AII) Alternative for individuals susceptible to both HAV and HBV: • Twinrix: 1.0 mL IM: three-dose series (0, 1, 6 months) (AII) Anti-HBs should be obtained 1 to 2 months after completion of the vaccine series. Vaccinate individuals with isolated anti-HBc with one standard dose of HepB (BII) and check anti-HBs titers 1–2 months afterward. If anti-HBs ≥100 mIU/mL, no further vaccination is needed, but if the titer is <100 mIU/mL, then vaccinate with a complete series of HepB (double dose) followed by anti-HBs testing (BII). If titers are not available, then give a complete vaccine series followed by anti-HBs testing (BII). Safety and efficacy of Heplisav has not yet been studied in people with HIV. If a two-dose vaccine is preferred, Heplisav is an option. If a significant delay occurs between doses, there is no need to restart the series. For travelers, some clinicians recommend: • Four-dose series (0, 7, 21–30 days, 12 months) of Twinrix (BII) ACIP does not recommend the use of double-dose Engerix-B or Recombivax for people with HIV. Vaccine nonresponder (if anti-HBs <10 mIU/mL after three-dose series) Revaccinate with either: • Second three-dose series of Engerix-B (40 mcg) or Recombivax (20 mcg) (BIII); or • Two-dose series of Heplisav-B (BIII) Delay repeat vaccination until after the CD4 count is ≥200 cells/mm3 (CIII). Post-exposure prophylaxis For exposed people who have been previously vaccinated with complete series and have documented antibody response, no additional vaccine is needed. Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-14 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations For exposed people who have received complete series without documentation of antibody response, administer a single dose of HepB vaccine. For exposed people who have not received a vaccine or have not received the complete series, administer or complete the HepB vaccine series and administer a dose of HBIG at a separate anatomical site as soon as possible after exposure (ideally within 24 hours, but up to 7 days after percutaneous exposure and up to 14 days after sexual exposure). Some experts consider that a four-dose vaccine series of recombinant hepatitis B vaccine (Engerix-B 40 mcg or Recombivax 20 mcg at 0, 1, 2, and 6 months) may produce a better immunologic response, but this approach has not been demonstrated to be superior to a double-dose, three-dose series. Human papillomavirus (HPV) Adults and adolescents through age 26 Recombinant 9-valent human papillomavirus vaccine (Gardasil 9): 0.5 mL IM three-dose series (0, 1–2, and 6 months) (AIII) If a significant delay occurs between doses, there is no need to restart the series. Routine vaccination is not recommended for people ages 27–45 years (AI). Some people with HIV may benefit from vaccination in this age group, and shared clinical decision-making between the provider and patient is recommended in these situations. No difference in recommendations Adults and adolescents who previously received bivalent or quadrivalent vaccine For patients who have completed a vaccination series with the recombinant bivalent or quadrivalent vaccine, no recommendations exist for additional vaccinations; some experts would give an additional full series of recombinant 9­valent vaccine, but no data currently define who might benefit or how cost effective this approach might be (CIII). Vaccination is not recommended during pregnancy (CIII). Delay until after pregnancy. Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-15 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Influenza All One dose of age appropriate IIV or RIV annually (AI) LAIV is contraindicated (AIII). Information on currently available influenza vaccines is available through the CDC recommendation Prevention and Control of Seasonal Influenza with Vaccines. Influenza vaccines are quadrivalent, with formulations that change from season to season. Adults age ≥65 years are recommended to receive high-dose IIV (Fluzone High-Dose) or adjuvanted IIV (FLUAD) over standard-dose unadjuvanted vaccine (AII). People age ≥18 years also may use RIV (Flublok Quadrivalent). For people with egg allergy, use IIV or RIV appropriate for age (if the allergy is more severe than hives, give the vaccine in a medical setting appropriate to manage severe allergic reaction). For pregnant individuals with HIV, administer inactivated influenza or recombinant vaccine at any time during pregnancy (AI). No difference in recommendations Measles, mumps, and rubella (MMR) CD4 count ≥200 cells/mm3 and no evidence of immunity to measles, mumps, or rubella Two-dose series of MMR vaccine at least 1 month apart (AIII) MMR is contraindicated if CD4 count <200 cells/mm3. MMR vaccine is contraindicated during pregnancy. Evidence of immunity to MMR: • Birth date before 1957, or • Documentation of receipt of MMR, or • Laboratory evidence of immunity or disease for each pathogen No difference in recommendations. Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-16 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations For pregnant people without immunity to rubella, after pregnancy, administer two doses of MMR vaccine at least 1 month apart if CD4 count ≥200 cells/mm3 (AIII). Post-exposure prophylaxis For measles, non-immune individuals with CD4 count >200 cells mm3, administer MMR vaccine within 72 hours of exposure or IG within 6 days of exposure. Do not administer MMR vaccine and IG simultaneously. For measles, non-immune individuals with CD4 count <200 cells mm3 or those who are pregnant, administer IG. Meningococcus serogroup A, C, W, Y (MenACWY) Not received any polyvalent meningococcal vaccine Menveo or MenQuadfi: • Two-dose series given at least 8 weeks apart (AII) • Booster dose of same MenACWY vaccine every 5 years (BIII) MenACWY vaccine is routinely recommended. No difference in recommendations Meningococcus serogroup B MenB is not routinely indicated for individuals with HIV, except for those at increased risk for serogroup B meningococcal disease (asplenia, complement deficiency, eculizumab use, occupational exposure). • Two-dose series of Bexsero or three-dose series of Trumenba Even if they are not at increased risk for serogroup B meningococcal disease, MenB may be given to adolescents and young adults ages 16–23 years (preferred age range, 16–18 years). Two MenB vaccines are available and not interchangeable, MenB-4C (Bexsero) and MenB-FHbp (Trumenba). No difference in recommendations Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-17 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Mpox All people who have potential for mpox exposure or anticipate potential exposure to mpox per CDC interim clinical considerations (BII), including those who request vaccination (CII) Administer two-dose series of JYNNEOS (0.5 mL SQ or 0.1 mL ID) given 28 days apart (AII). Administration of live replicating vaccinia vaccines (i.e., ACAM2000) to people with HIV is contraindicated (AII). SQ administration is the FDA-approved standard regimen for adults (≥18 years). SQ administration is authorized for people aged <18 years under an Emergency Use Authorization. ID administration is authorized as an alternative regimen for people age ≥18 years under an Emergency Use Authorization. The alternative regimen, when feasible, is preferred when the vaccine supply is scarce. People with a history of developing keloid scars should receive SQ administration. JYNNEOS can be co-administered with most other vaccines. Adolescent and young adult men might consider a 4-week interval between receiving JYNNEOS vaccine and a COVID-19 vaccine because of potential risk for myocarditis and pericarditis. JYNNEOS can be administered to people who are pregnant, breastfeeding, or trying to become pregnant and who require vaccination (BIII). No difference in recommendations Post-exposure prophylaxis For unvaccinated people with HIV who experience a known or presumed exposure, administer complete series (two doses 0, 4 weeks [28 days]) of JYNNEOS, with the first dose given as soon as possible within 4 to 14 days after exposure to mpox (BII). Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-18 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Pneumococcal No prior pneumococcal vaccine or vaccination history unknown Administer either of the following: • PCV20 (Prevnar20): 0.5 mL IM x 1 (AII); or • PCV15 (Vaxneuvance): 0.5 mL IM × 1 followed at least 8 weeks later by PPSV23 (Pneumovax): 0.5 mL IM × 1 (AII). While people with HIV with CD4 count <200 cells/mm3 can be offered PPSV23 at least 8 weeks after receiving PCV15 (CIII) (such as if there are concerns with retention in care), PPSV23 should preferably be deferred until after an individual’s CD4 count increases to >200 cells/mm3 while on ART (BIII). Previously received PCV13 and PPSV23 If <65 years when received dose of PPSV23: • Administer PCV20 0.5 mL IM x 1 at least 5 years after the last pneumococcal vaccine (CIII); or • Revaccinate the following with PPSV23 0.5 mL IM x 1 (BIII): o Adults aged 19–64 years if ≥5 years since the first PPSV23 dose o Adults aged ≥65 years if:  Previous PPSV23 administered at age <65, and  ≥5 years since the previous PPSV23 dose, and  At least 8 weeks after receipt of PCV13 Patients should receive a maximum of three doses of PPSV23. There is no need to give additional doses of PPSV23 every 5 years. Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-19 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations If ≥65 years when received dose of PPSV23: • No further doses of PPSV23 are required. • Shared decision-making is recommended regarding administration of PCV20 for adults aged ≥65 years who have completed both PCV13 and PPSV23. If PCV20 given, administer at least 5 years after last pneumococcal vaccine dose (CIII). Previously received only PCV13 Administer PCV20 0.5 mL IM x 1 at least 1 year after PCV13 (BIII); or Administer initial dose of PPSV23 0.5 mL IM × 1 at least 8 weeks after PCV13 (AII). Revaccinate the following with PPSV23 0.5 mL IM x 1 (BIII): • Adults aged 19–64 years if ≥5 years since the first PPSV23 dose • Adults aged ≥65 years if ≥5 years since the previous PPSV23 dose In patients who received PCV13 when their CD4 count was <200 cells/mm3 and PPSV23 will be given, some experts may choose to defer PPSV23 until CD4 count is >200 cells/mm3 to optimize vaccine efficacy (CIII). Previously received only PPSV23 Administer either of the following at least 1 year after last PPSV23 dose: • PCV20: 0.5 mL IM x 1 (BIII); or • PCV15: 0.5 mL IM × 1 (BIII) When PCV15 or PCV20 is used in those with history of PPSV23 receipt, it need not be followed by another dose of PPSV23. Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-20 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Polio Not routinely recommended (AIII) No difference in recommendations Those at higher risk for exposure to poliovirus— such as those traveling to countries where polio is epidemic or endemic—can be vaccinated with IPV (CIII). Three doses IPV IM at 0, 1–2 months, and third dose given 6–12 months after second dose (CIII) Previously vaccinated with one to two doses of vaccine Give remaining doses of vaccine at recommended intervals (CIII). Tetanus, diphtheria, and pertussis Did not receive Tdap at age 11 years or older One dose Tdap (Adacel or Boostrix), then Td or Tdap every 10 years (AII) If indicated, give Tdap regardless of when the last dose of Td was given. No difference in recommendations Pregnancy Give Tdap preferably in early part of gestational weeks 27–36 (AIII). One dose of Tdap is indicated for each pregnancy. Give Td or Tdap booster every 10 years after Tdap. Varicella (chickenpox) CD4 count ≥200 cells/mm3 with no evidence of immunity to varicella Two-dose series of VAR 3 months apart (BIII) VAR is contraindicated if CD4 count <200 cells/mm3 (AIII). Evidence of immunity to varicella: • Documented receipt of two doses of VAR or MMRV; or • Diagnosis of varicella or zoster by a health care provider; or • Laboratory evidence of immunity or disease If vaccination results in disease because of vaccine virus, treatment with acyclovir is recommended (AIII). No difference in recommendations Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-21 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Zoster Age ≥18 years, regardless of past episode of herpes zoster or receipt of attenuated ZVL (Zostavax) and regardless of CD4 count Give two-dose series of RZV (Shingrix) IM 2–6 months apart (AIII). Consider delaying vaccination until patient is virologically suppressed on ART (CIII) or wait for immune reconstitution in those who had a CD4 count <200 cells/mm3 (CIII) to maximize immunologic response to the vaccine. Do not give RZV (Shingrix) during an acute episode of herpes zoster (AIII). ACIP recommends RZV for adults ≥19 years who are or will be at risk for herpes zoster. (This difference in age selected by ACIP was made to align with the age range in the adult immunization schedule.) Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-22 Vaccine Preventable Infection Indication Recommendations Additional Comments ACIP Recommendations Immunizations for Travel Cholera Not routinely recommended for most travelers (CIII). Age 18–64 years old with CD4 count >200 cells/mm3 traveling to an area where cholera is epidemic or endemic within the past year Lyophilized CVD 103-HgR (Vaxchora) single oral dose at least 10 days prior to potential exposure (CIII) Safety and efficacy have not been established in individuals with HIV. No adverse effects reported with older formulation of vaccine in individuals with HIV infection without an AIDS diagnosis. No current recommendations for individuals with HIV infection Typhoid At risk of Salmonella serotype typhi infection (travel, intimate exposure to a chronic carrier, occupational exposure) Revaccination only if continued or renewed exposure to Salmonella serotype typhi is expected. One dose Vi capsular polysaccharide vaccine (Typhim Vi) via intramuscular injection at least 1 week before exposure (AIII) Revaccinate every 2 years if risk remains (BIII). The live attenuated oral typhoid vaccine (Vivotif) is contraindicated in people with HIV (AIII). Provide education on other preventive measures against foodborne illness in addition to typhoid vaccination (AIII). Safety of typhoid vaccination in pregnancy is unknown. Consider avoiding during pregnancy (AIII). ACIP has no position on the use of typhoid vaccine in people with HIV except not to give immunocompromised people the live attenuated vaccine. Yellow fever (YF) Age ≤59 years and at risk for YF virus acquisition (travel to or live in areas at risk based on season, location, activities, and duration) If indicated, provide vaccination at least 10 days prior to expected exposure. Age <59 years and asymptomatic with CD4 count >500 cells/mm3: One dose of YF vaccine, revaccinate in >10 years if risk remains (BIII). Provide vaccination as an adjunct to other protective measures against mosquito bites. Pregnancy and age ≥60 years may increase risk of complications from YF vaccine administration. No difference in recommendations Recommended Adult Immunization Schedule by Medical Condition and Other Indications Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-23 Any age and asymptomatic with CD4 count 200–499 cells/mm3: YF vaccine may be considered depending on risk (BIII). YF vaccine is contraindicated for people with CD4 count <200 cells/mm3. This recommendation is based on a theoretic increased risk for encephalitis in this population (AII). If international travel requirements rather than an increased risk for acquiring YF infection are the only reason to vaccinate people with HIV, excuse the person from vaccination and issue a medical waiver to fulfill health regulations. Closely monitor people with HIV who have received YF vaccine for evidence of adverse events. Key: ACIP = Advisory Committee on Immunization Practices; anti-HBc = hepatitis B core antibody; anti-HBs = hepatitis B surface antibody; ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CDC = Centers for Disease Control and Prevention; FDA = U.S. Food and Drug Administration; HAV = hepatitis A virus; HBIG = hepatitis B immune globulin; HBV = hepatitis B virus; HepA = hepatitis A vaccine; HepB = hepatitis B vaccine; HPV = human papillomavirus; IG = immunoglobulin; IgG = immunoglobulin G; IIV = inactivated influenza vaccine; IM = intramuscular; IPV = inactivated polio vaccine; LAIV = live attenuated influenza vaccine; MenACWY = meningococcus serogroup A, C, W, Y; MenB = serogroup B meningococcal vaccination; MMR = measles, mumps, and rubella; MMRV = measles, mumps, rubella, and varicella; PCV13 = 13-valent pneumococcal conjugate vaccine; PCV15 = 15-valent pneumococcal conjugate vaccine; PPSV23 = 23-valent pneumococcal polysaccharide vaccine; PVC13 = 13-valent pneumococcal conjugate vaccine; RIV = recombinant influenza vaccine; RZV = recombinant zoster vaccine; SQ = subcutaneous; Td = tetanus and diphtheria toxoids vaccine; Tdap = combination tetanus toxoid, reduced diphtheria toxoid, and acellular pertussis vaccine; VAR = varicella vaccine; YF = yellow fever; ZVL = zoster vaccine live Note: Recommendations may differ from the ACIP. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-24 Recommended Immunization Schedule for Adults and Adolescents with HIV Vaccine All People with HIV Where Varies by Age Where Varies by CD4 Cell Count (cells/mm3) <200 ≥200 Hepatitis A Two to three doses (varies by formulation) Hepatitis B Two to four doses (varies by formulation and indication) Human papillomavirus (HPV) Three doses for ages 18–26 Influenza One dose annually Measles, mumps, rubella (MMR) Contraindicated Two doses if born after 1956 with no history of vaccination or positive antibody titer Meningococcal A,C,W,Y conjugate (MenACWY) Two doses, booster every 5 years Meningococcal B (MenB) Two to three doses (varies by formulation) Mpox (MVA-BN, attenuated) Two doses Mpox (ACAM2000, live replicating) Contraindicated Pneumococcal conjugate (PCV15 or PCV20) One dose Pneumococcal polysaccharide (PPSV23) One dose (if conjugate vaccine was PCV-15) COVID-19 For current COVID-19 vaccination recommendations, please visit CDC.gov. Recommendations differ with advanced or untreated HIV infection Tetanus, diphtheria, pertussis (Tdap/Td) Tdap once, then Td or Tdap booster every 10 years Varicella (VAR) Contraindicated Two doses Zoster recombinant (RZV) Two doses for ages 18 and older Recommended for all adults and adolescents with HIV who meet the age requirement or lack documentation of vaccination or evidence of past infection. Recommended for adults and adolescents with HIV with another risk factor (medical, occupational, or other indication) or in select circumstances. Contraindicated Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV R-25 References 1. Bertagnolio S TS, Silva R, et al. Clinical characteristics and prognostic factors in people living with HIV hospitalized with COVID-19: findings from the WHO Global Clinical Platform. Presented at: International AIDS Society; 2021. Available at: 2. Dandachi D, Geiger G, Montgomery MW, et al. 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Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-1 Leishmaniasis Updated: July 29, 2024 Reviewed: July 29, 2024 Epidemiology Leishmaniasis is caused by protozoa that survive and replicate within macrophages and other mononuclear cells. There are over 20 species within the Leishmania (L.) genus that cause human disease, the main forms of which are visceral, cutaneous, and mucosal disease.1 Leishmaniasis occurs in 99 countries or territories in the tropics and subtropics (including the southern United States, most of Central and South America, and southern Europe), with an estimated incidence of 1 million new cases annually. In 2022, 12,842 incident cases of visceral leishmaniasis and 205,986 new cases of cutaneous leishmaniasis were reported to the World Health Organization (WHO).2 Prevalence of the different Leishmania species varies geographically. The main Leishmania species that cause visceral leishmaniasis are L. donovani, L. infantum (syn. L. chagasi), and the more recently recognized L. (Mundinia) martiniquensis. The visceral leishmaniasis-causing species in the Americas are L. infantum and L. martiniquensis. Cutaneous leishmaniasis acquired outside the Americas is commonly caused by L. tropica, L. major, and L. aethiopica. In the Americas, the prevalent species that cause cutaneous leishmaniasis are of the L. (Viannia) subgenera (braziliensis, guyanensis, panamensis, peruviana), L. mexicana and L. amazonensis.3 In the United States, there have been fewer than 100 recognized autochthonous cases in the past 100 years, mainly L. mexicana cutaneous leishmaniasis acquired in Texas.3 As of 2021, HIV-leishmaniasis coinfection has been reported in 45 countries,4 predominantly as HIV-visceral leishmaniasis coinfection.4,5 The first cases of HIV-leishmaniasis coinfection were described in Spain in the late 1980s.6 After the introduction of combination antiretroviral therapy (ART), the incidence decreased substantially in developed countries,7,8 but HIV-leishmaniasis coinfection poses a growing problem in parts of Asia, Africa, and Latin America.9-12 New species Leishmania (Mundinia) martiniquensis, associated with visceral and disseminated cutaneous leishmaniasis, and L. (Mundinia) orientalis, which causes cutaneous leishmaniasis, have been reported from Thailand in people with HIV.11-13 In endemic areas, leishmaniasis is usually spread by infected sand flies of the genera Phlebotomus and Lutzomyia. However, in southern Europe, HIV and L. infantum visceral leishmaniasis coinfections have been reported in association with injection drug use, suggesting that Leishmania (which can infrequently be transmitted via blood14,15) also may be acquired by needle sharing; contaminated syringes have been shown to be an epidemiologically significant component of the transmission cycle of Leishmania amastigotes.16,17 Clinical Manifestations The term leishmaniasis encompasses multiple syndromes—most notably, cutaneous leishmaniasis and visceral leishmaniasis, but also related syndromes such as mucosal (or mucocutaneous) leishmaniasis, disseminated cutaneous leishmaniasis, diffuse cutaneous leishmaniasis (an anergic form), and post-kala-azar dermal leishmaniasis.18 The most reported clinical presentation of leishmaniasis in people with HIV is a systemic visceral disease syndrome. However, the predominant Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-2 parasite species varies geographically. In Europe, visceral disease has been reported in 95% of people with HIV-leishmaniasis coinfection (87% typical visceral, 8% atypical visceral).6 In Brazil, mucosal, visceral, and cutaneous forms have accounted for 43%, 37%, and 20% of reported leishmaniasis cases in people with HIV, respectively.19 Most Leishmania infections in immunocompetent hosts are asymptomatic. In many disease-endemic areas, 30% or more of the population has evidence of latent infection, as demonstrated by a positive leishmanin skin test.20-22 After primary infection, Leishmania remain viable in healthy individuals for long periods, creating a population at risk of reactivation if CD4 T lymphocyte (CD4) cell depletion occurs. In people with HIV without severe CD4 cell depletion, disease manifestations are similar to those in immunocompetent individuals. In those with advanced immunosuppression (i.e., CD4 count <200 cells/mm3), manifestations of leishmaniasis can be both atypical and more severe. Dermotrophic species can disseminate both in skin and through the reticuloendothelial system to visceralize.23,24 Relapse after treatment—especially of visceral leishmaniasis—is common.25,26 Atypical disseminated leishmaniasis in people with HIV is considered a WHO clinical stage 4 HIV criterion.27 Visceral Leishmaniasis In people with HIV and visceral disease, the most common clinical and laboratory findings are fever (65% to 100%), systemic malaise (70% to 90%), splenomegaly (usually moderate) (54% to 90%), hepatomegaly without splenomegaly (34% to 85%), hepatosplenomegaly (68% to 73%), lymphadenopathy (12% to 57%), and pancytopenia (50% to 80%).6,26 Anemia is usually marked, with <10 g hemoglobin/dL (50% to 100%); leukopenia is moderate, with <2,400 leukocytes/µL (56% to 95%); and thrombocytopenia is usually present (52% to 93%). Splenomegaly is less pronounced in people with HIV than in immunocompetent patients with visceral leishmaniasis.26 In people with HIV with more profound CD4 cell depletion, atypical manifestations have been described, including mucosal involvement, such as masses, ulcers, mucositis of the upper and lower gastrointestinal tract, serositis in pleural and peritoneal cavities, and lung and skin lesions.6,7,26,28,29 Esophageal involvement can lead to dysphagia and odynophagia and must be distinguished from other causes of esophagitis in people with HIV, such as candidiasis.6 Amastigote infiltration of the duodenum often presents as chronic diarrhea.7 Nonulcerative cutaneous lesions that mimic Kaposi sarcoma (KS), nodular diffuse leishmaniasis, and post-kala-azar dermal leishmaniasis have been described in people with HIV and visceral leishmaniasis.30-32 However, the presence of Leishmania amastigotes in skin can occur in the absence of lesions or in combination with other pathology, such as KS, and does not prove that the parasite is the cause of the lesions.33,34 Cutaneous Leishmaniasis Cutaneous leishmaniasis in people with HIV varies depending on immune function. In people with HIV with well-controlled HIV and high CD4 counts, the presentation is not different than those without HIV except that there may be a higher rate of relapse.35,36 In those with lower CD4 counts (e.g., <200 cells/mm3), dermal leishmaniasis may disseminate in the skin, mucosa, and viscera.37 Most have multiple skin lesions, often atypical (unusual morphology) for localized cutaneous leishmaniasis, and genital involvement seems more frequent.37-39 Among people with HIV in Brazil, 68% had concomitant mucosal leishmaniasis, a rate much higher than those without HIV.18 Additionally, as mentioned above, people with HIV and visceral leishmaniasis may present with cutaneous lesions.40,41 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-3 Mucosal Leishmaniasis Mucosal leishmaniasis among people with HIV is most commonly associated with infections acquired in the New World, especially L. braziliensis and other species in the L. (Viannia) subgenera including L. guyanensis and L. panamensis.19 Additionally, mucosal disease also has been reported with species that have geographic distribution beyond the Americas, including L. infantum, L. aethiopica, and L. tropica.42 Presentation in people with HIV is similar to those without HIV and includes nasal septum destruction, obstructive masses in the nose, uvula erosion, ulcerated infiltrative lesions of the palate, and laryngeal involvement.19,43-49 Mucosal leishmaniasis may occur concomitantly with cutaneous leishmaniasis or years after resolution of localized cutaneous leishmaniasis.50 Diagnosis Demonstration of Leishmania parasites by histopathology, cultures, smears, and molecular methods in tissue specimens (such as scrapings, aspirates, and biopsies) is the standard for diagnosing cutaneous leishmaniasis in people with HIV. Coinfection of HIV and visceral leishmaniasis also can be diagnosed by demonstration of leishmanial parasites in the following: blood smears (approximately 50% sensitivity in expert hands); buffy-coat smear preparations; cultures from the peripheral blood; and smears, histopathology, and cultures from bone marrow (preferred) or splenic aspirates (significant procedural risk). Polymerase chain reaction (PCR) amplification can also be useful for detecting Leishmania nucleic acid in the blood or tissue of patients with HIV-leishmaniasis coinfection (>95% sensitivity).51 Generally, PCR and Leishmania culture require specialty reference laboratory support. Assistance for conducting diagnostic tests for Leishmania is available by contacting the Centers for Disease Control and Prevention (CDC) at parasiteslab@cdc.gov. Serologic tests that detect Leishmania antibodies have high sensitivity and can be used to support diagnosis of visceral leishmaniasis in immunocompetent patients.51 They should be used only in those with a compatible clinical picture and an exposure history suggestive of visceral leishmaniasis. Serology has a lower sensitivity in people with HIV such that parasitological diagnosis should be sought when clinical suspicion has been raised.6,52 The use of recombinant antigen in enzyme-linked immunosorbent assays (or ELISAs) may increase sensitivity for detection of Leishmania antibodies, but a proportion of people with HIV-leishmaniasis coinfection remain seronegative.53 Immunoblotting with L. infantum soluble antigen has been successful in detecting specific antileishmanial antibodies in up to 70% of patients.52 Preventing Exposure Prevention of exposure to leishmanial infection relies on reservoir host control in urban and periurban areas with zoonotic transmission (such as controlling visceral leishmaniasis in dogs) and vector control activities (such as indoor residual spraying, using insecticide-treated bed nets, and intervening in sand fly breeding sites).54,55 Optimal control measures rely on local transmission characteristics, which vary by vector. For travelers to leishmaniasis-endemic areas, the best way to prevent infection is to protect themselves from sand fly bites. Personal protective measures include minimizing nocturnal outdoor activities, wearing protective clothing, and applying insect repellent to exposed skin. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-4 People who inject drugs should undertake measures (such as the use of clean needles and injection equipment from syringe service programs) to decrease the risk of transmission of Leishmania parasites and other infectious agents. Preventing Disease Primary chemoprophylaxis to prevent leishmaniasis is not recommended. No screening or preemptive therapy is appropriate for people with HIV who may have been exposed to leishmanial infection. No vaccine against leishmaniasis is available. Treating Disease Recommendations for Treating Visceral and Cutaneous Leishmaniasis Treating Visceral Leishmaniasis • ART should be initiated as soon as possible (AIII). Initiation or optimization of ART may prevent reactivation of visceral leishmaniasis. Leishmania infantum/chagasi Preferred Therapy • Liposomal amphotericin B, achieving a total dose of 20–60 mg/kg (AII) via either o 3–5 mg/kg IV daily (AII), or o Interrupted schedule, such as 4 mg/kg IV on Days 1–5, 10, 17, 24, 31, and 38 (AII) Alternative Therapy • Amphotericin B deoxycholate 0.5–1.0 mg/kg IV daily for total dose of 1.5–2.0 grams (BII), or • Pentavalent antimony (meglumine antimoniate) 20 mg/kg IV or IM daily for 28 days (BII), currently available in the United States only by investigator-initiated investigational new drug application Leishmania donovani Preferred Therapy (Combination) • Liposomal amphotericin B 30 mg/kg IV total dose (5 mg/kg on Days 1, 3, 5, 7, 9, and 11), plus miltefosine 50 mg PO twice daily for 28 days (East Africa) or for 14 days (Southeast Asia) (BI) Alternative Therapy • Liposomal amphotericin B, achieving a total dose of 20–60 mg/kg (AII) via either o 3–5 mg/kg IV daily (AII), or o Interrupted schedule, such as 4 mg/kg IV on Days 1–5, 10, 17, 24, 31, and 38 (AII) • See Alternative Therapy for L. infantum, or • For Indian L. donovani o Miltefosine (BII) (available in the United States via www.profounda.com), aiming for 2.5–3 mg/kg daily (maximum of 150 mg daily)  For patients who weigh 30–44 kg: 50 mg PO two times daily for 28 days  For patients who weigh ≥45 kg: 50 mg PO three times daily for 28 days Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-5 Chronic Maintenance Therapy for Visceral Leishmaniasis Indication • For patients with visceral leishmaniasis and CD4 count <200 cells/mm3 (AII) Preferred Therapy • Liposomal amphotericin B 4 mg/kg IV every 2–4 weeks (AII) Alternative Therapy • Amphotericin B lipid complex 3 mg/kg every 21 days (BII), or • Pentavalent antimony (meglumine antimoniate) 20 mg/kg IV or IM every 4 weeks (BII), or • Pentamidine isethionate 4 mg/kg (maximum of 300 mg) IV every 2–4 weeks (BII) Discontinuation of Chronic Maintenance Therapy • Consider stopping secondary prophylaxis when the CD4 count is >350 cells/mm3, HIV viral load has been undetectable for 6 months, and there are no symptoms of visceral leishmaniasis relapse (CIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-6 Treating Cutaneous Leishmaniasis • ART should be initiated as soon as possible (AIII). Initiation or optimization of ART may prevent reactivation of cutaneous leishmaniasis. Preferred Therapy • Liposomal amphotericin B 4 mg/kg IV daily for 10 days or interrupted schedule (e.g., 4 mg/kg on days 1–5, 10, 17, 24, 31, 38) until a total dose of 20–60 mg/kg is achieved (BIII), or • Miltefosine 2.5 mg/kg/day PO in 2 or 3 divided doses for 28 days (Viannia subgenus); not well tolerated if more than 150 mg daily (BIII), or • Pentavalent antimony (meglumine antimoniate) 20 mg/kg IV or IM daily for 28 days (BIII) Alternative Therapy • Other options for individual cases may include cryotherapy, topical paromomycin, intralesional pentavalent antimony (meglumine antimoniate) or pentamidine, fluconazole for L. major and L. mexicana, intravenous pentamidine or local heat therapy. Chronic Maintenance Therapy for Cutaneous Leishmaniasis • Indicated for immunocompromised patients with multiple relapses (CIII) • See drugs and doses for Chronic Maintenance Therapy for Visceral Leishmaniasis. Pregnancy Considerations • Liposomal amphotericin B is the first choice for therapy of visceral leishmaniasis in pregnancy (AIII). Amphotericin B deoxycholate can be given as alternative therapy (AIII). • In many uncomplicated cutaneous leishmaniasis cases, treatment can be delayed until postpartum (CIII). • In cases of severe cutaneous leishmaniasis with multiple and/or very large lesions, shared decision making with the patient is recommended to discuss the potential risks and benefits of deferring treatment until after pregnancy, treating with systemic therapy, or using local therapy as a temporizing approach (followed by systemic therapy to be given after pregnancy if the lesions do not resolve) (CIII). • Liposomal amphotericin B IV is the first choice for therapy of mucosal or severe cutaneous leishmaniasis in pregnancy (CIII). Patients treated with amphotericin B formulations should be monitored for dose-dependent nephrotoxicity, electrolyte disturbances, and infusion-related adverse reactions (AII). Infusion-related adverse events may be ameliorated by pre-treatment with acetaminophen or diphenhydramine (CIII). An infusion of 1 L of saline 1 hour prior to drug infusion is recommended to help reduce the risk of renal dysfunction during treatment (BIII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; IM = intramuscular; IV = intravenous; PO = orally Visceral Leishmaniasis The following medications have been used to treat visceral leishmaniasis: amphotericin B deoxycholate, liposomal amphotericin B, pentavalent antimonial drugs (e.g., meglumine antimoniate), and miltefosine (for L. donovani). Lower cure rates, higher drug toxicity, more relapses, and higher mortality summarize the treatment outcomes for people with HIV with visceral leishmaniasis. Amphotericin deoxycholate and lipid formulations of amphotericin B appear to be at least as effective as pentavalent antimonials.56-58 Liposomal and lipid complex preparations of amphotericin B are typically better tolerated than amphotericin B deoxycholate or pentavalent antimony (meglumine antimoniate).59-61 The equivalent efficacy and better toxicity profile have led the Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-7 Adolescents With HIV (the Panel) to recommend liposomal amphotericin B as the preferred amphotericin formulation for treatment of visceral leishmaniasis in people with HIV (AII).62 The optimal amphotericin B dosage has not been determined.62,63 Recommended regimens include liposomal preparations of 3 to 5 mg/kg body weight administered on consecutive days or in an interrupted schedule (e.g., 4 mg/kg on Days 1–5, 10, 17, 24, 31, and 38) to achieve a total cumulative dose of 20 to 60 mg/kg body weight (AII). An alternative regimen of amphotericin B deoxycholate, 0.5 to 1.0 mg/kg body weight/day intravenously (IV), to achieve a total dose of 1.5 to 2.0 g, can be administered (BII).56,57,64-67 Pentavalent antimony (meglumine antimoniate) 20 mg/kg/day IV or intramuscular (IM) for 28 consecutive days, is an alternative (BII). Pentavalent antimonial drugs require an investigator-initiated investigational new drug application in the United States (see Instructions for Acquiring Glucantime [Meglumine antimoniate] for Treatment of Leishmaniasis). Due to toxicity concerns with pentavalent antimonial drugs, a pregnancy test (beta-human chorionic gonadotropin [β-hCG]) should be obtained by individuals of childbearing potential prior to start of therapy, and effective contraception during treatment is advised. Oral miltefosine monotherapy (available in the United States via www.profounda.com) is recommended as an alternative treatment option for Indian L. donovani visceral leishmaniasis in people with HIV63,68 at a dose of approximately 2.5 to 3 mg/kg daily (maximum of 150 mg daily) for 28 days (BII).69-72 Combination therapy using miltefosine and liposomal amphotericin in the treatment of HIV-L. donovani visceral leishmaniasis has also shown promise. A randomized clinical trial of liposomal amphotericin 30 mg/kg total dose and miltefosine 100 mg/day for 28 days was compared to liposomal amphotericin 40 mg/kg total dose monotherapy among patients with L. donovani visceral leishmaniasis and HIV coinfection in Ethiopia. Parasite clearance persisting to 58 days was found in 88% of the combination treatment group versus 55% in the monotherapy group.73 In India, 150 people with HIV with L. donovani visceral leishmaniasis received total doses of liposomal amphotericin 40 mg/kg IV versus liposomal amphotericin 30 mg/kg IV with oral miltefosine 50 mg twice daily for 14 days. At Day 210 follow-up, 7% of patients in the monotherapy arm died versus 1.3% in the combination arm.74 These data have led the WHO to update their 2022 HIV and visceral leishmaniasis coinfection treatment guidelines to conditionally recommend combination liposomal amphotericin and miltefosine treatment; those with HIV-visceral leishmaniasis coinfection in Eastern Africa (L. donovani) should be administered miltefosine for 28 days, and those with HIV-visceral leishmaniasis coinfection (L. donovani) in South East Asia should be administered miltefosine for 14 days.75 Since miltefosine is teratogenic and is contraindicated in pregnancy, β-hCG should be checked prior to initiation and effective contraception should be continued for 5 months.63 Data supporting the use of miltefosine monotherapy in people with HIV are relatively limited and restricted to Indian L. donovani. For visceral leishmaniasis caused by L. infantum (e.g., in the Americas, Europe), Pan American Health Organization guidelines recommend against miltefosine monotherapy due to lower efficacy and limited evidence.76 Further research is also needed to confirm the efficacy of drug combinations in people with HIV to treat other Leishmania species and severe or refractory cases of visceral leishmaniasis in other geographic regions. Currently, there is no recommendation for combination therapy in visceral leishmaniasis due to L. infantum. Cutaneous Leishmaniasis Few systematic data are available on the efficacy of treatment for cutaneous leishmaniasis, mucosal leishmaniasis, or diffuse cutaneous leishmaniasis in people with HIV. Based on data from individuals Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-8 without HIV with cutaneous leishmaniasis and case reports in people with HIV-cutaneous leishmaniasis, patients with HIV-cutaneous leishmaniasis should be treated with some form of systemic therapy, depending on the type of cutaneous leishmaniasis and the clinical response. Liposomal amphotericin B (BIII),67 miltefosine (Viannia subgenus infections) (BIII), or pentavalent antimony (meglumine antimoniate) (BIII) are options for treatment.77,78 Pentavalent antimonial drugs require an investigator-initiated investigational new drug application in the United States (see Instructions for Acquiring Glucantime [Meglumine antimoniate] for Treatment of Leishmaniasis). Potential alternatives for cutaneous leishmaniasis include cryotherapy, topical paromomycin, intralesional pentavalent antimony or pentamidine isoethionate, intravenous pentamidine isethionate,79,80 fluconazole for L. major and L. mexicana, or local heat therapy. The effectiveness of these modalities is known to be dependent upon the infecting species of Leishmania.66,81-83 However, these alternatives are based on data from people without HIV, not those with HIV-cutaneous leishmaniasis coinfection. For example, although the Pan American Health Organization 2022 guidelines recommend intralesional pentavalent antimonial treatment as first-line use in immunocompetent patients, this treatment has not been tested in people with HIV and New World cutaneous leishmaniasis; because of this, there are concerns about how effectively it will prevent dissemination like mucosal leishmaniasis in people with HIV, who may be at increased risk.76,84 Therefore, these alternatives could be considered in individualized circumstances in patients with high CD4 counts and controlled viral load. Special Considerations Regarding ART Initiation Appropriate use of ART has substantially improved the survival of patients with coinfection and decreased the likelihood of relapse after antileishmanial therapy.8,26,85 Therefore, ART should be started as soon as patients are able to tolerate it (AIII). Monitoring of Response to Therapy and Adverse Events (Including IRIS) Patients treated with liposomal amphotericin B should be monitored for dose-dependent nephrotoxicity, electrolyte disturbances, and infusion-related adverse reactions (AII). Infusion-related adverse events may be ameliorated by pre-treatment with acetaminophen or diphenhydramine (CIII). An infusion of 1 L of saline 1 hour prior to drug infusion is recommended to help reduce the risk of glomerular function decline during treatment (BIII). The frequency of nephrotoxicity is lower for liposomal or lipid-associated preparations than for amphotericin B deoxycholate.60 Adverse events associated with miltefosine use include gastrointestinal symptoms (more commonly nausea or vomiting than diarrhea) that can result in prerenal azotemia, motion sickness-like symptoms, scrotal pain, thrombocytopenia, and hepatotoxicity. To decrease gastrointestinal symptoms, which are usually worse at the beginning of therapy, miltefosine should be administered in divided 50 mg doses during the day and taken with food containing some fat. Weekly assessment of renal and hepatic function and platelet counts is recommended.67 Patients receiving parenteral pentavalent antimony (meglumine antimoniate) should be monitored closely for adverse reactions.77 Overall, at a dose of 20 mg/kg of body weight per day, more than 60% of patients have one or more of the following reactions: thrombophlebitis, anorexia, myalgia, arthralgia, abdominal pain, elevation of liver transaminases, amylase, or lipase, and clinical pancreatitis, in some patients. Weekly electrocardiograms are recommended during treatment, with careful monitoring for changes that may indicate early cardiotoxicity, such as prolonged QT intervals and T-wave inversion (CIII). Rarely, arrhythmias and sudden death have occurred.58,66 Severe Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-9 adverse reactions to pentavalent antimony, including acute pancreatitis and leukopenia, appear to be more common in patients with coinfection than in those who do not have HIV.86 Cases of newly symptomatic visceral leishmaniasis, mucosal leishmaniasis, and cutaneous leishmaniasis have been reported in association with immune reconstitution inflammatory syndrome (IRIS) following initiation of ART.87-90 Several of these cases have resembled post-kala-azar dermal leishmaniasis or disseminated cutaneous leishmaniasis.91-95 Existing experience with IRIS-associated leishmaniasis, however, is insufficient to provide data for specific management guidelines. People with HIV who respond to initial treatment should be clinically monitored for relapse (any recurrence or new consistent skin lesions) for at least 6 months to 1 year after treatment for cutaneous leishmaniasis; those with infection with L. (Viannia) subspecies also should be followed for 2 to 5 years for any signs or symptoms of inflammation of the nasal mucosa. People with HIV successfully treated for visceral leishmaniasis should be clinically monitored for symptoms or signs of recurrence such as fever, constitutional symptoms, hepatomegaly, splenomegaly, or cytopenia. Routine follow-up via parasitological testing with repeat biopsies or longitudinally tracking antibody levels is generally not recommended for people with HIV with treated leishmaniasis who do not demonstrate clinical signs or symptoms of recurrence. A positive peripheral blood PCR for Leishmania correlated with a high risk of relapse in people with HIV-visceral leishmaniasis coinfection.96 Managing Treatment Failure For patients who fail to respond to initial therapy or who experience a relapse after initial treatment, a repeat course of the initial regimen, or one of the recommended alternatives for initial therapy, should be used as previously outlined (AIII). The response rate for retreatment appears to be similar to that for initial therapy, although some patients evolve to a chronic disease state with serial relapses despite aggressive acute and maintenance therapies.97 In a pharmacokinetic substudy of antileishmanial drugs for treatment of visceral leishmaniasis in people with HIV, blood concentrations of amphotericin were found to be twofold-lower than those measured in studies among those with visceral leishmaniasis without HIV. Additionally, lower observed miltefosine concentrations were likely due in part to lower weight-based dosing when compared to other studies, emphasizing the need to use a weight-based dosage approximating 2.5 mg/kg/day in adults. However, no relationship between amphotericin and miltefosine concentrations and treatment outcome was observed.98 Expert assistance to health care providers for clinical care for leishmaniasis is available at the CDC’s Parasitic Diseases Hotline at (404) 718-4745 or parasites@cdc.gov. Preventing Recurrence Relapses, particularly of visceral leishmaniasis and disseminated cutaneous leishmaniasis, are common after cessation of antileishmanial therapy in people with HIV, and relapse is more frequent in those with lower CD4 count.99 Reported associations with relapse are prior episode of visceral leishmaniasis, CD4 count <100 cells/mm3 at time of primary visceral leishmaniasis, and no increase in CD4 count at follow-up.99 In people with HIV-visceral leishmaniasis coinfection who were not receiving or responding to ART, the risk of relapse at 6 and 12 months was 60% and 90%, respectively, in the absence of secondary prophylaxis (chronic maintenance therapy).6,100,101 In Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-10 Brazil, a relapse rate of 28.6% of patients with HIV-cutaneous leishmaniasis was reported, regardless of viral load and adherence to ART.35 Therefore, secondary prophylaxis with an effective antileishmanial drug administered at least every 4 weeks is recommended, particularly for patients with visceral leishmaniasis and CD4 counts <200 cells/mm3 (AII).6,26,100,102 The only published, randomized trial of secondary prophylaxis compared amphotericin B lipid complex (3 mg/kg every 21 days) in eight patients with no prophylaxis in nine patients; this trial reported relapse rates of 50% versus 78%, respectively, after 1 year of follow-up.102 In retrospective observational studies, monthly pentavalent antimony or lipid formulations of amphotericin every 2 to 4 weeks were also associated with decreased relapse rates.26,100 With a 2 year follow-up, 74 people with HIV-visceral leishmaniasis coinfection were given monthly intravenous pentamidine isethionate (4 mg/kg with a maximal dose 300 mg) and 71% were relapse-free after 12 months.103 In 54 persons followed for 390 days stratified for CD4 above and below 200, there was a reported overall relapse-free survival of 50% and 53% if CD4 ≥200 cells/µL.104 Liposomal amphotericin B (4 mg/kg every 2–4 weeks) (AII) is the preferred regimen for secondary prophylaxis. Amphotericin B lipid complex (3 mg/kg every 21 days) (BII) and pentavalent antimony (meglumine antimoniate, 20 mg/kg IV or IM every 4 weeks) are alternatives (BII). Although pentamidine isethionate is no longer recommended to treat primary visceral leishmaniasis, a dosage of 4 mg/kg IV (300 mg for adult) every 2 to 4 weeks has been suggested as another alternative for secondary prophylaxis (BII).105-107 Allopurinol, used for maintenance therapy, is less effective than monthly pentavalent antimony and is not recommended (BII).100 Although no published data on efficacy are available, maintenance therapy may be indicated for immunocompromised patients with cutaneous leishmaniasis who have multiple relapses after adequate treatment (CIII). When to Stop Secondary Prophylaxis Some investigations suggest that secondary antileishmanial prophylaxis can be discontinued in patients whose CD4 count is >200 to 350 cells/mm3 in response to ART.105,108 Others, however, suggest that secondary prophylaxis should be maintained indefinitely. Among 74 patients in Ethiopia with HIV-visceral leishmaniasis coinfection, who received monthly intravenous pentamidine for 12 to 18 months, a 36.9% relapse rate was identified over a 2-year follow-up, mainly among those with a low baseline CD4 count of ≤100 cells/mm3. All with CD4 count >200 cells/mm3 at Month 12 were relapse-free.105 In one study, a positive peripheral blood PCR for Leishmania correlated with a high risk of relapse.96 Therefore, the Panel recommends considering cessation of secondary prophylaxis when CD4 count is >350 cell/mm3 and HIV viral load has been undetectable for 6 months and there is no clinical evidence of visceral leishmaniasis relapse (CIII). Special Considerations During Pregnancy Diagnostic considerations in pregnant people are the same as in people who are not pregnant. Retrospective analyses suggest that rates of preterm birth and spontaneous abortion may be increased in women with visceral leishmaniasis during pregnancy, especially in the first trimester and when antimonial drugs are used.109,110 Because visceral leishmaniasis is a potentially lethal disease, postponing treatment until after delivery is not an option. Several small published series of pregnant women treated with amphotericin B deoxycholate or liposomal amphotericin B have demonstrated good clinical outcomes.111-115 Liposomal amphotericin B is the first choice for therapy of visceral leishmaniasis in pregnancy (AIII).111 Amphotericin B deoxycholate, which has demonstrated positive Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-11 clinical and pregnancy outcomes in a small group of pregnant people, can be given as an alternative therapy (AIII).111 There are concerns about toxicity and lack of experience with use of pentavalent antimony compounds in human pregnancy; labels for pentavalent antimony compounds state that these drugs are contraindicated for use in pregnant people, although various antimonial compounds were found to not be teratogenic in chickens, rats, or sheep.116-118 Therefore, pentavalent antimonial drugs are not recommended in individuals who are pregnant (BIII). Miltefosine is teratogenic and pentamidine is embryotoxic; therefore, both drugs are not recommended in pregnancy (AII).63,119 In a systematic review including 346 pregnant people with visceral leishmaniasis, 176 pregnant individuals treated with liposomal amphotericin were reported to have 4 (2.3%) maternal deaths, 5 (2.8%) miscarriages, and 2 (1.1%) fetal deaths/stillbirths versus 88 pregnant people receiving pentavalent antimonial drugs, where reported outcomes included 4 (4.5%) maternal deaths, 24 (27.3%) spontaneous abortions, and 2 (2.3%) miscarriages.115 In contrast to visceral leishmaniasis, the Panel recommends deferring treatment of cutaneous leishmaniasis until the postpartum period for most individuals with HIV-cutaneous leishmaniasis (CIII). One study suggests that lesions of cutaneous leishmaniasis may be larger and are more likely to be exophytic in pregnancy, and that untreated cutaneous leishmaniasis may be associated with an increased risk of preterm delivery and stillbirth.120 This is presumed to be related to transient modulation of maternal immune responses during pregnancy.121 In cases of severe cutaneous leishmaniasis with multiple and/or very large lesions, the Panel recommends shared decision making with the patient to discuss the potential risks and benefits of deferring treatment until after pregnancy, treating with systemic therapy, or using local therapy as a temporizing approach (followed by systemic therapy to be given after pregnancy if the lesions do not resolve) (CIII). Systemic therapy is recommended in most cases of mucosal leishmaniasis in patients with HIV (CIII). 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Visceral leishmaniasis in pregnancy and vertical transmission: a systematic literature review on the therapeutic orphans. PLoS Negl Trop Dis. 2021;15(8):e0009650. Available at: 116. James LF, Lazar VA, Binns W. Effects of sublethal doses of certain minerals on pregnant ewes and fetal development. Am J Vet Res. 1966;27(116):132-135. Available at: 117. Ridgway LP, Karnofsky DA. The effects of metals on the chick embryo: toxicity and production of abnormalities in development. Ann N Y Acad Sci. 1952;55(2):203-215. Available at: 118. Rossi F, Acampora R, Vacca C, et al. Prenatal and postnatal antimony exposure in rats: effect on vasomotor reactivity development of pups. Teratog Carcinog Mutagen. 1987;7(5):491-496. Available at: 119. Ito S, Koren G. Estimation of fetal risk from aerosolized pentamidine in pregnant healthcare workers. Chest. 1994;106(5):1460-1462. Available at: 120. Morgan DJ, Guimaraes LH, Machado PR, et al. Cutaneous leishmaniasis during pregnancy: exuberant lesions and potential fetal complications. Clin Infect Dis. 2007;45(4):478-482. Available at: 121. Conceicao-Silva F, Morgado FN, Pimentel MI, et al. Two women presenting worsening cutaneous ulcers during pregnancy: diagnosis, immune response, and follow-up. PLoS Negl Trop Dis. 2013;7(12):e2472. Available at: 122. Boehme CC, Hain U, Novosel A, Eichenlaub S, Fleischmann E, Loscher T. Congenital visceral leishmaniasis. Emerg Infect Dis. 2006;12(2):359-360. Available at: 123. Meinecke CK, Schottelius J, Oskam L, Fleischer B. Congenital transmission of visceral leishmaniasis (Kala Azar) from an asymptomatic mother to her child. Pediatrics. 1999;104(5):e65. Available at: 124. Zinchuk A, Nadraga A. Congenital visceral leishmaniasis in Ukraine: case report. Ann Trop Paediatr. 2010;30(2):161-164. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV R-23 125. Argy N, Lariven S, Rideau A, et al. Congenital leishmaniasis in a newborn infant whose mother was coinfected with leishmaniasis and HIV. J Pediatric Infect Dis Soc. 2020;9(2):277-280. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-1 Malaria Updated: March 28, 2017 Reviewed: January 10, 2024 Epidemiology Malaria continues to contribute disproportionately to the global burden of infectious diseases, especially in sub-Saharan Africa and Southeast Asia. In 2015, the World Health Organization estimated that 97 countries had ongoing malaria transmission, and almost half the world’s population, approximately 3.2 billion people, lived in areas with some risk of malaria transmission.1 Of the nearly 214 million cases of malaria worldwide in 2015 (based on reports and models), approximately 88% (188 million) occurred in Africa, the area of the world with the highest HIV prevalence.1 Approximately 438,000 deaths were attributable to malaria in 2015, with ~90% occurring in Africa and 74% of those deaths in children younger than 5 years of age. Fifteen countries, mainly in sub-Saharan Africa, account for 80% of malaria cases and 78% of deaths worldwide.1 Current attributable morbidity and mortality are likely underestimated, given our limited understanding, surveillance, and reporting of non-falciparum infections. Malaria typically is transmitted by the bite of an infected female Anopheles sp. mosquito. Reports of vertical transmission and infection after blood transfusion do exist, but these routes of transmission are uncommon in non-endemic areas.2-5 Malaria in humans can be caused by any one of five species: Plasmodium falciparum, Plasmodium vivax, Plasmodium ovale, Plasmodium malariae, and Plasmodium knowlesi (a zoonotic species that also infects macaques in Southeast Asia).4 Although P. vivax infections are more common and occur in a far wider geographic distribution,6 P. falciparum malaria represents the most serious public health problem because of its tendency toward severe or fatal infections. P. vivax, however, should not be discounted as a risk for travelers in many parts of the world. Malaria and HIV both cause substantial morbidity and mortality, particularly in sub-Saharan Africa. Given this substantial overlap, even modest interactions between them have public health importance.7,8 Malaria influences the natural history of HIV infection, and HIV infection alters the natural history and severity of malaria.9 Many foreign-born individuals develop malaria in the United States because of distant exposure before their arrival, or as a result of more recent travel for business or family reasons. Similarly, U.S.-born individuals can develop malaria during travel to endemic areas.10-13 Failure to take appropriate chemoprophylaxis is a common problem for both groups of individuals.14,15 People who formerly lived in malarious areas may believe that they are immune, and therefore do not need to take prophylaxis.16 Such patients are at high risk of infection, however, because they likely have lost partial immunity within 6 months after leaving endemic regions. Consideration of malaria in returning travelers who are febrile is important: Of the nearly 50 million individuals who travel to developing countries each year, between 5% and 11% develop a fever during or after travel.17-20 Malaria is a surprisingly common cause of these fevers.21 Clinical Manifestations The clinical syndromes caused by Plasmodium species depend on prior exposure.22 While many native U.S. travelers have no prior immunity, clinical manifestations in those who have resided in malarious areas depend Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-2 on whether they lived in an area with stable endemic malaria transmission (year round) or unstable (seasonal, infrequent or very low) transmission.23 In stable endemic areas, children younger than age 5 years may experience chronic infections with recurrent parasitemia, resulting in severe anemia and death. Children who survive these infections usually acquire partial immunity by age 5 years, and if they remain in the area where malaria is endemic, they maintain this immunity into adulthood. In stable endemic areas, adults usually experience asymptomatic or milder infections as a result of this acquired immune response. However, as noted previously, patients who leave endemic areas and subsequently return may be at high risk of disease because they likely have lost partial immunity 6 months after leaving endemic regions. In unstable transmission areas, protective immunity is not acquired. For populations in these areas, the overwhelming clinical manifestation is acute febrile disease that can be complicated by cerebral malaria, affecting persons of all ages. When pregnant women in areas of unstable transmission develop acute malaria, the consequences may include spontaneous abortion and stillbirth. In more stable transmission areas, pregnant women, particularly primigravidas, may lose some acquired immunity. Although infections may continue to be asymptomatic, infected pregnant women may acquire placental malaria that contributes to intrauterine growth retardation, low birth weight, and increased infant mortality. Patients with malaria can exhibit various symptoms and a broad spectrum of severity, depending upon factors such as the infecting species and level of acquired immunity in the host. HIV-immunosuppressed patients in endemic areas may lose acquired malarial immunity, and HIV-immunosuppressed adults with little or no previous malaria exposure (such as travelers) appear to be at increased risk of severe outcomes.24 The incubation period for P. falciparum is from a week to several months, but most often less than 60 days. Patients can present much later (>1 year), but this pattern is more common with other species, especially P. vivax. In non-immune patients, typical symptoms of malaria include fever, chills, myalgias and arthralgias, headache, diarrhea, vomiting, and other non-specific signs. Splenomegaly, anemia, thrombocytopenia, pulmonary or renal dysfunction, and neurologic findings also may be present. Classically, paroxysmal fevers occur every 48 hours for P. falciparum, P. vivax, and P. ovale malaria; those with P. malariae occur every 72 hours. This classic presentation is highly variable, however, and may not be present. P. knowlesi, known to cause human infection in Southeast Asia in travelers to jungle/forested areas, is clinically indistinguishable from other species of malaria, and the overwhelming majority of patients present with uncomplicated disease (~90%).25 Uncomplicated malaria infection can progress to severe disease or death within hours. Malaria with central nervous system symptoms can be particularly ominous. Cerebral malaria refers to unarousable coma not attributable to any other cause in patients infected with P. falciparum; in Africa, case fatality rates with cerebral malaria approach 40%.26-28 The risk of severe and complicated illness is increased in patients with high levels of parasitemia and without partial immunity. Metabolic acidosis is an important manifestation of severe malaria and an indicator of poor prognosis.29 Other acute complications include renal failure, hypoglycemia, disseminated intravascular coagulation, shock, and acute pulmonary edema.30 P. falciparum is the species most commonly responsible for severe disease and death, although the other species can cause severe disease and death as well.25,31 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-3 Effect of HIV on Parasitemia and Clinical Severity HIV infection impairs acquired immunity to malaria that is present in older children and adults in stable endemic areas. Large cohort studies have demonstrated the increased frequency (with rates one- to two-fold higher) of both parasitemia and clinical malaria in HIV-infected adults, with increasing risk and higher-density parasitemia associated with more advanced immunosuppression, particularly among those with CD4 T-lymphocyte (CD4) cell counts <350 cells/mm3.32-34 Increased rates of malaria among individuals with HIV do not appear to be as great as the rates observed with classic opportunistic infections such as tuberculosis and Pneumocystis jirovecii pneumonia.35 In a prospective cohort study in an area with unstable malaria transmission, HIV-infected non-immune adults were found to be at increased risk of severe malaria, and the risk was associated with a low CD4 cell count.36 Non-immune HIV-infected patients were substantially more likely to have severe clinical malaria than were non-immune patients without HIV. In KwaZulu Natal, an area of unstable malaria transmission, HIV-infected adults hospitalized for malaria were substantially more likely to die or require an intensive care unit admission than those who were not HIV-infected.37 In contrast, HIV infection did not confer an increased risk of poor outcomes among partially immune adults in areas with more stable transmission.32 In a cross-sectional study of travelers returning to France from malaria-endemic areas between 2000 and 2003, HIV-infected individuals with CD4 counts <350 cells/mm3 were at significantly higher risk of developing severe malaria, compared with those who were HIV-negative.34 Effects of Malaria on Mother-to-Child HIV Transmission Placental malaria also has been associated with increased expression of CCR5 receptors in placental macrophages38 and increased viral load,39 raising the possibility of placental malaria leading to increased mother-to-child transmission (MTCT) of HIV. In addition, fetal immune activation by malaria antigens may increase susceptibility to HIV infection.40 Data are conflicting concerning the effect of malaria during pregnancy on risk of MTCT in the pre-ART era and are limited since the widespread use of ART for prevention of MTCT.41-43 Diagnosis A malaria diagnosis must be considered in all febrile patients who have traveled to or lived in malaria-endemic areas or who have received blood products, tissues, or organs from individuals who have been to such areas. Several diagnostic methods are available, including microscopic diagnosis, antigen detection tests, polymerase chain reaction-based assays, and serologic tests, though serologic tests which detect host antibody are inappropriate for the diagnosis of acute malaria. Direct microscopic examination of intracellular parasites on stained blood films is the standard for definitive diagnosis in nearly all settings because it allows for identification of the species and provides a measure of parasite density. Microscopic diagnosis of P. knowlesi is difficult because it is commonly misidentified as P. malariae, which tends to follow a more benign course. Providers should have a high index of suspicion for P. knowlesi in travelers returning from Southeast Asia.31 In non-immune patients with all types of malaria, symptoms may develop before detectable levels of parasitemia are evident. For this reason, several blood smear examinations taken at 12- to 24-hour intervals may be needed to positively rule out a diagnosis of malaria in symptomatic patients. Guidelines for laboratory diagnosis are summarized elsewhere and are available at the Centers for Disease Control and Prevention Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-4 (CDC)’s malaria website ( Rapid diagnostic tests, particularly for the diagnosis of P. falciparum, can be used depending on the local expertise and practice and can facilitate prompt diagnosis and treatment of infected patients, but must be followed by microscopy. Preventing Exposure Pre-travel evaluation by a travel medicine specialist can provide specific education about risk of exposure in various geographic locales, the utility of insecticide-impregnated bed nets in the setting where the individual will be traveling or residing, and the use of DEET (N,N-diethyl-3-methyl-benzamide)-containing repellants. Infection with P. falciparum can be more severe in HIV-infected patients with low CD4 cell counts and in pregnant women regardless of HIV infection than in other individuals. Because no chemoprophylactic regimen is completely effective, HIV-infected patients with low CD4 cell counts and women who are pregnant or likely to become pregnant should be advised to avoid travel to areas with malaria transmission if possible (AIII). If travel to an endemic area cannot be deferred, use of an effective chemoprophylaxis regimen is essential, along with careful attention to personal protective measures to prevent mosquito bites. Preventing Disease For United States travelers (including HIV-infected patients) to endemic areas, a combination of chemoprophylaxis and personal protective measures can be highly effective in preventing malaria. Recommendations for prophylaxis are the same for HIV-infected patients as for those who are not HIV-infected and are available at CDC’s malaria website (AIII) ( Malaria incidence has been markedly reduced in African adults with HIV who receive cotrimoxazole (trimethoprim-sulfamethoxazole) prophylaxis.44 A recent study of HIV-infected patients in Uganda demonstrated that malaria burden was reduced by 70% with cotrimoxazole, and then reduced another 50% when antiretroviral (ARV) drugs were provided, and finally reduced another 50% with provision of insecticide-treated nets.45 However, cotrimoxazole is not as effective an antimalarial prophylactic regimen as the recommended antimalarials. Therefore, HIV-infected travelers should not rely on prophylaxis with cotrimoxazole for chemoprophylaxis against malaria (AIII). Treating Disease Because P. falciparum malaria can progress within hours from mild symptoms or low-grade fever to severe disease or death, all HIV-infected patients with confirmed or suspected P. falciparum infections should be admitted to the hospital for evaluation, initiation of treatment, and observation of response to treatment (AIII). Diagnosis prior to treatment should always be pursued; however, treatment should not be delayed when malaria is strongly suspected but laboratory services are unavailable or results will be delayed (AIII). Choice of treatment is guided by the degree of parasitemia, the species of Plasmodium, a patient’s clinical status, and the likely drug susceptibility of the infecting species (as determined by where the infection was acquired). For HIV-infected patients who do acquire Plasmodium infection, treatment recommendations are the same as for HIV-uninfected patients (AIII). CDC posts current treatment recommendations on its website ( and has clinicians on call 24 hours to provide advice to clinicians on diagnosing and treating malaria (CDC Malaria Hotline: (770) 488-7788; Monday through Friday. 8 a.m. to 4:30 p.m. EST. (770) 488-7100 after hours). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-5 Special Considerations with Regard to Starting Antiretroviral Therapy (ART) There is no reason to defer ART initiation after patients have recovered from acute malaria. Monitoring of Response to Therapy and Adverse Events (Including IRIS) Careful monitoring of patients (especially those with P. falciparum malaria) is necessary, including measurement of peripheral parasitemia and hemoglobin and blood glucose levels, as well as assessment of cerebral, pulmonary, and renal function. Frequency of monitoring depends on severity of disease, a patient’s immune status, and the species of Plasmodium. Chemoprophylaxis or treatment for malaria in patients receiving ARV agents requires attention to potential drug interactions. Several potential drug interactions can occur between antimalarial and HIV drugs as well as other medications used to treat HIV-associated opportunistic infections (see Table 4).46 Providers are also encouraged to check for drug-drug interactions by using an interactive web-based resource from the University of Liverpool at Mefloquine in repeated doses has been observed to reduce area under the concentration-time curve and maximal plasma concentrations of ritonavir by 31% and 36%, respectively. Insufficient data are available to suggest that dose adjustments are needed. Quinine levels may be increased by ritonavir-containing regimens or cobicistat; conversely, nevirapine and efavirenz can reduce plasma quinine levels. Potential interactions can occur between ritonavir or cobicistat and chloroquine, but their clinical significance is unclear, and until further data are available, no dose adjustments are recommended. Artemether-lumefantrine is now approved in the United States for treatment of uncomplicated P. falciparum infection. Data in children suggest that this combination is well tolerated and safe in HIV-infected children,47 however, efficacy data are conflicting in HIV-infected adults. An open-label trial in Tanzania demonstrated excellent efficacy (97.6%) of artemether-lumefantrine for treating uncomplicated P. falciparum malaria in HIV-infected adults on nevirapine-based ART.48 Conversely, 28-day clinical and parasitologic response was sub-optimal in the efavirenz-based ART group, with efficacy of 82.5%, and a 19-fold increased risk of recurrent parasitemia compared to the control group of HIV-infected adults not on ART.48 Artesunate is available for treatment of severe malaria through a compassionate use Investigational New Drug application. A trial in Uganda demonstrated the effectiveness of artesunate plus amodiaquine in HIV-infected children, but treatment was associated with increased risk of neutropenia in those on ART, particularly zidovudine, which was attributed to the amodiaquine component of therapy.49 Ritonavir or cobicistat-boosted ARV regimens and non-nucleoside reverse transcriptase inhibitors have the potential to affect metabolism of artemisinin-containing drugs,50 but the overall effect and clinical significance remain unclear. No dose alterations currently are recommended. No immune reconstitution inflammatory syndrome (IRIS) has been described in association with malaria. Managing Treatment Failure HIV-infected individuals are at increased risk of malaria treatment failure.51 Management of treatment failure is the same in HIV-infected and HIV-uninfected patients, except for considerations about drug interactions between ART and antimalarial drugs. Drug-resistant malaria and possible concomitant infections should be considered in HIV-infected patients whose malaria fails to respond to therapy. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-6 Preventing Recurrence If the species of malaria identified is P. vivax or P. ovale, which can cause recurrence due to hepatic phase of infection, then treatment with primaquine in addition to standard treatment is recommended to prevent recurrence (AI). Guidelines for primaquine treatment do not differ in HIV-infected individuals. Special Considerations During Pregnancy Malaria in pregnancy affects both mother and fetus. Infection with P. falciparum during pregnancy can increase maternal risk of severe disease and anemia and risk for stillbirth, preterm birth, and low birth weight.52 The diagnosis of malaria in pregnant women is the same as in women who are not pregnant. For pregnant women with a diagnosis of uncomplicated malaria caused by P. malariae, P. ovale, chloroquine-sensitive P. vivax, and chloroquine-sensitive P. falciparum, prompt treatment with chloroquine is recommended.53 For pregnant women with a diagnosis of chloroquine-resistant P. vivax, treatment with mefloquine for 7 days is recommended. For pregnant women with a diagnosis of uncomplicated chloroquine-resistant P. falciparum malaria, prompt treatment with mefloquine or quinine and clindamycin is recommended as per CDC guidelines.54 On the basis of extensive experience with its use, chloroquine is considered the drug of choice for prophylaxis and treatment of sensitive strains of malaria in pregnancy. Although quinine at high doses has been associated with an increased risk of birth defects (especially deafness) in some animal species and humans (usually during attempted abortion), use of therapeutic doses in pregnancy is considered safe.53,55 Because of the potential for hypoglycemia, glucose levels should be monitored in pregnant women treated with quinine and their neonates. Clindamycin use has not been associated with birth defects. Animal and human data on use of prophylactic and treatment doses of mefloquine do not suggest teratogenicity and the drug can be used safely during all trimesters.56 One randomized trial of mefloquine used in addition to daily cotrimoxazole for malaria prophylaxis in pregnant women living with HIV demonstrated an increased risk of transmission of HIV to the infant in the mefloquine arm, potentially because of drug interactions.57 Although experience is limited, available data on artemether-lumefantrine during pregnancy suggest that use is not associated with increased adverse events or birth defects.58 A pharmacokinetic study in HIV-uninfected persons found no difference in levels between pregnant and non-pregnant subjects except for small differences in elimination half-life of lumefantrine.59 Data on pharmacokinetics in HIV-infected pregnant women were not included. Because of limited data, atovaquone-proguanil is not recommended for treatment in pregnancy and should be used only if quinine plus clindamycin, quinine monotherapy, or mefloquine are unavailable or not tolerated.55 Tetracyclines are not recommended in pregnancy because of increased risk of maternal hepatotoxicity and staining of fetal teeth and bones. Primaquine use during pregnancy is not recommended because of limited experience with its use and the potential for fetal glucose-6-phosphate dehydrogenase (G6PD) deficiency. After treatment, all pregnant women with P. vivax and P. ovale should receive chloroquine prophylaxis for the duration of pregnancy to avoid relapses. Once-weekly mefloquine can be used for prophylaxis in pregnant women with P. vivax acquired in an area with chloroquine-resistant strains. Women who have normal G6PD screening tests can be treated with primaquine after delivery. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-7 Recommendations for Preventing and Treating Malaria Preventing Malaria in Patients Traveling to Endemic Areas: • Recommendations are the same for HIV-infected and HIV-uninfected patients. • Specific recommendations are based on region of travel, malaria risks, and drug susceptibility in the region. • Clinicians should refer to the following website for the most up-to-date recommendations: • TMP-SMX has been shown to reduce malaria in HIV-infected adults in Africa. However, it is not as effective as antimalarial prophylactic regimens. Therefore, HIV-infected travelers should not rely on TMP-SMX for prophylaxis against malaria (AIII). Treating Malaria • Because Plasmodium falciparum malaria can progress within hours from mild symptoms or low-grade fever to severe disease or death, all HIV-infected patients with confirmed or suspected P. falciparum infection should be admitted to the hospital for evaluation, initiation of treatment, and observation of response to therapy (AIII). • When suspicion of malaria is low, antimalarial treatment should not be initiated until the diagnosis has been confirmed by laboratory investigations. • Treatment should not be delayed when malaria is strongly suspected but laboratory services are unavailable or results will be delayed (AIII). • When malaria is strongly suspected, but not yet confirmed, clinicians are advised to consider and initiate treatment for other possible diagnoses in addition to malaria. • Treatment recommendations for HIV-infected patients are the same as HIV-uninfected patients (AIII). • Choice of therapy is guided by the degree of parasitemia, the species of Plasmodium, the patient’s clinical status, and the likely drug susceptibility of the infected species. • For treatment recommendations for specific region, clinicians should refer to o The CDC malaria website: o The CDC Malaria Hotline: (770) 488-7788; Monday through Friday. 8 a.m. to 4:30 p.m. EST. (770) 488-7100 after hours. Key: CDC = the Centers for Disease Control and Prevention; TMP-SMX = trimethoprim-sulfamethoxazole Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-8 References 1. World Health Organization. World Malaria Report 2015. 2015.Available at: Accessed: April 5, 2016. 2. Mungai M, Tegtmeier G, Chamberland M, Parise M. Transfusion-transmitted malaria in the United States from 1963 through 1999. N Engl J Med. 2001;344(26):1973-1978. Available at: 3. Austin SC, Stolley PD, Lasky T. The history of malariotherapy for neurosyphilis. Modern parallels. JAMA. 1992;268(4):516-519. Available at: 4. Mali S, Steele S, Slutsker L, Arguin PM, Centers for Disease Control and Prevention. Malaria surveillance - United States, 2008. MMWR Surveill Summ. 2010;59(7):1-15. Available at: 5. Centers for Disease Control and Prevention. Update: self-induced malaria associated with malariotherapy for Lyme disease--Texas. MMWR Morb Mortal Wkly Rep. 1991;40(39):665-666. Available at: 6. Guerra CA, Howes RE, Patil AP, et al. The international limits and population at risk of Plasmodium vivax transmission in 2009. PLoS Negl Trop Dis. 2010;4(8):e774. Available at: 7. Korenromp EL, Williams BG, de Vlas SJ, et al. Malaria attributable to the HIV-1 epidemic, sub-Saharan Africa. Emerg Infect Dis. 2005;11(9):1410-1419. Available at: 8. Van Geertruyden JP, Menten J, Colebunders R, Korenromp E, D'Alessandro U. The impact of HIV-1 on the malaria parasite biomass in adults in sub-Saharan Africa contributes to the emergence of antimalarial drug resistance. Malar J. 2008;7:134. Available at: 9. Slutsker L, Marston BJ. HIV and malaria: interactions and implications. Curr Opin Infect Dis. 2007;20(1):3-10. Available at: 10. Kemper CA, Linett A, Kane C, Deresinski SC. Frequency of Travel of Adults Infected with HIV. J Travel Med. 1995;2(2):85-88. Available at: 11. Simons FM, Cobelens FG, Danner SA. Common health problems in HIV-infected travelers to the (sub)tropics. J Travel Med. 1999;6(2):71-75. Available at: 12. Castelli F, Patroni A. The human immunodeficiency virus-infected traveler. Clin Infect Dis. 2000;31(6):1403-1408. Available at: 13. Bhadelia N, Klotman M, Caplivski D. The HIV-positive traveler. Am J Med. 2007;120(7):574-580. Available at: 14. Smego RA, Jr. Effectiveness of antimalarial drugs. N Engl J Med. 2005;353(4):420-422; author reply 420-422. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-9 15. Suh KN, Mileno MD. Challenging scenarios in a travel clinic: advising the complex traveler. Infect Dis Clin North Am. 2005;19(1):15-47. Available at: 16. Sherrard AW, McCarthy AE. Travel patterns and health risks for patients infected with HIV. Travel Med Infect Dis. 2009;7(5):291-295. Available at: 17. Ryan ET, Wilson ME, Kain KC. Illness after international travel. N Engl J Med. 2002;347(7):505-516. Available at: 18. Spira AM. Assessment of travellers who return home ill. Lancet. 2003;361(9367):1459-1469. Available at: 19. Steffen R, Rickenbach M, Wilhelm U, Helminger A, Schar M. Health problems after travel to developing countries. J Infect Dis. 1987;156(1):84-91. Available at: 20. Winer L, Alkan M. Incidence and precipitating factors of morbidity among Israeli travelers abroad. J Travel Med. 2002;9(5):227-232. Available at: 21. Wilson ME, Weld LH, Boggild A, et al. Fever in returned travelers: results from the GeoSentinel Surveillance Network. Clin Infect Dis. 2007;44(12):1560-1568. Available at: 22. Mackinnon MJ, Marsh K. The selection landscape of malaria parasites. Science. 2010;328(5980):866-871. Available at: 23. Snow RW, Marsh K. The consequences of reducing transmission of Plasmodium falciparum in Africa. Adv Parasitol. 2002;52:235-264. Available at: 24. Matteelli A, Casalini C, Bussi G, et al. Imported malaria in an HIV-positive traveler: a case report with a fatal outcome. J Travel Med. 2005;12(4):222-224. Available at: 25. Daneshvar C, Davis TM, Cox-Singh J, et al. Clinical and laboratory features of human Plasmodium knowlesi infection. Clin Infect Dis. 2009;49(6):852-860. Available at: 26. Severe and complicated malaria. World Health Organization, Division of Control of Tropical Diseases. Trans R Soc Trop Med Hyg. 1990;84 Suppl 2(Suppl 2):1-65. Available at: 27. Greenberg AE, Ntumbanzondo M, Ntula N, Mawa L, Howell J, Davachi F. Hospital-based surveillance of malaria-related paediatric morbidity and mortality in Kinshasa, Zaire. Bull World Health Organ. 1989;67(2):189-196. Available at: 28. Molyneux ME, Taylor TE, Wirima JJ, Borgstein A. Clinical features and prognostic indicators in paediatric cerebral malaria: a study of 131 comatose Malawian children. Q J Med. 1989;71(265):441-459. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-10 29. English M, Sauerwein R, Waruiru C, et al. Acidosis in severe childhood malaria. QJM. 1997;90(4):263-270. Available at: 30. Marsh K, Forster D, Waruiru C, et al. Indicators of life-threatening malaria in African children. N Engl J Med. 1995;332(21):1399-1404. Available at: 31. Cox-Singh J, Davis TM, Lee KS, et al. Plasmodium knowlesi malaria in humans is widely distributed and potentially life threatening. Clin Infect Dis. 2008;46(2):165-171. Available at: 32. Whitworth J, Morgan D, Quigley M, et al. Effect of HIV-1 and increasing immunosuppression on malaria parasitaemia and clinical episodes in adults in rural Uganda: a cohort study. Lancet. 2000;356(9235):1051-1056. Available at: 33. Patnaik P, Jere CS, Miller WC, et al. Effects of HIV-1 serostatus, HIV-1 RNA concentration, and CD4 cell count on the incidence of malaria infection in a cohort of adults in rural Malawi. J Infect Dis. 2005;192(6):984-991. Available at: 34. Mouala C, Guiguet M, Houze S, et al. Impact of HIV infection on severity of imported malaria is restricted to patients with CD4 cell counts < 350 cells/microl. AIDS. 2009;23(15):1997-2004. Available at: 35. Laufer MK, van Oosterhout JJ, Thesing PC, et al. Impact of HIV-associated immunosuppression on malaria infection and disease in Malawi. J Infect Dis. 2006;193(6):872-878. Available at: 36. Cohen C, Karstaedt A, Frean J, et al. Increased prevalence of severe malaria in HIV-infected adults in South Africa. Clin Infect Dis. 2005;41(11):1631-1637. Available at: 37. Grimwade K, French N, Mbatha DD, Zungu DD, Dedicoat M, Gilks CF. HIV infection as a cofactor for severe falciparum malaria in adults living in a region of unstable malaria transmission in South Africa. AIDS. 2004;18(3):547-554. Available at: 38. Tkachuk AN, Moormann AM, Poore JA, et al. Malaria enhances expression of CC chemokine receptor 5 on placental macrophages. J Infect Dis. 2001;183(6):967-972. Available at: 39. Mwapasa V, Rogerson SJ, Molyneux ME, et al. The effect of Plasmodium falciparum malaria on peripheral and placental HIV-1 RNA concentrations in pregnant Malawian women. AIDS. 2004;18(7):1051-1059. Available at: 40. Steiner K, Myrie L, Malhotra I, et al. Fetal immune activation to malaria antigens enhances susceptibility to in vitro HIV infection in cord blood mononuclear cells. J Infect Dis. 2010;202(6):899-907. Available at: 41. Msamanga GI, Taha TE, Young AM, et al. Placental malaria and mother-to-child transmission of human immunodeficiency virus-1. Am J Trop Med Hyg. 2009;80(4):508-515. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-11 42. Bulterys PL, Chao A, Dalai SC, et al. Placental malaria and mother-to-child transmission of human immunodeficiency virus-1 in rural Rwanda. Am J Trop Med Hyg. 2011;85(2):202-206. Available at: 43. Ezeamama AE, Duggan C, Manji KP, et al. Clinical malaria diagnosis in pregnancy in relation to early perinatal mother-to-child transmission of HIV: a prospective cohort study. HIV Med. 2014;15(5):276-285. Available at: 44. Anglaret X, Chene G, Attia A, et al. Early chemoprophylaxis with trimethoprim-sulphamethoxazole for HIV-1-infected adults in Abidjan, Cote d'Ivoire: a randomised trial. Cotrimo-CI Study Group. Lancet. 1999;353(9163):1463-1468. Available at: 45. Mermin J, Ekwaru JP, Liechty CA, et al. Effect of co-trimoxazole prophylaxis, antiretroviral therapy, and insecticide-treated bednets on the frequency of malaria in HIV-1-infected adults in Uganda: a prospective cohort study. Lancet. 2006;367(9518):1256-1261. Available at: 46. Khoo S, Back D, Winstanley P. The potential for interactions between antimalarial and antiretroviral drugs. AIDS. 2005;19(10):995-1005. Available at: 47. Katrak S, Gasasira A, Arinaitwe E, et al. Safety and tolerability of artemether-lumefantrine versus dihydroartemisinin-piperaquine for malaria in young HIV-infected and uninfected children. Malar J. 2009;8:272. Available at: 48. Maganda BA, Minzi OM, Kamuhabwa AA, Ngasala B, Sasi PG. Outcome of artemether-lumefantrine treatment for uncomplicated malaria in HIV-infected adult patients on anti-retroviral therapy. Malar J. 2014;13:205. Available at: 49. Gasasira AF, Kamya MR, Achan J, et al. High risk of neutropenia in HIV-infected children following treatment with artesunate plus amodiaquine for uncomplicated malaria in Uganda. Clin Infect Dis. 2008;46(7):985-991. Available at: 50. Parikh S, Gut J, Istvan E, Goldberg DE, Havlir DV, Rosenthal PJ. Antimalarial activity of human immunodeficiency virus type 1 protease inhibitors. Antimicrob Agents Chemother. 2005;49(7):2983-2985. Available at: 51. Van Geertruyden JP, Mulenga M, Mwananyanda L, et al. HIV-1 immune suppression and antimalarial treatment outcome in Zambian adults with uncomplicated malaria. J Infect Dis. 2006;194(7):917-925. Available at: 52. Desai M, ter Kuile FO, Nosten F, et al. Epidemiology and burden of malaria in pregnancy. Lancet Infect Dis. 2007;7(2):93-104. Available at: 53. Griffith KS, Lewis LS, Mali S, Parise ME. Treatment of malaria in the United States: a systematic review. JAMA. 2007;297(20):2264-2277. Available at: 54. Centers for Disease Control and Prevention. Part 3: Alternatives for Pregnant Women and Treatment of Severe Malaria. In: Secondary Centers for Disease Control and Prevention, ed^eds. Subsidiary Centers for Disease Control and Prevention, trans. Secondary Part 3: Alternatives for Pregnant Women and Treatment of Severe Malaria. Vol. ed.: 2013. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-12 55. McGready R, Thwai KL, Cho T, et al. The effects of quinine and chloroquine antimalarial treatments in the first trimester of pregnancy. Trans R Soc Trop Med Hyg. 2002;96(2):180-184. Available at: 56. Centers for Disease Control and Prevention. Update: New Recommendations for Mefloquine Use in Pregnancy. 2011. Available at: 57. Gonzalez R, Desai M, Macete E, et al. Intermittent preventive treatment of malaria in pregnancy with mefloquine in HIV-infected women receiving cotrimoxazole prophylaxis: a multicenter randomized placebo-controlled trial. PLoS Med. 2014;11(9):e1001735. Available at: 58. Manyando C, Kayentao K, D'Alessandro U, Okafor HU, Juma E, Hamed K. A systematic review of the safety and efficacy of artemether-lumefantrine against uncomplicated Plasmodium falciparum malaria during pregnancy. Malar J. 2012;11:141. Available at: 59. Nyunt MM, Nguyen VK, Kajubi R, et al. Artemether-Lumefantrine Pharmacokinetics and Clinical Response Are Minimally Altered in Pregnant Ugandan Women Treated for Uncomplicated Falciparum Malaria. Antimicrob Agents Chemother. 2015;60(3):1274-1282. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-1 Microsporidiosis Updated: November 14, 2023 Reviewed: January 10, 2024 Epidemiology Microsporidia are protists related to fungi, defined by the presence of a unique invasive organelle consisting of a single polar tube that coils around the interior of the spore. They are ubiquitous organisms and are likely zoonotic and/or waterborne in origin. Phylogenetic studies now place microsporidia with the Cryptomycota as the basal branch of the fungal kingdom (or alternatively as a sister phylum).1 The microsporidia reported as pathogens in humans include Encephalitozoon cuniculi, Encephalitozoon hellem, Encephalitozoon (syn Septata) intestinalis, Enterocytozoon bieneusi, Trachipleistophora hominis, Trachipleistophora anthropophthera, Pleistophora species, Pleistophora ronneafiei, Vittaforma (syn Nosema) corneae, Tubulonosema acridophagus, Endoreticulatus sp., Nosema ocularum, Anncaliia (syns Brachiola/Nosema) connori, Anncaliia (syn Brachiola) vesicularum, Anncaliia (syns Brachiola/Nosema) algerae, and Microsporidium sp.2-8 In the pre-antiretroviral therapy (ART) era, reported prevalence rates of microsporidiosis varied between 2% and 70% among people with HIV/AIDS with diarrhea, depending on the diagnostic techniques employed and the population described.3-5,8 The incidence of microsporidiosis has declined with the widespread use of effective ART, but it continues to occur among people with HIV who are unable to obtain ART or to remain on it.9 Microsporidiosis is increasingly recognized among people without HIV, including children, travelers, organ transplant recipients, contact lens wearers, and the elderly. In people with immune suppression, clinical signs related to microsporidiosis3-5,8 are most commonly observed when CD4 T lymphocyte (CD4) cell counts are <100 cells/mm3. Clinical Manifestations The most common manifestation of microsporidiosis is gastrointestinal tract infection with diarrhea; however, encephalitis, ocular infection, sinusitis, myositis, and disseminated infection have also been described.3-5,8 Clinical syndromes can vary by infecting species. E. bieneusi is associated with malabsorption, diarrhea, and cholangitis. E. cuniculi is associated with hepatitis, encephalitis, and disseminated disease. E. intestinalis is associated with diarrhea, disseminated infection, and superficial keratoconjunctivitis. E. hellem is associated with superficial keratoconjunctivitis, sinusitis, respiratory disease, prostatic abscesses, and disseminated infection. Anncaliia, Vittaforma, and Trachipleistophora are associated with keratoconjunctivitis. Nosema, Vittaforma, and Microsporidium are associated with stromal keratitis following trauma in immunocompetent hosts. Pleistophora, Anncaliia, and Trachipleistophora are associated with myositis. Trachipleistophora is associated with encephalitis and disseminated disease. Diagnosis Effective morphologic demonstration of microsporidia by light microscopy can be accomplished with staining methods that produce differential contrast between the spores of the microsporidia and the cells and debris in clinical samples, such as stool. In addition, because of the small size of the spores (1–5 mm), magnification up to 1,000 times is required for visualization. Chromotrope 2R and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-2 the fluorescent brighteners calcofluor white and Uvitex 2B are useful as selective stains for microsporidia in stool and other body fluids.7 In biopsy specimens, microsporidia can be visualized with Giemsa, tissue Gram stains (Brown-Hopps Gram stain), calcofluor white or Uvitex 2B (fluorescent brighteners) staining, Warthin-Starry silver staining, or Chromotrope 2A.7 In gastrointestinal disease, examination of three stools with chromotrope and chemofluorescent stains is often sufficient for diagnosis. If stool examination is negative and microsporidiosis is suspected, a small bowel biopsy may be useful. If the etiologic agent is Encephalitozoon or Trachipleistophora sp., examination of urine often also reveals the organism. Determination of the species of microsporidia causing disease can be made by the morphology of the organism demonstrated by transmission electron microscopy, by staining with species-specific antibodies, or by polymerase chain reaction using species- or genus-specific primers.7,10 The assistance of specialists familiar with the species differentiation of microsporidia should be sought. Preventing Exposure People with HIV who have CD4 counts <200 cells/mm3 should avoid untreated water sources (AIII). Additional recommendations include increasing attention to hand washing and personal hygiene, avoiding eating undercooked meat or seafood, and limiting exposure to animals known to be infected with microsporidia (BIII).11 The precautions described in the section on cryptosporidiosis also are applicable to microsporidiosis. Preventing Disease Preventing Chronic Microsporidiosis • Because chronic microsporidiosis occurs primarily in people with advanced immunodeficiency, initiate ART before severe immunosuppression occurs (AII). Key: ART = antiretroviral therapy Because chronic microsporidiosis occurs primarily in people with advanced immunodeficiency, appropriate initiation of ART before severe immunosuppression should prevent this disease (AII). No specific chemoprophylactic regimens are known to be effective in preventing microsporidiosis. Treating Disease Managing Microsporidiosis • Initiate or optimize ART with immune restoration to CD4 count >100 cells/mm3 (AII). • Manage severe dehydration, malnutrition, and wasting with fluid support (AII) and nutritional supplements (AIII). • Antimotility agents can be used for diarrhea control, if required (BIII). GI Infections Caused by Enterocytozoon bieneusi • The best treatment option is ART and fluid support (AII). • No specific therapeutic agent is available for this infection. • Fumagillin 60 mg PO daily (BII) and TNP-470 (BIII) (unavailable in the United States) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-3 • Nitazoxanide 500 mg twice daily for at least 14 days may resolve chronic diarrhea and is a reasonable alternative if fumagillin is not available (CIII), but the effect appeared to be minimal in people with low CD4 counts. Intestinal and Disseminated (Not Ocular) Infection Caused by Microsporidia Other Than E. bieneusi and Vittaforma corneae • Albendazole is recommended only for initial therapy of intestinal and disseminated microsporidiosis caused by microsporidia other than E. bieneusi and V. corneae (AII). Albendazole 400 mg PO twice daily (AII) for at least 14 days; continue therapy until the CD4 count is >200 cells/mm3 after initiation of ART (BIII). Disseminated Disease Caused by Trachipleistophora or Anncaliia • Itraconazole 400 mg PO daily plus albendazole 400 mg PO twice daily (CIII) Ocular Infection • Topical fumagillin bicylohexylammonium (Fumidil B) 3 mg/mL in saline (fumagillin 70 µg/mL) eye drops: 2 drops every 2 hours for 4 days, then 2 drops four times daily (investigational use only in the United States; needs to be prepared by a compounding pharmacy) (BII), and • Albendazole 400 mg PO twice daily for management of systemic infection (BIII) • For people with CD4 count >200 cells/mm3, therapy can be discontinued after ocular infection resolves (CIII). • For people with CD4 count ≤200 cells/mm3, therapy should be continued indefinitely as recurrence or relapse may occur when therapy is discontinued (BIII). Discontinuation of Chronic Maintenance Therapy for Non-Ocular Manifestations (BIII) • No longer have signs and symptoms of microsporidiosis, and • Sustained increase in CD4 count >200 cells/mm3 for ≥3 months after ART Pregnancy Considerations • Albendazole is not recommended for use during the first trimester (BIII); use in later pregnancy should be considered only if benefits outweigh potential risks (CIII). • Fumagillin has an antiangiogenic effect and should not be used systemically in pregnant people (AIII). Topical fumagillin has not been associated with embryotoxic or teratogenic effects and can be considered when therapy with this agent is appropriate (CIII). • Nitazoxanide has not been associated with adverse outcomes in pregnancy; however, data are very limited on its use during pregnancy (CIII). • Azole antifungals should be avoided during the first trimester (BIII). • Loperamide should be avoided in the first trimester unless benefits outweigh potential risks of congenital malformations (CIII). Loperamide is the preferred antimotility agent in late pregnancy (CIII). • Opiate exposure in late pregnancy has been associated with neonatal respiratory depression, and chronic exposure may result in neonatal withdrawal; therefore, tincture of opium is not recommended in late pregnancy (AIII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; GI = gastrointestinal; PO = orally Data suggest that treatment with ART enables a person’s own defenses to eradicate microsporidia,12,13 and administration of ART with immune restoration (an increase in CD4 count to >100 cells/mm3) is associated with resolution of symptoms of enteric microsporidiosis, including illness caused by E. bieneusi.12-15 Everyone, therefore, should be offered ART as part of the initial management of microsporidial infection (AII), and they should be given fluid support if they have signs of diarrhea and dehydration (AII). People with malnutrition and wasting should be treated with Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-4 nutritional supplementation (AIII). Antimotility agents can be used if required for diarrhea control (BIII). No specific therapeutic agent is available for E. bieneusi infection. Based on results from a controlled clinical trial, oral fumagillin (60 mg/day), a water-insoluble antibiotic made from Aspergillus fumigatus (BII),16,17 or to its synthetic analog, TNP-470 can be administered (BIII).18 Fumagillin and TNP-470 are not commercially available for systemic use in the United States, and Sanofi in France no longer produces FLISINT (fumagillin). One report indicated that treatment with nitazoxanide might resolve chronic diarrhea caused by E. bieneusi in the absence of ART;19 however, the effect appeared to be minimal among people with low CD4 counts. Based on the professional experience of several experts who have treated diarrhea caused by E. bieneusi with nitazoxanide in organ transplant recipients, nitazoxanide is a reasonable alternative for the treatment of diarrhea due to E. bieneusi if fumagillin is not available (CIII).20 Albendazole, a benzimidazole that binds to β-tubulin, has activity against many species of microsporidia, but it is not effective against E. bieneusi or V. corneae infections. The tubulin genes of both E. bieneusi21 and V. corneae22 have amino acid residues associated with albendazole resistance. Albendazole is recommended only for initial therapy of intestinal and disseminated microsporidiosis caused by microsporidia other than E. bieneusi and V. corneae (AII).23-25 Itraconazole may be useful in disseminated disease when combined with albendazole, especially in infections caused by Trachipleistophora or Anncaliia (CIII). Treatment with furazolidone (an agent that is not currently available in the United States) combined with albendazole was reported to improve clinical signs in four people with HIV with persistent diarrhea and E. bieneusi infection (CIII)26; however, furazolidone has not been demonstrated to be active in other case reports. Metronidazole and atovaquone are not active in vitro or in animal models and should not be used to treat microsporidiosis (AII). People with ocular infections caused by microsporidia should be administered topical Fumidil B (fumagillin bicylohexylammonium) in saline (to achieve a concentration of 70 µg/mL of fumagillin) (BII).23 Topical fumagillin solution needs to be made by a compounding pharmacy because it is not commercially available in the United States and is investigational. Although clearance of microsporidia from the eye can be demonstrated, the organism often is still present systemically and can be detected in urine or in nasal smears; therefore, the use of albendazole as a companion systemic agent to fumagillin is recommended in ocular infections (BIII). Special Considerations with Regard to Starting ART As noted above, people with HIV should be offered ART as part of the initial management of microsporidial infection, as well as fluid support if they have signs of diarrhea and dehydration (AII). Data suggest that treatment with ART, which results in immune reconstitution, enables a person’s own defenses to eradicate microsporidia.12,13 Monitoring of Response to Therapy and Adverse Events (Including IRIS) Although side effects with albendazole are rare, hepatic enzymes should be monitored because elevations have been reported. Albendazole is not known to be carcinogenic or mutagenic. Topical fumagillin has not been associated with substantial side effects. Oral fumagillin has been associated with thrombocytopenia, which is reversible after stopping the drug. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-5 One report of immune reconstitution inflammatory syndrome (IRIS) has been described in a person with HIV treated with ART in the setting of E. bieneusi infection;27 however, no IRIS reactions have been reported with other species of microsporidia or with other cases of E. bieneusi. Concerns about IRIS should not alter therapy or the use of ART (AIII). Managing Treatment Failure Supportive treatment and optimization of ART to attempt to achieve full virologic suppression are the only currently feasible approaches to managing treatment failure (AIII). Preventing Recurrence In individuals with relatively competent immune systems (>200 CD4 cells/mm3), treatment should be discontinued after ocular infection resolves (CIII); treatment should be continued indefinitely if CD4 counts fall below 200 cells/mm3 because recurrence or relapse may occur after treatment discontinuation (BIII). Whether it is safe to discontinue treatment for other manifestations after immune restoration with ART is unknown. Based on experience with discontinuation of secondary prophylaxis for other opportunistic infections, it is reasonable to discontinue chronic maintenance therapy in those who no longer have signs and symptoms of microsporidiosis and have a sustained increase in their CD4 counts to >200 cells/mm3 for 3 to 6 months after ART (BIII).13 Special Considerations During Pregnancy Rehydration and initiation of ART are the preferred initial treatment of microsporidiosis during pregnancy, as in nonpregnant people (AII). In rats and rabbits, albendazole is embryotoxic and teratogenic at exposure levels less than those estimated with therapeutic human dosing. There are no adequate and well-controlled studies of albendazole exposure in early human pregnancy. A recent randomized trial in which albendazole was used for second-trimester treatment of soil-transmitted helminth infections found no evidence of teratogenicity or other adverse pregnancy effects.28 Based on these data, albendazole is not recommended for use during the first trimester (BIII); use in later pregnancy should be considered only if benefits outweigh potential risks (CIII). Systemic fumagillin has been associated with increased resorption and growth retardation in rats. No data on use in human pregnancy are available. However, because of the antiangiogenic effect of fumagillin, this drug should not be used systemically in pregnant people (AIII). Topical fumagillin has not been associated with embryotoxic or teratogenic effects and can be considered when therapy with this agent is appropriate (CIII). Furazolidone is not teratogenic in animal studies, but human data are limited to a case series that found no association between first-trimester use of furazolidone and birth defects in 132 furazolidone-exposed pregnancies.29 Nitazoxanide has not been associated with adverse outcomes in pregnancy; however, data are very limited on its use during pregnancy (CIII). Case reports exist of birth defects in infants exposed to itraconazole, but prospective cohort studies of >300 women with first-trimester exposure did not show an increased risk of malformation.30,31 In general, however, azole antifungals should be avoided during the first trimester (BIII). Loperamide is poorly absorbed and has not been associated with birth defects in animal studies; however, a recent study identified an increased risk of congenital malformations, specifically hypospadias, among 683 women with exposure to loperamide in early pregnancy.32 Therefore, loperamide should be avoided in the first trimester unless benefits outweigh potential risks (CIII). Loperamide is the preferred antimotility agent in late pregnancy (CIII). Opiate exposure in late pregnancy has been Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-6 associated with neonatal respiratory depression, and chronic exposure may result in neonatal withdrawal; therefore, tincture of opium is not recommended in late pregnancy (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-7 References 1. James TY, Pelin A, Bonen L, et al. Shared signatures of parasitism and phylogenomics unite Cryptomycota and microsporidia. Curr Biol. 2013;23(16):1548-1553. Available at: 2. Beauvais B, Sarfati C, Molina JM, Lesourd A, Lariviere M, Derouin F. Comparative evaluation of five diagnostic methods for demonstrating microsporidia in stool and intestinal biopsy specimens. Ann Trop Med Parasitol. 1993;87(1):99-102. Available at: 3. Deplazes P, Mathis A, Weber R. Epidemiology and zoonotic aspects of microsporidia of mammals and birds. Contrib Microbiol. 2000;6:236-260. Available at: 4. Kotler DP, Orenstein JM. Clinical syndromes associated with microsporidiosis. Adv Parasitol. 1998;40:321-349. Available at: 5. Mathis A. Microsporidia: emerging advances in understanding the basic biology of these unique organisms. Int J Parasitol. 2000;30(7):795-804. Available at: 6. Weber R, Bryan RT, Owen RL, Wilcox CM, Gorelkin L, Visvesvara GS. Improved light-microscopical detection of microsporidia spores in stool and duodenal aspirates. The Enteric Opportunistic Infections Working Group. N Engl J Med. 1992;326(3):161-166. Available at: 7. Weiss LM, Vossbrinck CR. Microsporidiosis: molecular and diagnostic aspects. Adv Parasitol. 1998;40:351-395. Available at: 8. Wittner M, Weiss L. The microsporidia and microsporidiosis. Washington D.C.: ASM Press; 1999. 9. Stark D, Barratt JL, van Hal S, Marriott D, Harkness J, Ellis JT. Clinical significance of enteric protozoa in the immunosuppressed human population. Clin Microbiol Rev. 2009;22(4):634-650. Available at: 10. Sheoran AS, Feng X, Singh I, et al. Monoclonal antibodies against Enterocytozoon bieneusi of human origin. Clin Diagn Lab Immunol. 2005;12(9):1109-1113. Available at: 11. Didier ES, Weiss LM. Microsporidiosis: current status. Curr Opin Infect Dis. 2006;19(5):485-492. Available at: 12. Goguel J, Katlama C, Sarfati C, Maslo C, Leport C, Molina JM. Remission of AIDS-associated intestinal microsporidiosis with highly active antiretroviral therapy. AIDS. 1997;11(13):1658-1659. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-8 13. Miao YM, Awad-El-Kariem FM, Franzen C, et al. Eradication of cryptosporidia and microsporidia following successful antiretroviral therapy. J Acquir Immune Defic Syndr. 2000;25(2):124-129. Available at: 14. Conteas CN, Berlin OG, Speck CE, Pandhumas SS, Lariviere MJ, Fu C. Modification of the clinical course of intestinal microsporidiosis in acquired immunodeficiency syndrome patients by immune status and anti-human immunodeficiency virus therapy. Am J Trop Med Hyg. 1998;58(5):555-558. Available at: 15. Maggi P, Larocca AM, Quarto M, et al. Effect of antiretroviral therapy on cryptosporidiosis and microsporidiosis in patients infected with human immunodeficiency virus type 1. Eur J Clin Microbiol Infect Dis. 2000;19(3):213-217. Available at: 16. Molina JM, Goguel J, Sarfati C, et al. Trial of oral fumagillin for the treatment of intestinal microsporidiosis in patients with HIV infection. ANRS 054 Study Group. Agence Nationale de Recherche sur le SIDA. AIDS. 2000;14(10):1341-1348. Available at: 17. Molina JM, Tourneur M, Sarfati C, et al. Fumagillin treatment of intestinal microsporidiosis. N Engl J Med. 2002;346(25):1963-1969. Available at: 18. Didier PJ, Phillips JN, Kuebler DJ, et al. Antimicrosporidial activities of fumagillin, TNP-470, ovalicin, and ovalicin derivatives in vitro and in vivo. Antimicrob Agents Chemother. 2006;50(6):2146-2155. Available at: 19. Bicart-See A, Massip P, Linas MD, Datry A. Successful treatment with nitazoxanide of Enterocytozoon bieneusi microsporidiosis in a patient with AIDS. Antimicrob Agents Chemother. 2000;44(1):167-168. Available at: 20. Saffo Z, Mirza N. Successful treatment of Enterocytozoon bieneusi gastrointestinal infection with nitazoxanide in a immunocompetent patient. IDCases. 2019;18:e00586. Available at: 21. Akiyoshi DE, Weiss LM, Feng X, et al. Analysis of the beta-tubulin genes from Enterocytozoon bieneusi isolates from a human and rhesus macaque. J Eukaryot Microbiol. 2007;54(1):38-41. Available at: 22. Franzen C, Salzberger B. Analysis of the beta-tubulin gene from Vittaforma corneae suggests benzimidazole resistance. Antimicrob Agents Chemother. 2008;52(2):790-793. Available at: 23. Diesenhouse MC, Wilson LA, Corrent GF, Visvesvara GS, Grossniklaus HE, Bryan RT. Treatment of microsporidial keratoconjunctivitis with topical fumagillin. Am J Ophthalmol. 1993;115(3):293-298. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV T-9 24. Dieterich DT, Lew EA, Kotler DP, Poles MA, Orenstein JM. Treatment with albendazole for intestinal disease due to Enterocytozoon bieneusi in patients with AIDS. J Infect Dis. 1994;169(1):178-183. Available at: 25. Molina JM, Chastang C, Goguel J, et al. Albendazole for treatment and prophylaxis of microsporidiosis due to Encephalitozoon intestinalis in patients with AIDS: a randomized double-blind controlled trial. J Infect Dis. 1998;177(5):1373-1377. Available at: 26. Dionisio D, Manneschi LI, Di Lollo S, et al. Persistent damage to Enterocytozoon bieneusi, with persistent symptomatic relief, after combined furazolidone and albendazole in AIDS patients. J Clin Pathol. 1998;51(10):731-736. Available at: 27. Sriaroon C, Mayer CA, Chen L, Accurso C, Greene JN, Vincent AL. Diffuse intra-abdominal granulomatous seeding as a manifestation of immune reconstitution inflammatory syndrome associated with microsporidiosis in a patient with HIV. AIDS Patient Care STDS. 2008;22(8):611-612. Available at: 28. Ndyomugyenyi R, Kabatereine N, Olsen A, Magnussen P. Efficacy of ivermectin and albendazole alone and in combination for treatment of soil-transmitted helminths in pregnancy and adverse events: a randomized open label controlled intervention trial in Masindi district, western Uganda. Am J Trop Med Hyg. 2008;79(6):856-863. Available at: 29. Heinonen OP, Slone D, Shapiro S. Birth defects and drugs in pregnancy. Littleton: Publishing Sciences Group; 1977. 30. De Santis M, Di Gianantonio E, Cesari E, Ambrosini G, Straface G, Clementi M. First-trimester itraconazole exposure and pregnancy outcome: a prospective cohort study of women contacting teratology information services in Italy. Drug Saf. 2009;32(3):239-244. Available at: 31. Bar-Oz B, Moretti ME, Bishai R, et al. Pregnancy outcome after in utero exposure to itraconazole: a prospective cohort study. Am J Obstet Gynecol. 2000;183(3):617-620. Available at: 32. Kallen B, Nilsson E, Otterblad Olausson P. Maternal use of loperamide in early pregnancy and delivery outcome. Acta Paediatr. 2008;97(5):541-545. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-1 Mpox Updated: July 24, 2023 Reviewed: January 10, 2024 Epidemiology Mpox is a zoonotic viral disease caused by mpox virus, an enveloped double-stranded DNA virus that belongs to the same Orthopoxvirus genus of the Poxviridae family as the causative agent of smallpox. Mpox virus circulates among certain small mammals found in the forested regions of some parts of Africa, creating a reservoir of disease in the animal population. This reservoir is believed to have been the source of the sporadic human outbreaks that have occurred in certain African countries since the first cases were identified in the 1970s until the recent 2022 multinational mpox outbreak.1 Two distinct clades of mpox virus have been described in different geographic regions of Africa; Clade I (previously called Congo Basin clade) was classically associated with more severe disease and more human-to-human transmission than Clade II (previously called West African clade).2,3 Historically, risk for serious infection and death has been greatest for children <8 years of age as well as developing fetuses infected perinatally.4 The epidemiology of Clade II mpox has evolved as human cases of mpox outside of Africa have been identified.5 The first notable mpox outbreak occurred in the United States in 2003 and was associated with the importation of small African mammals; transmission occurred through direct contact or contaminated fomites.6 Mpox also re-emerged in countries like Nigeria, which saw a large outbreak in 2017 and 2018 after decades without human cases.7,8 However, from 2018 until May 2022, all cases involved persons traveling from endemic areas to other nations, including the United Kingdom (4 cases), Singapore (1 case), Israel (1 case), and the United States (2 cases).9-14 In May 2022, a large multinational outbreak of Clade II mpox was recognized. Multiple lineages of mpox virus were detected in the United States during the early months of the outbreak, suggesting multiple introductions of mpox worldwide and raising concerns for future outbreaks.15 The majority of infections in 2022 were transmitted sexually through intimate contact with one or more mpox lesions on the skin or mucosal surfaces of people with mpox infection.16 Infections have disproportionately affected gay, bisexual, same-gender-loving, and other men who have sex with men (MSM). Notably, infections in women and children and occupational infections transmitted to health care personnel through injury with contaminated sharps also have been reported.17-25 Among MSM, coinfection with HIV and other sexually transmitted infections (STIs) has been common.17 Across reports, around 40% to 50% of cases have been in people with HIV, and around 15% to 30% of cases have been diagnosed concomitantly with gonorrhea, syphilis, chlamydia, or other STIs.17,18,26,27 Severe and fatal cases have disproportionately been reported in people with HIV, especially among people with advanced or uncontrolled HIV.28-39 Although the overall mortality rate for Clade II infection is low (<1%), mortality among people with advanced HIV has been higher.8,36-39 Clinical Manifestations In outbreaks prior to 2022, mpox cases had been characterized by prodromal symptoms of fever, headache, lymphadenopathy, myalgias, or fatigue followed by a distinctive rash that progresses synchronously from macules to papules, vesicles, pustules, and, ultimately, crusted lesions. In prior Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-2 outbreaks, some cases among people with HIV were identified; these cases involved longer duration of illness, larger size of lesions, more frequent secondary bacterial infections, and presence of genital ulcers.8,38 In the 2022 multinational mpox outbreak, the clinical manifestations associated with Clade II infection were distinct in several respects.18,40 Prodromal symptoms have been mild or absent and have not always preceded the rash.40 Rash commonly occurs as anogenital or oropharyngeal/perioral lesions, with rash involving the limbs, face, and trunk also occurring.18,40 Lesions can be single or multiple and limited to a single body site and also can progress in varying stages.18,40 Inguinal, cervical, and/or axillary lymphadenopathy may be present, similar to historic outbreaks, but not as reliably as with classic presentations.40 Most patients, including those with well-controlled HIV, experience self-limiting disease and recover with supportive care alone.41 For a subset of patients, infection can be more severe.41 Pharyngeal involvement can result in tonsillitis or pharyngitis associated with odynophagia or dysphagia.18 Anorectal involvement has caused tenesmus, proctitis, and rectal bleeding, which can be severe.18,42 Inflammation from genital lesions can produce dysuria occasionally complicated by significant paraphimosis/phimosis or urethritis that limits the ability to urinate.39,43,44 Severe gastrointestinal manifestations, such as enteritis or colitis, and anogenital involvement can necessitate hospitalization for enhanced symptom control, including pain management.18,39,44 Lesions have led to stricture and scar formation, causing urethral or bowel obstruction.39,44 Ocular involvement from autoinoculation can result in conjunctivitis, blepharitis, keratitis, corneal ulcer with possible scarring, and, in rare cases, loss of vision.45-47 Bacterial superinfections (e.g., staphylococcal skin and soft tissue infections) can also occur.39 Other reported manifestations have included nodular pulmonary disease, encephalitis and transverse myelitis, myocarditis and pericarditis, septic arthritis, viral “cold abscesses,” and genital necrosis.39,48,49 During the current outbreak, cases among pediatric patients and pregnant people have been less common and have not yet been associated with severe disease.50,51 People who are significantly immunocompromised, most commonly from poorly controlled HIV (CD4 T lymphocyte [CD4] cell count <350 cells/mm3 and especially <50 cells/mm3), have experienced more severe infections, including increased likelihood of hospitalization and disseminated disease, likely because their weakened immune systems are unable to clear the virus.28-39 These more severe manifestations can include coalescing or necrotic lesions involving areas of skin (including genitalia) that require surgical debridement and that can continue to progress despite initiation of medical treatment for mpox (see Treating Disease below).52 Patients’ illness can continue to worsen if immune function is not restored, resulting in death.39 Diagnosis Clinical presentation with symptoms such as a characteristic rash associated with mpox lesions is strongly suggestive of mpox.53 However, diagnosis of mpox based solely on clinical presentation can be challenging due to the protean appearance of mpox lesions. Mpox lesions can mimic lesions seen in other infections such as herpes zoster, as well as STIs such as syphilis, herpes simplex, and molluscum contagiosum. For this reason, and due to the high frequency of coinfection with STIs seen during the multinational 2022 Clade II mpox outbreak, a broad differential diagnosis is encouraged for all people undergoing evaluation for mpox, and screening for STIs, including HIV, is recommended.17 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-3 Mpox is typically confirmed by the presence of mpox virus DNA in a clinical specimen using the polymerase chain reaction (PCR).16,53 The recommended specimen is skin lesion material, which can include swabs of a lesion’s surface, lesion exudate, or lesion crusts. In the absence of a lesion on epithelialized skin, specimens from mucosal (e.g., oropharynx, saliva, anorectum) lesions or tissues can support diagnosis of mpox. Unroofing or aspiration of lesions is neither required nor recommended and has led to occupational infections from injuries with contaminated sharps; vigorous swabbing of lesion surfaces alone is sufficient.22,23,54 Testing is available through state public health laboratories and multiple commercial laboratories. The diagnosis of mpox can also be established by serologic testing demonstrating detectable levels of anti-Orthopoxvirus immune globulin M antibody during the period of 4 to 56 days after rash onset in the absence of recent mpox vaccination.53 If there is high clinical suspicion for mpox and inconclusive or negative testing via PCR or antibody testing, additional testing—such as next-generation sequencing, viral culture to demonstrate the presence of replication-competent virus, biopsy with immunohistochemical staining to demonstrate the presence of viral antigen, or electron microscopy to demonstrate the presence of characteristic viral particles—can be used to confirm the diagnosis, but these diagnostic technologies have varying availability.53 Preventing Exposure Strategies to prevent mpox exposure are similar for people with and without HIV.55 Regardless of vaccination, people with HIV at risk for mpox should avoid skin-to-skin or other close intimate contact (including sex) with people who may have constitutional symptoms or a rash suspicious for mpox, avoid contact with contaminated surfaces or objects (including linens) used by a person with mpox, and perform frequent hand hygiene after touching rash material or surfaces that may have had contact with rash material (AIII). Condoms or other barrier methods may provide additional protection during sex or other intimate activity. During active mpox outbreaks when rates of community transmission may be high, it is recommended that people (including people with HIV) be counseled about the value of reducing their number of sexual partners and limiting visits to venues where group sex or other prolonged skin-to-skin contact is possible (CIII). Recommendations regarding the use of personal protective equipment and other infection control practices when clinically managing patients with mpox can be found at the CDC web page on Infection Prevention and Control of Mpox in Healthcare Settings. Of particular note, sharps should not be used to unroof lesions when collecting diagnostic samples. Self-inoculation with sharps contaminated with mpox via penetrating wound injuries has been the leading cause of health care-associated infections.22-25 Preventing Disease Recommendations for Preventing Mpox Infection Vaccination Before Mpox Exposure • Indications o Mpox vaccination should be offered to all people with HIV who have potential for mpox exposure or anticipate potential exposure to mpox per CDC interim clinical considerations (BII). o Mpox vaccination should be provided to any other people with HIV who request vaccination (CII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-4 • Vaccination o MVA-BN vaccine, sold in the United States as JYNNEOS, is the preferred vaccine before mpox exposure and is safe to use in people with HIV; administer JYNNEOS in two doses (0.1 mL ID or 0.5 mL SQ) 28 days apart (AII). o Administration of live, replicating vaccinia vaccines (i.e., ACAM2000) to pregnant or immunocompromised people, including people with HIV, is contraindicated (AII). Vaccination Following Mpox Exposure • Indications o For unvaccinated people with HIV who experience a known or presumed exposure, post-exposure vaccination is recommended as soon as possible, ideally within 4 days after exposure; however, administration 4 to 14 days after exposure may still provide some protection against mpox and should be offered (BII). • Vaccination o JYNNEOS is the preferred vaccine following mpox exposure and is safe to use in people with HIV; administer JYNNEOS in two doses (0.1 mL ID or 0.5 mL SQ) 28 days apart as soon as possible and within 14 days after exposure to mpox (AII). o Administration of live, replicating vaccinia vaccines (i.e., ACAM2000) to pregnant, breastfeeding, or immunocompromised individuals, including people with HIV, is contraindicated (AII). Alternative Post-Exposure Prophylaxis • On a case-by-case basis and in consultation with an infectious disease expert, people with HIV who have advanced immunosuppression or a contraindication to vaccination can consider— o Tecovirimat 600 mg PO every 12 hours (people weighing 40 kg to <120 kg) or every 8 hours (patients weighing ≥120 kg) for 14 days (CIII), or o VIGIV 6,000–9,000 units/kg IV single dose (CIII) • NOTE: There are no clinical data regarding the effectiveness of mpox post-exposure prophylaxis with these agents. Key: CDC = Centers for Disease Control and Prevention; ID = intradermal; MVA-BN = modified vaccinia Ankara-Bavarian Nordic; IV = intravenous; PO = orally; SQ = subcutaneous; VIGIV = vaccinia immune globulin intravenous Vaccination is the principal biomedical means of preventing mpox. Mpox vaccination should be offered to all people with HIV who have potential for mpox exposure or anticipate potential exposure to mpox per Centers for Disease Control and Prevention (CDC) interim clinical considerations (BII). Additionally, mpox vaccination should be provided to any other people with HIV who request vaccination (CII). For unvaccinated people with HIV who experience a known or presumed exposure, post-exposure vaccination is recommended as soon as possible, ideally within 4 days after exposure; however, administration 4 to 14 days after exposure may still provide some protection against mpox and should be offered (BII). At this time, vaccination recommendations are in the context of a rapidly evolving multinational mpox outbreak. For current mpox vaccination recommendations, please see CDC’s interim clinical considerations. People with HIV who are eligible for vaccination against mpox should receive modified vaccinia Ankara (MVA) vaccines (AII), a live, non-replicating viral vaccine sold as JYNNEOS in the United States and as IMVANEX or IMVAMUNE elsewhere. JYNNEOS consists of two doses given 4 weeks (28 days) apart. CDC’s interim clinical considerations for mpox vaccination recommend vaccine administration either subcutaneously or intradermally—both have been found to be effective.56 For JYNNEOS, if the second dose is not administered during the recommended interval, it should be administered as soon as possible (CIII). There is no need to restart or add doses to the Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-5 series if there is an extended interval between doses (CIII). People who have received smallpox vaccination more than 10 years ago should still receive two doses of JYNNEOS (CIII). Use of live, replicating vaccinia vaccines, such as ACAM2000, is contraindicated in immunocompromised individuals, including people with HIV, due to the risk of serious complications from the enhanced replication and dissemination of vaccinia virus (AII).57 JYNNEOS has been demonstrated to be both safe for people with HIV and equally immunogenic in people with HIV as in people without HIV.58-60 However, these studies were limited to people who were virologically suppressed and had CD4 counts ≥100 cells/mm3. Immunogenicity among people with HIV who are not virologically suppressed or have lower CD4 counts remains unknown. Several studies indicate that JYNNEOS is effective against mpox.61-67 Matched case control study data indicate that vaccine effectiveness against symptomatic infection ranges from 36-75% after one dose to 66-89% after two doses.65-67 However, all studies to date have had insufficient data to assess the effectiveness of JYNNEOS against mpox by HIV status or CD4 count, and immunologic correlates of protection have not yet been established. For people with HIV who have advanced immunosuppression or a contraindication to vaccination, tecovirimat or vaccinia immune globulin intravenous (VIGIV) can be used for mpox post-exposure prophylaxis on a case-by-case basis in consultation with an infectious diseases expert and CDC (CIII); however, there are no clinical data regarding the effectiveness of mpox post-exposure prophylaxis with these agents. Per U.S. Food and Drug Administration (FDA) labeling, VIGIV might theoretically impair the efficacy of live attenuated virus vaccines; however, the extent to which it might affect live but non-replicating vaccines, such as JYNNEOS, is unclear.68 Vaccination with any live virus vaccines should be delayed until 3 months after VIGIV administration (CIII).68 People who received VIGIV shortly after a live virus vaccination should be revaccinated 3 months after administration of the immune globulin (CIII).68 Treating Disease Recommendations for Treating Mpox • People not presently taking ART should initiate treatment as soon as possible (AIII). Preferred Therapy for Severe Disease or at Risk for Severe Disease • Tecovirimat 600 mg PO every 12 hours (<120 kg) or every 8 hours (≥120 kg) for 14 days (BIII) within 30 minutes of a fatty meal; or • Tecovirimat 200 mg IV every 12 hours for 14 days (<120 kg) or 300 mg IV every 12 hours (≥ 120 kg), if concern exists regarding altered gastrointestinal absorption capacity, the inability to take PO, or the extent of organ systems affected by mpox (BIII). • NOTE: Patients with severe immunocompromise might benefit from extended treatment (i.e., >14 days) of preferred or adjunctive therapies if new confirmed mpox lesions occur or existing lesions worsen despite treatment. • NOTE: For severe disease, the Panel recommends early intervention with combination therapy at the time of the first medical encounter, in consultation with CDC or an expert in mpox treatment (CIII). Adjunctive Therapy for Severe Disease or at Risk for Severe Disease Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-6 • Cidofovir 5 mg/kg/week IV for two doses with saline hydration before and after therapy and probenecid 2 g PO 3 hours before the dose followed by 1 g PO 2 hours after the dose, and 1 g PO 8 hours after the dose (total of 4 g) (BIII), or o Cidofovir is contraindicated in patients with a serum creatinine >1.5 mg/dL, a calculated creatinine clearance ≤55 mL/min, or a urine protein ≥100 mg/dL (equivalent to ≥2+ proteinuria). Given the nephrotoxic potential of cidofovir, cautious use of cidofovir with tenofovir is advised. This regimen should be avoided in patients with sulfa allergy because of cross-hypersensitivity with probenecid. • Brincidofovir 200 mg PO once weekly for two doses (BIII), or • VIGIV 6,000–9,000 units/kg IV single dose (BIII) o NOTE: Vaccination with any live virus vaccines should be delayed until 3 months after VIGIV administration (CIII). People who received VIGIV shortly after a live virus vaccination should be revaccinated 3 months after administration of the immune globulin (CIII). • NOTE: Consultation with local health department and/or CDC should be obtained prior to initiating the above therapies. Preferred Therapy for Ocular Mpox • Tecovirimat 600 mg PO every 12 hours (<120 kg) or every 8 hours (≥120 kg) for 14 days (CIII) within 30 minutes of a fatty meal, and • Trifluridine (Viroptic) 1 drop into affected eye(s) every 2 hours when awake (max: 9 drops/day) until reepithelialization, then every 4 hours (min: 5 drops/day) for 7 days or until all periocular lesions have healed (CIII) o Prolonged use of trifluridine beyond 21 days might cause corneal epithelial toxicity and should be avoided (AII). • NOTE: Trifluridine should be used in consultation with an ophthalmologist. Other Considerations • CDC offers a clinical consultation service (email eocevent482@cdc.gov), or health care providers may contact the CDC Emergency Operations Center (EOC) at 770-488-7100, where CDC can provide additional guidance to clinicians with patient management questions. • Patients with mpox benefit from supportive care and pain control that is implemented early in the illness (BIII). Pregnancy Considerations • Tecovirimat can be used as a first-line antiviral for people who are pregnant, recently pregnant, or breastfeeding (BIII). • In animal studies, cidofovir and brincidofovir have been shown to be teratogenic; therefore, these agents are not recommended for use in pregnancy (AIII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CDC = Centers for Disease Control and Prevention; IV = intravenous; the Panel = Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV; PO = orally; VIGIV = vaccinia immune globulin intravenous People with HIV who are not virologically suppressed or who have CD4 counts <350 cells/mm3 are considered at high risk for severe mpox. Severe mpox might manifest as hemorrhagic disease; a large number of lesions such that they are confluent; sepsis; encephalitis; ocular or periorbital infections; or other conditions requiring hospitalization. For people with well-controlled HIV, mpox is typically a self-limiting illness that resolves spontaneously without antiviral treatment. However, people with HIV who are not virologically suppressed, who have CD4 counts <350 cells/mm3, or who are otherwise severely immunocompromised can experience prolonged severe illness with serious sequelae and are therefore candidates for antiviral treatment.41 See the CDC’s Mpox Clinical Considerations for more information. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-7 If therapy is considered, oral tecovirimat should be administered as first-line treatment (BIII). Tecovirimat, which inhibits the Orthopoxvirus VP37 envelope-wrapping protein, is available as an oral capsule or intravenous (IV) injection. The decision to use oral or IV tecovirimat should be based on the severity of illness (e.g., extent of other organ systems affected by mpox, presence of coalescing non-healing lesions), other comorbidities that could contribute to greater severity of illness, expected adherence to the oral formulation, and gastrointestinal absorption capacity.41 Oral tecovirimat requires intact gastrointestinal absorption and the ability to consume a high-fat meal (600 calories and 25 g fat) to support absorption, which may pose a challenge.69 Tecovirimat should be administered early in the course of illness for patients with advanced HIV, along with supportive care and pain control (BIII). Studies using a variety of animal models have shown that tecovirimat is effective in treating Orthopoxvirus disease.70-72 Human clinical trials have demonstrated the drug had an acceptable safety profile.71,73,74 A case report from the United Kingdom has suggested that tecovirimat may shorten the duration of mpox illness and mpox viral shedding.75 There are ongoing clinical trials to assess the efficacy of tecovirimat to treat mpox.76-78 Tecovirimat can be provided under an expanded access investigational new drug (IND) protocol or through clinical trials. IV cidofovir or oral brincidofovir can be used as adjunctive therapy in people with severe manifestations of mpox or at risk of severe manifestations (BIII). Cidofovir, which acts via competitive inhibition of DNA polymerase to block DNA synthesis of many DNA viruses, is an FDA-approved antiviral medication for the treatment of cytomegalovirus (CMV) retinitis in people with advanced HIV. Brincidofovir, available orally as a tablet or suspension, is a prodrug of cidofovir that acts similarly and is thought to have less toxicity. Human data are not available on the effectiveness of cidofovir or brincidofovir to treat mpox in people with HIV. However, in vitro and animal studies have demonstrated that these drugs are effective against other Orthopoxviruses.79-84 Data from animal models suggest that the combination of tecovirimat and brincidofovir may act synergistically to improve outcomes and could be considered for patients with disseminated infection (CIII).85 Cidofovir or brincidofovir can be used for people with or at risk for severe disease or people who experience clinically significant progression while receiving tecovirimat, develop recrudescence of disease after an initial period of improvement while receiving tecovirimat, or are otherwise ineligible to receive oral or IV tecovirimat (BIII). Brincidofovir is available from federal partners to clinicians who request and obtain a single-patient emergency use IND authorization for treatment of mpox. Clinicians should consider the side effect profiles of both medications when deciding on their use. VIGIV can be used in severe cases where the development of a robust antibody response may be impaired (BIII). Data are not available on the effectiveness of VIGIV to treat mpox in people with HIV. In animal models using non-human primates, vaccine-induced vaccinia antibodies were protective against lethal challenge with mpox virus. The benefit of VIGIV for treatment of severe mpox is unknown. VIGIV is administered under an expanded access IND. Subsequent dosing (i.e., redosing) decisions should be made on a case-by-case basis in consultation with CDC and can be considered when: mpox lesions affect a large percentage of a patient’s body surface at the time of diagnosis; new lesions (or expanding borders on existing lesions) emerge several days after VIGIV; lesions affect mobility or are concerning for long-term sequelae, such as sexual dysfunction; or adverse events or contraindications preclude maximal use of other medical countermeasures.41 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-8 Depending on the severity of immunocompromise and uncontrolled viral replication, these additional therapies to tecovirimat (i.e., VIGIV and brincidofovir or cidofovir) can be considered after balancing the benefits and harms. In severe cases, the Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV recommends early intervention with combination therapy at the time of the first medical encounter, in consultation with CDC or an expert in mpox treatment (CIII). The role of topical therapy in the treatment of mpox remains unknown. Topical cidofovir has been used for skin lesions with mixed success.86,87 For ocular involvement, trifluridine, in addition to systemic therapy, can be used in cases of mpox virus conjunctivitis and is recommended in cases of mpox virus keratitis, in consultation with an ophthalmologist (CIII).45,88,89 Prolonged use of trifluridine beyond 21 days might cause corneal epithelial toxicity and should be avoided (AII).90 Treatments for mpox have the potential for complex and possibly bidirectional interactions with certain antiretroviral agents. Drug–Drug Interactions tables in the Adult and Adolescent Antiretroviral Guidelines describe such interactions and recommendations for therapeutic drug monitoring and dosage adjustments, where feasible. Special Considerations with Regard to Starting Antiretroviral Therapy People with HIV not presently taking antiretroviral therapy (ART) should initiate treatment as soon as possible to improve T and B cell function, which have key roles in modulating mpox disease severity and preventing mortality (AIII).41,91-93 In people with advanced HIV (e.g., CD4 count <350 cells/mm3), those whose HIV viral load is unsuppressed, or those who otherwise merit treatment for mpox, ART should ideally be started at the same time as mpox therapy (AIII). Monitoring of Response to Therapy and Adverse Events (Including Immune Reconstitution Inflammatory Syndrome) As with other opportunistic infections in people with advanced HIV, dysregulated immune responses, such as immune reconstitution inflammatory syndrome (IRIS), following initiation of ART have been raised as a potential concern.35 IRIS could lead to paradoxical worsening or a protracted course of mpox disease. Data are insufficient to inform recommendations on identification and management of dysregulated immune responses in the setting of mpox infection in people with advanced HIV. Providing passive immunity with the use of VIGIV and extending the duration of antivirals such as tecovirimat should be considered pending immune recovery (CIII). VIGIV has an estimated half-life of up to 3 weeks. If immune reconstitution is slow, repeat dosing should be considered on a case-by-case basis, as noted above (BIII). Monitoring is recommended during and after treatment of mpox to detect toxicity, as well as persistence or recurrence of mpox. The most common adverse effects of tecovirimat are headache and nausea.69 After the treating clinician has assessed the risks and benefits and determined that IV tecovirimat is clinically necessary, the IV formulation should be used with caution in patients with severe renal impairment (creatinine clearance [CrCl] <30 mL/min) due to accumulation of an excipient in the IV formulation (hydroxypropyl-beta-cyclodextrin) that has shown potential for nephrotoxicity at very high exposure levels. If the IV formulation is used, closely monitor renal function; if renal toxicity is suspected, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-9 switching to oral tecovirimat, if possible, or an alternative agent can be considered in consultation with CDC. Adverse effects of cidofovir include dose-related nephrotoxicity, neutropenia, uveitis, and hypotony (low intraocular pressure).94 The risk of severe renal injury from IV cidofovir can be reduced by prehydration and oral probenecid before and after cidofovir administration. In patients receiving IV cidofovir, analysis of blood urea nitrogen and creatinine levels and urinalysis should be performed before each infusion.94 Drug administration is contraindicated if renal dysfunction or substantial proteinuria is detected (a serum creatinine >1.5 mg/dL, creatinine clearance ≤55 mL/min, or a urine protein ≥100 mg/dL [equivalent to ≥2+ proteinuria]).94 Particular attention is needed for patients receiving other potentially nephrotoxic medications, including tenofovir disoproxil fumarate.94 Periodic ophthalmologic examinations are needed to monitor for cidofovir-associated uveitis or hypotony.94 Adverse effects of brincidofovir include diarrhea, nausea, and other gastrointestinal adverse events and elevations in hepatic enzymes (e.g., alanine transaminase, aspartate aminotransferase) and bilirubin.95 Brincidofovir-induced diarrhea may impair absorption of oral tecovirimat. Screening for liver test abnormalities should be performed before starting therapy and repeat testing for follow-up as clinically indicated.95 Since brincidofovir is usually given only in two doses 1 week apart, monitoring of liver function parameters is generally done before the second dose (Day 8).95 If serum aminotransferases are elevated and persist above 10 times the upper limit of normal, consider not giving the second dose of brincidofovir.95 The second and final dose of brincidofovir should not be given on Day 8 if elevation of serum aminotransferases is accompanied by clinical signs and symptoms of liver inflammation or increasing direct bilirubin, alkaline phosphatase, or international normalized ratio.95 Male patients should be counseled on the risk for irreversible effects on male fertility based on testicular toxicity observed in animal studies (AII).95 Individuals of childbearing potential should use effective contraception and/or condoms during treatment and for at least 4 months after the last dose (AIII).95 Managing Treatment Failure Clinical failure of therapy for mpox might be more likely in patients who do not have substantial immune reconstitution after initiation or optimization of ART or who are otherwise severely immunocompromised. Treatment failure can also result from inadequate tecovirimat levels secondary to inadequate gastrointestinal absorption, drug resistance, or nonadherence. Lesions may continue to develop after a 14-day course of tecovirimat. If clinical manifestations do not improve, symptoms progress despite the use of oral tecovirimat, or there are concerns about gastrointestinal absorption, IV tecovirimat should be initiated if not already being used (BIII). In these cases, the addition of other therapeutics, including brincidofovir or cidofovir and VIGIV should also be assessed. Extending the duration of tecovirimat treatment should be done carefully, through short increments of time and close clinical monitoring for safety signals and clinical response (BIII). The use of topical or ablative therapies for progressive hypertrophic lesions has been reported, but their role is still under exploration.96 Consultation with an infectious diseases specialist, dermatology, and wound care services should be sought. CDC offers a clinical consultation service (email eocevent482@cdc.gov), or health care providers may contact the CDC Emergency Operations Center (EOC) at 770-488-7100, where CDC can provide additional guidance to clinicians with patient management questions. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-10 Tecovirimat has a relatively low barrier to viral resistance. Single amino acid substitutions at various locations in the F13L gene coding the viral VP37 drug target confer substantial reductions in tecovirimat’s antiviral activity.69 Genotypic and phenotypic resistance to tecovirimat has been documented in patients with severe immunocompromising conditions who have disseminated and progressive mpox infection and have received or are undergoing prolonged tecovirimat treatment.97 Patients for whom resistance is suspected (e.g., new lesions form after at least 7 days of treatment) or documented can be considered for additional therapeutics, including cidofovir or brincidofovir, and VIGIV. Efforts should be made to restore immune function, such as ensuring people with HIV are receiving effective ART and limiting the use of immunocompromising therapies.41 Clinicians may consider sending repeat sample swabs to the CDC to assess for the continued presence of virus and to assess for evidence of potential viral resistance based on genetic sequencing. Formal tecovirimat sensitivity testing results cannot be used to guide treatment decisions for individual patients for two reasons: first, they require culture-based resistance testing techniques that take weeks to perform (i.e., results cannot be returned in a timely manner); and second, reporting of these results is not permitted under Clinical Laboratory Improvement Amendments. However, the results of tecovirimat susceptibility testing are helpful to public health efforts to monitor for the emergence of tecovirimat resistance. Persistently positive PCR test results are expected until lesions resolve; therefore, subsequent testing of lesion specimens may not be informative unless new lesions or progressive lesions are occurring despite 14 days of tecovirimat treatment. Evaluating trends in PCR cycle threshold (Ct) values may be informative; Ct values ≥35 might suggest that minimal replication-competent virus is present.98 Certain laboratories may be able to test for presence of viable virus with culture techniques, but these results may not be available in a clinically relevant timeframe. Other possible reasons for treatment failure may include a dysregulated immune response with associated inflammation or the presence of another opportunistic infection. If viable mpox virus is still detected by culture, viral replication and ongoing infection may be driving the disease process and antiviral medications should be continued. Biopsy of the affected tissue can be performed in cases with new or atypical lesions where it is unclear if the lesions are primarily due to mpox or another infectious cause, including secondary bacterial or fungal infections, and in cases with significant complications (e.g., mucosal or bowel lesions, severe lymphadenopathy, pulmonary nodular lesions, or severe conjunctivitis). Consultation with infectious diseases specialists and CDC is encouraged. Preventing Recurrence and Reinfection The durability of immunity after infection with mpox or after vaccination is unknown, including among people with HIV. No clinical correlates of immunity have yet been established to guide when booster vaccination may be needed following infection or a primary vaccination series. Special Considerations During Pregnancy Data regarding mpox infection in pregnancy are limited.99,100 It is unknown if pregnant people, including people with HIV, are more susceptible to mpox or if infection is more severe in pregnancy. Mpox can be transmitted to the fetus during pregnancy or to the newborn by close contact during and after birth. Adverse pregnancy outcomes, including spontaneous pregnancy loss and stillbirth, have Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-11 been reported in cases of confirmed mpox infection during pregnancy.4,101 Preterm delivery and neonatal mpox infection have also been reported.50 The signs and symptoms of mpox infection in pregnant people appear similar to those in non-pregnant people, including prodromal symptoms and rash. The approach to diagnosis of mpox in pregnant people is the same as in non-pregnant people. For people who are pregnant, breastfeeding, or trying to become pregnant and who require vaccination, JYNNEOS should be used because it is non-replication competent (AIII). Studies of JYNNEOS vaccine in animals have shown no evidence of harm to the developing fetus.102 Vaccination with ACAM2000, which contains a replication-competent virus, is contraindicated in people who are pregnant or breastfeeding due to risk of pregnancy loss, congenital defects, and vaccinia virus infection in fetuses and newborns and the availability of alternative non-replicating viral vaccine (AII).57 Treatment for mpox should be offered to people who are pregnant, recently pregnant, or breastfeeding (AIII). Tecovirimat can be used as a first-line antiviral for people who are pregnant, recently pregnant, or breastfeeding (BIII). Information about the impact of tecovirimat on reproductive development is limited to animal studies, in which no specific fetal effects were observed.69 It is not known if treatment with tecovirimat during pregnancy prevents congenital mpox. Animal reproduction studies have not been conducted with VIGIV; therefore, it is not known whether VIGIV can cause fetal harm when administered during pregnancy or affect future fertility.68 However, other immune globulins have been widely used during pregnancy for many years without any apparent negative reproductive effects. In animal studies, cidofovir and brincidofovir have been shown to be teratogenic; therefore, these agents are not recommended for use in pregnancy (AIII).94,95 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-12 References 1. Ladnyj ID, Ziegler P, Kima E. A human infection caused by monkeypox virus in Basankusu Territory, Democratic Republic of the Congo. Bull World Health Organ. 1972;46(5):593-597. Available at: 2. Chen N, Li G, Liszewski MK, et al. Virulence differences between monkeypox virus isolates from West Africa and the Congo basin. Virology. 2005;340(1):46-63. Available at: 3. Likos AM, Sammons SA, Olson VA, et al. A tale of two clades: monkeypox viruses. J Gen Virol. 2005;86(Pt 10):2661-2672. Available at: 4. Mbala PK, Huggins JW, Riu-Rovira T, et al. Maternal and fetal outcomes among pregnant women with human monkeypox infection in the Democratic Republic of Congo. J Infect Dis. 2017;216(7):824-828. Available at: 5. Bunge EM, Hoet B, Chen L, et al. The changing epidemiology of human monkeypox-a potential threat? A systematic review. PLoS Negl Trop Dis. 2022;16(2):e0010141. Available at: 6. Centers for Disease Control and Prevention. Update: multistate outbreak of monkeypox—Illinois, Indiana, Kansas, Missouri, Ohio, and Wisconsin, 2003. MMWR Morb Mortal Wkly Rep. 2003;52(27):642-646. Available at: 7. Ogoina D, Yinka-Ogunleye A. Sexual history of human monkeypox patients seen at a tertiary hospital in Bayelsa, Nigeria. Int J STD AIDS. 2022;33(10):928-932. Available at: 8. Yinka-Ogunleye A, Aruna O, Dalhat M, et al. Outbreak of human monkeypox in Nigeria in 2017–18: a clinical and epidemiological report. Lancet Infect Dis. 2019;19(8):872-879. Available at: 9. Vaughan A, Aarons E, Astbury J, et al. Two cases of monkeypox imported to the United Kingdom, September 2018. Euro Surveill. 2018;23(38). Available at: 10. European Centre for Disease Prevention and Control. Rapid risk assessment: monkeypox cases in the UK imported by travellers returning from Nigeria, 2018. 2018. Available at: 11. Erez N, Achdout H, Milrot E, et al. Diagnosis of imported monkeypox, Israel, 2018. Emerg Infect Dis. 2019;25(5):980-983. Available at: 12. Yong SEF, Ng OT, Ho ZJM, et al. Imported monkeypox, Singapore. Emerg Infect Dis. 2020;26(8):1826-1830. Available at: 13. Costello V, Sowash M, Gaur A, et al. Imported monkeypox from international traveler, Maryland, USA, 2021. Emerg Infect Dis. 2022;28(5):1002-1005. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-13 14. Rao AK, Schulte J, Chen TH, et al. Monkeypox in a traveler returning from Nigeria - Dallas, Texas, July 2021. MMWR Morb Mortal Wkly Rep. 2022;71(14):509-516. Available at: 15. Gigante CM, Korber B, Seabolt MH, et al. Multiple lineages of monkeypox virus detected in the United States, 2021–2022. Science. 2022;378(6619):560-565. Available at: 16. Centers for Disease Control and Prevention. Science brief: detection and transmission of monkeypox virus. Available at: 17. Curran KG, Eberly K, Russell OO, et al. HIV and sexually transmitted infections among persons with monkeypox - eight U.S. jurisdictions, May 17–July 22, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(36):1141-1147. Available at: 18. Thornhill JP, Barkati S, Walmsley S, et al. Monkeypox virus infection in humans across 16 countries - April–June 2022. N Engl J Med. 2022;387(8):679-691. Available at: 19. Saunders KE, Van Horn AN, Medlin HK, et al. Monkeypox in a young infant - Florida, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(38):1220-1221. Available at: 20. Aguilera-Alonso D, Alonso-Cadenas JA, Roguera-Sopena M, Lorusso N, Miguel LGS, Calvo C. Monkeypox virus infections in children in Spain during the first months of the 2022 outbreak. Lancet Child Adolesc Health. 2022;6(11):e22-e23. Available at: 21. Alonso-Cadenas JA, Andina-Martinez D, Garcia-Garcia CJ, Gaitero-Tristan J, Garcia-Ascaso MT, Torrelo A. Monkeypox disease in a breastfeeding infant. Pediatr Dermatol. 2022. Available at: 22. Carvalho LB, Casadio LVB, Polly M, et al. Monkeypox virus transmission to healthcare worker through needlestick injury, Brazil. Emerg Infect Dis. 2022;28(11):2334-2336. Available at: 23. Mendoza R, Petras JK, Jenkins P, et al. Monkeypox virus infection resulting from an occupational needlestick - Florida, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(42):1348-1349. Available at: 24. Choi Y, Jeon EB, Kim T, et al. Case report and literature review of occupational transmission of monkeypox virus to healthcare workers, South Korea. Emerg Infect Dis. 2023;29(5):997-1001. Available at: 25. Caldas JP, Valdoleiros SR, Rebelo S, Tavares M. Monkeypox after occupational needlestick injury from pustule. Emerg Infect Dis. 2022;28(12):2516-2519. Available at: 26. Tarin-Vicente EJ, Alemany A, Agud-Dios M, et al. Clinical presentation and virological assessment of confirmed human monkeypox virus cases in Spain: a prospective observational Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-14 cohort study. Lancet. 2022;400(10353):661-669. Available at: 27. Philpott D, Hughes CM, Alroy KA, et al. Epidemiologic and clinical characteristics of monkeypox cases - United States, May 17–July 22, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(32):1018-1022. Available at: 28. Philpott D, Bonacci R, Weidle P, et al. CD4 count <350 cells/mm3 increases risk of hospitalization with mpox in PWH. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: 29. Cholli PA, Miller MJ, Paromita P, et al. Characteristics of patients hospitalized with mpox during the 2022 U.S. outbreak. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: 30. Corma-Gómez A, Santos M, Cabello A, et al. Mpox virus infection is more severe in patients with uncontrolled HIV infection. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: 31. Garcia EA, Lash MK, McPherson TD, et al. Severe mpox among people living with HIV receiving tecovirimat in New York City. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: 32. Garneau WM, Jones JL, Dashler G, et al. Clinical outcomes among in- and outpatients with mpox in an urban health system. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: 33. Silva M, Coutinho C, Torres T, et al. Impact of HIV infection on mpox-related hospitalizations in Brazil. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: A3o_final-133209759446392218.pdf. 34. Vo C, Zomorodi R, Silvera R, et al. Demographic and clinical characteristics of mpox within a New York City health system. Presented at: Conference on Retroviruses and Opportunistic Infections 2023; 2023. Seattle, WA. Available at: 35. Mitja O, Alemany A, Marks M, et al. Mpox in people with advanced HIV infection: a global case series. Lancet. 2023. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-15 36. World Health Organization. Multi-country outbreak of mpox, external situation report #12 - 14 December 2022. 2022. Available at: 37. Nigeria Centre for Disease Control. Weekly Epidemiological Report week 51: 16th–22nd December 2019. Nigeria: Nigeria Centre for Disease Control and Prevention; January 3 2020. Available at: 38. Ogoina D, Iroezindu M, James HI, et al. Clinical course and outcome of human monkeypox in Nigeria. Clin Infect Dis. 2020;71(8):e210-e214. Available at: 39. Miller MJ, Cash-Goldwasser S, Marx GE, et al. Severe monkeypox in hospitalized patients - United States, August 10–October 10, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(44):1412-1417. Available at: 40. Centers for Disease Control and Prevention. Health Alert Network (HAN) no. 466: monkeypox virus infection in the United States and other non-endemic countries—2022. 2022. Available at: 41. Rao AK, Schrodt CA, Minhaj FS, et al. Interim clinical treatment considerations for severe manifestations of mpox - United States, February 2023. MMWR Morb Mortal Wkly Rep. 2023;72(9):232-243. Available at: 42. Lucar J, Roberts A, Saardi KM, Yee R, Siegel MO, Palmore TN. Monkeypox virus-associated severe proctitis treated with oral tecovirimat: a report of two cases. Ann Intern Med. 2022;175(11):1626-1627. Available at: 43. Patel A, Bilinska J, Tam JCH, et al. Clinical features and novel presentations of human monkeypox in a central London centre during the 2022 outbreak: descriptive case series. BMJ. 2022;378:e072410. Available at: 44. Centers for Disease Control and Prevention. Health Alert Network (HAN) no. 475: severe manifestations of monkeypox among people who are immunocompromised due to HIV or other conditions. 2022. Available at: 45. Cash-Goldwasser S, Labuda SM, McCormick DW, et al. Ocular monkeypox - United States, July–September 2022. MMWR Morb Mortal Wkly Rep. 2022;71(42):1343-1347. Available at: 46. Nogueira Filho PA, Lazari CDS, Granato CFH, et al. Ocular manifestations of monkeypox: a case report. Arq Bras Oftalmol. 2022;85(6):632-635. Available at: 47. Kaufman AR, Chodosh J, Pineda R 2nd. Monkeypox virus and ophthalmology-a primer on the 2022 monkeypox outbreak and monkeypox-related ophthalmic disease. JAMA Ophthalmol. 2022. Available at: 48. Pastula DM, Copeland MJ, Hannan MC, et al. Two cases of monkeypox-associated encephalomyelitis - Colorado and the District of Columbia, July–August 2022. MMWR Morb Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-16 Mortal Wkly Rep. 2022;71(38):1212-1215. Available at: 49. Fonti M, Mader T, Burmester-Kiang J, et al. Monkeypox associated acute arthritis. Lancet Rheumatol. 2022;4(11):e804. Available at: 50. Khalil A, Samara A, O’Brien P, et al. Monkeypox in pregnancy: update on current outbreak. Lancet Infect Dis. 2022;22(11):1534-1535. Available at: 51. Hennessee I, Shelus V, McArdle CE, et al. Epidemiologic and clinical features of children and adolescents aged <18 years with monkeypox - United States, May 17–September 24, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(44):1407-1411. Available at: 52. Carrubba S, Geevarghese A, Solli E, et al. Novel severe oculocutaneous manifestations of human monkeypox virus infection and their historical analogues. Lancet Infect Dis. 2023. Available at: 53. Centers for Disease Control and Prevention. Case definitions for use in the 2022 mpox response. 2022. Available at: 54. Centers for Disease Control and Prevention. Infection prevention and control of mpox in healthcare settings. 2022. Available at: 55. O’Shea J, Filardo TD, Morris SB, Weiser J, Petersen B, Brooks JT. Interim guidance for prevention and treatment of monkeypox in persons with HIV infection - United States, August 2022. MMWR Morb Mortal Wkly Rep. 2022;71(32):1023-1028. Available at: 56. Centers for Disease Control and Prevention. JYNNEOS vaccine. 2022. Available at: 57. Food and Drug Administration. ACAM2000 [package insert]. 2018. Available at: 58. Overton ET, Lawrence SJ, Stapleton JT, et al. A randomized phase II trial to compare safety and immunogenicity of the MVA-BN smallpox vaccine at various doses in adults with a history of AIDS. Vaccine. 2020;38(11):2600-2607. Available at: 59. Overton ET, Stapleton J, Frank I, et al. Safety and immunogenicity of modified vaccinia Ankara-Bavarian Nordic smallpox vaccine in vaccinia-naive and experienced human immunodeficiency virus-infected individuals: an open-label, controlled clinical phase II trial. Open Forum Infect Dis. 2015;2(2):ofv040. Available at: 60. Greenberg RN, Overton ET, Haas DW, et al. Safety, immunogenicity, and surrogate markers of clinical efficacy for modified vaccinia Ankara as a smallpox vaccine in HIV-infected subjects. J Infect Dis. 2013;207(5):749-758. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-17 61. Centers for Disease Control and Prevention. Preliminary JYNNEOS vaccine effectiveness estimates against medically attended mpox disease in the U.S., August 15, 2022–October 29, 2022. 2022. Available at: 62. Payne AB, Ray LC, Cole MM, et al. Reduced risk for mpox after receipt of 1 or 2 doses of JYNNEOS vaccine compared with risk among unvaccinated persons - 43 U.S. jurisdictions, July 31–October 1, 2022. MMWR Morb Mortal Wkly Rep. 2022;71(49):1560-1564. Available at: 63. Bertran M, Andrews N, Davison C, et al. Effectiveness of one dose of MVA-BN smallpox vaccine against mpox in England using the case-coverage method: an observational study. Lancet Infect Dis. 2023. Available at: 64. Arbel R, Sagy YW, Zucker R, et al. Effectiveness of a single-dose modified vaccinia Ankara in human monkeypox: an observational study. Research Square. 2022. Available at: 65. Dalton AF, Diallo AO, Chard AN, et al. Estimated effectiveness of JYNNEOS vaccine in preventing mpox: a multijurisdictional case-control study - United States, August 19, 2022– March 31, 2023. MMWR Morb Mortal Wkly Rep. 2023;72(20):553-558. Available at: 66. Deputy NP, Deckert J, Chard AN, et al. Vaccine effectiveness of JYNNEOS against mpox disease in the United States. N Engl J Med. 2023. Available at: 67. Rosenberg ES, Dorabawila V, Hart-Malloy R, et al. Effectiveness of JYNNEOS vaccine against diagnosed mpox infection—New York, 2022. MMWR Morb Mortal Wkly Rep. 2023;72(20):559– 563. Available at: 68. Food and Drug Administration. Vaccine Immune Globulin Intravenous [package insert]. 2005. Available at: 69. Food and Drug Administration. TPOXX (tecovirimat) [package insert]. 2018. Available at: 70. Merchlinsky M, Albright A, Olson V, et al. The development and approval of tecoviromat (TPOXX®), the first antiviral against smallpox. Antiviral Res. 2019;168:168-174. Available at: 71. Grosenbach DW, Honeychurch K, Rose EA, et al. Oral tecovirimat for the treatment of smallpox. N Engl J Med. 2018;379(1):44-53. Available at: 72. Smith SK, Self J, Weiss S, et al. Effective antiviral treatment of systemic orthopoxvirus disease: ST-246 treatment of prairie dogs infected with monkeypox virus. J Virol. 2011;85(17):9176-9187. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-18 73. Desai AN, Thompson GR 3rd, Neumeister SM, Arutyunova AM, Trigg K, Cohen SH. Compassionate use of tecovirimat for the treatment of monkeypox infection. JAMA. 2022;328(13):1348-1350. Available at: 74. O’Laughlin K, Tobolowsky FA, Elmor R, et al. Clinical use of tecovirimat (TPOXX) for treatment of monkeypox under an Investigational New Drug protocol - United States, May– August 2022. MMWR Morb Mortal Wkly Rep. 2022;71(37):1190-1195. Available at: 75. Adler H, Gould S, Hine P, et al. Clinical features and management of human monkeypox: a retrospective observational study in the UK. Lancet Infect Dis. 2022;22(8):1153-1162. Available at: 76. National Institutes of Health. Study of tecovirimat for human monkeypox virus (STOMP). 2022. Available at: 77. National Institutes of Health. Tecovirimat for treatment of monkeypox virus. 2022. Available at: 78. National Institute for Health and Care Research. New clinical trial to test treatment for mpox (PLATINUM). 2022. Available at: 79. Rice AD, Adams MM, Wallace G, et al. Efficacy of CMX001 as a post exposure antiviral in New Zealand White rabbits infected with rabbitpox virus, a model for orthopoxvirus infections of humans. Viruses. 2011;3(1):47-62. Available at: 80. Parker S, Chen NG, Foster S, et al. Evaluation of disease and viral biomarkers as triggers for therapeutic intervention in respiratory mousepox - an animal model of smallpox. Antiviral Res. 2012;94(1):44-53. Available at: 81. Baker RO, Bray M, Huggins JW. Potential antiviral therapeutics for smallpox, monkeypox and other orthopoxvirus infections. Antiviral Res. 2003;57(1-2):13-23. Available at: 82. Smee DF. Progress in the discovery of compounds inhibiting orthopoxviruses in animal models. Antivir Chem Chemother. 2008;19(3):115-124. Available at: 83. Stittelaar KJ, Neyts J, Naesens L, et al. Antiviral treatment is more effective than smallpox vaccination upon lethal monkeypox virus infection. Nature. 2006;439(7077):745-748. Available at: 84. Hutson CL, Kondas AV, Mauldin MR, et al. Pharmacokinetics and efficacy of a potential smallpox therapeutic, brincidofovir, in a lethal monkeypox virus animal model. mSphere. 2021;6(1). Available at: 85. Quenelle DC, Prichard MN, Keith KA, et al. Synergistic efficacy of the combination of ST-246 with CMX001 against orthopoxviruses. Antimicrob Agents Chemother. 2007;51(11):4118-4124. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-19 86. Sobral-Costas TG, Escudero-Tornero R, Servera-Negre G, et al. Human monkeypox outbreak: epidemiological data and therapeutic potential of topical cidofovir in a prospective cohort study. J Am Acad Dermatol. 2022. Available at: 87. Rubio-Muniz CA, Montero-Menárguez J, López-Valle A, et al. Monkeypox: is topical cidofovir a good idea? Clin Exp Dermatol. 2022. Available at: 88. Parkhurst JR, Danenberg PV, Heidelberger C. Growth inhibition of cells in cultures and of vaccinia virus infected HeLa cells by derivatives of trifluorothymidine. Chemotherapy. 1976;22(3-4):221-231. Available at: 89. Hyndiuk RA, Seideman S, Leibsohn JM. Treatment of vaccinial keratitis with trifluorothymidine. Arch Ophthalmol. 1976;94(10):1785-1786. Available at: 90. Maudgal PC, Van Damme B, Missotten L. Corneal epithelial dysplasia after trifluridine use. Graefes Arch Clin Exp Ophthalmol. 1983;220(1):6-12. Available at: 91. Agrati C, Cossarizza A, Mazzotta V, et al. Immunological signature in human cases of monkeypox infection in 2022 outbreak: an observational study. Lancet Infect Dis. 2022. Available at: 92. Lum FM, Torres-Ruesta A, Tay MZ, et al. Monkeypox: disease epidemiology, host immunity and clinical interventions. Nat Rev Immunol. 2022;22(10):597-613. Available at: 93. Hermanussen L, Grewe I, Tang HT, et al. Tecovirimat therapy for severe monkeypox infection: longitudinal assessment of viral titers and clinical response pattern-a first case-series experience. J Med Virol. 2022. Available at: 94. Food and Drug Administration. Cidofovir [package insert]. 2000. Available at: 95. Food and Drug Administration. Brincidofovir [package insert]. 2021. Available at: 96. Scotti B, Piraccini BM, Gaspari V. Hypertrophic verrucous lesions after monkeypox virus infection. Lancet Infect Dis. 2022. Available at: 97. Centers for Disease Control and Prevention. Update on managing monkeypox in patients receiving therapeutics. 2022. Available at: 98. Paran N, Yahalom-Ronen Y, Shifman O, et al. Monkeypox DNA levels correlate with virus infectivity in clinical samples, Israel, 2022. Euro Surveill. 2022;27(35). Available at: 99. Jamieson DJ, Cono J, Richards CL, Treadwell TA. The role of the obstetrician-gynecologist in emerging infectious diseases: monkeypox and pregnancy. Obstet Gynecol. 2004;103(4):754-756. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV V-20 100. Meaney-Delman DM, Galang RR, Petersen BW, Jamieson DJ. A primer on monkeypox virus for obstetrician-gynecologists: diagnosis, prevention, and treatment. Obstet Gynecol. 2022;140(3):391-397. Available at: 101. Jezek Z; Fenner Z. Human monkeypox. Monographs in Virology. 1988;17:127-140. Available at: 102. Food and Drug Administration. JYNNEOS [package insert]. 2022. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-1 Disseminated Mycobacterium avium Complex Disease Updated: August 15, 2024 Reviewed: August 15, 2024 Epidemiology Organisms of the Mycobacterium avium complex (MAC) are ubiquitous in the environment.1-6 In the era before effective antiretroviral therapy (ART) was available, M. avium was the etiologic agent in >95% of people with HIV with advanced immunosuppression who acquired disseminated MAC disease.4,7-12 Newer bacterial typing technology suggests organisms causing bacteremia in people with HIV represent a diversity of species, including the M. avium subspecies hominissuis and M. colombiense and other non-MAC species, including M. genavense, M. kansasii, M. simiae, M. mycogenicum, and others.13-16 These comprise what was historically referred to as disseminated MAC. An estimated 7% to 12% of adults with HIV have been previously infected with MAC, although rates of disease vary in different geographic locations.2,4,8,11,12 In particular, disseminated MAC in people with HIV has been described more frequently in the United States and Europe than in resource-limited settings.17 Although epidemiologic associations with infection have been identified, no singular environmental exposure or behavior has been consistently linked to subsequent increased risk of developing MAC disease. The mode of MAC infection is thought to be through repeated inhalation or ingestion of MAC bacteria via the respiratory or gastrointestinal (GI) tract, likely from environmental exposure.1,18 Household or close contacts of those with MAC disease do not appear to be at increased risk of disease, and person-to-person transmission is unlikely.19 MAC disease typically occurs in people with HIV with CD4 T lymphocyte (CD4) cell counts <50 cells/mm3. The previously reported incidence of disseminated MAC disease ranged from 20% to 40% in people with HIV with advanced immunosuppression in the absence of effective ART or chemoprophylaxis.20,21 However, the overall incidence of MAC disease among people with HIV has declined substantially in the modern ART era to current levels of <2 cases of MAC as the first opportunistic infection [OI] per 1,000 person-years for individuals in care, even among those not receiving effective ART.22-26 In addition to a CD4 count <50 cells/mm3, factors associated with increased risk for MAC disease are ongoing HIV viral replication despite ART, previous or concurrent OIs, reduced in vitro lymphoproliferative immune responses to M. avium antigens (possibly reflecting defects in T-cell repertoire), and genetic predisposition in some populations.24-27 While effective ART has clearly been associated with dramatic reductions in risk of developing MAC disease, MAC disease still can occur in people with HIV on suppressive ART, and the clinical presentation may differ from what is seen in people with untreated HIV. In one retrospective case series following people with HIV mostly on ART, nontuberculous mycobacterial (NTM) disease occurred in nine people who were virologically suppressed on ART at the time of their diagnosis— seven with pulmonary NTM only and two with extrapulmonary disease. MAC was the most common NTM pathogen, isolated in 19 of the 34 cases.13 Those with extrapulmonary disease were younger and had higher viral loads and lower CD4 counts at diagnosis. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-2 Clinical Manifestations In people with HIV with advanced immunosuppression who are not on ART, MAC disease generally presents as a disseminated, multi-organ infection, although localized disease may also be seen.28-32 Early symptoms may be minimal and can precede mycobacteremia or positive tissue cultures by several weeks. Symptoms are nonspecific and include fever, night sweats, weight loss, fatigue, diarrhea, and abdominal pain.8,13-15 Laboratory abnormalities particularly associated with disseminated MAC disease include anemia (often out of proportion to that expected for the stage of HIV disease) and elevated liver alkaline phosphatase levels.4,5,7-12,20,21,33,34 Hepatomegaly, splenomegaly, or lymphadenopathy (paratracheal, retroperitoneal, para-aortic, or less commonly peripheral) may be identified on physical examination or by radiographic or other imaging studies. Other focal physical findings or laboratory abnormalities may occur with localized disease. Localized MAC disease occurs more often in people with HIV on suppressive ART with increased CD4 counts than in people with HIV not on ART, suggesting improved immune function is associated with more localized disease. Localized syndromes include cervical, intraabdominal, or mediastinal lymphadenitis; pneumonia; pericarditis; osteomyelitis; skin or soft-tissue abscesses; bursitis; genital ulcers; and central nervous system infection. Localized syndromes may also be manifestations of immune reconstitution inflammatory syndrome (IRIS), as discussed below. Diagnosis A confirmed diagnosis of disseminated MAC disease is based on compatible clinical signs and symptoms coupled with the isolation of MAC from cultures of blood, lymph fluid, bone marrow, or other normally sterile tissue or body fluids, although data suggest that bone marrow cultures have low yield for detection of MAC in this setting, particularly if blood cultures are negative.21,31,32,35-40 Species identification should be performed using molecular techniques, polymerase chain reaction-based assays, whole-genome sequencing, high-performance liquid chromatography, or biochemical tests. Other ancillary studies provide supportive diagnostic information, including acid-fast bacilli smear and culture of tissue, radiographic imaging, or other studies aimed at isolating organisms from focal infection sites. Although isolated pulmonary MAC disease is not often observed in people with advanced HIV-associated immunosuppression, occasionally MAC disease may be limited to the lung in people with HIV who are virologically suppressed on ART. Diagnostic criteria for disease limited to the lung in this setting should follow those established by the American Thoracic Society (ATS), European Respiratory Society (ERS), European Society of Clinical Microbiology and Infectious Diseases (ESCMID), and the Infectious Disease Society of America (IDSA) joint guideline on Treatment of Nontuberculous Mycobacterial Pulmonary Disease, which include pulmonary clinical signs and symptoms, exclusion of other alternative diagnoses, nodular or cavitary disease on lung imaging, and a positive culture for MAC from at least two sputum specimens or at least one bronchoalveolar lavage or biopsy sample.41 Detection of MAC organisms in the respiratory or GI tract may represent colonization of these sites and may be a harbinger of disseminated MAC infection. However, no data are available regarding Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-3 efficacy of treatment for asymptomatic colonization with MAC organisms at these sites. Therefore, routine screening of respiratory or GI specimens and preemptive treatment for MAC is not recommended. Preventing Exposure MAC organisms commonly contaminate environmental sources of infection, such as food and water. Available information does not support specific recommendations regarding avoidance of exposure. Preventing Disease Recommendations for Preventing Disseminated Mycobacterium avium Complex Disease Preventing First Episode of Disseminated MAC Disease (Primary Prophylaxis) • Primary prophylaxis is not recommended for adults and adolescents who immediately initiate ART (AII). Indications for Primary Prophylaxis • CD4 count <50 cells/mm3 AND not receiving ART or remains viremic on ART or has no options for a fully suppressive ART regimen (AI) • Before primary prophylaxis is initiated, disseminated MAC disease should be ruled out by clinical assessment, and if appropriate, by obtaining a blood culture for MAC (AI). If blood culture is obtained, prophylaxis should be delayed until results are available to avoid exposing patients to monotherapy and the attendant risk of drug resistance (AI). Preferred Therapy • Azithromycin 1,200 mg PO once weekly (AI), or • Clarithromycin 500 mg PO twice daily (AI), or • Azithromycin 600 mg PO twice weekly (BIII) Alternative Therapy • Rifabutin 300 mg PO daily (BI) in people who cannot tolerate azithromycin or clarithromycin o Dose adjustment of rifabutin may be necessary based on drug–drug interactions, please refer to Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines for dosing recommendation when used with certain ARV drugs. o Active TB should be ruled out before starting rifabutin to avoid monotherapy in the setting of active TB. Indication for Discontinuing Primary Prophylaxis • If previously initiated, primary prophylaxis should be discontinued if the patient is continuing on a fully suppressive ART regimen (AI). Pregnancy Considerations • Primary prophylaxis for MAC disease in pregnant people who immediately initiate ART is not recommended (AIII). • When primary prophylaxis is required for a pregnant person who is not being treated with effective ART, azithromycin is the preferred agent (BIII). Key: ART = antiretroviral therapy; ARV = antiretroviral; CD4 = CD4 T lymphocyte; MAC = Mycobacterium avium complex; PO = orally; TB = tuberculosis Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-4 Indication for Primary Prophylaxis Primary prophylaxis against disseminated MAC disease is not recommended for adults and adolescents with HIV who immediately initiate ART, regardless of CD4 count (AII). People with HIV who have CD4 counts <50 cells/mm3 and who are not receiving ART, remain viremic on ART, or have no options for a fully suppressive ART regimen should receive chemoprophylaxis against disseminated MAC (AI). Before prophylaxis is initiated, disseminated MAC disease should be ruled out by clinical assessment and, if appropriate based on that assessment, by obtaining a blood culture for MAC. MAC prophylaxis should be delayed until results are available to avoid exposing patients to monotherapy and the attendant risk of drug resistance (AI). When to Stop Primary Prophylaxis Primary MAC prophylaxis, if previously initiated, should be discontinued in adults and adolescents who are continuing on a fully suppressive ART regimen (AI). Two randomized, placebo-controlled trials and several large observational cohort studies have demonstrated that people with HIV taking ART can discontinue primary prophylaxis with minimal risk of developing MAC disease, particularly if they are virologically suppressed.42-47 Conclusions from these studies indicate that the overall incidence of disseminated MAC within 6 to 12 months after stopping primary prophylaxis in these circumstances, regardless of CD4 count, was 0.6 to 0.8 per 100 person-years. In each of these studies, plasma HIV RNA level >1,000 copies/mL was the principal risk factor for developing MAC disease regardless of MAC prophylaxis. However, in a study from the TREAT Asia HIV Observational Database, which evaluated the impact of MAC prophylaxis on AIDS-defining conditions and HIV-associated mortality in people with HIV on ART from September 2015 onward, macrolide use within 3 months of starting ART for those with a CD4 count <50 at ART initiation was associated with a decreased risk of HIV-associated mortality (HR 0.10; 95% CI, 0.01–0.80; P = 0.031) but not with the combined outcome of developing an AIDS-defining condition or death.48 Despite this finding, only 10.6% of the 1,345 participants in the cohort eligible for MAC prophylaxis received it. The authors concluded that there may be an additive protective effect of macrolide prophylaxis in reducing overall HIV-related mortality among Asians with HIV and CD4 counts <50 even though they received effective ART. Despite some differences among these published data, for most individuals, particularly in higher resourced settings, the preponderance of current data suggest that primary MAC prophylaxis provides no additional benefit in people started on effective ART that results in viral suppression. Additional arguments against primary MAC prophylaxis while prioritizing effective ART to achieve viral suppression include (1) the potential for adding additional cost and adverse effects of the drugs used for prophylaxis; (2) the likelihood that only a small number of people with HIV will develop “unmasking MAC IRIS” (i.e., active MAC disease after starting ART); (3) the potential for acquired drug resistance if people fail monotherapy for MAC prophylaxis; and (4) limiting polypharmacy to assist with adherence to ART.49-51 Preferred and Alternative Drugs for Prophylaxis As previously stated, primary prophylaxis for MAC is not recommended for people on effective ART, but for those for whom prophylaxis is being considered, azithromycin52 and clarithromycin5,53 are the preferred prophylactic agents (AI).1,54 The combination of clarithromycin and rifabutin is no more effective than clarithromycin alone for chemoprophylaxis, is associated with a higher rate of adverse effects than either drug alone, and should not be used (AI).5 The combination of azithromycin and rifabutin is more effective than azithromycin alone in preventing MAC disease.52 However, based on the additional cost, increased occurrence of adverse effects, potential for drug Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-5 interactions, and lack of greater survival benefit than with azithromycin alone, the combination regimen of azithromycin and rifabutin is not recommended (AI). In people with HIV who cannot tolerate azithromycin or clarithromycin, rifabutin can be used as a prophylactic agent for MAC disease (BI), although drug interactions may complicate use of this agent. Moreover, tuberculosis (TB) should be excluded before rifabutin is used to avoid monotherapy in the setting of active TB, which could result in acquired rifamycin resistance. Treating Disease Recommendations for Treating Disseminated Mycobacterium avium Complex Disease Treating Disseminated MAC Disease Preferred Therapy • At least two drugs as initial therapy to prevent or delay emergence of resistance (AI) o Clarithromycin 500 mg PO twice daily (AI) plus ethambutol 15 mg/kg PO daily (AI), or o Azithromycin 500–600 mg (AII) plus ethambutol 15 mg/kg PO daily (AI) when drug interactions or intolerance precludes the use of clarithromycin (AII) o Note: Testing of susceptibility to clarithromycin or azithromycin is recommended. • Some experts would add rifabutin when more severe disease manifestations are present. o Rifabutin 300 mg PO daily (CI). Dose adjustment of rifabutin may be necessary based on drug–drug interactions. Refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB table in the Mycobacterium tuberculosis section for more information. • Some experts would also add a fourth drug if more severe disease is present, the risk of mortality is high, emergence of drug resistance is likely (e.g., after failure of MAC prophylaxis), CD4 count is <50 cells/mm3, mycobacterial loads are high (>2 log10 CFU/mL of blood), or effective ART is absent (CIII). Fourth drug options may include: o A fluoroquinolone (CIII) (e.g., levofloxacin 500 mg PO daily or moxifloxacin 400 mg PO daily), or o An injectable aminoglycoside (CIII) (e.g., amikacin 10–15 mg/kg IV daily or streptomycin 1 g IV or IM daily) (generally avoided unless in the setting of refractory disease when other alternatives are not available or tolerated) o Bedaquiline, tedizolid, linezolid, and omadacycline have demonstrated in vitro activity against clinical isolates of MAC; these might also be considered in people with refractory MAC disease. Duration of Therapy • At least 12 months (AII) • Shorter duration may be considered depending on the degree of immunologic recovery following initiation of ART. CD4 count should be >100 cells/mm3 for ≥6 months before discontinuation of therapy (CIII). Chronic Maintenance Therapy (Secondary Prophylaxis) • Same as treatment regimens • If ART does not result in immune reconstitution, people with HIV and disseminated MAC disease should continue chronic maintenance therapy (AII). Criteria for Discontinuing Chronic Maintenance Therapy (Secondary Prophylaxis) (AI) • Completed at least 12 months of therapy, and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-6 • No signs or symptoms of MAC disease, and • Have sustained (≥6 months) CD4 count >100 cells/mm3 in response to ART Indication for Restarting Chronic Maintenance Therapy (Secondary Prophylaxis) • If a fully suppressive ART regimen is not possible and CD4 is consistently <100 cells/mm3 (BIII) Pregnancy Considerations • For secondary prophylaxis (chronic maintenance therapy), azithromycin plus ethambutol is the preferred drug combination (BIII). Other Considerations • NSAIDs may be used for people with HIV who experience moderate to severe symptoms attributed to IRIS (BIII). • If IRIS symptoms persist, a short-term course (4–8 weeks) of systemic corticosteroid therapy (equivalent to prednisone 20–40 mg/day) can be used (BII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CFU = colony-forming units; IM = intramuscular; IRIS = immune reconstitution inflammatory syndrome; IV = intravenous; MAC = Mycobacterium avium complex; NSAID = nonsteroidal anti-inflammatory drug; PO = orally Initial treatment of MAC disease should consist of two or more antimycobacterial drugs to prevent or delay the emergence of resistance (AI).1,6,11,12,18,55-63 Clarithromycin (AI) or azithromycin (AII) are preferred first agents; published data are more extensive for clarithromycin than for azithromycin in people with advanced HIV disease, and clarithromycin appears to be associated with more rapid clearance of MAC from the blood.6,55,57,61,62,64 However, azithromycin is acceptable when drug interactions or intolerance preclude the use of clarithromycin (AII). Doses of clarithromycin >1 g/day for treatment of disseminated MAC disease have been associated with increased mortality and should not be used (AI).65 Testing MAC isolates for susceptibility to clarithromycin or azithromycin is recommended for all people with HIV, particularly those who developed MAC disease while receiving prophylaxis with one of these agents.66,67 In three randomized clinical trials, clarithromycin-resistant isolates were reported in 29% and 58% of people with HIV who developed MAC bacteremia during prophylaxis with clarithromycin, and azithromycin-resistant isolates were recovered from 11% of those who developed bacteremia while on azithromycin prophylaxis.5,52,53,68 More advanced immunosuppression at prophylaxis initiation and longer duration of MAC prophylaxis are associated with higher rates of clarithromycin resistance at the time of MAC prophylaxis failure.68 Ethambutol is the recommended second drug for the initial treatment of MAC disease (AI) based on randomized trials of MAC therapy that indicate its use in the regimen is associated with lower rates of relapse.56,58,64,69 Rifabutin can be used as a third drug (CI) with or without a fluoroquinolone (levofloxacin or moxifloxacin) (CIII), or an injectable aminoglycoside (amikacin or streptomycin) (CIII) can be used as a fourth drug if more severe disease is present; the risk of mortality is high; emergence of drug resistance is likely (e.g., after failure of MAC prophylaxis); or in the setting of advanced immunosuppression (CD4 count <50 cells/mm3), high mycobacterial loads (>2 log10 colony-forming units/mL of blood), or the absence of effective ART (CIII). One randomized clinical trial demonstrated that adding rifabutin to the combination of clarithromycin and ethambutol improved survival, and in two randomized clinical trials, this approach reduced emergence of drug resistance6,57 in individuals with advanced HIV and disseminated MAC disease. These studies were completed before the availability of effective ART. It has not been established whether similar results would be observed for people with HIV receiving effective ART. The fluoroquinolones levofloxacin and moxifloxacin and amikacin have in vitro and animal model Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-7 activity against MAC, although randomized trials evaluating the efficacy of adding a fluoroquinolone or injectable aminoglycoside as part of a multidrug regimen for treatment of MAC have not been done. Injectable aminoglycosides should generally be avoided except in the setting of refractory disease when other alternative agents are not available or tolerated.66,70 Additional drugs with in vitro activity against clinical isolates of MAC include bedaquiline, tedizolid, linezolid, and omadacycline; these might also be considered in people with refractory MAC disease.71-75 While not specifically applicable to people with HIV (who more often have disseminated MAC disease than isolated pulmonary disease), in 2020, the ATS/ERS/ESCMID/IDSA updated their jointly sponsored clinical guideline for treatment of nontuberculous mycobacterial pulmonary disease, including pulmonary MAC.41 People with HIV fully suppressed on ART with higher CD4 counts may present with localized pulmonary or other local organ system MAC disease that may clinically resemble such disease in people without HIV. Following the ATS/ERS/ESCMID/IDSA guidelines would be reasonable in such settings. The recommended treatment includes an initial three-drug regimen containing a macrolide and ethambutol for those with macrolide-susceptible pulmonary MAC disease. Addition of an aminoglycoside, which in refractory cases can be given as inhalation suspension, is recommended if cavitary or severe bronchiectatic disease is present or if macrolide resistance is suspected.76 People with HIV and disseminated MAC disease should be treated for a minimum duration of 12 months (AII). Shorter duration of treatment may be considered depending on the degree of immunologic recovery following initiation of ART (CIII); the CD4 count should be maintained above 100 cells/mm3 for at least 6 months before discontinuing MAC treatment.77-79 Special Considerations Regarding Antiretroviral Therapy Initiation ART should be started as soon as possible after the diagnosis of MAC disease, preferably at the same time as initiation of antimycobacterial therapy in people with HIV and disseminated MAC disease who are not receiving effective ART (BIII). ART is recommended as soon as possible to reduce the risk of further AIDS-defining OIs and to further improve the response to antimycobacterial therapy in the setting of advanced immunosuppression (BIII). If ART has already been initiated, it should be continued. The regimens should be modified when there is any potential for an adverse drug–drug interaction(s) between the antiretroviral (ARV) and antimycobacterial drugs (BIII). Information on drug–drug interactions can be found in the Adult and Adolescent Antiretroviral Guidelines. People with HIV will need continuous antimycobacterial treatment until ART results in sustained immune reconstitution, as indicated above (CD4 count maintained above 100 cells/mm3 for at least 6 months). Monitoring of Response to Therapy and Adverse Events (Including IRIS) A repeat blood culture for MAC should be obtained 4 to 8 weeks after initiating antimycobacterial therapy in people with HIV who do not have a clinical response to their initial treatment regimens. Improvement in fever and other systemic symptoms and a decline in quantity of mycobacteria in blood or tissue can be expected within 2 to 4 weeks after initiation of appropriate therapy; clinical response may be delayed, however, in those with more extensive MAC disease or advanced immunosuppression. Adverse effects of clarithromycin and azithromycin include GI upset, metallic taste, elevations in liver transaminase levels, and hypersensitivity reactions. Clarithromycin’s adverse effects may be exacerbated when drug levels are increased due to drug interactions associated with some ARV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-8 drugs. Doses of clarithromycin >1 g/day for treatment of disseminated MAC disease have been associated with increased mortality and should not be used (AI).65 Protease inhibitors (PIs) can increase clarithromycin levels; clarithromycin dose adjustment or switching clarithromycin to azithromycin may be necessary. Azithromycin metabolism is not affected by the cytochrome P450 (CYP) system; azithromycin can be used safely in the presence of PIs, non-nucleoside reverse transcriptase inhibitors, or integrase inhibitors without concerns about drug interactions. When used with clarithromycin or other drugs that inhibit CYP isoenzyme 3A4, rifabutin has been associated with a higher risk of adverse drug interactions, in particular sight-threatening uveitis and neutropenia.80-82 Rifabutin adverse effects are concentration related; therapeutic drug level monitoring may be considered to reduce the potential for adverse effects. Rifabutin must be dose adjusted in people with HIV receiving PIs or efavirenz. Rifabutin should not be coadministered with cobicistat-boosted PIs, long-acting injectable cabotegravir/rilpivirine, bictegravir, elvitegravir/cobicistat, fostemsavir, or lenacapavir.82-86 Rilpivirine and doravirine must be dose adjusted if either is coadministered with rifabutin. No dose adjustment for rifabutin or the integrase inhibitors dolutegravir or raltegravir or injectable cabotegravir alone is currently recommended, although at least one study suggested that compared with people without TB or MAC, lower trough concentrations were observed when once daily dolutegravir was used together with rifabutin.87-89 The most updated drug–drug interaction information can be found in the Adult and Adolescent Antiretroviral Guidelines. Therapeutic drug monitoring may be helpful for optimizing drug dosing in the context of complex drug–drug interactions.90 IRIS associated with MAC disease is recognized as a systemic inflammatory syndrome, with signs and symptoms clinically indistinguishable from active MAC infection, although bacteremia is generally absent. Similar to TB, MAC-associated IRIS can occur as “unmasking” IRIS in people with HIV with subclinical (undiagnosed) MAC or “paradoxical” IRIS in those with previously established MAC disease.91-95 Both variants occur primarily in those with advanced immunosuppression who begin ART and have a rapid and marked reduction in plasma HIV RNA.95,96 Elevated alkaline phosphatase levels may be a predictor of MAC-associated IRIS.97 The syndrome may be benign and self-limited or may result in severe, unremitting symptoms that improve with the use of systemic anti-inflammatory therapy or corticosteroids. People with HIV on ART who develop moderate to severe symptoms typical of IRIS should receive initial treatment with nonsteroidal anti-inflammatory drugs (NSAIDs) (BIII). If IRIS symptoms do not improve, short-term (4–8 weeks) systemic corticosteroid therapy, in doses equivalent to 20 to 40 mg of oral prednisone daily, can be used to reduce symptoms and morbidity (BII).92,98 Severe forms of MAC IRIS with a hemophagocytic lymphohistiocytosis (HLH) phenotype may occur, and a lower hemoglobin prior to ART may help predict this more severe form of IRIS.97,99 Patients with this more severe form may have a genetic predisposition, and cases of MAC IRIS and other NTM IRIS requiring additional immunosuppression in addition to corticosteroids have been reported.99,100 Managing Treatment Failure MAC treatment failure is defined by the absence of a clinical response and the persistence of mycobacteremia (or persistently positive tissue cultures from other sites) after 4 to 8 weeks of treatment. Repeat testing of MAC isolates for susceptibility to clarithromycin or azithromycin is recommended for people with HIV whose disease relapses after an initial response to treatment. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-9 Because the number of drugs with demonstrated clinical activity against MAC is limited, results of susceptibility testing should be used to construct a new multidrug regimen. The regimen should consist of at least two new drugs (i.e., not previously used) to which the isolate is susceptible. Drugs from which to choose include rifabutin, fluoroquinolone (levofloxacin or moxifloxacin), an injectable aminoglycoside (amikacin or streptomycin), or possibly bedaquiline, tedizolid, linezolid, or omadacycline, although data supporting a survival or microbiologic benefit when these agents are added are limited.11,12,41,56-60,64,69,72-75,101-104 Continuing clarithromycin or azithromycin despite resistance is not recommended (BIII), as there is likely to be no additional benefit and may have added toxicity. Clofazimine should generally not be used because randomized trials have demonstrated lack of efficacy and an association with increased mortality (AI).56,58,69 Optimization of ART is an important adjunct to second-line or salvage therapy for MAC disease in people with HIV for whom initial treatment is unsuccessful or who have disease that is resistant to antimycobacterial drugs (AIII). Although anecdotal data and individual case reports suggest potential benefit, adjunctive treatment of MAC disease with immunomodulators has not been thoroughly studied, and data are insufficient to support a recommendation for routine use, except in the setting of familial immunodeficiencies associated with increased risk of MAC disease.105 Preventing Recurrence As indicated above, people with HIV and disseminated MAC disease should be treated for a minimum duration of 12 months (AII). Shorter duration of treatment may be considered depending on the degree of immunologic recovery following initiation of ART; the CD4 count should be maintained above 100 cells/mm3 for at least 6 months before discontinuing MAC treatment. If ART initiation does not result in immune reconstitution, people with HIV and disseminated MAC disease should continue chronic maintenance therapy (AII).77-79 When to Stop Secondary Prophylaxis or Chronic Maintenance Therapy The risk of MAC recurrence is low in people with HIV who have completed at least a 12-month MAC treatment course, remain asymptomatic with respect to MAC signs and symptoms, and sustain an increase in CD4 count to >100 cells/mm3 for ≥6 months after initiation of ART. In this setting, it is reasonable to discontinue maintenance therapy based on data from studies in people with HIV and inferences from more extensive study data that indicate the safety of discontinuing secondary prophylaxis for other OIs (AI).44,60,77-79,106-108 Reintroducing chronic maintenance therapy or secondary prophylaxis for people with HIV for whom a fully suppressive ART regimen is not possible and who have a decline in their CD4 count to levels consistently below 100 cells/mm3 may be indicated (BIII). Special Considerations During Pregnancy Primary prophylaxis for MAC disease in pregnant people who immediately initiate ART is not recommended (AIII). When primary prophylaxis is required for a pregnant person who is not being treated with effective ART, azithromycin is the preferred agent (BIII). For secondary prophylaxis (chronic maintenance therapy), azithromycin plus ethambutol is the preferred drug combination (BIII). Because clarithromycin is associated with an increased risk of birth defects based on evidence from certain animal studies, it is not recommended as the first-line agent for prophylaxis or treatment of MAC in pregnancy (BIII). Two studies, each with slightly more than 100 women with Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-10 first-trimester exposure to clarithromycin, did not demonstrate an increase in or specific pattern of defects, although an increased risk of spontaneous abortion was noted in one study.109,110 Azithromycin did not produce defects in animal studies, but experience with use in humans during the first trimester is limited. A nested case-control study conducted within the large Quebec Pregnancy cohort found an association between azithromycin use and spontaneous miscarriage111; however the authors were not able to adjust for severity of infection, an important confounder. Multiple studies, including large cohort studies, have found no association between the use of azithromycin in the first trimester and major congenital malformations, including heart defects.112-114 A systematic review of pregnancy outcomes following macrolide use found no significant increased risks for major congenital malformations or congenital heart defects following all macrolide use in the first trimester, but a small but significant increased rate of major congenital malformations with azithromycin though maternal confounders could not be excluded. In a Cochrane systematic review of Chlamydia trachomatis infection treatment in pregnancy, there was no apparent difference between azithromycin and other agents in terms of efficacy and pregnancy complications.115 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-11 References 1. Karakousis PC, Moore RD, Chaisson RE. 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Available at: 29. Hellyer TJ, Brown IN, Taylor MB, Allen BW, Easmon CS. Gastro-intestinal involvement in Mycobacterium avium-intracellulare infection of patients with HIV. J Infect. 1993;26(1):55-66. Available at: 30. Torriani FJ, McCutchan JA, Bozzette SA, Grafe MR, Havlir DV. Autopsy findings in AIDS patients with Mycobacterium avium complex bacteremia. J Infect Dis. 1994;170(6):1601-1605. Available at: 31. Roth RI, Owen RL, Keren DF, Volberding PA. Intestinal infection with Mycobacterium avium in acquired immune deficiency syndrome (AIDS): histological and clinical comparison with Whipple’s disease. Dig Dis Sci. 1985;30(5):497-504. Available at: 32. Gillin JS, Urmacher C, West R, Shike M. Disseminated Mycobacterium avium-intracellulare infection in acquired immunodeficiency syndrome mimicking Whipple’s disease. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-14 Gastroenterology. 1983;85(5):1187-1191. Available at: 33. Inderlied CB, Kemper CA, Bermudez LE. The Mycobacterium avium complex. Clin Microbiol Rev. 1993;6(3):266-310. Available at: 34. Packer SJ, Cesario T, Williams JH, Jr. Mycobacterium avium complex infection presenting as endobronchial lesions in immunosuppressed patients. Ann Intern Med. 1988;109(5):389-393. Available at: 35. Shanson DC, Dryden MS. Comparison of methods for isolating Mycobacterium avium-intracellulare from blood of patients with AIDS. J Clin Pathol. 1988;41(6):687-690. Available at: 36. Hafner R, Inderlied CB, Peterson DM, et al. Correlation of quantitative bone marrow and blood cultures in AIDS patients with disseminated Mycobacterium avium complex infection. J Infect Dis. 1999;180(2):438-447. Available at: 37. Cornejo-Juárez P, Islas-Muñoz B, Ramírez-Ibarguen AF, et al. Bone marrow culture yield for the diagnosis of opportunistic diseases in patients with AIDS and disseminated Kaposi sarcoma. Curr HIV Res. 2020;18(4):277-282. Available at: 38. Prabhu V, Coelho S, Achappa B, Baliga S, Sharon L, Shah J. Role of fluorescence in situ hybridization in detecting Mycobacterium avium complex presenting as fever in treatment failure HIV. J Clin Tuberc Other Mycobact Dis. 2020;21:100188. Available at: 39. Sharma S, Latawa R, Wanchu A, Verma I. Differential diagnosis of disseminated Mycobacterium avium and Mycobacterium tuberculosis infection in HIV patients using duplex PCR. Future Microbiol. 2021;16(3):159-173. Available at: 40. Sharvit G, Schwartz D, Heering G, et al. Evaluation of the clinical impact of bone marrow cultures in current medical practice. Sci Rep. 2022;12(1):9664. Available at: 41. Daley CL, Iaccarino JM, Lange C, et al. Treatment of nontuberculous mycobacterial pulmonary disease: an official ATS/ERS/ESCMID/IDSA Clinical Practice Guideline. Clin Infect Dis. 2020;71(4):e1-e36. Available at: 42. Dworkin MS, Hanson DL, Kaplan JE, Jones JL, Ward JW. Risk for preventable opportunistic infections in persons with AIDS after antiretroviral therapy increases CD4+ T lymphocyte counts above prophylaxis thresholds. J Infect Dis. 2000;182(2):611-615. Available at: 43. El-Sadr WM, Burman WJ, Grant LB, et al. Discontinuation of prophylaxis for Mycobacterium avium complex disease in HIV-infected patients who have a response to Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-15 antiretroviral therapy. Terry Beirn Community Programs for Clinical Research on AIDS. N Engl J Med. 2000;342(15):1085-1092. Available at: 44. Currier JS, Williams PL, Koletar SL, et al. Discontinuation of Mycobacterium avium complex prophylaxis in patients with antiretroviral therapy-induced increases in CD4+ cell count: a randomized, double-blind, placebo-controlled trial. AIDS Clinical Trials Group 362 Study Team. Ann Intern Med. 2000;133(7):493-503. Available at: 45. Furrer H, Telenti A, Rossi M, Ledergerber B. Discontinuing or withholding primary prophylaxis against Mycobacterium avium in patients on successful antiretroviral combination therapy. The Swiss HIV Cohort Study. AIDS. 2000;14(10):1409-1412. Available at: 46. Brooks JT, Song R, Hanson DL, et al. Discontinuation of primary prophylaxis against Mycobacterium avium complex infection in HIV-infected persons receiving antiretroviral therapy: observations from a large national cohort in the United States, 1992–2002. Clin Infect Dis. 2005;41(4):549-553. Available at: 47. Chene G, Phillips A, Costagliola D, et al. Cohort profile: Collaboration of Observational HIV Epidemiological Research Europe (COHERE) in EuroCoord. Int J Epidemiol. 2017;46(3):797-797n. Available at: 48. Pasayan MKU, ML SM, Boettiger D, et al. Effect of macrolide prophylactic therapy on AIDS-defining conditions and HIV-associated mortality. J Acquir Immune Defic Syndr. 2019;80(4):436-443. Available at: 49. Lange CG, Woolley IJ, Brodt RH. Disseminated Mycobacterium avium-intracellulare complex (MAC) infection in the era of effective antiretroviral therapy: is prophylaxis still indicated? Drugs. 2004;64(7):679-692. Available at: 50. Sax PE. “Choosing wisely” in HIV medicine — should we stop giving MAC prophylaxis? HIV and ID Observations. 2016;2018(3/20/2016). Available at: 51. Vervoort SC, Borleffs JC, Hoepelman AI, Grypdonck MH. Adherence in antiretroviral therapy: a review of qualitative studies. AIDS. 2007;21(3):271-281. Available at: 52. Havlir DV, Dube MP, Sattler FR, et al. Prophylaxis against disseminated Mycobacterium avium complex with weekly azithromycin, daily rifabutin, or both. California Collaborative Treatment Group. N Engl J Med. 1996;335(6):392-398. Available at: 53. Pierce M, Crampton S, Henry D, et al. A randomized trial of clarithromycin as prophylaxis against disseminated Mycobacterium avium complex infection in patients with advanced Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-16 acquired immunodeficiency syndrome. N Engl J Med. 1996;335(6):384-391. Available at: 54. Uthman MM, Uthman OA, Yahaya I. Interventions for the prevention of Mycobacterium avium complex in adults and children with HIV. Cochrane Database Syst Rev. 2013(4):CD007191. Available at: 55. Chaisson RE, Benson CA, Dube MP, et al. Clarithromycin therapy for bacteremic Mycobacterium avium complex disease. A randomized, double-blind, dose-ranging study in patients with AIDS. AIDS Clinical Trials Group Protocol 157 Study Team. Ann Intern Med. 1994;121(12):905-911. Available at: 56. May T, Brel F, Beuscart C, et al. Comparison of combination therapy regimens for treatment of human immunodeficiency virus-infected patients with disseminated bacteremia due to Mycobacterium avium. ANRS Trial 033 Curavium Group. Agence Nationale de Recherche sur le Sida. Clin Infect Dis. 1997;25(3):621-629. Available at: 57. Gordin FM, Sullam PM, Shafran SD, et al. A randomized, placebo-controlled study of rifabutin added to a regimen of clarithromycin and ethambutol for treatment of disseminated infection with Mycobacterium avium complex. Clin Infect Dis. 1999;28(5):1080-1085. Available at: 58. Dube MP, Sattler FR, Torriani FJ, et al. A randomized evaluation of ethambutol for prevention of relapse and drug resistance during treatment of Mycobacterium avium complex bacteremia with clarithromycin-based combination therapy. California Collaborative Treatment Group. J Infect Dis. 1997;176(5):1225-1232. Available at: 59. Cohn DL, Fisher EJ, Peng GT, et al. A prospective randomized trial of four three-drug regimens in the treatment of disseminated Mycobacterium avium complex disease in AIDS patients: excess mortality associated with high-dose clarithromycin. Terry Beirn Community Programs for Clinical Research on AIDS. Clin Infect Dis. 1999;29(1):125-133. Available at: 60. Aberg JA, Yajko DM, Jacobson MA. Eradication of AIDS-related disseminated Mycobacterium avium complex infection after 12 months of antimycobacterial therapy combined with highly active antiretroviral therapy. J Infect Dis. 1998;178(5):1446-1449. Available at: 61. Ward TT, Rimland D, Kauffman C, Huycke M, Evans TG, Heifets L. Randomized, open-label trial of azithromycin plus ethambutol vs. clarithromycin plus ethambutol as therapy for Mycobacterium avium complex bacteremia in patients with human immunodeficiency virus infection. Veterans Affairs HIV Research Consortium. Clin Infect Dis. 1998;27(5):1278-1285. Available at: 62. Dunne M, Fessel J, Kumar P, et al. A randomized, double-blind trial comparing azithromycin and clarithromycin in the treatment of disseminated Mycobacterium avium infection in patients with human immunodeficiency virus. Clin Infect Dis. 2000;31(5):1245-1252. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-17 63. Xu HB, Jiang RH, Li L. Treatment outcomes for Mycobacterium avium complex: a systematic review and meta-analysis. Eur J Clin Microbiol Infect Dis. 2014;33(3):347-358. Available at: 64. Shafran SD, Singer J, Zarowny DP, et al. A comparison of two regimens for the treatment of Mycobacterium avium complex bacteremia in AIDS: rifabutin, ethambutol, and clarithromycin versus rifampin, ethambutol, clofazimine, and ciprofloxacin. Canadian HIV Trials Network Protocol 010 Study Group. N Engl J Med. 1996;335(6):377-383. Available at: 65. Food and Drug Administration. Clarithromycin [package insert]. 2017. Accessed May 25. Available at: 5s026lbl.pdf. 66. Griffith DE, Aksamit T, Brown-Elliott BA, et al. An official ATS/IDSA statement: diagnosis, treatment, and prevention of nontuberculous mycobacterial diseases. Am J Respir Crit Care Med. 2007;175(4):367-416. Available at: 67. Gardner EM, Burman WJ, DeGroote MA, Hildred G, Pace NR. Conventional and molecular epidemiology of macrolide resistance among new Mycobacterium avium complex isolates recovered from HIV-infected patients. Clin Infect Dis. 2005;41(7):1041-1044. Available at: 68. Craft JC, Notario GF, Grosset JH, Heifets LB. Clarithromycin resistance and susceptibility patterns of Mycobacterium avium strains isolated during prophylaxis for disseminated infection in patients with AIDS. Clin Infect Dis. 1998;27(4):807-812. Available at: 69. Chaisson RE, Keiser P, Pierce M, et al. Clarithromycin and ethambutol with or without clofazimine for the treatment of bacteremic Mycobacterium avium complex disease in patients with HIV infection. AIDS. 1997;11(3):311-317. Available at: 70. Koh WJ, Hong G, Kim SY, et al. Treatment of refractory Mycobacterium avium complex lung disease with a moxifloxacin-containing regimen. Antimicrob Agents Chemother. 2013;57(5):2281-2285. Available at: 71. Chapagain M, Pasipanodya JG, Athale S, et al. Omadacycline efficacy in the hollow fibre system model of pulmonary Mycobacterium avium complex and potency at clinically attainable doses. J Antimicrob Chemother. 2022;77(6):1694-1705. Available at: 72. Litvinov V, Makarova M, Kudlay D, Nikolenko N, Mikhailova J. In vitro activity of bedaquiline against Mycobacterium avium complex. J Med Microbiol. 2021;70(10). Available at: 73. Lin S, Hua W, Wang S, et al. In vitro assessment of 17 antimicrobial agents against clinical Mycobacterium avium complex isolates. BMC Microbiol. 2022;22(1):175. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-18 74. Gil E, Sweeney N, Barrett V, et al. Bedaquiline as treatment for disseminated nontuberculous mycobacteria infection in 2 patients co-infected with HIV. Emerg Infect Dis. 2021;27(3):944-948. Available at: 75. Philley JV, Wallace RJ, Jr., Benwill JL, et al. Preliminary results of bedaquiline as salvage therapy for patients with nontuberculous mycobacterial lung disease. Chest. 2015;148(2):499-506. Available at: 76. Shirley M. Amikacin liposome inhalation suspension: a review in Mycobacterium avium complex lung disease. Drugs. 2019;79(5):555-562. Available at: 77. Aberg JA, Williams PL, Liu T, et al. A study of discontinuing maintenance therapy in human immunodeficiency virus-infected subjects with disseminated Mycobacterium avium complex: AIDS Clinical Trial Group 393 Study Team. J Infect Dis. 2003;187(7):1046-1052. Available at: 78. Shafran SD, Mashinter LD, Phillips P, et al. Successful discontinuation of therapy for disseminated Mycobacterium avium complex infection after effective antiretroviral therapy. Ann Intern Med. 2002;137(9):734-737. Available at: 79. Kirk O, Reiss P, Uberti-Foppa C, et al. Safe interruption of maintenance therapy against previous infection with four common HIV-associated opportunistic pathogens during potent antiretroviral therapy. Ann Intern Med. 2002;137(4):239-250. Available at: 80. Shafran SD, Deschenes J, Miller M, Phillips P, Toma E. Uveitis and pseudojaundice during a regimen of clarithromycin, rifabutin, and ethambutol. MAC Study Group of the Canadian HIV Trials Network. N Engl J Med. 1994;330(6):438-439. Available at: 81. Hafner R, Bethel J, Power M, et al. Tolerance and pharmacokinetic interactions of rifabutin and clarithromycin in human immunodeficiency virus-infected volunteers. Antimicrob Agents Chemother. 1998;42(3):631-639. Available at: 82. Panel on Antiretroviral Guidelines for Adults and Adolescents. Guidelines for the use of antiretroviral agents in adults and adolescents with HIV. 2023. Available at: 83. Hennig S, Svensson EM, Niebecker R, et al. Population pharmacokinetic drug-drug interaction pooled analysis of existing data for rifabutin and HIV PIs. J Antimicrob Chemother. 2016;71(5):1330-1340. Available at: 84. Naiker S, Connolly C, Wiesner L, et al. Randomized pharmacokinetic evaluation of different rifabutin doses in African HIV-infected tuberculosis patients on lopinavir/ritonavir-based Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-19 antiretroviral therapy. BMC Pharmacol Toxicol. 2014;15:61. Available at: 85. Kakuda TN, Woodfall B, De Marez T, et al. Pharmacokinetic evaluation of the interaction between etravirine and rifabutin or clarithromycin in HIV-negative, healthy volunteers: results from two phase 1 studies. J Antimicrob Chemother. 2014;69(3):728-734. Available at: 86. Ramanathan S, Mathias AA, German P, Kearney BP. Clinical pharmacokinetic and pharmacodynamic profile of the HIV integrase inhibitor elvitegravir. Clin Pharmacokinet. 2011;50(4):229-244. Available at: 87. Dooley KE, Sayre P, Borland J, et al. Safety, tolerability, and pharmacokinetics of the HIV integrase inhibitor dolutegravir given twice daily with rifampin or once daily with rifabutin: results of a phase 1 study among healthy subjects. J Acquir Immune Defic Syndr. 2013;62(1):21-27. Available at: 88. Brainard DM, Kassahun K, Wenning LA, et al. Lack of a clinically meaningful pharmacokinetic effect of rifabutin on raltegravir: in vitro/in vivo correlation. J Clin Pharmacol. 2011;51(6):943-950. Available at: 89. Le X, Guo X, Sun J, et al. Pharmacokinetic features of dolutegravir with rifampicin and rifabutin among patients coinfected with human immunodeficiency virus and tuberculosis/Mycobacterium avium complex. Int J Infect Dis. 2022;116:147-150. Available at: 90. Alffenaar JW, Martson AG, Heysell SK, et al. Therapeutic drug monitoring in non-tuberculosis mycobacteria infections. Clin Pharmacokinet. 2021;60(6):711-725. Available at: 91. Phillips P, Kwiatkowski MB, Copland M, Craib K, Montaner J. Mycobacterial lymphadenitis associated with the initiation of combination antiretroviral therapy. J Acquir Immune Defic Syndr. 1999;20(2):122-128. Available at: 92. Phillips P, Bonner S, Gataric N, et al. Nontuberculous mycobacterial immune reconstitution syndrome in HIV-infected patients: spectrum of disease and long-term follow-up. Clin Infect Dis. 2005;41(10):1483-1497. Available at: 93. Race EM, Adelson-Mitty J, Kriegel GR, et al. Focal mycobacterial lymphadenitis following initiation of protease-inhibitor therapy in patients with advanced HIV-1 disease. Lancet. 1998;351(9098):252-255. Available at: 94. Cabie A, Abel S, Brebion A, Desbois N, Sobesky G. Mycobacterial lymphadenitis after initiation of highly active antiretroviral therapy. Eur J Clin Microbiol Infect Dis. 1998;17(11):812-813. Available at: 95. Smibert OC, Trubiano JA, Cross GB, Hoy JF. Short communication: Mycobacterium avium complex infection and immune reconstitution inflammatory syndrome remain a challenge in Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-20 the era of effective antiretroviral therapy. AIDS Res Hum Retroviruses. 2017;33(12):1202-1204. Available at: 96. Barber DL, Andrade BB, McBerry C, Sereti I, Sher A. Role of IL-6 in Mycobacterium avium—associated immune reconstitution inflammatory syndrome. J Immunol. 2014;192(2):676-682. Available at: 97. Breglio KF, Vinhaes CL, Arriaga MB, et al. Clinical and immunologic predictors of Mycobacterium avium complex immune reconstitution inflammatory syndrome in a contemporary cohort of patients with human immunodeficiency virus. J Infect Dis. 2021;223(12):2124-2135. Available at: 98. Wormser GP, Horowitz H, Dworkin B. Low-dose dexamethasone as adjunctive therapy for disseminated Mycobacterium avium complex infections in AIDS patients. Antimicrob Agents Chemother. 1994;38(9):2215-2217. Available at: 99. Rocco JM, Laidlaw E, Galindo F, et al. Severe mycobacterial immune reconstitution inflammatory syndrome (IRIS) in advanced human immunodeficiency virus (HIV) has features of hemophagocytic lymphohistiocytosis and requires prolonged immune suppression. Clin Infect Dis. 2023;76(3):e561-e570. Available at: 100. Rocco JM, Laidlaw E, Galindo F, et al. Mycobacterial immune reconstitution inflammatory syndrome in HIV is associated with protein-altering variants in hemophagocytic lymphohistiocytosis-related genes. J Infect Dis. 2023;228(2):111-115. Available at: 101. Masur H. Recommendations on prophylaxis and therapy for disseminated Mycobacterium avium complex disease in patients infected with the human immunodeficiency virus. Public Health Service Task Force on Prophylaxis and Therapy for Mycobacterium avium Complex. N Engl J Med. 1993;329(12):898-904. Available at: 102. Kemper CA, Meng TC, Nussbaum J, et al. Treatment of Mycobacterium avium complex bacteremia in AIDS with a four-drug oral regimen: rifampin, ethambutol, clofazimine, and ciprofloxacin. The California Collaborative Treatment Group. Ann Intern Med. 1992;116(6):466-472. Available at: 103. Chiu J, Nussbaum J, Bozzette S, et al. Treatment of disseminated Mycobacterium avium complex infection in AIDS with amikacin, ethambutol, rifampin, and ciprofloxacin. California Collaborative Treatment Group. Ann Intern Med. 1990;113(5):358-361. Available at: 104. Rodriguez Diaz JC, Lopez M, Ruiz M, Royo G. In vitro activity of new fluoroquinolones and linezolid against non-tuberculous mycobacteria. Int J Antimicrob Agents. 2003;21(6):585-588. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV W-21 105. Liu L, Song Z, Xun J, et al. PD-1 inhibitor for disseminated Mycobacterium avium infection in a person with HIV. Open Forum Infect Dis. 2023;10(1):ofac700. Available at: 106. Aberg J, Powderly W. HIV: primary and secondary prophylaxis for opportunistic infections. BMJ Clin Evid. 2010;2010. Available at: 107. Green H, Hay P, Dunn DT, McCormack S, Investigators S. A prospective multicentre study of discontinuing prophylaxis for opportunistic infections after effective antiretroviral therapy. HIV Med. 2004;5(4):278-283. Available at: 108. El-Sadr WM, Murphy RL, Yurik TM, et al. Atovaquone compared with dapsone for the prevention of Pneumocystis carinii pneumonia in patients with HIV infection who cannot tolerate trimethoprim, sulfonamides, or both. Community Program for Clinical Research on AIDS and the AIDS Clinical Trials Group. N Engl J Med. 1998;339(26):1889-1895. Available at: 109. Einarson A, Phillips E, Mawji F, et al. A prospective controlled multicentre study of clarithromycin in pregnancy. Am J Perinatol. 1998;15(9):523-525. Available at: 110. Drinkard CR, Shatin D, Clouse J. Postmarketing surveillance of medications and pregnancy outcomes: clarithromycin and birth malformations. Pharmacoepidemiol Drug Saf. 2000;9(7):549-556. Available at: 111. Muanda FT, Sheehy O, Berard A. Use of antibiotics during pregnancy and risk of spontaneous abortion. CMAJ. 2017;189(17):E625-E633. Available at: 112. Berard A, Sheehy O, Zhao JP, Nordeng H. Use of macrolides during pregnancy and the risk of birth defects: a population-based study. Pharmacoepidemiol Drug Saf. 2015;24(12):1241-1248. Available at: 113. Lin KJ, Mitchell AA, Yau WP, Louik C, Hernandez-Diaz S. Safety of macrolides during pregnancy. Am J Obstet Gynecol. 2013;208(3):221 e221-228. Available at: 114. Bahat Dinur A, Koren G, Matok I, et al. Fetal safety of macrolides. Antimicrob Agents Chemother. 2013;57(7):3307-3311. Available at: 115. Cluver C, Novikova N, Eriksson DO, Bengtsson K, Lingman GK. Interventions for treating genital chlamydia trachomatis infection in pregnancy. Cochrane Database Syst Rev. 2017;9(9):CD010485. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-1 Mycobacterium tuberculosis Infection and Disease Updated: May 2, 2024 Reviewed: May 2, 2024 Epidemiology Tuberculosis (TB) is the leading cause of morbidity and mortality among people with HIV worldwide. In 2020 and 2021, progress towards reducing TB morbidity and mortality slowed amidst the widespread disruption of health services from the COVID-19 pandemic. Globally, the annual number of estimated TB deaths increased in 2020 and 2021, to 1.5 million and 1.6 million, respectively.1,2 Among people with HIV, there were an estimated 703,000 people who had TB, but only 52% were diagnosed and reported. A total of 187,000 deaths among people with HIV were attributed to TB in 2021, the first time there has been an increase in HIV-associated TB deaths since 2006.2 People with HIV still account for a disproportionate number of TB deaths worldwide (11.8% of deaths vs. 6.7% of TB cases); however, a 47% reduction in deaths has occurred since 2010.2 In the United States, more than two-thirds (5,456; 71.4%) of people newly reported with TB in 2021 were born outside the United States, similar to 2019 and 2020 proportions.3 The incidence of HIV-related TB in the United States has declined substantially, in part because of the widespread use of antiretroviral therapy (ART).4,5 Among all people reported with TB with known HIV status in the United States in 2021, 293 people (4.2%) were coinfected with HIV (6.3% among people with TB aged 25–44 years vs. 5.6% among those aged 45–64 years).6 Overall, the proportion of reported people with TB and HIV co-infection has been steadily declining over the past decade (7.4% in 2011). Latent TB Infection TB infection occurs when a person inhales droplet nuclei containing Mycobacterium tuberculosis organisms. Usually within 2 to 12 weeks after infection, the immune response limits the multiplication of tubercle bacilli. However, viable bacilli can persist for years, a condition referred to as latent TB infection (LTBI). People with LTBI are asymptomatic and are not infectious. TB disease (defined as clinically active disease, often with positive smears and cultures) can develop soon after exposure to M. tuberculosis organisms (primary disease) or after reactivation of latent infection.7,8 The risk of TB disease due to reactivation of LTBI for people with untreated HIV has been estimated as 3% to 16% per year, which approximates the lifetime risk of TB disease for people with LTBI who do not have HIV (approximately 5%).9-14 The risk of TB disease begins in the first year following HIV infection.15 TB disease can occur at any CD4 T lymphocyte (CD4) cell count, although the risk increases with progressive immunodeficiency.15,16 The estimated annual risk of developing TB disease among people with LTBI (diagnosed by a positive tuberculin skin test [TST] or interferon-gamma release assay [IGRA] in the absence of a TB disease diagnosis) is 3 to 12 times greater for people with untreated HIV than for those without HIV.17 Even with effective ART, the risk of TB disease among people with HIV remains greater than that among the general population.18 Since 2006, the TB incidence rate in people with HIV has been lower than in previous years, but the TB risk is still substantially higher than among people without HIV.19 In the United States, the most common predisposing factor for TB infection is birth or residence outside of the United States.20 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-2 The risk of progression from LTBI to TB disease in people with HIV is reduced both by ART and by the treatment of LTBI.18,21-24 In combination with ART, isoniazid preventive therapy decreased the risk of TB disease by 76% among people with HIV in Brazil.25 Furthermore, isoniazid preventive therapy and ART independently and additively decreased the risk of death and severe HIV-related illness.21,23 Diagnosing Latent TB Infection All people with HIV should be evaluated for LTBI at the time of HIV diagnosis, regardless of their epidemiological risk of TB exposure. In programmatic settings in the United States, TB screening has been suboptimal, with only 47% to 69% of people with HIV presenting to care completing initial screening, and 42% of those with LTBI initiating therapy.26-30 The two current diagnostics available for the detection of M. tuberculosis infection in the United States, IGRA and TST, help differentiate those with and without TB infection. However, the diagnostic accuracy of TST and IGRA is limited; a negative test does not exclude the diagnosis of LTBI or TB disease, and a positive test does not, by itself, mean LTBI therapy is warranted. Decisions about medical and public health management should include epidemiological risk factors, medical history, and other clinical information when interpreting IGRA or TST results. People with advanced HIV (CD4 count <200 cells/mm3) and negative diagnostic tests for LTBI, and no indications for initiating empiric LTBI treatment (i.e., no recent exposure to a culture-confirmed TB case) should be retested for LTBI once they start ART and attain a CD4 count ≥200 cells/mm3 to ensure that the initial test result was a true negative result.31-33 Annual testing for LTBI using TST or IGRA is recommended only for people with HIV who have a history of a negative test for infection and are at high risk for repeated or ongoing exposure to people with active TB disease (e.g., during incarceration, travel to a high-TB incidence country, homelessness, living in a congregate setting).34 Traditionally, LTBI has been defined by the presence of a positive TST (≥5 mm of induration at 48– 72 hours in people with HIV) in people with no clinical or radiographic evidence of TB disease. Despite the extensive experience with the TST among people with HIV, the test has several disadvantages: the requirement for two visits to place and read the test, decreased specificity (false positive results) among people who received Bacillus Calmette-Guérin (BCG) vaccination, and decreased sensitivity (false negative results) among people with advanced immunodeficiency.33,35 The first two limitations of the TST have led to broader use of IGRAs for the detection of LTBI. IGRAs include the T-SPOT.TB and QFT-TB Gold Plus (QFT-Plus). Systematic reviews and meta-analyses, as well as a large study in the United States, have found that IGRAs generally have higher specificity than the TST, may correlate better with exposure to M. tuberculosis, and are less likely to cross-react with BCG vaccination or exposure to nontuberculous mycobacteria.19,36,37 A systematic review among people with HIV did not find robust evidence that IGRAs were superior to TST in diagnosing either active TB or LTBI.33 However, in a prospective study of 1,510 people with HIV in the United States (median CD4 count of 532 cells/mm3), T.SPOT.TB was significantly more specific (99.7%) and had a significantly higher positive predictive value (PPV; 90.0%) than the older QuantiFERON Gold In-Tube (QFT-GIT) (96.5% specificity, 50.7% PPV) and TST (96.8% specificity, 45.4% PPV). QFT-GIT was significantly more sensitive (72.2%) than TST (54.2%) and T.SPOT.TB (51.9%).38 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-3 As with the TST, progressive immunodeficiency is associated with decreased sensitivity of IGRAs.39 In addition, the reproducibility of positive results of IGRAs may be limited. Among 46 people with HIV who had initial positive tests with the QFT-GIT assay, 33 (72%) had negative repeat tests, particularly those whose responses were at the lower range of the manufacturer’s suggested range of positive results.40 Similar to recommendations for healthcare workers, annual testing for people with HIV is no longer recommended unless high risk exists for repeated or ongoing exposure to people with active TB disease.41 Among people with HIV, the correlation between the TST and IGRA test results is poor to moderate.42,43 In prospective studies not limited to people with HIV, positive results with either the TST or IGRA were associated with an increased risk of developing TB disease.19,44-46 In some studies (again not limited to people with HIV), patients with a positive IGRA were at a higher risk of subsequently developing TB disease than those with a positive TST.19,47,48 Despite its limitations, a positive TST result strongly predicts that the treatment of LTBI will decrease the risk of TB progression among people with HIV.18 Studies are underway to formally evaluate if IGRAs are similarly predictive.49 Although no definitive comparisons of the TST and IGRAs for screening people with HIV in low-burden settings have been published, both the TST and the approved IGRAs are considered appropriate for TB screening among people with HIV in the United States.17,38 Some experts have suggested using both the TST and an IGRA in a stepwise or sequential manner to screen for LTBI, but the predictive value of this approach is not clear, and it may be challenging to implement. The routine use of both TST and IGRAs in a single patient to screen for LTBI is not recommended in the United States.50 As tests of immune reactivity against M. tuberculosis, TST and IGRAs are often positive among people with TB disease. Therefore, all people with a positive TST or IGRA should be evaluated for the possibility of active TB disease.17 Most, but not all, people with HIV and TB disease have symptoms (e.g., cough, fever, sweats, weight loss, lymphadenopathy); the absence of these symptoms had a 98% negative predictive value for culture-positive TB in low-resource settings, although this varied depending on pretest probability.51 The addition of a chest radiograph improved the sensitivity of this screening algorithm but decreased specificity.52 It is important to note that in a symptomatic patient with clinical suspicion of TB disease, a negative TST or IGRA does not rule out TB disease, particularly in those with CD4 count <200 cells/mm3. Obtaining a sputum specimen for M. tuberculosis identification is the gold standard for diagnosing pulmonary TB disease, but it is not high yield in screening people with HIV without pulmonary symptoms, particularly in low-prevalence settings. Therefore, a negative symptom screen (including absent cough of any duration) coupled with a normal chest radiograph is usually sufficient to exclude TB disease in a patient with a positive TST or IGRA in low TB incidence settings.17 Sub-clinical TB among people with HIV is of greater concern in high TB burden settings.53 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-4 Treating Latent TB Infection Recommendations for Treating LTBI to Prevent TB Disease in People with HIV Indications • Positive screening testa for LTBI (≥5 mm of induration at 48–72 hours in people with HIV or positive IGRA) regardless of BCG status, no evidence of active TB disease, and no prior history of treatment for active disease or latent TB infection (AI). • Close contact with a person with infectious TB (such as someone who has shared air space, such as in a household or close congregate setting, with a person with active pulmonary TB according to the Centers for Disease Control and Prevention Guidelines for the Investigation of Contacts of Persons with Infectious Tuberculosis) regardless of screening test result and CD4 count (AII). Preferred Therapy • Isoniazid 15 mg/kg PO once weekly (900 mg maximum) plus rifapentine (see weight-based dosing below) PO once weekly plus pyridoxine 50 mg PO once weekly (3HP) for 12 weeks (AI). Note: 3HP is recommended only for virally-suppressed patients receiving an efavirenz-, raltegravir-, or once-daily dolutegravir-based ARV regimen (AII). o Rifapentine Weekly Dose (maximum 900 mg)  Weighing 25.1–32 kg: 600 mg  Weighing 32.1–49.9 kg: 750 mg  Weighing ≥50.0 kg: 900 mg • Isoniazid 300 mg PO daily plus rifampin 600 mg PO daily plus pyridoxine 25–50 mg PO daily (AI) for 3 months (3HR). See the Dosing Recommendations for use of ARV and Anti-TB Drugs When Treating Latent TB table for the list of ARV drugs not recommended for use with rifampin (e.g., protease inhibitors, bictegravir) and those which require dosage adjustment (i.e., raltegravir, dolutegravir, or maraviroc). Alternative Therapy • Isoniazid 300 mg PO daily plus pyridoxine 25–50 mg PO daily for 6–9 months (AII) or • Rifampin 600 mg PO daily for 4 months (BI) (4R) o Consult the Tuberculosis/HIV Coinfection section of the Adult and Adolescent Antiretroviral Guidelines for the list of ARV drugs not recommended for use with rifampin (e.g., protease inhibitors, bictegravir) and those which require dosage adjustment (e.g., raltegravir, dolutegravir, or maraviroc). • Isoniazid 300 mg PO daily plus rifapentine (see weight-based dosing below) PO daily plus pyridoxine 25–50 mg PO daily for 4 weeks (BI) (1HP) Note: 1HP is recommended only for patients receiving an efavirenz-based ARV regimen (AI). o Rifapentine Daily Dose (maximum 600 mg)  Weighing <35 kg: 300 mg  Weighing 35–45 kg: 450 mg  Weighing >45 kg: 600 mg • For people exposed to drug-resistant TB, select drugs for prevention of TB after consultation with experts and with public health authorities (AIII). Pregnancy Considerations • 4R and 3HR are acceptable alternative regimens for pregnant people with HIV (BIII). • For pregnant people receiving effective ART and without close household contact with infectious TB or recent test for TB infection (TST or IGRA) conversion from negative to positive, therapy for LTBI may be deferred until after delivery (BIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-5 • Although rifampin generally is considered safe in pregnancy, data on the use of rifapentine are extremely limited and its use in pregnant people is not currently recommended (BIII). Additional Considerations • Deferring ART until after completion of treatment for LTBI is not recommended (AI). • Given the important drug–drug interactions between rifamycins and several antiretroviral (ARV) agents, selection of an LTBI regimen will depend on a patient’s current or planned ARV regimen. a Screening tests for LTBI include a tuberculin skin test (TST) or interferon-gamma release assay (IGRA); see text for details regarding these tests. Key: H = Isoniazid; P = Rifapentine; R = Rifampin; ARV = antiretroviral; CDC = Centers for Disease Control and Prevention; CD4 = CD4 T lymphocyte; CNS = central nervous system; DOT = directly observed therapy; IRIS = immune reconstitution inflammatory syndrome; IPT = isoniazid preventive therapy; LTBI = latent tuberculosis infection; PI = protease inhibitor; PO = orally; TB = tuberculosis Once active TB disease is excluded and in the absence of other medical contraindications, people with HIV with a positive TB screening test should receive LTBI treatment (AI), unless there is documentation of prior treatment for active TB or LTBI.54 Additionally, people with HIV who are in close contact with anyone with infectious TB should receive LTBI treatment, regardless of their TB screening test results and CD4 count (AII). Selection of an LTBI regimen may depend on the potential for drug interactions, toxicity concerns, as well as medication availability and/or cost (see Recommendations for Treating LTBI to Prevent TB Disease in People with HIV table above). People with HIV who have been treated successfully for LTBI should not have repeat testing with TST or IGRA; a previously positive test result generally will not revert to negative. People with HIV in the United States who have a negative TST or IGRA and no recent contact with a person with infectious TB likely will not benefit from the treatment of LTBI, and preventive therapy is not generally recommended (AIII); this is in contrast to high TB prevalence countries where isoniazid (i.e., isoniazid preventive therapy; IPT) decreased TB risk and mortality in people with HIV, regardless of TST or IGRA result.24 LTBI treatment and ART act independently to decrease the risk of TB disease.22,23,25,55,56 Therefore, the use of both interventions is recommended for people with LTBI and HIV (AI). Given the important drug–drug interactions between rifamycins and several antiretroviral (ARV) agents, selection of an LTBI regimen will depend on a patient’s current or planned ARV regimen. Deferring ART until after completion of treatment for LTBI is not recommended (AI).23 Preferred Drugs for Treatment of Latent TB Infection 3HP • Rifapentine (weight-based dosing) orally (PO) once weekly plus isoniazid 15 mg/kg PO once weekly (900 mg maximum) plus pyridoxine 50 mg PO once weekly for 12 weeks is one of two preferred regimens for the treatment of LTBI (AI).54 In two randomized controlled trials, rifapentine plus isoniazid once weekly for 12 weeks (3HP) was as effective and well-tolerated as 6 to 9 months of daily isoniazid, including in people with HIV whose CD4 counts were generally >350 cells/mm3 and who were not yet on ART.57,58 3HP treatment completion rates with self-administered therapy were inferior to those with directly observed therapy (DOT) but non-inferior among study participants enrolled in the United States—and generally high overall.59 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-6 Although individuals taking ART were not included in the Phase 3 trial of 3HP,57 the pharmacokinetic (PK) profile of efavirenz with daily rifapentine and isoniazid is favorable.60,61 Raltegravir concentrations were modestly increased when it was given with once-weekly rifapentine in healthy volunteers.62 In a Phase 1/2 single-arm study of people with HIV treated with dolutegravir and 3HP, rifapentine decreased dolutegravir exposure by 26%. However, trough concentrations remained above the 90% maximum inhibitory concentration for all but one participant, and all participants maintained an undetectable viral load throughout the study period.63 Based on these PK data and limited outcome data, 3HP is recommended in virally suppressed people receiving efavirenz, raltegravir, or once-daily dolutegravir without dose adjustment of rifapentine, isoniazid, or ART (AII).64 A trial is currently underway examining the use of 3HP in ART-naive participants who are initiating therapy with a dolutegravir-based regimen.65 3HP has not been studied in patients receiving twice-daily dolutegravir and is therefore not recommended (AIII). 3HR • Daily isoniazid 300 mg PO daily plus rifampin 600 mg PO daily plus pyridoxine 25 mg to 50 mg PO daily for 3 months is also a preferred option for the treatment of LTBI in people with HIV (AI). In studies of adults and children without HIV who had a positive TST, those who received 3HR had a similar decreased risk of TB disease, hepatotoxicity, and adverse effects requiring treatment discontinuation compared with those who received ≥6 months of daily isoniazid.66-70 Among people with HIV, several studies found no difference in the incidence of TB disease between those who received 3HR and those who received ≥6 months of daily isoniazid, regardless of TST status;71-74 hepatotoxicity was less frequent among those receiving 3HR, but treatment-limiting adverse effects were more common.54 When using rifampin for LTBI treatment, either dose adjustment or substitution of many commonly used ARVs may be needed (see Dosing Recommendations for Use of ARV and Anti-TB Drugs When Treating Latent TB table). Alternative Drugs for Treatment of Latent TB Infection Isoniazid • Isoniazid 300 mg PO daily plus pyridoxine 25 mg to 50 mg PO daily for 6 to 9 months is an alternative regimen for the treatment of LTBI, particularly when drug–drug interactions between rifamycins and ARV regimens limit the use of rifamycin-containing LTBI therapies (AII). Daily isoniazid for 6 to 9 months is effective and reasonably well-tolerated; severe toxicity is infrequent.23,74-78 However, treatment completion rates are suboptimal, decreasing its effectiveness.79 Longer courses of isoniazid (e.g., 12 months) are more effective at preventing TB but carry a higher risk of toxicity80,81 and patients are more likely to complete shorter regimens.57,59,79,82-85 Peripheral neuropathy, hepatitis, and rash may be caused by either isoniazid or some ARV drugs. Isoniazid, when used, should be supplemented with pyridoxine at a dose of 25 to 50 mg per day to prevent peripheral neuropathy (AIII). 4R • Rifampin 600 mg PO daily for 4 months (4R) is an alternative regimen for the treatment of LTBI in people with HIV (BI). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-7 A large trial compared 4 months of daily rifampin (4R) to 9 months of daily isoniazid (9H) in more than 6,000 participants who were predominantly HIV-seronegative.77 Although rates of incident active TB were low in both arms, the 4R regimen was non-inferior to 9H. Treatment completion rates were significantly higher and adverse events were less common in the 4R arm than in the 9H arm (78.8% vs. 63.2%; P < 0.001 and 1.5% vs. 2.6%; P = 0.003, respectively). However, only 255 participants were people with HIV, which limits the generalizability of the findings for this population. Although the National Tuberculosis Controllers Association (NTCA)/CDC guidelines recommend 4R as a preferred treatment for LTBI in people without HIV,54 given the lack of trial data in people with HIV, the 4R regimen is recommended only as an alternative to 3HP, 3HR, and 6 or 9 months of isoniazid in people with HIV (BI). When using rifampin for LTBI treatment, either dose adjustment or substitution of key ARVs may be needed. Given the theoretical but unproven risk of selecting for drug-resistant TB with rifamycin monotherapy in undiagnosed early-stage TB disease and the relatively poor performance of symptom screens alone in people with HIV on ART,86,87 some clinicians would obtain a specimen for M. tuberculosis testing before starting 4R for LTBI. Due to limited data on 4R in people with HIV, concerns about using this regimen in people with low CD4 cell counts, and an absence of data on the use of 4 months of rifabutin either in people with or without HIV, rifabutin monotherapy is not recommended (AIII).88-90 1HP • Isoniazid 300 mg PO daily plus rifapentine (weight-based dosing to a maximum of 600 mg) PO daily plus pyridoxine 25 mg to 50 mg PO daily for 4 weeks (1HP) is an alternative therapy for the treatment of LTBI in people with HIV treated with efavirenz (BI). The BRIEF-TB study (AIDS Clinical Trials Group [ACTG] 5279) evaluated 1 month of daily rifapentine plus isoniazid (1HP) versus 9 months of daily isoniazid (9H) in people with HIV residing in mostly high TB burden settings (TB incidence >60 per 100,000 population).83 The median CD4 count of study participants was 470 cells/mm3, 50% of the study population was on efavirenz or nevirapine-based ART regimens at study entry, and 21% of the study population was TST positive. 1HP was non-inferior to 9H when comparing the composite outcome of confirmed or probable TB, death due to TB, and death due to unknown cause. Treatment completion rates (by self-report) were 97% in the 1HP arm and 90% in the 9H arm. Of note, although the population of people with HIV enrolled was at increased risk for LTBI due to high endemic exposure, the number of participants with documented LTBI based on TST or IGRA testing was low (23%), and the overall event rate (i.e., the number of participants who developed active TB in either arm) was also low (0.56/100 person-years) after more than 3 years of follow-up. Based on these data, 1HP is recommended as an alternative regimen for treatment of LTBI in people with HIV (BI). The NTCA/CDC guidelines do not include 1HP as a preferred or alternative regimen given that the BRIEF-TB study was performed largely in people with HIV living in high TB burden settings, most of whom did not have positive tests for LTBI.54 In light of the strengths of the study results and the convenience and safety of the regimen, some clinicians may choose to use 1HP for treatment of LTBI as an alternative option to those recommended in the current NTCA/CDC guidelines. If ART is administered together with 1HP, an efavirenz-based regimen should be used (AI).60,91 A study evaluating co-administration of 1HP with dolutegravir is in progress; the use of dolutegravir-based ART should await results from this trial.92 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-8 Dosing Recommendations for Use of ARV and Anti-TB Drugs When Treating Latent TB Infection TB Drug ARV Drugs Dose of TB Drug Isoniazid (INH) • All ARVs • Note: for information on coadministration of ARVs with rifampin or rifapentine, see entries below Use INH with pyridoxine 25–50 mg PO daily (50 mg once weekly if used with 3HP) For 3HP (weekly INH + rifapentine x 12 weeks) • 15 mg/kg PO once weekly (900 mg maximum) For 3HR (daily INH + rifampin x 3 months), or 1HP (daily INH + rifapentine x 4 weeks), or INH alone (daily INH x 6–9 months) • 300 mg PO daily Rifampina • NRTIs (TAF with cautionb) • EFV 600 mg • DTG, RAL (twice daily), and MVC without a strong CYP3A4 inhibitor (note: doses of these ARV drugs need to be adjusted when used with rifampin) • IBA, T-20 For 3HR (daily rifampin + INH x 3 months), or 4R (daily rifampin x 4 months) • 600 mg PO daily • All other ARVs Not recommended Rifapentinea 3HP Weekly rifapentine + INH x 12 weeks • EFV 600 mg, RAL or once daily DTG • NRTIs (TAF with cautionb) • IBA, T-20 • Weighing 32.1–49.9 kg: 750 mg PO weekly • Weighing ≥50.0 kg: 900 mg PO weekly • All other ARVs Not recommended Rifapentinea 1HP Daily rifapentine + INH x 4 weeks • NRTIs (TAF with cautionb) • EFV 600 mg • IBA, T-20 • Weighing <35 kg: 300 mg PO daily • Weighing 35–45 kg: 450 mg PO daily • Weighing >45 kg: 600 mg PO daily • All other ARVs Not Recommended a For additional drug—drug interaction information between antiretrovirals and anti-TB drugs, see Drug-Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines. b If TAF and rifamycins are coadministered, monitor for HIV treatment efficacy. Note that FDA labeling recommends not to coadminister. See Drug-Drug Interactions in the Treatment of HIV-Related TB below and Significant Pharmacokinetic Interactions between Drugs Used to Treat or Prevent Opportunistic Infections table for more information. Key: ARV = antiretroviral; BIC = bictegravir; DTG = dolutegravir; EFV = efavirenz; IBA = ibalizumab; IM = intramuscular; INH = isoniazid; MVC = maraviroc; NRTI = nucleoside reverse transcriptase inhibitor; PO = oral; RAL = raltegravir; RTV = ritonavir; T-20 = enfuvirtide; TAF = tenofovir alafenamide; TB = tuberculosis Treatment of LTBI Following Exposure to Drug-Resistant TB For people exposed to drug-resistant TB, a regimen for LTBI should be selected after consultation with experts or with public health authorities (AIII).93 A large randomized clinical trial of 26 weeks of either isoniazid or delamanid for people at high risk for TB, including people with HIV, following household exposure to drug-resistant TB is in progress.94 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-9 Monitoring for Adverse Events Related to Treating Latent TB Infection Individuals receiving TB-preventive therapy should be evaluated by a clinician monthly to assess adherence and evaluate for possible drug toxicity. Although people with HIV may not have a higher risk of hepatitis from isoniazid than people without HIV, people with HIV should have serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) and total bilirubin levels measured before starting LTBI treatment and repeated if abnormal.54 People with concomitant chronic viral hepatitis and older individuals have an increased risk of isoniazid-related hepatotoxicity, and such people should be monitored closely when being treated for LTBI.95,96 Following initiation of isoniazid, ALT and AST levels often increase during the first 3 months of treatment but return to normal despite continued therapy. Hepatotoxicity also can occur with rifamycins, although it is less common than with isoniazid.78,83 Factors that increase the risk of drug-induced clinical hepatitis include daily alcohol consumption, underlying liver disease, pregnancy and early postpartum, and concurrent treatment with other hepatotoxic drugs.97 At each visit, patients should be asked about adherence, new medications, and alcohol use and should be screened for potential adverse effects of treatment for LTBI (e.g., unexplained anorexia, nausea, vomiting, dark urine, icterus, rash, persistent paresthesia of the hands and feet, persistent fatigue, weakness or fever lasting 3 or more days, abdominal tenderness, easy bruising or bleeding, arthralgia) and told to stop medications immediately and return to the clinic for an assessment should any of these occur (AIII). If the serum ALT or AST levels increase to (1) greater than five times the upper limit of normal without symptoms or (2) greater than three times the upper limit of normal AND total bilirubin greater than two times the upper limit of normal without symptoms or (3) greater than three times the upper limit of normal with symptoms (or greater than two times the baseline value for patients with baseline abnormal transaminases), LTBI treatment should be stopped (AIII). The ultimate decision regarding resumption of therapy with the same or different agents for LTBI treatment should be made after weighing the risk for additional hepatic injury against the benefit of preventing progression to TB disease,97 and ideally in consultation with an expert in treating LTBI in people with HIV. If a local expert is not available through the public health department, clinicians and TB programs can contact the CDC (tbinfo@cdc.gov) and utilize remote TB medical consultation services available through the CDC-funded TB Center of Excellence that serves their region. Clinical Manifestations of TB Disease Similar to people without HIV, people with HIV and TB disease may be asymptomatic but have positive sputum cultures with or without abnormal findings on chest radiograph (subclinical TB).98,99 In ambulatory people with HIV, the presence of any one of the classic symptoms of TB disease (i.e., cough, fever, night sweats, weight loss) has high sensitivity but low specificity for diagnosing TB as assessed in resource-limited settings.51 Compared to treatment-naive patients with HIV, the sensitivity of classic TB symptoms is lower in people with HIV on ART.86 The presentation of TB disease is influenced by the degree of immunodeficiency.100-102 In people with HIV and CD4 counts >200 cells/mm3, HIV-related TB generally resembles TB among people without HIV. Most people with or without HIV have disease limited to the lungs, and common chest radiographic manifestations are upper lobe infiltrates with or without cavitation.103 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-10 In people with HIV and CD4 counts <200 cells/mm3, the chest radiographic findings of pulmonary TB are markedly different, with infiltrates showing no predilection for the upper lobes, and cavitation uncommon.100,103,104 Normal chest radiographs can be seen in some people with respiratory symptoms and positive sputum cultures. Thoracic CT scans may demonstrate mild reticulonodular infiltrates despite a normal chest radiograph.105 With increasing degrees of immunodeficiency, extrapulmonary (especially lymphadenitis, pleuritis, pericarditis, and meningitis) or disseminated TB are more common. In people with HIV who are markedly immune-suppressed, TB can be a severe systemic disease with high fevers, rapid progression, and features of sepsis.106 Clinical manifestations of extrapulmonary TB in people with HIV are not substantially different from those described in people without HIV. TB must be considered in disease processes involving any site in the body,107 especially in those with central nervous system (CNS) disease, when early TB treatment is essential to improve outcomes.108-111 After initiation of ART, immune reconstitution can unmask subclinical TB disease, resulting in pronounced inflammatory reactions at the sites of infection (see Unmasking TB-IRIS below). Diagnosis Initial diagnostic testing for TB disease should be directed at the anatomic site of symptoms or signs (e.g., lungs, lymph nodes, urine, cerebrospinal fluid).17 Pulmonary involvement is common at all CD4 counts.99,112 The initial evaluation of a person suspected of having HIV-related TB should always include chest imaging, even in the absence of pulmonary symptoms or signs. However, chest radiography is an imperfect screen for pulmonary TB, particularly among individuals with advanced immunodeficiency who can have TB culture-positive sputum despite normal chest radiographs.113,114 Therefore, sputum acid-fast bacilli (AFB) smear, nucleic acid amplification (NAA) testing, and AFB culture should be performed in people with HIV with symptoms of TB disease who have a normal chest radiograph, as well as in those with no pulmonary symptoms but evidence of TB disease elsewhere in the body.17 Sputum culture yield is not affected by HIV or the degree of immunodeficiency. Sputum smear-negative, culture-positive TB disease is common among people with HIV, particularly those with advanced immunodeficiency and non-cavitary disease.115,116 NAA tests have a higher sensitivity for culture-positive disease than smear.17,117 Smear and culture of three sputum specimens is recommended based on a large study in people with HIV that showed a 10% incremental yield for broth culture between the second and third specimens.118 Additionally, up-front NAA testing for M. tuberculosis can expedite diagnosis.17 Lymph node involvement is common in HIV-related TB, and the combined yield of histopathology, smear, and culture from needle aspirates of enlarged lymph nodes is quite high.119,120 While NAA testing on specimens other than sputum is an off-label use of the test, a positive NAA test result can be useful as evidence of extrapulmonary TB and for clinical decision-making.121 Histopathologic findings also are affected by the degree of immunodeficiency. People with relatively intact immune function have typical granulomatous inflammation associated with TB disease. With progressive immunodeficiency, granulomas become poorly formed or can be completely absent.101,122 Pleural fluid, pericardial fluid, ascites, and cerebrospinal fluid should be sampled if there is clinical evidence of involvement. Polymerase chain reaction (PCR) testing to aid with molecular identification of M. tuberculosis on formalin-fixed tissue is available through reference laboratories Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-11 and, in special situations, through the CDC. Clinical providers and pathologists should contact their state or local health department for consultation with the CDC (tbinfo@cdc.gov) and the CDC-funded TB Center of Excellence for assistance with referring specimens for evaluation. The yield of mycobacterial urine and blood cultures depends on the clinical setting; among people with HIV and advanced immunodeficiency, the yield of culture from these two readily available body fluids can be relatively high101,107 and may allow definitive diagnosis and be the only source of an isolate for drug-susceptibility testing (DST).123 Nucleic-Acid Amplification Testing NAA tests provide rapid diagnosis of TB, and some assays also provide rapid detection of drug resistance. NAA assays, if positive, are highly predictive of TB disease when performed on Acid-Fast Bacillus (AFB) smear-positive specimens. However, because nontuberculous mycobacterial infections (NTM) may occur in people with HIV with advanced immunodeficiency, negative NAA results in the setting of smear-positive specimens may indicate NTM infection and can be used to direct further workup and guide decisions about the need for respiratory isolation. NAA tests are more sensitive than AFB smears, being positive in 50% to 80% of smear-negative, culture-positive sputum specimens124,125 and up to 90% when three NAA tests are performed. Therefore, it is recommended that for all patients with suspected pulmonary TB, an NAA test be performed on at least one sputum specimen.17,126 NAA tests also can be used on extrapulmonary specimens with the caveat that the sensitivity is often lower than with sputum specimens.17 Importantly, a smear-negative specimen with a negative NAA test result does not rule out active TB disease. The Xpert MTB/RIF assay is an automated NAA test that can detect both M. tuberculosis and mutations in the rpoB gene associated with rifampin resistance. It has been implemented widely in resource-limited settings with high TB prevalence and as a frontline TB diagnostic test in people with HIV.127 This assay combines simple processing requirements in the laboratory and rapid turnaround (results within 2 hours). In a meta-analysis, the overall sensitivity and specificity of the Xpert MTB/RIF assay were 88% (95% confidence interval [CI], 83% to 92%) and 98% (95% CI, 97% to 99%), respectively. The assay is somewhat less sensitive among people with HIV overall,128 however, this may be, in part, attributed to a higher prevalence of smear-negative disease in people with HIV.129 In one key study from South Africa, the sensitivity of Xpert MTB/RIF a relationship with CD4 count was demonstrated, indicating higher sensitivity among people with HIV as the CD4 count declined below 500 cells/mm3.130 Importantly, patients in this study with the lowest CD4 count (<100 cells/mm3) actually had higher rates of smear-positivity and higher markers of severe TB disease (C-reactive protein, anemia, and WHO symptom screen). Xpert MTB/RIF sensitivity in extrapulmonary specimens is up to 95% in smear-positive specimens and 69% in smear-negative specimens.131 Median sensitivity varied by specimen type, with higher yield from lymph nodes (96%), cerebrospinal fluid (85%), and gastric aspirates (78%) and lower yield from pleural fluid (34%) and other non-pleural serous fluids (67%). Xpert MTB/RIF also has been applied with excellent diagnostic accuracy to stool specimens in people with pulmonary TB,132 which may provide an alternative for people with HIV who are being evaluated for TB and unable to expectorate. The next-generation Xpert MTB/RIF Ultra improved the sensitivity of the existing test platform, but it is not currently approved by the U.S. Food and Drug Administration (FDA) or available in the Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-12 United States. Similarly, the Xpert MTB/XDR cartridge incorporates other drug-resistance targets that may be relevant for constructing a treatment regimen for drug-resistant TB, particularly in settings without access to conventional growth-based or sequencing-based DST, but is also not currently approved by the U.S. FDA and is unavailable in the United States (see Drug-Resistance Testing, below).133 Lipoarabinomannan (LAM) LAM is an M. tuberculosis cell wall polysaccharide that can be detected in the urine of people with TB.134-137 LAM has been shown to be more sensitive and specific as an adjunct diagnostic test in people with HIV with advanced immunosuppression. The Alere Determine TB LAM is a lateral flow strip applied to a urine sample and recommended by the WHO as an additional diagnostic test for TB among people with HIV.138 Newer generation LAM assays have increased sensitivity and may be particularly useful in paucibacillary clinical specimens such as cerebrospinal fluid. In a study of 101 patients with suspected TB meningitis, 95 of whom were people with HIV, the SILVAMP TB LAM (Fujifilm) sensitivity from cerebrospinal fluid was 52% for definite or probable TB meningitis (with specificity of 98%), which compared favorably to the sensitivity of 55% for Xpert Ultra. LAM assays are not commercially available in the United States at this time.139 Drug-Resistance Testing Evaluation for TB drug resistance should be considered in all people with HIV, especially those who meet any of the following criteria: • Known exposure to a person with drug-resistant TB, • Residence in a setting with high rates of primary drug-resistant TB, • Persistently positive smear or culture results at or after 4 months of treatment, or • Previous TB treatment, particularly if it was not directly observed or was interrupted for any reason. Rapid molecular DST for rifampin (and isoniazid, if available) should be performed on the initial isolates from all patients suspected of having TB, because resistance to rifampin is associated with an increased risk of treatment failure, recurrent TB, and amplification of resistance to additional TB medications.140,141 The presence of multidrug-resistant TB (MDR TB; defined as resistance to at least isoniazid and rifampin) or extensively drug-resistant TB (XDR TB; defined as MDR TB with additional resistance to a fluoroquinolone and either bedaquiline or linezolid) is associated with a markedly increased risk of death.142-144 Therefore, early identification of drug resistance, with appropriate adjustment of the treatment regimen based on both full molecular and conventional DST results, is critical to the successful treatment of TB disease and to curbing transmission of drug-resistant M. tuberculosis.17 For all patients with TB disease, phenotypic DST to first-line TB drugs (isoniazid, rifampin, ethambutol, and pyrazinamide) should be performed, regardless of the source of the specimen. Given the alternative of a shorter drug-susceptible TB regimen containing moxifloxacin (see Treating TB Disease), public health laboratories in the U.S. may add routine moxifloxacin susceptibility testing as well. Molecular resistance testing should be performed, and resistance testing should be repeated if Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-13 sputum cultures remain positive for M. tuberculosis at or after 4 months of treatment or become positive again 1 month or longer after culture conversion to negative. Resistance testing for second-line TB medications (including bedaquiline, linezolid, clofazimine, pretomanid, cycloserine, ethionamide, and others) should be limited to specimens with resistance to first-line TB medications and should be performed in reference laboratories with substantial experience in these techniques.126 Conventional Growth-Based Drug-Susceptibility Testing Conventional DST is used widely and has been validated for first-line drugs. The disadvantage of this technique, however, is that the combined turnaround time of a conventional broth or agar-based culture followed by DST may be as long as 8 weeks,145 due to the slow growth of M. tuberculosis. During this time, people with drug-resistant TB may be receiving ineffective, empiric first-line TB therapy, which could allow ongoing transmission, further clinical deterioration, acquisition of additional drug resistance, and death, particularly in individuals with HIV.144 Yet, for many second-line drugs used to treat MDR and XDR TB, conventional DST remains either the gold standard or the only available technique because molecular correlates of phenotypic drug resistance are incomplete. Molecular Tests for Drug Resistance Genotypic testing to identify mutations that confer drug resistance allows rapid detection of resistance. The relationship between these mutations and drug resistance has been studied for a number of TB medications.146,147 Commercial NAA tests—such as Xpert MTB/RIF—identify resistance mutations associated with rifampin, and commercially available line probe assays (LPAs) identify genotypic resistance to other drugs.129,148 All probe-based assays, including Xpert MTB/RIF and LPAs, should be confirmed with sequence-based tests and growth-based DST. For initial evaluation of drug resistance or confirmation of drug resistance identified by the aforementioned assays, the CDC Division of Tuberculosis Elimination has a Molecular Detection of Drug Resistance (MDDR) service that offers rapid sequencing-based testing for first-and second-line TB medications at no charge for providers evaluating people for drug-resistant TB. State TB programs and state laboratories also should be consulted for resistance testing options. Several assays can be performed on cultured isolates or directly on sputum specimens. Molecular resistance testing also can be performed on extrapulmonary specimens that are NAA-positive; if unable to be performed by local or state public health laboratories, this testing can be arranged through the CDC’s Division of TB Elimination Laboratory (TBLab@cdc.gov). In low TB prevalence settings—such as the United States—the positive predictive value for NAA tests of rifampin resistance is low.149 False-positive rifampin resistance on Xpert MTB/RIF is associated with lower sputum bacillary burden (i.e., high cycle thresholds on Xpert).150 Therefore, isolates with an initial reading of rifampin resistance by commercial NAA test should always undergo confirmatory testing (rpoB gene sequencing and phenotypic DST), with results taken into consideration for treatment decisions. Clinicians who suspect drug-resistant TB in a patient with HIV should make every effort to expedite a diagnosis and consult with their state TB program and then the CDC as needed. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-14 Treating TB Disease Treating Active TB Disease in People with HIV • After collecting a specimen for culture and molecular diagnostic tests, empiric treatment should be initiated in people with HIV with clinical and radiographic presentation suggestive of HIV-related TB (AIII). • DOT is recommended for all patients requiring treatment for HIV-related TB (AII). • Please refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB (below) for specific TB drug dosing recommendations and the Tuberculosis/HIV Coinfection section of the Adult and Adolescent Antiretroviral Guidelines for dosing recommendations of ARV drugs when used with rifampin or rifabutin. • Recommendations for monitoring during TB treatment and when to start ART in the context of TB treatment are described in the text. For Drug-Susceptible TB Preferred Therapy Intensive Phase (8 weeks) • Isoniazid plus pyridoxine plus (rifampin or rifabutin) plus pyrazinamide plus ethambutol 25–50 mg PO daily (AI) • If molecular or phenotypic drug susceptibility reports show sensitivity to isoniazid and rifampin, then ethambutol may be discontinued before the end of 8 weeks (AI). Continuation Phase (for Drug-Susceptible TB) • Isoniazid plus pyridoxine plus (rifampin or rifabutin) 25–50 mg PO daily (AII) Total Duration of Therapy • Pulmonary, drug-susceptible, uncomplicated TB: 6 months (BII) • Pulmonary TB and positive culture at 8 weeks of TB treatment, severe cavitary disease or disseminated extrapulmonary TB: 9 months (BII) • Extrapulmonary TB with TB meningitis: 9–12 months (BII) • Extrapulmonary TB in other sites: 6 months (BII) Alternative Therapy (only for patients receiving an efavirenz-based ARV regimen; not recommended for extrapulmonary TB) Intensive Phase (8 weeks) • Isoniazid plus pyridoxine plus rifapentine 1,200 mg plus moxifloxacin 400 mg plus pyrazinamide 25–50 mg PO daily (AI).a Continuation Phase (9 weeks) • Isoniazid plus pyridoxine plus rifapentine 1,200 mg plus moxifloxacin 400 mg 25–50 mg PO daily (AI). For Drug-Resistant TB Empiric Therapy for Suspected Resistance to Rifamycin With or Without Resistance to Other Drugs • Isoniazidb plus pyrazinamide plus ethambutol plus (moxifloxacin or levofloxacin) plus (linezolid or amikacinc) (BII) Resistant to Isoniazid • (Moxifloxacin or levofloxacin) plus (rifampin or rifabutin) plus ethambutol plus pyrazinamide for 6 months (BII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-15 Resistant to Rifamycins With or Without Other Antimycobacterial Agents Preferred Therapy • For 14 days: pretomanid 200 mg plus linezolid 600 mg plus moxifloxacin 400 mg plus bedaquiline 400 PO daily, followed by • For 24 weeks: pretomanid 200 mg plus linezolid 600 mg plus moxifloxacin 400 mg daily, and bedaquiline 200 mg PO three times per week • Note: Omit moxifloxacin if resistant to fluoroquinolones (AI). Alternative Therapy • An individualized regimen including based on drug susceptibility test results and clinical and microbiological responses, to include ≥5 active drugs, and with close consultation with experienced specialists (BIII). Duration • 6–24 months (see Managing Drug-Resistant TB section below for discussion of treatment duration) Treatment of TB for Pregnant People • TB therapy should not be withheld because of pregnancy (AIII). • Treatment of TB disease for pregnant people should be the same as for nonpregnant people, but with attention to the following considerations (AIII): o Monthly monitoring of liver transaminases during pregnancy and the postpartum period is recommended (BIII). o If pyrazinamide is not included in the initial treatment regimen, the minimum duration of TB therapy with isoniazid, rifampin, and ethambutol should be 9 months for drug-susceptible TB (AII). The decision regarding whether to include pyrazinamide in treatment regimens for a pregnant person should be made after consultation among obstetricians, TB specialists, and the patient, while considering gestational age and likely susceptibility pattern of the TB strain. o Fluoroquinolones are typically not recommended for pregnant people because arthropathy has been noted in immature animals exposed to fluoroquinolones in utero (CIII). Fluoroquinolones can, however, be used in pregnancy for drug-resistant TB if they are required on the basis of susceptibility testing (BII). o Based on data derived from studies of streptomycin and kanamycin, and the theoretical risk of ototoxicity with in utero exposure to amikacin, aminoglycosides should be avoided during pregnancy, if possible (AIII). TB-Associated IRIS Preventing Paradoxical TB-IRIS • In high-risk patients (i.e., starting ART within 30 days after TB treatment initiation and a CD4 count ≤100/mm3) who are responding well to TB therapy and who do not have rifampin resistance, Kaposi sarcoma, or active hepatitis B (BI): prednisone 40 mg/day for 2 weeks, then 20 mg/day for 2 weeks Managing Paradoxical TB-IRIS • Paradoxical reaction/IRIS that is not severe may be treated symptomatically (CIII). • For moderately severe paradoxical TB-IRIS, use of prednisone is recommended (AI). • In patients on a rifampin-based regimen: prednisone 1.5 mg/kg/day for 2 weeks, then 0.75 mg/kg/day for 2 weeks • In patients on a rifabutin plus boosted PI-based regimen: prednisone 1.0 mg/kg/day for 2 weeks, then 0.5 mg/kg/day for 2 weeks • Taper over 4 weeks (or longer) based on clinical symptoms; a more gradual tapering schedule over 2 to 3 months is recommended for patients whose signs and symptoms have not improved or have worsened due to tapering (BIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-16 Other Considerations in TB Management • Adjunctive corticosteroid is recommended for patients with HIV-related TB involving the CNS (AII). • Dexamethasone has been used for CNS disease with the following dosing schedule: 0.3–0.4 mg/kg/day for 2–4 weeks, then taper by 0.1 mg/kg per week until 0.1 mg/kg, then 4 mg per day and taper by 1 mg/week; total duration of 12 weeksd • Despite the potential of drug–drug interactions, rifamycins remain the most potent TB drug and should remain as part of the TB regimen, unless a rifamycin-resistant isolate is detected or the patient has a severe adverse effect that is likely due to the rifamycin (please refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB below and the Tuberculosis/HIV Coinfection section of the Adult and Adolescent Antiretroviral Guidelines for dosing recommendations involving concomitant use of rifampin or rifabutin and different ARV drugs). • Intermittent rifamycin use can result in the development of resistance in patients with HIV and is not recommended (AI). a This regimen was not studied and is not recommended for people who are pregnant, breastfeeding, <40kg, or who have most types of extrapulmonary TB (other than pleural TB or lymphadenitis). b Many patients with rifampin resistance also have resistance to isoniazid. Susceptibility should be confirmed in any patient with rifampin resistance to determine if isoniazid can be included in the treatment regimen. c Given the risk of ototoxicity and nephrotoxicity with aminoglycosides, use of amikacin should generally be restricted to bridging regimens, while awaiting availability of less toxic medications and/or results of drug-susceptibility testing. d At doses above 16 mg, dexamethasone is a CYP3A4 inducer and can decrease certain ARVs that are substrates of CYP3A4 (e.g., DOR, RPV, and protease inhibitors). Consultation with a pharmacist is recommended. Key: ARV = antiretroviral; CNS = central nervous system; DOT = directly observed therapy; IRIS = immune reconstitution inflammatory syndrome; LTBI = latent tuberculosis infection; PI = protease inhibitor; PO = orally TB among people with advanced immunodeficiency can be a rapidly progressive and fatal illness if treatment is delayed. Therefore, after collection of available specimens for culture and molecular diagnostic tests, empiric treatment for TB is recommended in patients with clinical and radiographic findings suggestive of HIV-related TB (AIII). Treatment of TB for people with HIV is the same as for individuals without HIV151 although the current standard of care continues to evolve as new data emerge from clinical trials. Recommended dosing of drugs for treating active TB disease is summarized in the following table. Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB TB Drug ARV Drugs Daily Dose of TB Drug Isoniazid • All ARVs 5 mg/kg (usual dose 300 mg) Use INH with pyridoxine 25–50 mg PO daily Rifampina,b • NRTIs (use TAF with cautionc) • EFV 600 mg • DTG, RAL (twice daily), MVC without a strong CYP3A4 inhibitor (note: doses of these ARVs need to be adjusted when used with rifampin) • IBA, T-20 10 mg/kg (usual dose 600 mg) • DOR, ETR, EFV 400 mg, NVP, RPV (PO) • BIC, EVG/c, RAL (daily) • CAB/RPV (IM/PO) • HIV PIs Not recommended Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-17 TB Drug ARV Drugs Daily Dose of TB Drug • LEN (SC/PO), FTR, MVC with a strong CYP3A4 inhibitor Rifabutina • NRTIs (use TAF with cautionc) • ETR without boosted PIs • DOR and RPV (PO) (note: doses need to be adjusted when used with rifabutin) • DTG, RAL • MVC without a strong CYP3A4 inhibitor • IBA, T-20, FTR 5 mg/kg (usual dose 300 mg) • PIs with RTV • MVC with a strong CYP3A4 inhibitor 150 mg dailye • EFV 450–600 mg • ETR with boosted PIs • BIC, EVG/c • CAB/RPV (IM/PO) • PIs with COBI • LEN (SC/PO) Not recommended Rifapentine • EFV • NRTIs (use TAF with cautionc) 1,200 mg/day for people weighing ≥40 kg • All other ARVs Not recommended Pyrazinamide • All ARVs Weight-based dosing • 40–55 kg: 1,000 mg • 56–75 kg: 1,500 mg • 76–90 kg: 2,000 mg • >90 kg: 2,000 mgf Ethambutol • All ARVs Weight-based dosing • 40–55 kg: 800 mg • 56–75 kg: 1,200 mg • 76–90 kg: 1,600 mg • >90 kg: 1,600 mgf Moxifloxacin • All ARVs • 400 mg daily for those weighing ≥40 kg a For more detailed guidelines on use of different ARV drugs with rifamycin, clinicians should refer to the Drug–Drug Interactions section of the Adult and Adolescent Antiretroviral Guidelines. b Higher doses may be needed in the treatment of TB meningitis. Expert consultation is advised. c If TAF and rifamycins are coadministered, monitor for HIV treatment efficacy. Note that FDA labeling recommends not to coadminister. See text below and Table 4 for more information. e Acquired rifamycin resistance has been reported in patients with inadequate rifabutin levels while on 150 mg three times per week dosing together with RTV-boosted PIs. May consider therapeutic drug monitoring (TDM) when rifabutin is used with an RTV-boosted PI and adjust dose accordingly. f Monitor for therapeutic response and consider TDM to assure dosage adequacy in patients weighing >90 kg. Note: For drug-drug interaction information between antiretrovirals and anti-TB drugs for treatment of drug-resistant TB, see the Adult and Adolescent Antiretroviral Guidelines. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-18 Key: ARV = antiretroviral; BIC = bictegravir; BID = twice a day; CAB = cabotegravir; COBI = cobicistat; DOR = doravirine; DTG = dolutegravir; EFV = efavirenz; ETR = etravirine; EVG/c = elvitegravir/cobicistat; FTR = fostemsavir; IBA = ibalizumab; IM = intramuscular; INH = isoniazid; LEN = lenacapavir; MVC = maraviroc; NRTI = nucleoside reverse transcriptase inhibitor; PI = protease inhibitor; PO = oral; RAL = raltegravir; RPV = rilpivirine; RTV = ritonavir; SC = subcutaneous; T-20 = enfuvirtide; TAF = tenofovir alafenamide; TB = tuberculosis; TDM = Therapeutic Drug Monitoring The preferred regimen for drug-susceptible TB includes a 2-month (8-week) intensive phase of isoniazid, rifampin, ethambutol, and pyrazinamide (AI). Ethambutol can be discontinued when susceptibility to isoniazid and rifampin has been confirmed. Thereafter, isoniazid and a rifamycin are used in the continuation phase of therapy, generally recommended as an additional 4 months (18 weeks) of treatment for uncomplicated TB (AI).151 Extension of therapy to 9 months is recommended for patients who have a positive sputum culture after 2 months of treatment or severe cavitary or disseminated extrapulmonary disease (BII). A recently completed large, randomized clinical trial that enrolled 2,516 participants at 34 clinical sites in 13 countries established that a 4-month regimen of 2 months (8 weeks) of rifapentine, moxifloxacin, isoniazid, and pyrazinamide followed by 2 months (9 weeks) of rifapentine, moxifloxacin, and isoniazid was as effective as the standard 6-month regimen of isoniazid, rifampin, ethambutol, and pyrazinamide for two months followed by isoniazid and rifampin for an additional four months.152 In this study, the four-month regimen was non-inferior to the control regimen in both the microbiologically eligible and the assessable populations, with unfavorable outcome rates of 15.5% vs. 14.6% (95% CI, -2.6 to 4.5) and 11.6% vs. 9.6% (95% CI, -1.1 to 5.1) respectively. Additionally, the four-month regimen had slightly lower rates of grade 3 or higher adverse events than the control arm. While participants with HIV were included in the trial, the only antiretroviral therapy regimen allowed during the study was efavirenz-containing.153 This four-month regimen is now recommended as an alternative option for people with and without HIV who are 12 years of age or older (AI). It is not recommended for children under 12 years of age, pregnant people, people with extrapulmonary TB, or people with HIV who are taking a non-efavirenz-based antiretroviral regimen (AI).154 The trial also evaluated a four-month regimen with the same high dose of rifapentine but without moxifloxacin, which was found to be inferior to the control arm. If rapid DST results indicate resistance to rifampin, with or without resistance to other drugs, an initial MDR TB regimen, as indicated below, should be used (BIII) and adjusted as molecular sequencing and conventional DST results become available. Directly Observed Therapy (DOT) DOT monitored by trained health care workers, who can be community-based or clinic-based, is recommended for all people with HIV-related TB (AII). Digital technology—such as video-DOT and pill sensors—may be useful alternatives to clinic-based or health care worker–based DOT.155-160 The likelihood of treatment success is further enhanced with comprehensive case management; assistance with housing and other social support; and, if needed, assistance to help people establish or re-engage with HIV care.151 Dosing and Duration of Therapy Although intermittent dosing (administration less often than daily) facilitates DOT, regimens that included twice- or thrice-weekly dosing during the intensive or continuation phase have been Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-19 associated with an increased risk of treatment failure or relapse with acquired drug resistance to the rifamycin class, particularly in people with HIV.161-169 Intermittent rifamycin use can result in the development of resistance in patients with HIV and is not recommended (AI). Therefore, daily therapy is recommended during both the intensive and continuation treatment phases (AII).151,167,168,170 Earlier recommendations171 for TB treatment in people without HIV indicated that therapy should be based on the number of doses received rather than the duration of therapy. However, no data substantiate the minimum number of doses needed within a specified time interval in people with HIV.151 Every effort should be made to ensure that people with HIV receive daily therapy as previously described. The optimal duration of TB treatment for people with HIV and drug-susceptible TB disease has not been fully established. In general, the outcomes of 6-month regimens given as DOT to people with HIV have been favorable.2,151 A 1998 randomized but underpowered trial in the United States showed excellent and comparable outcomes of TB therapy among people with HIV assigned to 6 months or 9 months of therapy.172 Two trials in high-burden settings showed a higher risk of recurrent TB among people treated with 6 months of therapy than among those assigned to 9-month161 or 12-month regimens.173 However, the applicability of these two trials to low-burden settings—such as the United States—and in the context of universal ART is uncertain. In people with HIV receiving an efavirenz-based ART regimen, the 4-month alternative regimen of rifapentine, moxifloxacin, isoniazid, and pyrazinamide previously described was not associated with a higher rate of recurrent TB compared to the standard of care arm after follow-up out to at least 18 months post-TB treatment initiation.152,154 Whether outcomes with this 4-month regimen will be similar to standard 6-month anti-TB therapy in people with HIV treated with non-efavirenz-based ART is not known. Additional TB treatment shortening trials using alternative strategies in participants with HIV and TB coinfection are ongoing. Treatment of TB Meningitis With regard to the treatment of tuberculous meningitis, data regarding optimal drugs and doses to use are sparse. Many experts suggest that TB meningitis should be treated for an extended period of 9 to 12 months, but there is no evidence to support this recommended treatment duration.174 Recent clinical trials have suggested that the use of higher rifampin doses (up to 30–35 mg/kg/day) or the addition of fluoroquinolones or linezolid to initial treatment for TB meningitis may be beneficial, but the data are limited, particularly in people with HIV, and are insufficient to support a clear recommendation at this time.175-183 Adjunctive corticosteroid therapy is recommended for all individuals who have TB involving the CNS (AII) including those with HIV, as indicated below. Adjunctive Corticosteroid Use in TB Treatment Several clinical trials have demonstrated that adjunctive corticosteroid therapy increases survival overall for people with TB meningitis, improves treatment effectiveness, and reduces adverse event rates. These trials, however, either excluded people with HIV or were underpowered for detecting statistically significant outcome benefits in that group.111,184,185 A recent clinical trial compared adjunctive corticosteroids to placebo in people with HIV—the majority of whom had advanced HIV (52% of participants had a CD4 ≤50 cells/mm3)—and failed to find a statistically significant benefit (HR for death 0.85 [95% CI, 0.66–1.10]).186 The trial was powered to detect a 31% improvement in Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-20 survival and it is possible that corticosteroids have a more modest effect. Importantly, the study found no evidence of harm with corticosteroids and, given the high morbidity and mortality associated with TB meningitis, adjunctive corticosteroids are still recommended in people with HIV and TB meningitis. Dexamethasone should be administered in a dose of 0.3 mg/kg/day to 0.4 mg/kg/day for 2 to 4 weeks, then tapered by 0.1 mg/kg per week until a dose of 0.1 mg/kg is reached, then 4 mg per day and tapered by 1 mg/week) for a total duration of 12 weeks (BII).111,151 TB involving the CNS is currently the only organ system manifestation for which corticosteroids are recommended.151 Adjunctive corticosteroid therapy is not recommended in the treatment of TB pericarditis (AI). In a randomized trial that compared adjunctive prednisolone with placebo—each administered for 6 weeks in individuals with tuberculous pericarditis, with and without HIV— prednisolone was not associated with a significant reduction in the composite endpoint of death, cardiac tamponade, or constrictive pericarditis. Those receiving prednisolone also had a higher incidence of some cancers.187 A Cochrane review similarly found no mortality benefit from adjunctive corticosteroids and a nonsignificant reduction in constrictive pericarditis. Notably, however, <20% of people with HIV in the trials analyzed were receiving ART.188 No trials have been conducted comparing different doses and treatment durations of adjunctive corticosteroids. Special Considerations Regarding ART Initiation The preponderance of data from several large randomized trials in people with HIV and TB, as well as subsequent systematic reviews and meta-analyses, supports the recommendation that ART should not be withheld until completion of TB treatment (AI).108,189-196 ART is recommended for all people with HIV and TB (AI). For ART-naive patients, ART should be started within 2 weeks after TB treatment initiation in those with CD4 count <50 cells/mm3 when TB meningitis is not suspected (AI). For ART-naive patients with higher CD4 cell counts, ART should be started within 2-8 weeks of starting anti-TB treatment when TB meningitis is not suspected (AI). For ART-naïve patients with TB meningitis, ART should be started once the TB meningitis is under control—with either clinical improvement or improvement in CSF parameters—after at least 2 weeks of anti-TB treatment, to reduce the risk of immune reconstitution causing life-threatening inflammation in a closed space (AIII). Rifamycin-associated drug interactions should be considered when selecting the ARV drug regimen. Preemptive prednisone therapy should be offered to patients starting ART within 30 days after TB treatment initiation, have a CD4 count ≤100/mm3, are responding well to TB therapy and who do not have rifampin resistance, Kaposi sarcoma, or active hepatitis B (BI) (see TB-Associated IRIS below for details).197 American Thoracic Society (ATS)/CDC/Infectious Diseases Society of America (IDSA) guidelines recommend that people with TB meningitis should not start ART before 8 weeks of TB treatment is completed, regardless of CD4 count, based primarily on a randomized trial in 253 people with HIV and TB meningitis conducted in Vietnam. This trial compared immediate ART within 7 days of starting TB treatment with delayed ART started two months after starting TB treatment.151,193 The study showed no difference in mortality or TB outcomes, but those receiving immediate ART had a higher rate of severe adverse events. It is unclear whether the study’s findings are generalizable to higher-resourced settings with access to frequent monitoring and adjustment of dosing. We recommend that for ART-naive people with HIV and TB meningitis, ART should be started once the TB meningitis is under control, after at least 2 weeks of anti-TB treatment (AIII). The greatest risk of early ART is the occurrence of intracerebral TB-IRIS after starting ART, which has been reported in up to 50% of people with HIV and TB meningitis and may increase morbidity and mortality198 (although mortality was similar in both early and delayed ART arms in the only randomized trial Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-21 completed to date).193 However, adjunctive corticosteroid therapy is recommended for all people with HIV and TB meningitis (AII) and precludes the need for pre-emptive use of prednisone to prevent IRIS. Whether the corticosteroid regimen recommended as adjunctive therapy for TB meningitis also further reduces the risk of TB IRIS and its consequences has not been evaluated. In summary, early ART initiation requires close collaboration between HIV and TB care clinics, expertise in the management of ARV regimen selection, close monitoring, potential adjunctive corticosteroid therapy, and support and adherence services. The prevention and management of IRIS are discussed in detail below (see TB-Associated IRIS, below). When TB occurs in people already on ART, treatment for TB must be started immediately (AIII), and ART should be modified to reduce the risk of drug interactions and to maintain virologic suppression. When TB occurs in the setting of virologic failure, ART drug-resistance testing should be performed, and intensified adherence counseling should be provided. A new ARV regimen may be required to achieve virologic suppression and minimize drug interactions with the anti-TB regimen. Drug–Drug Interactions in the Treatment of HIV-Related TB Dolutegravir in combination with two nucleoside(tide) reverse transcriptase inhibitors, including tenofovir disoproxil fumarate (TDF), tenofovir alafenamide (TAF), abacavir, emtricitabine, or lamivudine, is the preferred regimen for co-treatment of HIV in most ART-naive people with TB (AI). This regimen can be managed with rifamycin-based anti-TB treatment (see Integrase Inhibitor section below for recommendations about dolutegravir dose adjustment if coadministered with rifampin). The following text summarizes the most important drug-drug interactions for antiretroviral drugs and anti-TB drugs to guide choices if other ART regimens are considered. The rifamycin class of antibiotics is the cornerstone of effective and shorter-course first-line treatments for drug-sensitive TB. The currently available rifamycins (rifampin, rifabutin, and rifapentine) have clinically significant interactions with several ARV drugs. Most of these result from the rifamycin’s potent induction of genes involved in the metabolism and transport of ARV agents, and these interactions should be taken into consideration before initiating therapy (see Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB above, and the Tuberculosis/HIV Coinfection section of the Adult and Adolescent Antiretroviral Guidelines). Every effort should be made to include a rifamycin in the TB treatment regimen. Rifamycins remain the most potent drug class for TB treatment. Older regimens that included only 2 months of rifampin were associated with increased risks of treatment failure and TB recurrence among people with HIV-related TB.199,200 If a rifamycin cannot be used, TB treatment duration must be extended, and treatment complexity increases substantially. Thus, individuals with rifamycin-susceptible M. tuberculosis isolates should be treated with a regimen that includes a rifamycin unless a serious adverse event is highly likely due to a rifamycin (AIII). No clinical trial has specifically compared rifampin- and rifabutin-containing anti-TB regimens among people with HIV and TB taking ART. Rifabutin is generally regarded as a reasonable substitute for rifampin for the treatment of active TB disease in people with HIV who concurrently receive ARVs that have adverse drug interactions with rifamycins, because rifabutin is a less potent inducer of CYP3A4 than rifampin.201 Although clinical trial data among people with HIV are limited to one small study, observational data among people with HIV, and several trials among people without HIV have found similar outcomes between those treated with rifampin or rifabutin.202-205 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-22 Nucleoside Reverse Transcriptase Inhibitor Backbone Nucleoside(tide) backbone drugs—including tenofovir disoproxil fumarate (TDF), abacavir, emtricitabine, and lamivudine—can be given together with rifampin-containing TB treatment without dose adjustment. Tenofovir alafenamide (TAF), a substrate of drug transporters including P-glycoprotein, may be more likely to have drug–drug interactions than TDF. A study conducted among healthy volunteers without HIV showed that concentrations of intracellular tenofovir-diphosphate (TFV-DP) were higher with TAF/emtricitabine given with rifampin than with TDF given alone, suggesting that TAF may be given together with rifampin-containing TB treatment without dose adjustment.206 Neither TDF nor TAF has been fully evaluated with rifabutin. In one small study, though, HIV virologic suppression was sustained during TAF-rifabutin co-administration.207 In one study of TAF (as part of Biktarvy™) taken with daily high-dose rifapentine and isoniazid (1HP) for the treatment of LTBI, plasma tenofovir concentration was similar when TAF was taken alone versus together with 1HP, suggesting that TAF can be taken with rifapentine for short periods of time for prevention of TB.208 Non-Nucleoside Reverse Transcriptase Inhibitors—Efavirenz, Nevirapine, Etravirine, Doravirine, and Rilpivirine One alternative co-treatment regimen for HIV-related TB disease is rifampin-based TB therapy with an ARV regimen of efavirenz (600 mg daily) plus two nucleoside(tide) analogues (AII). Studies in people with HIV and TB (including patients with higher body weight) have not shown a significant effect of rifampin-containing TB treatment on efavirenz plasma concentrations when used at the standard 600 mg per day dose in the majority of patients.209-211 Given the preponderance of data and the excellent treatment outcomes of co-treatment with standard-dose efavirenz,212,213 the 600 mg daily dose of efavirenz is recommended (AII). A small study among people with HIV found similar efavirenz concentrations when the 400 mg dose was taken with isoniazid and rifampicin versus when it was taken alone,214 suggesting that, while not recommended, rifampicin-based TB treatment could be given with efavirenz without a need for efavirenz dose adjustment. Pharmacokinetic studies also support the use of the 600mg efavirenz dose with the new 4-month rifapentine-moxifloxacin-isoniazid-pyrazinamide regimen.215 Nevirapine is not recommended for HIV and TB co-treatment (AII).216 The use of rifampin or rifapentine with doravirine, etravirine, or rilpivirine is not recommended (AIII) (see Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB, above, and the Tuberculosis/HIV Coinfection section of the Adult and Adolescent Antiretroviral Guidelines). Some experts might consider substitution of rifabutin for rifampin with an appropriate dose adjustment of rifabutin (e.g., increasing to 450–600 mg daily when given with efavirenz) or of the non-nucleoside reverse transcriptase inhibitors (NNRTIs) (e.g., increasing doravirine dosing to 100 mg twice daily and increasing oral rilpivirine to 50 mg daily), where appropriate,217,218 for patients who require one of these NNRTIs;219 however, IM rilpivirine, as used in long-acting ARV combinations, is not recommended (AIII). Rifabutin has not been evaluated in combination with rilpivirine, doravirine, or etravirine in people with HIV requiring treatment for active TB disease. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-23 Integrase Inhibitors—Bictegravir, Dolutegravir, Elvitegravir, Raltegravir, and Cabotegravir As indicated above, dolutegravir in combination with nucleoside reverse transcriptase inhibitors is the preferred option for co-treatment of HIV in most patients with TB (AI). A PK study in healthy volunteers showed that increasing the dose of dolutegravir to 50 mg twice a day with rifampin resulted in similar exposure to dolutegravir dosed 50 mg daily without rifampin, and that rifabutin 300 mg daily did not significantly reduce the area under the concentration curve of dolutegravir.220 A Phase 2 trial in people with HIV and TB (INSPIRING) demonstrated that PK targets and virologic suppression were favorable at 24 and 48 weeks when dolutegravir 50 mg twice daily was administered with rifampin-containing TB treatment.221 Dolutegravir is currently recommended at a dose of 50 mg twice daily when used together with a rifampin-containing TB regimen (AI) (and for two weeks following the completion of TB therapy), though randomized trials evaluating standard once-daily dosing are underway.222 Dolutegravir should be used at a standard 50 mg once-daily dose when used with rifabutin (AII). Another alternative co-treatment regimen is the combination of raltegravir-based ART, using raltegravir 800 mg twice daily, with standard rifampin dosing (BI).223 Raltegravir concentrations are decreased significantly when co-administered with rifampin. Increasing the dose of raltegravir to 800 mg twice daily mitigates this PK interaction.224 No PK or clinical data exist regarding the use of rifampin with the once-daily, extended-release 600 mg formulation of raltegravir, and co-administration is not recommended (AIII). Alternatively, raltegravir can be given with a rifabutin-containing TB regimen without a dose adjustment of either drug (BII).225 At this time, bictegravir should not be used together with rifamycin-containing TB treatment (rifampin, rifabutin, or rifapentine) (AII). A trial conducted among healthy participants without HIV evaluated bictegravir concentrations when given twice daily together with rifampin versus once daily alone.226 Bictegravir trough concentrations, with the dose adjustment, were reduced by 80%. Although studied only with rifabutin, elvitegravir/cobicistat is not recommended with TB treatment that contains rifamycins (AII).227,228 When given at steady-state with oral cabotegravir, rifampin decreased cabotegravir AUC by 59% in healthy volunteers.229 The long-acting injectable formulation of cabotegravir has not been studied with rifamycins, but a pharmacokinetic model of long-acting, injectable, co-formulated cabotegravir-rilpivirine predicted that concurrent rifampin would decrease cabotegravir AUC by 41% to 46%.230 As a result, oral and long-acting injectable cabotegravir is not recommended for use with rifampin or rifapentine (AII).229 Oral and long-acting injectable cabotegravir may be coadministered with rifabutin (AIII); however, long-acting injectable cabotegravir plus rilpivirine is not recommended for use with rifabutin due to the rilpivirine component (AIII). Protease Inhibitors with Rifampin or Rifabutin Rifampin decreases the plasma concentrations and exposure of co-administered PIs by >75%.231-234 One trial tested adjusted doses of ritonavir-boosted darunavir (1600/200 mg once daily and 800/100 mg twice daily) with rifampicin in people with HIV without TB.235 The trial was stopped early because of high rates of hepatotoxicity, and trough concentrations in the once-daily group were reduced substantially. Thus, boosted darunavir is not recommended for use together with rifampin, even with dose adjustment (AI). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-24 The effects of rifampin on lopinavir/ritonavir PK may be overcome by doubling the dose of lopinavir/ritonavir.233,236 In a study of 71 people with HIV and TB, double doses of lopinavir/ritonavir were reasonably well tolerated in those on rifampin-based TB treatment.205 Some experts would consider this an alternative when a PI-based ART regimen is required during TB treatment (BI). Regular monitoring of transaminases and HIV RNA is recommended when double-dose lopinavir/ritonavir is used (e.g., more frequently initially, then monthly once transaminase levels are stable on full dose). Use of rifabutin with a boosted PI is preferred to the use of rifampin with double-dose PI in settings where rifabutin is readily available. Co-administered rifabutin has little effect on ritonavir-boosted lopinavir205,237 or atazanavir238 and only moderately increases concentrations of ritonavir-boosted darunavir239 and fosamprenavir.240 However, all PIs markedly increase serum concentrations of rifabutin (and one of its principal active metabolites, 25-O-desacetyl-rifabutin). Therefore, the dose of rifabutin must be decreased from 300 mg to 150 mg daily with all ritonavir-boosted PIs to avoid dose-related toxicity, such as uveitis and neutropenia (AI).205,241 Coadministration of cobicistat-boosted PIs with rifabutin is not recommended (AII). In studies in people with HIV, rifabutin exposures were significantly lower when rifabutin was dosed at 150 mg three times weekly (with lopinavir/ritonavir) than when dosed at 300 mg daily without a PI, but concentrations of the active desacetyl metabolite were high.242,243 Among people with HIV and TB, cases have been reported of acquired rifamycin resistance when doses of rifabutin of 150 mg three times weekly were co-administered with a boosted PI-based ARV regimen.244,245 Based on available PK data, it is generally recommended that rifabutin be dosed 150 mg daily in patients who are on a ritonavir-boosted PI-containing ARV regimen (AI). However, given the potential risk of adverse events related to high levels of rifabutin’s metabolite with this dosing strategy, close monitoring for toxicity (especially neutropenia and uveitis) is required.205 Close monitoring of adherence to ART is essential because these reduced doses of rifabutin would be inadequate if the patient stopped taking the PI, putting the patient at risk of rifamycin-resistant TB. Monitoring the Response to Therapy Patients with pulmonary TB should have at least monthly sputum smears and cultures performed to document culture conversion on therapy (defined as two consecutive negative cultures) (AII). Sputum cultures from patients with susceptible TB typically convert to negative within 2 months of first-line TB therapy, although sputum culture conversion to negative may take longer for people with cavitary TB disease.246-248 Sputum cultures that do not convert to negative at or after 4 months of therapy indicate treatment failure and should prompt further evaluation, including drug-resistance testing of available specimens. In patients with extrapulmonary TB, obtaining follow-up specimens can be challenging, making it difficult to assess a bacteriologic response to therapy. Instead, the response typically is measured by an improvement in clinical and radiographic findings, but the frequency of such evaluations will depend on the infected sites, the severity of disease, and the ease with which specimens can be obtained. Managing Suspected Treatment Failure The causes of treatment failure include undetected primary drug resistance, inadequate adherence to therapy, incorrect or inadequate prescribed regimen, subtherapeutic drug levels due to malabsorption Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-25 or drug interactions, reinfection or mixed infection with drug-resistant M. tuberculosis, and acquired drug resistance. People with suspected treatment failure should be evaluated with a medical history, physical exam, and chest radiograph to determine whether a clinical response to therapy has occurred despite the absence of sputum culture conversion. The initial culture results and drug-resistance tests, treatment regimen, and adherence to the regimen also should be reviewed. Some experts would perform therapeutic drug monitoring to determine if serum concentrations of the TB drugs are within expected ranges and adjust dosage as necessary.151,249 In addition, samples from all available sites (e.g., sputum, blood, urine) should be collected for repeat culture and DST, and strong consideration should be given to performing rapid resistance testing on direct specimens or positive cultures to identify acquired drug resistance or mixed infection with a drug-resistant strain. While awaiting results of repeat cultures and rapid resistance testing, broadening empiric TB treatment to include at least two additional second-line TB drugs should be considered in consultation with an expert in the field (BIII). Adverse Drug Reactions in TB Patients on Antiretroviral Therapy Retrospective observational studies reported an increased risk of adverse drug reactions in patients treated with concomitant ART and anti-TB therapy. Many of these studies, however, included patients receiving older antiretrovirals which carried more frequent side effects.250 Three later randomized controlled trials reported similar rates of adverse events during anti-TB therapy with and without concomitant ART, suggesting no significant additive toxicity when ART is co-administered with anti-TB therapy.153,189,191 Nevertheless, managing suspected adverse drug reactions in this setting is complex because assigning causality to individual drugs in patients on anti-TB drugs, ART, and other agents is very difficult. Because first-line anti-TB drugs are more effective and have fewer toxicities than alternative drugs, first-line drugs (especially isoniazid and rifampin or rifabutin) should not be stopped permanently, unless strong evidence exists that a severe drug reaction was caused by a specific anti-TB drug (AIII). In such situations, decisions regarding rechallenge with first-line drugs and/or substitution of second-line drugs may be made in consultation with a specialist in treating TB disease in people with HIV. Liver transaminases should be monitored at baseline and monthly for those with underlying risk factors for hepatotoxicity.151 Drug-induced liver injury (DILI) can be caused by isoniazid, rifamycins, pyrazinamide, some ARV drugs, and trimethoprim-sulfamethoxazole (TMP-SMX). Anti-TB DILI is defined as an ALT elevation ≥3 times the upper limit of normal (ULN) in the presence of symptoms (e.g., fever, rash, fatigue, nausea, anorexia, jaundice); ALT ≥3 times the ULN plus total bilirubin 2 times the ULN in the absence of symptoms; or ALT ≥5 times the ULN alone in the absence of symptoms. An increase in ALT concentration occurs in approximately 5% to 30% of people treated with the standard four-drug anti-TB regimen,97,251 but many of these have only transient, mild elevations of ALT.97 If the criteria for anti-TB DILI are fulfilled, all potentially hepatotoxic drugs should be stopped, and the patient should be evaluated immediately (AIII). Serologic testing for syphilis and hepatitis A, B, and C should be performed, and the patient should be questioned regarding symptoms suggestive of biliary tract disease and exposures to alcohol and other hepatotoxins. At least three anti-TB drugs not Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-26 associated with hepatoxicity should be started (e.g., ethambutol, linezolid, and moxifloxacin or levofloxacin)252 as a “bridging regimen” until the specific cause of hepatotoxicity can be determined and an alternative longer-term regimen constructed (BIII). After the ALT level returns to <2.5 times the ULN (or to near baseline for those with preexisting abnormalities), rechallenge with the hepatotoxic first-line anti-TB medications can be started by adding each drug individually to the bridging regimen at 7-day intervals. During the rechallenge, ALT levels should be monitored frequently. Rechallenge was successful in almost 90% of people without HIV in one randomized controlled trial of different rechallenge regimens.252 Because the rifamycins are a critical part of the TB regimen, they should be restarted first. Rechallenge with pyrazinamide is controversial because some studies have reported high rates of recurrent ALT elevations with reintroduction of the drug. Other studies, however, have demonstrated successful reintroduction of pyrazinamide,253,254 and some experts would therefore recommend rechallenge with pyrazinamide in people with severe forms of TB (e.g., meningitis or disseminated TB). Bridging drugs can be stopped once three active nonbridging drugs are reinstated successfully. Depending on the outcome of the rechallenge, the anti-TB therapy regimen and duration may need to be altered, in which case, expert consultation is advised. After successful anti-TB drug rechallenge (i.e., if appropriate), relevant ARV drugs and TMP-SMX may be restarted. Cutaneous adverse drug reactions may occur with all anti-TB drugs, notably rifampin and isoniazid255; some ARV drugs, notably the NNRTIs; and TMP-SMX. If the rash is minor, affects a limited area, and causes pruritus, antihistamines should be administered for symptomatic relief and all anti-TB medications should be continued. If the rash is generalized or associated with fever or DILI or involves mucous membrane or desquamation, all anti-TB medications, relevant ARVs, and TMP-SMX should be stopped. When the rash improves substantially, the TB drugs should be restarted as described in the section on DILI above. If the rash recurs, the last drug that had been added should be stopped and the TB regimen modified. Thereafter, if appropriate, relevant ARV drugs and TMP-SMX may be restarted. Managing Drug-Resistant TB Although drug-resistant TB represents a small fraction of the TB cases in the United States, the increasing number of people with drug-resistant TB globally plus the high proportion of TB cases in the United States in people who are from TB-endemic areas make it increasingly likely that local TB programs will be faced with this complex disease. The most active and effective TB drugs are those used in first-line TB treatment regimens. When resistance to these medications develops, alternative combinations of TB medications must be used, but clinical trial data on their optimal use are limited, and most recent studies have been conducted primarily in TB-endemic resource-constrained settings. In the United States, approximately 7% of people with TB have baseline isoniazid mono-resistance.256 Growing evidence demonstrates an increased risk of treatment failure associated with isoniazid monoresistance,257 particularly in people with HIV and TB.258 For people with isoniazid monoresistance, it is recommended that a fluoroquinolone (levofloxacin or moxifloxacin) be substituted for isoniazid and given together with rifampin or rifabutin, pyrazinamide, and ethambutol for 6 months (BII).93,259-261 Though rifampin reduces concentrations of moxifloxacin by 20% to 40%, there is no clinical evidence that a moxifloxacin dose adjustment improves outcomes.262-264 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-27 The treatment of rifampin-resistant (RR) and MDR TB (resistance to both isoniazid and rifampin) is an area of active investigation and is evolving rapidly. Historically, RR/MDR TB has been treated with individualized regimens taking into account the results of drug resistance testing and prior treatment exposure. In 2019, ATS, CDC, IDSA, and the European Respiratory Society (ERS) issued MDR TB treatment guidelines recommending a fully oral regimen consisting of at least 5 active drugs for most patients with drug-resistant TB, including people with HIV.93 Since the publication of the 2019 guidelines, however, several clinical trials have examined the efficacy and safety of a 6-month, all-oral regimen comprised of bedaquiline, pretomanid, and linezolid (“BPaL"). Pretomanid is a novel oral antimycobacterial agent that was approved by the FDA in 2019 exclusively as part of the BPaL regimen. The initial study (“Nix-TB”) on which approval was based, was a single-arm study in 109 patients, of whom 51% were people with HIV.265 Although the study had no control arm, 90% of participants had a favorable outcome. High rates of peripheral neuropathy were seen in Nix-TB study participants, and this was attributed to the high dose of linezolid used (1200 mg daily). The follow-up ZeNix study (n=181) compared outcomes of patients receiving the BPaL regimen at different linezolid doses and showed similarly favorable outcomes with a lower dose of 600 mg daily.266 The TB-PRACTECAL study compared a regimen in which moxifloxacin was added to BPaL (aka “BPaLM”) to longer injectable-based regimens, which were the standard of care at the time.267,268 In modified intention-to-treat analyses, 121 of 138 (88%) participants in the BPaLM arm achieved treatment success compared with 81 of 137 (59%) of those receiving standard of care. Disease recurrence occurred in one participant in the BPaLM group (n=151) and four in the BPaL group (n=123); new resistance to bedaquiline was observed in the BPaL group in isolates from three of four recurrences, with no new resistance to other drugs in the regimens.267 The BPaL and BPaLM regimens have been used in the United States, and treatment outcomes thus far have been very successful among 152 patients with culture-positive pulmonary TB, most of whom received the 600 mg daily dose of linezolid.269,270 Three recurrences after treatment completion were reported among 116 who received BPaL and none among 36 patients who received BPaLM. Based on these data, BPaLM is recommended as the preferred therapy for people with HIV with pulmonary RR-TB and without known resistance to the component medications (AI).271 Patients with RR-TB with fluoroquinolone resistance should receive BPaL without moxifloxacin (AI). This recommendation is similar to that of WHO, which conditionally recommends both the BPaL and BPaLM regimens to patients ≥15 years of age with RR-TB who have not had previous exposure or resistance to the drugs in the regimen.272 BPaLM and BPaL regimens should be given for a total of 26 weeks (6 months) (AI). Treatment should be extended up to a total of 39 weeks (9 months) if sputum cultures are positive between months 4 and 6 (AI). For patients who have not been included in BPaL or BPaLM studies—such as those with extrapulmonary TB or those with known or suspected resistance to bedaquiline, pretomanid, or linezolid—we recommend an individualized regimen consisting of at least 5 active drugs, based on the results of resistance testing and prior treatment exposure (AI). Component medications should be selected using the ranking outlined in the ATS/CDC/IDSA/ERS guidelines.93 When possible, an initial individualized regimen should contain bedaquiline, linezolid, a fluoroquinolone (levofloxacin or moxifloxacin), clofazimine, and a D-alanine analog (cycloserine or terizidone). All remaining drugs should be used to complete the regimen only when the recommended drugs cannot be used. Kanamycin and capreomycin are no longer recommended due to the increased risk of treatment Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-28 failure and relapse with their use.273 Such an association was not seen for amikacin, which may be used when other, less toxic drugs cannot be used. The duration of therapy with such a regimen will depend on the component drugs and the patient’s response to therapy. The ATS/CDC/IDSA/ERS guidelines currently recommend a treatment duration of 15 to 24 months after culture conversion when using an individualized regimen, although these guidelines are currently undergoing revision.93 Several clinical trials have examined different regimens with total durations as short as 9 months and show TB treatment success rates comparable to or better than longer duration therapy.274-278 Consultation with an expert who has experience managing drug-resistant TB is advised. An important concern regarding BPaL(M) regimens is the growing prevalence of bedaquiline resistance and the lack of widespread availability of phenotypic second-line TB drug susceptibility testing.279,280 Rapid molecular testing with confirmatory sequencing for fluoroquinolones and first-line drugs should ideally be performed prior to the initiation of treatment for RR/MDR TB; phenotypic testing should also be undertaken. This testing, as well as susceptibility testing for second-line agents, is available at many local or state public health laboratories or through the CDC’s Molecular Detection of Drug Resistance (MDDR) service. To submit a sample for the MDDR service, complete the CDC’s MDDR Request Form. Importantly, as with all TB drugs, there is incomplete concordance between purported bedaquiline resistance-conferring mutations and phenotypic resistance.281 If bedaquiline is being used, then bedaquiline phenotypic testing should be pursued, if available. Treatment with BPaLM need not be delayed, however, while awaiting the results of bedaquiline susceptibility testing. Of note, pretomanid resistance testing is not currently available. For people with HIV with RR-TB, several important drug–drug interactions occur between bedaquiline and some ARV drugs. Specifically, efavirenz decreases bedaquiline plasma concentrations.282 For people with HIV with RR-TB, efavirenz should not be used concurrently with bedaquiline (AI). Lopinavir/ritonavir increases bedaquiline plasma concentrations approximately twofold when given at steady-state,283,284 but this has not been associated with additional prolongation of the QT-interval or other adverse events.285 Given the options for regimen choice and individual drug dosing within regimens, as well as variations in local drug susceptibilities, the treatment of RR-TB should involve an expert with experience in treating drug-resistant TB.267,269 If a local expert is not available through the public health department, clinicians and TB programs can contact the CDC (tbinfo@cdc.gov) and one of the CDC’s TB Centers of Excellence for Training, Education, and Medical Consultation. TB-Associated IRIS TB-IRIS is a frequent, early complication of ART in people with HIV with active TB. The condition is thought to result from the recovering immune system driving inflammatory reactions directed at M. tuberculosis antigen present at sites of disease.286-288 TB-IRIS is characterized by excessive local or systemic inflammation. Two forms of TB-IRIS are recognized: paradoxical TB-IRIS and unmasking TB-IRIS. Proposed clinical case definitions for these syndromes have been published.289 Paradoxical TB-IRIS Paradoxical TB-IRIS occurs in people who are diagnosed with active TB disease before starting ART. Typically, people experiencing paradoxical TB-IRIS have had clinical improvement on TB Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-29 treatment before starting ART, and within the first 1 to 4 weeks of ART (though sometimes later), they develop new or recurrent symptoms and worsening or recurrent clinical and radiologic features of TB. Common and important manifestations of paradoxical TB-IRIS include fevers, new or enlarging lymphadenopathy, and new or worsening pulmonary infiltrates. Mortality due to paradoxical TB-IRIS is uncommon,287,290 but life-threatening manifestations include enlarging cerebral tuberculomas, meningitis, enlargement of pericardial effusions causing cardiac tamponade, extensive pulmonary involvement with respiratory failure, nodal enlargement causing airway obstruction, and splenic rupture due to rapid enlargement.287,291,292 In people with disseminated TB, hepatic TB-IRIS is common, manifesting with nausea and vomiting, tender hepatic enlargement, cholestatic liver function derangement, and occasionally jaundice.288,293 A liver biopsy often reveals granulomatous hepatitis.294 Hepatic TB-IRIS may be difficult to differentiate from drug-induced liver injury. Paradoxical TB-IRIS is relatively common among patients starting ART while on TB treatment. A meta-analysis of 40 studies reported a pooled incidence of TB-IRIS of 18% in adults with HIV-associated TB initiating ART, with death attributed to TB-IRIS in 2% of the cases.295 The onset of paradoxical TB-IRIS symptoms is typically between 1 to 4 weeks after ART is initiated.296-301 The syndrome lasts for 2 to 3 months on average,300,302 but in some cases, symptoms may continue for several more months, and in rare cases, local manifestations may persist or recur over a year after onset.289,302,303 In such cases of prolonged TB-IRIS, manifestations usually include suppurative lymphadenitis and abscess formation. The most consistently identified risk factors for paradoxical TB-IRIS are a low CD4 count at the start of ART, especially a CD4 count239,244 <100 cells/mm3;299,304 high HIV viral load before ART305,306; disseminated or extrapulmonary TB291,298,300,304; and a short interval between starting TB treatment and initiating ART, particularly if ART is started within the first 1 to 2 months of TB treatment.291,297,299 Although early ART increases the risk for TB-IRIS, ART should be started within 2 weeks of TB diagnosis in patients with CD4 counts <50 cells/mm3 and within 2 to 8 weeks of TB diagnosis in those with higher CD4 counts, as previously discussed, to reduce the risk of HIV progression and death (see Special Considerations Regarding ART Initiation, above) (AI).295 The diagnosis of paradoxical TB-IRIS may be challenging, and no definitive confirmatory test exists. Thus, diagnosis relies upon a characteristic clinical presentation: improvement of TB symptoms with treatment before ART, deterioration with inflammatory features of TB soon after starting ART, or demonstration of a response to ART (CD4 rise and/or HIV viral load reduction). In addition, diagnosis of paradoxical TB-IRIS requires investigations to exclude alternative causes for deterioration, particularly another opportunistic infection, undetected TB drug resistance, or other cause of treatment failure (see Managing Suspected Treatment Failure, above).307 Prevention of Paradoxical TB-IRIS Pre-emptive treatment with prednisone may prevent or reduce the consequences of TB-IRIS. A randomized, double-blind, placebo-controlled trial of prednisone (40 mg/day for 2 weeks, then 20 mg/day for 2 weeks) versus placebo in 240 ART-naive adults at high risk of developing IRIS at the time of ART initiation demonstrated that preemptive prednisone treatment was effective in reducing the risk of paradoxical TB-IRIS.197 The incidence of TB-IRIS was 47% in the placebo arm and 33% in the prednisone arm (RR = 0.70; 95% CI, 0.51–0.96). No excess risk was observed for malignancy, severe infections, or other complications. Based on these study findings, preemptive prednisone therapy should be offered for high-risk patients as defined in this study (i.e., starting ART Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-30 within 30 days after TB treatment initiation and a CD4 count ≤100/mm3) who are responding well to TB therapy and who do not have rifampin resistance, Kaposi sarcoma, or active hepatitis B (BI). Managing Paradoxical TB-IRIS Most cases of paradoxical TB-IRIS are self-limiting. Many people require symptomatic therapy (e.g., analgesia, anti-emetics), and if symptoms are significant, anti-inflammatory therapy is appropriate. Clinicians may use non-steroidal anti-inflammatory drugs to provide symptomatic relief in patients with mild TB-IRIS (CIII). Needle aspiration of enlarging serous effusions, large tuberculous abscesses, or suppurative lymphadenitis may also provide symptom relief (CIII). Repeated aspirations may be required as abscesses and effusions often re-accumulate.291 In people with moderately severe paradoxical TB-IRIS, treatment with prednisone is recommended (AI). One randomized, placebo-controlled trial among patients with moderately severe paradoxical TB-IRIS showed that treatment with prednisone (1.5 mg/kg/day for 2 weeks followed by 0.75 mg/kg/day for 2 weeks) resulted in a reduction in a combined endpoint of days hospitalized plus outpatient therapeutic procedures.308 In that study, however, 4 weeks of prednisone treatment was insufficient in a subset of participants. If clinical assessment indicates that signs and symptoms have not improved or have worsened as corticosteroids are tapered, a more gradual tapering of steroids over 2 to 3 months is recommended (BIII).308 Patients on prednisone experienced more rapid symptoms and radiographic improvement. No reduction in mortality was demonstrated, but immediately life-threatening cases (e.g., those with neurological involvement) were excluded from this study.111,292,308 Rifampin increases the clearance of prednisolone (the active metabolite of prednisone),309 but no such effect is expected with rifabutin; dosing of prednisone should therefore be adjusted in patients receiving rifampin or rifabutin-containing regimens (See the Treating TB-Associated IRIS section of the Treating TB Disease table). Corticosteroids should be avoided in people with Kaposi sarcoma because life-threatening exacerbations can occur. Case reports have been published of patients with steroid-refractory and prolonged IRIS or paradoxical reactions responding to TNF-blockers, IL-1 inhibitors, JAK inhibitors, or thalidomide.310-317 Unmasking TB-IRIS Unmasking TB-IRIS may occur in people who have unrecognized TB (because TB is either symptomatic or it has eluded diagnosis) at the start of ART. These people may present with a particularly accelerated and inflammatory presentation of TB in the first weeks of ART.289 A common presentation is pulmonary TB with rapid symptom onset and clinical features similar to bacterial pneumonia with high fever, respiratory distress, sepsis syndrome, and consolidation on chest radiograph.289,308,318-320 Focal inflammatory manifestations—such as abscesses and lymphadenitis— also may develop.321 In cases of unmasking TB-IRIS, the treatment should be standard TB treatment and, if the manifestations are life-threatening, adjunctive corticosteroid therapy is recommended, although steroid use in this setting has not been studied in a clinical trial (BIII). Prevention of Recurrent TB Among patients receiving the same TB treatment regimen in the same setting, the risk of recurrent TB appears to be higher among those with HIV than among those without HIV.322,323 In TB-endemic settings, much of the increased risk of recurrent TB appears to be due to the higher risk of re-infection with a new strain of M. tuberculosis, with subsequent rapid progression to TB disease.324,325 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-31 In settings with low rates of TB—such as the United States—recurrent TB due to re-infection is uncommon, even among people with HIV.326 Several interventions may decrease the risk of recurrent TB among people with HIV: longer TB treatment regimens, administering therapy daily throughout the course of the intensive and continuation phases, post-treatment isoniazid therapy, and use of ART. None of these interventions has been adequately evaluated in randomized trials in settings with low TB burdens. Post-treatment isoniazid (6–9 months of daily isoniazid therapy after the completion of standard multidrug therapy) has been shown to be effective in high-burden settings in which the risk of re-exposure is high,327,328 suggesting that this intervention decreases the risk of re-infection. Post-treatment isoniazid is not recommended for patients in the United States or other low-burden settings due to a lack of evidence of effectiveness supporting a reduced risk of re-infection for these settings (AIII). Given that ART reduces the risk of initially developing TB disease, it is likely that ART also decreases the risk of re-infection with TB. Special Considerations During Pregnancy Pregnant people with HIV who do not have documentation of a prior negative TB screening test result or who are at high risk for repeated or ongoing exposure to individuals with active TB disease should be tested for TB during pregnancy (AIII). TB rates in pregnant and postpartum women are higher than in non-pregnant adults, after adjusting for age,329 and this is likely due to pregnancy-related immunologic shifts.330-334 Several studies have examined the performance of IGRAs for diagnosis of LTBI in pregnant women. In pregnant women with or without HIV, the test appears to perform well.335,336 Longitudinal studies conducted in high-burden countries, however, suggest that test performance may be compromised in late pregnancy versus postpartum, especially at delivery.337-343 A clinical trial of isoniazid preventive therapy (IPT) among HIV-infected women in high TB prevalence settings (TB APPRISE) found increased adverse pregnancy outcomes in women treated with isoniazid during pregnancy compared to postpartum initiation of isoniazid.344 Importantly, however, none of the women were close household TB contacts, and most of the women in the trial were IGRA-negative and were receiving efavirenz-based ART. Two smaller observational studies of isoniazid given to pregnant women with HIV in South Africa did not find an increased risk of adverse pregnancy outcomes with isoniazid.345,346 Similarly, a study of participants in Botswana who became pregnant in a trial of 36 months of isoniazid for people with HIV also did not report increased adverse pregnancy outcomes.347 A subsequent systematic review of the association of adverse pregnancy outcomes and isoniazid found inconsistent associations.348 Among people enrolled in the BRIEF-TB study who became pregnant while taking isoniazid for TB prevention, first-trimester IPT exposure was associated with increased risk of fetal demise, though this association was attenuated when adjusted for covariates proximal to pregnancy outcome including ART use. 349 Studies in individuals with HIV who are not receiving ART have shown a high risk of progression from LTBI to active TB disease (10% per year), and a high risk exists for maternal and infant mortality in pregnant women with HIV who have active TB disease.350,351 Although the risk of progression from LTBI to active TB disease in individuals on ART is decreased significantly, risk in these individuals with HIV appears higher than in pregnant and postpartum people without HIV.337,352 Pregnant people with HIV should be receiving ART both for their own health and for prevention of perinatal transmission (AI). In the United States, isoniazid preventive therapy is Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-32 recommended for pregnant women with HIV whose close household contacts include a person with active TB disease (AI). For those receiving effective ART and without recent TST or IGRA conversion or close household contacts with infectious TB, therapy for LTBI may be deferred until after delivery (BIII). The risk of isoniazid-associated hepatotoxicity may be increased in pregnancy and in the first 2 to 3 months post-partum.344 Therefore, if isoniazid is prescribed, frequent monitoring is needed.34 Pregnant people receiving isoniazid should receive daily pyridoxine supplementation (AII) because they are at risk of isoniazid-associated peripheral neuropathy.151,353 Limited data exist on alternatives to isoniazid for LTBI therapy in pregnant people with HIV. In the IMPAACT 2001 study, pregnant women with and without HIV received 3HP and no serious adverse pregnancy outcomes were observed. Drug exposures were similar to non-pregnant adults, suggesting this regimen does not require dose adjustment in pregnancy.354 Despite these promising data and although rifampin generally is considered safe in pregnancy, data on the use of rifapentine remain extremely limited and the use of rifapentine in pregnant people is not currently recommended (BIII).355-357 The DOLPHIN Moms trial (NCT05122026) currently underway is examining the pharmacokinetics and safety of 3HP and 1HP in pregnant people with HIV who are virally suppressed on a dolutegravir-based regimen. The diagnostic evaluation for TB disease in pregnant people is the same as for nonpregnant adults. It is important to recognize that standard symptom screens have lower sensitivity in pregnant women than in non-pregnant adults, and that some TB symptoms may be masked by common symptoms of pregnancy (e.g. poor appetite).358-360 In addition to standard sputum testing, chest radiographs with abdominal shielding are recommended and result in minimal fetal radiation exposure.361 An increase in pregnancy complications—including preterm birth, low birthweight, and fetal growth restriction— can be seen among pregnant women with either pulmonary or extrapulmonary TB not confined to the lymph nodes, especially when TB treatment is delayed until late in pregnancy.34,330,333,335,336,339,344,351,362-366 Congenital TB infection has been reported, although it appears relatively uncommon; history of maternal infertility and acid-fast bacilli from placenta or endometrial biopsy may be found with this rare diagnosis.367-372 While rare, congenital TB might be more common among children born to mothers with TB/HIV coinfection, especially when those children also have perinatally acquired HIV.373,374 TB therapy should not be withheld because of pregnancy (AIII). Treatment of TB disease should be the same for pregnant people and nonpregnant people, but with attention to the following considerations (AIII): • Although isoniazid is not teratogenic in animals or humans, hepatotoxicity caused by isoniazid might occur more frequently during pregnancy and the postpartum period.375 Monthly monitoring of liver transaminases during pregnancy and the postpartum period is recommended (BIII). • Rifampin is not teratogenic in humans. • Ethambutol is teratogenic in rodents and rabbits at doses that are much higher than those used in humans. No evidence of teratogenicity has been observed in humans. Ocular toxicity has been reported in adults taking ethambutol but changes in visual acuity have not been detected in infants exposed to ethambutol in utero. • Pyrazinamide is not teratogenic in animals. The WHO and the International Union Against Tuberculosis and Lung Diseases have made recommendations for the routine use of pyrazinamide in pregnant individuals.272,376 Pyrazinamide has been recommended for use in pregnant people in the United States, although data characterizing its safety in this setting are Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-33 limited and the CDC guidance suggests that clinicians consider the use of this agent based on individual patient considerations weighing benefit and risks.151,377 If pyrazinamide is not included in the initial treatment regimen, the minimum duration of TB therapy with isoniazid, rifampin, and ethambutol should be 9 months for drug-susceptible TB (AII). The decision regarding whether to include pyrazinamide in treatment regimens for a pregnant person should be made after consultation among obstetricians, TB specialists, and the patient, while considering gestational age and likely susceptibility pattern of the TB strain. Experience using the majority of the second-line drugs for TB during pregnancy is limited.378-381 MDR TB in pregnancy should be managed in consultation with a specialist. In a small prospective study of pregnant patients who received second-line MDR/RR-TB regimens that contained bedaquiline or delamanid (including linezolid, clofazimine, amikacin, capreomycin, and kanamycin) 98% had successful treatment outcomes, and at least 81% of continued pregnancies resulted in live births with 68% normal birthweight neonates.378 The following concerns should be considered when selecting second-line anti-TB drugs for use in pregnant people: • Bedaquiline: Data on the use of bedaquiline in pregnancy are limited, but a study of 108 pregnant women from South Africa found an increased frequency of low birthweight (<2,500 g) among children exposed to bedaquiline in utero compared to those who were not exposed (45% vs. 26%; P = 0.034).382 The median birthweight between the two groups, however, was not statistically significant (2690 vs. 2900 grams [P = 0.18]) and after 1 year, most children exposed to bedaquiline had gained weight and were doing well. Bedaquiline concentrations in breast milk may be as high or higher than concentrations in maternal plasma, which may have implications for the infant.383,384 • Cycloserine: No data are available from animal studies or reports of cycloserine use in humans during pregnancy. • Ethionamide has been associated with an increased risk for several anomalies in rats after high-dose exposure, but not in mice or rabbits.385-387 Case reports have documented cases of CNS defects in humans and hypothyroidism, but overall experience is limited with use during human pregnancy.388 Ethionamide is likely present in the breast milk, which could be associated with thyroid issues in the infant. Thus, ethionamide should be avoided, unless its use is required on the basis of susceptibility testing (CIII). • Fluoroquinolones: Because arthropathy has been noted in immature animals exposed to fluoroquinolones in utero, quinolones are typically not recommended for pregnant people or children aged <18 years (CIII). However, studies evaluating fluoroquinolone use in pregnant women did not find an increased risk of birth defects or congenital musculoskeletal abnormalities.389-393 Furthermore, fluoroquinolones were used in a larger South African case series of MDR TB treatment in pregnancy with generally good outcomes.382 Thus, fluoroquinolones can be used in pregnancy for drug-resistant TB if they are required on the basis of susceptibility testing (BII).394 • Linezolid: Animal studies of linezolid in pregnancy report decreased fetal body weight and increased fusion of costal cartilage.395 There are few studies in human pregnancy, but linezolid has been used for the treatment of DR-TB in some high-burden countries.378,382 In these case studies, monitoring complete blood counts for anemia and thrombocytopenia and advising iron supplementation has been recommended.384,396 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-34 • Delamanid: Delamanid appears to be safe in animal reproductive toxicity studies. It has been used in small cohorts of pregnant women for DR-TB with favorable outcomes.378,397 • Pretomanid: Animal studies of pretomanid do not indicate direct or indirect harmful effects with respect to embryo-fetal development. However, pretomanid has been associated with reproductive toxicity in animal models; specifically, reduced fertility in male rats.398 There has been very limited use in human pregnancies. Therefore, pretomanid should be avoided in pregnancy until more data is available (AIII). • Para-aminosalicylic acid is not teratogenic in rats or rabbits.377 In one study, a possible increase in limb and ear anomalies was reported among 143 infants delivered by women who were exposed to para-aminosalicylic acid during the first trimester of pregnancy.399 No specific pattern of defects and no increase in the rate of defects have been detected in other human studies, indicating that this agent can be used with caution, if needed (CIII). • Aminoglycosides/polypeptides: Streptomycin use has been associated with a 10% rate of vestibulocochlear nerve toxicity in infants exposed to the drug in utero; its use during pregnancy should be avoided, if possible (AIII). Hearing loss has been detected in approximately 2% of children exposed to long-term kanamycin therapy in utero; like streptomycin, this agent should typically be avoided, if possible (AIII). 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Mycobacterium tuberculosis infection in pregnant and nonpregnant women infected with HIV in the Women and Infants Transmission Study. Arch Intern Med. 1995;155(10):1066-1072. Available at: 331. Eriksen NL, Helfgott AW. Cutaneous anergy in pregnant and nonpregnant women with human immunodeficiency virus. Infect Dis Obstet Gynecol. 1998;6(1):13-17. Available at: 332. Jana N, Vasishta K, Jindal SK, Khunnu B, Ghosh K. Perinatal outcome in pregnancies complicated by pulmonary tuberculosis. Int J Gynaecol Obstet. 1994;44(2):119-124. Available at: 333. Jana N, Vasishta K, Saha SC, Ghosh K. Obstetrical outcomes among women with extrapulmonary tuberculosis. N Engl J Med. 1999;341(9):645-649. Available at: 334. Kourtis AP, Read JS, Jamieson DJ. Pregnancy and infection. N Engl J Med. 2014;370(23):2211-2218. Available at: 335. Jonnalagadda S, Lohman Payne B, Brown E, et al. Latent tuberculosis detection by interferon gamma release assay during pregnancy predicts active tuberculosis and mortality in human immunodeficiency virus type 1-infected women and their children. J Infect Dis. 2010;202(12):1826-1835. Available at: 336. Jonnalagadda SR, Brown E, Lohman-Payne B, et al. Consistency of Mycobacterium tuberculosis-specific interferon-gamma responses in HIV-1-infected women during pregnancy and postpartum. Infect Dis Obstet Gynecol. 2012;2012:950650. Available at: 337. Bhosale R, Alexander M, Deshpande P, et al. Stages of pregnancy and HIV affect diagnosis of tuberculosis infection and Mycobacterium tuberculosis (MTB)-induced immune response: Findings from PRACHITi, a cohort study in Pune, India. Int J Infect Dis. 2021;112:205-211. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-67 338. Kaplan SR, Escudero JN, Mecha J, et al. Interferon gamma release assay and tuberculin skin test performance in pregnant women living with and without HIV. J Acquir Immune Defic Syndr. 2022;89(1):98-107. Available at: 339. Lighter-Fisher J, Surette AM. Performance of an interferon-gamma release assay to diagnose latent tuberculosis infection during pregnancy. Obstet Gynecol. 2012;119(6):1088-1095. Available at: 340. Mathad JS, Bhosale R, Balasubramanian U, et al. Quantitative IFN-γ and IL-2 response associated with latent tuberculosis test discordance in HIV-infected pregnant women. Am J Respir Crit Care Med. 2016;193(12):1421-1428. Available at: 341. Mathad JS, Bhosale R, Sangar V, et al. Pregnancy differentially impacts performance of latent tuberculosis diagnostics in a high-burden setting. PLoS One. 2014;9(3):e92308. Available at: 342. LaCourse SM, Cranmer LM, Matemo D, et al. Effect of pregnancy on interferon gamma release assay and tuberculin skin test detection of latent TB infection among HIV-infected women in a high burden setting. J Acquir Immune Defic Syndr. 2017;75(1):128-136. Available at: 343. Weinberg A, Aaron L, Montepiedra G, et al. Effects of pregnancy and isoniazid preventive therapy on Mycobacterium tuberculosis interferon gamma response assays in women with HIV. Clin Infect Dis. 2021;73(9):e3555-e3562. Available at: 344. Gupta A, Montepiedra G, Aaron L, Theron G. isoniazid preventive therapy in HIV-infected pregnant and postpartum women. N Engl J Med. 2019;381:1333-1346. Available at: 345. Salazar-Austin N, Cohn S, Lala S, et al. Isoniazid preventive therapy and pregnancy outcomes in women living with human immunodeficiency virus in the Tshepiso cohort. Clin Infect Dis. 2020;71(6):1419-1426. Available at: 346. Kalk E, Heekes A, Mehta U, et al. Safety and effectiveness of isoniazid preventive therapy in pregnant women living with human immunodeficiency virus on antiretroviral therapy: An Observational Study Using Linked Population Data. Clin Infect Dis. 2020;71(8):e351-e358. Available at: 347. Taylor AW, Mosimaneotsile B, Mathebula U, et al. Pregnancy outcomes in HIV-infected women receiving long-term isoniazid prophylaxis for tuberculosis and antiretroviral therapy. Infect Dis Obstet Gynecol. 2013;2013:195637. Available at: 348. Hamada Y, Figueroa C, Martín-Sánchez M, Falzon D, Kanchar A. The safety of isoniazid tuberculosis preventive treatment in pregnant and postpartum women: systematic review and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-68 meta-analysis. Eur Respir J. 2020;55(3). Available at: 349. Gupta A, Hughes MD, Cruz JL, et al. Adverse pregnancy outcomes among HIV-infected women taking isoniazid preventive therapy during the first trimester. Clin Infect Dis. 2023. Available at: 350. Lawn SD, Wood R, De Cock KM, Kranzer K, Lewis JJ, Churchyard GJ. Antiretrovirals and isoniazid preventive therapy in the prevention of HIV-associated tuberculosis in settings with limited health-care resources. Lancet Infect Dis. 2010;10(7):489-498. Available at: 351. Gupta A, Nayak U, Ram M, et al. Postpartum tuberculosis incidence and mortality among HIV-infected women and their infants in Pune, India, 2002-2005. Clin Infect Dis. 2007;45(2):241-249. Available at: 352. Middelkoop K, Bekker LG, Myer L, et al. Antiretroviral program associated with reduction in untreated prevalent tuberculosis in a South African township. Am J Respir Crit Care Med. 2010;182(8):1080-1085. Available at: 353. Miele K, Bamrah Morris S, Tepper NK. Tuberculosis in pregnancy. Obstet Gynecol. 2020;135(6):1444-1453. Available at: 354. Mathad JS, Savic R, Britto P, et al. Pharmacokinetics and safety of 3 months of weekly rifapentine and isoniazid for tuberculosis prevention in pregnant women. Clin Infect Dis. 2022;74(9):1604-1613. Available at: 355. Moro RN, Scott NA, Vernon A, et al. Exposure to latent tuberculosis treatment during pregnancy. the PREVENT TB and the iAdhere Trials. Ann Am Thorac Soc. 2018;15(5):570-580. Available at: 356. Food and Drug Administration. PRIFTIN (rifapentine). 2010. Available at: 357. Mathad JS, Savic R, Britto P, et al. Pharmacokinetics and safety of three months of weekly rifapentine and isoniazid for tuberculosis prevention in pregnant women. Clin Infect Dis. 2021. Available at: 358. Hoffmann CJ, Variava E, Rakgokong M, et al. High prevalence of pulmonary tuberculosis but low sensitivity of symptom screening among HIV-infected pregnant women in South Africa. PLoS One. 2013;8(4):e62211. Available at: 359. LaCourse SM, Cranmer LM, Matemo D, et al. Tuberculosis case finding in HIV-infected pregnant women in Kenya reveals poor performance of symptom screening and rapid diagnostic tests. J Acquir Immune Defic Syndr. 2016;71(2):219-227. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-69 360. Kosgei RJ, Szkwarko D, Callens S, et al. Screening for tuberculosis in pregnancy: do we need more than a symptom screen? Experience from western Kenya. Public Health Action. 2013;3(4):294-298. Available at: 361. Committee Opinion. Committee Opinion No. 723: Guidelines for diagnostic imaging during pregnancy and lactation. Obstet Gynecol. 2017;130(4):e210-e216. Available at 362. Mnyani CN, McIntyre JA. Tuberculosis in pregnancy. BJOG. 2011;118(2):226-231. Available at: 363. Brost BC, Newman RB. The maternal and fetal effects of tuberculosis therapy. Obstet Gynecol Clin North Am. 1997;24(3):659-673. Available at: 364. Bothamley G. Drug treatment for tuberculosis during pregnancy: safety considerations. Drug Saf. 2001;24(7):553-565. Available at: 365. Czeizel AE, Rockenbauer M, Olsen J, Sorensen HT. A population-based case-control study of the safety of oral anti-tuberculosis drug treatment during pregnancy. Int J Tuberc Lung Dis. 2001;5(6):564-568. Available at: 366. Efferen LS. Tuberculosis and pregnancy. Curr Opin Pulm Med. 2007;13(3):205-211. Available at: 367. Vilarinho LC. Congenital tuberculosis: a case report. Braz J Infect Dis. 2006;10(5):368-370. Available at: 368. Lee LH, LeVea CM, Graman PS. Congenital tuberculosis in a neonatal intensive care unit: case report, epidemiological investigation, and management of exposures. Clin Infect Dis. 1998;27(3):474-477. Available at: 369. Cantwell MF, Shehab ZM, Costello AM, et al. Brief report: congenital tuberculosis. N Engl J Med. 1994;330(15):1051-1054. Available at: 370. Rinsky JL, Farmer D, Dixon J, et al. Notes from the field: contact investigation for an infant with congenital tuberculosis infection - North Carolina, 2016. MMWR Morb Mortal Wkly Rep. 2018;67(23):670-671. Available at: 371. Chang CW, Wu PW, Yeh CH, Wong KS, Wang CJ, Chang CC. Congenital tuberculosis: case report and review of the literature. Paediatr Int Child Health. 2018;38(3):216-219. Available at: 372. Stuart RL, Lewis A, Ramsden CA, Doherty RR. Congenital tuberculosis after in-vitro fertilisation. Med J Aust. 2009;191(1):41-42. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-70 373. Pillay T, Sturm AW, Khan M, et al. Vertical transmission of Mycobacterium tuberculosis in KwaZulu Natal: impact of HIV-1 co-infection. Int J Tuberc Lung Dis. 2004;8(1):59-69. Available at: 374. Adhikari M, Pillay T, Pillay DG. Tuberculosis in the newborn: an emerging disease. Pediatr Infect Dis J. 1997;16(12):1108-1112. Available at: 375. Franks AL, Binkin NJ, Snider DE, Jr., Rokaw WM, Becker S. Isoniazid hepatitis among pregnant and postpartum Hispanic patients. Public Health Rep. 1989;104(2):151-155. Available at: 376. Dlodlo RA, Brigden G, Heldal E, et al. Management of tuberculosis: a guide to essential practice. Paris, France: International Union Against Tuberculosis and Lung Disease; October 2019. Available at: 377. Dluzniewski A, Gastol-Lewinska L. The search for teratogenic activity of some tuberlostatic drugs. Diss Pharm Pharmacol. 1971;23:383-392. 378. Lotia Farrukh I, Lachenal N, Adenov MM, et al. Pregnancy and birth outcomes in patients with multidrug-resistant tuberculosis treated with regimens that include new and repurposed drugs. Clin Infect Dis. 2023. Available at: 379. Lessnau KD, Qarah S. Multidrug-resistant tuberculosis in pregnancy: case report and review of the literature. Chest. 2003;123(3):953-956. Available at: 380. Drobac PC, del Castillo H, Sweetland A, et al. Treatment of multidrug-resistant tuberculosis during pregnancy: long-term follow-up of 6 children with intrauterine exposure to second-line agents. Clin Infect Dis. 2005;40(11):1689-1692. Available at: 381. Alene KA, Murray MB, van de Water BJ, et al. Treatment outcomes among pregnant patients with multidrug-resistant tuberculosis: a systematic review and meta-analysis. JAMA Netw Open. 2022;5(6):e2216527. Available at: 382. Loveday M, Hughes J, Sunkari B, et al. Maternal and infant outcomes among pregnant women treated for multidrug/rifampicin-resistant tuberculosis in South Africa. Clinical Infectious Diseases. 2020;72(7):1158-1168. Available at: 383. Court R, Gausi K, Mkhize B, et al. Bedaquiline exposure in pregnancy and breastfeeding in women with rifampicin-resistant tuberculosis. Br J Clin Pharmacol. 2022;88(8):3548-3558. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-71 384. Jaspard M, Elefant-Amoura E, Melonio I, De Montgolfier I, Veziris N, Caumes E. Bedaquiline and linezolid for extensively drug-resistant tuberculosis in pregnant woman. Emerg Infect Dis. 2017;23(10):1731-1732. Available at: 385. Fujimori H, et al. The effect of tuberculostatics on the fetus: an experimental production of congenital anomaly in rats by ethionamide. Proc Congen Anom Res Assoc Jpn. 1965;5:34-35. 386. Takekoshi S. Effects of hydroxymethylpyrimidine on isoniazid- and ethionamide-induced teratosis. Gunma J Med Sci. 1965;14:233-244. 387. Khan I, Azam A. Study of teratogenic activity of trifluoperazine, amitriptyline, ethionamide and thalidomide in pregnant rabbits and mice. Proc Eur Soc Study Drug Toxic. 1969;10:235-242. 388. Potworowska M, Sianoz-Ecka E, Szufladowica R. Treatment with ethionamide in pregnancy. Pol Med J. 1966;5(5):1152-1158. Available at: 389. Schaefer C, Amoura-Elefant E, Vial T, et al. Pregnancy outcome after prenatal quinolone exposure. Evaluation of a case registry of the European Network of Teratology Information Services (ENTIS). Eur J Obstet Gynecol Reprod Biol. 1996;69(2):83-89. Available at: 390. Yefet E, Schwartz N, Chazan B, Salim R, Romano S, Nachum Z. The safety of quinolones and fluoroquinolones in pregnancy: a meta-analysis. BJOG. 2018;125(9):1069-1076. Available at: 391. Loebstein R, Addis A, Ho E, et al. Pregnancy outcome following gestational exposure to fluoroquinolones: a multicenter prospective controlled study. Antimicrob Agents Chemother. 1998;42(6):1336-1339. Available at: 392. Ziv A, Masarwa R, Perlman A, Ziv D, Matok I. Pregnancy Outcomes Following exposure to quinolone antibiotics - a systematic-review and meta-analysis. Pharm Res. 2018;35(5):109. Available at: 393. Acar S, Keskin-Arslan E, Erol-Coskun H, Kaya-Temiz T, Kaplan YC. Pregnancy outcomes following quinolone and fluoroquinolone exposure during pregnancy: A systematic review and meta-analysis. Reprod Toxicol. 2019;85:65-74. Available at: 394. Nahum GG, Uhl K, Kennedy DL. Antibiotic use in pregnancy and lactation: what is and is not known about teratogenic and toxic risks. Obstet Gynecol. 2006;107(5):1120-1138. Available at: 395. ZYVOX [package insert]. Food and Drug Administration. 2008. Available at: 4lbl.pdf. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV X-72 396. Van Kampenhout E, Bolhuis MS, Alffenaar JC, et al. Pharmacokinetics of moxifloxacin and linezolid during and after pregnancy in a patient with multidrug-resistant tuberculosis. Eur Respir J. 2017;49(3). Available at: 397. Acquah R, Mohr-Holland E, Daniels J, et al. Outcomes of children born to pregnant women with drug-resistant tuberculosis treated with novel drugs in Khayelitsha, South Africa: A Report of Five Patients. Pediatr Infect Dis J. 2021;40(5):e191-e192. Available at: 398. PRETOMANID [package insert]. Food and Drug Administration. 2022. Available at: 399. Varpela E. On the effect exerted by first-line tuberculosis medicines on the foetus. Acta Tuberc Pneumol Scand. 1964;45:53-69. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-1 Pneumocystis Pneumonia Updated: September 16, 2024 Reviewed: September 16, 2024 Epidemiology Pneumocystis pneumonia (PCP) is caused by Pneumocystis jirovecii, a ubiquitous fungus. The taxonomy of the organism has been changed; Pneumocystis carinii now refers only to the Pneumocystis that infects rats, and P. jirovecii refers to the distinct species that infects humans. However, the abbreviation PCP is still the preferred acronym to designate the clinical syndrome of Pneumocystis pneumonia,1 although PJP is commonly used. Initial infection with P. jirovecii usually occurs in early childhood; two-thirds of healthy children have antibodies to P. jirovecii by age 2 years to 4 years.2 Rodent studies and case clusters in immunosuppressed patients suggest that Pneumocystis spreads by the airborne route. Disease probably occurs by both new acquisition of infection and by reactivation of latent infection.3-12 Before the widespread use of PCP prophylaxis and antiretroviral therapy (ART), PCP occurred in 70% to 80% of people with advanced HIV,13 with a 20% to 40% mortality rate in individuals despite anti-Pneumocystis therapy. Approximately 90% of PCP cases occur in people with HIV with CD4 T lymphocyte (CD4) cell counts <200 cells/mm3. The incidence of PCP has declined substantially with widespread use of PCP prophylaxis and ART; incidence among people with HIV in Western Europe and the United States is <1 case per 100 person-years.14-16 Most cases of PCP now occur in people with HIV who are unaware of their HIV status or are not receiving ongoing care for HIV,17 and in those with advanced immunosuppression (i.e., CD4 counts <100 cells/mm3).18 Clinical Manifestations In people with HIV, the most common manifestations of PCP are subacute onset of progressive dyspnea, fever, non-productive cough, and chest discomfort that worsens within days to weeks. The fulminant pneumonia observed in people who do not have HIV is less common among people with HIV. A more fulminant course can occur particularly after initiation of therapy.19-21 In mild cases, pulmonary examination while the patient is at rest usually is normal. With exertion, tachypnea, tachycardia, and diffuse dry (cellophane) rales may be observed.20 Fever is present in most cases and may be the predominant symptom in some people. Pneumonia limited to the apices and extrapulmonary disease, which can occur in any organ, are rare and have been associated with use of aerosolized pentamidine prophylaxis.22 Hypoxemia, the most characteristic laboratory abnormality, can range from mild (room air arterial oxygen partial pressure [PaO2] ≥70 mmHg or alveolar-arterial gradient [A-a gradient] <35 mmHg) to moderate (A-a gradient ≥35 to <45 mmHg) to severe (A-a gradient ≥45 mmHg). Oxygen desaturation with exercise is often abnormal but is non-specific.23 Elevation of lactate dehydrogenase levels to >500 mg/dL is common but also non-specific.24 The chest radiograph typically demonstrates diffuse, bilateral, symmetrical “ground-glass” interstitial infiltrates emanating from the hila in a butterfly pattern20; however, in people with HIV with early disease, a chest radiograph may Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-2 be normal.25 Atypical radiographic presentations (such as nodules, blebs and cysts, asymmetric disease, upper lobe localization, intrathoracic adenopathy, and pneumothorax) also occur. Spontaneous pneumothorax in a person with HIV should raise the suspicion of PCP.26,27 Cavitation and pleural effusion are uncommon in the absence of other pulmonary pathogens or malignancies, and their presence may indicate an alternative diagnosis or an additional pathology. People with HIV who have documented PCP may have another concurrent cause of pulmonary dysfunction, such as tuberculosis (TB), Kaposi sarcoma, toxoplasmosis, or fungal or bacterial pneumonia.28,29 Thin-section computed tomography (CT) without contrast is a useful adjunctive study, since even in patients with mild-to-moderate symptoms and a normal chest radiograph, a CT scan will be abnormal, demonstrating “ground-glass” attenuation that may be patchy. A normal CT has a high negative predictive value, and alternate diagnoses should be excluded.30,31 Diagnosis Because clinical presentation, blood tests, and chest radiographs are not pathognomonic for PCP (and because the organism cannot be cultivated routinely), histopathologic or cytopathologic demonstration of organisms in tissue, bronchoalveolar lavage (BAL) fluid, or induced sputum samples19,28,29,32 is required for a definitive diagnosis of PCP. Spontaneously expectorated sputum has low sensitivity for the diagnosis of PCP and should not be submitted to the laboratory to diagnose PCP. Giemsa, Diff-Quik, and Wright stains detect both main life forms of P. jirovecii—cysts and trophic forms—but do not stain the cyst wall; Grocott-Gomori methenamine silver, Gram-Weigert, cresyl violet, and toluidine blue stain only the cyst wall. Some laboratories prefer direct immunofluorescent staining, which has higher sensitivity than the colorimetric stains.33 The sensitivity and specificity of respiratory samples for PCP depend on the stain being used, the experience of the microbiologist or pathologist, the pathogen load, and specimen quality. Studies of stained respiratory tract samples obtained by various methods indicate the following relative diagnostic sensitivities: <50% to >90% for induced sputum, 90% to 99% for bronchoscopy with BAL, 95% to 100% for transbronchial biopsy, and 95% to 100% for open lung biopsy.34-40 Polymerase chain reaction (PCR) is an increasingly utilized method for diagnosing PCP and has replaced staining methods in many laboratories. PCR is highly sensitive and specific for detecting Pneumocystis. While PCR cannot reliably distinguish colonization from active disease, quantitative PCR (qPCR) is favored over qualitative assays, as a higher organism load by qPCR is likely to represent clinically significant disease.41-43 However, the broad range of organism loads in patients with PCP and the lack of commercially available U.S. Food and Drug Administration (FDA)– approved qPCR kits for diagnosis makes establishment of cutoffs for colonization versus disease difficult to standardize. 1,3 β-D-glucan (β-glucan), which is a component of the cell wall of Pneumocystis cysts, is often elevated in people with HIV who also have PCP. The sensitivity of the β-glucan assay for diagnosis of PCP appears to be high, thus PCP is less likely in people with HIV with a low level of β-glucan (e.g., <80 pg/mL using the Fungitell assay). However, the specificity of β-glucan testing for establishing a PCP diagnosis is low,44-48 since many other fungal diseases, cellulose membranes used for hemodialysis, and some drugs can elevate β-glucan levels.47,48 Because the clinical manifestations of several disease processes are similar, it is important to seek a definitive diagnosis of PCP disease rather than rely on a presumptive diagnosis, especially in patients with moderate-to-severe disease. However, PCP treatment should be initiated before a definitive Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-3 diagnosis is established if clinical suspicion is high. P. jirovecii persist in clinical specimens for days or weeks after effective therapy is initiated, allowing definitive diagnosis to be established even after initiating therapy.32 Preventing Exposure There are insufficient data to support isolation as standard practice to prevent PCP (CIII). Pneumocystis can be quantified in the air near people with PCP,49 and multiple outbreaks, each caused by a distinct strain of Pneumocystis, have been documented among kidney transplant patients as well as other immunosuppressed populations.6-12,50 Although these findings strongly suggest that isolating people with known PCP from people at high risk for PCP may be beneficial, no study to date has documented the benefit of such an approach. Preventing Disease Recommendations for Preventing First Episode of Pneumocystis Pneumonia (Primary Prophylaxis) Indications for Initiating Primary Prophylaxis • CD4 count 100–200 cells/mm3, if plasma HIV RNA level above detection limits (AI), or • CD4 count <100 cells/mm3, regardless of plasma HIV RNA level (AIII) • Note: Patients who are receiving pyrimethamine-sulfadiazine for treatment or suppression of toxoplasmosis do not require additional prophylaxis for PCP (AII). Preferred Therapy • TMP-SMX, 1 DS tablet PO daily (AI), or • TMP-SMX, 1 SS tablet PO daily (AI) • Note: TMP-SMX also confers protection against toxoplasmosis and some protection against many respiratory bacterial infections. Alternative Therapy • The following regimens can be used for people who are seropositive or seronegative for Toxoplasma gondii: o TMP-SMX 1 DS tablet PO three times weekly (BI), or o Dapsonea 50 mg PO daily with pyrimethamine 50 mg plus leucovorin 25 mg PO weekly (BI), or o Dapsonea 200 mg plus pyrimethamine 75 mg plus leucovorin 25 mg PO weekly (BI), or o Atovaquone 1,500 mg PO daily with food (BI) • The following regimens should only be used in people who are seronegative for Toxoplasma gondii: o Dapsonea 100 mg PO daily or dapsone 50 mg PO twice a day (BI), or o Aerosolized pentamidine 300 mg via Respirgard II nebulizer every month (BI), or o Intravenous pentamidine 300 mg every 28 days (CIII) Indication for Discontinuing Primary Prophylaxis • CD4 count increased from <200 cells/mm3 to ≥200 cells/mm3 for ≥3 months in response to ART (AI) • Can consider when CD4 count is 100–200 cells/mm3 and HIV RNA remains below limit of detection of the assay used for ≥3 to 6 months (BII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-4 Indication for Restarting Primary Prophylaxis • CD4 count <100 cells/mm3 regardless of HIV RNA (AIII) • CD4 count 100–200 cells/mm3 and HIV RNA consistently above detection limit of the assay used (AIII) Pre-pregnancy and Pregnancy Considerations • Clinicians who are providing pre-pregnancy care for people with HIV receiving PCP prophylaxis can discuss the option of deferring pregnancy until PCP prophylaxis can be safely discontinued with their patients (BIII). • Chemoprophylaxis for PCP should be administered to pregnant adults and adolescents as for nonpregnant adults and adolescents (AIII). TMP-SMX is the recommended prophylactic agent (AIII). Clinicians should consider giving supplemental folic acid 4 mg/day to people who are on TMP-SMX if they are capable of becoming pregnant prior to pregnancy or as soon as possible in their first trimester (BIII). • Given theoretical concerns about possible teratogenicity associated with first-trimester TMP-SMX exposure, clinicians may consider using alternative prophylactic regimens such as aerosolized pentamidine or oral atovaquone during the first trimester (CIII) rather than withholding chemoprophylaxis. Other Considerations/Comments • For people with HIV with non-life-threatening adverse reactions to TMP-SMX, the drug should be continued if clinically feasible. • If TMP-SMX is discontinued because of a mild adverse reaction, reinstitution of therapy should be considered after the reaction has resolved (AII). The dose of TMP-SMX can be increased gradually (desensitization) (BI) or the drug can be given at a reduced dose or frequency (CIII). • TMP-SMX should be permanently discontinued, with no rechallenge, in people with HIV with life-threatening adverse reactions including suspected or confirmed Stevens-Johnson Syndrome or toxic epidermal necrolysis (AIII). See above for alternative options for primary PCP prophylaxis. a G6PD levels should be checked before administration of dapsone. An alternative agent should be used if the patient is found to have G6PD deficiency. Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; DS = double strength; G6PD = glucose-6-phosphate dehydrogenase; PCP = Pneumocystis pneumonia; PO = orally; SS = single strength; TMP-SMX = trimethoprim-sulfamethoxazole Indication for Primary Prophylaxis Chemoprophylaxis against PCP should be given to adults and adolescents with HIV (including pregnant people) with CD4 counts <100 cells/mm3 regardless of plasma HIV levels (AIII) and those with CD4 counts between 100 and 200 cells/mm3 with plasma HIV RNA levels above detection limits (AI).13,51 Patients receiving pyrimethamine-sulfadiazine for treatment or suppression of toxoplasmosis do not require additional prophylaxis for PCP (AII).52 Trimethoprim-sulfamethoxazole (TMP-SMX) is the recommended prophylactic agent for PCP (AI).51,53-55 One double-strength TMP-SMX tablet daily or one single-strength tablet daily55 are the preferred regimens (AI); there is greater experience with the double-strength tablet, but the single-strength tablet may be better tolerated. One double-strength TMP-SMX tablet three times weekly is also effective (BI).56 TMP-SMX confers cross-protection against toxoplasmosis57 and many respiratory bacterial infections.53,58 TMP-SMX chemoprophylaxis should be continued, when clinically feasible, in people with HIV who have non-life-threatening adverse reactions. In those who discontinue TMP-SMX because of a mild adverse reaction (e.g., rash without vesicles, bullae, or ulcerations), reinstitution of the drug should be considered after the reaction has resolved (AII).59 Therapy should be permanently discontinued (with no rechallenge) in people with HIV with life-Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-5 threatening adverse reactions, including possible or definite Stevens-Johnson syndrome or toxic epidermal necrolysis (AIII). Patients who have experienced adverse events, including fever and rash, may better tolerate reinstitution of TMP-SMX if the dose is gradually increased according to published regimens (BI)60,61 or if the drug is given at a reduced dose or frequency (CIII). As many as 70% of people with HIV can tolerate such reinstitution of TMP-SMX therapy.58 For people with HIV in whom TMP-SMX use may need to be avoided (e.g., intolerance, severe renal dysfunction, early pregnancy, significant myelosuppression), alternative prophylactic regimens include dapsone (BI),53 dapsone plus pyrimethamine plus leucovorin (BI),62-64 aerosolized pentamidine administered with the Respirgard II nebulizer (manufactured by Marquest; Englewood, Colorado) (BI),54 intravenous (IV) pentamidine (CIII),65-67 and atovaquone (BI).68,69 For people with HIV who are seropositive for Toxoplasma gondii and cannot tolerate TMP-SMX, recommended alternatives for prophylaxis against both PCP and toxoplasmosis include dapsone plus pyrimethamine plus leucovorin (BI)62-64 or atovaquone (CIII). Dapsone alone and pentamidine (aerosol or IV) have not been shown to have activity against toxoplasmosis, and should only be used in people who are seronegative for anti-Toxoplasma antibodies.57,70,71 Glucose-6-phosphate dehydrogenase (G6PD) levels should be checked prior to starting dapsone, and an alternative regimen should be used if G6PD deficiency is present, given the risks of hemolysis and methemoglobinemia in patients with G6PD deficiency.72 The utility of IV pentamidine as PCP prophylaxis has been evaluated primarily in retrospective/observational studies in immunosuppressed patients without HIV, especially in pediatric populations; experience in people with HIV is limited. Aerosolized pentamidine should be administered in an appropriately configured negative pressure room.73 Pyrimethamine has become extremely expensive and can be difficult to obtain in the United States, and atovaquone has variable and unpredictable bioavailability. Atovaquone is as effective as aerosolized pentamidine68 or dapsone69 but substantially more expensive than the other regimens, and less preferred by patients due to the taste of the suspension. The following regimens are NOT recommended as alternatives to TMP-SMX for PCP prophylaxis (AIII): • Aerosolized pentamidine administered by nebulization devices other than the Respirgard II nebulizer74 • Oral clindamycin plus primaquine, given that this regimen has not been studied for PCP prophylaxis, and clindamycin alone was poorly tolerated as a potential prophylactic regimen for toxoplasmosis.75 Discontinuing Primary Prophylaxis Primary Pneumocystis prophylaxis should be discontinued in adult and adolescent people with HIV who have responded to ART with an increase in CD4 counts from <200 cells/mm3 to ≥200 cells/mm3 for ≥3 months (AI). In observational and randomized studies whose findings support this recommendation, most people with HIV had CD4 counts >200 cells/mm3 for >3 months before discontinuing PCP prophylaxis.76-85 At discontinuation of prophylaxis, the median CD4 count was >300 cells/mm3, most participants had a CD4 cell percentage ≥14%, and many had sustained suppression of HIV plasma RNA levels below detection limits for the assay employed. Median follow-up was 6 to 19 months. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-6 A combined analysis of European cohorts,86,87 a small randomized trial,88 and a case series89 found a low incidence of PCP in people with HIV with CD4 counts between 100 cells/mm3 and 200 cells/mm3, who were receiving ART and had HIV plasma viral loads <50 to <400 copies/mL, and who had stopped or never received PCP prophylaxis; this suggests that primary and secondary PCP prophylaxis can be safely discontinued in people with HIV with CD4 counts between 100 cells/mm3 to 200 cells/mm3 and HIV plasma RNA levels below limits of detection of commercial assays. Data on which to base specific recommendations are inadequate, but some clinicians would stop primary prophylaxis in people with HIV with CD4 counts of 100 cells/mm3 to 200 cells/mm3 if HIV plasma RNA levels remain below limits of detection for ≥3 months to 6 months (BII). Similar observations have been made with regard to stopping primary prophylaxis for Toxoplasma encephalitis.90 Prophylaxis should be reintroduced if the patient’s CD4 count decreases to 100 to 200 cells/mm3 in the setting of sustained increases in plasma HIV RNA levels (AIII) and in any people with HIV whose CD4 count drops to <100 cells/mm3 (AIII). Treating Disease Recommendations for Treating Pneumocystis Pneumonia People with HIV who develop PCP despite TMP-SMX prophylaxis usually can be treated effectively with standard doses of TMP-SMX (BIII). If not already started, ART should be initiated in patients within 2 weeks of diagnosis of PCP, if possible (AI). For Moderate-to-Severe PCP Preferred Therapy • TMP-SMX: (TMP 15–20 mg/kg/day and SMX 75–100 mg/kg/day) IV given in divided doses every 6 or 8 hours (AI); may switch to PO formulation after clinical improvement (AI) Alternative Therapy • Primaquinea 30 mg (base) PO once daily plus clindamycin (IV [600 mg every 6 hours or 900 mg every 8 hours] or PO [450 mg every 6 hours or 600 mg every 8 hours]) (AI), or • Pentamidine 4 mg/kg IV once daily infused over ≥60 minutes (AI); may reduce the dose to pentamidine 3 mg/kg IV once daily in the event of toxicities (BI) • Note: Some clinicians prefer primaquine plus clindamycin because it is more effective and less toxic than pentamidine. Adjunctive Corticosteroids For Moderate-to-Severe PCP Based on the Following Criteria (AI) • PaO2 <70 mmHg at room air, or • A-a gradient ≥35 mmHg Corticosteroid Dosing Schedule • Prednisone doses (beginning as soon as possible and ideally within 72 hours of initiating PCP therapy) (AI) o Days 1–5: 40 mg PO twice daily o Days 6–10: 40 mg PO daily o Days 11–21: 20 mg PO daily • IV methylprednisolone can be given as 80% of prednisone dose. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-7 • Benefit of corticosteroid if started after 72 hours of treatment is unknown, but some clinicians will use it for moderate-to-severe PCP (BIII). For Mild-to-Moderate PCP Preferred Therapy • TMP-SMX: (TMP 15–20 mg/kg/day and SMX 75–100 mg/kg)/day) PO given in three divided doses (AI), or • TMP-SMX, two DS tablets PO three times daily (AI) Alternative Therapy • Dapsonea 100 mg PO daily plus TMP 15 mg/kg/day PO given in three divided doses (BI), or • Primaquinea 30 mg (base) PO daily plus clindamycin PO (450 mg every 6 hours or 600 mg every 8 hours) (BI), or • Atovaquone 750 mg PO twice daily with food (BI) Duration of Therapy • The recommended duration of therapy (irrespective of regimen) is 21 days (AII). • Secondary prophylaxis should be initiated immediately after completion of treatment (see Recurrence table below). Pregnancy Considerations For Moderate-to-Severe PCP Preferred Therapy • TMP-SMX, regardless of disease (AI) • Although a small increased risk of birth defects may be associated with first-trimester exposure to trimethoprim, people in their first trimester with PCP should be treated with TMP-SMX because of its considerable benefit in reducing morbidity and mortality, which outweighs potential risk (AIII). • Clinicians should consider giving supplemental folic acid 4 mg/day to people who are on TMP-SMX before pregnancy if they are capable of becoming pregnant, or as soon as possible in their first trimester (BIII). Doses of supplemental folic acid of 4 mg/day should be limited to the first trimester during the teratogenic window and can be reduced to 0.4 mg at 12 weeks continuing to 4–6 weeks postpartum or discontinuation of breastfeeding (AIII). • Whether or not a person receives supplemental folic acid during the first trimester, a follow-up ultrasound is recommended at 18 weeks to 20 weeks to assess fetal anatomy with consideration for follow-up scans subsequently (BIII). Alternative Therapy • IV pentamidine (BIII) • If other alternatives are not available or tolerated, primaquine plus clindamycin (BIII) o Because of concerns about hemolytic anemia in exposed fetuses who are G6PD deficient (which cannot be diagnosed antenatally), primaquine (plus clindamycin) should be used in pregnancy only if other alternatives are not available or tolerated and benefit is felt to outweigh the risk (AIII). For Mild-to-Moderate PCP Preferred Therapy • TMP-SMX, regardless of disease (AI) Alternative Therapy • Atovaquone suspension (BIII) • If atovaquone is not available or tolerated, dapsone plus TMX (BIII) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-8 o Because of concerns about hemolytic anemia in exposed fetuses who are G6PD deficient, primaquine or dapsone should be used in pregnancy only if other alternatives are not available or tolerated and benefit is felt to outweigh the risk (AIII). Note: As with nonpregnant adults, G6PD levels should be checked before administration of primaquine or dapsone. While the G6PD level in a fetus generally is unknown during pregnancy, G6PD deficiency is an X-linked inherited condition and primaquine or dapsone can be considered if both the pregnant person and biologic father have normal G6PD activity. Adjunctive Corticosteroid Therapy • Adjunctive corticosteroid therapy should be used to improve the pregnant person’s treatment outcome as indicated in nonpregnant adults (AIII). Maternal glucose levels and blood pressure should be monitored closely when corticosteroids are used in pregnancy, as well as fetal growth (AIII). • Pregnant persons who are on chronic steroid therapy during pregnancy for non-hypothalamic-pituitary-adrenal axis disorders do not need stress doses of steroids for vaginal or cesarean delivery but should be continued on their therapeutic dose of steroids without interruption (BIII). Other Considerations/Comments • For people with HIV with non-life-threatening adverse reactions to TMP-SMX, the drug should be continued if clinically feasible. • If TMP-SMX is discontinued because of a mild adverse reaction, reinstitution of therapy should be considered after the reaction has resolved (AII). The dose of TMP-SMX can be increased gradually (desensitization) (BI) or the drug can be given at a reduced dose or frequency (CIII). • TMP-SMX should be permanently discontinued, with no rechallenge, in people with HIV with life-threatening adverse reactions including suspected or confirmed Stevens-Johnson Syndrome or toxic epidermal necrolysis (AIII). See above for alternative options for PCP treatment. a G6PD levels should be checked before administration of dapsone or primaquine. An alternative agent should be used if the patient is found to have G6PD deficiency. Key: A-a gradient = alveolar-arterial gradient; ART = antiretroviral therapy; DS = double strength; G6PD = glucose-6-phosphate dehydrogenase; IV = intravenously; PaO2 = room air arterial oxygen partial pressure; PCP = Pneumocystis pneumonia; PO = orally; SMX = sulfamethoxazole; TMP = trimethoprim; TMP-SMX = trimethoprim-sulfamethoxazole TMP-SMX is the treatment of choice for PCP (AI).91,92 Standard doses are summarized in the table above; lower doses may also be effective, potentially with less toxicity, though randomized controlled data addressing this possibility are unavailable.93 The dose must be adjusted for abnormal renal function. Multiple randomized clinical trials indicate that TMP-SMX is as effective as parenteral pentamidine and more effective than other regimens for PCP treatment.91,92,94 Adding leucovorin to prevent myelosuppression during acute treatment is not recommended because efficacy in preventing this toxicity is questionable and some evidence exists for a higher failure rate in preventing PCP (AII).95 Outpatient therapy with oral TMP-SMX is highly effective in people with HIV with mild-to-moderate PCP (AI).92 TMP-SMX should be permanently discontinued (with no rechallenge) in people with HIV who experience life-threatening adverse reactions including possible or definite Stevens-Johnson syndrome or toxic epidermal necrolysis (AIII). Mutations associated with resistance to sulfa drugs have been documented, but their effect on clinical outcome is uncertain.96-99 Patients who have PCP despite TMP-SMX prophylaxis usually can be treated effectively with standard doses of TMP-SMX (BIII). Patients with documented or suspected PCP and moderate-to-severe disease, defined by room air PaO2 <70 mmHg or A-a gradient ≥35 mmHg, should receive adjunctive corticosteroids as soon as possible and certainly within 72 hours after starting specific PCP therapy (AI).100-105 The benefits of starting steroids later are unclear, but most clinicians would administer them even after 72 hours for Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-9 people with HIV who have moderate-to-severe PCP (BIII). Intravenous methylprednisolone at 80% of the corresponding oral prednisone dose can be used if parenteral administration is necessary. Alternative therapeutic regimens for mild-to-moderate disease include: dapsone plus trimethoprim (TMP) (BI),92,106 which may have efficacy similar to TMP-SMX with fewer side effects, but is less convenient given the number of pills; primaquine plus clindamycin (BI)107-109 (clindamycin can be administered IV for more severe cases, but primaquine is only available in an oral formulation); and atovaquone suspension (BI),91,110 which is less effective than TMP-SMX for mild-to-moderate PCP but has fewer side effects. Clinicians should be aware that the absorption of atovaquone is highly variable; plasma concentrations ≥15 µg/mL are associated with an improved response rate, but atovaquone therapeutic drug monitoring is not routinely available.91,111 People with HIV should be tested for G6PD levels before primaquine or dapsone is administered. An alternative agent should be used if the patient is found to have G6PD deficiency. Alternative therapeutic regimens for people with HIV who have moderate-to-severe PCP include primaquine plus clindamycin (AI) or IV pentamidine (AI).109,112,113 Some clinicians prefer primaquine plus clindamycin because this combination is more effective and less toxic than pentamidine.109,114-116 Aerosolized pentamidine should not be used to treat PCP because it has limited efficacy and is associated with more frequent relapse (AI).112,117,118 The recommended duration of therapy for PCP (irrespective of regimen) is 21 days (AII)19; shorter durations may also be effective but have not been systematically studied.119 The probability and rate of response to therapy depend on the agent used, number of previous PCP episodes, severity of pulmonary illness, degree of immunodeficiency, timing of initiation of therapy, and comorbidities. Although the overall prognosis for people with HIV with PCP-associated respiratory failure is poor, over the past decades, survival for people with HIV who require intensive care unit (ICU) care has improved as management of respiratory failure and HIV comorbidities has improved.120-123 Special attention is necessary regarding the use of ART in such critically ill patients.124 Special Considerations With Regards to Starting ART (Including IRIS) If not already started, ART should be initiated in patients, when possible, within 2 weeks of PCP diagnosis (AI). In a randomized controlled trial of 282 people with HIV with opportunistic infections (OIs) other than TB, 63% of whom had definite or presumptive PCP, the incidence of AIDS progression or death (a secondary study endpoint) was significantly lower among participants who initiated ART early than among those who delayed ART (median 12 days and 45 days after OI therapy initiation, respectively).125 Of note, none of the participants with PCP enrolled in the study had respiratory failure requiring intubation.125 Initiating ART in such people with HIV can be managed with attention to formulations that can be crushed for administration, awareness of the unpredictable absorption of oral medications, and potential drug–drug or drug–nutrient interactions commonly encountered in the ICU.126 Paradoxical immune reconstitution inflammatory syndrome (IRIS) following an episode of PCP is rare but has been reported.127,128 Most cases occurred within weeks of the PCP episode; symptoms included fever and recurrence or exacerbation of pulmonary symptoms including cough and shortness of breath, as well as worsening of a previously improving chest radiograph. Although IRIS Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-10 in the setting of PCP has rarely been life-threatening,129 people with HIV should be closely followed for recurrence of symptoms after initiation of ART. Management of PCP-associated IRIS is not well defined; some experts recommend use of corticosteroids in people with HIV with respiratory deterioration if other causes are ruled out. Monitoring of Response to Pneumocystis Pneumonia Therapy and Adverse Events Careful monitoring during PCP therapy is important to evaluate treatment response and to detect toxicity as soon as possible. Follow-up after therapy includes assessment for early relapse, especially if therapy has been with an agent other than TMP-SMX or was shortened because of toxicity. In people with HIV, rates of adverse reactions to TMP-SMX are high (20% to 85% of patients).91,92,106,108,113,130-134 Common adverse effects are rash (30% to 55% of patients) (including Stevens-Johnson syndrome), fever (30% to 40% of patients), leukopenia (30% to 40% of patients), thrombocytopenia (15% of patients), azotemia (1% to 5% of patients), hepatitis (20% of patients), hyperkalemia, and rarely, aseptic meningitis. Supportive care for common adverse effects should be attempted before TMP-SMX is discontinued (AIII). Mild rashes (e.g., rash without vesicles, bullae, or ulcerations), nausea, and fever can often be “treated through” with antihistamines, antiemetics, and antipyretics, respectively.59 High-dose trimethoprim inhibits tubular secretion of creatinine without affecting glomerular filtration rate, and this may be additive with other medications. As noted above, therapy should be permanently discontinued in the setting of life-threatening adverse reactions including possible or definite Stevens-Johnson syndrome or toxic epidermal necrolysis (AIII). The most common adverse effects of alternative therapies include methemoglobinemia and hemolysis with dapsone or primaquine (especially in those with G6PD deficiency); rash and fever with dapsone92,106; azotemia, pancreatitis, hypoglycemia or hyperglycemia, leukopenia, electrolyte abnormalities, and cardiac dysrhythmia with pentamidine110,112,113,133; anemia, rash, fever, and diarrhea with primaquine and clindamycin92,107,108; and headache, nausea, diarrhea, rash, and transaminase elevations with atovaquone.91,132 Patients who exhibit persistent hypoxemia despite an apparent positive clinical response should undergo evaluation for methemoglobinemia if they are taking potentially causative medications. Managing Treatment Failure Clinical failure is defined as lack of improvement or worsening of respiratory function documented by arterial blood gases after 4 to 8 days of anti-PCP treatment. Failure attributed to lack of drug efficacy occurs in approximately 10% of people with HIV with mild-to-moderate PCP disease.91,92 However, there are not any convincing clinical trial data on which to base recommendations for the management of PCP treatment failure due to lack of drug efficacy. Clinicians should wait 4 to 8 days before switching therapy for lack of clinical improvement (BIII). In the absence of corticosteroid therapy, early and reversible deterioration within the first 3 to 5 days of therapy is typical, probably because of the inflammatory response caused by antibiotic-induced lysis of organisms in the lung. Other concomitant infectious and non-infectious processes must be excluded as a cause of clinical failure28,29; bronchoscopy with BAL should be strongly considered to evaluate for this possibility, even if bronchoscopy was used to make the initial diagnosis. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-11 Treatment-limiting toxicities occur in up to one-third of patients.92 Switching to another regimen is the appropriate management for treatment-related toxicity (BII). When TMP-SMX is not effective or cannot be used for moderate-to-severe disease because of toxicity, the common practice is to use parenteral pentamidine (BII) or oral primaquine combined with IV clindamycin (BII).108,109,113 For mild disease, atovaquone is a reasonable alternative (BII). Although a meta-analysis, systematic review, and cohort study concluded that the combination of primaquine and clindamycin might be the most effective regimen for salvage therapy,109,115,116 no prospective clinical trials have evaluated the optimal approach for people with HIV who experience a therapy failure with TMP-SMX. Preventing Recurrence Recommendations for Preventing Recurrence of Pneumocystis Pneumonia (Secondary Prophylaxis) Indications for Initiating Secondary Prophylaxis • Prior PCP Preferred Therapy • TMP-SMX, 1 DS tablet PO dailya (AI), or • TMP-SMX, 1 SS tablet PO dailya (AI) • Note: TMP-SMX also confers protection against toxoplasmosis and some protection against many respiratory bacterial infections. Patients who are receiving pyrimethamine/sulfadiazine for treatment or suppression of toxoplasmosis do not require additional prophylaxis for PCP (AII). Alternative Therapy • The following regimens can be used for people who are seropositive or seronegative for Toxoplasma gondii: o TMP-SMX one DS tablet PO three times weekly (BI), or o Dapsonea 50 mg PO daily with pyrimethamine 50 mg plus leucovorin 25 mg PO weekly (BI), or o Dapsonea 200 mg plus pyrimethamine 75 mg plus leucovorin 25 mg PO weekly (BI), or o Atovaquone 1,500 mg PO daily with food (BI) • The following regimens should only be used in people who are seronegative for Toxoplasma gondii: o Dapsonea 100 mg PO daily (BI), or o Aerosolized pentamidine 300 mg via Respirgard II nebulizer every month (BI), or o Intravenous pentamidine 300 mg every 28 days (CIII) Indications for Discontinuing Secondary Prophylaxis • CD4 count increased from <200 cells/mm3 to ≥200 cells/mm3 for ≥3 months as a result of ART (AII), or • Can consider if CD4 count is 100–200 cells/mm3 and HIV RNA remains below limits of detection of assay used for 3 to 6 months (BII) • For people with HIV in whom PCP occurs at a CD4 count >200 cells/mm3 while not on ART, discontinuation of prophylaxis can be considered once HIV RNA levels are suppressed to below limits of detection of the assay used for ≥3 to 6 months, although there are no data to support recommendations in this setting (CIII). • Note: If an episode of PCP occurs at a CD4 count >200 cells/mm3 while a patient is on ART, it would be prudent to continue PCP prophylaxis for life, especially with plasma HIV RNA below level of detection, regardless of how high the CD4 cell count rises as a consequence of ART (BIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-12 Indications for Restarting Secondary Prophylaxis • CD4 count <100 cells/mm3 regardless of HIV RNA (AIII), or • CD4 count 100–200 cells/mm3 and HIV RNA above detection limit of the assay used (AIII) Pre-pregnancy and Pregnancy Considerations • Clinicians who are providing pre-pregnancy care for people with HIV receiving PCP prophylaxis can discuss with their patients the option of deferring pregnancy until PCP prophylaxis can be safely discontinued (BIII) due to potential concerns about possible adverse effects of trimethoprim on the fetus. • Persons of childbearing potential who choose not to defer pregnancy while on TMP-SMX should consider increasing the dose of folic acid to 4 mg/day (BIII). • Chemoprophylaxis for PCP should be administered to pregnant adults and adolescents as for nonpregnant adults and adolescents (AIII). TMP-SMX is the recommended prophylactic agent (AIII). Clinicians should consider giving supplemental folic acid 4 mg/day to people in their first trimester who are on TMP-SMX (BIII). • Given theoretical concerns about possible teratogenicity associated with first-trimester TMP-SMX exposures, alternative prophylactic regimens such as aerosolized pentamidine or oral atovaquone can be used in during the first trimester (BII). • Dapsone should be used in the first trimester only if the other alternatives are not available or tolerated due to concerns about hemolytic anemia in mothers or exposed fetuses (BIII). Note regarding G6PD deficiency and use of primaquine or dapsone in pregnancy: As with nonpregnant adults, G6PD levels should be checked before administration of primaquine or dapsone. While G6PD level in a fetus are generally unknown during pregnancy, G6PD deficiency is an X-linked inherited condition and primaquine or dapsone can be considered if both the pregnant person and biologic father have normal G6PD activity. Other Considerations/Comments • For people with HIV with non-life-threatening adverse reactions to TMP-SMX, the drug should be continued if clinically feasible. • If TMP-SMX is discontinued because of a mild adverse reaction, reinstitution of therapy should be considered after the reaction has resolved (AII). The dose of TMP-SMX can be increased gradually (desensitization) (BI) or the drug can be given at a reduced dose or frequency (CIII). • TMP-SMX should be permanently discontinued, with no rechallenge, in people with HIV with life-threatening adverse events, including suspected or confirmed Stevens-Johnson Syndrome or toxic epidermal necrolysis (AIII). See above for alternative options for secondary PCP prophylaxis. a Whenever possible, people with HIV should be tested for G6PD deficiency before administration of dapsone. An alternative agent should be used if the patient is found to have G6PD deficiency. Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte cell; DS = double strength; G6PD = glucose-6-phosphate dehydrogenase; IV = intravenously; PCP = Pneumocystis pneumonia; PO = orally; SS = single strength; TMP-SMX = trimethoprim-sulfamethoxazole When to Start Secondary Prophylaxis Secondary PCP prophylaxis with TMP-SMX should be initiated immediately upon successful completion of PCP therapy and maintained until immune reconstitution occurs as a result of ART (see below) (AI).135 For people with HIV who are intolerant of TMP-SMX, the alternatives are dapsone (BI), dapsone plus pyrimethamine plus leucovorin (BI), atovaquone (BI), and aerosolized (BI) or IV pentamidine (CIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-13 When to Stop Secondary Prophylaxis Secondary prophylaxis should be discontinued in adult and adolescent patients whose CD4 counts have increased from <200 cells mm3 to ≥200 cells mm3 for ≥3 months as a result of ART (AII). Reports from observational studies77,83,136,137 and from two randomized trials84,138 and a combined analysis of European cohorts being followed prospectively139,140 support this recommendation. In these studies, people with HIV responded to ART with an increase in CD4 counts to ≥200 cells/mm3 for ≥3 months. At the time secondary PCP prophylaxis was discontinued, the median CD4 count was >300 cells/mm3 and most people with HIV had a CD4 cell percentage >14%. Most people with HIV had sustained suppression of plasma HIV RNA levels below the limits of detection for the assay employed; the longest follow-up was 40 months. Based on results from the COHERE study, secondary prophylaxis in people with HIV with CD4 counts of 100 cells/mm3 to 200 cells/mm3 can potentially be discontinued if HIV plasma RNA levels remain below limits of detection for 3 to 6 months (BII).141 When to Restart Primary or Secondary Prophylaxis Primary or secondary PCP prophylaxis should be reintroduced if the patient’s CD4 count decreases to <100 cells/mm3 (AIII) regardless of the HIV plasma viral load. Prophylaxis should also be reintroduced for people with HIV with CD4 counts of 100 cells/mm3 to 200 cells/mm3 with HIV plasma viral load above detection limits of the assay used (AIII). Based on results from the COHERE study, primary or secondary PCP prophylaxis may not need to be restarted in people with HIV with CD4 counts of 100 cells/mm3 to 200 cells/mm3 who have had HIV plasma RNA levels below limits of detection for 3 to 6 months (BII).86,139 If an episode of PCP occurs at a CD4 count >200 cells/mm3 while a patient is on ART, it would be prudent for the patient to continue PCP prophylaxis for life, regardless of how high their CD4 cell count rises as a consequence of ART (BIII). For people with HIV in whom PCP occurs at a CD4 count >200 cells/mm3 while not on ART, discontinuation of prophylaxis can be considered once HIV plasma RNA levels are suppressed to below limits of detection for 3 to 6 months, although there are no data to support recommendations in this setting (CIII). Special Considerations Regarding Pregnancy Some data suggest an increased risk of PCP-associated mortality in pregnancy.142 All-cause pneumonia during pregnancy increases rates of preterm labor and delivery.143 People at >20 weeks gestation who have PCP should be closely monitored for signs or symptoms of preterm labor (e.g., abdominal cramping, uterine tightening, fluid leakage) (BIII). Pre-pregnancy Care Clinicians who are providing pre-pregnancy care for people with HIV receiving PCP prophylaxis can discuss with their patients the option of deferring pregnancy until PCP prophylaxis can be safely discontinued (BIII) due to concerns about possible adverse effects of trimethoprim on the fetus (see the Primary and Secondary Prophylaxis section below). All persons of childbearing potential should take supplemental folic acid at a dose of 0.4 mg/day (AI); those who choose not to defer pregnancy while on TMP-SMX should consider increasing the dose of folic acid to 4 mg/day (BIII) (see below). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-14 Pregnancy Care Note: Specific drugs recommended for prophylaxis are discussed in the section on Primary and Secondary Prophylaxis. This information is not repeated in the Treating Disease section and only medications recommended exclusively for treatment are discussed in this section. Primary and Secondary Prophylaxis Chemoprophylaxis for PCP should be administered to pregnant adults and adolescents as for nonpregnant adults and adolescents (AIII). The preferred regimen for prophylaxis is TMP-SMX (AIII). Given concerns about possible teratogenicity associated with first-trimester TMP-SMX exposure, alternative prophylactic regimens such as aerosolized pentamidine or oral atovaquone can be used during the first trimester (BII). Dapsone should be used in the first trimester only if the other alternatives are not available or tolerated due to concerns about hemolytic anemia in pregnant persons or exposed fetuses (BIII). As with nonpregnant adults, G6PD levels should be checked before dapsone administration. No adequate and well-controlled large studies of pregnancy outcomes after exposure to sulfamethoxazole and trimethoprim have been published. Trimethoprim is classified as a folic acid antagonist, acting as a dihydrofolate reductase inhibitor; older case-control studies found that first-trimester exposure has been associated with an increased risk of neural tube defects and cardiovascular, oral clefts, urinary tract, and multiple anomalies.144-146 A systematic review and meta-analysis in 2014, including 24 studies,147 reported congenital anomalies in 232 infants among 4,196 women receiving TMP-SMX in pregnancy, with a pooled prevalence of 3.5% (95% confidence interval [CI], 1.8% to 5.1%) and three studies reported 31 infants with neural tube defects associated with first-trimester exposure, with a crude prevalence of 0.7% (95% CI, 0.5% to 1.0%). The quality of the evidence was considered very low and the authors supported continued recommendation for TMP-SMX when indicated for pregnant persons with HIV. A recent systematic review of antimicrobials used for management of plague during pregnancy included 23,602 prenatal exposures to TMP-SMX found that first-trimester exposure was associated with an increased risk of neural tube defects (pooled odds ratio [OR] 2.5; 95% CI, 1.4–4.3).148 This study also found increased odds of spontaneous abortion (OR 3.5; 95% CI, 2.3–5.6), preterm delivery (OR 1.5; 95% CI, 1.1–2.1) and the fetus being small for gestational age (OR 1.6; 95% CI, 1.2–2.2). In a nested case-control study (n = 77,429; 7,039 cases of spontaneous abortion) based on prescription fills, first-trimester exposure to TMP-SMX, after adjusting for potential confounders, was associated with increased odds of spontaneous abortion (adjusted odds ratio [aOR] 2.94, 95% CI, 1.89–4.57, including 25 exposed cases and 77 controls).149 Exposure to TMP-SMX in the last two trimesters of pregnancy was associated with low birth weight, adjusted for gestational age and gender (OR 1.61; 95% CI, 1.16–2.23) in a case-control study within the Quebec Pregnancy Registry (8,192 cases, 55,146 controls).150 Data from a large Canadian administrative database was used to retrospectively compare the occurrence of placenta-mediated adverse pregnancy outcomes between pregnant women exposed to folic acid antagonists and women without exposure to these agents.151 TMP-SMX was the most frequently prescribed dihydrofolate reductase inhibitor (11,386 exposures during the preconception period and all three trimesters compared to 45,456 unexposed women) and exposure was associated with increased odds of preeclampsia (aOR 1.13; 95% CI, 1.01–1.26), placental abruption (aOR 1.26; 95% CI, 1.03–1.55), and fetal growth restriction defined as less than the third percentile (aOR 1.20; 95% CI, 1.07–1.33). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-15 Folic acid supplementation at 0.4 mg/day is routinely recommended for all women of reproductive potential,152 to reduce the risk of neural tube defects (AI). Since neural tube closure occurs early in pregnancy, often before pregnancy is diagnosed, all persons planning a pregnancy or with reproductive potential should take daily folic acid supplementation. There is also evidence that folic acid supplementation may decrease risk of congenital heart defects, cleft lip and palate,153 preterm birth,154 low birth weight, and the fetus being small for gestational age.155,156 There are no trials evaluating whether supplementation at higher levels (e.g., 4 mg/day as recommended for pregnant women who previously had an infant with a neural tube defect) would reduce the risk of birth defects associated with first-trimester TMP-SMX use. A multicenter double-blind randomized clinical trial in women of childbearing age who planned pregnancy within 12 months failed to show an advantage of folic acid 4 mg versus 0.4 mg daily on the occurrence of congenital malformations; however, the higher dose was associated with lower occurrence of spontaneous abortion, the fetus being small for gestational age, and preterm delivery.157 The authors noted that the study was underpowered for the outcome of congenital malformations.157 Other studies have found that higher doses of folic acid (4–6 mg/day) are associated with less frequent neural tube defects, oral clefts, and recurrent preeclampsia.158-160 In a large, population-based, case-control study, the increased odds of congenital cardiovascular anomalies associated with TMP-SMX use in pregnancy were not seen in women also receiving folic acid supplementation, most of whom received folic acid 6 mg/day (OR 1.24; 95% CI, 0.94–1.62).144 Although the risk of multiple congenital abnormalities associated with TMP-SMX use persisted despite supplemental folic acid, the OR decreased from 6.4 for TMP-SMX without folic acid to 1.9 for TMP-SMX plus folic acid. Based on these findings, with the suggestion of a dose-response effect of folic acid supplementation and the known effects of TMP-SMX as a folic acid antagonist, clinicians should consider giving supplemental folic acid 4 mg/day to people who are on TMP-SMX prior to pregnancy in those who are capable of becoming pregnant, or as soon as possible in the first trimester in those who are pregnant (BIII). Leucovorin (folinic acid) is an active form of folate and is commonly used to counteract the effect of folic acid antagonists, especially as an adjunct in the treatment of various cancers. However, it is chemically different from folic acid and is not interchangeable. A randomized, controlled trial demonstrated that adding leucovorin to TMP-SMX for the treatment of PCP was associated with an increased risk of therapeutic failure and death.95 In addition, there are case reports of failure of TMP-SMX prophylaxis in the setting of concurrent leucovorin use.161 If a higher dose of supplemental folic acid is given, its use should be limited to the first trimester (AIII). Whether or not a person receives supplemental folic acid during the first trimester, a follow-up ultrasound is recommended at 18 weeks to 20 weeks to assess fetal anatomy with consideration for subsequent follow-up scans (BIII). Although historically there has been concern about the risk of neonatal kernicterus in the setting of maternal sulfonamide or dapsone use near delivery, reviews have found no cases of kernicterus reported in neonates after maternal ingestion of sulfonamides or with the use of TMP-SMX in neonates.162-164 For several decades, dapsone has been used safely to treat leprosy, malaria, and various dermatologic conditions during pregnancy.165,166 Long-term therapy is associated with a risk of mild maternal hemolysis, and exposed fetuses with G6PD deficiency are at potential risk (albeit extremely low) of acute hemolytic anemia.167 Data on atovaquone in human pregnancy are limited but preclinical studies have not demonstrated teratogenicity in rats or rabbits at plasma concentrations corresponding to estimated human exposure during malaria treatment.168 A systematic review of the safety of atovaquone-proguanil for the prevention and treatment of malaria in pregnancy found miscarriages in 21 of 260 women (8.08%; Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-16 95% CI, 5.07% to 12.08%) and congenital anomalies in 11 of 430 women (2.56%; 95% CI, 1.28% to 4.53%), both well within expected rates.169 When considering only results from this one randomized clinical trial of atovaquone-proguanil, there was no significant difference in these outcomes when compared to quinine, although the number was extremely small (n = 81).170 Pentamidine is embryotoxic but not teratogenic in rats and rabbits.171 There is limited experience with systemic use in human pregnancy and no human studies of pregnancy outcomes after exposure to pentamidine have been published. It is unknown if pentamidine crosses the placental barrier at significant concentrations when administered via the aerosolized route. Given anecdotal experience to date during pregnancy without signs of adverse effects or teratogenicity, pentamidine should be considered an alternative when indicated either via aerosolized or IV route. Treating Disease The preferred initial therapy for PCP during pregnancy, regardless of disease severity, is TMP-SMX (AI).134 Although a small increased risk of birth defects may be associated with first-trimester exposure to trimethoprim, people with PCP in the first trimester should be treated with TMP-SMX because of its considerable benefit in reducing morbidity and mortality, which outweighs the potential risk (AIII). Clinicians should consider giving supplemental folic acid 4 mg/day to people who are on TMP-SMX and capable of pregnancy or as soon as possible in the first trimester (BIII). Doses of supplemental folic acid of 4 mg/day should be limited to the first trimester during the teratogenic window and can be reduced to 0.4 mg at 12 weeks continuing to 4 to 6 weeks postpartum or discontinuation of breastfeeding (AIII). If an alternative therapeutic regimen is required for moderate-to-severe PCP, IV pentamidine is preferred (BIII). Primaquine plus clindamycin should be used only if other alternatives are not available or tolerated (BIII). If an alternative therapeutic regimen is required for mild-to-moderate PCP, atovaquone suspension is preferred (BIII); dapsone plus TMP can be used if atovaquone is not available or tolerated (BIII). As with nonpregnant adults, G6PD levels should be checked before administration of dapsone. Because of concerns about hemolytic anemia in exposed fetuses who are G6PD-deficient (which cannot be diagnosed antenatally), primaquine or dapsone should be used in pregnancy only if other alternatives are not available or tolerated and benefit is felt to outweigh the risk (AIII). Adjunctive corticosteroid therapy should be used to improve the mother’s treatment outcome as indicated in nonpregnant adults (AIII).172-175 Patients with documented or suspected PCP and moderate-to-severe disease, as defined by room air PO2 <70 mmHg or A-a gradient PO2 ≥35 mmHg, should receive adjunctive corticosteroids as early as possible. Corticosteroids have commonly been used in pregnancy for autoimmune conditions and are considered low risk for use in pregnancy.176 Although an earlier systematic review of case-control studies evaluating women with first-trimester exposure to corticosteroids found a 3.4-fold increase in the odds of delivering a baby with an oral cleft,177 more recent data from a prospective controlled study in Israel, a large population-based registry in Sweden,178 and an updated analysis from the National Birth Defect Prevention Study,179,180 have failed to demonstrate an association between first-trimester corticosteroids and major congenital anomalies, including orofacial clefts. A recent systematic review and meta-analysis also found no association between first-trimester corticosteroid exposure and risk of congenital heart defects.181 Long-term corticosteroid use in pregnancy may be associated with an increased risk of maternal Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV Y-17 hypertension, preeclampsia, hyperglycemia, premature rupture of membranes, intrauterine growth restriction,182 and infection, although the magnitude is not known.183 Maternal glucose levels and blood pressure as well as fetal growth should be monitored closely when corticosteroids are used in pregnancy (AIII). Based on available observational data from pregnant and nonpregnant surgical patients, pregnant persons who are on chronic steroid therapy during pregnancy for non-hypothalamic-pituitary-adrenal axis disorders do not need stress doses of steroids for vaginal or cesarean delivery, but they should be continued on their therapeutic dose of steroids without interruption (BIII). HPA axis suppression is rarely seen among neonates born to women who received chronic corticosteroids during pregnancy. Clindamycin is considered safe for use throughout pregnancy (BIII). Clindamycin is recommended as an alternative antibiotic for prevention of group B streptococcal disease in newborns and for antimicrobial prophylaxis during cesarean delivery.184,185 However, there are no well-controlled studies of clindamycin use in pregnant women during the first trimester. In animal studies, clindamycin was not teratogenic following oral doses up to six times the maximum recommended adult human dose.186 During clinical trials, the systemic administration of clindamycin to pregnant women during the second and third trimesters did not increase the frequency of congenital abnormalities.186 There are no adequate or well-controlled studies of primaquine use in pregnant women, and animal data is scant. Although some data from animal studies suggest evidence of genotoxicity, as well as fetal abnormalities at doses multiple times the maximal dose in humans,187 another animal study at doses 0.25 to 3.0 mg/kg early in gestation found no harmful effects on mother or offspring.188 In an observational study from Brazil, 59 women were found to have been prescribed primaquine for malaria during pregnancy, approximately one-third in the first trimester; no adverse birth outcomes were found, although G6PD testing was not done on the infants.189 The Centers for Disease Control and Prevention recommend that primaquine not be administered during pregnancy because of the risk of hemolytic anemia in a G6PD-deficient fetus.190 The degree of intravascular hemolysis appears to be associated with both the dose of primaquine and severity of G6PD deficiency.168 G6PD deficiency is an X-linked inherited condition and primaquine can be considered if both the pregnant person and biologic father have normal G6PD activity.191 Primaquine should be used in pregnancy only if other alternatives are not available or tolerated and the benefit is felt to outweigh the risk (AIII). 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Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-1 Progressive Multifocal Leukoencephalopathy/JC Virus Infection Updated: October 19, 2022 Reviewed: January 10, 2024 Epidemiology Progressive multifocal leukoencephalopathy (PML) is an opportunistic infection of the central nervous system (CNS), caused by the human polyoma virus JC virus (JCV) and characterized by focal demyelination.1,2 JCV has a worldwide distribution, and 20% to 70% of people exhibit serologic evidence of exposure by their late teens or as adults.3-7 Primary JCV infection usually occurs asymptomatically in childhood resulting in a chronic carrier state in most individuals. Viral DNA is detected in the urine of 20% to 30% of healthy adults.4,8-12 PML is a rare manifestation of JCV reactivation and characteristically manifests as a complication of HIV-1 infection and other immunocompromising diseases or therapies.13-16 In recent years, PML has been reported in patients treated with immunomodulatory humanized antibodies, including natalizumab17 and efalizumab.18 Concern has been raised about a possible increased risk of PML in persons with HIV (PWH) treated with rituximab for non-Hodgkin lymphoma,19,20 but PML has not been documented in that setting. PML can occur during chronic immunosuppression after organ transplantation and often has a poor prognosis.21 Before the advent of combination antiretroviral therapy (ART), PML developed in 3% to 7% of patients with AIDS22-24 and was almost invariably fatal; spontaneous remissions were rare.25 With the widespread use of ART, incidence of PML decreased substantially,26,27 and mortality in PWH who develop the disease has declined.28-30 Although most CNS opportunistic infections are effectively prevented when CD4 T lymphocyte (CD4) cell counts are maintained above 100 to 200 cells/mm3, PML still occurs occasionally in patients treated with ART.2,31,32 PML also can develop in the setting of immune reconstitution after ART initiation, which is discussed below.2,30,33 Clinical Manifestations PML manifests as focal neurological deficits, usually with insidious onset and steady progression. Because the demyelinating lesions can involve different brain regions, specific deficits vary from patient to patient. Although some regions seem to be more favored, any region of the CNS can be involved, including the occipital lobes (hemianopsia), frontal and parietal lobes (aphasia, hemiparesis, and hemisensory deficits), and cerebellar peduncles and deep white matter (dysmetria and ataxia).13 Spinal cord involvement is rare, and the optic nerves are not involved.34 Although lesions can be multiple, one lesion is clinically predominant. Initial symptoms and signs usually begin as partial deficits (e.g., weakness in one leg) that worsen over time and involve a larger territory (e.g., evolution to hemiparesis), as individual lesions expand concentrically or along white matter tracts. Less localized clinical syndromes—such as behavioral changes, dementia, or encephalopathy—result from multiple lesions in the setting of PML and are rarely the presenting clinical phenotype.35 The time course of evolving demyelination, with clinical progression over several weeks, often provides a clue to diagnosis because the other major opportunistic focal brain disorders (cerebral toxoplasmosis and primary CNS lymphoma) characteristically progress in hours to days and cerebral Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-2 infarcts begin even more abruptly. Nonetheless, PML is sometimes mistaken for an evolving stroke, which, like PML, is bright on diffusion-weighted magnetic resonance imaging (MRI). Focal brain lesion can mimic strokes; however, the progressive course should make this diagnosis less likely, and PML must be considered. Headache and fever are not characteristic of PML, and when present may indicate presence of another opportunistic infection. Seizures occur in nearly 20% of PML cases and are associated with lesions immediately adjacent to the cortex.36,37 Diagnosis Initial recognition of PML relies on a combination of clinical and neuroimaging findings: steady progression of focal neurological deficits with MRI almost always demonstrating distinct white matter lesions in areas of the brain corresponding to the clinical deficits. The lesions are hyperintense (white) on T2-weighted and fluid-attenuated inversion recovery sequences and hypointense (dark) on T1-weighted sequences.2 The T1 findings can be subtle and may help distinguish lesions due to PML from those of other pathologies, including the white matter lesions of HIV encephalitis. A linear, paramagnetic band or rim in the paralesional U-fibers has been described as a common finding in PML and has been proposed to have diagnostic value independent of underlying predisposing disease. Histopathological studies show this band corresponds to iron accumulation within phagocytic cells, although the pathophysiology leading to this remains unclear.38,39 Brain imaging with magnetic resonance (MR) or computed tomography is critical to identifying PML and differentiating it from other important treatable diseases that occur in advanced HIV. In contrast to cerebral toxoplasmosis and primary CNS lymphoma, no mass effect or displacement of normal structures is usually evident in PML imaging. Although contrast enhancement is present in 10% to 15% of cases, it is usually sparse with a thin or reticulated appearance adjacent to the edge of the lesions. Exceptions to these characteristic imaging findings can occur when the inflammatory form of PML develops in the setting of immune reconstitution after initiation of ART (see below). Advanced neuroimaging techniques—such as diffusion-weighted imaging (DWI) and MR spectroscopy—may provide additional diagnostic information.40-42 New PML lesions and the advancing edge of large lesions have a high signal on DWI and a normal-to-low apparent diffusion coefficient, signifying restricted diffusion. These changes relate to regions of active infection and oligodendrocyte swelling. MR spectroscopy can show areas of decreased N-acetylaspartate and increased choline related to axonal loss and cell membrane and myelin breakdown, respectively, with the greatest changes at the center of lesions.43 Recently, a hyperintense cortical signal seen on MRI scan in non-enhanced T1-weighted cortex images has been associated with seizures complicating inflammatory PML.37 In most cases of PML, the combined clinical and radiographic presentations support a presumptive diagnosis. Because the primary treatment method for PML is restoring the patient’s immune function, confirming the diagnosis is especially important to ensure ART is initiated rapidly. JCV DNA is virtually never detected in normal cerebrospinal fluid (CSF) samples. Thus, the usual first step in confirming the diagnosis is to test CSF by polymerase chain reaction (PCR) for the presence of JCV DNA. The assay is positive in approximately 70% to 90% of patients not taking ART, for whom a positive result can be considered diagnostic in the appropriate clinical context— namely, subacute onset of focal neurological abnormalities and suggestive imaging findings.10,44 JCV may be detectable in the CSF of as few as 60% of ART-treated patients.45 In patients not taking ART, the number of JCV DNA copies can add additional information for prognosis, although the relationship between copy number and prognosis is less clear in patients taking ART.46,47 CSF analysis can be repeated if JCV PCR is negative yet suspicion of PML remains high and alternative diagnoses have been excluded. Given that in AIDS patients, multiple opportunistic conditions are sometimes encountered, evaluation of CSF is often indicated to rule out Cryptococcus, neurosyphilis, Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-3 cytomegalovirus encephalitis, varicella-zoster encephalitis, herpes simplex encephalitis, and tuberculosis. Further, CSF PCR analyses for Toxoplasma and consideration of Epstein-Barr virus generally associated with primary CNS lymphoma is often indicated with progressive multifocal brain disease in the setting of AIDS. Because JCV DNA viral load in CSF may be very low even with active PML, highly sensitive PCR performance is desirable. Sensitive assays that detect as few as 50 copies/mL are now available, with some research laboratories exceeding this level of sensitivity; detection of JCV virus in CSF in any amount with the appropriate clinical and imaging findings strongly supports the diagnosis of PML.48 Analysis of plasma samples for detection of JCV by PCR when positive are relatively specific for PML (~92% in patients with HIV), while the sensitivity is less than 40% in this setting.49 In some instances, brain biopsy is required in order to rule out other diagnoses. PML usually can be identified by the characteristic tissue cytopathology—including oligodendrocytes with intranuclear inclusions, bizarre astrocytes, and lipid-laden macrophages—with identification of JCV or cross-reacting polyoma virus by immunohistochemistry, in situ nucleic acid hybridization, or electron microscopy.13,50,51 Generally, serologic testing is not useful because of high anti-JCV seroprevalence in the general population. Recently, however, antibody testing has been assessed for stratifying risk of PML with natalizumab treatment.6 Significant increases in JCV-specific antibody titers52 and detection of intrathecally produced anti-JCV antibodies may prove useful for diagnostic testing53 but require further prospective study. The value of anti-JCV antibodies in stimulating Fc receptor-bearing effector cell activity contributing to outcome of PML requires further studies.54 Preventing Exposure Currently, no known way exists to prevent exposure to the virus because most individuals are infected in childhood. Preventing Disease In many individuals, JCV infection is likely latent and intermittently productive, although clinically silent, in the kidney or other anatomic sites. Systemic infection may increase in the presence of immunosuppression. It remains a subject of debate whether JCV infection is also latent in the CNS or whether PML results from hematogenous dissemination of infection to the brain resulting in subsequent PML lesion development within months of entry to the CNS.55,56 Therefore, the only known way to prevent disease is to prevent progression of HIV-related immunosuppression with ART (AII). Treating Disease No specific therapy exists for JCV infection or PML. The main approach to treatment involves ART to reverse the immunosuppression that interferes with the normal host response to this virus.57 In patients with PML who are not on therapy, ART should be started immediately (AII). In this setting, more than half of PML patients with HIV experience a remission in which disease progression stops. Although neurological deficits often persist, some patients experience clinical improvement.28,29,58-63 In one retrospective study of 118 consecutive patients with PML who received ART, 75 patients (63.6%) survived for a median of 114 weeks (2.2 years) after diagnosis of PML.63 Neurological function in the survivors was categorized as cure or improvement in 33, stabilization or worsening in 40, and unknown in 2. Another retrospective case series reported that 42% of PML survivors on ART had moderate or severe disability.64 Peripheral blood CD4 count at presentation was the only variable Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-4 that predicted survival; the odds ratio for death was 2.7 among patients with CD4 counts <100 cells/mm3 compared with patients who had higher CD4 counts. In other case series, worse prognosis also was associated with high plasma HIV RNA levels at the time of presentation, poor virologic responses to ART, and presence of lesions in the brain stem.29,32,59,60,62,63,65 Contrast enhancement on imaging may predict better outcomes, as it is indicative of an immune response to the virus.31 In multiple sclerosis patients with PML, younger age, more restricted unilobar disease, and lower CSF JCV DNA copy numbers are associated with better outcomes; whether these associations are true for PML in PWH is unknown.66 ART should be optimized for HIV virologic suppression in patients with PML who have received ART but remain viremic because of inadequate adherence or ARV resistance (AIII). More problematic are patients who develop PML despite successful HIV virologic suppression while taking ART. A preliminary report of PML with patients treated intensively with four classes of ART (including enfuvirtide) suggested that the strategy might offer higher-than-anticipated survival,67 but it has not yet been followed by structured trial. Therefore, no evidence supports ART intensification for PML (BII). The use of ARV drugs that better penetrate the CNS also has been proposed, with use of the CNS Penetration Effectiveness (CPE) score of drug regimens as a guide. This score is based on the pharmacology of ARV drugs with respect to their chemical characteristics as well as demonstrated entry into the CNS (or, more often, the CSF) and, where available, on their CNS anti-HIV activity.68 One report found at the beginning of the combination ART era that a high CPE score was associated with longer survival after a PML diagnosis, whereas in the late, more recent ART period, the effect of the CPE score disappeared as more potent ARV regimens led to more effective plasma viral load control.69 Hence, in the current era, the effectiveness of selecting a treatment regimen with a high CPE score is not established. It seems likely that systemic rather than CNS efficacy is the salient aspect of ART in this setting because ART’s most important effect on PML may be restoration of effective anti-JCV immunity that can limit CNS infection.70,71 ART regimens should be selected based on likelihood of achieving virologic suppression and not CPE score (BII). Several studies have evaluated targeted treatments for PML. However, many anecdotal reports of efficacy have not been confirmed by controlled studies and are therefore not recommended. Based on case reports and demonstration of in vitro inhibitory activity against JCV, intravenous (IV) and intrathecal cytarabine (cytosine arabinoside) were tested in a clinical trial, but neither demonstrated clinical benefit.72 Therefore, treatment with cytarabine is not recommended (AII). Similarly, cidofovir initially was reported to have a salutary clinical effect, but several large studies—including retrospective case-control studies, an open-label clinical trial, and a meta-analysis that included patients from five large studies—demonstrated no benefit.45,61-63,73 Thus, treatment with cidofovir is also not recommended (AII). On the basis of a report indicating that the serotonergic 5HT2a receptor can serve as a cellular receptor for JCV in a glial cell culture system,74,75 drugs that block the 5HT2a receptor, including olanzapine, ziprasidone, mirtazapine, cyproheptadine, and risperidone, have been suggested as treatment for PML,76 although the rationale for this practice has been questioned.77 Again, anecdotes about favorable outcomes1,78-81 have not been substantiated by reports of genuine benefit in larger case series, cohort studies, or formal clinical trials. Thus, at this time, treatment with serotonergic 5HT2a receptor blockers is not recommended (BIII). After a cell-culture study indicated that JCV replication could be inhibited by a topoisomerase inhibitor,82 an analogue, topotecan, was studied in a small trial. Results suggested a salutary effect in some patients, although the outcome likely was little different from the natural course in other Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-5 patients with AIDS, and the main toxicities were hematologic.83 At this time, topotecan is not recommended (BIII). A Phase I/II clinical trial of the antimalarial drug mefloquine was initiated based on its demonstrated in vitro anti-JCV activity. The trial was later halted by the sponsor because demonstration of efficacy was futile.84 Mefloquine use for PML treatment is not recommended (BIII). Immunomodulatory approaches to the treatment of PML in PWH also have been tried, but none has yet been studied in a prospective, controlled clinical trial. Although an initial retrospective analysis suggested that interferon-alpha might improve survival,85 a subsequent retrospective analysis did not demonstrate benefit beyond that afforded by ART; therefore, interferon-alpha is not recommended (BIII).86 A single report described failure of interferon-beta treatment of HIV-associated PML87 and natalizumab-related PML developed in patients given interferon-beta for multiple sclerosis.17 Case reports have described improvement or recovery in PML-related neurological dysfunction in three patients who were not HIV infected and were treated with IL-2: one with Hodgkin lymphoma treated with autologous bone marrow transplantation, one with low-grade lymphoma and allogeneic stem cell transplantation, and one with myelodysplastic syndrome.88-90 Like the other reports, these too have not been followed up with more substantial trials; therefore, treatment of PML with IL-2 is not recommended (BIII). Recent interest in recombinant IL-7 for treatment of PML when CD4 lymphopenia is persistent, sometimes in combination with VP-1 vaccination strategy, are under consideration as an alternative adjuvant immune therapy to improve PML outcomes.91-95 Checkpoint inhibitor therapy has been considered recently as a means of enhancing the immune response to JCV most commonly in settings outside of HIV where immune reconstitution may be futile. The outcome of reports is conflicting, and further research is required.96,97 Use of checkpoint inhibitors for PML in the setting of HIV is not recommended (BIII). Adoptive transfer of autologous or allogeneic virus-specific T cells, either against JCV or the closely related BK virus, have been used for the treatment of PML. Across the several small case series published to date, a single patient with HIV-associated PML was treated with benefit.98-100 Use of disease-specific T cells is actively being explored, but at present cannot be recommended for HIV-associated PML. In summary, immunomodulatory agents are not recommended (BIII). Special Considerations for ART ART should be (re)started as soon as possible for all patients, ideally before PML develops. For patients with suspected PML, it is especially imperative to start ART quickly (AII). For patients already on treatment who have demonstrated plasma HIV viremia and are adherent to therapy, ART should be adjusted, if possible, based on plasma virus susceptibility (AII). Monitoring of Response to Therapy and Adverse Events (Including Immune Reconstitution Inflammatory Syndrome) Treatment response should be monitored with clinical examination and brain MRI. In patients with detectable JCV DNA in their CSF before initiation of ARV treatment, quantification of CSF JCV DNA may prove useful as an index to follow for assessing treatment response. No clear guidelines exist for the timing of follow-up assessments, but it is reasonable to be guided by clinical progress (BIII). Often disease progression occurs before stabilization and improvement occurs.67 In patients who appear stable or improved, neuroimaging can be obtained 6 to 8 weeks after ART initiation to screen for radiographic signs of progression or of immune response and can serve as a further baseline for subsequent scans should the patient begin to deteriorate (BIII). In patients who clinically Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-6 worsen before or after this 6- to 8-week period, repeat neuroimaging should be obtained as soon as worsening is recognized (BIII). PML-Immune Reconstitution Inflammatory Syndrome PML has been reported to occur within the first weeks to months after initiating ART2,32,33,101-103 with clinical and radiographic features that differ from classical PML, including lesions with contrast enhancement, edema and mass effect, and a more rapid clinical course.38,104 As with other presentations of immune reconstitution inflammatory syndrome (IRIS), it is more likely after advanced HIV with low CD4 counts and greater decline in HIV viral load on initiation of ARV. This presentation has been referred to as inflammatory PML or PML-IRIS. Both unmasking of cryptic PML and paradoxical worsening in a patient with an established PML diagnosis have been observed. Histopathology typically demonstrates perivascular mononuclear inflammatory infiltration.105-108 Unmasked PML-IRIS is presumed to represent the effects of a restored immune response to JCV infection in the context of ART, with resultant local immune and inflammatory responses. Because ART-induced immune reconstitution may be associated with both onset and paradoxical worsening of PML, corticosteroids have been used empirically in this setting with reported benefit.2,102,109 Further study of corticosteroids for treatment of PML-IRIS is needed to confirm efficacy and refine dosage and duration. At present, however, use of corticosteroids to treat of PML-IRIS may be justified in some PML where edema or mass effect causes serious clinical deterioration (BIII). The decision to use steroids can be difficult because it is the immune response to JCV that controls the infection and treatments that blunt that response could be deleterious. Nevertheless, the inflammatory response against PML can, at times, be more damaging than the virus itself, and corticosteroids appear to have a role in treatment of these patients. The dosage and duration of corticosteroids for PML-IRIS have not been established. In the absence of comparative data, adjuvant corticosteroid therapy should be tailored to individual patients. One approach, modeled on treatment of multiple sclerosis flairs, is to begin with a 3- to 5-day course of IV methylprednisolone dosed at 1 g per day, followed by an oral prednisone taper, dosed according to clinical response. A taper may begin with a dose of 60 mg per day in a single dose, tapered over 1 to 6 weeks. Clinical status should be monitored carefully during this taper in an attempt to minimize systemic and immune effects while avoiding IRIS recrudescence. Contrast-enhanced MRI at 2 to 6 weeks may be helpful in documenting resolution of inflammation and edema and to obtain a new baseline, recognizing that the MRI appearance may worsen despite clinical improvement and that clinical status is likely the best indicator of treatment efficacy. Importantly, ART should be continued (AIII). Several case reports suggest that maraviroc might be beneficial for PML-IRIS,110 presumably related to the immunomodulatory rather than ARV properties of the CCR5 inhibitor. However, no comparative studies in HIV-associated PML have confirmed benefit of inclusion of maraviroc in HIV therapy in this setting.110,111 A retrospective cohort study of 27 patients with PML in whom maraviroc was used failed to show utility in preventing PML-IRIS.112 Maraviroc is not recommended as a component of treatment of PML (BIII). Managing Treatment Failure PML remission can take several weeks, and no strict criteria exist to define treatment failure. However, a working definition of treatment failure may be continued clinical worsening after 3 months of ART initiation. Changes in plasma HIV RNA levels and blood CD4 count responses provide ancillary predictive information. Failing ART regimens should be changed based on standard Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-7 guidelines for the use of ART (see Virologic Failure in the Adult and Adolescent Antiretroviral Guidelines). When PML continues to worsen despite fully suppressive ART, one of the unproven therapies described above could be considered after consultation with an expert (CIII), although the possibility of toxicity must be balanced against the unproven benefits of these treatments. The search for other potentially treatable comorbid conditions, like hepatitis C virus and associated cirrhosis, also should be considered in this setting.113 Preventing Recurrence Patients who experience remission of PML after ART rarely suffer subsequent recrudescence unless ART is interrupted.61,114 The main preventive measure, based on its role in reversing the disease, is treatment with an effective ART regimen that suppresses viremia and maintains CD4 counts (AII). Special Considerations During Pregnancy Diagnostic evaluation of PML should be the same in pregnant or nonpregnant individuals. Therapy during pregnancy should consist of initiating or optimizing the ARV regimen. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-8 Recommendations for Treating and Monitoring PML Treatment The main approach to treatment is to preserve immune function and reverse HIV-associated immunosuppression with effective ART. • In patients not on ART who are diagnosed with PML, ART should be (re)started immediately (AII). • In patients who are receiving ART but remain viremic because of inadequate adherence or drug resistance, ART should be optimized to achieve HIV suppression (AIII). • No role for ART intensification in patients with HIV viral suppression (BII). • ART regimens should be selected based on likelihood of achieving virologic suppression and not CPE score (BII). • No effective direct-acting antiviral therapy exists for preventing or treating JCV infections or PML. • The following agents are not recommended for the treatment of PML: cytarabine (AII), cidofovir (AII), interferon-alpha (BIII), interleukin-2 (BIII), topotecan (BIII), pembrolizumab (BIII). • The following agents are not recommended due to limited data: 5HT2a receptor antagonist (e.g., olanzapine, ziprasidone, mirtazapine, cyproheptadine, risperidone) (BIII), mefloquine (BIII). Expert consultation is recommended prior to initiation of these agents. • PML-IRIS may require administration of corticosteroid therapy (BIII). The optimal corticosteroid regimen has not been established but should be tailored to individual patients. ART should NOT be discontinued during PML-IRIS (AIII). Monitoring • Timing of follow-up assessments (clinical, lumbar puncture, and MRI) should be guided by clinical progress (BIII). • In patients who appear stable or improved, neuroimaging can be obtained 6 to 8 weeks after ART initiation (BIII). • In patients who clinically worsen before or after this 6- to 8-week period, repeat MRI should be obtained as soon as worsening is recognized (BIII). Key: ART = antiretroviral therapy; CPE = Central Nervous System (CNS) Penetration Effectiveness; IRIS = immune reconstitution inflammatory syndrome; JCV = JC virus; MRI = magnetic resonance imaging; PML = progressive multifocal leukoencephalopathy. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-9 References 1. Koralnik IJ. Progressive multifocal leukoencephalopathy revisited: has the disease outgrown its name? Ann Neurol. 2006;60(2):162-173. Available at: 2. Cinque P, Koralnik IJ, Gerevini S, Miro JM, Price RW. Progressive multifocal leukoencephalopathy in HIV-1 infection. Lancet Infect Dis. 2009;9(10):625-636. Available at: 3. Kean JM, Rao S, Wang M, Garcea RL. Seroepidemiology of human polyomaviruses. PLoS Pathog. 2009;5(3):e1000363. Available at: 4. Egli A, Infanti L, Dumoulin A, et al. Prevalence of polyomavirus BK and JC infection and replication in 400 healthy blood donors. J Infect Dis. 2009;199(6):837-846. Available at: 5. Antonsson A, Green AC, Mallitt KA, et al. Prevalence and stability of antibodies to the BK and JC polyomaviruses: a long-term longitudinal study of Australians. J Gen Virol. 2010;91(Pt 7):1849-1853. Available at: 6. 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Prolonged survival and partial recovery in AIDS-associated progressive multifocal leukoencephalopathy. Neurology. 1988;38(7):1060-1065. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-11 26. d'Arminio Monforte A, Cinque P, Mocroft A, et al. Changing incidence of central nervous system diseases in the EuroSIDA cohort. Ann Neurol. 2004;55(3):320-328. Available at: 27. Casado JL, Corral I, Garcia J, et al. Continued declining incidence and improved survival of progressive multifocal leukoencephalopathy in HIV/AIDS patients in the current era. Eur J Clin Microbiol Infect Dis. 2014;33(2):179-187. Available at: 28. Clifford DB, Yiannoutsos C, Glicksman M, et al. HAART improves prognosis in HIV-associated progressive multifocal leukoencephalopathy. Neurology. 1999;52(3):623-625. Available at: 29. Antinori A, Cingolani A, Lorenzini P, et al. Clinical epidemiology and survival of progressive multifocal leukoencephalopathy in the era of highly active antiretroviral therapy: data from the Italian Registry Investigative Neuro AIDS (IRINA). J Neurovirol. 2003;9 Suppl 1:47-53. Available at: 30. Melliez H, Mary-Krause M, Bocket L, et al. Risk of progressive multifocal leukoencephalopathy in the combination antiretroviral therapy era in the French Hospital Database on Human Immunodeficiency Virus (ANRS-C4). Clin Infect Dis. 2018;67(2):275-282. Available at: 31. Berger JR, Levy RM, Flomenhoft D, Dobbs M. Predictive factors for prolonged survival in acquired immunodeficiency syndrome-associated progressive multifocal leukoencephalopathy. Ann Neurol. 1998;44(3):341-349. Available at: 32. Cinque P, Bossolasco S, Brambilla AM, et al. The effect of highly active antiretroviral therapy-induced immune reconstitution on development and outcome of progressive multifocal leukoencephalopathy: study of 43 cases with review of the literature. J Neurovirol. 2003;9 Suppl 1:73-80. Available at: 33. Du Pasquier RA, Koralnik IJ. Inflammatory reaction in progressive multifocal leukoencephalopathy: harmful or beneficial? J Neurovirol. 2003;9 Suppl 1:25-31. Available at: 34. Bernal-Cano F, Joseph JT, Koralnik IJ. Spinal cord lesions of progressive multifocal leukoencephalopathy in an acquired immunodeficiency syndrome patient. J Neurovirol. 2007;13(5):474-476. Available at: 35. Zunt JR, Tu RK, Anderson DM, Copass MC, Marra CM. Progressive multifocal leukoencephalopathy presenting as human immunodeficiency virus type 1 (HIV)-associated dementia. Neurology. 1997;49(1):263-265. Available at: 36. Lima MA, Drislane FW, Koralnik IJ. Seizures and their outcome in progressive multifocal leukoencephalopathy. Neurology. 2006;66(2):262-264. Available at: 37. Khoury MN, Alsop DC, Agnihotri SP, et al. Hyperintense cortical signal on magnetic resonance imaging reflects focal leukocortical encephalitis and seizure risk in progressive Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-12 multifocal leukoencephalopathy. Ann Neurol. 2014;75(5):659-669. Available at: 38. Post MJ, Thurnher MM, Clifford DB, et al. CNS-immune reconstitution inflammatory syndrome in the setting of HIV infection, part 2: discussion of neuro-immune reconstitution inflammatory syndrome with and without other pathogens. AJNR Am J Neuroradiol. 2013;34(7):1308-1318. Available at: 39. Mahajan KR, Amin M, Poturalski M, et al. Juxtacortical susceptibility changes in progressive multifocal leukoencephalopathy at the gray-white matter junction correlates with iron-enriched macrophages. Mult Scler. 2021;27(14):2159-2169. Available at: 40. Chang L, Ernst T, Tornatore C, et al. Metabolite abnormalities in progressive multifocal leukoencephalopathy by proton magnetic resonance spectroscopy. Neurology. 1997;48(4):836-845. Available at: 41. Mader I, Herrlinger U, Klose U, Schmidt F, Kuker W. Progressive multifocal leukoencephalopathy: analysis of lesion development with diffusion-weighted MRI. Neuroradiology. 2003;45(10):717-721. Available at: 42. da Pozzo S, Manara R, Tonello S, Carollo C. Conventional and diffusion-weighted MRI in progressive multifocal leukoencephalopathy: new elements for identification and follow-up. Radiol Med. 2006;111(7):971-977. Available at: 43. Shah R, Bag AK, Chapman PR, Cure JK. Imaging manifestations of progressive multifocal leukoencephalopathy. Clin Radiol. 2010;65(6):431-439. Available at: 44. Cinque P, Scarpellini P, Vago L, Linde A, Lazzarin A. Diagnosis of central nervous system complications in HIV-infected patients: cerebrospinal fluid analysis by the polymerase chain reaction. AIDS. 1997;11(1):1-17. Available at: 45. De Luca A, Ammassari A, Pezzotti P, et al. Cidofovir in addition to antiretroviral treatment is not effective for AIDS-associated progressive multifocal leukoencephalopathy: a multicohort analysis. AIDS. 2008;22(14):1759-1767. Available at: 46. Yiannoutsos CT, Major EO, Curfman B, et al. Relation of JC virus DNA in the cerebrospinal fluid to survival in acquired immunodeficiency syndrome patients with biopsy-proven progressive multifocal leukoencephalopathy. Ann Neurol. 1999;45(6):816-821. Available at: 47. Bossolasco S, Calori G, Moretti F, et al. Prognostic significance of JC virus DNA levels in cerebrospinal fluid of patients with HIV-associated progressive multifocal leukoencephalopathy. Clin Infect Dis. 2005;40(5):738-744. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-13 48. Berger JR, Aksamit AJ, Clifford DB, et al. PML diagnostic criteria: consensus statement from the AAN Neuroinfectious Disease Section. Neurology. 2013;80(15):1430-1438. Available at: 49. Ferretti F, Bestetti A, Yiannoutsos CT, et al. Diagnostic and prognostic value of JC virus DNA in plasma in progressive multifocal leukoencephalopathy. Clin Infect Dis. 2018;67(1):65-72. Available at: 50. Silver SA, Arthur RR, Erozan YS, Sherman ME, McArthur JC, Uematsu S. Diagnosis of progressive multifocal leukoencephalopathy by stereotactic brain biopsy utilizing immunohistochemistry and the polymerase chain reaction. Acta Cytol. 1995;39(1):35-44. Available at: 51. Jochum W, Weber T, Frye S, Hunsmann G, Luke W, Aguzzi A. Detection of JC virus by anti-VP1 immunohistochemistry in brains with progressive multifocal leukoencephalopathy. Acta Neuropathol. 1997;94(3):226-231. Available at: 52. Viscidi RP, Khanna N, Tan CS, et al. JC virus antibody and viremia as predictors of progressive multifocal leukoencephalopathy in human immunodeficiency virus-1-infected individuals. Clin Infect Dis. 2011;53(7):711-715. Available at: 53. Knowles WA, Luxton RW, Hand JF, Gardner SD, Brown DW. The JC virus antibody response in serum and cerebrospinal fluid in progressive multifocal leucoencephalopathy. Clin Diagn Virol. 1995;4(2):183-194. Available at: 54. Tan CS, Ghofrani J, Geiger E, Koralnik IJ, Jost S. Brief report: decreased JC virus-specific antibody-dependent cellular cytotoxicity in HIV-seropositive PML survivors. J Acquir Immune Defic Syndr. 2019;82(2):220-224. Available at: 55. Perez-Liz G, Del Valle L, Gentilella A, Croul S, Khalili K. Detection of JC virus DNA fragments but not proteins in normal brain tissue. Ann Neurol. 2008;64(4):379-387. Available at: 56. Tan CS, Ellis LC, Wuthrich C, et al. JC virus latency in the brain and extraneural organs of patients with and without progressive multifocal leukoencephalopathy. J Virol. 2010;84(18):9200-9209. Available at: 57. Dunham SR, Schmidt R, Clifford DB. Treatment of progressive multifocal leukoencephalopathy using immune restoration. Neurotherapeutics. 2020;17(3):955-965. Available at: 58. Dworkin MS, Wan PC, Hanson DL, Jones JL. Progressive multifocal leukoencephalopathy: improved survival of human immunodeficiency virus-infected patients in the protease inhibitor era. J Infect Dis. 1999;180(3):621-625. Available at: 59. Gasnault J, Taoufik Y, Goujard C, et al. Prolonged survival without neurological improvement in patients with AIDS-related progressive multifocal leukoencephalopathy on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-14 potent combined antiretroviral therapy. J Neurovirol. 1999;5(4):421-429. Available at: 60. Tassie JM, Gasnault J, Bentata M, et al. Survival improvement of AIDS-related progressive multifocal leukoencephalopathy in the era of protease inhibitors. Clinical Epidemiology Group. French Hospital Database on HIV. AIDS. 1999;13(14):1881-1887. Available at: 61. Cinque P, Pierotti C, Vigano MG, et al. The good and evil of HAART in HIV-related progressive multifocal leukoencephalopathy. J Neurovirol. 2001;7(4):358-363. Available at: 62. Marra CM, Rajicic N, Barker DE, et al. A pilot study of cidofovir for progressive multifocal leukoencephalopathy in AIDS. AIDS. 2002;16(13):1791-1797. Available at: 63. Berenguer J, Miralles P, Arrizabalaga J, et al. Clinical course and prognostic factors of progressive multifocal leukoencephalopathy in patients treated with highly active antiretroviral therapy. Clin Infect Dis. 2003;36(8):1047-1052. Available at: 64. Lima MA, Bernal-Cano F, Clifford DB, Gandhi RT, Koralnik IJ. Clinical outcome of long-term survivors of progressive multifocal leukoencephalopathy. J Neurol Neurosurg Psychiatry. 2010;81(11):1288-1291. Available at: 65. Pazzi AL, Galli M, et al. The relationship between outcome of progressive multifocal leukoencephalopathy and type and response to ART in previously HAART-untreated patients. Presented at: 14th Conference on Retroviruses and Opportunistic Infections; 2007. Los Angeles, CA. 66. Dong-Si T, Gheuens S, Gangadharan A, et al. Predictors of survival and functional outcomes in natalizumab-associated progressive multifocal leukoencephalopathy. J Neurovirol. 2015;21(6):637-644. Available at: 67. Gasnault J, Costagliola D, Hendel-Chavez H, et al. Improved survival of HIV-1-infected patients with progressive multifocal leukoencephalopathy receiving early 5-drug combination antiretroviral therapy. PLoS One. 2011;6(6):e20967. Available at: 68. Letendre S, Marquie-Beck J, Capparelli E, et al. Validation of the CNS Penetration-Effectiveness rank for quantifying antiretroviral penetration into the central nervous system. Arch Neurol. 2008;65(1):65-70. Available at: 69. Lanoy E, Guiguet M, Bentata M, et al. Survival after neuroAIDS: association with antiretroviral CNS Penetration-Effectiveness score. Neurology. 2011;76(7):644-651. Available at: 70. Garvey L, Winston A, Walsh J, et al. Antiretroviral therapy CNS penetration and HIV-1-associated CNS disease. Neurology. 2011;76(8):693-700. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-15 71. Fanjul F, Riveiro-Barciela M, Gonzalez J, et al. Evaluation of progressive multifocal leukoencephalopathy treatments in a Spanish cohort of HIV-infected patients: do protease inhibitors improve survival regardless of central nervous system penetration-effectiveness (CPE) score? HIV Med. 2013;14(5):321-325. Available at: 72. Hall CD, Dafni U, Simpson D, et al. Failure of cytarabine in progressive multifocal leukoencephalopathy associated with human immunodeficiency virus infection. AIDS Clinical Trials Group 243 Team. N Engl J Med. 1998;338(19):1345-1351. Available at: 73. Gasnault J, Kousignian P, Kahraman M, et al. Cidofovir in AIDS-associated progressive multifocal leukoencephalopathy: a monocenter observational study with clinical and JC virus load monitoring. J Neurovirol. 2001;7(4):375-381. Available at: 74. Elphick GF, Querbes W, Jordan JA, et al. The human polyomavirus, JCV, uses serotonin receptors to infect cells. Science. 2004;306(5700):1380-1383. Available at: 75. O'Hara BA, Atwood WJ. Interferon beta1-a and selective anti-5HT(2a) receptor antagonists inhibit infection of human glial cells by JC virus. Virus Res. 2008;132(1-2):97-103. Available at: 76. Altschuler EL, Kast RE. The atypical antipsychotic agents ziprasidone [correction of zisprasidone], risperdone and olanzapine as treatment for and prophylaxis against progressive multifocal leukoencephalopathy. Med Hypotheses. 2005;65(3):585-586. Available at: 77. Santagata S, Kinney HC. Mechanism of JCV entry into oligodendrocytes. Science. 2005;309(5733):381-382. Available at: 78. Focosi D, Fazzi R, Montanaro D, Emdin M, Petrini M. Progressive multifocal leukoencephalopathy in a haploidentical stem cell transplant recipient: a clinical, neuroradiological and virological response after treatment with risperidone. Antiviral Res. 2007;74(2):156-158. Available at: 79. Vulliemoz S, Lurati-Ruiz F, Borruat FX, et al. Favourable outcome of progressive multifocal leucoencephalopathy in two patients with dermatomyositis. J Neurol Neurosurg Psychiatry. 2006;77(9):1079-1082. Available at: 80. Lanzafame M, Ferrari S, Lattuada E, et al. Mirtazapine in an HIV-1 infected patient with progressive multifocal leukoencephalopathy. Infez Med. 2009;17(1):35-37. Available at: 81. Cettomai D, McArthur JC. Mirtazapine use in human immunodeficiency virus-infected patients with progressive multifocal leukoencephalopathy. Arch Neurol. 2009;66(2):255-258. Available at: 82. Kerr DA, Chang CF, Gordon J, Bjornsti MA, Khalili K. Inhibition of human neurotropic virus (JCV) DNA replication in glial cells by camptothecin. Virology. 1993;196(2):612-618. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-16 83. Royal W, 3rd, Dupont B, McGuire D, et al. Topotecan in the treatment of acquired immunodeficiency syndrome-related progressive multifocal leukoencephalopathy. J Neurovirol. 2003;9(3):411-419. Available at: 84. Clifford DB, Nath A, Cinque P, et al. A study of mefloquine treatment for progressive multifocal leukoencephalopathy: results and exploration of predictors of PML outcomes. J Neurovirol. 2013;19(4):351-358. Available at: 85. Huang SS, Skolasky RL, Dal Pan GJ, Royal W, 3rd, McArthur JC. Survival prolongation in HIV-associated progressive multifocal leukoencephalopathy treated with alpha-interferon: an observational study. J Neurovirol. 1998;4(3):324-332. Available at: 86. Geschwind MD, Skolasky RI, Royal WS, McArthur JC. The relative contributions of HAART and alpha-interferon for therapy of progressive multifocal leukoencephalopathy in AIDS. J Neurovirol. 2001;7(4):353-357. Available at: 87. Nath A, Venkataramana A, Reich DS, Cortese I, Major EO. Progression of progressive multifocal leukoencephalopathy despite treatment with beta-interferon. Neurology. 2006;66(1):149-150. Available at: 88. Przepiorka D, Jaeckle KA, Birdwell RR, et al. Successful treatment of progressive multifocal leukoencephalopathy with low-dose interleukin-2. Bone Marrow Transplant. 1997;20(11):983-987. Available at: 89. Buckanovich RJ, Liu G, Stricker C, et al. Nonmyeloablative allogeneic stem cell transplantation for refractory Hodgkin's lymphoma complicated by interleukin-2 responsive progressive multifocal leukoencephalopathy. Ann Hematol. 2002;81(7):410-413. Available at: 90. Kunschner L, Scott TF. Sustained recovery of progressive multifocal leukoencephalopathy after treatment with IL-2. Neurology. 2005;65(9):1510. Available at: 91. Sospedra M, Schippling S, Yousef S, et al. Treating progressive multifocal leukoencephalopathy with interleukin 7 and vaccination with JC virus capsid protein VP1. Clin Infect Dis. 2014;59(11):1588-1592. Available at: 92. Pavlovic D, Patera AC, Nyberg F, Gerber M, Liu M, Progressive Multifocal Leukeoncephalopathy Consortium. Progressive multifocal leukoencephalopathy: current treatment options and future perspectives. Ther Adv Neurol Disord. 2015;8(6):255-273. Available at: 93. Soleimani-Meigooni DN, Schwetye KE, Angeles MR, et al. JC virus granule cell neuronopathy in the setting of chronic lymphopenia treated with recombinant interleukin-7. J Neurovirol. 2017;23(1):141-146. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-17 94. Miskin DP, Chalkias SG, Dang X, Bord E, Batson S, Koralnik IJ. Interleukin-7 treatment of PML in a patient with idiopathic lymphocytopenia. Neurol Neuroimmunol Neuroinflamm. 2016;3(2):e213. Available at: 95. Ray U, Cinque P, Gerevini S, et al. JC polyomavirus mutants escape antibody-mediated neutralization. Sci Transl Med. 2015;7(306):306ra151. Available at: 96. Cortese I, Muranski P, Enose-Akahata Y, et al. Pembrolizumab treatment for progressive multifocal leukoencephalopathy. N Engl J Med. 2019;380(17):1597-1605. Available at: 97. Clifford DB. Checkpoint therapy for progressive multifocal leukoencephalopathy: pointless? Eur J Neurol. 2020;27(11):2114-2116. Available at: 98. Berzero G, Basso S, Stoppini L, et al. Adoptive transfer of JC virus-specific T lymphocytes for the treatment of progressive multifocal leukoencephalopathy. Ann Neurol. 2021;89(4):769-779. Available at: 99. Muftuoglu M, Olson A, Marin D, et al. Allogeneic BK virus-specific T cells for progressive multifocal leukoencephalopathy. N Engl J Med. 2018;379(15):1443-1451. Available at: 100. Cortese I, Beck ES, Al-Louzi O, et al. BK virus-specific T cells for immunotherapy of progressive multifocal leukoencephalopathy: an open-label, single-cohort pilot study. Lancet Neurol. 2021;20(8):639-652. Available at: 101. Vendrely A, Bienvenu B, Gasnault J, Thiebault JB, Salmon D, Gray F. Fulminant inflammatory leukoencephalopathy associated with HAART-induced immune restoration in AIDS-related progressive multifocal leukoencephalopathy. Acta Neuropathol. 2005;109(4):449-455. Available at: 102. Tan K, Roda R, Ostrow L, McArthur J, Nath A. PML-IRIS in patients with HIV infection: clinical manifestations and treatment with steroids. Neurology. 2009;72(17):1458-1464. Available at: 103. Sainz-de-la-Maza S, Casado JL, Perez-Elias MJ, et al. Incidence and prognosis of immune reconstitution inflammatory syndrome in HIV-associated progressive multifocal leucoencephalopathy. Eur J Neurol. 2016;23(5):919-925. Available at: 104. Clifford DB. Neurological immune reconstitution inflammatory response: riding the tide of immune recovery. Curr Opin Neurol. 2015;28(3):295-301. Available at: 105. Miralles P, Berenguer J, Lacruz C, et al. Inflammatory reactions in progressive multifocal leukoencephalopathy after highly active antiretroviral therapy. AIDS. 2001;15(14):1900-1902. Available at: 106. Safdar A, Rubocki RJ, Horvath JA, Narayan KK, Waldron RL. Fatal immune restoration disease in human immunodeficiency virus type 1-infected patients with progressive Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-18 multifocal leukoencephalopathy: impact of antiretroviral therapy-associated immune reconstitution. Clin Infect Dis. 2002;35(10):1250-1257. Available at: 107. Hoffmann C, Horst HA, Albrecht H, Schlote W. Progressive multifocal leucoencephalopathy with unusual inflammatory response during antiretroviral treatment. J Neurol Neurosurg Psychiatry. 2003;74(8):1142-1144. Available at: 108. Di Giambenedetto S, Vago G, Pompucci A, et al. Fatal inflammatory AIDS-associated PML with high CD4 counts on HAART: a new clinical entity? Neurology. 2004;63(12):2452-2453. Available at: 109. Fournier A, Martin-Blondel G, Lechapt-Zalcman E, et al. Immune reconstitution inflammatory syndrome unmasking or worsening AIDS-related progressive multifocal leukoencephalopathy: a literature review. Front Immunol. 2017;8:577. Available at: 110. Martin-Blondel G, Cuzin L, Delobel P, et al. Is maraviroc beneficial in paradoxical progressive multifocal leukoencephalopathy-immune reconstitution inflammatory syndrome management? AIDS. 2009;23(18):2545-2546. Available at: 111. Januel E, Martin-Blondel G, Lamirel C, et al. Do CCR5 antagonists improve the overall survival of patients with AIDS-related progressive multifocal leucoencephalopathy? J Neurol Neurosurg Psychiatry. 2018;89(10):1125-1126. Available at: 112. Bernard-Valnet R, Moisset X, Maubeuge N, et al. CCR5 blockade in inflammatory PML and PML-IRIS associated with chronic inflammatory diseases' treatments. Neurol Neuroimmunol Neuroinflamm. 2022;9(1). Available at: 113. Hentzien M, Guihot A, de Maindreville D, et al. Progressive multifocal leukoencephalopathy despite immune recovery in a HIV/HCV co-infected patient. J Neurovirol. 2020;26(4):607-610. Available at: 114. Crossley KM, Agnihotri S, Chaganti J, et al. Recurrence of progressive multifocal leukoencephalopathy despite immune recovery in two HIV seropositive individuals. J Neurovirol. 2016;22(4):541-545. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-1 Syphilis Updated: September 25, 2023 Reviewed: January 10, 2024 Epidemiology Syphilis, caused by Treponema pallidum, is associated with an increased risk of sexual acquisition and transmission of HIV.1-8 In the United States, the national rate of primary and secondary syphilis has increased since 2001.9-12 Although HIV infection, particularly in the advanced stages, may modify the diagnosis, natural history, or management of T. pallidum infection, the principles of syphilis management remain the same for people with and without HIV.13-18 Clinical Manifestations The effects of HIV on the protean manifestations of syphilis have been documented in multiple case reports and small case series, and in a limited number of large studies. In most people with HIV and syphilis, the clinical manifestations of syphilis are similar to those observed in people without HIV. Some studies suggest that infection with HIV may affect the clinical presentation of syphilis, as atypical or multiple genital lesions are more apparent, and accelerated progression of syphilis may be seen in people with advanced immunosuppression.16,17,19-22 Primary or secondary syphilis also may cause a transient decrease in CD4 T lymphocyte (CD4) cell count and an increase in HIV viral load that improves with recommended syphilis treatment regimens.13,23-27 Independent of HIV, previous syphilis can attenuate the clinical and laboratory manifestations of incident infection with T. pallidum.28-30 Primary syphilis commonly presents as a single painless nodule at the site of contact that rapidly ulcerates to form a classic chancre; however, multiple or atypical painful chancres may occur, and primary lesions may be absent or missed in people with HIV.16,21,31 Progression to secondary syphilis typically follows 2 to 8 weeks after primary syphilis, but an overlap in primary and secondary manifestations can occur, especially in people with HIV. The most common manifestations of secondary syphilis are mucocutaneous lesions that are macular, maculopapular, papulosquamous, or pustular. These lesions can involve the palms and soles and are often accompanied by generalized lymphadenopathy, fever, malaise, anorexia, arthralgias, and headache.13,17,18 Mpox (formerly known as monkeypox) lesions can have a similar appearance and can occur simultaneously with early syphilis.32 Condylomata lata (moist, flat papular lesions in warm intertriginous regions) can occur and may resemble condylomata acuminata caused by human papillomavirus. Lues maligna is a rare manifestation of secondary syphilis, characterized by papulopustular skin lesions that can evolve into ulcerative lesions with sharp borders and a dark central crust.33-35 Manifestations of secondary syphilis involving other locations can occur (e.g., ocular and otic syphilis, meningoencephalitis, hepatitis, nephrotic syndrome, gastritis, pneumonia). In people with secondary syphilis, non-focal central nervous system (CNS) symptoms and cerebrospinal fluid (CSF) abnormalities, such as lymphocytic pleocytosis with a mildly elevated CSF protein, can occur.19,22,31,36-40 Signs and symptoms of primary and secondary syphilis can overlap or persist from a few days to several weeks before resolving. In some instances, recrudescence of symptoms may occur after secondary infection with subsequent evolution to latent stages. Latent syphilis is defined as serologic reactivity without clinical signs and symptoms of infection. Latent syphilis can be categorized as early latent syphilis if ≤1 year duration, late latent syphilis if Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-2 >1 year duration, or latent syphilis of unknown duration if there is insufficient information to determine the duration of infection. Tertiary syphilis refers to gumma, cardiovascular syphilis, psychiatric manifestations (e.g., memory loss, personality changes), or late neurosyphilis that can develop 10 to 30 years after untreated infection. Neurosyphilis, similar to ocular and otic syphilis, can occur at any stage of syphilis with different clinical presentations, including cranial nerve dysfunction, meningitis, stroke, acute or chronic change in mental status, and loss of vibration sense. Manifestations of neurosyphilis in people with HIV are similar to those in individuals who do not have HIV. However, clinical manifestations of neurosyphilis, such as concomitant ocular syphilis (including uveitis) or meningitis, may be more common in people with HIV.19,22,40-46 Syphilitic uveitis or other ocular syphilis manifestations (e.g., neuroretinitis and optic neuritis) can occur during any stage of syphilis and can manifest as isolated abnormalities or can be associated with neurosyphilis. Syphilis can involve almost any ocular structure, but posterior uveitis and panuveitis are the most common presentations. Other common manifestations can include interstitial keratitis, recurrent anterior uveitis, retinal vasculitis, and optic neuropathy.47 All people with ocular symptoms and reactive syphilis serology need a full ocular examination, including cranial nerve evaluation. If cranial nerve dysfunction is present, a CSF evaluation is needed. Among people with isolated ocular symptoms (no cranial nerve dysfunction or other neurologic abnormalities), reactive syphilis serology, and confirmed ocular abnormalities on examination, CSF examination is unnecessary before treatment. CSF analysis might be helpful in evaluating people with ocular symptoms and reactive syphilis serology who do not have ocular findings on examination. If ocular syphilis is suspected, immediate referral to and management in collaboration with an ophthalmologist is crucial. Ocular syphilis should be treated similarly to neurosyphilis, even if a CSF examination is normal. Isolated hearing loss or other otologic symptoms can occur at any stage of syphilis or can be associated with neurosyphilis. Among people with isolated auditory abnormalities and reactive syphilis serology, CSF evaluation is likely to be normal and is not necessary before treatment.48 Diagnosis Direct Detection Darkfield microscopy and molecular tests to detect T. pallidum in lesion exudates or tissue (e.g., biopsy with silver stain) are definitive for diagnosing early syphilis.49 Although T. pallidum direct antigen detection tests are no longer commercially available, some laboratories provide locally developed and validated polymerase chain reaction (PCR) tests for the direct detection of T. pallidum. Serologic Testing Serologic diagnosis of syphilis traditionally has involved screening for nontreponemal antibodies with confirmation of reactive tests by treponemal-based assays.13,50,51 A serologic diagnosis of syphilis is based on nontreponemal tests (i.e., Venereal Disease Research Laboratory [VDRL] and rapid plasma reagin [RPR]), followed by confirmation with treponemal tests (i.e., T. pallidum particle agglutination [TP-PA], enzyme immunoassays [EIAs], chemiluminescence Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-3 immunoassays [CIAs], fluorescent treponemal antibody absorbed [FTA-ABS], or immunoblots). Rapid treponemal assays are also available to screen for syphilis; however, these tests can not differentiate recent or past infection, so testing with a nontreponemal test is indicated to inform further patient management.50-52 Use of only one type of serologic test (nontreponemal or treponemal) is insufficient for diagnosis and can result in false-negative results among people tested during primary syphilis and false-positive results among people without syphilis or previously treated syphilis. Traditional Algorithm False-positive nontreponemal test results can be associated with medical conditions and other factors unrelated to syphilis, including HIV, autoimmune disease, vaccinations, injection drug use, pregnancy, and older age.50 Individuals with a reactive nontreponemal test should always receive a treponemal test to confirm the syphilis diagnosis. Nontreponemal test antibody titers can correlate with disease activity and are used for monitoring treatment response. Sequential serologic tests should be performed using the same testing method (VDRL or RPR), preferably by the same laboratory. VDRL and RPR are equally valid assays; however, quantitative results from the two tests cannot be compared directly with each other because the methods are different, and RPR titers frequently are slightly higher than VDRL titers. Nontreponemal test titers usually decrease after treatment and can become nonreactive with time. However, in some instances nontreponemal antibodies might decrease less than fourfold after treatment (i.e., inadequate serologic response) or might decline appropriately but fail to serorevert and persist for a long period. Atypical nontreponemal serologic test results (e.g., unusually high, unusually low, or fluctuating titers) might occur regardless of HIV status. When serologic tests do not correspond with clinical findings indicative of primary, secondary, or latent syphilis, presumptive treatment is recommended for people with risk factors for syphilis, and use of other tests (e.g., biopsy for histology and immunostaining and PCR of lesion) should be considered. For most people with HIV, serologic tests are accurate and reliable for diagnosing syphilis and evaluating response to treatment.28 Reverse-Sequence Algorithm Most people who have reactive treponemal tests will have reactive tests for the remainder of their lives, regardless of adequate treatment or disease activity and do not predict treatment response. Some laboratories have initiated a reverse-sequence screening algorithm using treponemal EIA or CIA as a screening test, followed by a reflex-quantitative nontreponemal test if the EIA or CIA is positive. This reverse-sequence algorithm can identify people previously treated for syphilis, those with untreated or incompletely treated syphilis, and those with false-positive results that can occur with a low likelihood of infection.13,53 People with a positive treponemal screening test should have a standard quantitative nontreponemal test with titer performed reflexively by the laboratory to guide patient management decisions. In the reverse-sequence screening strategy, having a positive treponemal EIA or CIA and a negative reflex-quantitative nontreponemal test requires a second treponemal test (based on different antigens from the initial test) to confirm the results of the positive initial treponemal test. If a second Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-4 treponemal test is positive, people who have been treated appropriately for their stage of syphilis will require no further treatment unless sexual risk history suggests likelihood of re-exposure or there is a sustained fourfold increase in nontreponemal antibody titers. In this instance, a repeat nontreponemal test 2 to 4 weeks after the most recent possible exposure is recommended to evaluate for early infection. Those without a history of treatment for syphilis should be offered treatment. Unless history or results of a physical examination suggest a recent infection (e.g., early-stage syphilis), previously untreated people should be treated for late latent syphilis. If the second treponemal test is negative and the risk of syphilis is low, no treatment is indicated.13,54 However, if the risk of syphilis is high, treatment should be considered. Multiple studies demonstrate that high quantitative index values or high signal-to-cutoff ratio from treponemal EIA or CIA tests correlate with TP-PA positivity, which might eliminate the need for additional confirmatory testing; however, the range of index values varies among different treponemal immunoassays, and the values that correspond to high levels of reactivity with confirmatory testing might differ by immunoassay.51,55,56 In the absence of neurologic signs or symptoms, risk of neurosyphilis is low in people with a reactive treponemal test and a nonreactive nontreponemal test55,57; examination of CSF is not recommended. Early-stage disease (i.e., primary, secondary, and early latent syphilis) is identified using the same diagnostic tests used in people without HIV: standard serologic tests and darkfield microscopy of mucocutaneous lesions, if available. VDRL and RPR titers may be higher, lower (in rare instances), or delayed in people with HIV with early-stage syphilis.58-62 No data indicate that treponemal tests perform differently among people with HIV51; although uncommon, false-negative serologic tests for syphilis can occur with documented T. pallidum infection.61,62 When serologic tests do not correspond with clinical findings indicative of primary or secondary syphilis, presumptive treatment is recommended for people with risk factors for syphilis, and dilution of the sample for prozone phenomenon should be considered. For most people with HIV, serologic tests are accurate and reliable for diagnosing syphilis and for determining response to treatment. By definition, people with latent syphilis have serological evidence of syphilis (nontreponemal and treponemal testing) in the absence of clinical manifestations. Early latent syphilis may occur in the interval between the primary and secondary stage of infection or following resolution of secondary manifestations and is defined by evidence of infection during the preceding year by— • A documented seroconversion or fourfold or greater increase in nontreponemal titer; or • Symptoms of primary or secondary syphilis; or • A sex partner with documented primary, secondary, or early latent syphilis.13 Late latent syphilis is defined as syphilis in a person who does not have evidence of acquiring infection in the preceding year. All people with syphilis and signs or symptoms suggesting neurologic disease (e.g., cranial nerve dysfunction, meningitis, stroke, altered mental status) warrant evaluation for neurosyphilis. CSF abnormalities (i.e., elevated protein and mononuclear pleocytosis) are common in early-stage syphilis36 and in people with HIV, even those with no neurologic symptoms. The clinical and prognostic significance of CSF laboratory abnormalities with early-stage syphilis in people without neurologic symptoms is unknown. Several studies have demonstrated that in people with syphilis and HIV, CSF laboratory abnormalities are associated with CD4 counts ≤350 cells/mm3 or in combination with RPR titers ≥1:32.39,40,63,64 However, unless neurologic signs and symptoms are Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-5 present, a CSF examination has not been associated with improved clinical outcomes. Although laboratory testing is helpful in supporting the diagnosis of neurosyphilis, no single test can be used to diagnose neurosyphilis. The diagnosis of neurosyphilis depends on a combination of CSF tests (CSF cell count, CSF protein, and CSF-VDRL) in the setting of reactive serologic test results and neurologic signs and symptoms. CSF examination may indicate mononuclear pleocytosis (6–200 cells/mm3), mildly elevated protein concentration, or a reactive CSF-VDRL. Among people with HIV, the CSF leukocyte count can be elevated (>5 white blood cell count [WBC]/mm3); using a higher cutoff (>20 WBC/mm3) may improve the specificity of neurosyphilis diagnosis.39 In people with neurologic signs or symptoms, a reactive CSF-VDRL (in a specimen not contaminated with blood) is considered diagnostic of neurosyphilis; however, it is thought to have a very low sensitivity and therefore may miss true disease. Therefore, in people with neurologic signs or symptoms, reactive serologic test results, lymphocytic pleocytosis, or elevated protein, neurosyphilis should be considered even when the CSF-VDRL is negative. In that instance, additional evaluation by using FTA-ABS or TP-PA testing on CSF might be warranted.13 The CSF FTA-ABS test is less specific for neurosyphilis than the CSF-VDRL but is highly sensitive. Fewer data are available regarding CSF TP-PA; however, the sensitivity and specificity appears similar to the CSF FTA-ABS.65,66 Neurosyphilis is highly unlikely with a negative CSF FTA-ABS or TP-PA test, especially among people with nonspecific neurologic signs and symptoms. RPR tests of the CSF have been associated with a high false-negative rate and are not recommended.67 PCR-based diagnostic methods are not currently recommended as diagnostic tests for neurosyphilis. Preventing Disease Recommendations for Preventing Syphilis Management of Sexual Partners After Exposure to Treponema pallidum (Syphilis) to Prevent Disease Indication for Treatment • Individuals exposed sexually within 90 days preceding the diagnosis of primary, secondary, or early latent syphilis in a sex partner regardless of syphilis serologic status (AII) • Individuals exposed >90 days before syphilis diagnosis in a sex partner, if syphilis serologic test results are not available immediately and the opportunity for follow-up is uncertain (AIII) Treatment • See therapy for early-stage syphilis in the Recommendations for Treating Syphilis table. Note: Additional logistical information is available from the Centers for Disease Control and Prevention at The resurgence of syphilis and other sexually transmitted infections (STIs), as well as the emergence of mpox, in men who have sex with men (MSM) with HIV underscores the importance of primary prevention of syphilis in this population, which should begin with a behavioral risk assessment and routine discussion of sexual behaviors. Health care providers should discuss patient-centered risk reduction messages and advise specific actions that can reduce the risk of acquiring STIs and of transmitting HIV.13,68-72 Routine serologic screening for syphilis is recommended at least annually for all people with HIV who are sexually active, with more frequent screening (every 3–6 months) for those who have multiple or anonymous partners.13,73-75 The occurrence of syphilis or any other STI in a person with HIV is an indication of risk behaviors that should prompt intensified risk assessment Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-6 and counseling messages about the manifestations of syphilis, risk of HIV transmission, and prevention strategies with strong consideration for behavioral intervention.76,77 People undergoing screening or treatment for syphilis also should be evaluated for other STIs, including mpox, chlamydia, and gonorrhea at anatomic sites of exposure in men and chlamydia, gonorrhea, and trichomonas infections in women.13,78 Frequent serologic screening can identify people with recent infection and, in some instances, before infectious lesions develop. Treatment can prevent disease progression in the individual and transmission to their partners. Studies in the pre-HIV era demonstrated that approximately one-third of the sexual partners of people who have primary syphilis will develop syphilis within 30 days of exposure; empiric treatment of sexual partners exposed to syphilis will prevent the development of disease and onward syphilis transmission.79-82 Individuals with recent sexual contact with a person with syphilis in any stage should be evaluated clinically and serologically and treated presumptively. People who have had sexual contact with an individual diagnosed with primary, secondary, or early latent syphilis during the 90 days preceding the diagnosis should be treated presumptively for early syphilis, even if serologic test results are negative (AII). People who have had sexual contact with a person who receives a diagnosis of primary, secondary, or early latent syphilis >90 days before the diagnosis should be treated presumptively for early syphilis if serologic test results are not immediately available and the opportunity for follow-up is uncertain (AIII). If serologic tests are negative, no treatment is needed. If serologic tests are positive, treatment should be based on clinical and serologic evaluation and the stage of syphilis. Long-term sexual partners of people who have late latent syphilis should be evaluated clinically and serologically for syphilis and treated on the basis of the evaluation’s findings. Sexual partners of people with syphilis should be notified of their exposure and the importance of evaluation for testing and empiric therapy.13 The following sex partners of people with syphilis are considered at risk for infection and should be confidentially notified of the exposure and need for evaluation: partners who have had sexual contact within (1) 3 months plus the duration of symptoms for people who receive a diagnosis of primary syphilis, (2) 6 months plus the duration of symptoms for those diagnosed with secondary syphilis, and (3) 1 year for people diagnosed with early latent syphilis. Pre-Exposure Prophylaxis and Post-Exposure Prophylaxis for Prevention Doxycycline pre-exposure prophylaxis (PrEP) has been examined for prevention of bacterial STIs. In a pilot study, 30 MSM with HIV with previous syphilis were randomly assigned to doxycycline 100 mg daily for 48 weeks versus a financial incentive–based behavioral intervention; doxycycline was associated with a lower incidence of syphilis, but this did not reach statistical significance due to small sample size.83 Post-exposure prophylaxis (doxycycline 200 mg after unprotected anal sex) has been studied among MSM and transgender women, with a reduction in incident syphilis by 73%.84 Several recent randomized open-label clinical trials have found that doxycycline 200 mg after condomless sex among MSM or transgender women with HIV or on HIV PrEP significantly reduced chlamydia, gonorrhea, and syphilis acquisition; a randomized trial of cisgender women on HIV PrEP administered doxycycline 200 mg within 72 hours after sex did not reduce chlamydia, gonorrhea, or syphilis acquisition.85 There is ongoing evaluation regarding the potential impact of STI postexposure prophylaxis on antimicrobial resistance and the microbiome. Other studies are underway or in development regarding doxycycline prophylaxis for bacterial STIs.86,87 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-7 Targeted mass treatment of high-risk populations with azithromycin has not been demonstrated to be effective.88 Azithromycin is not recommended as secondary prevention because of azithromycin treatment failures reported in people with HIV and reports of chromosomal mutations associated with macrolide-resistant T. pallidum.89-93 Treatment Recommendations for Treating Syphilis General Considerations for Treating Syphilis • Selection of the appropriate penicillin preparation is important because T. pallidum can reside in sequestered sites (e.g., the CNS and aqueous humor) that are poorly accessed by certain forms of penicillin. • Combinations of oral benzathine penicillin and procaine penicillin or short-acting benzathine-procaine penicillin (Bicillin C-R) preparations are not appropriate for syphilis treatment. • The efficacy of non-penicillin alternatives has not been well evaluated in people with HIV and should be undertaken only with close clinical and serologic monitoring. • The Jarisch-Herxheimer reaction is an acute febrile reaction accompanied by headache, fever, and myalgias that can occur within the first 24 hours after therapy. It occurs more frequently in people with early syphilis and can induce early labor or cause fetal distress during pregnancy. Patients should be informed about this potential reaction to treatment and that it is not an allergic reaction to penicillin. Treating Treponema pallidum Infections (Syphilis) Depending on Stage of Disease Primary, Secondary, and Early Latent Syphilis [<1 year] Recommended Therapy • Benzathine penicillin G 2.4 million units IM in a single dose (AII)a Alternative Therapy (For Penicillin-Allergic Patients; See Note Below) • Doxycycline 100 mg PO twice daily for 14 days (BII),b or • Ceftriaxone 1 g IM or IV daily for 10–14 days (BII)b Note: People with penicillin allergy whose compliance or follow-up cannot be ensured and who have syphilis during pregnancy should undergo penicillin desensitization and treatment with benzathine penicillin. For management of early syphilis during pregnancy, limited evidence indicates a second dose of benzathine penicillin G 2.4 million units IM 1 week after the single dose treatment may be of benefit for congenital syphilis prevention (BII). Late Latent (>1 year) or Latent of Unknown Duration Recommended Therapy • Benzathine penicillin G 2.4 million units IM weekly for three doses (AII)a Alternative Therapy (For Penicillin-Allergic Patients) • Doxycycline 100 mg PO twice daily for 28 days (BIII) Note: People with penicillin allergy whose compliance or follow-up cannot be ensured should be desensitized and treated with benzathine penicillin (AII). Recommendations for Preventing and Treating Syphilis Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-8 Tertiary—Cardiovascular or Gummatous Disease • Perform CSF examination and obtain infectious diseases consultation to guide management. • People with CSF abnormalities should be treated with a regimen for neurosyphilis (AII). Recommended Therapy • Benzathine penicillin G 2.4 million units IM weekly for three doses for people without neurosyphilis (AII)a Neurosyphilis, Otic, or Ocular Syphilis Recommended Therapy • Aqueous crystalline penicillin G 18–24 million units per day, administered as 3–4 million units IV every 4 hours or by continuous IV infusion for 10–14 days (AII), with or without • Benzathine penicillin G 2.4 million units IM x 1 after completion of aqueous crystalline penicillin G infusion (CIII)a Alternative Therapy • Procaine penicillin G 2.4 million units IM daily plus probenecid 500 mg PO four times a day for 10–14 days (BII). Procaine penicillin has been discontinued by the manufacturer as of June 13, 2023 (see FDA Drug Shortages). Note: People who are allergic to sulfa-containing medications should not be given probenecid; thus, the procaine penicillin regimen is not recommended (AIII). For Penicillin-Allergic Patients with Neurosyphilis, Otic, or Ocular Syphilis Recommended Therapy • Desensitization to penicillin Alternative Therapy (If Desensitization Is Not Feasible and Not Pregnant) • Ceftriaxone 2 g IV daily for 10–14 days (BII) Note: People who have a history of IgE-mediated penicillin hypersensitivity may lose their sensitivity after 10 years, and a subsequent negative skin test evaluation followed by oral challenge can be considered. Among people for whom the only option is penicillin (e.g., syphilis in pregnancy) and among those with a positive skin test, desensitization to penicillin is the preferred approach. a Benzathine penicillin is currently on the FDA drug shortage webpage due to limited supply. Updates on the expected duration for the shortage are available on the FDA Drug Shortage webpage. b Skin testing for penicillin allergy can be useful in circumstances in which the reagents and expertise are available. Note: Additional logistical information is available from the Centers for Disease Control and Prevention at Key: CNS = central nervous system; CSF = cerebrospinal fluid; FDA = U.S. Food and Drug Administration; IgE = immunoglobulin E; IM = intramuscular; IV = intravenously; PO = orally Treatment regimens for syphilis demonstrate that most people with HIV respond appropriately to single dose benzathine penicillin G after exposure to syphilis and for primary, secondary, and early latent syphilis (within the previous 12 months).13,59,94,95 However, in people with HIV, more frequent clinical and serologic evaluation is recommended—at least every 3 months rather than every 6 months—because serologic nonresponse and neurologic complications may be more frequent.19,96,97 Use of antiretroviral therapy (ART) in people with syphilis has also been associated with a reduced risk of serologic failure of syphilis treatment22 and a lower risk of developing neurosyphilis.22 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-9 Benzathine penicillin G remains the treatment of choice for syphilis. People with HIV with early-stage (primary, secondary, or early latent) syphilis should receive a single intramuscular (IM) injection of 2.4 million units of benzathine penicillin G (AII).13 High-dose amoxicillin given with probenecid in addition to benzathine penicillin G in early syphilis is not associated with improved clinical outcomes.59 People with a penicillin allergy whose compliance or follow-up cannot be ensured should be desensitized and treated with benzathine penicillin G (AIII). The efficacy of alternative non-penicillin regimens in people with HIV and early syphilis has not been well studied. The use of any alternative penicillin treatment regimen should be undertaken only with close clinical and serologic monitoring. The Panel on Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV (the Panel) supports the use of doxycycline, 100 mg orally twice daily for 14 days, to treat early syphilis (BII).98,99 Based on limited clinical studies in people with and without HIV, ceftriaxone (1 g daily either IM or intravenously [IV] for 10–14 days) is also recommended for treating early-stage syphilis (BII), but the optimal dose and duration of therapy have not been defined.100-102 There are limited data suggesting a single 2-g oral dose of oral azithromycin can be effective for treating early syphilis103-105; however, T. pallidum chromosomal mutations associated with azithromycin resistance and treatment failures have been reported most commonly in MSM.89-93,106 Azithromycin has not been well studied in people with HIV or among pregnant people. Therefore, azithromycin should not be used as treatment for syphilis (AII). In people with HIV who have late latent syphilis, treatment with three weekly IM injections of 2.4 million units of benzathine penicillin G is recommended (AII). Alternative therapy is doxycycline, 100 mg orally twice daily for 28 days; however, it has not been sufficiently evaluated in people with HIV (BIII). Limited clinical studies and biologic and pharmacologic evidence suggest that ceftriaxone may be effective, but the optimal dose and duration of therapy have not been determined.107,108 If the clinical situation requires use of an alternative to penicillin, treatment should be undertaken with close clinical and serologic monitoring. People with HIV who have clinical evidence of tertiary syphilis (cardiovascular or gummatous disease) should have CSF examination to rule out CSF abnormalities before therapy is initiated. If the CSF evaluation is normal, the recommended treatment of late-stage syphilis is three weekly IM injections of 2.4 million units of benzathine penicillin G (AII).13 However, due to the complexity of tertiary syphilis management, especially cardiovascular syphilis, health care providers are advised to consult an infectious disease specialist. People with HIV diagnosed with neurosyphilis or ocular or otic syphilis should receive IV aqueous crystalline penicillin G, 18 to 24 million units daily, administered 3 to 4 million units IV every 4 hours or by continuous infusion for 10 to 14 days (AII), or procaine penicillin, 2.4 million units IM once daily plus probenecid 500 mg orally four times a day for 10 to 14 days (BII).13 However, procaine penicillin has been recently discontinued by the manufacturer.109 People with HIV who are allergic to sulfa-containing medications should not be given probenecid because of potential allergic reaction; therefore, IV penicillin is recommended (AIII). Although systemic steroids are used frequently as adjunctive therapy for otic syphilis, such therapy has not been proven beneficial. Because neurosyphilis treatment regimens are of shorter duration than those used in late latent syphilis, 2.4 million units of benzathine penicillin IM once after completion of IV penicillin G can be considered to provide a comparable duration of therapy (CIII).13 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-10 People who have a history of immunoglobulin E mediated penicillin hypersensitivity may lose their sensitivity after 10 years,110,111 and a subsequent negative skin test evaluation followed by oral challenge can be considered. Among people for whom the only option is penicillin (e.g., syphilis in pregnancy) and among those with a positive skin test, desensitization to penicillin is the preferred approach. However, based on limited data, ceftriaxone (2 g daily IV for 10–14 days) is recommended as an acceptable alternative regimen (BII).100,101,108 Other alternative regimens for neurosyphilis have not been evaluated adequately. Syphilis treatment recommendations are available in the 2021 Centers for Disease Control and Prevention STI Treatment Guidelines.13 Special Considerations with Regard to Starting Antiretroviral Therapy There are no special considerations regarding the initiation of ART in patients with syphilis. Specifically, there is no evidence that treatment with ART needs to be delayed until treatment for syphilis has been completed. Immune reconstitution inflammatory syndrome in association with syphilis following treatment with ART in people with HIV is uncommon.112,113 Monitoring and Adverse Events Clinical and serologic responses (fourfold decrease from the nontreponemal titer at the time of treatment) to treatment of early-stage (primary, secondary, and early latent) disease should be performed at 3, 6, 9, 12, and 24 months after therapy to ensure resolution of signs and symptoms within 3 to 6 months and seroreversion or a fourfold decline in nontreponemal titers within 24 months. Clinical and serologic responses to treatment are similar in people with HIV; subtle variations can occur, however, including a slower temporal pattern of serologic response in people with HIV.13,59,79,94,95 Factors associated with the serologic response to treatment in people without HIV include younger age, earlier syphilis stage, and higher RPR titer.114-116 If clinical signs and symptoms persist, treatment failure should be considered. If clinical signs or symptoms recur or there is a sustained fourfold increase in nontreponemal titers of greater than 2 weeks, treatment failure or reinfection should be considered and managed per recommendations (see Managing Possible Treatment Failure or Reinfection). The potential for reinfection should be based on the sexual history and risk assessment. Clinical trial data have demonstrated that 15% to 20% of people (including people with HIV) treated with recommended therapy for early-stage syphilis will not achieve the fourfold decline in nontreponemal titer used to define treatment response at 1 year.13,59 Serum nontreponemal test titers may remain reactive, usually ≤1:8, although can be higher, for prolonged periods. In addition, people treated for early-stage syphilis who have a fourfold decline in titer may not serorevert to a negative nontreponemal test, which does not represent treatment failure but an inadequate serologic response.117 Response to therapy for late latent syphilis should be monitored using nontreponemal serologic tests at 6, 12, 18, and 24 months to ensure at least a fourfold decline in titer, if initially high (≥1:32), within 24 months of therapy. However, data to define the precise time intervals for adequate serologic responses are limited. Many people with low titers and late latent syphilis do not have a fourfold decline in the initial titer. If clinical symptoms develop or a fourfold increase in nontreponemal titers is sustained over 2 weeks, then treatment failure or reinfection should be considered and managed per recommendations (see Managing Possible Treatment Failure or Reinfection). The potential for reinfection should be based on sexual history and risk assessment.13 The earliest CSF indicator of response to neurosyphilis treatment is a decline in CSF lymphocytosis. The CSF-VDRL may respond more slowly. Limited data suggest that changes in CSF parameters Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-11 may occur more slowly in people with HIV, especially with advanced immunosuppression.22,39 Among people with HIV who are on effective ART and people without HIV, normalization of the serum RPR titer predicts normalization of abnormal CSF parameters after neurosyphilis treatment.118,119 Therefore, repeated CSF examinations are unnecessary for people without HIV or among people with HIV who are on ART and who exhibit serologic and clinical responses to treatment.13 The Jarisch-Herxheimer reaction is an acute febrile reaction frequently accompanied by headache, rigors, transient worsening of rash, myalgia, and sometimes even a sepsis-like syndrome, that can occur within the first 24 hours after initiation of treatment for syphilis. Antipyretics can be used to manage symptoms but have not been proven to prevent this reaction. The Jarisch-Herxheimer reaction occurs most frequently in people with early syphilis, high nontreponemal antibody titers, and prior penicillin treatment.120 People with syphilis should be warned about this reaction, instructed how to manage it, and informed that it is not an allergic reaction to penicillin. Managing Possible Treatment Failure or Reinfection Retreatment should be considered for people with early-stage syphilis who have persistent or recurring clinical signs or symptoms of disease, or a sustained fourfold increase in serum nontreponemal titers after an initial fourfold decrease following treatment. The assessment for potential reinfection should be informed by a sexual history and syphilis risk assessment including information about a recent sexual partner with signs or symptoms or recent treatment for syphilis. People who have had syphilis are at increased risk for reinfection. One study showed that 6% of MSM had a repeat early-stage syphilis infection within 2 years of initial infection; HIV infection and multiple sexual partners were associated with increased risk of reinfection.11 Serologic response should be compared to the titer at the time of treatment. However, assessing serologic response to treatment can be difficult, as definitive criteria for cure or failure have not been well established. People with HIV may be at increased risk of treatment failure, but the magnitude of these risks is not precisely defined and is likely low.13,38,97 People who meet the criteria for treatment failure (i.e., signs or symptoms that persist or recur, or a fourfold increase or greater in titer sustained for more than 2 weeks) and who are at low risk for reinfection should be managed for possible treatment failure. If neurologic symptoms or signs are identified, a CSF evaluation is recommended, with findings guiding management. People with nontreponemal titers that do not decrease fourfold within 12 to 24 months of therapy should also be managed as a possible treatment failure. Management should include neurologic examination and retreatment with benzathine penicillin G, 2.4 million units at 1-week intervals for 3 weeks (BIII). If titers do not respond appropriately after retreatment, the value of repeated CSF examination or additional therapy is unclear, but it is generally not recommended. The Panel supports benzathine penicillin treatment (2.4 million units IM) without a CSF examination (unless signs or symptoms of neurosyphilis are present) and close clinical follow-up in people with recurrent signs and symptoms of primary or secondary syphilis or a fourfold increase in nontreponemal titers within the past year who are at high risk of syphilis reinfection (CIII). People treated for late latent syphilis should have a CSF examination and be re-treated if they develop clinical signs or symptoms of syphilis or have a sustained fourfold increase in serum nontreponemal test titer and are at low risk for reinfection; this can also be considered if they experience an inadequate serologic response (i.e., less than fourfold decline in an initially high [≥1:32] nontreponemal test titer) within 12 months for early syphilis and 24 months for late latent Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-12 syphilis. If CSF examination is consistent with CNS involvement, retreatment should follow the recommendations for treatment of neurosyphilis. People with a normal CSF examination or without ocular or otic symptoms should be treated with benzathine penicillin 2.4 million units IM weekly for three doses (BIII). The Panel supports benzathine penicillin treatment (2.4 million units IM) without a CSF examination (unless signs or symptoms of neurosyphilis are present) and close clinical follow-up in people with signs or symptoms of primary or secondary syphilis or a fourfold increase in nontreponemal titers within the past year who are at high risk of reinfection (CIII). Among people with HIV who are on effective ART and people without HIV, normalization of the serum RPR titer predicts normalization of abnormal CSF parameters after neurosyphilis treatment.118,119 Therefore, repeated CSF examinations are unnecessary for people with HIV who are on ART and who exhibit serologic and clinical responses after treatment. Special Considerations During Pregnancy In recent years, there has been a resurgence in neonatal syphilis in the United States. Syphilis in pregnancy is associated with increased risk of several adverse outcomes, including pregnancy loss, preterm birth, stillbirth, impaired fetal growth, neonatal mortality, and congenital infection, which can cause abnormalities in multiple organ systems. The clinical manifestations of syphilis in pregnancy are similar in people with and without HIV. Serologic screening for syphilis should be conducted at the first prenatal visit and at 28 weeks. In communities and populations in which the prevalence of syphilis is high and in people at increased risk of infection (i.e., sex with multiple partners or new partner, sex in conjunction with drug use or transactional sex, late entry or no prenatal care, methamphetamine or heroin use, hepatitis C, alcohol misuse,121 incarceration, STI in pregnancy or partner with STI, unstable housing or homelessness),122 serologic testing should also be performed at delivery.13 Providers should consider offering screening for syphilis to sexual partners of pregnant people. Screening for syphilis during pregnancy should be offered at sites providing episodic care, including emergency departments, jails, and prisons.123 Antepartum screening with nontreponemal testing is typical, but treponemal screening is being used in some settings. If a treponemal EIA or CIA test is used for antepartum syphilis screening, all positive EIA or CIA tests should be confirmed with a quantitative nontreponemal test (RPR or VDRL), as titers are essential to monitoring treatment response. If the nontreponemal test is negative and the prozone reaction is ruled out (false-negative nontreponemal test that results from high antibody titer) then the results are discordant; a second treponemal test should be performed, preferably on the same specimen (see Diagnosis section above).124 If the second treponemal test is negative (i.e., EIA positive, RPR negative, and TP-PA negative), the positive EIA or CIA is more likely to represent a false-positive test result for people who are living in communities with low rates of syphilis, have a partner who is uninfected, and have no history of treated syphilis.55,124 During pregnancy, if there is a low risk for syphilis, there are no signs or symptoms of primary syphilis, the partner has no clinical or serologic evidence of syphilis, and the pregnant person is likely to follow up with clinical care, repeat serologic testing within 4 weeks can be considered to determine whether the EIA or CIA remains positive or whether the RPR, VDRL, or TP-PA result becomes positive. If both the RPR and TP-PA remain negative, no further treatment is necessary. If follow-up is not likely, treatment appropriate for the stage of syphilis is recommended for people with an isolated reactive treponemal test without a history of syphilis treatment. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-13 No postpartum individual or neonate should leave the hospital without documentation of maternal syphilis serologic status determined at least once during pregnancy.13 All individuals who have a fetal death after 20 weeks of gestation also should be tested for syphilis. Rates of transmission to the fetus and adverse pregnancy outcomes for untreated syphilis are highest with primary, secondary, and early latent syphilis and decrease with increasing duration of infection. Pregnancy does not appear to alter the clinical course, manifestations, or diagnostic test results for syphilis infection in adults. Concurrent syphilis infection has been associated with increased risk of perinatal transmission of HIV to the infant.125-131 Syphilis infection during pregnancy should be considered in those with reactive syphilis serology unless an adequate treatment history is documented clearly in the medical records and sequential serologic antibody titers have declined appropriately for the stage of syphilis. In general, the risk of antepartum fetal infection or congenital syphilis at delivery is related to the quantitative maternal nontreponemal titer, especially if ≥1:8. However, risk for fetal infection is still substantial among pregnant people with late latent syphilis and low titers. All neonates born to people with syphilis should be evaluated for congenital syphilis regardless of maternal treatment or response. Sustained low nontreponemal titers after documented treatment for the appropriate stage of infection might not require additional treatment; however, rising or persistently high antibody titers may indicate reinfection or treatment failure, and retreatment should be considered.13 Benzathine penicillin G is recommended for the treatment of syphilis during pregnancy. Penicillin is the only known effective antimicrobial for preventing transmission to the fetus and for treatment of fetal infection; however, evidence is insufficient to determine the optimal penicillin regimen.132 For management of early syphilis during pregnancy, limited evidence indicates that a second dose of benzathine penicillin G 2.4 million units IM 1 week after the single dose treatment may be of benefit for congenital syphilis prevention.13,129,133-135 If a second dose of benzathine penicillin is administered, it should be provided no later than 9 days after the first dose.13 Sexual partners of pregnant individuals with syphilis should be referred for evaluation and treatment. Since no alternatives to penicillin have been proven effective and safe for prevention of fetal infection, desensitization and treatment with penicillin should be performed in pregnancy for those who have a history of penicillin allergy (AIII).13 Erythromycin and azithromycin should not be used because these regimens do not reliably cure infection in the pregnant individual or the fetus (AII)132; tetracyclines should be avoided in the second and third trimesters of pregnancy (AII).129,136 Data are insufficient to recommend ceftriaxone137,138 for treatment of antenatal infection and prevention of congenital syphilis (BIII). Treatment of syphilis during the second half of pregnancy may precipitate preterm labor or fetal distress if a Jarisch-Herxheimer reaction occurs.139,140 Obstetric attention is advised if contractions develop or a decrease in fetal movement is noted after treatment. During the second half of pregnancy, syphilis management can be facilitated with sonographic fetal evaluation for congenital syphilis, but this evaluation should not delay therapy. Sonographic signs of fetal or placental syphilis (e.g., hepatomegaly, ascites, fetal hydrops, thickened placenta) indicate a greater risk of fetal treatment failure.141 Such cases should be managed in consultation with high-risk obstetric specialists. After 20 weeks of gestation, fetal and contraction monitoring for 24 hours after initiation of treatment for early syphilis should be considered when sonographic findings indicate fetal infection. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-14 Coordinated prenatal care and treatment are vital because providers should document that treatment is adequate for the syphilis stage and ensure that the clinical and antibody responses are appropriate for the patient’s disease stage. Maternal serologic response during pregnancy after adequate therapy varies by stage of disease and timing of treatment.142 If syphilis is diagnosed and treated at or before 24 weeks’ gestation, serologic titers should not be repeated before 8 weeks after treatment but should be repeated again at delivery. Titers should be repeated sooner if reinfection or treatment failure is suspected. For syphilis diagnosed and treated after 24 weeks’ gestation, serologic titers should be repeated at delivery.13 A majority of women will not achieve a fourfold decrease in titers before delivery, although this does not indicate treatment failure. Inadequate antenatal treatment is likely if delivery occurs within 30 days of therapy, clinical signs of infection are present at delivery, or the maternal nontreponemal titer at delivery is fourfold higher than the pre-treatment titer. 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Ghanem KG, Hook EW, 3rd. The terms “serofast” and “serological nonresponse” in the modern syphilis era. Sex Transm Dis. 2021;48(6):451-452. Available at: 118. Marra CM, Maxwell CL, Tantalo LC, Sahi SK, Lukehart SA. Normalization of serum rapid plasma reagin titer predicts normalization of cerebrospinal fluid and clinical abnormalities after treatment of neurosyphilis. Clin Infect Dis. 2008;47(7):893-899. Available at: 119. Xiao Y, Tong ML, Lin LR, et al. Serological response predicts normalization of cerebrospinal fluid abnormalities at six months after treatment in HIV-negative neurosyphilis patients. Sci Rep. 2017;7(1):9911. Available at: 120. Yang CJ, Lee NY, Lin YH, et al. Jarisch-Herxheimer reaction after penicillin therapy among patients with syphilis in the era of the hiv infection epidemic: incidence and risk factors. Clin Infect Dis. 2010;51(8):976-979. Available at: 121. Aaron KJ, Brill I, Causey-Pruitt Z, et al. Factors associated with syphilis seroprevalence in women with and at-risk for HIV infection in the Women’s Interagency HIV Study (1994– 2015). Sex Transm Infect. 2022;98(1):4-10. Available at: 122. Trivedi S, Williams C, Torrone E, Kidd S. National trends and reported risk factors among pregnant women with syphilis in the United States, 2012–2016. Obstet Gynecol. 2019;133(1):27-32. Available at: 123. U.S. Preventive Services Task Force, Curry SJ, Krist AH, et al. Screening for syphilis infection in pregnant women: U.S. Preventive Services Task Force reaffirmation recommendation statement. JAMA. 2018;320(9):911-917. Available at: 124. Mmeje O, Chow JM, Davidson L, Shieh J, Schapiro JM, Park IU. Discordant syphilis immunoassays in pregnancy: perinatal outcomes and implications for clinical management. Clin Infect Dis. 2015;61(7):1049-1053. Available at: 125. Adachi K, Xu J, Yeganeh N, et al. Combined evaluation of sexually transmitted infections in HIV-infected pregnant women and infant HIV transmission. PLoS One. 2018;13(1):e0189851. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-26 126. Berman SM. Maternal syphilis: pathophysiology and treatment. Bull World Health Organ. 2004;82(6):433-438. Available at: 127. Tess BH, Rodrigues LC, Newell ML, Dunn DT, Lago TD. Breastfeeding, genetic, obstetric and other risk factors associated with mother-to-child transmission of HIV-1 in Sao Paulo State, Brazil. Sao Paulo Collaborative Study for Vertical Transmission of HIV-1. AIDS. 1998;12(5):513-520. Available at: 128. Lee MJ, Hallmark RJ, Frenkel LM, Del Priore G. Maternal syphilis and vertical perinatal transmission of human immunodeficiency virus type-1 infection. Int J Gynaecol Obstet. 1998;63(3):247-252. Available at: 129. Wendel GD, Jr., Sheffield JS, Hollier LM, Hill JB, Ramsey PS, Sanchez PJ. Treatment of syphilis in pregnancy and prevention of congenital syphilis. Clin Infect Dis. 2002;35(Suppl 2):S200-209. Available at: 130. Kreitchmann R, Fuchs SC, Suffert T, Preussler G. Perinatal HIV-1 transmission among low income women participants in the HIV/AIDS Control Program in Southern Brazil: a cohort study. BJOG. 2004;111(6):579-584. Available at: 131. Mwapasa V, Rogerson SJ, Kwiek JJ, et al. Maternal syphilis infection is associated with increased risk of mother-to-child transmission of HIV in Malawi. AIDS. 2006;20(14):1869-1877. Available at: 132. Walker GJ. Antibiotics for syphilis diagnosed during pregnancy. Cochrane Database Syst Rev. 2001(3):CD001143. Available at: 133. Donders GG, Desmyter J, Hooft P, Dewet GH. Apparent failure of one injection of benzathine penicillin G for syphilis during pregnancy in human immunodeficiency virus-seronegative African women. Sex Transm Dis. 1997;24(2):94-101. Available at: 134. Sheffield JS, Sanchez PJ, Morris G, et al. Congenital syphilis after maternal treatment for syphilis during pregnancy. Am J Obstet Gynecol. 2002;186(3):569-573. Available at: 135. Zhu L, Qin M, Du L, Xie RH, Wong T, Wen SW. Maternal and congenital syphilis in Shanghai, China, 2002 to 2006. Int J Infect Dis. 2010;14 Suppl 3:e45-48. Available at: 136. Ramsey PS, Vaules MB, Vasdev GM, Andrews WW, Ramin KD. Maternal and transplacental pharmacokinetics of azithromycin. Am J Obstet Gynecol. 2003;188(3):714-718. Available at: 137. Zhou P, Gu Z, Xu J, Wang X, Liao K. A study evaluating ceftriaxone as a treatment agent for primary and secondary syphilis in pregnancy. Sex Transm Dis. 2005;32(8):495-498. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV AA-27 138. Katanami Y, Hashimoto T, Takaya S, et al. Amoxicillin and ceftriaxone as treatment alternatives to penicillin for maternal syphilis. Emerg Infect Dis. 2017;23(5):827-829. Available at: 139. Klein VR, Cox SM, Mitchell MD, Wendel GD, Jr. The Jarisch-Herxheimer reaction complicating syphilotherapy in pregnancy. Obstet Gynecol. 1990;75(3 Pt 1):375-380. Available at: 140. Butler T. The Jarisch-Herxheimer reaction after antibiotic treatment of spirochetal infections: a review of recent cases and our understanding of pathogenesis. Am J Trop Med Hyg. 2017;96(1):46-52. Available at: 141. Hollier LM, Harstad TW, Sanchez PJ, Twickler DM, Wendel GD, Jr. Fetal syphilis: clinical and laboratory characteristics. Obstet Gynecol. 2001;97(6):947-953. Available at: 142. Rac MW, Bryant SN, Cantey JB, McIntire DD, Wendel GD, Jr., Sheffield JS. Maternal titers after adequate syphilotherapy during pregnancy. Clin Infect Dis. 2015;60(5):686-690. Available at: 143. Webster CM, Kasaro MP, Price JT, et al. Seroreduction of syphilis non-treponemal titers during pregnancy for women with and without HIV co-infection. Int J Gynaecol Obstet. 2022. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-1 Talaromycosis (formerly Penicilliosis) Updated: November 21, 2019 Reviewed: January 10, 2024 Epidemiology Talaromycosis is an invasive fungal infection caused by the dimorphic fungus Talaromyces marneffei (formerly Penicillium marneffei), which is endemic in Southeast Asia (northern Thailand, Vietnam, and Myanmar), East Asia (southern China, Hong Kong, and Taiwan), and South Asia (northeastern India) (see the geographic distribution of talaromycosis in Figure 1).1-4 T. marneffei was formerly classified under the Penicillium subgenus Biverticillium based on morphological characteristics. In 2011, the subgenus Biverticillium was found to form a monophyletic group with Talaromyces that is distinct from Penicillium, and it was taxonomically unified with the Talaromyces genus.5 Hence, P. marneffei was changed to T. marneffei, and the disease penicilliosis is now called talaromycosis. HIV is a major risk factor for talaromycosis in highly endemic regions, accounting for approximately 88% of disease.2 The fungus is also a major cause of HIV-associated opportunistic infections in these regions, making up to 16% of hospital admissions due to AIDS,2,3,6-8 and is a leading cause of HIV-associated blood stream infections and deaths in Vietnam and southern China.6,9-11 Infection occurs predominantly in individuals2,3,12 who have very advanced HIV disease with a CD4 T lymphocyte (CD4) cell count of <100 cells/mm3. Talaromycosis is increasingly diagnosed in immunocompromised individuals who are returning travelers or immigrants from the endemic regions, and it has been reported in Japan, Australia, Belgium, France, Germany, the Netherlands, Sweden, Switzerland, the United Kingdom, Oman (in the Middle East), and the United States.13,14 Talaromycosis is increasingly recognized in individuals who have a primary immunodeficiency condition (e.g., idiopathic CD4 lymphopenia; anti-interferon-gamma autoantibody-associated immunodeficiency; conditions due to mutations in CYBB or CD40L; or gain-of-function mutation in STAT1/STAT3 pathways) or secondary immunodeficiency conditions (e.g., autoimmune diseases in people on corticosteroids and/or other immunosuppressive therapy; solid and hematological malignancies; solid organ transplantation; hematopoietic stem cell transplantation; and therapy with novel target therapies, such as monoclonal antibodies against CD20 and kinase inhibitors).15 Talaromycosis-related mortality, despite antifungal therapy in people both with and without HIV, is up to 30%.2,3,12,16,17 Similar to other endemic mycoses, talaromycosis is a saprozoonotic infection, meaning the transmissible source has a reservoir both in an abiotic environment and in an animal host. The wild bamboo rat in highland areas in the endemic regions is the known animal reservoir of T. marneffei18,19; however, case-control studies suggest that human infection results from inhalation of fungal spores released from a soil-related environmental reservoir (plants and farmed animals) rather than from direct bamboo rat–to-human transmission.20,21 Talaromycosis incidence increased 30% to 50% during the rainy months in southern Vietnam and northern Thailand3,22 and was associated with increased humidity and not precipitation,23,24 which suggests that humidity facilitates an expansion of the environmental reservoir, resulting in increased exposure to the fungus. Reactivation of latent infections has been demonstrated in non-autochthonous cases with a history of remote travel to the endemic countries and can occur many years after exposure.13,14,25 One case of presumed laboratory-acquired talaromycosis was reported in an African man with HIV who was at Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-2 the Pasteur Institute in Paris26; however, laboratory-acquired infection has never been reported from the endemic regions. Donor-acquired transmission has been reported in a lung-transplant recipient from Belgium.27 Clinical Manifestations Disseminated infection involving multiple organ systems is the most common manifestation of talaromycosis in people with advanced HIV disease. The infection frequently begins as a subacute illness characterized by fever, weight loss, hepatosplenomegaly, lymphadenopathy, and respiratory and gastrointestinal abnormalities.3,28 These clinical features are nonspecific and are indistinguishable from those of disseminated tuberculosis, other systemic mycoses, or infections due to intracellular pathogens such as Salmonella species. Skin lesions are the most specific but late manifestations of talaromycosis, with central-necrotic papules on the face, trunk, and extremities occurring in 40% to 70% of patients.1,3,29 Pulmonary involvement manifested as cough or shortness of breath occurs in 40% of patients. Gastrointestinal involvement presenting as diarrhea or abdominal pain occurs in 30% of patients. Significant hepatosplenomegaly is present in 70% of patients and together with intra-abdominal lymphadenopathy cause abdominal distention and pain.3,7 Meningoencephalitis is a rare manifestation that occurs in <1% of patients and has a rapid disease course with a mortality of 80%.30 Concurrent infections with other opportunistic pathogens occur in up to 60% of patients, with oropharyngeal candidiasis being the most common.2 Tuberculosis coinfection is common (occurring in up to 22% of patients in highly endemic regions) and complicates disease management because of itraconazole and rifampin drug interactions.3 Common laboratory findings associated with talaromycosis include anemia and thrombocytopenia due to bone marrow infiltration. Anemia can be profound and may require multiple red cell transfusions. Elevation of aminotransferase is common, with a serum aspartate aminotransferase (AST) over alanine aminotransferase (ALT) ratio of approximately 2.3 The median CD4 count in multiple cohorts2,3 is <50 cells/mm3. The chest radiographical findings are broad, ranging from diffuse interstitial disease to reticulonodular infiltrates to alveola infiltrates causing respiratory failure.31 Diagnosis A diagnosis of talaromycosis should be considered in all people with HIV with CD4 count <100 cells/mm3 who have traveled to or have lived in talaromycosis-endemic areas and present with a systemic infection involving the reticuloendothelial system (i.e., lymph nodes, liver, spleen, and bone marrow). Skin lesions in talaromycosis have typical central-necrotic appearance and can be a diagnostic sign. However, skin lesions are a late manifestation of talaromycosis and are absent in up to 60% of patients.1,3,29 The current diagnostic methods for talaromycosis are still based on conventional microscopy, histology, and culture. Culture results usually return within 4 to 5 days but can take up to 28 days. Diagnostic delay, particularly in patients presenting without fever or skin lesions, is Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-3 associated with increased mortality.2,3,15,32 Antigen detection and polymerase chain reaction (PCR)– based methods are promising rapid diagnostics currently being evaluated. Microscopy, Histology, and Culture Are the Current Gold Standard Diagnostic Methods A presumptive diagnosis of talaromycosis can be made based on the microscopic examination of Giemsa-, Wright-, or Gomori Methenamine Silver (GMS)–stained samples of skin lesion scrapings, lymph node aspirate, bone marrow aspirate, or tissue sections showing round-to-oval extracellular and intramacrophage yeast-like organisms measuring 3 to 6 µm in diameter. Identification of a clear midline septum in a dividing yeast cell is what distinguishes T. marneffei from Histoplasma or Candida species.1 In some patients, the fungus can be identified by microscopic examination of a Wright-stained peripheral blood smear.33 A definitive diagnosis of talaromycosis can be made by the histopathologic demonstration of the organism in biopsy specimens. There are three histopathological forms. The granulomatous reaction is formed by histiocytes, lymphocytes, and plasma; epithelioid and giant cells and can be seen in reticuloendothelial organs in patients who are HIV-negative or immunocompetent. The suppurative reaction develops with the joining of multiple abscesses seen in the lung and subcutaneous tissues of immunocompetent patients. The anergic and necrotizing reaction is characterized by focal necrosis surrounded by distended histiocytes containing proliferating fungi seen in the lung, liver, and spleen of immunocompromised patients.34 Most frequently, a definitive diagnosis of talaromycosis is based on isolation of the organism from cultures of clinical specimens. Compared to other endemic dimorphic fungi, T. marneffei grows more readily in standard BACTEC blood culture media and Sabouraud dextrose agar but takes 5 to 14 days to grow and to demonstrate temperature dimorphism. At 25 °C to 30 °C, the fungus grows as a mold, producing yellow-green colonies with sulcate folds and a red diffusible pigment in the media. Microscopically, filamentous hyphae with characteristic spore-bearing structures called conidiophores and conidia can be seen. At 32 °C to 37 °C, the fungus makes the morphological transition from a mold to a yeast, producing tan-colored colonies without a red diffusible pigment. In laboratory media, only the transitional sausage-shaped cells can be seen microscopically. The round-to-oval yeast cells are only seen in natural tissue.1 Culture yield is the highest from bone marrow (100%), followed by skin lesions (90%) and blood (70%).3,35 Less commonly, talaromycosis has been diagnosed from sputum, pleural fluid, peritoneal fluid, cerebrospinal fluid, pericardium fluid, stool, and urine. Molecular Diagnosis Molecular diagnostics for talaromycosis have been based on PCR amplification and sequence identification of specific regions within the fungal ribosome’s internally transcribed spacer regions, the 5.8S rRNA, and the 18S rRNA genes of T. marneffei.36-39 These assays have high specificity (100%) but limited sensitivity (60% to 70%). At present, none of the real-time PCR assays have been prospectively validated, standardized, or commercially developed for clinical use. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-4 Antigen Detection The commercial assay for the detection of Aspergillus galactomannan cross-reacts with T. marneffei and has a sensitivity of 95.8% (23 of 24 patients with culture-positive talaromycosis were correctly identified) and a specificity of 90.9% (30 of 33 people without talaromycosis were correctly identified) for the detection of talaromycosis (at cutoff index = 1.0).40 However, the galactomannan test also cross reacts with other endemic fungi, such as Histoplasma and Blastomyces, and has not been evaluated prospectively. The Mp1p enzyme-linked immunosorbent assay (ELISA) has been shown to be more sensitive than blood culture (in 372 culture-proven talaromycosis cases, sensitivity was 86.3% for the Mp1p ELISA and 74% for blood culture) and is highly specific (98.1% specificity in 338 healthy controls and 179 people without HIV but with other infections).41 This assay was used to screen a large serum bank of 8,131 people with HIV in Guangzhou, China, and showed a Mp1p antigenemia prevalence of 9.4%, with prevalence of antigenemia increased from 4.5% to 28.4% as the CD4 count decreased from 200 cells/mm3 to 50 cells/mm3, demonstrating a significant burden of disease in southern China.24 In Vietnam, the Mp1p ELISA identified 4.2% antigenemia in 1,123 asymptomatic people with HIV who had a CD4 count <100 cells/mm3 initiating antiretroviral therapy (ART) in 22 HIV clinics across Vietnam. Antigenemia was found to be independently associated with 12-month mortality.42 These data demonstrate that the Mp1p ELISA has the potential to detect infection earlier than culture allows and can potentially be used as a screening tool for subclinical infection, thereby permitting pre-emptive antifungal therapy to prevent disease development. This is an area of active research. Matrix-Assisted Laser Desorption/Ionization-Time of Flight Method The matrix-assisted laser desorption/ionization-time of flight (MALDI-TOF) method recently has been used for identification of Talaromyces to the species level from cultured specimens based on either an in-house database generated from an institution’s T. marneffei clinical strain collection43,44 or from the comprehensive National Institutes of Health MDL Mold Library.45 The MALDI-TOF represents a rapid and reliable tool for downstream fungal identification, eliminating the need to demonstrate thermal dimorphism. Antifungal Susceptibility Testing The minimum inhibitory concentrations (MICs) have been consistently low for itraconazole, intermediate for amphotericin B, and high for fluconazole. Thus far, only one retrospective case series from Chiang Mai in Thailand correlated MIC data of 30 clinical isolates with patient outcomes. More recent studies reported low MIC values for the newer generation azole drugs voriconazole (MICs 0.016–0.063 µg/mL) and posaconazole (MICs 0.001–0.002 µg/ml), and intermediate to high MIC values of 2 µg/ml to 8 µg/mL for anidulafungin.46 A later study utilized a commercial Sensititre YeastOne YO10 assay.47 These results suggest promising activity of voriconazole and posaconazole for the treatment of talaromycosis and suggest that the echinocandins are less effective against T. marneffei. Preventing Exposure Two case-controls studies in Thailand and Vietnam demonstrated that people with World Health Organization Stage 4 HIV disease or a CD4 count <100 cells/mm3 who had an occupational exposure Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-5 to plants and farmed animals were at increased risk for infection.20,21 The risk was higher in the rainy and humid months.3,22 Residency or a history of traveling to the highland regions (as short as 3 days) was a risk factor for talaromycosis in people with advanced HIV disease in southern Vietnam.20 These data suggest that people with advanced HIV should avoid visiting the areas where talaromycosis is highly endemic, particularly highland regions during the rainy and humid months (BIII). Preventing Disease Preventing First Episode of Talaromycosis (Primary Prophylaxis) Indication for Primary Prophylaxis • People with a CD4 count <100 cells/mm3 who are unable to have ART or have treatment failure without access to effective ART options and who either: o Reside in the highly endemic regions in northern Thailand, throughout Vietnam, and in southern China (particularly in highland regions during the rainy humid months) (BI), or o Are from countries outside of the endemic region and must travel to the region (BIII). Primary Prophylaxis • For Individuals Residing in Endemic Areas o Preferred Therapy: Itraconazole 200 mg PO once daily (BI) o Alternative Therapy: Fluconazole 400 mg PO once weekly (BII) • For Individuals Traveling to Endemic Areas o Preferred Therapy: Begin itraconazole 200 mg PO once daily 3 days before travel and continue for 1 week after leaving the endemic area (BIII). o Alternative Therapy: Begin fluconazole 400 mg 3 days before travel, then continue 400 mg once weekly while in the area and take final dose after leaving the endemic area (BIII). Indication for Discontinuing Primary Prophylaxis for People Who Reside in Endemic Areas • CD4 count >100 cells/mm3 for ≥6 months in response to ART (BII) • Viral load suppression for ≥6 months on ART (BIII) Indication for Restarting Primary Prophylaxis • CD4 count decreases to <100 cells/mm3 (BIII) and the person still resides in or travels to high-risk areas. Primary prophylaxis for travelers may begin 3 days prior to travel to allow serum drug level to reach steady state and may continue for 1 week after travel (BIII). Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; PO = orally Primary prophylaxis has been shown to reduce the incidence of talaromycosis and other invasive fungal infections. A double-blind, placebo-controlled trial48 in Chiang Mai, Thailand, demonstrated that oral itraconazole 200 mg daily for primary prophylaxis significantly reduced the occurrence of invasive fungal infections (predominantly cryptococcosis and talaromycosis) in people with HIV with a CD4 count <200 cells/mm3. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-6 In a retrospective study also in Chiang Mai, fluconazole (400 mg weekly) was shown to be as effective as itraconazole (200 mg daily) for primary prophylaxis.49 However, these studies were conducted prior to the widespread use of ART and had small sample sizes, and a mortality benefit was not observed. Therefore, primary prophylaxis has not been widely adopted given concerns about long-term toxicity, drug–drug interactions, and costs. Indication for Primary Prophylaxis Primary prophylaxis is only recommended for people with HIV with CD4 counts <100 cells/mm3 who reside in the highly endemic regions in northern Thailand, southern China, and northern and southern Vietnam who are unable to have ART for whatever reasons or have treatment failure without access to effective antiretroviral (ARV) options (BI). The drug choices for prophylaxis are oral itraconazole 200 mg once daily (BI) or oral fluconazole 400 mg once weekly (BII). Primary prophylaxis is not recommended in people with HIV who are on or about to start effective ART and is not recommended in geographic areas outside of the mentioned highly endemic regions (AIII). For people with HIV who are from the United States and from countries outside of the endemic region who are not on effective ART, have a CD4 count <100 cells/mm3, and must travel to the highly endemic areas mentioned, primary prophylaxis with either itraconazole or fluconazole should begin 3 days prior to travel to allow serum drug level to reach steady state and may continue for 1 week after travel (BIII). Discontinuation of Primary Prophylaxis Primary prophylaxis for talaromycosis can reasonably be discontinued in people with HIV who are ART adherent and have a sustained CD4 count ≥100 cells/mm3 for more than 6 months (BII). In areas where viral load monitoring has replaced CD4 count monitoring, primary prophylaxis can reasonably be discontinued in people with HIV who achieve sustained virologic suppression at least 6 months (BIII). Treating Disease Treating Acute Infection in Severely Ill Patients Preferred Therapy • Induction Therapy o Liposomal amphotericin B 3–5 mg/kg/day IV for 2 weeks, followed by • Consolidation Therapy o Itraconazole 200 mg PO twice daily for 10 weeks (AI), followed by • Maintenance Therapy or Secondary Prophylaxis o Itraconazole 200 mg PO daily (AII) Alternative Therapy (If Liposomal Amphotericin B Is Not Available) • Induction Therapy Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-7 o Deoxycholate amphotericin B 0.7 mg/kg/day IV for 2 weeks, followed by • Consolidation Therapy o Itraconazole 200 mg PO twice daily for 10 weeks (AI), followed by • Maintenance Therapy or Secondary Prophylaxis o Itraconazole 200 mg PO daily (AII) Alternative Therapy (If Amphotericin B Is Not Available) • Induction Therapy o Voriconazole 6 mg/kg IV every 12 hours for 1 day (loading dose) and then voriconazole 4 mg/kg IV every 12 hours for 2 weeks, or o Oral voriconazole 600 mg every 12 hours on day 1 (loading dose) and then voriconazole 400 mg PO every 12 hours for 2 weeks; followed by • Consolidation Therapy o Voriconazole 200 mg PO twice daily, or o Itraconazole 200 mg PO twice daily for a maximum of 10 weeks (BII); followed by • Maintenance Therapy or Secondary Prophylaxis o Itraconazole 200 mg PO daily (AII) Note: Itraconazole is not recommended as induction therapy for talaromycosis (AI). Criteria for Discontinuing Chronic Maintenance Therapy • CD4 count >100 cells/mm3 for ≥6 months in response to ART (BII) • Virologic suppression for ≥6 months on ART (BIII) Criteria for Restarting Chronic Maintenance Therapy • CD4 count decreases to <100 cells/mm3 (AIII) Other Considerations • To improve outcomes, ART can be initiated as early as 1 week after the initiation of treatment for talaromycosis with amphotericin B induction therapy (BII). • Given erratic absorption of itraconazole, extensive interindividual variability and nonlinear PK of voriconazole, and the potential for drug interactions with ARV drugs, itraconazole and voriconazole concentrations should be monitored, and serum trough concentration should be >0.5 µg/mL for itraconazole and >1 µg/mL for voriconazole (BIII). Both itraconazole and voriconazole can have significant drug–drug interactions with various ARV drugs; dosage adjustment may be necessary, and TDM to guide therapy can be considered (see the Drug–Drug Interactions tables in the Adult and Adolescent Antiretroviral Guidelines for further recommendations). • Substitution of amphotericin B for high-dose azoles in the first trimester is recommended (BIII). People on secondary prophylaxis with itraconazole or other azoles should postpone pregnancy until their CD4 counts have been restored with ART, such that prophylaxis can be discontinued (BIII). Key: ART = antiretroviral therapy; ARV = antiretroviral; CD4 = CD4 T lymphocyte; IV = intravenously; PK = pharmacokinetics; PO = orally; TDM = therapeutic drug monitoring Disseminated talaromycosis is fatal if untreated.50 The case fatality rates with antifungal therapy range from 10% to 30%.2,3,6,16 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-8 Antifungal therapy for talaromycosis is divided into induction, consolidation, and maintenance phases. The treatment recommendations are based on several observational studies in Thailand and China51-54 and the recent Itraconazole versus Amphotericin B for Penicilliosis (IVAP) randomized, controlled trial in Vietnam.55 In an earlier noncomparative prospective study of 74 patients in Thailand, induction therapy with deoxycholate amphotericin B for 2 weeks followed by consolidation therapy with itraconazole for 10 weeks was shown to be highly effective. Treatment success rate (defined by negative blood culture and resolution of fever and skin lesions at the end of a 12-week treatment course) was 97%.51 Voriconazole has been used for induction therapy in patients who could not tolerate amphotericin B and was shown to have favorable clinical and microbiological outcomes in 8 of 9 patients in Thailand53 and 10 of 14 patients in China.52 The IVAP trial randomized 440 patients across 5 hospitals in Vietnam and demonstrated that induction therapy with amphotericin B was superior to itraconazole with respect to 6-month mortality (absolute risk of death was 11% and 21%, respectively; hazard ratio of death in the itraconazole arm was 1.88 [95% confidence interval, 1.15–3.09; P = 0.012]). Patients in the amphotericin B arm had significantly lower rates of disease complications, including disease relapse and immune reconstitution inflammatory syndrome (IRIS), and had a fourfold faster rate of blood fungal clearance. The difference in mortality between the arms was not dependent on disease severity (based on positive blood culture, blood fungal count, or requirement for oxygen support at presentation) or by a participant’s immune status (CD4 count <50 cells/mm3 or ≥50 cells/mm3), ART status, or intravenous (IV) drug use.55 The recommended induction therapy for all patients, regardless of disease severity, is amphotericin B, preferably liposomal amphotericin B 3 to 5 mg/kg/day where available, or deoxycholate amphotericin B 0.7 mg/kg body weight/day, IV for 2 weeks (AI). Induction therapy should be followed by consolidation therapy with oral itraconazole, 200 mg every 12 hours for a subsequent duration of 10 weeks (AI).55 After this period, maintenance therapy (or secondary prophylaxis) with oral itraconazole 200 mg/day is recommended to prevent recurrence until the CD4 count rises above 100 cells/mm3 for ≥6 months (AI).56 For patients who are unable to tolerate any form of amphotericin, induction therapy with IV voriconazole 6 mg/kg every 12 hours on Day 1 (loading dose), then 4 mg/kg every 12 hours or with oral voriconazole 600 mg every 12 hours on Day 1 (loading dose), then 400 mg every 12 hours for 2 weeks is recommended (BII).52,53 Thereafter, either oral voriconazole or oral itraconazole 200 mg every 12 hours can be used for consolidation therapy for 10 weeks, followed by itraconazole 200 mg/day for secondary prophylaxis. The optimal dose of voriconazole for secondary prophylaxis beyond 12 weeks has not been studied. Itraconazole is not recommended as an induction therapy for talaromycosis, regardless of disease severity (AI).55 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-9 Special Considerations with Regard to Starting ART No studies exist regarding the optimal time to start ART in people with HIV who have talaromycosis. In the IVAP trial, the median time to ART initiation, which was similar in both arms, was 3 weeks (range: 1–5 weeks). Paradoxical IRIS events occurred only in the itraconazole arm (in 11.4% of patients), suggesting that ART can be safely initiated as early as 1 week after starting effective antifungal therapy with amphotericin B (BIII).55 Monitoring of Response to Therapy and Adverse Events (Including IRIS) Adverse Event Monitoring Patients treated with amphotericin B should be monitored for infusion-related adverse reactions (fever, rigors, nausea, vomiting), electrolyte disturbances (particularly hypokalemia and hypomagnesemia), nephrotoxicity (rise in creatinine), and anemia. Hydration with 500 mL to 1,000 mL of normal saline and potassium supplementation before each amphotericin B infusion reduces the risk of nephrotoxicity during treatment (AII). Infusion-related adverse reactions can be ameliorated by pre-treatment with acetaminophen and diphenhydramine. Drug–Drug Interactions and Therapeutic Drug Monitoring Itraconazole and voriconazole and ARV drugs—such as protease inhibitors, some integrase strand transfer inhibitors, and non-nucleoside reverse transcriptase inhibitors—can have bidirectional interactions with each other, leading to increased or decreased drug concentrations (see Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines). Close monitoring is recommended when using these drugs together. In settings where therapeutic drug monitoring (TDM) is available, serum itraconazole and voriconazole levels should be obtained in all patients to ensure adequate drug exposure (BIII). This is because itraconazole and voriconazole can interact with some ARV drugs and absorption of itraconazole can be erratic, and because of the extensive interindividual variability and nonlinear pharmacokinetics of voriconazole. The target serum trough concentration should be >0.5 μg/mL for itraconazole and >1 μg/mL for voriconazole (BIII). Because it is more bioavailable, itraconazole solution is preferred over the capsule formulation. Prevention and Management of IRIS Both unmasking and paradoxical IRIS have been described in patients with talaromycosis when ART is initiated.57-59 In the IVAP trial, 188 of 432 (44%) patients had started ART a median of 3 to 4 months before developing talaromycosis, indicating the role of ART in the unmasking of subclinical infection in a significant proportion of patients.55 This finding highlights the need for a sensitive assay to screen for subclinical infection and the importance of pre-emptive antifungal therapy to prevent disease and unmasking IRIS. In patients starting ART after a diagnosis of talaromycosis, paradoxical IRIS events only occurred in patients treated with itraconazole induction therapy,55 demonstrating the role of effective induction therapy with amphotericin B in the prevention of paradoxical IRIS. ART should not be withheld because of concerns for possible development of IRIS (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-10 Patients with paradoxical IRIS typically present with inflammatory manifestations that include erythematous or immunological skin lesions, such as erythema nodosum, as well as large and painful peripheral lymph nodes and synovitis of small joints. Most symptoms can be managed by judicious use of nonsteroid anti-inflammatory medicine. Corticosteroids are reserved for synovitis that interferes with daily function.59 Although the IRIS events in the IVAP trial were not associated with increased mortality and were managed effectively with continuation of ART and antifungal therapy, they were associated with higher morbidity, including lower quality of life and increased diagnostic testing, duration of hospitalization, and cost.55 Managing Treatment Failure and Relapse Talaromycosis treatment failure and disease relapse were associated with ineffective induction therapy with itraconazole, highlighting the importance of amphotericin B induction therapy.55 On the basis of case series that included very few patients and on clinical experiences, voriconazole is an alternative therapy for patients who are unable to tolerate amphotericin B treatment (BII). Disease relapse is associated with higher mortality55 and occurs mainly in patients who are not adherent to ART or have virologic failure, as well as in those who are not adherent to itraconazole consolidation or maintenance therapy. Therapy adherence counseling and TDM for itraconazole and voriconazole, if available, are recommended (AIII). Preventing Recurrence When to Start Secondary Prophylaxis/Chronic Maintenance Therapy A study showed that >50% of patients not treated with ART had disease relapse within 6 months after discontinuation of antifungal therapy. A double-blind, placebo-controlled study conducted in Chiang Mai, Thailand, demonstrated that secondary prophylaxis with oral itraconazole 200 mg daily in patients with AIDS reduced the talaromycosis relapse rate from 57% to 0% (p < 0.001).56 All patients who successfully complete induction and consolidation treatment for talaromycosis should receive secondary prophylaxis (maintenance therapy) with oral itraconazole 200 mg/day until they reach criteria for stopping secondary prophylaxis (AI). When to Stop Secondary Prophylaxis/Chronic Maintenance Therapy No randomized, controlled study has demonstrated the safety of discontinuation of secondary prophylaxis for talaromycosis. However, a retrospective cohort study60 reported no relapse of talaromycosis after itraconazole was discontinued in patients receiving ART whose CD4 counts were >100 cells/mm3. Therefore, secondary prophylaxis for talaromycosis can be discontinued in patients who are ART adherent and have CD4 counts >100 cells/mm3 for at least 6 months (BII). Secondary prophylaxis can reasonably be discontinued in patients with sustained virologic suppression for ≥6 months (BIII). Secondary prophylaxis/chronic maintenance therapy should be reintroduced if the CD4 count decreases to <100 cells/mm3 (BIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-11 Special Considerations During Pregnancy The diagnosis and treatment of talaromycosis during pregnancy is similar to that in nonpregnant adults, with the following considerations regarding antifungal use in pregnancy. Amphotericin B has not been shown to be teratogenic in animals, and no increase in fetal anomalies has been seen with its use in humans. Neonates born to people on chronic amphotericin B at delivery should be evaluated for renal dysfunction and hypokalemia. Itraconazole at high doses has been shown to be teratogenic in animals, but because humans lack the metabolic mechanism accounting for these defects, the animal teratogenicity data are not applicable to humans. Case series in humans do not suggest an increased risk of birth defects with itraconazole, but experience is very limited.61 Voriconazole is Food and Drug Administration Category D because of teratogenicity (cleft palate and renal defects) seen in rats and embryotoxicity in rabbits. No human data on use of voriconazole are available, so use in the first trimester is not recommended. Substitution of amphotericin B for high-dose azoles in the first trimester is recommended (BIII). People on secondary prophylaxis with itraconazole or other azoles should postpone pregnancy until their CD4 counts have been restored with ART, such that prophylaxis can be discontinued (BIII). If a person becomes pregnant while receiving itraconazole prophylaxis, the decision as to whether to continue should be individualized based on current CD4 count and viral suppression and patient preference. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-12 Figure 1. Geographic Distribution of Talaromycosis Figure courtesy of Dr. Thuy Le, Division of Infectious Diseases and International Health, Duke University School of Medicine. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-13 References 1. Vanittanakom N, Cooper CR, Jr., Fisher MC, Sirisanthana T. Penicillium marneffei infection and recent advances in the epidemiology and molecular biology aspects. Clin Microbiol Rev. 2006;19(1):95-110. Available at: 2. Hu Y, Zhang J, Li X, et al. Penicillium marneffei infection: an emerging disease in mainland China. Mycopathologia. 2013;175(1-2):57-67. Available at: 3. Le T, Wolbers M, Chi NH, et al. Epidemiology, seasonality, and predictors of outcome of AIDS-associated Penicillium marneffei infection in Ho Chi Minh City, Viet Nam. Clin Infect Dis. 2011;52(7):945-952. Available at: 4. Ranjana KH, Priyokumar K, Singh TJ, et al. Disseminated Penicillium marneffei infection among HIV-infected patients in Manipur state, India. J Infect. 2002;45(4):268-271. Available at: 5. Samson RA, Yilmaz N, Houbraken J, et al. Phylogeny and nomenclature of the genus Talaromyces and taxa accommodated in Penicillium subgenus Biverticillium. Stud Mycol. 2011;70(1):159-183. Available at: 6. Jiang J, Meng S, Huang S, et al. Effects of Talaromyces marneffei infection on mortality of HIV/AIDS patients in southern China: a retrospective cohort study. Clin Microbiol Infect. 2019;25(2):233-241. Available at: 7. Larsson M, Nguyen LH, Wertheim HF, et al. Clinical characteristics and outcome of Penicillium marneffei infection among HIV-infected patients in northern Vietnam. AIDS Res Ther. 2012;9(1):24. Available at: 8. Wu TC, Chan JW, Ng CK, Tsang DN, Lee MP, Li PC. Clinical presentations and outcomes of Penicillium marneffei infections: a series from 1994 to 2004. Hong Kong Med J. 2008;14(2):103-109. Available at: 9. Feng RF, Ma Y, Liu ZF, et al. [Specific causes of death among 381 AIDS patients who died in hospitals]. Zhonghua Liu Xing Bing Xue Za Zhi. 2013;34(12):1237-1241. Available at: 10. Nga TV, Parry CM, Le T, et al. The decline of typhoid and the rise of non-typhoid salmonellae and fungal infections in a changing HIV landscape: bloodstream infection trends over 15 years in southern Vietnam. Trans R Soc Trop Med Hyg. 2012;106(1):26-34. Available at: 11. Qi T, Zhang R, Shen Y, et al. Etiology and clinical features of 229 cases of bloodstream infection among Chinese HIV/AIDS patients: a retrospective cross-sectional study. Eur J Clin Microbiol Infect Dis. 2016;35(11):1767-1770. Available at: 12. Supparatpinyo K, Khamwan C, Baosoung V, Nelson KE, Sirisanthana T. Disseminated Penicillium marneffei infection in southeast Asia. Lancet. 1994;344(8915):110-113. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-14 13. Antinori S, Gianelli E, Bonaccorso C, et al. Disseminated Penicillium marneffei infection in an HIV-positive Italian patient and a review of cases reported outside endemic regions. J Travel Med. 2006;13(3):181-188. Available at: 14. Cristofaro P, Mileno MD. Penicillium marneffei infection in HIV-infected travelers. AIDS Alert. 2006;21(12):140-142. Available at: 15. Chan JF, Lau SK, Yuen KY, Woo PC. Talaromyces (Penicillium) marneffei infection in non-HIV-infected patients. Emerg Microbes Infect. 2016;5:e19. Available at: 16. Son VT, Khue PM, Strobel M. Penicilliosis and AIDS in Haiphong, Vietnam: evolution and predictive factors of death. Med Mal Infect. 2014;44(11-12):495-501. Available at: 17. Kawila R, Chaiwarith R, Supparatpinyo K. Clinical and laboratory characteristics of penicilliosis marneffei among patients with and without HIV infection in Northern Thailand: a retrospective study. BMC Infect Dis. 2013;13:464. Available at: 18. Cao C, Liang L, Wang W, et al. Common reservoirs for Penicillium marneffei infection in humans and rodents, China. Emerg Infect Dis. 2011;17(2):209-214. Available at: 19. Huang X, He G, Lu S, Liang Y, Xi L. Role of Rhizomys pruinosus as a natural animal host of Penicillium marneffei in Guangdong, China. Microb Biotechnol. 2015;8(4):659-664. Available at: 20. Le T, Jonat B, Kim Cuc N, al E. The exposure and geospatial risk factors for AIDS-associated penicilliosis in Vietnam. Presented at: Conference on Retroviruses and Opportunistic Infections; 2015. Seattle, WA. 21. Chariyalertsak S, Sirisanthana T, Supparatpinyo K, Praparattanapan J, Nelson KE. Case-control study of risk factors for Penicillium marneffei infection in human immunodeficiency virus-infected patients in northern Thailand. Clin Infect Dis. 1997;24(6):1080-1086. Available at: 22. Chariyalertsak S, Sirisanthana T, Supparatpinyo K, Nelson KE. Seasonal variation of disseminated Penicillium marneffei infections in northern Thailand: a clue to the reservoir? J Infect Dis. 1996;173(6):1490-1493. Available at: 23. Bulterys PL, Le T, Quang VM, Nelson KE, Lloyd-Smith JO. Environmental predictors and incubation period of AIDS-associated penicillium marneffei infection in Ho Chi Minh City, Vietnam. Clin Infect Dis. 2013;56(9):1273-1279. Available at: 24. Wang YF, Xu HF, Han ZG, et al. Serological surveillance for Penicillium marneffei infection in HIV-infected patients during 2004–2011 in Guangzhou, China. Clin Microbiol Infect. 2015;21(5):484-489. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-15 25. Castro-Lainez MT, Sierra-Hoffman M, J LL-Z, et al. Talaromyces marneffei infection in a non-HIV non-endemic population. IDCases. 2018;12:21-24. Available at: 26. Hilmarsdottir I, Coutellier A, Elbaz J, et al. A French case of laboratory-acquired disseminated Penicillium marneffei infection in a patient with AIDS. Clin Infect Dis. 1994;19(2):357-358. Available at: 27. Hermans F, Ombelet S, Degezelle K, et al. First-in-man observation of Talaromyces marneffei-transmission by organ transplantation. Mycoses. 2017;60(3):213-217. Available at: 28. Sirisanthana T. Penicillium marneffei infection in patients with AIDS. Emerg Infect Dis. 2001;7(3 Suppl):561. Available at: 29. Chen J, Zhang R, Shen Y, et al. Clinical Characteristics and Prognosis of Penicilliosis Among human immunodeficiency virus-infected patients in eastern China. Am J Trop Med Hyg. 2017;96(6):1350-1354. Available at: 30. Le T, Huu Chi N, Kim Cuc NT, et al. AIDS-associated Penicillium marneffei infection of the central nervous system. Clin Infect Dis. 2010;51(12):1458-1462. Available at: 31. Limper AH, Adenis A, Le T, Harrison TS. Fungal infections in HIV/AIDS. Lancet Infect Dis. 2017;17(11):e334-e343. Available at: 32. Zheng J, Gui X, Cao Q, et al. A clinical study of acquired immunodeficiency syndrome associated Penicillium marneffei infection from a non-endemic area in China. PLoS One. 2015;10(6):e0130376. Available at: 33. Supparatpinyo K, Sirisanthana T. Disseminated Penicillium marneffei infection diagnosed on examination of a peripheral blood smear of a patient with human immunodeficiency virus infection. Clin Infect Dis. 1994;18(2):246-247. Available at: 34. Deng Z, Ribas JL, Gibson DW, Connor DH. Infections caused by Penicillium marneffei in China and Southeast Asia: review of eighteen published cases and report of four more Chinese cases. Rev Infect Dis. 1988;10(3):640-652. Available at: 35. Supparatpinyo K, Chiewchanvit S, Hirunsri P, Uthammachai C, Nelson KE, Sirisanthana T. Penicillium marneffei infection in patients infected with human immunodeficiency virus. Clin Infect Dis. 1992;14(4):871-874. Available at: 36. LoBuglio KF, Taylor JW. Phylogeny and PCR identification of the human pathogenic fungus Penicillium marneffei. J Clin Microbiol. 1995;33(1):85-89. Available at: 37. Pornprasert S, Praparattanapan J, Khamwan C, et al. Development of TaqMan real-time polymerase chain reaction for the detection and identification of Penicillium marneffei. Mycoses. 2009;52(6):487-492. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-16 38. Hien HTA, Thanh TT, Thu NTM, et al. Development and evaluation of a real-time polymerase chain reaction assay for the rapid detection of Talaromyces marneffei MP1 gene in human plasma. Mycoses. 2016;59(12):773-780. Available at: 39. Dankai W, Pongpom M, Vanittanakom N. Validation of reference genes for real-time quantitative RT-PCR studies in Talaromyces marneffei. J Microbiol Methods. 2015;118:42-50. Available at: 40. Huang YT, Hung CC, Liao CH, Sun HY, Chang SC, Chen YC. Detection of circulating galactomannan in serum samples for diagnosis of Penicillium marneffei infection and cryptococcosis among patients infected with human immunodeficiency virus. J Clin Microbiol. 2007;45(9):2858-2862. Available at: 41. Thu NT, Chan JF, Hien HTA, et al. Clinical performance of the Mp1p immunoassay for rapid diagnosis of Talaromyces marneffei infection. Presented at: Conference on Retroviruses and Opportunistic Infections; 2017. Seattle, WA. 42. Thu N, Dat V, Chan J, et al. Asymptomatic Talaromyces marneffei infection is associated with HIV mortality. Presented at: Asia Pacific AIDS and CoInfection Conference; 2018. Hong Kong, China. 43. Borman AM, Fraser M, Szekely A, Johnson EM. Rapid and robust identification of clinical isolates of Talaromyces marneffei based on MALDI-TOF mass spectrometry or dimorphism in Galleria mellonella. Med Mycol. 2019;57(8):969-975. Available at: 44. Lau SK, Lam CS, Ngan AH, et al. Matrix-assisted laser desorption ionization time-of-flight mass spectrometry for rapid identification of mold and yeast cultures of Penicillium marneffei. BMC Microbiol. 2016;16:36. Available at: 45. Li L, Chen K, Dhungana N, Jang Y, Chaturvedi V, Desmond E. Characterization of clinical isolates of Talaromyces marneffei and related species, California, USA. Emerg Infect Dis. 2019;25(9):1765-1768. Available at: 46. Lau SK, Lo GC, Lam CS, et al. In vitro activity of posaconazole against Talaromyces marneffei by broth microdilution and Etest methods and comparison to itraconazole, voriconazole, and anidulafungin. Antimicrob Agents Chemother. 2017;61(3). Available at: 47. Lei HL, Li LH, Chen WS, et al. Susceptibility profile of echinocandins, azoles and amphotericin B against yeast phase of Talaromyces marneffei isolated from HIV-infected patients in Guangdong, China. Eur J Clin Microbiol Infect Dis. 2018;37(6):1099-1102. Available at: 48. Chariyalertsak S, Supparatpinyo K, Sirisanthana T, Nelson KE. A controlled trial of itraconazole as primary prophylaxis for systemic fungal infections in patients with advanced human immunodeficiency virus infection in Thailand. Clin Infect Dis. 2002;34(2):277-284. Available at: 49. Chaiwarith R, Fakthongyoo A, Praparattanapan J, Boonmee D, Sirisanthana T, Supparatpinyo K. Itraconazole vs fluconazole as a primary prophylaxis for fungal infections in HIV-infected patients in Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-17 Thailand. Curr HIV Res. 2011;9(5):334-338. Available at: 50. Supparatpinyo K, Nelson KE, Merz WG, et al. Response to antifungal therapy by human immunodeficiency virus-infected patients with disseminated Penicillium marneffei infections and in vitro susceptibilities of isolates from clinical specimens. Antimicrob Agents Chemother. 1993;37(11):2407-2411. Available at: 51. Sirisanthana T, Supparatpinyo K, Perriens J, Nelson KE. Amphotericin B and itraconazole for treatment of disseminated Penicillium marneffei infection in human immunodeficiency virus-infected patients. Clin Infect Dis. 1998;26(5):1107-1110. Available at: 52. Ouyang Y, Cai S, Liang H, Cao C. Administration of voriconazole in disseminated Talaromyces (Penicillium) marneffei infection: a retrospective study. Mycopathologia. 2017;182(5-6):569-575. Available at: 53. Supparatpinyo K, Schlamm HT. Voriconazole as therapy for systemic Penicillium marneffei infections in AIDS patients. Am J Trop Med Hyg. 2007;77(2):350-353. Available at: 54. Supparatpinyo K, Chiewchanvit S, Hirunsri P, et al. An efficacy study of itraconazole in the treatment of Penicillium marneffei infection. J Med Assoc Thai. 1992;75(12):688-691. Available at: 55. Le T, Kinh NV, Cuc NTK, et al. A trial of itraconazole or amphotericin B for HIV-associated talaromycosis. N Engl J Med. 2017;376(24):2329-2340. Available at: 56. Supparatpinyo K, Perriens J, Nelson KE, Sirisanthana T. A controlled trial of itraconazole to prevent relapse of Penicillium marneffei infection in patients infected with the human immunodeficiency virus. N Engl J Med. 1998;339(24):1739-1743. Available at: 57. Hall C, Hajjawi R, Barlow G, Thaker H, Adams K, Moss P. Penicillium marneffei presenting as an immune reconstitution inflammatory syndrome (IRIS) in a patient with advanced HIV. BMJ Case Rep. 2013;2013. Available at: 58. Liu X, Wu H, Huang X. Disseminated Penicillium marneffei infection with IRIS. IDCases. 2015;2(4):92-93. Available at: 59. Thanh NT, Vinh LD, Liem NT, et al. Clinical features of three patients with paradoxical immune reconstitution inflammatory syndrome associated with Talaromyces marneffei infection. Med Mycol Case Rep. 2018;19:33-37. Available at: 60. Chaiwarith R, Charoenyos N, Sirisanthana T, Supparatpinyo K. Discontinuation of secondary prophylaxis against penicilliosis marneffei in AIDS patients after HAART. AIDS. 2007;21(3):365-367. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV Z-18 61. Pilmis B, Jullien V, Sobel J, Lecuit M, Lortholary O, Charlier C. Antifungal drugs during pregnancy: an updated review. J Antimicrob Chemother. 2015;70(1):14-22. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-1 Toxoplasmosis Updated: September 16, 2024 Reviewed: September 16, 2024 Toxoplasma gondii is a protozoan that can commonly cause asymptomatic infection, a mononucleosis-like syndrome, retinochoroiditis, or congenital infection in immunocompetent individuals, but it presents most often as toxoplasma encephalitis (TE) in people with HIV who are severely immunocompromised.1-4 Toxoplasmosis in people with HIV appears to occur mainly due to reactivation of latent tissue cysts from a prior infection; primary infection is occasionally associated with acute cerebral or disseminated disease. Epidemiology Primary infection occurs most commonly after consumption of undercooked meat, unwashed fruits or vegetables, water, or unpasteurized milk containing viable organisms, or ingesting oocysts that have been shed in cat feces and sporulated in the environment, a process that takes at least 24 hours. In up to 50% of individuals, primary infection can occur in the absence of conventional risk factors.5 Infection can also be transmitted congenitally, or rarely following organ transplant or blood transfusion.6-9 The organism is not transmitted through direct person-to-person contact. Seroprevalence of anti-Toxoplasma antibody, indicating prior infection, can vary substantially within the United States based on geography and demographics, with an overall prevalence of approximately 11%, versus 40% to 80% in certain European, Latin American, Asian, and African countries.10-12 In the era before antiretroviral therapy (ART), the 12-month incidence of TE was approximately 33% in patients with advanced immunodeficiency who were seropositive for T. gondii and not receiving prophylaxis with drugs active against the disease. A very low incidence of toxoplasmosis is seen in people with HIV who are seronegative for T. gondii. In these individuals, their toxoplasmosis presumably represents primary infection, reactivation of latent disease in individuals who cannot produce detectable antibodies, or the use of insensitive assays.13,14 Clinical Manifestations Clinical disease related to immunodeficiency is rare among people with HIV with CD4 T lymphocyte (CD4) cell counts >200 cells/mm3. People with CD4 counts <50 cells/mm3 are at greatest risk.1,3,14,15 Among people with HIV, the most common clinical presentation of T. gondii infection is focal encephalitis, with subacute onset of headache, focal neurologic deficits (e.g., hemiparesis), and sometimes fever.1,3,15 People with HIV also may present with non-focal encephalitis, with manifestations including isolated headache and generalized seizures.16 Focal neurological abnormalities may be present on physical examination. In the absence of treatment, disease progression may result in seizures, stupor, coma, and death. Computed tomography (CT) scan or magnetic resonance imaging (MRI) of the brain following intravenous contrast administration will typically show multiple contrast-enhancing lesions, with a predilection for the basal ganglia, often with edema and associated mass effect.1,15,17-19 Toxoplasmosis can more rarely manifest as a single brain lesion or diffuse encephalitis without evidence of focal brain lesions on imaging studies.16 The latter presentation tends to be rapidly progressive and fatal. Retinochoroiditis, pneumonia, adenopathy, and evidence of other multifocal organ system involvement can occur but are uncommon in people with HIV. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-2 Diagnosis People with HIV and concomitant TE are usually seropositive for anti-toxoplasma immunoglobulin G (IgG) antibodies.1,3,15,20 The absence of IgG antibody makes a diagnosis of toxoplasmosis unlikely but not impossible. Anti-toxoplasma immunoglobulin M (IgM) antibodies are usually absent and should not be requested unless primary infection is suspected. Quantitative antibody titers are not useful for diagnosis. Definitive diagnosis of TE requires a compatible clinical syndrome, identification of one or more mass lesions by CT or MRI, and detection of the organism in a clinical sample. A presumptive diagnosis is based on a consistent clinical and radiographic presentation, presence of anti-Toxoplasma IgG antibodies, and response to anti-Toxoplasma therapy, but without detection of the organism. Most diagnoses are made either presumptively or based on a positive cerebrospinal fluid (CSF) toxoplasma polymerase chain reaction (PCR). On imaging studies, toxoplasmosis presents as contrast-enhancing lesions (typically ring-enhancing), with a predilection for the basal ganglia. MRI has sensitivity superior to that of CT and should be obtained in patients with equivocal or negative CT studies. Positron emission tomography18 or single-photon emission CT scanning19 may be helpful in distinguishing between TE and primary central nervous system (CNS) lymphoma, but no imaging technique is completely specific. For TE, detection of the organism requires either a brain biopsy, most commonly stereotactic, or a positive CSF PCR test. Hematoxylin and eosin stains can be used for detection of T. gondii in biopsies, but sensitivity is significantly increased if immunoperoxidase staining is used and if experienced laboratories process the specimens.21 If safe and feasible, a lumbar puncture should be performed for T. gondii PCR, as well as for cytology, culture, cryptococcal antigen, and PCR for Mycobacterium tuberculosis, Epstein-Barr virus (EBV), and JC virus (JCV) depending on imaging findings. PCR for cytomegalovirus and varicella-zoster virus, as well as testing for syphilis, may also be considered. Detection of T. gondii by PCR in CSF has high specificity (96% to 100%), but low sensitivity (50%), especially once specific anti-Toxoplasma therapy has been started.22-25 The differential diagnosis of CNS lesions with mass effect in patients with AIDS most often includes primary CNS lymphoma, tuberculosis, and endemic fungal infection (e.g., cryptococcosis). Lymphoma can be indistinguishable from TE radiographically, both frequently presenting with ring-enhancing lesions, although lymphoma presents more often with a single lesion.26 In the absence of immune reconstitution inflammatory syndrome (IRIS), progressive multifocal leukoencephalopathy (PML) can be distinguished based on imaging studies. PML lesions typically involve white matter rather than gray matter, are usually non-contrast-enhancing, and produce no mass effect. There are a large number of less common causes of focal neurologic disease in people with AIDS including Chagas disease, metastatic tumors, and pyogenic brain abscess, particularly in people who inject drugs. Given the risks associated with a brain biopsy, and the difficulty in obtaining one at many centers, a presumptive diagnosis of TE is established based on an objective response to empiric therapy.27 Brain biopsy is then reserved for patients who fail to respond to specific therapy, although earlier biopsy should be strongly considered if results from imaging, serology, or CSF PCR do not confirm toxoplasmosis or suggest an etiology other than toxoplasmosis. In patients with contrast-enhancing lesions, detection of EBV in the CSF by PCR should raise concern for CNS lymphoma, especially Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-3 when quantitative results show CSF levels above 10,000 EBV copies/mL; however, it is not diagnostic by itself.28-30 In people with HIV receiving ART, PML-IRIS may also present with contrast-enhancing lesions, in which case JCV by PCR in CSF is highly suggestive of PML.31 Preventing Exposure People with HIV should be counseled regarding sources of Toxoplasma infection. Those with CD4 counts <200 cells/mm3 should be tested for IgG antibody to Toxoplasma soon after they are diagnosed with HIV to detect latent infection with T. gondii (BIII). To minimize risk of acquiring toxoplasmosis, people with HIV, especially those with CD4 counts <200 cells/mm3, should be advised not to eat raw or undercooked meat, including undercooked lamb, beef, pork, or venison, and not to eat raw shellfish, including oysters, clams, and mussels (BIII). Lamb, beef, venison, and pork should be cooked to an internal temperature of 165 °F to 170 °F;32 meat cooked until it is no longer pink inside usually has an internal temperature of 165 °F to 170 °F, and therefore, from a more practical perspective, satisfies this requirement. People with HIV should wash their hands after contact with raw meat and after gardening or other contact with soil; they should also wash fruits and vegetables well before eating them raw (BIII). Cat owners with HIV whose CD4 counts are <200 cells/mm3 and who are seronegative should be advised to have a nonpregnant person without HIV change the litter box daily. If a person with HIV must change the litter box themselves, they should wear gloves and wash their hands thoroughly afterward (BIII). They also should be encouraged to keep their cats inside and not to adopt or handle stray cats (BIII). Cats should be fed only canned or dried commercial food or well-cooked table food, not raw or undercooked meats (BIII). People with HIV do not need to be advised to part with their cats or to have their cats tested for toxoplasmosis (BIII). Preventing Disease Recommendations for Preventing Toxoplasma gondii Encephalitis Preventing 1st Episode of Toxoplasma gondii Encephalitis (Primary Prophylaxis) Indications for Initiating Primary Prophylaxis • Toxoplasma IgG positive patients with CD4 count <100 cells/mm3 (AII) Note: Listed regimens are also effective against PCP. Preferred Regimen • TMP-SMX one DS PO daily (AII) Alternative Regimens • TMP-SMX one DS PO three times weekly (BII), or • TMP-SMX one SS PO daily (BIII), or • Dapsonea 50 mg PO daily + (pyrimethamine 50 mg + leucovorin 25 mg) PO weekly (BI), or • (Dapsonea 200 mg + pyrimethamine 75 mg + leucovorin 25 mg) PO weekly (CI), or • Atovaquoneb 1,500 mg PO daily (CIII), or Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-4 • (Atovaquoneb 1,500 mg + pyrimethamine 25 mg + leucovorin 10 mg) PO daily (CIII) Indication for Discontinuing Primary Prophylaxis • CD4 count >200 cells/mm3 for >3 months and sustained HIV RNA below limits of detection in response to ARV therapy (AI); or • Can consider if CD4 count is 100–200 cells/mm3 and HIV RNA remains below limits of detection for at least 3–6 months (BII) Indication for Restarting Primary Prophylaxis • CD4 count <100 cells/mm3 (AIII) • CD4 count 100–200 cells/mm3 and HIV RNA above detection limits (AIII) Pregnancy Considerations Indication, drugs, and doses are the same as for nonpregnant individuals. a Whenever possible, patients should be tested for G6PD deficiency before administrating dapsone. Alternative agent should be used if the patient is found to have G6PD deficiency. b Atovaquone should be taken with meals or nutritional supplement to ensure adequate oral absorption. Key: ARV = antiretroviral; CD4 = CD4 T lymphocyte; DS = double-strength; G6PD = glucose-6-phosphate dehydrogenase; IgG = immunoglobulin G; PCP = Pneumocystis pneumonia; PO = orally; SS = single-strength; TMP-SMX = trimethoprim-sulfamethoxazole Indication for Primary Prophylaxis Toxoplasma-seropositive people who have CD4 counts <100 cells/mm3 should receive prophylaxis against TE (AII).33,34 The preferred primary prophylaxis regimen is one double-strength tablet daily of TMP-SMX (AII). This is also the preferred prophylaxis regimen for Pneumocystis jirovecii pneumonia (PCP), which all people at risk for toxoplasmosis are also at risk for developing. TMP-SMX, one double-strength tablet three times weekly, is an alternative (BII). TMP-SMX, one single-strength tablet daily, is also an option (BIII). If TMP-SMX cannot be tolerated, the recommended alternative is dapsone plus pyrimethamine plus leucovorin, which also is effective against PCP (see table for rating based on dapsone and pyrimethamine doses).35-37 Atovaquone with or without pyrimethamine plus leucovorin is active against PCP and can also be considered for toxoplasmosis (CIII). For people in whom other alternatives are not possible, pyrimethamine (plus leucovorin) alone may have some efficacy as primary prophylaxis (CIII).14 Aerosolized pentamidine does not protect against TE and is not recommended for anti-Toxoplasma prophylaxis (AI).33,38 Discontinuing Primary Prophylaxis Prophylaxis against TE should be discontinued in adults and adolescents with HIV receiving ARV therapy with sustained suppression of plasma HIV RNA levels below the detection limits of available assays whose CD4 counts increase to >200 cells/mm3 for more than 3 months (AI).39-43 In this setting primary TE prophylaxis should be discontinued because it adds little value in preventing toxoplasmosis and increases pill burden, potential for drug toxicity and interaction, likelihood of development of drug-resistant pathogens, and cost. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-5 A combined analysis of 10 European cohorts found a low incidence of TE in patients with CD4 counts between 100 and 200 cells/mm3, who were receiving ARVs and had HIV RNA plasma viral loads <400 copies/mL, and who had stopped or never received TE prophylaxis; this suggests that primary TE prophylaxis can be safely discontinued in patients with CD4 counts 100 to 200 cells/mm3 and HIV plasma RNA levels below limits of detection with commercial assays.44 Similar observations have been made with regard to stopping primary or secondary prophylaxis for PCP.44-46 Data on which to base specific recommendations are inadequate, but one approach would be to stop primary prophylaxis in patients with CD4 counts of 100 to 200 cells/mm3 if HIV plasma RNA levels remain below limits of detection for at least 3 to 6 months (BII).44 Treating Disease Recommendations for Treating Toxoplasma gondii Encephalitis Treating Toxoplasma gondii Encephalitis Preferred Regimens for Acute Infection • Pyrimethamine 200 mg PO once, followed by weight-based dosing (AI): o Body weight ≤60 kg: pyrimethamine 50 mg PO daily + sulfadiazine 1,000 mg PO every 6 hours + leucovorin 10–25 mg PO daily (can increase to 50 mg daily or twice daily) o Body weight >60 kg: pyrimethamine 75 mg PO daily + sulfadiazine 1,500 mg PO every 6 hours + leucovorin 10–25 mg PO daily (can increase to 50 mg daily or twice daily) or • TMP-SMX (TMP 5 mg/kg and SMX 25 mg/kg) (IV or PO) twice daily (AII) Note: If pyrimethamine is unavailable or cannot be obtained without delay due to costs or other factors, TMP-SMX should be used in place of pyrimethamine-sulfadiazine (AII). Alternative Regimens for Acute Infection • (Pyrimethamine + leucovorin)c plus clindamycin 600 mg IV or PO every 6 hours (AI); preferred alternative for patients intolerant of sulfadiazine or who do not respond to pyrimethamineb-sulfadiazine; must add additional agent for PCP prophylaxis (AII), or • Atovaquoneb 1,500 mg PO twice daily + (pyrimethamine +leucovorin)c (BII), or • Atovaquoneb 1,500 mg PO twice daily + sulfadiazined (BII), or • Atovaquoneb 1,500 mg PO twice daily (BII) • For patients with a history of sulfa allergy, rapid sulfa desensitization may be attempted using one of several published strategies (BI). • During the desensitization phase, atovaquone 1,500 mg PO should be administered twice daily until therapeutic doses of TMP-SMX (TMP 5 mg/kg and SMX 25 mg/kg) twice daily are achieved (CIII). Total Duration for Treating Acute Infection • At least 6 weeks (BII); longer duration if clinical or radiologic disease is extensive or response is incomplete at 6 weeks • After completion of the acute therapy, all patients should be continued on chronic maintenance therapy as outlined below. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-6 Chronic Maintenance Therapy for Toxoplasma gondii Encephalitis Preferred Regimens • Pyrimethamine 25–50 mg PO daily + sulfadiazine 2,000–4,000 mg PO daily (in 2 to 4 divided doses) + leucovorin 10–25 mg PO daily (AI), or • TMP-SMX DS one tablet twice daily (AII) Alternative Regimens • (Pyrimethamine 25–50 mg + leucovorin 10–25 mg) PO daily plus clindamycin 1,800 mg PO daily dose (in 3 or 4 divided doses) (BI); must add additional agent to prevent PCP (AII), or • Atovaquoneb 750–1,500 mg PO twice daily + (pyrimethamine 25 mg + leucovorin 10 mg) PO daily (BII), or • Atovaquoneb 750–1,500 mg PO twice daily + sulfadiazine 2,000–4,000 mg PO daily (in 2 to 4 divided doses) (BII), or • Atovaquoneb 750–1,500 mg PO twice daily (BII) Criteria for Discontinuing Chronic Maintenance Therapy (BI) • Successfully completed initial therapy, and • Asymptomatic of signs and symptoms of TE, and • CD4 count >200 cells/mm3 for >6 months in response to ARVs Criteria for Restarting Secondary Prophylaxis/Chronic Maintenance • CD4 count <200 cells/mm3 regardless of HIV RNA level (AIII) Other Considerations • Adjunctive corticosteroids (e.g., dexamethasone) should only be administered when clinically indicated to treat a mass effect associated with focal lesions or associated edema (BIII) or for control of clinically significant IRIS symptoms in conjunction with ART and anti-toxoplasma therapy (CIII); discontinue as soon as clinically feasible. For patients in whom the diagnosis of TE is presumptive based in part on clinical response, one needs to be careful as CNS lymphoma may also respond to steroids clinically and radiologically. • Antiseizure medications should be administered to patients with TE and associated seizures (AII) and continued through at least the period of acute treatment (BII); antiseizure medications should not be used as prophylaxis in patients without seizures (BII). Pregnancy Considerations Suspected or Confirmed Acute Toxoplasmosis During Pregnancy Initial Therapy (primary infection during pregnancy or symptomatic reactivation of T. gondii without encephalitis) • Initiation of therapy before 14 weeks of pregnancy: spiramycin administered orally at a dosage of 1.0 g (or 3 million U) every 8 hours (total dosage of 3 g or 9 million U per day) (AII) • Initiation of therapy on or after 14 weeks of pregnancy: pyrimethamine (50 mg PO twice daily x 2 days, then 50 mg PO daily) + sulfadiazine (75 mg/kg PO x 1 day, then 50 mg/kg PO twice daily) + leucovorin (10–20 mg/day during and 1 week after pyrimethamine use) (AII) Fetal Assessment • Amniocentesis for toxoplasmosis PCR to be done at 18 weeks gestation or later (BIII) • Fetal ultrasonography every 4 weeks until delivery (AIII) • If no evidence of fetal infection (negative amniotic fluid PCR, no fetal ultrasonographic abnormalities), continue initial therapy. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-7 Treatment of Toxoplasma gondii Encephalitis During Pregnancy • Treatment regimen is the same as for nonpregnant individuals (BIII). • In general, pyrimethamine should be avoided in the first trimester of pregnancy because of teratogenicity concerns, but in the case of TE, the benefit of using pyrimethamine to the pregnant individual outweighs the risk to the fetus. Fetal Infection Criteria for Initiating Treatment for Fetal Infection • Positive amniotic fluid PCR, and/or • Fetal ultrasonographic findings suggestive of congenital toxoplasmosis Treatment for Fetal Infection • Pyrimethamine + sulfadiazine + leucovorin until delivery (AII) Note: If pyrimethamine is unavailable or cannot be obtained without delay due to costs or other factors, TMP-SMX DS one tablet twice daily plus spiramycin 1 g PO three times a day plus leucovorin 4 mg daily should be utilized in place of pyrimethamine-sulfadiazine (BII). a Whenever possible, patients should be tested for G6PD deficiency before administrating dapsone. Alternative agent should be used if the patient is found to have G6PD deficiency. b Atovaquone should be taken with meals or nutritional supplement to ensure adequate oral absorption. c Pyrimethamine and leucovorin doses: Same doses and frequency as listed in Preferred Regimen for Acute Infection d Sulfadiazine dose: Same as weight-based dose and frequency listed in Preferred Regimen for Acute Infection Key: ART = antiretroviral therapy; ARV = antiretroviral; CD4 = CD4 T lymphocyte; CNS = central nervous system; DS = double-strength; G6PD = glucose-6-phosphate dehydrogenase; IRIS = immune reconstitution inflammatory syndrome; IV = intravenous; PCP = Pneumocystis pneumonia; PCR = polymerase chain reaction; PO = orally; SMX = sulfamethoxazole; TE = toxoplasma encephalitis; TMP = trimethoprim; TMP-SMX = trimethoprim-sulfamethoxazole For many years, the initial therapy of choice for TE has been the combination of pyrimethamine plus sulfadiazine plus leucovorin (AI).2,47-49 Pyrimethamine penetrates the brain parenchyma efficiently even in the absence of inflammation.50 Leucovorin reduces the likelihood of hematologic toxicities associated with pyrimethamine therapy.51 Pyrimethamine, however, has become extremely expensive and can be difficult to obtain in the United States. TMP-SMX has been used with increasing frequency as a preferred regimen (AII), although large, randomized trials comparing TMP-SMX to pyrimethamine plus sulfadiazine have not been performed. In a small (77 patients) randomized trial, TMP-SMX was reported to be as effective and better tolerated than pyrimethamine-sulfadiazine.52 Others have reported similar efficacy of TMP-SMX to pyrimethamine plus sulfadiazine in open-label observational studies.53,54 A recent meta-analysis found that TMP-SMX was as effective as pyrimethamine plus sulfadiazine, but was associated with less toxicity.55 If pyrimethamine is unavailable or cannot be obtained without delay due to costs or other factors, TMP-SMX should be utilized (AII). Pyrimethamine plus leucovorin plus clindamycin47,48 is the preferred alternative regimen for patients with TE who cannot tolerate sulfa drugs or do not respond to first-line therapy (AI). This combination, however, does not prevent PCP, therefore additional PCP prophylaxis must be administered when it is used (AII) (see discussion under Preventing Recurrence).56 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-8 For patients with a history of sulfa allergy, rapid sulfa desensitization may be attempted using one of several published strategies (BI).57-62 During the desensitization period, atovaquone with or without pyrimethamine should be administered until therapeutic doses of TMP-SMX are achieved (CIII). No well-studied options exist for patients who cannot take an oral regimen. No parenteral formulation of pyrimethamine exists and the only widely available parenteral sulfonamide is the sulfamethoxazole component of TMP-SMX. Some specialists will use parenteral TMP-SMX (BII) or oral pyrimethamine plus parenteral clindamycin (CIII) as initial treatment in severely ill patients who require parenteral therapy. Atovaquone (with meals or oral nutritional supplements) plus pyrimethamine plus leucovorin, atovaquone plus sulfadiazine, or (for patients intolerant of both pyrimethamine and sulfadiazine) atovaquone as a single agent also have been shown to be effective in treating TE (BII).63,64,65 However, the relative efficacy of atovaquone-containing regimens compared with other regimens is unknown. Clinicians should be aware that the absorption of the drug varies substantially from patient to patient; plasma levels >18.5 µg/mL are associated with an improved response rate but atovaquone therapeutic drug monitoring is not routinely available.64-66 The following regimens have been reported to have activity in treatment of TE in small cohorts of patients or in case reports of one or several patients: azithromycin plus pyrimethamine plus leucovorin (CII)67,68; clarithromycin plus pyrimethamine plus leucovorin (CIII)69; 5-fluorouracil plus clindamycin (CIII)70; dapsone plus pyrimethamine plus leucovorin (CIII)71; and minocycline or doxycycline combined with either pyrimethamine plus leucovorin, sulfadiazine, or clarithromycin (CIII).72,73 There is rarely a reason to use one of these regimens. Clinical response to acute therapy occurs in ~90% of patients with TE within 14 days of initiating appropriate anti-Toxoplasma treatment.2 The reasons why some patients fail therapy are not clearly proven; whether such failures are due to poor adherence, other host factors, or antimicrobial resistance has not been well delineated. Acute therapy for TE should be continued for 6 weeks, if there is clinical and radiologic improvement (BII).1-4 Longer courses may be necessary if clinical or radiologic disease is extensive or response is incomplete at 6 weeks. After completion of the acute therapy, all patients should be continued on chronic maintenance therapy as outlined below (see Preventing Recurrence section below). The radiologic goals for treatment include resolution of the lesion(s) in terms of size, contrast enhancement, and associated edema, although residual contrast-enhancing lesions may persist for prolonged periods, especially in people with HIV receiving ARVs.74 Adjunctive Therapies Adjunctive corticosteroids such as dexamethasone should only be used for treatment of patients with TE when they are clinically indicated to treat a mass effect associated with focal lesions or associated edema (BIII). In those treated with corticosteroids, caution may be needed in diagnosing CNS toxoplasmosis on the basis of treatment response, since primary CNS lymphoma may respond clinically and radiographically to corticosteroids alone; these patients should be monitored carefully as corticosteroids are tapered. In addition, corticosteroids should be discontinued as soon as clinically feasible because of their potential to cause immunosuppression. Patients receiving corticosteroids should be monitored closely for development of other opportunistic infections (OIs), including cytomegalovirus retinitis and tuberculosis. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-9 Antiseizure medications should be administered to patients with TE associated with seizures (AII) but should not be administered prophylactically to patients without seizures (BII). Anticonvulsants, if indicated, should be continued at least through the period of acute therapy (BII). Special Considerations Regarding ART Initiation There are no data on which to base a recommendation regarding when to start ARV therapy in people with HIV and TE. However, many physicians would initiate ARV therapy within 2 to 3 weeks after the diagnosis of toxoplasmosis, based on the significantly lower incidence of AIDS progression or death (a secondary study endpoint) seen in the early ARV therapy arm of a controlled trial of 282 patients with OIs other than tuberculosis (only 5% of whom had toxoplasmosis) who were randomized to early (median 12 days after initiation of OI therapy) versus deferred (median 45 days) initiation of ARV therapy.75 IRIS IRIS associated with TE has been reported but appears to be rare (~5% in one report).76-78 Most cases develop as paradoxical worsening with increase in the size and number of lesions, peri-lesional edema, and an increase in contrast enhancement on MRI.77,79,80 As for IRIS with other infections, corticosteroid therapy, dosed to control symptoms, can be administered in patients with clinically significant symptoms in conjunction with ARVs and anti-Toxoplasma therapy (CIII). Monitoring of Response to Therapy and Adverse Events (Including IRIS) Changes in antibody titers are not useful for monitoring responses to therapy. People with HIV with TE should be monitored routinely for adverse events and clinical and radiologic improvement (AIII). Neurological improvement will occur by 14 days in over 90% of patients2; if no improvement is seen by that time, other diagnoses should be considered. Repeat imaging can be considered at 3 and 6 weeks, or sooner for clinical deterioration.2 After 6 weeks, maintenance therapy at ~50% of treatment doses should be initiated assuming a clinical response has been seen. Common pyrimethamine toxicities such as rash, nausea, and bone marrow suppression (neutropenia, anemia, and thrombocytopenia) often can be reversed by increasing the leucovorin dose to 10, 25, or 50 mg four times daily (CIII). Common sulfadiazine toxicities include rash, fever, leukopenia, hepatitis, nausea, vomiting, diarrhea, renal insufficiency, and crystalluria. Common clindamycin toxicities include fever, rash, nausea, diarrhea (including pseudomembranous colitis or diarrhea related to Clostridium difficile toxin), and hepatotoxicity. Common TMP-SMX toxicities include rash, fever, leukopenia, thrombocytopenia, and hepatotoxicity. Common atovaquone toxicities include nausea, vomiting, diarrhea, rash, headache, hepatotoxicity, and fever. Drug interactions between certain anticonvulsants (e.g., phenytoin, phenobarbital, carbamazepine), dexamethasone and antiretroviral (ARV) agents should be evaluated carefully; if necessary, doses should be adjusted, or alternative anticonvulsants or ARV agents should be used. Managing Treatment Failure A brain biopsy should be strongly considered in patients who did not have an initial biopsy prior to therapy and who fail to respond to initial therapy for TE (BII) as defined by clinical or radiologic deterioration during the first week despite adequate therapy, or who do not show clinical Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-10 improvement within 10 to 14 days. A switch to an alternative regimen, as previously described, should be considered for those who undergo brain biopsy and have confirmed histopathologic evidence of TE, or who have a CSF PCR positive for T. gondii (BIII). In patients who adhere to their regimens, disease recurrence is unusual in the setting of chronic maintenance therapy after an initial clinical and radiographic response. Preventing Recurrence When to Start Chronic Maintenance Therapy Patients who have completed initial therapy for TE should be given chronic maintenance therapy to suppress infection (AI)47,48 until immune reconstitution occurs as a consequence of ARV therapy. The combination of pyrimethamine plus sulfadiazine plus leucovorin is highly effective as suppressive therapy for patients with TE (AI) and provides protection against PCP (AII). Although sulfadiazine is routinely dosed as a four-times-a-day regimen, a pharmacokinetic study suggests bioequivalence for the same total daily dose when given either twice or four times a day,81 and limited clinical experience suggests that twice-daily dosing is effective.82 For patients being treated with TMP-SMX, this drug should be continued as chronic maintenance at a reduced dose of one double-strength tablet twice daily (AII).52 A small, uncontrolled study in patients who had been receiving ART for a median of 13 months suggested that TMP-SMX could be used as a suppressive regimen in place of pyrimethamine-sulfadiazine or pyrimethamine-clindamycin to reduce pill burden.83 Pyrimethamine plus leucovorin plus clindamycin is commonly used as suppressive therapy for patients with TE who cannot tolerate sulfa drugs (BI). Because of the high failure rate observed with lower doses,47 a dose of 1,800 mg clindamycin daily in 3 or 4 divided doses is recommended. Because this regimen does not provide protection against PCP (AII),56 an additional agent, such as dapsone or aerosol pentamidine, must be used. Atovaquone also is active against both TE65,66 and PCP84 and can be used alone, with sulfadiazine, or with pyrimethamine and leucovorin in patients with TE (BII). When to Stop Chronic Maintenance Therapy Chronic maintenance therapy for TE can be discontinued in adults and adolescents with HIV, if they have successfully completed initial therapy for TE, remain asymptomatic with regard to signs and symptoms of TE, and have an increased CD4 count to >200 cells/mm3 for >6 months in response to ARV therapy (BI), although occasional recurrences have been reported.40,43,85,86 As part of the evaluation to determine whether discontinuation of therapy is appropriate, some specialists recommend obtaining an MRI of the brain to assess for resolution of brain lesions, although residual contrast-enhancing lesions can be seen for prolonged periods in some ARV-treated patients. When to Restart Primary Prophylaxis or Maintenance Therapy Primary prophylaxis should be reintroduced if the CD4 count decreases to <100 cells/mm3 (AIII) regardless of the HIV plasma viral load. Based on results from the COHERE study, an observational study of multiple cohorts, primary prophylaxis may not need to be restarted in patients with CD4 counts of 100 to 200 cells/mm3 who have had HIV plasma RNA levels below limits of detection for at least 3 to 6 months (BII).44,45 For patients with CD4 counts of 100 to 200 cells/mm3 with HIV plasma viral load above detection limits of the utilized assay, PCP prophylaxis should be Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-11 reintroduced, and most, but not all, regimens will provide prophylaxis for toxoplasmosis as well (AIII). Because there are no published data examining the risk of recurrence in patients stopping chronic maintenance therapy for TE when the CD4 count is between 100 and 200 cells/mm3, and recurrent TE can be debilitating and potentially life-threatening, maintenance therapy should be reintroduced if the CD4 count decreases to <200 cells/mm3 (AIII) regardless of the HIV plasma viral load.87 Special Considerations During Pregnancy Diagnosis During Pregnancy Documentation of baseline T. gondii serologic status (IgG only) should be obtained in people with HIV who become pregnant because of concerns regarding congenital toxoplasmosis. Although perinatal transmission of T. gondii normally occurs only with acute infection in the immunocompetent host, case reports have documented transmission with reactivation of chronic infection in pregnant people with HIV with severe immunosuppression.88,89 Knowing toxoplasmosis sero-status at the beginning of pregnancy may be helpful in delineating future risks and interpreting serologic testing performed later in pregnancy should there be heightened concerns for maternal infection and/or fetal transmission. Toxoplasma infection during pregnancy is usually asymptomatic. Non-specific symptoms may include fever, fatigue, headache, and myalgia after a 5- to 23-day incubation period. In the setting of parasitemia during pregnancy, the placenta may become infected and result in fetal infection. The risk of congenital toxoplasmosis (infection of the fetus) is highest in the setting of a primary infection during pregnancy as compared to reactivation. While the risk of transmission to the fetus increases with gestational age, with the highest risk in the third trimester, the sequelae to the fetus are more severe when toxoplasmosis is acquired early in gestation.90,91 Toxoplasmosis diagnostic considerations are not affected by pregnancy. Primary T. gondii infection can typically be distinguished from chronic infection with the use of multiple serologic assays, including IgG, IgM, immunoglobulin A, and immunoglobulin E antibodies; IgG avidity; and the differential agglutination tests.92,93 Because serologic testing is often difficult to interpret and prompt treatment and counseling is particularly important during pregnancy, people with HIV with suspected primary T. gondii infection during pregnancy should be managed in consultation with a maternal-fetal medicine specialist where available. The care team may elect to access specialized laboratory testing93,94 (e.g., the Palo Alto Medical Foundation Toxoplasmosis Serology Laboratory [PAMF-TSL], Palo Alto, CA, at 650-853-4828 and toxolab@pamf.org; and the National Collaborative Chicago-based Congenital Toxoplasmosis Study [NCCCTS], Toxoplasmosis Center, Chicago, IL, 773-834-4130, eFax 773-834 3577 and rmcleod@midway.uchicago.edu). Screening The value of routine toxoplasmosis screening programs is debated in the United States but generally accepted in other countries. In countries such as France where pregnant people are universally screened and treated, offspring who acquire toxoplasmosis are reported to have primarily mild disease and rarely severe disease. In contrast, in countries without a universal screening program (e.g., United States), offspring who acquire toxoplasmosis mostly present with severe disease.95 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-12 Toxoplasmosis is not a nationally notifiable illness, is only reportable in eight states, and case definitions vary.12 Preventing Congenital Infection: Initial Therapy and Surveillance Pregnant people with HIV who have evidence of primary toxoplasmic infection, without TE, should be evaluated and managed during pregnancy in consultation with appropriate specialists (BIII). Recent studies support treatment of toxoplasmosis during pregnancy in an effort to decrease congenital transmission and reduce the severity of clinical signs in the offspring.96-102 In the setting of primary infection during pregnancy or symptomatic reactivation of T. gondii, initial therapy depends on the gestational age at time of acquisition/reactivation. • For patients presumed to have acquired/reactivated infection at less than 14 weeks gestation, spiramycin is recommended to prevent congenital transmission (AII). Spiramycin is not commercially available in the United States. To obtain spiramycin, the provider must call the U.S. Food and Drug Administration directly (301-796-1400) after consultation with PAMF-TSL or NCCCTS (see Diagnosis During Pregnancy for contact information). A clinical pharmacist will assist with the proper paperwork. • For patients presumed to have acquired/reactivated infection at 14 weeks gestation or beyond, pyrimethamine plus sulfadiazine plus leucovorin is recommended, as the risk of fetal transmission is higher (AII). If pyrimethamine is unavailable or cannot be obtained without delay due to costs or other factors, a combination of TMP-SMX, spiramycin, and leucovorin should be utilized in place of pyrimethamine-sulfadiazine (BII).103,104 For pregnant people with suspected primary or symptomatic reactivation of T. gondii during pregnancy, detailed ultrasound examination of the fetus specifically evaluating for hydrocephalus, cerebral calcifications, and growth restriction should be done monthly regardless of gestational age at the time of diagnosis (AIII).93 In addition, patients should undergo an amniocentesis with PCR testing for T. gondii DNA in the amniotic fluid.105 Amniocentesis does not appear to increase the risk of perinatal HIV transmission, particularly in people receiving ARV therapy.106 Therefore, PCR of amniotic fluid can be considered during gestation in pregnant people on ARV therapy with serologic evidence of recently acquired Toxoplasma infection; people suspected to have reactivated their Toxoplasma latent infection during pregnancy; and those with ultrasound findings suggestive of fetal T. gondii infection (BIII).93 In an effort to minimize false-negative results, amniotic fluid testing for T. gondii PCR should be avoided at less than 18-week gestation.107 Congenital Infection For patients whose evaluations do not suggest congenital infection (i.e., no ultrasound findings and negative amniotic fluid PCR), initial therapy should be continued until delivery. For patients started on spiramycin as initial therapy who are found to have a positive PCR in the amniotic fluid and/or ultrasound findings concerning for congenital transmission, therapy should be escalated to pyrimethamine/sulfadiazine/leucovorin (AII), or if pyrimethamine is unavailable, TMP-SMX, spiramycin, and leucovorin (AII). Pediatric-care providers should be informed about birthing parents with HIV who have suspected or confirmed T. gondii infection to allow evaluation of their neonates for evidence of congenital infection (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-13 Toxoplasma Encephalitis During Pregnancy Treatment of pregnant people with TE should be the same as in nonpregnant adults (BIII), including pyrimethamine plus sulfadiazine plus leucovorin (AI), and in consultation with appropriate specialists (BIII).2,47-49 In general pyrimethamine should be avoided in the first trimester of pregnancy because of teratogenicity concerns, but in the case of TE, the benefit of using pyrimethamine to the mother outweighs the risk to the fetus. Of note, this regimen is often used in the treatment of fetuses with toxoplasmosis.93 The preferred alternative regimen for pregnant patients with TE who are unable to tolerate or who fail to respond to first-line therapy is pyrimethamine plus clindamycin plus leucovorin (AI).47,48 If pyrimethamine is unavailable or cannot be obtained without delay due to costs or other factors, TMP-SMX should be utilized in place of pyrimethamine-sulfadiazine or pyrimethamine-clindamycin (BI). Prophylaxis During Pregnancy The indications for primary prophylaxis for TE during pregnancy, and the medications and dosages used, are the same as for nonpregnant individuals with HIV. TMP-SMX is the preferred therapy. The risks of TMP-SMX in the first trimester, as discussed for PCP, must be balanced against the risk of TE. Secondary prophylaxis should be provided, using the same indications as for nonpregnant people. Over the past several decades, dapsone (also used for primary prophylaxis) has been used safely in pregnancy to treat leprosy, malaria, and various dermatologic conditions.108,109 Dapsone appears to cross the placenta.108,110 When providing preconception care for people of pregnancy potential with HIV and receiving TE prophylaxis, providers should discuss the option of deferring pregnancy until TE prophylaxis can be safely discontinued (BIII). Pregnancy-Specific Medication Concerns Spiramycin is recommended to prevent transmission at <14 weeks gestation in the setting of acute primary infection during pregnancy or symptomatic reactivation of T. gondii (AII).101,103,111 Spiramycin is not commercially available in the United States. Please see Preventing Congenital Infection: Initial Therapy and Surveillance on how to obtain spiramycin. Pyrimethamine to prevent transmission should be avoided in the first trimester because of teratogenicity concerns with birth defects in animals, however it is recommended as first-line treatment for maternal TE (BIII), where the benefit of using pyrimethamine in a pregnant person outweighs the risk to the fetus. Additionally, pyrimethamine is often used in the setting of a positive fetal diagnosis.112,113 Pyrimethamine can be administered to pregnant people after the first trimester since human data have not suggested an increased risk of birth defects.89,114-117 Sulfadiazine appears safe in pregnancy, without clear evidence of adverse fetal or neonatal outcome.118,119 Although there are no studies published to date directly linking late third-trimester maternal sulfadiazine to neonatal death or kernicterus, the infant’s care provider should be notified of maternal sulfa use in late pregnancy. Clindamycin, suggested as part of an alternative regimen for patients with TE, is considered safe throughout pregnancy. Atovaquone, used both for prophylaxis and treatment of TE, may be used if indicated. While there are limited data on atovaquone safety in human pregnancy, preclinical studies Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-14 have not demonstrated maternal or fetal toxicity.115 As noted above, dapsone has been used safely in pregnant persons for TE prophylaxis though with long-term therapy, there is a risk of mild hemolysis and a potential—although extremely low—risk of hemolytic anemia in exposed fetuses with glucose-6-phosphate dehydrogenase (or G6PD) deficiency.108,120 A detailed discussion of TMP-SMX and pregnancy is reviewed in the PCP chapter. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV CC-15 References 1. 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Amsterdam: Elsevier; 2007:947. 947. 113. Practice bulletin no. 151: cytomegalovirus, parvovirus B19, varicella zoster, and toxoplasmosis in pregnancy. Obstet Gynecol. 2015;125(6):1510-1525. Available at: 114. Peters PJ, Thigpen MC, Parise ME, Newman RD. Safety and toxicity of sulfadoxine/pyrimethamine: implications for malaria prevention in pregnancy using intermittent preventive treatment. Drug Saf. 2007;30(6):481-501. Available at: 115. Nosten F, McGready R, d’Alessandro U, et al. Antimalarial drugs in pregnancy: a review. Curr Drug Saf. 2006;1(1):1-15. Available at: 116. Wong SY, Remington JS. Toxoplasmosis in pregnancy. Clin Infect Dis. 1994;18(6):853-861; quiz 862. Available at: 117. Deen JL, von Seidlein L, Pinder M, Walraven GE, Greenwood BM. The safety of the combination artesunate and pyrimethamine-sulfadoxine given during pregnancy. Trans R Soc Trop Med Hyg. 2001;95(4):424-428. Available at: 118. Baskin CG, Law S, Wenger NK. Sulfadiazine rheumatic fever prophylaxis during pregnancy: does it increase the risk of kernicterus in the newborn? Cardiology. 1980;65(4):222-225. Available at: 119. Yu PA, Tran EL, Parker CM, et al. Safety of antimicrobials during pregnancy: a systematic review of antimicrobials considered for treatment and postexposure prophylaxis of plague. Clin Infect Dis. 2020;70(70 Suppl 1):S37-S50. Available at: 120. Thornton YS, Bowe ET. Neonatal hyperbilirubinemia after treatment of maternal leprosy. South Med J. 1989;82(5):668. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-1 Varicella-Zoster Virus Diseases Updated: September 7, 2022 Reviewed: January 10, 2024 Epidemiology More than 95% of adults (aged >20 years) born in the United States have immunity to varicella-zoster virus (VZV), mostly due to primary VZV infection, known as varicella (or chickenpox).1 A varicella vaccine became available in the United States in 1995; most children born in the United States after 2005 are immune to varicella as a result of vaccination.2 Reactivation of latent VZV results in herpes zoster (shingles). In the general population, the incidence of herpes zoster is about 3.6 cases per 1,000 person-years, with much higher incidence seen among elderly and immunocompromised individuals. Before the availability of antiretroviral therapy (ART), the incidence of herpes zoster was more than 15-fold higher among adults with HIV than among age-matched controls without HIV.3,4 Herpes zoster can occur in adults with HIV at any CD4 T lymphocyte (CD4) cell count, but with CD4 counts <200 cells/mm3, the risk of disease is higher.5-8 In addition, HIV viremia is associated with an increased risk for incident herpes zoster.9 ART has been shown to reduce the incidence of herpes zoster in adults with HIV, presumably because of immune restoration, although the risk of herpes zoster remains threefold higher in adults with HIV than in the general population.7,10-13 Several studies have demonstrated that the risk of herpes zoster in adults with HIV is increased in the 6-month period immediately after initiation of ART, possibly because of an immune reconstitution inflammatory syndrome (IRIS)-related mechanism.7,10,13,14 Clinical Manifestations Varicella rash tends to have a central distribution, with lesions first appearing on the head, then the trunk, and finally the extremities, evolving through stages of macules, papules, vesicles, pustules, and crusts. The rash is characterized by rapid evolution of lesions during the initial 8 to 12 hours after onset, by successive crops of new lesions, and by the presence of lesions in different stages of development. New vesicle formation continues for 2 to 4 days, accompanied by pruritus, fever, headache, malaise, and anorexia.15 Primary varicella can cause substantial morbidity in adolescents and adults with HIV. Visceral dissemination, especially VZV pneumonitis, is well documented.15 Because most adults with HIV in the United States are VZV seropositive, primary varicella is an uncommon occurrence in this population. Herpes zoster manifests as a painful cutaneous eruption in a dermatomal distribution, often preceded by prodromal pain. The most common sites for herpes zoster are the thoracic dermatomes (40% to 50% of cases), followed by cranial nerve (20% to 25%), cervical (15% to 20%), lumbar (15%), and sacral (5%) dermatomes.16 Skin changes begin with an erythematous maculopapular rash, followed by the appearance of clear vesicles and accompanied by pain, which may be severe. New vesicle formation typically continues for 3 to 5 days, followed by lesion pustulation and scabbing. Crusts typically persist for 2 to 3 weeks. About 20% to 30% of people with HIV have one or more subsequent episodes of herpes zoster, which may involve the same or different dermatomes. The probability of a recurrence of herpes zoster within 1 year of the index episode is approximately 10%.5,17 Approximately 10% to 15% of people with HIV report post-herpetic neuralgia as a complication following herpes zoster.5,18 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-2 When herpes zoster involves the nasociliary branch of the trigeminal nerve, the eye can be affected (herpes zoster ophthalmicus [HZO]), resulting in keratitis (inflammation of the cornea) or anterior uveitis (inflammation of the iris and anterior ciliary body) or both. Vesicles on the tip of the nose (Hutchinson sign) are a clue that the nasociliary branch is involved. With corneal involvement, there may be an initial brief period during which the corneal epithelium is infected with VZV, but the major problem is inflammation of the corneal stroma, which can result in scarring, neovascularization, or necrosis with loss of vision. Stromal keratitis can be chronic. Once it occurs, VZV-associated anterior uveitis also tends to be chronic and can result in increased intraocular pressure or glaucoma, scarring of intraocular tissues, and cataract. Stromal keratitis and anterior uveitis may not develop immediately after the appearance of skin vesicles on the forehead and scalp; therefore, patients with normal eye examinations initially should receive follow-up eye examinations, even after the skin lesions heal. Antiviral treatment of herpes zoster at the onset of cutaneous lesions reduces the incidence and severity of ophthalmic involvement. Some patients with HZO may develop late dendriform lesions of the corneal epithelium that contain virus and will respond rapidly to systemic or topical anti-herpetic medications. These lesions are usually painful. In one study, the median time from onset of HZO to development of late dendriform lesions was 5 months, and the risk of recurrences decreased over time.19 The frequency with which these late infectious lesions occur has not been determined. Acute retinal necrosis (ARN) and progressive outer retinal necrosis (PORN) are variants of necrotizing retinopathy caused by VZV. Although ARN can occur in both immunocompetent and immunocompromised patients, PORN occurs almost exclusively20 in patients with AIDS with CD4 counts <100 cells/mm3. In contrast to ARN, PORN is characterized by minimal inflammation in the aqueous and vitreous humor, absence of occlusive retinal vasculitis, and multiple discrete peripheral lesions that manifest initially as yellow foci of retinal opacification in the outer retinal layers.21 PORN lesions rapidly coalesce, causing full-thickness retinal necrosis and subsequent retinal detachment.22 Both ARN and PORN are associated with high rates of loss of vision. People with HIV who have CD4 counts <200 cells/mm3 are at highest risk of herpes zoster–related complications, including disseminated herpes zoster.23 The central nervous system (CNS) is a target organ for herpes zoster dissemination in patients coinfected with HIV. Various VZV-related neurologic syndromes occur in people with HIV, including CNS vasculitis, multifocal leukoencephalitis, ventriculitis, myelitis and myeloradiculitis, optic neuritis, cranial nerve palsies and focal brain-stem lesions, and aseptic meningitis.24 Diagnosis Varicella and herpes zoster are typically distinctive in appearance and usually can be diagnosed clinically. Varicella also can be diagnosed retrospectively by documenting seroconversion (i.e., immunoglobulin G [IgG] antibody negative to positive). In immunocompromised persons, varicella may be difficult to distinguish from disseminated herpes zoster (as opposed to dermatomal herpes zoster); a history of VZV exposure, a rash that began with a dermatomal pattern, and VZV serologic testing to assess prior VZV infection may be helpful to distinguish disseminated herpes zoster from varicella. When lesions are atypical or difficult to distinguish from those due to other potential etiologies (including herpes simplex virus [HSV]), swabs of vesicular fluid from a fresh lesion or tissue biopsies can be submitted for viral culture, direct fluorescent antigen testing, or polymerase Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-3 chain reaction (PCR). Additionally, scabs may be adequate specimens for PCR testing. PCR of lesions is the most sensitive and specific method for diagnosis of VZV infections. Histopathology and PCR (of blood or fluids, such as cerebrospinal fluid or vitreous humor) can aid with diagnosis of VZV infections of visceral organs (e.g., pneumonitis, encephalitis, retinitis).25 Preventing Exposure People with HIV who are susceptible to VZV (i.e., people who have no history of chickenpox or shingles, who are seronegative for VZV, and who have no history of vaccination against VZV) should avoid exposure to individuals with varicella or herpes zoster (CIII). Household contacts of people with HIV without evidence of immunity to VZV should be vaccinated to prevent acquisition of varicella and potential transmission of wild-type VZV to susceptible contacts with HIV (BIII). Preventing Disease Vaccination to Prevent Primary Infection (Varicella) The live attenuated varicella vaccine (Varivax®) has been documented to be safe and immunogenic in children with HIV who have relatively preserved immune systems (CD4 percentage ≥15%)26-29 and is recommended for this population of children with HIV.30 Varicella vaccination of children with HIV also reduces the risk of subsequent herpes zoster.29,31 VZV-seronegative adults are potential candidates for varicella vaccination. Some experts would serologically screen adults with HIV without a history of prior varicella or varicella vaccination for VZV IgG. However, the value of this approach may be limited by the lack of sensitivity of commercially available VZV antibody assays (particularly for vaccine-induced antibody).32,33 No studies have evaluated the vaccine in adolescents or adults with HIV, but many experts recommend varicella vaccination (2 doses, administered 3 months apart) for VZV-susceptible people with HIV aged ≥18 years with CD4 counts ≥200 cells/mm3 (BIII).34 If varicella vaccination results in disease caused by vaccine virus (a rare event), therapy with acyclovir is recommended (AIII). Administration of varicella vaccine to more severely immunocompromised people with HIV (CD4 counts <200 cells/mm3) is contraindicated (AIII). Given the high prevalence of VZV seropositivity in adults, administration of varicella vaccine for adults will be infrequent. If post-exposure varicella-zoster immune globulin (VariZIG™) has been administered, an interval of at least 5 months is recommended before varicella vaccination (CIII).35 If post-exposure acyclovir has been administered, an interval of at least 3 days is recommended before varicella vaccination (CIII). Pre-Exposure Prophylaxis to Prevent Primary Infection (Varicella) Long-term prophylaxis with anti-VZV drugs, such as acyclovir or valacyclovir, to prevent varicella is not recommended (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-4 Post-Exposure Prophylaxis to Prevent Primary Infection (Varicella) For people with HIV who are susceptible to VZV, post-exposure prophylaxis following known or suspected VZV exposure is recommended (AII). After close contact with a person who has active varicella or herpes zoster, adolescents and adults with HIV who are susceptible to VZV (particularly those with CD4 counts <200 cells/mm3) should receive VariZIG as soon as possible (preferably within 96 hours), but up to 10 days after exposure (AIII).36 Given the cost of obtaining VariZIG, it is reasonable to check VZV serology before administering VariZIG to people who do not have a clinical history of chickenpox or shingles and no documentation of varicella vaccination (AIII). The risk of VZV transmission is greater with exposure to varicella than localized herpes zoster. In the United States, VariZIG is commercially available from a broad network of specialty distributers (listed at: www.varizig.com). The duration of protection from VariZIG is at least 3 weeks. Patients receiving monthly infusions of high-dose intravenous immune globulin (IVIG >400 mg/kg) are likely to be protected and probably do not require VariZIG if they received a dose of IVIG <3 weeks before VZV exposure. A 5- to 7-day course of post-exposure acyclovir or valacyclovir beginning 7 to 10 days after exposure is recommended by some experts to prevent varicella among VZV-susceptible adolescents or adults with HIV, but this intervention has not been studied in these populations (BIII).37 Among VZV-susceptible immunocompetent children, post-exposure varicella vaccination has been shown to reduce the risk for varicella and is more effective than pre-emptive therapy with antiviral drugs; however, the efficacy of post-exposure varicella vaccination for people with HIV has not been studied and is not recommended. Antiviral Prophylaxis to Prevent Re-Activation Disease (Herpes Zoster) Long-term administration of anti-VZV drugs to individuals with HIV to prevent episodes of herpes zoster is not routinely recommended (AII). However, in a randomized, placebo-controlled study in Africa that evaluated daily acyclovir prophylaxis (acyclovir 400 mg orally [PO] twice a day) administered to people with HIV/HSV-2 coinfection who were not taking ART, acyclovir prophylaxis reduced the rate of herpes zoster by 62%.38 Acyclovir did not prevent recurrent zoster episodes in patients with prior history of herpes zoster.38 People with HIV who are taking suppressive anti-herpes medications (i.e., acyclovir, valacyclovir, or famciclovir) for other indications—such as prevention of genital herpes—may receive some additional benefit in reduction of risk of herpes zoster, but the relative risk reduction in people who are receiving ART is unknown. Vaccination to Prevent Reactivation Disease (Herpes Zoster) One U.S. Food and Drug Administration (FDA)-approved vaccine is currently available for the prevention of herpes zoster in immunocompetent adults. In 2017, a subunit vaccine containing recombinant VZV glycoprotein E (gE) and adjuvant AS01B (i.e., recombinant zoster vaccine [RZV] Shingrix) was FDA approved and recommended by the Advisory Committee on Immunization Practices (ACIP) to prevent herpes zoster in immunocompetent adults aged ≥50 years, given on a 2-dose schedule.39 The approval and recommendation for the vaccine were based on pivotal Phase 3 randomized, placebo-controlled clinical trials involving >30,000 participants aged ≥50 years in which the vaccine efficacy against herpes zoster in vaccinated participants was 97.2% overall and 91.3% in those aged ≥70 years.40,41 The most common solicited adverse reactions in vaccine recipients were pain (78% of recipients), myalgia (45%), and fatigue (45%), with Grade 3 injection site reactions (pain, redness, and swelling) reported in 9.4% of vaccine recipients and Grade 3 solicited systemic events (myalgia, fatigue, headache, fever, and gastrointestinal symptoms) reported Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-5 by 10.8% of vaccine recipients.39,42 Systemic Grade 3 reactions were reported more frequently after Dose 2 than after Dose 1.42 Data on use of RZV in people with HIV are limited. A Phase 1/2 randomized, placebo-controlled study enrolled 94 adults with HIV receiving ART43 with CD4 count ≥200 cells/mm3, 14 adults receiving ART with CD4 count <200 cells/mm3, and 15 ART-naive adults with CD4 count ≥500 cells/mm3. The participants’ median age was 46 years. Participants received the vaccine in three doses administered at 0, 2, and 6 months. The vaccine increased humoral and cell-mediated immunity to VZV gE after two doses, including among people with CD4 counts <200 cells/mm3. The most common side effects included pain at the injection sites (98.6% of participants, 16.4% Grade 3), fatigue (75.3%, 16.4% Grade 3), myalgia (74.0%, 13.7% Grade 3), and headache (64.4%, 8.2% Grade 3). No vaccine-related severe adverse events occurred during follow-up. Based on these very limited data in people with HIV, the vaccine appears safe and immunogenic. No efficacy data are available for the RZV among people with HIV. Given that the risk of herpes zoster is high among people with HIV, and the vaccine appears safe, administration of RZV to people with HIV 18 years of age and older is recommended following the FDA-approved schedule for persons without HIV (intramuscular [IM] dose at 0 and 2–6 months) (AIII). No data identify the optimal timing of vaccination for persons who have a CD4 count <200 cells/mm3 or who are not suppressed virologically on ART. Following initiation of ART, some experts would administer the RZV vaccination series after CD4 count recovery (CIII), and others would administer the series after virologic suppression was achieved (CIII). RZV is not a treatment of herpes zoster and should not be given during acute episodes (AIII). It also should not be given to individuals with VZV-related inflammatory eye disease (keratitis or anterior uveitis) during episodes of active inflammation (AIII). A 1-dose attenuated live-zoster virus vaccine (i.e., zoster vaccine live [ZVL], Zostavax®) for prevention of herpes zoster was FDA approved for use in immunocompetent adults aged ≥50 years. However, as of November 18, 2020, it is no longer available for use in the United States, and recommendations for its use have been removed from these guidelines. Those who previously received ZVL should be revaccinated with RZV. Treating Disease Varicella No controlled prospective studies of antiviral therapy for varicella in adults with HIV have been reported. For uncomplicated varicella, the preferred treatment options are valacyclovir (1 g PO three times daily) or famciclovir (500 mg PO three times daily), initiated as early as possible after lesion onset and continued for 5 to 7 days (AII). Oral acyclovir (20 mg/kg body weight up to a maximum dose of 800 mg five times daily) is an alternative (BII). Intravenous (IV) acyclovir 10 mg/kg every 8 hours for 7 to 10 days is the recommended initial treatment for people with HIV with severe or complicated varicella (AIII).15,44,45 If no evidence of visceral involvement with VZV is apparent, many experts recommend switching from IV to oral antiviral therapy after the patient has defervesced (BIII).46 Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-6 Herpes Zoster Antiviral therapy should be instituted as soon as possible for all people with HIV with herpes zoster diagnosed within 1 week of rash onset (or any time prior to full crusting of lesions). The recommended treatment options for acute localized dermatomal herpes zoster in people with HIV are oral valacyclovir (AII), famciclovir (AII), or acyclovir (BII) (doses as above) for 7 to 10 days, although longer durations of therapy should be considered if lesions resolve slowly. Valacyclovir or famciclovir are preferred because of their improved pharmacokinetic properties and simplified dosing schedule. If cutaneous lesions are extensive or if visceral involvement is suspected, IV acyclovir should be initiated and continued until clinical improvement is evident (AII).47 A switch from IV acyclovir to oral antiviral therapy (to complete a 10- to 14-day treatment course) is reasonable when formation of new cutaneous lesions has ceased and the signs and symptoms of visceral VZV infection are improving (BIII). Adjunctive corticosteroid therapy for herpes zoster in people with HIV is not recommended because no data support its benefit in this population (AIII). In patients with HZO, both stromal keratitis and anterior uveitis require treatment with topical corticosteroids; in many cases, chronic, low-dose topical corticosteroid therapy is necessary to maintain suppression of inflammation. Recurrences or exacerbations of inflammation are common. A role for antiviral agents in the management of chronic keratitis and uveitis has not been established. ARN should be treated promptly with antiviral therapy. One treatment recommended by some experts is high-dose IV acyclovir (10 mg/kg every 8 hours for 10 to 14 days), followed by prolonged high-dose oral valacyclovir (1 g three times daily) (AIII). High-dose oral antiviral treatment for at least 14 weeks has been shown to decrease the risk of second eye involvement among those who present with unilateral ARN syndrome;48,49 (AIII) however, many ophthalmologists and infectious disease specialists will continue oral antiviral therapy for much longer. Many experts would also include an intravitreous injection of ganciclovir as part of the initial induction therapy. Additional intravitreous injections can be given if there is concern for lack of treatment response, but injections should not be more frequent than twice weekly (BIII). Use of oral valaciclovir instead of IV acyclovir for initial treatment has been reported. This approach should be used with caution because serum drug levels with oral treatment will not be as high as those achieved with IV administration (CIII). Involvement of an experienced ophthalmologist in the management of patients with VZV ocular disease is strongly recommended (AIII). Optimal antiviral therapy for PORN remains undefined and should be managed in consultation with an experienced ophthalmologist (AIII).50-52 Outcomes with IV acyclovir or ganciclovir monotherapy were poor. Better results were obtained with IV ganciclovir (or the combination of ganciclovir plus foscarnet), along with intravitreal antiviral drug injections.22,51,53 Specific treatment should include systemic therapy with at least one IV drug (either acyclovir or ganciclovir) (AIII) coupled with injections of at least one intravitreal drug (ganciclovir or foscarnet) (BIII).53,54 Intravitreal cidofovir should not be used because such injections may be associated with loss of intraocular pressure and other adverse effects. Ganciclovir ocular implants previously recommended by some experts are no longer manufactured. The prognosis for visual preservation in involved eyes is poor, despite aggressive antiviral therapy. When to Start Antiretroviral Therapy All people with HIV should receive ART as soon as possible after diagnosis of HIV infection. The presence of disease caused by VZV is not an indication to defer or discontinue ART (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-7 Monitoring of Response to Therapy and Adverse Events (Including IRIS) For monitoring and adverse event recommendations related to anti-herpesvirus drugs, see preceding guideline sections on Herpes Simplex Virus and Cytomegalovirus. Initiation of ART appears to be associated with an increased frequency of VZV reactivation, peaking at about 3 months after ART initiation.7,13,14,55,56 Observational studies have shown the risk of herpes zoster to increase twofold to fourfold between 4 and 16 weeks after initiating ART. The clinical presentation and natural history of herpes zoster in the setting of immune reconstitution is similar to that observed in other people with HIV, and episodes of herpes zoster in either setting should be managed in the same manner. Managing Treatment Failure Treatment failure caused by resistance of VZV to acyclovir and related drugs (e.g., famciclovir, ganciclovir) is rare, but should be suspected when clinical findings do not improve within 7 days of initiation of therapy or when skin lesions have an atypical (e.g., verrucous) appearance. A viral culture should be obtained, and if VZV is isolated, susceptibility testing performed to establish antiviral drug susceptibility and to document the need for alternative therapy. Among patients with suspected or proven acyclovir-resistant VZV infections, treatment with IV foscarnet is recommended (AII).57 IV cidofovir is a potential alternative (CIII). Both foscarnet and cidofovir are nephrotoxic agents and should be given in consultation with an expert in infectious diseases. Special Considerations During Pregnancy Pregnant women with HIV who are susceptible to VZV and are in close contact with a person with active varicella or herpes zoster should receive VariZIG as soon as possible (within 10 days)36 after exposure to VZV (AIII). If oral acyclovir is used for post-exposure prophylaxis, VZV serology should be performed so that the drug can be discontinued if the patient is seropositive for VZV (CIII). Pregnant women should not receive varicella vaccine (AIII). For pregnant women without HIV with varicella, the risk of transmitting VZV to the infant resulting in congenital varicella syndrome is 0.4% when varicella infection occurs at or before 12 weeks gestation, 2.2% with infection at 13 to 20 weeks, and negligible with infection after 20 weeks.58 Women with varicella during the first half of pregnancy should be counseled about the risks to the fetus and offered detailed ultrasound surveillance for findings indicative of fetal congenital varicella syndrome.58 Administration of VariZIG is recommended primarily to prevent complications in the mother; whether it has any benefit in prevention of congenital varicella syndrome is unknown. VariZIG should be administered to infants born to women who have varicella from 5 days before delivery to 2 days after delivery to reduce the severity and mortality of neonatal varicella acquired by exposure to maternal viremia (AIII). Oral acyclovir or valacyclovir are the preferred treatments for pregnant women with HIV who have uncomplicated varicella during pregnancy (BIII). Pregnant women with HIV who have severe varicella or who exhibit signs or symptoms of VZV pneumonitis should be hospitalized and treated with IV acyclovir (10 mg/kg every 8 hours) (AII). No controlled studies of antiviral therapy of herpes zoster during pregnancy have been reported. Recommended therapy for uncomplicated herpes zoster in pregnant women with HIV is oral Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-8 acyclovir or valacyclovir (BIII). Pregnant women should not receive the herpes zoster vaccine (AIII). Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-9 Recommendations for Preventing and Treating Varicella-Zoster Virus Infections Pre-Exposure Prevention of VZV Primary Infection Indications • Adults and adolescents with HIV who have CD4 counts ≥200 cells/mm3 and who do not have documentation of varicella vaccination, a history or diagnosis of varicella or herpes zoster confirmed by a health care provider, or laboratory confirmation of VZV disease; and anyone with HIV who is VZV seronegative should avoid exposure to persons with varicella or herpes zoster (CIII). Vaccination • Household contacts who are VZV-susceptible should be vaccinated to prevent potential transmission of VZV to at-risk people with HIV (BIII). • In VZV-seronegative persons aged ≥18 years with CD4 counts ≥200 cells/mm3, administer primary varicella vaccination (Varivax™) in two doses (0.5 mL SQ) 3 months apart (BIII). • If vaccination results in disease due to live-attenuated vaccine virus, treatment with acyclovir is recommended (AIII). • If post-exposure VariZIG™ has been administered, wait ≥5 months before varicella vaccination (CIII). • If post-exposure acyclovir has been administered, wait ≥3 days before varicella vaccination (CIII). • Administration of varicella vaccine to severely immunocompromised people with HIV (CD4 counts <200 cells/mm3) is contraindicated (AIII). Post-Exposure Prophylaxis of VZV Primary Infection Indications • Close contact with a person who has active varicella or herpes zoster, and • Susceptible to VZV (i.e., no history of varicella vaccination, no history of varicella or herpes zoster, or known to be VZV seronegative) Preferred Prophylaxis • VariZIG 125 IU/10 kg (maximum of 625 IU) IM, administered as soon as possible and within 10 days after exposure to a person with active varicella or herpes zoster (AIII) • If post-exposure VariZIG has been administered, wait ≥5 months before varicella vaccination (CIII). Note: Patients receiving monthly high-dose IVIG (i.e., >400 mg/kg) are likely protected against VZV and probably do not require VariZIG if the last dose of IVIG they received was administered <3 weeks before VZV exposure. Alternative Prophylaxis (Begin 7-10 Days After Exposure) • Acyclovir 800 mg PO 5 times daily for 5 to 7 days (BIII), or • Valacyclovir 1 gm PO 3 times daily for 5 to 7 days (BIII) Note: Neither these pre-emptive interventions nor post-exposure varicella vaccination have been studied in adults and adolescents with HIV. If acyclovir or valacyclovir is used, varicella vaccines should not be given <72 hours after the last dose of the antiviral drug. Recommendations for Preventing and Treating Varicella-Zoster Virus Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-10 Preventing Herpes Zoster (Shingles) Vaccination Recombinant zoster vaccine (RZV, Shingrix) is the only available vaccine for prevention of shingles in the United States. As of November 18, 2020, attenuated zoster vaccine live (ZVL, Zostavax) is no longer available for use in the United States. RZV Recommended in adults with HIV aged ≥18 years, regardless of CD4 count: • RZV 0.5 mL IM injection—2-dose series at 0 and then at 2 to 6 months (AIII). • RZV should not be given during an acute episode of herpes zoster (AIII). • Following initiation of ART, some experts would delay RZV vaccination until patients are suppressed virologically on ART (CIII) or until CD4 count recovery (CIII) to maximize immunologic response to the vaccine. Treating Varicella Infections Primary Varicella Infection (Chickenpox) Uncomplicated Cases Preferred Therapy • Valacyclovir 1 g PO 3 times a day (AII), or • Famciclovir 500 mg PO 3 times a day (AII) Alternative Therapy • Acyclovir 800 mg PO 5 times daily (BII) Duration • 5 to 7 days Severe or Complicated Cases • Acyclovir 10 mg/kg IV every 8 hours for 7 to 10 days (AIII) • May switch to oral famciclovir, valacyclovir, or acyclovir after defervescence if there is no evidence of visceral involvement (BIII) Herpes Zoster (Shingles) Acute, Localized, Dermatomal Preferred Therapy • Valacyclovir 1,000 mg PO 3 times a day (AII), or • Famciclovir 500 mg PO 3 times a day (AII) Alternative Therapy • Acyclovir 800 mg PO 5 times daily (BII) Duration • 7 to 10 days; longer duration should be considered if lesions resolve slowly Recommendations for Preventing and Treating Varicella-Zoster Virus Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-11 Herpes Zoster Ophthalmitis (HZO) Late dendriform lesions of the corneal epithelium should be treated with systemic or topical anti-herpetic medications (AIII). Extensive Cutaneous Lesion or Visceral Involvement • Acyclovir 10 mg/kg IV every 8 hours until clinical improvement is evident (AII). • Switch to oral therapy (valacyclovir 1 g 3 times a day, famciclovir 500 mg 3 times a day, or acyclovir 800 mg PO 5 times daily to complete a 10- to 14-day course) when formation of new lesions has ceased and signs and symptoms of visceral VZV infection are improving (BIII). Acute Retinal Necrosis (ARN) • Acyclovir 10 mg/kg IV every 8 hours for 10 to 14 days, followed by valacyclovir 1 g PO 3 times a day for ≥14 weeks (AIII). In addition, an intravitreous injection of ganciclovir (2 mg/0.05 mL) can be given as a part of initial treatment, and injections can be repeated at a frequency of twice weekly until there is evidence of a treatment response (BIII). Involvement of an experienced ophthalmologist is recommended (AIII). • Use of oral valaciclovir instead of IV acyclovir for initial treatment has been reported, but this approach should be used with caution, because serum drug levels with oral treatment will not be as high as those achieved with IV administration (CIII). Progressive Outer Retinal Necrosis (PORN) • Involvement of an experienced ophthalmologist is strongly recommended (AIII). • Acyclovir 10 mg/kg IV every 8 hours or ganciclovir 5 mg/kg every 12 hours plus ganciclovir 2 mg/0.05 mL and/or foscarnet 1.2 mg/0.05 mL intravitreal twice weekly (AIII) • Optimize ARV regimen (AIII). • Duration of therapy is not well defined and should be determined based on clinical, virologic, and immunologic responses in consultation with an ophthalmologist. Note: Ganciclovir ocular implants are no longer commercially available. Key: ARN = acute retinal necrosis; ART = antiretroviral therapy; ARV = antiretroviral; CD4 = CD4 T lymphocyte; HZO = herpes zoster ophthalmicus; IM = intramuscular; IU = international unit; IV = intravenous; IVIG = intravenous immunoglobulin; PO = orally; PORN = progressive outer retinal necrosis; RZV = recombinant zoster vaccine; SQ = subcutaneous; VariZIG = varicella zoster immune globulin; VZV = varicella zoster virus; ZVL = zoster vaccine live Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-12 References 1. Reynolds MA, Kruszon-Moran D, Jumaan A, Schmid DS, McQuillan GM. Varicella seroprevalence in the U.S.: data from the National Health and Nutrition Examination Survey, 1999-2004. Public Health Rep. 2010;125(6):860-869. Available at: 2. Guris D, Jumaan AO, Mascola L, et al. Changing varicella epidemiology in active surveillance sites—United States, 1995-2005. J Infect Dis. 2008;197 Suppl 2:S71-75. Available at: 3. 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J Acquir Immune Defic Syndr. 2012;61(2):203-207. Available at: 12. Moanna A, Rimland D. Decreasing incidence of herpes zoster in the highly active antiretroviral therapy era. Clin Infect Dis. 2013;57(1):122-125. Available at: 13. Nacher M, Basurko C, Adenis A, et al. Predictive factors of herpes zoster HIV-infected patients: another adverse effect of crack cocaine. PLoS One. 2013;8(11):e80187. Available at: 14. Domingo P, Torres OH, Ris J, Vazquez G. Herpes zoster as an immune reconstitution disease after initiation of combination antiretroviral therapy in patients with human immunodeficiency virus type-1 infection. Am J Med. 2001;110(8):605-609. Available at: 15. Wallace MR, Hooper DG, Pyne JM, Graves SJ, Malone JL. Varicella immunity and clinical disease in HIV-infected adults. South Med J. 1994;87(1):74-76. Available at: 16. Schmader KE, Dworkin RH. Natural history and treatment of herpes zoster. J Pain. 2008;9(1 Suppl 1):S3-9. Available at: 17. Gnann JW, Jr., Crumpacker CS, Lalezari JP, et al. Sorivudine versus acyclovir for treatment of dermatomal herpes zoster in human immunodeficiency virus-infected patients: results from a randomized, controlled clinical trial. Collaborative Antiviral Study Group/AIDS Clinical Trials Group, Herpes Zoster Study Group. Antimicrob Agents Chemother. 1998;42(5):1139-1145. Available at: 18. Harrison RA, Soong S, Weiss HL, Gnann JW, Jr., Whitley RJ. A mixed model for factors predictive of pain in AIDS patients with herpes zoster. J Pain Symptom Manage. 1999;17(6):410-417. Available at: 19. Hu AY, Strauss EC, Holland GN, Chan MF, Yu F, Margolis TP. Late varicella-zoster virus dendriform keratitis in patients with histories of herpes zoster ophthalmicus. Am J Ophthalmol. 2010;149(2):214-220 e213. Available at: 20. Engstrom RE, Jr., Holland GN, Margolis TP, et al. The progressive outer retinal necrosis syndrome. A variant of necrotizing herpetic retinopathy in patients with AIDS. Ophthalmology. 1994;101(9):1488-1502. Available at: 21. Ormerod LD, Larkin JA, Margo CA, et al. Rapidly progressive herpetic retinal necrosis: a blinding disease characteristic of advanced AIDS. Clin Infect Dis. 1998;26(1):34-45; discussion 46-37. Available at: 22. Yin PD, Kurup SK, Fischer SH, et al. Progressive outer retinal necrosis in the era of highly active antiretroviral therapy: successful management with intravitreal injections and Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-14 monitoring with quantitative PCR. J Clin Virol. 2007;38(3):254-259. Available at: 23. Veenstra J, van Praag RM, Krol A, et al. Complications of varicella zoster virus reactivation in HIV-infected homosexual men. AIDS. 1996;10(4):393-399. Available at: 24. Gray F, Belec L, Lescs MC, et al. Varicella-zoster virus infection of the central nervous system in the acquired immune deficiency syndrome. Brain. 1994;117 ( Pt 5):987-999. Available at: 25. Leung J, Harpaz R, Baughman AL, et al. Evaluation of laboratory methods for diagnosis of varicella. Clin Infect Dis. 2010;51(1):23-32. Available at: 26. Levin MJ, Gershon AA, Weinberg A, et al. Administration of live varicella vaccine to HIV-infected children with current or past significant depression of CD4(+) T cells. J Infect Dis. 2006;194(2):247-255. Available at: 27. Armenian SH, Han JY, Dunaway TM, Church JA. Safety and immunogenicity of live varicella virus vaccine in children with human immunodeficiency virus type 1. Pediatr Infect Dis J. 2006;25(4):368-370. Available at: 28. Bekker V, Westerlaken GH, Scherpbier H, et al. Varicella vaccination in HIV-1-infected children after immune reconstitution. AIDS. 2006;20(18):2321-2329. Available at: 29. Son M, Shapiro ED, LaRussa P, et al. Effectiveness of varicella vaccine in children infected with HIV. J Infect Dis. 2010;201(12):1806-1810. Available at: 30. Marin M, Guris D, Chaves SS, et al. Prevention of varicella: recommendations of the Advisory Committee on Immunization Practices (ACIP). MMWR Recomm Rep. 2007;56(RR-4):1-40. Available at: 31. Wood SM, Shah SS, Steenhoff AP, Rutstein RM. Primary varicella and herpes zoster among HIV-infected children from 1989 to 2006. Pediatrics. 2008;121(1):e150-156. Available at: 32. Breuer J, Schmid DS, Gershon AA. Use and limitations of varicella-zoster virus-specific serological testing to evaluate breakthrough disease in vaccinees and to screen for susceptibility to varicella. J Infect Dis. 2008;197 Suppl 2:S147-151. Available at: 33. Ludwig B, Kraus FB, Allwinn R, Keim S, Doerr HW, Buxbaum S. Loss of varicella zoster virus antibodies despite detectable cell mediated immunity after vaccination. Infection. 2006;34(4):222-226. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-15 34. Centers for Disease Control and Prevention. Recommended adult immunization schedule: United States, 2010. Ann Intern Med. 2010;152(1):36-39. Available at: 35. Centers for Disease Control and Prevention. A new product (VariZIG) for postexposure prophylaxis of varicella available under an investigational new drug application expanded access protocol. MMWR Morb Mortal Wkly Rep. 2006;55(8):209-210. Available at: 36. Centers for Disease C, Prevention. FDA approval of an extended period for administering VariZIG for postexposure prophylaxis of varicella. MMWR Morb Mortal Wkly Rep. 2012;61(12):212. Available at: 37. American Academy of Pediatrics. Varicella-zoster virus infections. In: Red Book: 2018–2021 Report of the Committee on Infectious Diseases. 31st ed. 2018:869-883. Available at: 38. Barnabas RV, Baeten JM, Lingappa JR, et al. Acyclovir prophylaxis reduces the incidence of herpes zoster among HIV-infected individuals: results of a randomized clinical trial. J Infect Dis. 2016;213(4):551-555. Available at: 39. Dooling KL, Guo A, Patel M, et al. Recommendations of the Advisory Committee on Immunization Practices for use of herpes zoster vaccines. MMWR Morb Mortal Wkly Rep. 2018;67(3):103-108. Available at: 40. Lal H, Cunningham AL, Godeaux O, et al. Efficacy of an adjuvanted herpes zoster subunit vaccine in older adults. N Engl J Med. 2015;372(22):2087-2096. Available at: 41. Cunningham AL, Lal H, Kovac M, et al. Efficacy of the herpes zoster subunit vaccine in adults 70 years of age or older. N Engl J Med. 2016;375(11):1019-1032. Available at: 42. U.S. Food and Drug Administration. Shingrix [package insert]. 2017. Available at: 581605.pdf. 43. Berkowitz EM, Moyle G, Stellbrink HJ, et al. Safety and immunogenicity of an adjuvanted herpes zoster subunit candidate vaccine in HIV-infected adults: a phase 1/2a randomized, placebo-controlled study. J Infect Dis. 2015;211(8):1279-1287. Available at: 44. Prober CG, Kirk LE, Keeney RE. Acyclovir therapy of chickenpox in immunosuppressed children—a collaborative study. J Pediatr. 1982;101(4):622-625. Available at: 45. Arvin AM. Antiviral therapy for varicella and herpes zoster. Semin Pediatr Infect Dis. 2002;13(1):12-21. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-16 46. Carcao MD, Lau RC, Gupta A, Huerter H, Koren G, King SM. Sequential use of intravenous and oral acyclovir in the therapy of varicella in immunocompromised children. Pediatr Infect Dis J. 1998;17(7):626-631. Available at: 47. Balfour HH, Jr., Bean B, Laskin OL, et al. Acyclovir halts progression of herpes zoster in immunocompromised patients. N Engl J Med. 1983;308(24):1448-1453. Available at: 48. Palay DA, Sternberg P, Jr., Davis J, et al. Decrease in the risk of bilateral acute retinal necrosis by acyclovir therapy. Am J Ophthalmol. 1991;112(3):250-255. Available at: 49. Jeon S, Kakizaki H, Lee WK, Jee D. Effect of prolonged oral acyclovir treatment in acute retinal necrosis. Ocul Immunol Inflamm. 2012;20(4):288-292. Available at: 50. Scott IU, Luu KM, Davis JL. Intravitreal antivirals in the management of patients with acquired immunodeficiency syndrome with progressive outer retinal necrosis. Arch Ophthalmol. 2002;120(9):1219-1222. Available at: 51. Moorthy RS, Weinberg DV, Teich SA, et al. Management of varicella zoster virus retinitis in AIDS. Br J Ophthalmol. 1997;81(3):189-194. Available at: 52. Austin RB. Progressive outer retinal necrosis syndrome: a comprehensive review of its clinical presentation, relationship to immune system status, and management. Clin Eye Vis Care. 2000;12(3-4):119-129. Available at: 53. Kim SJ, Equi R, Belair ML, Fine HF, Dunn JP. Long-term preservation of vision in progressive outer retinal necrosis treated with combination antiviral drugs and highly active antiretroviral therapy. Ocul Immunol Inflamm. 2007;15(6):425-427. Available at: 54. Gore DM, Gore SK, Visser L. Progressive outer retinal necrosis: outcomes in the intravitreal era. Arch Ophthalmol. 2012;130(6):700-706. Available at: 55. Dunic I, Djurkovic-Djakovic O, Vesic S, Zerjav S, Jevtovic D. Herpes zoster as an immune restoration disease in AIDS patients during therapy including protease inhibitors. Int J STD AIDS. 2005;16(7):475-478. Available at: 56. Espinosa E, Pena-Jimenez A, Ormsby CE, Vega-Barrientos R, Reyes-Teran G. Later onset of herpes zoster-associated immune reconstitution inflammatory syndrome. HIV Med. 2009;10(7):454-457. Available at: 57. Breton G, Fillet AM, Katlama C, Bricaire F, Caumes E. Acyclovir-resistant herpes zoster in human immunodeficiency virus-infected patients: results of foscarnet therapy. Clin Infect Dis. 1998;27(6):1525-1527. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV DD-17 58. Pastuszak AL, Levy M, Schick B, et al. Outcome after maternal varicella infection in the first 20 weeks of pregnancy. N Engl J Med. 1994;330(13):901-905. Available at: Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV EE-1 Table 1. Chemoprophylaxis to Prevent First Episode of Opportunistic Disease Updated: September 16, 2024 Reviewed: September 16, 2024 This table provides recommendations for the use of chemoprophylaxis to prevent the first episode of opportunistic disease. For the use of immunizations to prevent certain infections in people with HIV, please refer to the Immunizations for Preventable Diseases in Adults and Adolescents With HIV section. Opportunistic Infections Indication Preferred Alternative Coccidioidomycosis A new positive IgM or IgG serologic test in patients who live in a disease-endemic area and with CD4 count <250 cells/mm3 (BIII) Fluconazole 400 mg PO daily (BIII) Histoplasma capsulatum Infection CD4 count ≤150 cells/µL and at high risk because of occupational exposure or living in a community with a hyperendemic rate of histoplasmosis (>10 cases/100 patient-years) (BI) Itraconazole 200 mg PO daily (BI) Malaria Travel to disease-endemic area Recommendations are the same for HIV-infected and HIV-uninfected patients. Recommendations are based on the region of travel, malaria risks, and drug susceptibility in the region. Refer to the Centers for Disease Control and Prevention webpage for the most recent recommendations based on region and drug susceptibility: Malaria. Mycobacterium avium Complex (MAC) Disease CD4 count <50 cells/mm3 AND not receiving ART or remains viremic on ART or has no options for a fully suppressive ART regimen (AI) Not recommended for those who immediately initiate ART after HIV diagnosis (AII) Disseminated MAC disease should be ruled out before starting primary prophylaxis. See the MAC section for more information. Azithromycin 1,200 mg PO once weekly (AI), or Clarithromycin 500 mg PO twice daily (AI), or Azithromycin 600 mg PO twice weekly (BIII) Rifabutin (dose adjustment may be necessary with some ARV drugs, and rifabutin is not recommended if used with certain ARV drugs)a (BI); rule out active TB before starting rifabutin to avoid monotherapy in the setting of TB. Table 1. Chemoprophylaxis to Prevent First Episode of Opportunistic Disease Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV EE-2 Opportunistic Infections Indication Preferred Alternative Mycobacterium tuberculosis Infection (TB) (i.e., treatment of latent TB infection [LTBI]) Positive screening test for LTBI,b no evidence of active TB, and no prior treatment for active TB or LTBI (AI), or Close contact with a person with infectious TB (with no evidence of active TB), regardless of screening test results and CD4 count (AII) For recommendations on management of drug interactions with ARVs, see the Dosing Recommendations for Use of ARV and Anti-TB Drugs When Treating Latent TB Infection table in the Mycobacterium tuberculosis Infection and Disease section and the Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines. 3HP: Rifapentine (see weight-based dosing below) plus INH 15 mg/kg (900 mg maximum) plus pyridoxine 50 mg PO once weekly for 12 weeks (AI) Weight-Based Rifapentine Dose Weighing 25.1–32 kg: 600 mg PO once weekly Weighing 32.1–49.9 kg: 750 mg PO once weekly Weighing >50 kg: 900 mg PO once weekly Note: 3HP is recommended only for virally-suppressed persons receiving EFV, RAL, or once daily DTG-based ARV regimen (AII). or 3HR: INH 300 mg plus rifampin 600 mg plus pyridoxine 25–50 mg PO daily for 3 months (AI) INH 300 mg plus pyridoxine 25–50 mg PO daily for 6–9 months (AII), or 4R: Rifampin 600 mg PO daily for 4 months (BI), or 1HP: Rifapentine (see weight-based dosing below) plus INH 300 mg plus pyridoxine 25–50 mg) PO once daily for 4 weeks (BI) Weight-Based Rifapentine Dose Weighing <35 kg: 300 mg PO once daily Weighing 35–45 kg: 450 mg PO once daily Weighing >45 kg: 600 mg PO once daily Note: 1HP is recommended only for patients receiving an efavirenz-based ARV regimen (AI). For persons exposed to drug-resistant TB, select anti-TB drugs after consultation with experts and public health authorities (AIII). Pneumocystis pneumonia (PCP) CD4 count 100–200 cells/mm3, if plasma HIV RNA level is above detection limits (AI), or CD4 count <100 cells/mm3, regardless of plasma HIV RNA level (AIII) Note: Patients who are receiving pyrimethamine/ sulfadiazine for treatment or suppression of toxoplasmosis do not require additional PCP prophylaxis (AII). TMP-SMX 1 DS tablet PO daily (AI), or TMP-SMX 1 SS tablet PO daily (AI) Note: TMP-SMX also confers protection against toxoplasmosis and some protection against many respiratory bacterial infections. The following regimens can be used for people who are seropositive or seronegative for Toxoplasma gondii: • TMP-SMX 1 DS PO three times weekly (BI), or • Dapsonec 50 mg PO daily with pyrimethamined 50 mg plus leucovorin 25 mg PO weekly (BI), or • Dapsonec 200 mg plus pyrimethamined 75 mg plus leucovorin 25 mg PO weekly (BI), or • Atovaquone 1,500 mg PO daily with food (BI) The following regimens should only be used if the person is seronegative for Toxoplasma gondii: • Dapsonec 100 mg PO daily or 50 mg PO twice daily (BI), or Table 1. Chemoprophylaxis to Prevent First Episode of Opportunistic Disease Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV EE-3 Opportunistic Infections Indication Preferred Alternative • Aerosolized pentamidine 300 mg via Respigard II nebulizer every month (BI), or • Intravenous pentamidine 300 mg every 28 days (CIII) Syphilis Individuals exposed sexually within ≤90 days of the diagnosis of primary, secondary, or early latent syphilis in a sex partner, regardless of serologic status (AII), or Individuals exposed >90 days before syphilis diagnosis in a sex partner, if serologic test results are not available immediately and the opportunity for follow-up is uncertain (AIII) Benzathine penicillin G 2.4 million units IM for one dose (AII) For penicillin-allergic patients: Doxycycline 100 mg PO twice daily for 14 days (BII), or Ceftriaxone 1 g IM or IV daily for 10–14 days (BII) Talaromycosis (Penicilliosis) Persons with HIV and CD4 cell counts <100 cells/mm3, who are unable to have ART, or have treatment failure without access to effective ART options, and— Who reside in the highly endemic regions in northern Thailand, northern or southern Vietnam, or southern China (BI), or Who are from countries outside of the endemic region, and must travel to the region (BIII) Particularly in highland regions during the rainy and humid months For persons who reside in endemic areas, itraconazole 200 mg PO once daily (BI) For those traveling to the highly endemic regions, begin itraconazole 200 mg PO once daily 3 days before travel, and continue for 1 week after leaving the endemic area (BIII). For persons who reside in endemic areas, fluconazole 400 mg PO once weekly (BII) For those traveling to the highly endemic regions, take the first dose of fluconazole 400 mg 3 days before travel, continue 400 mg once weekly, and take the final dose after leaving the endemic area (BIII). Toxoplasma gondii encephalitis Toxoplasma IgG-positive patients with CD4 count <100 cells/mm3 (AII) Note: All regimens recommended for primary prophylaxis against toxoplasmosis also are effective as PCP prophylaxis. TMP-SMX 1 DS PO daily (AII) TMP-SMX 1 DS PO three times weekly (BII), or TMP-SMX 1 SS PO daily (BIII), or Dapsonec 50 mg PO daily plus (pyrimethamined 50 mg plus leucovorin 25 mg) PO weekly (BI), or Table 1. Chemoprophylaxis to Prevent First Episode of Opportunistic Disease Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV EE-4 Opportunistic Infections Indication Preferred Alternative (Dapsonec 200 mg plus pyrimethamined 75 mg plus leucovorin 25 mg) PO weekly (CI), or Atovaquone 1,500 mg PO daily (CIII), or (Atovaquone 1,500 mg plus pyrimethamined 25 mg plus leucovorin 10 mg) PO daily (CIII) a Refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB table in the Mycobacterium tuberculosis section for dosing recommendations. b Screening tests for LTBI include tuberculin skin test and interferon-gamma release assays. c Patients should be tested for glucose-6-phosphate dehydrogenase (G6PD) before administration of dapsone. An alternative agent should be used in patients found to have G6PD deficiency. d Refer to Daraprim Direct for information regarding how to access pyrimethamine. For information regarding the evidence ratings, refer to the Rating System for Prevention and Treatment Recommendations in the Introduction section of the Adult and Adolescent Opportunistic Infection Guidelines. Key: ART = antiretroviral therapy; ARV = antiretroviral; CD4 = CD4 T lymphocyte; DS = double strength; DTG = dolutegravir; EFV = efavirenz; IgG = immunoglobulin G; IgM = immunoglobulin M; IM = intramuscular; INH = isoniazid; IV = intravenously; LTBI = latent tuberculosis infection; MAC = Mycobacterium avium complex; PCP = Pneumocystis pneumonia; PO = orally; RAL= raltegravir; SS = single strength; TB = tuberculosis; TMP-SMX = trimethoprim-sulfamethoxazole Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-1 Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Updated: October 8, 2024 Reviewed: October 8, 2024 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Bacterial Enteric Infections Empiric Therapy Pending Definitive Diagnosis For People With HIV and CD4 >500 cells/mm3, 1–2 Days of Loose Stool Without Fever or Blood in Stool • Oral hydration, no further workup, and no antibiotics For People With HIV and CD4 200–500 cells/mm3 With Diarrhea Severe Enough to Compromise Quality of Life or the Ability to Work • Azithromycin 500 mg PO daily for 5 days (BIII), or • Ciprofloxacin 500–750 mg PO every 12 hours for 5 days (BIII) For People With HIV and Severe Disease (e.g., CD4 <200 cells/mm3 or Concomitant AIDS-Defining Illness and With Clinically Severe Diarrhea [≥6 Liquid Stools Per Day or Bloody Stool and/or Accompanying Fever or Chills]) • Hospitalization for diagnostic evaluation and IV antibiotics • Ceftriaxone IV 1–2 g every 24 hours (BIII) Note: If Campylobacter or Shigella bacteremia is suspected, a carbapenem is preferred (BIII). Therapy and duration should be adjusted based on microbiology and antibiotic sensitivity results. If no pathogen is identified and the patient recovers quickly, 5 days of therapy is recommended. For patients with persistent diarrhea (>14 days) without severe clinical signs, antibiotics therapy Diagnostic fecal specimens should be obtained before initiation of empiric antimicrobial therapy. If a pathogen is identified, antibiotic susceptibilities should be performed to confirm and inform antibiotic choices, given increased reports of antibiotic resistance. Oral or IV rehydration (if indicated) should be given to patients with diarrhea (AIII). Antimotility agents should be avoided if there is concern about inflammatory diarrhea, including CDI (BIII). Risk of bacteremia increases with decreasing CD4 count. If no clinical response is observed after 3–4 days, consider a follow-up stool culture with antibiotic susceptibility testing or alternative diagnostic tests (e.g., toxin assays, molecular testing) to evaluate alternative diagnoses, antibiotic resistance, or drug–drug interaction (BIII). MSM may be at increased risk for antibiotic resistant enteric infections. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-2 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments can be withheld until a diagnosis is made. Campylobacteriosis For Mild Disease If CD4 Count >200 cells/mm3 • No therapy unless symptoms persist for more than several days (CIII) For Mild to Moderate Disease (If Susceptible) • Azithromycin 500 mg PO daily for 5 days (BIII) (not recommended for patients with bacteremia [AIII]), or • Ciprofloxacin 500–750 mg PO (or 400 mg IV) every 12 hours for 7–10 days (BIII) For Campylobacter Bacteremia • Ciprofloxacin 500–750 mg PO (or 400 mg IV) every 12 hours for ≥14 days if the isolate is sensitive (BIII) plus an aminoglycoside (BIII) to limit the emergence of antibiotic resistance For Recurrent Infections • Duration of therapy may be extended to 2–6 weeks (BIII). For Mild to Moderate Disease (If Susceptible) • Levofloxacin 750 mg (PO or IV) every 24 hours (BIII) • Add an aminoglycoside to fluoroquinolone in bacteremic patients (BIII) to limit the emergence of antibiotic resistance. Oral or IV rehydration if indicated (AIII) Antimotility agents should be avoided (BIII). Third-generation cephalosporins are not reliably active and use of alternative cell wall–active agents, such as carbapenems, may be necessary in severely ill people who require empiric IV therapy until antimicrobial susceptibilities return. In the United States in 2018, 29% of C. jejuni isolates were resistant to ciprofloxacin and 2% were resistant to azithromycin; among C. coli isolates, 40.5% were resistant to fluoroquinolone and 13.3% were resistant to azithromycin. Effective ART may reduce the frequency, severity, and recurrence of Campylobacter infections. Clostridium difficile Infection (CDI) For Severe or Nonsevere CDI • Fidaxomicin 200 mg PO twice daily for 10 days (AI) Recurrent CDI • 2021 IDSA CDI Guidelines suggest use of fidaxomicin over oral vancomycin because it has a greater likelihood for a sustained clinical response at 30 days (AI). For Severe or Nonsevere CDI • Vancomycin 125 mg PO four times daily for 10 days (AI) For Nonsevere CDI If Neither Fidaxomicin nor Vancomycin Is Available • Metronidazole 500 mg (PO) three times daily for 10 days (CI) Recurrent CDI • Vancomycin is an acceptable option (see IDSA Guideline Severe CDI: white blood cell count ≥15,000 cells/mL or serum creatinine concentrations >1.5 mg/dL; nonsevere CDI: white blood cell count <15,000 cells/mL and serum creatinine concentrations <1.5 mg/dL Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-3 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments for tapered and pulsed regimens) (AI). • FMT may be considered after three CDI episodes (i.e. an initial and two recurrent episodes) (CIII). Salmonellosis All people with HIV and salmonellosis should receive antimicrobial treatment due to an increase of bacteremia (by 20-fold to 100-fold) and mortality (by up to sevenfold) compared to individuals without HIV (AIII). Oral or IV rehydration if indicated (AIII) Antimotility agents should be avoided (BIII). The role of long-term secondary prophylaxis in patients with recurrent Salmonella bacteremia is not well established. Must weigh the benefits against the risks of long-term antibiotic exposure (BIII). Effective ART may reduce the frequency, severity, and recurrence of salmonella infections. For Invasive Disease (Suspected or Confirmed) • Ceftriaxone IV 1–2 g every 24 hours pending susceptibilities (BIII) For Nontyphoidal Salmonella Gastroenteritis (With or Without Bacteremia) (If Susceptible) • Ciprofloxacin 500–750 mg PO (or 400 mg IV) every 12 hours (AIII) Duration of Therapy For Gastroenteritis Without Bacteremia • If CD4 count ≥200 cells/mm3: 7–14 days (BIII) • If CD4 count <200 cells/mm3: minimum of 2 weeks (may extend to up to 6 weeks if with severe disease) (BIII) For Gastroenteritis With Bacteremia • If CD4 count ≥200/mm3: 14 days or longer duration if bacteremia persists or if the infection is complicated (e.g., if metastatic foci of infection are present) (BIII) • If CD4 count <200 cells/mm3: 2–6 weeks (BIII) Secondary Prophylaxis Should Be Considered For Patients With For Nontyphoidal Salmonella Gastroenteritis (With or Without Bacteremia) (If Susceptible) • Levofloxacin 750 mg (PO or IV) every 24 hours (BIII), or • Moxifloxacin 400 mg (PO or IV) every 24 hours (BIII), or • TMP-SMX (160 mg/800 mg) PO (or IV) every 12 hours (BIII), or • Ceftriaxone 1–2 g IV every 24 hours (BIII) • Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-4 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments • Recurrent Salmonella bacteremia (BIII), or • Recurrent gastroenteritis (with or without bacteremia) with CD4 count <200 cells/mm3 with severe diarrhea (BIII) Shigellosis • Ciprofloxacin 500–750 mg PO (or 400 mg IV) every 12 hours (if MIC <0.12 µg/mL) (AIII) Duration of Therapy • Gastroenteritis: 5–7 days (AIII) (except ciprofloxacin [5–10 days] and azithromycin [5 days]) • Bacteremia: ≥14 days (BIII) • Recurrent infections: Up to 6 weeks (BIII) In Severely Ill Patients Requiring Empiric Parenteral Therapy While Awaiting Susceptibility • Consider initiating a carbapenem until antimicrobial susceptibilities are available (BIII). Note: Increased resistance of Shigella to fluoroquinolones in the United States. Alternative antibiotics should be considered if ciprofloxacin MIC is ≥0.12 µg/mL (BIII). • Levofloxacin 750 mg (PO or IV) every 24 hours (BIII), or • Trimethoprim 160 mg/sulfamethoxazole 800 mg PO or IV every 12 hours for 5–7 days (BIII), or • Azithromycin 500 mg PO daily for 5 days (BIII), or • Ceftriaxone 1–2 g IV every 24 hours (BIII) Note: Azithromycin and TMP-SMX are not recommended for treatment of bacteremia. Note: Azithromycin-resistant Shigella spp. has been reported in MSM with HIV. Therapy may slightly shorten the duration of illness and/or prevent the spread of infection (AIII). Oral or IV rehydration if indicated (AIII) Anti-motility agents should be avoided (BIII). Many Shigella strains that are resistant to fluoroquinolones exhibit resistance to other commonly used antibiotics. Antibiotic sensitivity testing of Shigella isolates from individuals with HIV should be performed routinely. Given increasing antimicrobial resistance and limited data showing that antibiotic therapy limits transmission, antibiotic treatment may be withheld in patients with CD4 count >500 cells/mm3 whose diarrhea resolves prior to culture confirmation of Shigella infection (CIII). Effective ART may decrease the risk of recurrence of Shigella infections. Bartonellosis For Bacillary Angiomatosis, Peliosis Hepatis, Bacteremia, and Osteomyelitis • Doxycycline 100 mg PO or IV every 12 hours (AII), or For Bacillary Angiomatosis, Peliosis Hepatis, Bacteremia, Osteomyelitis, and Other Severe Infection When RIF is used, take into consideration the potential for significant interaction with ARV drugs and other medications Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-5 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments • Erythromycin 500 mg PO or IV every 6 hours (AII) CNS Infections • (Doxycycline 100 mg +/- RIF 300 mg) PO or IV every 12 hours (AIII) Confirmed Bartonella Endocarditis • (Doxycycline 100 mg IV plus RIF 300 mg PO or IV) every 12 hours for 6 weeks, then continue with doxycycline 100 mg IV or PO every 12 hours (BII) Other Severe Infections • (Doxycycline 100 mg PO or IV +/- RIF 300 mg PO or IV) every 12 hours (BIII), or • (Erythromycin 500 mg PO or IV every 6 hours) +/- RIF 300 mg PO or IV every 12 hours (BIII) Duration of Therapy • At least 3 months (AII) • Azithromycin 500 mg PO daily (BIII) • Clarithromycin 500 mg PO twice a day (BIII) Confirmed Bartonella Endocarditis • (Doxycycline 100 mg IV every 12 hours plus gentamicin 1 mg/kg IV every 8 hours) for 2 weeks, then continue with doxycycline 100 mg IV or PO every 12 hours (BII) (see Table 4 for dosing recommendations). If relapse occurs after initial (>3 month) course of therapy, long-term suppression with doxycycline or a macrolide is recommended as long as the CD4 count is <200 cells/mm3 (AIII). Candidiasis (Mucocutaneous) For Oropharyngeal Candidiasis—Initial Episodes (For 7–14 Days) • Fluconazole 200 mg PO loading dose, followed by 100–200 mg PO daily (AI) For Esophageal Candidiasis (For 14–21 Days) • Fluconazole 200-mg loading dose, followed by 100–200 mg (up to 400 mg) PO or IV daily (AI). (Consider oral suspension for people with difficulty swallowing.) For Uncomplicated Vulvovaginal Candidiasis • Fluconazole 150 mg PO for one dose (AII), or • Topical azoles (clotrimazole, butoconazole, miconazole, For Oropharyngeal Candidiasis—Initial Episodes (For 7–14 Days) Oral Therapy • Itraconazole oral solution 200 mg PO daily (BI), or • Posaconazole oral suspension 400 mg PO twice a day for 1 day, then 400 mg daily (BI), or • Posaconazole tablet 300 mg PO twice a day for 1 day, then 300 mg daily (BI) Topical Therapy • Miconazole mucoadhesive buccal 50-mg tablet once daily; apply to mucosal surface over the canine fossa once daily (do not Chronic or prolonged use of azoles may promote the development of resistance. Systemic azoles may have significant drug– drug interactions with ARV drugs. A higher relapse rate for esophageal candidiasis is seen with echinocandins use than with fluconazole. Suppressive therapy is usually not recommended (CIII) unless patients have frequent or severe recurrences. If the Decision Is to Use Suppressive Therapy Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-6 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments tioconazole, or terconazole) for 3–7 days (AII), or • Ibrexafungerp 300 mg PO twice daily for 1 day (BI) For Severe or Recurrent Vulvovaginal Candidiasis • Fluconazole 100–200 mg PO daily for ≥7 days (AII), or • Topical antifungal ≥7 days (AII) For Recurrent Vulvovaginal Candidiasis Only (the following regimens include treatment for the acute episode plus treatment to reduce recurrence) • Oteseconazole 600 mg PO at Day 1, 450 mg at Day 2, followed by once weekly 150-mg dosing starting at Day 14 for 11 weeks (AI) (for those who are not of reproductive potential); or • Fluconazole 150 mg PO at Days 1, 4, and 7, followed by oteseconazole 150 mg PO daily at Days 14–20, followed by oteseconazole 150 mg once weekly starting at Day 28 for 11 weeks (Weeks 4–14) (AI) (for those who are not of reproductive potential); or • Fluconazole 150 mg PO every 72 hours for three doses, followed by ibrexafungerp 300 mg PO twice daily 1 day per month for 6 months (BI). (Use an effective form of contraception during treatment and for 4 days after the last dose.) swallow, chew, or crush tablet.) (BI), or • Clotrimazole troches 10 mg PO five times daily (BI), or • Nystatin suspension 4–6 mL four times a day (BII) For Esophageal Candidiasis (For 14–21 Days) • Itraconazole oral solution 200 mg PO daily (AI), or • Isavuconazole 400 mg PO loading dose, followed by 100 mg PO daily (BI), or • Isavuconazole 400 mg PO once weekly (BI), or • Voriconazole 200 mg PO or IV twice a day (BI), or • Posaconazole oral suspension 400 mg PO twice a day for 1 day, then 400 mg daily (BI), or • Posaconazole tablet 300 mg PO twice a day for 1 day, then 300 mg daily (BI), or • Lipid formulation of amphotericin B 3–4 mg/kg IV daily (BI), or • Caspofungin 70 mg IV loading dose, followed by 50 mg IV daily (BI), or • Micafungin 150 mg IV daily (BI), or • Anidulafungin 100 mg IV once, then 50 mg IV daily (BI) For Azole-Refractory Candida glabrata Vaginitis • Boric acid vaginal suppository 600 mg once daily for 14 days (BII) Oropharyngeal Candidiasis • Fluconazole 100 mg PO once daily or three times weekly (BI) Esophageal Candidiasis • Fluconazole 100–200 mg PO daily (BI), or • Posaconazole oral suspension 400 mg PO twice a day (BII), or • Posaconazole tablet 300 mg PO daily (BII) Vulvovaginal Candidiasis • Fluconazole 150 mg PO once weekly (BII), or • Oteseconazole 600 mg at Day 1 and 450 mg at Day 2 for treatment of the acute episode, followed by once-weekly 150-mg doses starting at Day 14 for 11 weeks (AI) (for those who are not of reproductive potential); or • Fluconazole 150 mg at Days 1, 4, and 7 for treatment of the acute episode, followed by oteseconazole 150 mg daily at Days 14–20, followed by oteseconazole 150 mg once weekly starting at Day 28 for 11 weeks (Weeks 4–14) (AI) (for those who are not of reproductive potential); or • Ibrexafungerp 300 mg twice daily 1 day per month for 6 months (BI). (Use an effective form of contraception Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-7 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments during treatment and for 4 days after the last dose.) Chagas Disease (American Trypanosomiasis) For Acute or Reactivated Disease • Benznidazole 5–8 mg/kg/day PO in two divided doses for 60 days (BIII) (commercially available at com/en; most experts recommend a daily maximum of 300 mg), or • Nifurtimox (Lampit®) 8–10 mg/kg/day PO in three divided doses for 60 days (BIII) (commercially available through retail sources) None Treatment is effective in reducing parasitemia and preventing clinical symptoms or slowing disease progression; however, these drugs have limited efficacy in achieving parasitological cure. Treatment is not recommended for patients with advanced chagasic cardiomyopathy. Duration of therapy has not been studied in patients with HIV. Initiation or optimization of ART is recommended for all people with HIV with concomitant Trypanosoma cruzi (AIII). Coccidioidomycosis Mild to Moderate Pulmonary Infection • Fluconazole 400 mg PO daily (AII), or • Itraconazole 200 mg three times a day for 3 days, then 200 mg PO twice a day (AII) • Duration of therapy: clinical response to 3–6 months of therapy, CD4 count ≥250 cells/mm3, and viral suppression on ARV (AII) Mild to Moderate Pulmonary Infection For Patients Who Failed to Respond to Fluconazole or Itraconazole • Posaconazole delayed release tablet 300 mg PO twice a day for first day, then 300 mg PO once daily (BIII), or • Voriconazole 400 mg PO twice daily for first day, then 200 mg PO twice a day (BIII) Some patients with meningitis may develop hydrocephalus and require CSF shunting. Therapy should be lifelong in patients with meningeal infections because relapse occurs in 80% of patients with HIV after discontinuation of triazole therapy (AII). See Table 4 for antifungal drug–drug interactions. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-8 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Severe Pulmonary or Extrapulmonary Infection (Except Meningitis) • Lipid formulation amphotericin B 3–5 mg/kg IV daily (AIII), or • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV daily (AII) • Continue until clinical improvement, then switch to an azole (BIII). Therapy should be continued for at least 12 months and usually much longer, and should be continued in patients with HIV viremia or with CD4 count <250 cells/mm3 (BIII) Meningeal Infections • Fluconazole 400–800 mg IV or PO daily (AII) • Duration of therapy: lifelong (AII) Severe Pulmonary or Extrapulmonary Infection (Except Meningitis) • Some specialists will add a triazole (fluconazole or itraconazole, with itraconazole preferred for bone disease) 400 mg per day to amphotericin B therapy and continue triazole once amphotericin B is stopped (CIII). Meningeal Infections • Itraconazole 200 mg PO two or three times daily (BII), or • Voriconazole 200–400 mg PO twice a day (BIII), or • Posaconazole delayed release tablet 300 mg PO twice on first day, then 300 mg PO daily (CIII), or • Isavuconazole sulfate 372 mg PO every 8 hrs for six doses, then 372 mg daily (CIII) • Intrathecal amphotericin B deoxycholate when triazole antifungals are ineffective (AIII) Itraconazole, posaconazole, and voriconazole may have significant interactions with certain ARV agents. These interactions are complex and can be bidirectional. Refer to Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines for dosage recommendations. Therapeutic drug monitoring and dosage adjustment may be necessary to ensure triazole antifungal and antiretroviral efficacy and reduce concentration-related toxicities. Intrathecal amphotericin B should only be given in consultation with a specialist and administered by an individual with experience with the technique. Community-Acquired Pneumonia (CAP) Empiric antibiotic therapy should be initiated promptly for patients presenting with clinical and radiographic evidence consistent with bacterial pneumonia. The recommendations listed are suggested empiric therapy. The regimen should be modified as needed once microbiologic results are available (BIII). Providers must also consider the risk of opportunistic lung infections (e.g., PCP, TB), which may alter the empiric therapy. Empiric antibiotic therapy should be initiated promptly for patients presenting with clinical and radiographic evidence consistent with bacterial pneumonia. The recommendations listed are suggested empiric therapy. The regimen should be modified as needed once microbiologic results are available (BIII). Providers must also consider the risk of opportunistic lung infections (e.g., PCP, TB), which may alter the empiric therapy. Duration For most patients, 5–7 days Patients should be afebrile for 48–72 hours and clinically stable before stopping antibiotics. Longer duration is often required if severe CAP or bacteremia is present, and particularly if due to S. pneumoniae or complicated S. aureus pneumonia. Fluoroquinolones should be used with caution in Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-9 Empiric Outpatient Therapy • A PO beta-lactam plus a PO macrolide (azithromycin or clarithromycin) (AII) Preferred Beta-Lactams • High-dose amoxicillin or amoxicillin/clavulanate Alternative Beta-Lactams • Cefpodoxime or cefuroxime, or • Levofloxacin 750 mg PO once daily (AII), or moxifloxacin 400 mg PO once daily (AII), especially for patients with penicillin allergies Empiric Therapy for Hospitalized Patients with Nonsevere CAP • An IV beta-lactam plus a macrolide (azithromycin or clarithromycin) (AI) Preferred Beta-Lactams • Ceftriaxone, cefotaxime, or ampicillin-sulbactam • Levofloxacin 750 mg IV once daily (AI), or moxifloxacin, 400 mg IV once daily (AI), especially for patients with penicillin allergies. Empiric Therapy for Hospitalized Patients with Severe CAP • An IV beta-lactam plus IV azithromycin (AI), or • An IV beta-lactam plus (levofloxacin 750 mg IV once daily or moxifloxacin 400 mg IV once daily) (AI) Preferred Beta-Lactams • Ceftriaxone, cefotaxime, or ampicillin-sulbactam Empiric Therapy for Patients at Risk of Pseudomonas Pneumonia • An IV antipneumococcal, antipseudomonal beta-lactam Empiric Outpatient Therapy • A PO beta-lactam plus PO doxycycline (CIII) Preferred Beta-Lactams • High-dose amoxicillin or amoxicillin/clavulanate Alternative Beta-Lactams • Cefpodoxime or cefuroxime Empiric Therapy for Hospitalized Patients with Nonsevere CAP • An IV beta-lactam plus doxycycline (CIII) Empiric Therapy for Hospitalized Patients with Severe CAP For Penicillin-Allergic Patients • Aztreonam IV plus (levofloxacin 750 mg IV once daily or moxifloxacin 400 mg IV once daily) (BIII) Empiric Therapy for Patients at Risk of Pseudomonas Pneumonia • An IV antipneumococcal, antipseudomonal beta-lactam plus an IV aminoglycoside plus azithromycin (BII), or • An IV antipneumococcal, antipseudomonal beta-lactam plus an aminoglycoside plus (levofloxacin 750 mg IV once daily or moxifloxacin 400 mg IV once daily) (BIII) For Penicillin-Allergic Patients • Replace the beta-lactam with aztreonam (BIII). patients in whom TB is suspected but is not being treated. Empiric therapy with a macrolide alone is not routinely recommended, because of increasing pneumococcal resistance (up to 30%) (BIII). Patients receiving a macrolide for MAC prophylaxis may have bacterial resistance to macrolide due to chronic exposure. For patients begun on IV antibiotic therapy, switching to PO should be considered when they are clinically improved and able to tolerate oral medications. Antibiotic chemoprophylaxis is generally not recommended because of the potential for developing drug resistance and drug toxicities (AI). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-10 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments plus (ciprofloxacin 400 mg IV every 8–12 hours or levofloxacin 750 mg IV once daily) (AI) Preferred Beta-Lactams • Piperacillin-tazobactam, cefepime, imipenem, or meropenem Empiric Therapy for Patients at Risk for Methicillin-Resistant Staphylococcus aureus Pneumonia • Add vancomycin IV or linezolid (IV or PO) to the baseline regimen (AII). • Addition of clindamycin to vancomycin (but not to linezolid) can be considered for severe necrotizing pneumonia to minimize bacterial toxin production (CII). Cryptococcosis Cryptococcal Meningitis Induction Therapy (for 2 weeks, followed by consolidation therapy) • Liposomal amphotericin B 3–4 mg/kg IV daily plus flucytosine 25 mg/kg PO four times a day (AI) (Note: Flucytosine dose should be adjusted in patients with renal dysfunction.) • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV daily plus flucytosine 25 mg/kg PO four times a day (AI) (if cost is an issue and the risk of renal dysfunction is low), or • If not improved clinically or remain clinically unstable, continue induction therapy until the CSF culture is confirmed to be negative (BIII). Cryptococcal Meningitis Induction Therapy (for at least 2 weeks, followed by consolidation therapy) • Amphotericin B lipid complex 5 mg/kg IV daily plus flucytosine 25 mg/kg PO four times a day (BII), or • Liposomal amphotericin B 3–4 mg/kg IV daily plus fluconazole 800–1,200 mg PO or IV daily (BIII), or • Fluconazole 1,200 mg PO or IV daily plus flucytosine 25 mg/kg PO four times a day (BII), or • Fluconazole 800 mg PO or IV daily plus flucytosine 25 mg/kg PO four times a day (BIII), or Addition of flucytosine to amphotericin B has been associated with more rapid sterilization of CSF and decreased risk for subsequent relapse. Patients receiving flucytosine should have either blood levels monitored (peak level 2 hours after dose should be 25–100 mcg/mL) or at least twice weekly monitoring of complete blood counts for cytopenia. Dosage should be adjusted in patients with renal insufficiency (BII). In resource-limited settings, induction of 1 week of amphotericin B deoxycholate with flucytosine followed by high-dose fluconazole is preferred (BIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-11 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Consolidation Therapy (for at least 8 weeks (AI), followed by maintenance therapy) • Fluconazole 800 mg PO (or IV) daily (AI) • For clinically stable patients with negative CSF cultures, dose can be reduced to 400 mg PO once daily (AII) • If CSF remains positive (but clinically stable) after 2 weeks of induction therapy, increase fluconazole dose to 1,200 mg and perform LP 2 weeks later (BIII); duration of consolidation therapy should be 8 weeks from the time of negative CSF culture (AI). Maintenance Therapy • Fluconazole 200 mg PO daily for ≥1 year from initiation of antifungal therapy (AI) For Non-CNS, Extrapulmonary Cryptococcosis and Diffuse Pulmonary Disease or Patients with Isolated Asymptomatic Antigenemia Without Meningitis and Serum CrAg ≥1:640 by LFA • Treatment same as for cryptococcal meningitis (BIII) Non-CNS Cryptococcosis with Mild-to-Moderate Symptoms and Focal Pulmonary Infiltrates, or Patients with Isolated Asymptomatic Antigenemia Without Meningitis and Serum CrAg ≤1:320 by LFA • Fluconazole, 400 to 800 mg PO daily for 10 weeks, followed by 200 mg daily for a total of 6 months (BIII) • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV daily plus fluconazole 800–1,200 mg PO or IV daily (BI), or • Liposomal amphotericin B 3–4 mg/kg IV daily (BI), or • Amphotericin B deoxycholate 0.7–1.0 mg/kg IV once daily alone (BI), or • Liposomal amphotericin B 3–4 mg/kg IV once daily plus flucytosine 25 mg/kg PO four times a day for 1 week followed by fluconazole 1,200 mg PO once daily (BIII), or • Fluconazole 1,200 mg PO or IV daily (CI) Consolidation Therapy (for at least 8 weeks [AI], followed by maintenance therapy) • If patient’s CSF culture remains positive at the end of 2 weeks, but the patient is not ill enough to be hospitalized, continue flucytosine for an additional 2 weeks with fluconazole 1,200 mg daily before starting a single-drug consolidation regimen. • Itraconazole 200 mg PO twice a day for 8 weeks— less effective than fluconazole (CI) Maintenance Therapy • No alternative therapy recommendation Opening pressure should always be measured when an LP is performed. Repeated LPs or CSF shunting are essential to effectively managing increased intracranial pressure. Corticosteroids and mannitol are ineffective in reducing ICP and are not recommended (AIII). Some specialists recommend a brief course of tapering dose of corticosteroid for management of severe IRIS symptoms (BIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-12 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Cryptosporidiosis • Aggressive oral and/or IV rehydration and replacement of electrolyte loss (AIII), and • Symptomatic treatment of diarrhea with anti-motility agents (AIII), and • ART initiation to achieve immune restoration to CD4 count >100 cells/mm3 (AII). No therapy has been shown to be effective without ART. Consider trial of these agents in conjunction with ART, rehydration, and symptomatic treatment: • Nitazoxanide 500–1,000 mg PO twice a day with food for at least 14 days (CIII), or • Paromomycin 500 mg PO four times daily for 14–21 days (CIII) Tincture of opium may be more effective than loperamide in management of diarrhea (CIII). Because diarrhea can cause lactase deficiency, patients should avoid milk products (CIII). Cytomegalovirus (CMV) Disease CMV Retinitis Induction Therapy (Followed by Chronic Maintenance Therapy) For Immediate Sight-Threatening Lesions (within 1,500 microns of the fovea) • Ganciclovir 5 mg/kg every 12 hours IV or valganciclovir 900 mg PO twice a day or for 14–21 days (AI) (some prefer IV ganciclovir initially and transition to PO valganciclovir when there is evidence of clinical response) with or without • Intravitreal injections of ganciclovir (2 mg) or foscarnet (2.4 mg) to rapidly achieve high intraocular concentration, continued weekly until lesion inactivity is achieved (AIII); plus For Peripheral Lesions • Valganciclovir 900 mg PO twice a day for 14–21 days, then 900 mg once daily (AI) Maintenance Therapy • Valganciclovir 900 mg PO daily (AI) for 3–6 months until ART-induced immune recovery CMV Esophagitis or Colitis • Ganciclovir 5 mg/kg IV every 12 hours; may switch to valganciclovir 900 mg PO every CMV Retinitis For Immediate Sight-Threatening Lesions (within 1,500 microns of the fovea): Intravitreal therapy as listed in the Preferred section, plus one of the following: Alternative Systemic Induction Therapy (Followed by Chronic Maintenance Therapy) • Foscarnet 90 mg/kg IV every 12 hours or 60 mg/kg every 8 hours for 14–21 days (BI), or • Cidofovir 5 mg/kg/week IV for 2 weeks; saline hydration before and after therapy and probenecid, 2 g PO 3 hours before dose, followed by 1 g PO 2 hours and 8 hours after the dose (total of 4 g) (CI) (Note: This regimen should be avoided in patients with sulfa allergy because of cross hypersensitivity with probenecid.) Chronic Maintenance (For 3–6 Months Until ART-Induced Immune Recovery) • Foscarnet 90–120 mg/kg IV once daily (AI), or • Cidofovir 5 mg/kg IV every other week with saline The choice of therapy for CMV retinitis should be individualized, based on tolerance of systemic medications, prior exposure to anti-CMV drugs, and location of the lesion (AIII). Initial therapy in patients with CMV retinitis, esophagitis, colitis, and pneumonitis should include initiation or optimization of ART (BIII). Given the evident benefits of systemic therapy in preventing contralateral eye involvement, reduce CMV visceral disease and improve survival. Whenever feasible, treatment should include systemic therapy. The ganciclovir ocular implant, which is effective for treatment of CMV retinitis, is no longer available. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-13 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments 12 hours once the patient can tolerate oral therapy (BI) • Valganciclovir 900 mg PO every 12 hours may be considered as initial therapy in mild diseases (CIII). • Duration: 21–42 days or until symptoms have resolved (CII) • Maintenance therapy is usually not necessary but should be considered after relapses (BII). Well-Documented, Histologically Confirmed CMV Pneumonia • Experience for treating CMV pneumonitis in HIV patients is limited. Use of IV ganciclovir or IV foscarnet is reasonable (doses same as for CMV retinitis) (CIII). • The optimal duration of therapy and the role of oral valganciclovir have not been established. CMV Neurological Disease Note: Treatment should be initiated promptly. • Ganciclovir 5 mg/kg IV every 12 hours plus (foscarnet 90 mg/kg IV every 12 hours or 60 mg/kg IV every 8 hours) to stabilize disease and maximize response. Continue until there is symptomatic improvement and resolution of neurologic symptoms (CIII). • The optimal duration of therapy and the role of oral valganciclovir have not been established. hydration and probenecid as above (BI) CMV Esophagitis or Colitis • Foscarnet 90 mg/kg IV every 12 hours or 60 mg/kg every 8 hours (BI) for patients with treatment-limiting toxicities to ganciclovir or with ganciclovir resistance, or • Valganciclovir 900 mg PO every 12 hours in milder disease and if able to tolerate PO therapy (BII), or • Duration: 21–42 days or until symptoms have resolved (CII) • For mild disease, if ART can be initiated without delay, consider withholding CMV therapy (CIII). Routine (i.e., every 3 months) ophthalmologic follow-up is recommended after stopping chronic maintenance therapy for early detection of relapse or IRU, and then periodically after sustained immune reconstitution (AIII). IRU may develop in the setting of immune reconstitution. Treatment of IRU Periocular, intravitreal, or short courses of systemic steroid (BIII) Hepatitis B Virus (HBV) Disease ART is recommended for all patients with HIV/HBV coinfection regardless of CD4 cell count and HBV DNA level (AIII). The ART regimen must include two drugs that are active against both HBV and HIV (AIII). For People Not on ART • Anti-HBV therapy is indicated for those who meet criteria for treatment according to the AASLD Hepatitis B Guidance. Directly acting HBV drugs—such as adefovir, emtricitabine, entecavir, lamivudine, telbivudine, or tenofovir—must not be given in the absence of a fully suppressive ART regimen to avoid selection of drug-resistant HIV (AII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-14 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments If CrCl ≥60 mL/min: • (TDF 300 mg plus [FTC 200 mg or 3TC 300 mg]) or (TAF [10 or 25 mg]a plus FTC 200 mg) PO once daily (AII) Note: TAF 10 mg is in the STR tablets of EVG/COBI/TAF/FTC and DRV/COBI/TAF/FTC; when TAF is used with other ARVs, the dose is 25 mg. If CrCl 30–59 mL/min: • TAF (10 or 25 mg)a plus FTC 200 mg PO once daily (AII) If CrCl <30 mL/min, not on HD: • Renally dosed entecavir (in place of TDF or TAF), with a fully suppressive ART regimen, or • ART with renally dose-adjusted TDF and FTC or 3TC can be used (BIII) if recovery of renal function is unlikely. If on HD: • (TDF or TAF) plus (FTC or 3TC) can be used. Refer to Table 6 for dosing recommendations. TAF and FTC do not require renal dose adjustment in people receiving HD. Duration • Continue treatment indefinitely (BIII). • Peginterferon alfa-2a 180 mcg SQ once weekly for 48 weeks (CIII), or • Peginterferon alfa-2b 1.5 mcg/kg SQ once weekly for 48 weeks (CIII) Chronic administration of 3TC or FTC as the only active drug against HBV should be avoided because of the high rate of selection of HBV drug-resistance mutations (AI). People with 3TC-resistant HBV will have cross-resistance to telbivudine and FTC and partial resistance to entecavir. These agents should not be used among people found to have 3TC-resistant HBV (AI). If 3TC resistance is suspected or documented, TDF or TAF should be added to the ART regimen (BIII). When changing ART regimens, continue agents with anti-HBV activity (AIII). If anti-HBV therapy is discontinued and a flare occurs, therapy should be reinstituted because it can be potentially lifesaving (AIII). Because HBV reactivation can occur during treatment for HCV with direct-acting antivirals in the absence of anti-HBV therapy, all people with HIV/HBV coinfection who will be treated for HCV infection should be on HBV-active ART at the time of HCV treatment initiation (AIII). If immunosuppressive therapy is given, HBV reactivation can occur. For people who are HBsAg-positive, treatment for Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-15 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments HBV infection should be administered (AII). Hepatitis C Virus (HCV) Disease For Treatment-Naive Patients Without Cirrhosis (Any Genotype or No Pre-treatment Genotype) • Glecaprevir/pibrentasvir FDC (100 mg/40 mg per tablet), three tablets daily for 8 weeks (AI), or • Sofosbuvir/velpatasvir FDC (400 mg/100 mg per tablet), one tablet daily for 12 weeks (AI) Characteristics that exclude patients from receiving simplified approach to therapy are outlined in Box 1 of the Hepatitis C Virus section. For Treatment-Naive Patients with Compensated Cirrhosis (Recommendations Based on Genotypes) Genotypes 1, 2, 4–6 • Glecaprevir/pibrentasvir FDC (100 mg/40 mg per tablet), three tablets daily for 8 weeks (AIII), or • Sofosbuvir/velpatasvir FDC (400 mg/100 mg per tablet), one tablet daily for 12 weeks (AI) Genotype 3 • Glecaprevir/pibrentasvir FDC (100 mg/40 mg per tablet), three tablets daily for 8 weeks (AIII) For Treatment of Acute HCV Infection • Glecaprevir/pibrentasvir FDC (100 mg/40 mg per tablet), three tablets daily for 8 weeks (AII), or • Sofosbuvir/velpatasvir FDC (400 mg/100 mg per tablet), one tablet daily for 12 weeks (AII) For Treatment-Naive Patients with Compensated Cirrhosis (Recommendations Based on Genotypes) Genotypes 1, 2, 4–6 • Glecaprevir/pibrentasvir FDC (100 mg/40 mg per tablet), three tablets daily for 12 weeks (CI) Genotype 3 • Glecaprevir/pibrentasvir FDC (100 mg/40 mg per tablet), three tablets daily for 12 weeks (CI), or • Sofosbuvir/velpatasvir FDC (400 mg/100 mg per tablet), one tablet daily with or without ribavirin for 12 weeks, pending results of NS5A RAS testing (CI) A simplified approach to HCV treatment can be used in treatment-naive patients with any genotype and without cirrhosis. This approach includes standardized treatment with no on-treatment testing or in-person follow-up and limited follow-up to confirm SVR. See Hepatitis C Virus section to review a summary of drug–drug interactions between HCV therapy and ARV drugs. HCV treatment should not be withheld solely due to perceived lack of adherence to ART or untreated HIV (BIII). Effort should be made to document SVR (HCV RNA less than lower limits of quantification) at least 12 weeks after completion of therapy (AI). Patients without cirrhosis who achieve SVR do not require continued liver disease monitoring. Recommendations for treatment after DAA failure are not provided. The reader is referred to the corresponding section in the AASLD/IDSA HCV treatment guidance. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-16 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Herpes Simplex Virus (HSV) Disease Orolabial Lesions (for 5–10 days) • Valacyclovir 1 g PO twice a day (AIII), or • Famciclovir 500 mg PO twice a day (AIII), or • Acyclovir 400 mg PO three times a day (AIII) Initial or Recurrent Genital HSV (for 5–14 days) • Valacyclovir 1 g PO twice a day (AI), or • Famciclovir 500 mg PO twice a day (AI), or • Acyclovir 400 mg PO three times a day (AI) Severe Mucocutaneous HSV • Initial therapy acyclovir 5 mg/kg IV every 8 hours (AIII) • After lesions begin to regress, change to PO therapy as above. Continue until lesions are completely healed. Chronic Suppressive Therapy For Patients with Severe Recurrences of Genital Herpes (AI) or Patients Who Want to Minimize Frequency of Recurrences (AI) • Valacyclovir 500 mg PO twice a day (AI), or • Famciclovir 500 mg PO twice a day (AI), or • Acyclovir 400 mg PO twice a day (AI) • Continue indefinitely, regardless of CD4 count. For Acyclovir-Resistant HSV Preferred Therapy • Foscarnet 80–120 mg/kg/day IV in two to three divided doses until clinical response (AI) Alternative Therapy (CIII) • IV cidofovir (dosage as in CMV retinitis), or • Topical trifluridine 1% three times a day, or • Topical cidofovir 1% once daily, or • Topical imiquimod 5% three times weekly, or • Topical foscarnet 1% five times daily Duration of Therapy • 21–28 days or longer Patients with HSV infection can be treated with episodic therapy when symptomatic lesions occur, or with daily suppressive therapy to prevent recurrences. Extemporaneous compounding of topical products can be prepared using trifluridine ophthalmic solution and the IV formulation of cidofovir and foscarnet. An expanded access program of oral pritelivir is now available for immunocompromised patients with acyclovir-resistant HSV infection. For more information, see the AiCuris Pritelivir website. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-17 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Histoplasmosis Moderately Severe to Severe Disseminated Disease Induction Therapy • For at least 2 weeks or until clinically improved • Liposomal amphotericin B 3 mg/kg IV daily (AI) Maintenance Therapy • Itraconazole 200 mg PO three times a day for 3 days, then 200 mg PO twice a day (AII) Less Severe Disseminated Disease Induction and Maintenance Therapy • Itraconazole 200 mg PO three times a day for 3 days, then 200 mg PO twice a day (AII) Duration of Therapy • At least 12 months Meningitis Induction Therapy (4–6 weeks) • Liposomal amphotericin B 5 mg/kg/day (AIII) Maintenance Therapy • Itraconazole 200 mg PO twice a day to three times a day for ≥12 months and until resolution of abnormal CSF findings (AII) Long-Term Suppression Therapy For patients with severe disseminated or CNS infection (AIII) after completion of at least 12 months of therapy and who relapse despite appropriate therapy (BIII) • Itraconazole 200 mg PO daily (AIII) Moderately Severe to Severe Disseminated Disease Induction Therapy (for at least 2 weeks or until clinically improved) • Amphotericin B lipid complex 5 mg/kg IV daily (AIII), or Alternatives to Itraconazole for Maintenance Therapy or Treatment of Less Severe Disease • Posaconazole extended release 300 mg PO twice a day for 1 day, then 300 mg PO once daily (BIII) • Voriconazole 400 mg PO twice a day for 1 day, then 200 mg twice a day (BIII), or • Fluconazole 800 mg PO daily (CII) Meningitis (These Recommendations Are Based on Limited Clinical Data for Patients with Intolerance to Itraconazole) • Posaconazole extended release 300 mg PO twice a day for 1 day, then 300 mg PO once daily (BIII) • Voriconazole 400 mg PO twice a day for 1 day, then 200 mg twice a day (BIII), or • Fluconazole 800 mg PO daily (CII) Long-Term Suppression Therapy • Posaconazole 300 mg extended release tablet PO once daily (BIII) • Voriconazole 200 mg PO twice daily (BIII) • Fluconazole 400 mg PO once daily (CII) Itraconazole, posaconazole, and voriconazole may have significant interactions with certain ARV agents. These interactions are complex and can be bidirectional. Refer to Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines for dosage recommendations. Therapeutic drug monitoring and dosage adjustment may be necessary to ensure triazole antifungal and ARV efficacy and reduce concentration-related toxicities. Random serum concentration of itraconazole between 1–2 mcg/mL is recommended. Frequency and severity of toxicities increase when concentration is >4 mcg/mL. Acute pulmonary histoplasmosis in patients with HIV with CD4 counts >300 cells/mm3 should be managed as non-immunocompromised host (AIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-18 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Human Herpesvirus-8 (HHV-8) Diseases (Kaposi Sarcoma [KS], Primary Effusion Lymphoma [PEL], Multicentric Castleman’s Disease [MCD]) Mild to Moderate KS (Localized Involvement of Skin and/or Lymph Nodes) • Initiate or optimize ART (AII). Advanced KS (Visceral [AI] or Disseminated Cutaneous KS [BIII]) • Chemotherapy (per oncology consult) plus ART • Liposomal doxorubicin first-line chemotherapy (AI) Primary Effusion Lymphoma • Chemotherapy (per oncology consult) plus ART (AIII) • PO valganciclovir or IV ganciclovir can be used as adjunctive therapy (CIII) MCD Therapy Options (In Consultation with Specialist, Depending on HIV/HHV-8 Status, Presence of Organ Failure, and Refractory Nature of Disease) ART (AIII) along with one of the following: • Valganciclovir 900 mg PO twice a day for 3 weeks (CII), or • Ganciclovir 5 mg/kg IV every 12 hours for 3 weeks (CII), or • Valganciclovir PO or Ganciclovir IV plus zidovudine 600 mg PO every 6 hours for 7–21 days (CII) • Rituximab +/- Prednisone (CII) • Monoclonal antibody targeting IL-6 or IL-6 receptor (BII) Concurrent KS and MCD • Rituximab plus liposomal doxorubicin (BII) MCD • Rituximab (375 mg/m2 given weekly for 4–8 weeks) may be an alternative to or used adjunctively with antiviral therapy (CII). Corticosteroids should be avoided in patients with KS, including those with KS-IRIS (AIII). Corticosteroids are potentially effective as adjunctive therapy for MCD, but should be used with caution, especially in patients with concurrent KS. Patients who received rituximab for MCD may experience subsequent exacerbation or emergence of KS. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-19 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Human Papillomavirus (HPV) Disease Treatment of Genital Warts Patients with HIV may have larger or more numerous warts and may not respond as well to therapy for genital warts when compared to individuals without HIV. Intralesional interferon is usually not recommended because of high cost, difficult administration, and potential for systemic side effects (CIII). In patients with HIV, the rate of recurrence of genital warts despite treatment is high. There is no consensus on the treatment of oral warts. Many treatments for anogenital warts cannot be used in the oral mucosa. Surgery is the most common treatment for oral warts that interfere with function or for aesthetic reasons. Patient-Applied Treatment Options for Uncomplicated External Warts That Can Be Easily Identified by Patients • Topical imiquimod 5% cream: Apply to genital warts at bedtime on 3 nonconsecutive nights per week for up to 16 weeks, until lesions are no longer visible. Each treatment should be washed with soap and water 6–10 hours after application (BII); or • Topical podophyllotoxin (e.g., podofilox 0.5% solution or 0.5% gel): Apply to genital warts twice a day for 3 days, followed by 4 days of no therapy. Can be repeated weekly for up to 4 cycles (BIII); or • Topical sinecatechins 15% ointment: Apply to affected areas three times a day for up to 16 weeks, until warts are completely cleared and not visible (BIII); or • Topical cidofovir 1%: Daily for 5 days per week for 8 weeks (CIII). Topical formulation is not commercially available but may be compounded. Provider-Applied Therapy for Complex or Multicentric Lesions, or Lesions Inaccessible to Patient, or Due to Patient or Provider Preference • Cryotherapy (liquid nitrogen or cryoprobe): Apply until each lesion is thoroughly frozen. Repeat every 1–2 weeks for up to 4 weeks, until lesions are no longer visible (BIII). Some specialists allow the lesion to thaw, then freeze a second time in each session (BIII); or • Trichloroacetic acid or bichloroacetic acid cauterization (80% to 90% aqueous solution): Apply to warts only and allow to dry until a white frost develops. Repeat weekly for up to 6 weeks, until lesions are no longer visible (BIII); or • Intralesional cidofovir (15 mg/mL solution) injected directly into the wart (maximum 1 mL per session). May be repeated every 4 weeks for total of 3–4 treatments (CIII). • Surgical excision (BIII) or laser surgery (CIII) for external or anal warts Isosporiasis (Cystoisosporiasis) For Acute Infection • TMP-SMX (160 mg/800 mg) PO (or IV) four times a day for 10 days (AII), or • TMP-SMX (160 mg/800 mg) PO (or IV) twice a day for 7–10 days (BI) For Acute Infection • Pyrimethamineb 50–75 mg PO daily plus leucovorin 10–25 mg PO daily (BIII), or • Ciprofloxacin 500 mg PO twice a day for 7 days (CI) as a second-line alternative Fluid and electrolyte management in patients with dehydration (AIII). Nutritional supplementation for malnourished patients (AIII). Immune reconstitution with ART may result in fewer relapses (AIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-20 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments • Can start with twice a day dosing first and increase daily dose and/or duration (up to 3–4 weeks) if symptoms worsen or persist (BIII) • IV therapy may be used for patients with potential or documented malabsorption. Chronic Maintenance Therapy (Secondary Prophylaxis) • In patients with CD4 count <200 cells/mm3, TMP-SMX (160 mg/800 mg) PO three times weekly (AI) Chronic Maintenance Therapy (Secondary Prophylaxis) • TMP-SMX (160 mg/800 mg) PO daily or (320 mg/1,600 mg) three times weekly (BIII) • Pyrimethamineb 25 mg PO daily plus leucovorin 5–10 mg PO daily (BIII) • Ciprofloxacin 500 mg three times weekly (CI) as a second-line alternative Leishmaniasis Visceral For Leishmania infantum/chagasi • Liposomal amphotericin B 3–5 mg/kg IV daily (AII), or • Liposomal amphotericin B interrupted schedule (e.g., 4 mg/kg on Days 1–5, 10, 17, 24, 31, 38) (AII) • To achieve total dose of 20–60 mg/kg (AII) For Leishmania donovani • Liposomal amphotericin B 5 mg/kg on Days 1, 3, 5, 7, 9, and 11 plus miltefosine 50 mg PO twice daily (for 28 days if from East Africa or 14 days if from Southeast Asia) (BI) Chronic Maintenance Therapy For Patients With CD4 Count <200 cells/mm3 (AII) • Liposomal amphotericin B 4 mg/kg IV every 2–4 weeks (AII) For Leishmania infantum/chagasi or donovani • Amphotericin B deoxycholate 0.5–1.0 mg/kg IV daily for total dose of 1.5–2.0 g (BII), or • Pentavalent antimony (meglumine antimoniate) 20 mg/kg IV or IM daily for 28 days (BII) For Leishmania donovani • Liposomal amphotericin B 3–5 mg/kg IV daily to achieve total dose of 20–60 mg/kg (AII), or • Liposomal amphotericin B interrupted schedule (e.g., 4 mg/kg on Days 1–5, 10, 17, 24, 31, 38) to achieve total dose of 20–60 mg/kg (AII), or • For Indian L. donovani: Miltefosine ~2.5–3.0 mg/kg PO daily in 2–3 divided doses (maximum 150 mg daily) for 28 days (BII) Chronic Maintenance Therapy (Secondary Prophylaxis) ART should be initiated or optimized as soon as possible (AIII). Pentavalent antimony is for investigational use only. For miltefosine, visit www.profounda.com. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-21 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments • Amphotericin B lipid complex 3 mg/kg IV every 21 days (BII), or • Pentavalent antimony (meglumine antimoniate) 20 mg/kg IV or IM every 4 weeks (BII), or • Pentamidine 4 mg/kg (maximum 300 mg) IV every 2–4 weeks (BII) Cutaneous For Initial Infection • Liposomal amphotericin B 4 mg/kg IV daily for 10 days (BIII) to achieve total dose of 20–60 mg/kg, or • Liposomal amphotericin B interrupted schedule (e.g., 4 mg/kg on Days 1–5, 10, 17, 24, 31, 38) to achieve total dose of 20–60 mg/kg (BIII), or • Miltefosine 2.5 mg/kg/day PO in 2–3 divided doses for 28 days (maximum 150 mg per day) (BIII), or • Pentavalent antimony (meglumine antimoniate) 20 mg/kg IV or IM daily for 28 days (BIII) Chronic Maintenance Therapy • May be indicated in immunocompromised patients with multiple relapses (CIII) • Drugs and doses same as for visceral leishmaniasis Possible Options • Cryotherapy, or • Topical paromomycin, or • Intralesional pentavalent antimony (meglumine antimoniate) or pentamidine, or • PO or IV fluconazole (L. major & L. mexicana) • IV pentamidine • Local heat therapy No data exist for any of these agents in patients with HIV; choice and efficacy are dependent on species of Leishmania. ART should be initiated or optimized as soon as possible (AIII). Pentavalent antimony is for investigational use only. For miltefosine, visit www.profounda.com. Malaria Because Plasmodium falciparum malaria can progress within hours from mild symptoms or low-grade fever to severe disease or death, all patients with HIV with confirmed or suspected P. falciparum infection should be hospitalized for evaluation, initiation of treatment, and observation (AIII). When suspicion for malaria is low, antimalarial treatment should not be initiated until the diagnosis is confirmed. For treatment recommendations for specific regions, clinicians should refer to ia or call the CDC Malaria Hotline: 770-488-7788, Monday–Friday, 8 a.m.– 4:30 p.m. ET, or 770­488­7100 after hours. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-22 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Treatment recommendations for patients with HIV are the same as for patients without HIV (AIII). Choice of therapy is guided by the degree of parasitemia, the species of Plasmodium, the patient’s clinical status, region of infection, and the likely drug susceptibility of the infected species, and can be found at Microsporidiosis For GI Infections Caused by Enterocytozoon bienuesi • Initiate or optimize ART with immune restoration to CD4 count >100 cells/mm3 (AII), plus • Manage dehydration and diarrhea with fluid support (AII) and malnutrition and wasting with nutritional supplements (AIII). For Intestinal and Disseminated (Not Ocular) Infections Caused by Microsporidia Other Than E. bienuesi and Vittaforma corneae • Albendazole 400 mg PO twice daily (AII), continue until CD4 count >200 cells/mm3 for >6 months after initiation of ART (BIII) For Disseminated Disease Caused by Trachipleistophora or Anncaliia • Itraconazole 400 mg PO daily plus albendazole 400 mg PO twice daily (CIII) For GI Infections Caused by E. bienuesi • Fumagillin 60 mg/day (BII) and TNP-470 (a synthetic analog of fumagillin) (BIII) may be effective, but neither is available in the United States. • Nitazoxanide (1,000 mg twice daily) may have some effect, but response may be minimal in patients with low CD4 counts (CIII). Anti-motility agents can be used for diarrhea control if required (BIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-23 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments For Ocular Infection • Topical fumagillin bicylohexylammonium (Fumidil B) eyedrops 3 mg/mL in saline (fumagillin 70 µg/mL): two eyedrops every 2 hours for 4 days, then two eyedrops four times daily (investigational use only in United States) (BII) plus albendazole 400 mg PO twice daily, for management of systemic infection (BIII) If CD4 Count >200 Cells/mm3 • Continue until symptoms resolve (CIII). If CD4 Count ≤200 Cells/mm3 • Continue until resolution of ocular symptoms and CD4 count increases to >200 cells/mm3 for >6 months in response to ART (BIII). Mpox For Severe Disease or at Risk for Severe Disease (See Other Comments for Definition) • Tecovirimat 600 mg PO every 12 hours (<120 kg) or every 8 hours (≥120 kg) for 14 days (BIII) within 30 minutes of a fatty meal, or • Tecovirimat 200 mg IV every 12 hours for 14 days (<120 kg) or 300 mg IV every 12 hours (≥120 kg) if concern exists regarding altered GI absorption capacity, inability to take PO, or extent of organ systems affected by mpox (BIII) Adjunctive Therapy for Severe Disease or at Risk for Severe Disease • Cidofovir 5 mg/kg/week IV for two doses with saline hydration before and after therapy and probenecid 2 g PO 3 hours before the dose followed by 1 g PO 2 hours after the dose and ART should be initiated as soon as possible (AIII). For severe disease, consider early intervention by adding one of the adjunctive therapies at the time of first medical encounter, in consultation with CDC or an expert in mpox treatment (CIII). Patients with severe immunocompromise might benefit from extended treatment (i.e., >14 days) of preferred and/or adjunctive therapies if new confirmed mpox lesions occur or existing lesions worsen despite treatment. Vaccination with any live virus vaccines should be delayed until 3 months after VIGIV administration (CIII). People who received VIGIV shortly after a live virus vaccination should be Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-24 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments 1 g PO 8 hours after the dose (total of 4 g) (BIII), or • Brincidofovir 200 mg PO once weekly for two doses (BIII), or • VIGIV 6,000–9,000 units/kg IV single dose (BIII) Preferred Therapy for Ocular Mpox • Tecovirimat 600 mg PO every 12 hours (<120 kg) or every 8 hours (≥120 kg) for 14 days (CIII) within 30 minutes of a fatty meal, and • Trifluridine (Viroptic) 1 drop into affected eye(s) every 2 hours when awake (max: 9 drops/day) until reepithelialization, then every 4 hours (min: 5 drops/day) for 7 days, or until all periocular lesions have healed (CIII) o Prolonged use of trifluridine beyond 21 days might cause corneal epithelial toxicity and should be avoided (AII). revaccinated 3 months after administration of the immune globulin (CIII). Definition for Severe Disease or at Risk for Severe Disease: People with HIV who are not virologically suppressed or who have CD4 counts <350 cells/mm3 are considered at high risk for severe mpox. Severe mpox might manifest as hemorrhagic disease; large number of lesions, such that they are confluent; sepsis; encephalitis; ocular or periorbital infections; or other conditions requiring hospitalization. Mycobacterium avium Complex (MAC) Disease At Least Two Drugs as Initial Therapy to Prevent or Delay Emergence of Resistance (AII) • Clarithromycin 500 mg PO twice daily (AI) plus ethambutol 15 mg/kg PO daily (AI), or • Azithromycin 500–600 mg plus ethambutol 15 mg/kg PO daily (AII) if drug interaction or intolerance precludes the use of clarithromycin. Duration • At least 12 months (AII) • Shorter duration may be considered. CD4 count should be >100 cells/mm3 for ≥6 months in response to ART before discontinuation of MAC therapy (CIII). Some experts would add a third drug if more severe disease is present. • Rifabutin 300 mg PO daily (dose adjustment may be necessary based on drug interactions) (CI) o Refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB table of the Mycobacterium tuberculosis section for dosing recommendations. Testing of susceptibility to clarithromycin and azithromycin is recommended. NSAIDs can be used for moderate to severe symptoms attributed to IRIS (BIII). If IRIS symptoms persist, a short course (i.e., 4–8 weeks) of a systemic corticosteroid (equivalent to 20–40 mg of prednisone daily) can be used (BII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-25 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Some experts would add a fourth drug if the risk of mortality is high, emergence of drug resistance is likely, CD4 count <50 cells/mm3, high mycobacterial loads (>2 log10 CFU/mL of blood) are present, or effective ART is absent (CIII). • A fluoroquinolone (CIII) (e.g., moxifloxacin 400 mg PO daily or levofloxacin 500 mg PO daily), or • An injectable aminoglycoside (CIII) (e.g., amikacin 10–15 mg/kg IV daily or streptomycin 1 g IV or IM daily). Bedaquiline, tedizolid, linezolid, and omadacycline have demonstrated in vitro activity against clinical isolates of MAC; these might also be considered in people with refractory MAC disease. Mycobacterium tuberculosis (TB) Disease: Drug-Susceptible TB Refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB table in the Mycobacterium tuberculosis section for dosing recommendations. Intensive Phase (8 Weeks) • INH (plus pyridoxine) plus (RIF or RFB) plus PZA plus EMB PO daily (AI) • If drug susceptibility report shows sensitivity to INH and RIF, then EMB may be discontinued before the end of 2 months (AI). Continuation Phase (Duration Depends on Site and Severity of Infection as noted below) • INH (plus pyridoxine) plus (RIF or RFB) PO daily (AII) Total Duration of Therapy for Drug-Susceptible TB • Pulmonary, Uncomplicated TB: 6 months (BII) Only for Patients Receiving an Efavirenz-based ARV Regimen; Not Recommended for Extrapulmonary TB Intensive Phase (8 Weeks) INH plus RPT 1200 mg plus moxifloxacin 400 mg plus PZA plus pyridoxine 25–50mg PO daily (AI)c Continuation Phase (9 Weeks) • INH plus RPT 1200 mg plus moxifloxacin 400 mg plus pyridoxine 25–50mg PO daily (AI) DOT is recommended for all patients (AII). All rifamycins may have significant pharmacokinetic interactions with ARV drugs; please refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB table in the Mycobacterium tuberculosis section and the Drug–Drug Interactions section of the Adult and Adolescent Antiretroviral Guidelines for dosing recommendations. Therapeutic drug monitoring should be considered in patients receiving rifamycin and interacting ART. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-26 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments • Pulmonary TB with Positive Culture at 8 Weeks of TB Treatment, or Severe Cavitary or Disseminated Extrapulmonary TB: 9 months (BII) • TB Meningitis: 9–12 months (BII) • Extrapulmonary TB in Other Sites: 6 months (BII) Adjunctive corticosteroids for TB meningitis (AII): Dexamethasone 0.3–0.4mg/kg/day for 2–4 weeks, then taper by 0.1 mg/kg per week until 0.1 mg/kg, then 4 mg per day, and taper by 1 mg/week for total of 12 weeks. At doses above 16 mg, dexamethasone is a CYP3A4 inducer and can decrease certain ARVs that are substrates of CYP3A4 (e.g., DOR, RPV, and protease inhibitors). Consultation with a pharmacist is recommended. Adjunctive corticosteroid is not recommended for patients with TB pericarditis (AI). See text for recommendations on preventing and managing paradoxical TB-IRIS, including prednisone dosing recommendations. Mycobacterium tuberculosis (TB) Disease: Drug-Resistant TB Refer to the Dosing Recommendations for Use of ARV and Anti-TB Drugs for Treatment of Active Drug Sensitive TB table in the Mycobacterium tuberculosis section for dosing recommendations. Empiric Therapy for Suspected Resistance to Rifamycind +/- Resistance to Other Drugs • INH (plus pyridoxine) plus PZA plus EMB plus (moxifloxacin or levofloxacin) plus (linezolid or amikacine) (BII) Confirmed Resistance to INH • (Moxifloxacin or levofloxacin) plus (RIF or RFB) plus EMB plus PZA for 6 months (BII) Confirmed Resistance to Rifamycin +/- Other Drugs (AI) For 14 Days • Pretomanid 200 mg plus linezolid 600 mg plus moxifloxacin 400 mg daily plus bedaquiline 400 PO daily, followed by For 24 Weeks • Pretomanid 200 mg plus linezolid 600 mg plus moxifloxacin 400 mg daily, and • Bedaquiline 200 mg PO three times per week Omit moxifloxacin if resistant to fluoroquinolones (AI). Confirmed Resistance to Rifamycin +/- Other Drugs • Therapy should be individualized based on drug susceptibility results and clinical and microbiologic responses, to include ≥5 active drugs, and with close consultation with experienced specialists (BIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-27 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Duration • 6–24 months (see Managing Drug-Resistant TB in the Mycobacterium tuberculosis section for discussion) Pneumocystis Pneumonia (PCP) People with HIV who develop PCP despite TMP-SMX prophylaxis can usually be treated with standard doses of TMP-SMX (BIII). Duration of PCP treatment: 21 days (AII) For Moderate to Severe PCP • TMP-SMX: (TMP 15–20 mg/kg/day and SMX 75–100 mg/kg/day) IV given in divided doses every 6 or 8 hours (AI); may switch to PO formulations after clinical improvement (AI) For Mild to Moderate PCP • TMP-SMX: (TMP 15–20 mg/kg/day and SMX 75–100 mg/kg/day) PO given in three divided doses (AI), or • TMP-SMX: (160 mg/800 mg or DS) two tablets PO three times daily (AI) Secondary Prophylaxis, After Completion of PCP Treatment • TMP-SMX DS: one tablet PO daily (AI), or • TMP-SMX (80 mg/400 mg or SS): one tablet PO daily (AI) For Moderate to Severe PCP • Primaquine 30 mg (base) PO daily plus (clindamycin 600 mg IV every 6 hours or 900 mg IV every 8 hours) or (clindamycin 450 mg PO every 6 hours or 600 mg PO every 8 hours) (AI) (some clinicians prefer this option because it is more effective and less toxic than pentamidine), or • Pentamidine 4 mg/kg IV daily infused over ≥60 minutes (AI); can reduce dose to 3 mg/kg IV daily in the event of toxicities (BI) For Mild to Moderate PCP • Dapsone 100 mg PO daily plus TMP 15 mg/kg/day PO given in three divided doses (BI), or • Primaquine 30 mg (base) PO daily plus (clindamycin 450 mg PO every 6 hours or 600 mg PO every 8 hours) (BI), or • Atovaquone 750 mg PO twice daily with food (BI) Secondary Prophylaxis, After Completion of PCP Treatment The following regimens can be used for people who are seropositive or seronegative for Toxoplasma gondii: • TMP-SMX DS: one tablet PO three times weekly (BI), or Indications for Adjunctive Corticosteroids for Moderate to Severe PCP (AI) • PaO2 <70 mmHg at room air, or • A-a gradient ≥35 mmHg Prednisone Doses (Beginning as Early as Possible and Within 72 Hours of PCP Therapy) (AI) • Days 1–5: 40 mg PO twice daily • Days 6–10: 40 mg PO daily • Days 11–21: 20 mg PO daily IV methylprednisolone can be administered as 80% of prednisone dose. Benefit of using a corticosteroid if started after 72 hours of treatment is unknown, but some clinicians will use it for moderate to severe PCP (BIII). Whenever possible, patients should be tested for G6PD before use of dapsone or primaquine. Alternative therapy should be used in patients found to have G6PD deficiency. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-28 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments • Dapsone 50 mg PO daily with pyrimethamineb 50 mg plus leucovorin 25 mg PO weekly (BI), or • Dapsone 200 mg plus pyrimethamineb 75 mg plus leucovorin 25 mg PO weekly (BI), or • Atovaquone 1,500 mg PO daily with food (BI) The following regimens should only be used if the person is seronegative for Toxoplasma gondii: • Dapsone 100 mg PO daily (BI), or • Aerosolized pentamidine 300 mg monthly via Respirgard II nebulizer (BI), or • Intravenous pentamidine 300 mg every 28 days (CIII) Patients who are receiving pyrimethamineb/sulfadiazine for the treatment or suppression of toxoplasmosis do not require additional PCP prophylaxis (AII). If TMP-SMX is discontinued because of a mild adverse reaction, reinstitution should be considered after the reaction resolves (AII). The dose can be increased gradually (desensitization) (BI) or the drug can be given at a reduced dose or frequency (CIII). TMP-SMX should be permanently discontinued in patients with possible or definite Stevens-Johnson syndrome or toxic epidermal necrosis (AIII). See alternative options. Progressive Multifocal Leukoencephalopathy (PML)/JC Virus Infections There is no specific antiviral therapy for JC virus infection. The main treatment approach is to reverse the immunosuppression caused by HIV. Initiate ART immediately in ART-naive patients (AII). Optimize ART to achieve viral suppression in patients who develop PML and receive ART but remain viremic (AIII). None Corticosteroids may be used for PML-IRIS (BIII). The optimal corticosteroid regimen has not been established but should be tailored to individual patients. ART should not be discontinued during PML-IRIS (AIII). Syphilis (Treponema pallidum Infection) Early-Stage (Primary, Secondary, and Early-Latent Syphilis) • Benzathine penicillin G 2.4 million units IM for one dose (AII) Early-Stage (Primary, Secondary, and Early-Latent Syphilis) For Penicillin-Allergic Patients • Doxycycline 100 mg PO twice daily for 14 days (BII), or • Ceftriaxone 1 g IM or IV daily for 10–14 days (BII) The efficacy of non-penicillin alternatives has not been evaluated in patients with HIV, and they should be used only with close clinical and serologic monitoring. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-29 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Late-Latent Disease (>1 Year) or of Unknown Duration • Benzathine penicillin G 2.4 million units IM weekly for three doses (AII) Late-Stage (Tertiary– Cardiovascular or Gummatous Disease) • Benzathine penicillin G 2.4 million units IM weekly for three doses (AII) Note: Rule out neurosyphilis before initiation of benzathine penicillin. People with CSF abnormalities should be treated with a regimen for neurosyphilis [AII]. Neurosyphilis, Otic, or Ocular Syphilis • Aqueous crystalline penicillin G 18–24 million units per day (administered as 3–4 million units IV every 4 hours or by continuous IV infusion) for 10–14 days (AII) +/- benzathine penicillin G 2.4 million units IM x 1 dose after completion of IV therapy (CIII) Late-Latent Disease (>1 Year) or of Unknown Duration For Penicillin-Allergic Patients • Doxycycline 100 mg PO twice a day for 28 days (BIII) Neurosyphilis • Procaine penicillin 2.4 million units IM daily plus probenecid 500 mg PO four times a day for 10–14 days (BII), or • For penicillin-allergic patients, desensitization to penicillin is the preferred approach (BIII); if not feasible and the patient is not pregnant, ceftriaxone 2 g IV daily for 10–14 days (BII). People with penicillin allergy whose compliance or follow-up cannot be ensured should be desensitized and treated with benzathine penicillin (AII). For management of early syphilis during pregnancy, limited evidence indicates a second dose of benzathine penicillin G 2.4 million units IM one week after the single dose treatment may be of benefit for congenital syphilis prevention (BII). The Jarisch-Herxheimer reaction is an acute febrile reaction accompanied by headache and myalgia that can occur within the first 24 hours after therapy for syphilis. This reaction occurs most frequently in patients with early syphilis, high non-treponemal titers, and prior penicillin treatment. Procaine penicillin has been discontinued by the manufacturer as of June 13, 2023 (see FDA Drug Shortages). Talaromycosis (Penicilliosis) Induction Therapy • Liposomal amphotericin B 3–5 mg/kg/day IV (AI) Duration • 2 weeks (AI), followed by consolidation therapy Consolidation Therapy • Itraconazole 200 mg PO twice daily for 10 weeks (AI), followed by chronic maintenance therapy Induction Therapy • Amphotericin B deoxycholate 0.7 mg/kg/day IV for 2 weeks (if liposomal amphotericin B is not available) (AI) If Amphotericin B Is Not Available • Voriconazole 6 mg/kg IV every 12 hours for 1 day (loading dose), then 4 mg/kg IV every 12 hours (BII), or Itraconazole is not recommended as induction therapy for talaromycosis (AI). ART can be initiated as early as 1 week after initiation of treatment for talaromycosis (BIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-30 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Chronic Maintenance Therapy • Itraconazole 200 mg PO once daily, until CD4 count >100 cells/mm3 for ≥6 months (AII) • Voriconazole 600 mg PO twice daily for 1 day (loading dose), then 400 mg PO twice daily (BII) Duration • 2 weeks (BII), followed by consolidation therapy with itraconazole (preferred) or voriconazole Consolidation Therapy • Voriconazole 200 mg PO twice daily for 10 weeks (BII), followed by chronic maintenance therapy Chronic Maintenance Therapy • Itraconazole should be used (AII). Chronic maintenance therapy with voriconazole has not been studied. Itraconazole and voriconazole may have significant interactions with certain ARV agents. These interactions are complex and can be bidirectional. Refer to Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines for dosage recommendations. TDM and dosage adjustment may be necessary to ensure triazole antifungal and ARV efficacy and reduce concentration-related toxicities. The goals of itraconazole and voriconazole trough concentrations are >0.5 mcg/mL and >1.0 mcg/mL, respectively. Toxoplasma gondii Encephalitis Treatment of Acute Infection • Pyrimethamineb 200 mg PO one time, followed by weight-based therapy (AI): o If ≤60 kg: Pyrimethamineb 50 mg PO once daily plus sulfadiazine 1,000 mg PO every 6 hours plus leucovorin 10–25 mg PO once daily o If >60 kg: Pyrimethamineb 75 mg PO once daily plus sulfadiazine 1,500 mg PO every 6 hours plus leucovorin 10–25 mg PO once daily Note: Leucovorin dose can be increased to 50 mg daily or twice a day. • TMP-SMX (TMP 5 mg/kg and SMX 25 mg/kg) IV or PO twice a day (AII) Treatment of Acute Infection • Pyrimethamineb (leucovorin) plus clindamycin 600 mg IV or PO every 6 hours (AI), or • Atovaquone 1,500 mg PO twice a day with food plus pyrimethamineb (leucovorin) (BII), or • Atovaquone 1,500 mg PO twice a day with food plus sulfadiazine 1,000–1,500 mg PO every 6 hours (weight-based dosing, as in preferred therapy) (BII), or • Atovaquone 1,500 mg PO twice a day with food (BII) If pyrimethamine is unavailable or there is a delay in obtaining it, TMP-SMX should be used in place of pyrimethamine-sulfadiazine (AII). For patients with a history of sulfa allergy, sulfa desensitization should be attempted using one of several published strategies (BI). Atovaquone should be administered until therapeutic doses of TMP-SMX are achieved (CIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-31 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Duration for Acute Therapy • At least 6 weeks (BII); longer duration if clinical or radiologic disease is extensive or response is incomplete at 6 weeks • After completion of acute therapy, all patients should be initiated on chronic maintenance therapy. Chronic Maintenance Therapy • Pyrimethamineb 25–50 mg PO daily plus sulfadiazine 2,000–4,000 mg PO daily (in 2–4 divided doses) plus leucovorin 10–25 mg PO daily (AI), or • TMP-SMX DS one tablet twice a day (AII) Chronic Maintenance Therapy • (Pyrimethamineb 25–50 mg plus leucovorin 10–25 mg) PO daily plus clindamycin 600 mg PO every 8 hours plus (BI), or • Atovaquone 750–1,500 mg PO twice a day plus (pyrimethamineb 25 mg plus leucovorin 10 mg) PO daily (BII), or • Atovaquone 750–1,500 mg PO twice a day plus sulfadiazine 2,000–4,000 mg PO daily (in two to four divided doses) (BII), or • Atovaquone 750–1,500 mg PO twice a day with food (BII) Pyrimethamineb and leucovorin doses are the same as for preferred therapy. Adjunctive corticosteroids (e.g., dexamethasone) should only be administered when clinically indicated to treat mass effect associated with focal lesions or associated edema (BIII); discontinue as soon as clinically feasible. Antiseizure medications should be administered to patients with a history of seizures (AII) and continued through acute treatment (BII) but should not be used as seizure prophylaxis (BII). If clindamycin is used in place of sulfadiazine, additional therapy must be added to prevent PCP (AII). Varicella Zoster Virus (VZV) Disease Primary Varicella Infection (Chickenpox) Uncomplicated Cases • Initiate as soon as possible after symptom onset and continue for 5–7 days: o Valacyclovir 1 g PO three times a day (AII), or o Famciclovir 500 mg PO three times a day (AII) Severe or Complicated Cases • Acyclovir 10 mg/kg IV every 8 hours for 7–10 days (AIII) • May switch to oral valacyclovir, famciclovir, or acyclovir after defervescence if no evidence of visceral involvement (BIII). Primary Varicella Infection (Chickenpox) Uncomplicated Cases (for 5–7 Days) • Acyclovir 800 mg PO five times a day (BII) Herpes Zoster (Shingles) Acute Localized Dermatomal • For 7–10 days; consider longer duration if lesions are slow to resolve • Acyclovir 800 mg PO five times a day (BII) In managing VZV of the eyes, consultation with an ophthalmologist experienced in management of VZV retinitis is strongly recommended (AIII). Duration of therapy for VZV retinitis is not well defined and should be determined based on clinical, virologic, and immunologic responses and ophthalmologic responses. Optimization of ART is recommended for serious and difficult-to-treat VZV infections (e.g., retinitis, encephalitis) (AIII). Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-32 Opportunistic Infection Preferred Therapy Alternative Therapy Other Comments Herpes Zoster (Shingles) Acute Localized Dermatomal • For 7–10 days; consider longer duration if lesions are slow to resolve. • Valacyclovir 1 g PO three times a day (AII), or • Famciclovir 500 mg three times a day (AII) Extensive Cutaneous Lesion or Visceral Involvement • Acyclovir 10 mg/kg IV every 8 hours until clinical improvement is evident (AII) • May switch to PO therapy (valacyclovir, famciclovir, or acyclovir) after clinical improvement (i.e., when no new vesicle formation or improvement of signs and symptoms of visceral VZV) to complete a 10- to 14-day course (BIII). ARN • Acyclovir 10 mg/kg IV every 8 hours for 10–14 days, followed by valacyclovir 1 g PO three times a day for >14 weeks (AIII), plus • Intravitreal ganciclovir 2 mg/0.05 mL twice weekly for 1–2 doses (BIII) PORN • Acyclovir 10 mg/kg IV every 8 hours or ganciclovir 5 mg/kg IV every 12 hours (AIII), plus • ≥1 intravitreal antiviral injection: ganciclovir 2 mg/0.05 mL or foscarnet 1.2 mg/0.05 mL twice weekly (AIII) • Initiate or optimize ART (AIII). In patients with herpes zoster ophthalmicus who have stromal keratitis and anterior uveitis, topical corticosteroids to reduce inflammation may be necessary. The role of ART has not been established in these cases. a TAF 10-mg dose is in the FDC tablets of EVG/c/TAF/FTC and DRV/c/TAF/FTC; when TAF is used with other antiretrovirals, the dose is 25 mg. b Refer to Daraprim Direct for information on accessing pyrimethamine. Table 2. Treatment of HIV-Associated Opportunistic Infections (Includes Recommendations for Acute Treatment and Secondary Prophylaxis/Chronic Suppressive/Maintenance Therapy) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV FF-33 c This regimen was not studied and is not recommended for people who are pregnant, breastfeeding, <40 kg, or who have most types of extrapulmonary TB (other than pleural TB or lymphadenitis). d Many patients with RIF resistance also have resistance to isoniazid. Susceptibility should be confirmed in any patient with RIF resistance to determine if isoniazid can be included in the treatment regimen. e Given the risk of ototoxicity and nephrotoxicity with aminoglycosides, use of amikacin should generally be restricted to bridging regimens, while awaiting availability of less toxic medications and/or results of drug-susceptibility testing. For information regarding the evidence ratings, refer to the Rating System for Prevention and Treatment Recommendations in the Introduction section of the Adult and Adolescent Opportunistic Infection Guidelines. Key: +/- = with or without; 3TC = lamivudine; A-a = alveolar-arterial; AASLD = American Association for the Study of Liver Diseases; ARN = acute retinal necrosis; ART = antiretroviral therapy; ARV = antiretroviral; CD4 = CD4 T lymphocyte; CDC = Centers for Disease Control and Prevention; CDI = Clostridium difficile infection; CFU = colony-forming unit; CNS = central nervous system; COBI = cobicistat; CrCl = creatinine clearance; CSF = cerebrospinal fluid; DAA = direct-acting antiviral; DOT = directly observed therapy; DRV = darunavir; DS = double strength; EMB = ethambutol; EVG = elvitegravir; FDA = U.S. Food and Drug Administration; FDC = fixed-dose combination; FMT = fecal microbiota therapy; FTC = emtricitabine; G6PD = glucose-6-phosphate dehydrogenase; GI = gastrointestinal; HBeAg = hepatitis B e antigen; HBsAg = hepatitis B surface antigen; HBV = hepatitis B virus; HCV = hepatitis C virus; HD = hemodialysis; ICP = intracranial pressure; IDSA = Infectious Diseases Society of America; IL-6 = interleukin-6; IM = intramuscular; INH = isoniazid; IRIS = immune reconstitution inflammatory syndrome; IRU = immune reconstitution uveitis; IV = intravenous; LFA = lateral flow assay; LP = lumbar puncture; MIC = minimum inhibitory concentration; MSM = men who have sex with men; NSAID = nonsteroidal anti-inflammatory drugs; PaO2 = partial pressure of oxygen; PCP = Pneumocystis pneumonia; PCR = polymerase chain reaction; PO = oral; PORN = progressive outer retinal necrosis; PZA = pyrazinamide; RFB = rifabutin; RIF = rifampin; RPT = rifapentine; SMX = sulfamethoxazole; SQ = subcutaneous; SS = single strength; STR = single-tablet regimen; SVR = sustained virologic response; TAF = tenofovir alafenamide; TB = tuberculosis; TDF = tenofovir disoproxil fumarate; TDM = therapeutic drug monitoring; TMP = trimethoprim; VIGIV = vaccinia immune globulin intravenous Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV GG-1 Table 3. Indications for Discontinuing and Restarting Opportunistic Infection Secondary Prophylaxis or Chronic Maintenance in Adults and Adolescents With HIV Updated: September 16, 2024 Reviewed: September 16, 2024 Opportunistic Infection Indication for Discontinuing Primary Prophylaxis Indication for Restarting Primary Prophylaxis Indication for Discontinuing Secondary Prophylaxis/Chronic Maintenance Therapy Indication for Restarting Secondary Prophylaxis/Chronic Maintenance Bacterial Enteric Infections: Salmonellosis Not applicable Not applicable Resolution of Salmonella infection and after response to ART with sustained viral suppression and CD4 counts >200 cells/mm3 (CII) No recommendation Bartonellosis Not applicable Not applicable • Received at least 3–4 months of treatment, and • CD4 count >200 cells/mm3 for ≥6 months (CIII) Some specialists would only discontinue therapy if Bartonella titers have also decreased by fourfold (CIII). No recommendation Candidiasis (Mucocutaneous) Not applicable Not applicable If used, reasonable to discontinue when CD4 count >200 cells/mm3 (AIII) No recommendation Coccidioidomycosis CD4 count ≥250 cells/mm3 for ≥6 months (CIII) Restart at CD4 count <250 cells/mm3 (BIII). Only for patients with focal coccidioidal pneumonia (AII): • Clinically responded to ≥12 months antifungal therapy, with CD4 count >250 cells/mm3, and receiving effective ART • Should continue monitoring for recurrence with serial chest radiographs and coccidioidal serology For patients with diffuse pulmonary (BIII), disseminated non-meningeal (BIII), or meningeal diseases (AII): • Suppressive therapy should be continued indefinitely, even with increase in CD4 count on ART. No recommendation Table 3. Indications for Discontinuing and Restarting Opportunistic Infection Secondary Prophylaxis or Chronic Maintenance in Adults and Adolescents With HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV GG-2 Opportunistic Infection Indication for Discontinuing Primary Prophylaxis Indication for Restarting Primary Prophylaxis Indication for Discontinuing Secondary Prophylaxis/Chronic Maintenance Therapy Indication for Restarting Secondary Prophylaxis/Chronic Maintenance Cryptococcal Meningitis Not applicable Not applicable If the following criteria are fulfilled (BII): • Completed initial (induction and consolidation) therapy, and • Received at least 1 year of antifungal therapy, and • Remain asymptomatic of cryptococcal infection, and • CD4 count ≥100 cells/mm3 and with suppressed plasma HIV RNA in response to ART CD4 count <100 cells/mm3 (AIII) Cytomegalovirus Retinitis Not applicable Not applicable • CMV treatment for at least 3 to 6 months and with CD4 count >100 cells/mm3 for >3 to 6 months in response to ART (AII) • Therapy should be discontinued only after consultation with an ophthalmologist, taking into account anatomic location of lesions, vision in the contralateral eye, and feasibility of regular ophthalmologic monitoring. • Routine (i.e., every 3 months) ophthalmologic follow-up is recommended after stopping therapy for early detection of relapse or immune restoration uveitis, and then periodically after sustained immune reconstitution (AIII). CD4 count <100 cells/mm3 (AIII) Histoplasma capsulatum Infection On ART, with CD4 count >150 cells/mm3 and undetectable HIV-1 viral load for 6 months (BIII) For patients at high risk of acquiring histoplasmosis, restart if CD4 count falls to <150 cells/mm3 (CIII). If the following criteria (AI) are fulfilled: • Received azole therapy for >1 year, and • Negative fungal blood cultures, and CD4 count <150 cells/mm3 (BIII) Table 3. Indications for Discontinuing and Restarting Opportunistic Infection Secondary Prophylaxis or Chronic Maintenance in Adults and Adolescents With HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV GG-3 Opportunistic Infection Indication for Discontinuing Primary Prophylaxis Indication for Restarting Primary Prophylaxis Indication for Discontinuing Secondary Prophylaxis/Chronic Maintenance Therapy Indication for Restarting Secondary Prophylaxis/Chronic Maintenance • Serum or urine Histoplasma antigen below the level of quantification, and • Undetectable HIV viral load, and • CD4 count ≥150 cells/mm3 for ≥6 months in response to ART Isospora belli Infection Not applicable Not applicable Sustained increase in CD4 count to >200 cells/mm3 for >6 months in response to ART and without evidence of I. belli infection (BIII) No recommendation Leishmaniasis: Visceral (and possibly cutaneous leishmaniasis in immunocompromised patients with multiple relapses) Not applicable Not applicable If CD4 count increases to >350 cells/mm3 and HIV viral load is suppressed for 6 months in response to ART and there is no evidence of clinical relapse of visceral leishmaniasis (CIII) No recommendation Microsporidiosis Not applicable Not applicable If there are no signs or symptoms of non-ocular (BIII) or ocular (CIII) microsporidiosis and CD4 count is >200 cells/mm3 for >6 months in response to ART. No recommendation Mycobacterium avium Complex Disease Continuing a fully suppressive ART regimen (AI) CD4 count <50 cells/mm3 and not on fully suppressive ART (AIII) If the following criteria are fulfilled (AI): • Completed ≥12 months of therapy, and • No signs and symptoms of MAC disease, and • Have sustained (>6 months) CD4 count >100 cells/mm3 in response to ART. If a fully suppressive ART regimen is not possible and CD4 count is consistently <100 cells/mm3 (BIII) Pneumocystis Pneumonia CD4 count increased from <200 to ≥200 cells/mm3 for ≥3 months in response to ART (AI). CD4 count <100 cells/mm3 regardless of HIV RNA level (AIII) CD4 count 100–200 cells/mm3 and HIV RNA above CD4 count increased from <200 cells/mm3 to ≥200 cells/mm3 for ≥3 months in response to ART (AII). Can consider when CD4 count is 100–200 cells/mm3 if HIV RNA CD4 count <100 cells/mm3 regardless of HIV RNA level (AIII) CD4 count 100–200 cells/mm3 and with HIV RNA above Table 3. Indications for Discontinuing and Restarting Opportunistic Infection Secondary Prophylaxis or Chronic Maintenance in Adults and Adolescents With HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV GG-4 Opportunistic Infection Indication for Discontinuing Primary Prophylaxis Indication for Restarting Primary Prophylaxis Indication for Discontinuing Secondary Prophylaxis/Chronic Maintenance Therapy Indication for Restarting Secondary Prophylaxis/Chronic Maintenance Can consider when CD4 count is 100–200 cells/mm3 if HIV RNA remains below limits of detection for ≥3 to 6 months (BII). detection limit of the assay (AIII) remains below limits of detection for 3–6 months (BII). If PCP occurs at a CD4 count >200 cells/mm3 while on ART, continue PCP prophylaxis for life, regardless of how high the CD4 cell count rises as a consequence of ART (BIII). If PCP occurs at a CD4 count >200 cells/mm3 while not on ART, discontinuation of prophylaxis can be considered when HIV RNA levels are suppressed to below limits of detection for ≥3 to 6 months (CIII). detection limit of the assay (AIII) Talaromycosis (Penicilliosis) CD4 count >100 cells/mm3 for >6 months in response to ART (BII) or If achieved sustained HIV viral suppression for >6 months (BIII) CD4 count <100 cells/mm3 (BIII)— if patient is unable to have ART, or has treatment failure without access to effective ART options, and still resides in or travels to the endemic area CD4 count >100 cells/mm3 for ≥6 months in response to ART (BII) or If achieved sustained HIV viral suppression for >6 months (BIII) CD4 count <100 cells/mm3 (BIII) Toxoplasma gondii Encephalitis CD4 count increased to >200 cells/mm3 for >3 months and sustained HIV RNA below limits of detection in response to ART (AI) Can consider when CD4 count is 100–200 cells/mm3 if HIV RNA remains below limits of detection for at least 3–6 months (BII) CD4 count <100 cells/mm3 (AIII) CD4 count 100–200 cells/mm3 and with HIV RNA above detection limit of the assay (AIII) If the following criteria are fulfilled (BI): • Successfully completed initial therapy, • Receiving maintenance therapy and remaining free of signs and symptoms of TE, and • CD4 count >200 cells/mm3 for >6 months in response to ART CD4 count <200 cells/mm3 (AIII) For information regarding the evidence ratings, refer to the Rating System for Prevention and Treatment Recommendations in the Introduction section of the Adult and Adolescent Antiretroviral Guidelines. Table 3. Indications for Discontinuing and Restarting Opportunistic Infection Secondary Prophylaxis or Chronic Maintenance in Adults and Adolescents With HIV Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV GG-5 Key: ART = antiretroviral therapy; CD4 = CD4 T lymphocyte; CMV = cytomegalovirus; MAC = Mycobacterium avium complex; PCP = Pneumocystis pneumonia; TE = Toxoplasma encephalitis Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-1 Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Updated: September 25, 2023 Reviewed: January 10, 2024 This table lists the known, predicted, or suspected pharmacokinetic (PK) interactions between drugs used for the treatment or prevention of HIV-associated opportunistic infections (OIs). Many of the drugs listed in this table may also interact with antiretroviral (ARV) drugs. Clinicians should see the Drug–Drug Interactions tables in the most current Adult and Adolescent Antiretroviral Guidelines to assess interaction potentials between OI drugs and ARV drugs. Throughout the table, three recommendations are commonly used when concomitant administration of two drugs may lead to untoward consequences. The rationales for these recommendations are summarized below: Do not coadminister. There is either strong evidence or strong likelihood that the PK interaction cannot be managed with a dose modification of one or both drugs and will or may result in either— • Increase in concentrations of one or both drugs, which may lead to excessive risk of toxicity; or • Decrease in concentrations of one or both drugs, which may render one or both drugs ineffective. Coadministration should be avoided, if possible. There is a potential for significant PK interactions. If other more favorable options exist, clinicians are advised to consider changing components of the regimen to accommodate a safer or more effective regimen. However, coadministration of the drugs may be necessary when there are no other acceptable therapeutic options that provide a more favorable benefit-to-risk ratio. Therapeutic drug monitoring, if available, may facilitate any necessary dose adjustments. Use with caution. Drug combinations are recommended to be used with caution when— • PK studies have shown a moderate degree of interaction of unknown clinical significance; or • Based on the known metabolic pathway of the two drugs, there is a potential for PK interaction of unknown clinical significance. Rifamycin-Related Induction Interactions Rifamycin antibiotics are potent inducers of Phase 1 and Phase 2 drug metabolizing reactions. They also affect various transporters. When a rifamycin antibiotic must be combined with an interacting drug, close monitoring for clinical efficacy of the coadministered agent is advised. Therapeutic drug monitoring, if available, may facilitate any necessary dose adjustments. • Rifampin (also known as rifampicin): Interactions may not be apparent in the first several days of rifampin therapy. However, with daily doses of rifampin, enzyme induction increases over a week or more. Based on Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-2 limited data, larger daily doses of rifampin (e.g., 1,200 mg or more) appear to produce the same maximum induction as lower doses, but the induction effect occurs more rapidly. • Rifabutin: In general, rifabutin as a cytochrome P450 3A4 (CYP3A4) inducer is about 40% of the potency of rifampin, but this can vary by substrate and enzymatic reaction. Rifabutin is also a substrate of CYP3A4 and may be subject to changes in drug exposure when given concomitantly with 3A4 inhibitors or inducers. Rifabutin dosage modification, therapeutic drug monitoring, and/or more frequent monitoring for rifabutin-related toxicities may be needed. • Rifapentine: In general, daily rifapentine is at least as potent an inducer as rifampin. However, the potential for drug interactions with once-weekly rifapentine is not well studied. Reduced exposure of concurrent drugs that are CYP3A4 substrates is likely to occur with once-weekly rifapentine, with the extent varying by drug. Azole- and Macrolide-Related Inhibition Interactions Azole antifungals, including fluconazole, isavuconazole, itraconazole, posaconazole, and voriconazole, are substrates and potent inhibitors of metabolic pathways, including cytochrome P450 enzymes and/or drug transporters (e.g., p-glycoprotein). Interactions involving azole antifungals are common. When an azole antifungal must be combined with an interacting drug, close monitoring for clinical toxicity and efficacy of the azole and/or the coadministered agent may be needed. Therapeutic drug monitoring, if available, may facilitate any necessary dose adjustments. Macrolides have been shown to form complexes with drug-oxidizing enzymes, including cytochrome P450 enzymes, which render an inhibitory effect. In general, erythromycin and clarithromycin are moderate to strong inhibitors, while azithromycin’s propensity for causing clinically relevant drug interactions is lowest, as it does not form complexes with cytochrome P450 enzymes that lead to enzyme inactivation. Pharmacodynamic Interactions Pharmacodynamic interactions are not addressed in this table. For example, many of the drug classes listed below independently possess a risk for QTc prolongation, including azoles, macrolides, and certain anti-tuberculosis and antimalarial medications. Coadministration of drugs in these classes may require monitoring for QTc prolongation, particularly in patients with predisposing risk factors. Therapeutic Drug Monitoring Drug interactions can alter oral absorption or systemic clearance of drugs. More than one interaction can occur at the same time, with potentially opposing effects. Therapeutic drug monitoring (TDM), if available, may facilitate any necessary dose adjustments in these complicated patients. TDM allows the clinician to make informed, individualized decisions about dose adjustments that are more precise than standardized dose adjustments based upon anticipated, average effects. Drugs that are marked with an asterisk () in the table below are known to have assays (for clinical and/or research purposes) available within the United States and typically in Europe as well. When TDM is appropriate, clinicians should contact their clinical laboratory to determine assay availability and turnaround time for their institution. Note: To avoid redundancy, drug–drug interactions are listed only once by primary drug (listed alphabetically). Subsequently, when an interacting agent becomes the primary drug, guideline users are referred to the entry for the initial primary drug. See the Clarithromycin row for the first example of this format. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-3 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Artemether/ Lumefantrine Clarithromycin ↑ lumefantrine expected Coadministration should be avoided, if possible. Consider azithromycin in place of clarithromycin. Erythromycin ↑ lumefantrine expected Coadministration should be avoided, if possible. Consider azithromycin in place of erythromycin. Fluconazole ↑ lumefantrine possible Coadministration should be avoided, if possible. If coadministered, monitor for lumefantrine toxicities. Isavuconazole ↑ lumefantrine possible Coadministration should be avoided, if possible. If coadministered, monitor for lumefantrine toxicities. Itraconazole ↑ lumefantrine expected Coadministration should be avoided, if possible. If coadministered, monitor for lumefantrine toxicities. Mefloquine ↓ lumefantrine possible If mefloquine is administered immediately before artemether/lumefantrine, monitor for decreased efficacy of artemether/lumefantrine and encourage food intake. Posaconazole ↑ lumefantrine expected Coadministration should be avoided, if possible. If coadministered, monitor for lumefantrine toxicities. Rifabutina ↓ artemether, DHA, and lumefantrine expected Use with caution. Monitor for antimalarial efficacy. Rifampina Artemether AUC ↓ 89% DHA AUC ↓ 85% Lumefantrine AUC ↓ 68% Do not coadminister. Rifapentinea Daily and Weekly Rifapentine ↓ artemether, DHA, and lumefantrine expected Do not coadminister. Voriconazole ↑ lumefantrine expected Coadministration should be avoided, if possible. If coadministered, monitor for lumefantrine toxicities. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-4 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Atovaquone Doxycycline Atovaquone concentration ↓ approximately equal to 40% with tetracycline No interaction study with doxycycline Dose adjustment not established; if coadministered, instruct patient to take atovaquone with fatty meal and monitor for decreased atovaquone efficacy. Rifabutina Atovaquone Css ↓ 34% Rifabutin Css ↓ 19% Dose adjustment not established; if coadministered, instruct patient to take atovaquone with fatty meal and monitor for decreased atovaquone efficacy. Rifampina Atovaquone Css ↓ 52% Rifampin Css ↑ 37% Do not coadminister. Rifapentinea Daily and Weekly Rifapentine ↓ atovaquone expected Do not coadminister. Bedaquiline Clarithromycin ↑ bedaquiline expected Do not coadminister. Consider azithromycin in place of clarithromycin. Erythromycin ↑ bedaquiline expected Do not coadminister. Consider azithromycin in place of erythromycin. Fluconazole ↑ bedaquiline possible Coadministration should be avoided, if possible. If coadministered, monitor for bedaquiline toxicities. Isavuconazole ↑ bedaquiline possible Coadministration should be avoided, if possible. If coadministered, monitor for bedaquiline toxicities. Itraconazole ↑ bedaquiline expected Coadministration should be avoided, if possible. If coadministered, monitor for bedaquiline toxicities. If coadministration is required for >14 days, weigh the benefits of therapy against the risks of bedaquiline toxicities. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-5 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Posaconazole ↑ bedaquiline expected Coadministration should be avoided, if possible. If coadministered, monitor for bedaquiline toxicities. Rifabutina ↔ bedaquiline ↓ rifabutin possible If coadministered, separate time of administration; perform rifabutin TDM and adjust dose accordingly. Rifampina Bedaquiline AUC ↓ 53% Do not coadminister. Rifapentinea Daily Rifapentine Bedaquiline AUC ↓ 55% Weekly Rifapentine ↓ bedaquiline expected Do not coadminister. Voriconazole ↑ bedaquiline expected Coadministration should be avoided, if possible. If coadministered, monitor for bedaquiline toxicities. Brincidofovir Clarithromycin ↑ brincidofovir expected Coadministration should be avoided, if possible. If coadministered, postpone clarithromycin for at least 3 hours after brincidofovir and monitor for brincidofovir toxicities. Consider azithromycin in place of clarithromycin. Erythromycin ↑ brincidofovir expected Coadministration should be avoided, if possible. If coadministered, postpone erythromycin for at least 3 hours after brincidofovir and monitor for brincidofovir toxicities. Consider azithromycin in place of erythromycin. Rifampin ↑ brincidofovir expected Coadministration should be avoided, if possible. If coadministered, postpone rifampin for at least 3 hours after brincidofovir and monitor for brincidofovir toxicities. Caspofungin Rifabutina ↓ caspofungin possible Monitor for antifungal efficacy. Dose not established. Consider increasing caspofungin dose to 70 mg/day or switch to another echinocandin (e.g., micafungin or anidulafungin). Rifampina Caspofungin Cmin ↓ 30% If coadministered, caspofungin dose should be increased to 70 mg/day. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-6 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Consider alternative echinocandin (e.g., micafungin or anidulafungin). Rifapentinea Daily Rifapentine ↓ caspofungin expected Weekly Rifapentine ↓ caspofungin possible Monitor for antifungal efficacy. Dose not established. Consider increasing caspofungin dose to 70 mg/day or switch to another echinocandin (e.g., micafungin or anidulafungin). Chloroquine Clarithromycin ↑ chloroquine expected Do not coadminister. Consider azithromycin in place of clarithromycin. Erythromycin ↑ chloroquine expected Do not coadminister. Consider azithromycin in place of erythromycin. Fluconazole ↑ chloroquine possible Coadministration should be avoided, if possible. If coadministered, monitor for chloroquine toxicities. Isavuconazole ↑ chloroquine possible Coadministration should be avoided, if possible. If coadministered, monitor for chloroquine toxicities. Itraconazole ↑ chloroquine expected Coadministration should be avoided, if possible. If coadministered, monitor for chloroquine toxicities. Posaconazole ↑ chloroquine expected Coadministration should be avoided, if possible. If coadministered, monitor for chloroquine toxicities. Rifabutina ↓ chloroquine expected Monitor for chloroquine efficacy. Rifampina ↓ chloroquine expected Monitor for chloroquine efficacy. Rifapentinea Daily and Weekly Rifapentine ↓ chloroquine expected Monitor for chloroquine efficacy. Voriconazole ↑ chloroquine expected Coadministration should be avoided, if possible. If coadministered, monitor for chloroquine toxicities. Clarithromycin Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-7 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Fluconazole Clarithromycin AUC ↑ 18% and Cmin↑ 33% No dose adjustment necessary in patients with normal renal function. Monitor for clarithromycin toxicity. Isavuconazole ↑ isavuconazole and clarithromycin expected Coadministration should be avoided, if possible. Consider azithromycin in place of clarithromycin. If coadministered, monitor for toxicities of both isavuconazole and clarithromycin. Role of isavuconazole TDM has not been established. Itraconazole ↑ itraconazole and clarithromycin expected Coadministration should be avoided, if possible. Consider azithromycin in place of clarithromycin. If coadministered, monitor for toxicities of both itraconazole and clarithromycin; perform itraconazole and clarithromycin TDM and adjust dose accordingly. Mefloquine ↑ mefloquine expected Use with caution. Consider azithromycin in place of clarithromycin. If coadministered, monitor for mefloquine toxicity. Posaconazole ↑ clarithromycin expected Coadministration should be avoided, if possible. Consider azithromycin in place of clarithromycin. If coadministered, monitor for toxicities of clarithromycin; perform clarithromycin TDM and adjust dose accordingly. Quinine ↑ quinine expected ↑ clarithromycin possible Do not coadminister. Consider azithromycin in place of clarithromycin. Rifabutina Clarithromycin AUC ↓ 44% 14-OH clarithromycin AUC ↑ 57% Rifabutin AUC ↑ 76% to 99% des-Rbt AUC ↑ 375% Use with caution. Consider azithromycin in place of clarithromycin. If coadministered, consider reducing rifabutin dose, perform clarithromycin and rifabutin TDM and adjust dose accordingly. Monitor for rifabutin toxicities. Rifampina Clarithromycin concentration ↓ 87% Rifampin AUC ↑ 60% Do not coadminister. Use azithromycin in place of clarithromycin. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-8 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Rifapentinea Daily and Weekly Rifapentine ↓ clarithromycin expected ↑ 14-OH clarithromycin and rifapentine expected Daily Rifapentine Do not coadminister. Use azithromycin in place of clarithromycin. Weekly Rifapentine Use with caution. Consider azithromycin in place of clarithromycin. If coadministered, monitor for rifapentine toxicities and clarithromycin efficacy; perform clarithromycin and rifapentine TDM and adjust doses accordingly. Voriconazole ↑ clarithromycin expected Coadministration should be avoided, if possible. Consider azithromycin in place of clarithromycin. If coadministered, monitor for toxicities of clarithromycin; perform clarithromycin TDM and adjust dose accordingly. Dapsone Rifabutina Dapsone AUC ↓ 27% to 40% Coadministration should be avoided, if possible. Consider alternatives for dapsone. Rifampina Dapsone concentration ↓ 7-fold to 10-fold and t1/2 ↓ from 24 hours to 11 hours Coadministration should be avoided, if possible. Consider alternatives for dapsone. Rifapentinea Daily and Weekly Rifapentine ↓ dapsone expected Coadministration should be avoided, if possible. Consider alternatives for dapsone. Doxycycline Atovaquone See Atovaquone. See Atovaquone. Rifabutina ↓ doxycycline possible Monitor closely for doxycycline efficacy or consider alternative therapy. Rifampina Doxycycline AUC ↓ 59% Use with caution. Monitor closely for doxycycline efficacy or consider alternative therapy. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-9 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Rifapentinea Daily Rifapentine ↓ doxycycline expected Weekly Rifapentine ↓ doxycycline possible Use with caution. Monitor closely for doxycycline efficacy or consider alternative therapy. Erythromycin Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Fluconazole ↑ erythromycin possible Do not coadminister. Consider azithromycin in place of erythromycin. Isavuconazole ↑ erythromycin and isavuconazole possible Do not coadminister. Consider azithromycin in place of erythromycin. Itraconazole Itraconazole AUC ↑ 36% ↑ erythromycin possible Do not coadminister. Consider azithromycin in place of erythromycin. Mefloquine ↑ mefloquine possible Do not coadminister. Consider azithromycin in place of erythromycin. Posaconazole ↑ erythromycin expected Do not coadminister. Consider azithromycin in place of erythromycin. Quinine ↑ quinine expected ↑ erythromycin possible Do not coadminister. Consider azithromycin in place of erythromycin. Rifabutina ↓ erythromycin possible ↑ rifabutin possible Use with caution. Consider azithromycin in place of erythromycin. If coadministered, monitor for erythromycin efficacy and rifabutin toxicities; perform rifabutin TDM and adjust dose accordingly. Rifampina ↓ erythromycin expected Consider azithromycin in place of erythromycin. If coadministered, monitor for erythromycin efficacy. Rifapentinea Daily and Weekly Rifapentine ↓ erythromycin expected Consider azithromycin in place of erythromycin. If coadministered, monitor for erythromycin efficacy. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-10 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Voriconazole ↑ erythromycin expected Do not coadminister. Consider azithromycin in place of erythromycin. Fluconazole Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Mefloquine ↑ mefloquine possible Coadministration should be avoided, if possible. If coadministered, monitor for mefloquine toxicities. Quinine ↑ quinine expected ↑ fluconazole possible Coadministration should be avoided, if possible. If coadministered, monitor for quinine and fluconazole toxicity. Rifabutina Rifabutin AUC ↑ 80% ↔ fluconazole expected Use with caution. Monitor for rifabutin toxicities. Perform rifabutin TDM; may need to decrease rifabutin dose to 150 mg/day. Rifampina Fluconazole AUC ↓ 23% to 56% Monitor for antifungal efficacy; may need to increase fluconazole dose. Rifapentinea Daily and Weekly Rifapentine ↓ fluconazole expected Monitor for antifungal efficacy; may need to increase fluconazole dose. Glecaprevir/ Pibrentasvir Rifabutina ↓ glecaprevir and pibrentasvir possible Coadministration should be avoided, if possible. Consider alternative agents. Rifampina Glecaprevir AUC ↓ 88% Pibrentasvir AUC ↓ 87% Do not coadminister. Rifapentinea Daily and Weekly Rifapentine ↓ glecaprevir and pibrentasvir expected Do not coadminister. Consider alternative agents. TDF TFV AUC ↑ 29% when coadministered as EFV/TDF/FTC Use usual dose. Monitor renal function or consider TAF. TAF ↔ TFV concentration when coadministered as EVG/c/TAF/FTC No dose adjustment necessary Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-11 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Isavuconazole Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Mefloquine ↑ mefloquine expected Coadministration should be avoided, if possible. If coadministered, monitor for mefloquine toxicities. Quinine ↑ quinine expected ↑ isavuconazole possible Coadministration should be avoided, if possible. If coadministered, monitor for quinine and isavuconazole toxicities. Rifabutina ↓ isavuconazole expected ↑ rifabutin expected Consider alternative agent(s). If alternative agents are not available, use with close monitoring for isavuconazole antifungal activity and rifabutin toxicity. Perform rifabutin TDM and adjust dose accordingly. Rifampina Isavuconazole AUC ↓ 97% Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Rifapentinea Daily and Weekly Rifapentine ↓ isavuconazole expected Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Itraconazole Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Mefloquine ↑ mefloquine expected Coadministration should be avoided, if possible. If coadministered, monitor for mefloquine toxicities. Quinine ↑ quinine expected ↑ itraconazole possible Coadministration should be avoided, if possible. If coadministered, monitor for quinine and itraconazole toxicities; perform itraconazole TDM and adjust dose accordingly. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-12 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Rifabutina Itraconazole AUC ↓ 70% ↑ rifabutin expected Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Rifampina Itraconazole AUC ↓ 64% to 88% Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Rifapentinea Daily and Weekly Rifapentine ↓ itraconazole expected Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Linezolid Rifabutina ↓ linezolid possible Monitor for linezolid efficacy. Rifampina Linezolid AUC ↓ 32% Monitor for linezolid efficacy. Perform linezolid TDM and adjust dose accordingly. Rifapentinea Daily Rifapentine ↓ linezolid expected Weekly Rifapentine ↓ linezolid possible Daily Rifapentine Monitor for linezolid efficacy. Perform linezolid TDM and adjust dose accordingly. Weekly Rifapentine Monitor for linezolid efficacy. Mefloquine Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Fluconazole See Fluconazole. See Fluconazole. Isavuconazole See Isavuconazole. See Isavuconazole. Itraconazole See Itraconazole. See Itraconazole. Posaconazole ↑ mefloquine expected Coadministration should be avoided, if possible. If coadministered, monitor for mefloquine toxicities. Rifabutina ↓ mefloquine possible Monitor for mefloquine efficacy. Rifampina Mefloquine AUC ↓ 68% Do not coadminister. Use alternative antimalarial drug or rifabutin. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-13 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Rifapentinea Daily and Weekly Rifapentine ↓ mefloquine expected Do not coadminister. Use alternative antimalarial drug or rifabutin. Voriconazole ↑ mefloquine expected Coadministration should be avoided, if possible. If coadministered, monitor for mefloquine toxicities. Posaconazole Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Mefloquine See Mefloquine. See Mefloquine. Quinine ↑ quinine expected ↑ posaconazole possible Coadministration should be avoided, if possible. If coadministered, monitor for quinine toxicities. Rifabutina Posaconazole AUC ↓ 49% Rifabutin AUC ↑ 72% Coadministration should be avoided, if possible. If coadministered, perform posaconazole and rifabutin TDM and adjust doses accordingly; monitor for clinical response to posaconazole and rifabutin toxicities. Rifampina ↓ posaconazole expected Do not coadminister when treating invasive fungal infections. If coadministered for treatment of noninvasive fungal infections, perform posaconazole TDM and adjust dose accordingly; monitor for clinical response. Rifapentinea Daily and Weekly Rifapentine: ↓ posaconazole expected Daily Rifapentine Do not coadminister when treating invasive fungal infections. If coadministered for treatment of noninvasive fungal infections, perform posaconazole TDM and adjust dose accordingly; monitor for clinical response. Weekly Rifapentine Coadministration should be avoided, if possible. If coadministered, perform posaconazole TDM and Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-14 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations adjust dose accordingly; monitor clinical response. Quinine Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Fluconazole See Fluconazole. See Fluconazole. Itraconazole See Itraconazole. See Itraconazole. Posaconazole See Posaconazole. See Posaconazole. Rifabutina ↓ quinine possible ↑ rifabutin possible Monitor for quinine efficacy. Monitor for rifabutin toxicity. Rifampina Quinine AUC ↓ 75% to 85% Do not coadminister. Rifapentinea Daily and Weekly Rifapentine ↓ quinine expected Do not coadminister. Voriconazole ↑ quinine expected Coadministration should be avoided, if possible. If coadministered, monitor for quinine toxicities. Rifabutina Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Atovaquone See Atovaquone. See Atovaquone. Bedaquiline See Bedaquiline. See Bedaquiline. Caspofungin See Caspofungin. See Caspofungin. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Dapsone See Dapsone. See Dapsone. Doxycycline See Doxycycline. See Doxycycline. Erythromycin See Erythromycin. See Erythromycin. Fluconazole See Fluconazole. See Fluconazole. Glecaprevir/Pibrentasvir See Glecaprevir/Pibrentasvir. See Glecaprevir/Pibrentasvir. Isavuconazole See Isavuconazole. See Isavuconazole. Itraconazole See Itraconazole. See Itraconazole. Linezolid See Linezolid. See Linezolid. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-15 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Mefloquine See Mefloquine. See Mefloquine. Posaconazole See Posaconazole. See Posaconazole. Quinine See Quinine. See Quinine. Sofosbuvir/Velpatasvir ↓ velpatasvir, sofosbuvir expected Do not coadminister. TAF ↓ TAF, TFV, TFV-DP expected ↑ TFV-DP expected versus TDF alone If coadministered, monitor for HIV and HBV treatment efficacy. Note: Interpretation extrapolated from TAF and rifampin (see Rifampin). FDA labeling recommends not to coadminister. TDF ↔ TDF, TFV, TFV-DP expected No dosage adjustment necessary. Voriconazole Voriconazole AUC ↓ 79% Rifabutin AUC ↑ 4-fold Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Coadministration may be considered if both voriconazole and rifabutin TDM is available to guide therapy. Rifampina Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Atovaquone See Atovaquone. See Atovaquone. Bedaquiline See Bedaquiline. See Bedaquiline. Caspofungin See Caspofungin. See Caspofungin. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Dapsone See Dapsone. See Dapsone. Doxycycline See Doxycycline. See Doxycycline. Erythromycin See Erythromycin. See Erythromycin. Fluconazole See Fluconazole. See Fluconazole. Glecaprevir/Pibrentasvir See Glecaprevir/Pibrentasvir. See Glecaprevir/Pibrentasvir. Isavuconazole See Isavuconazole. See Isavuconazole. Itraconazole See Itraconazole. See Itraconazole. Linezolid See Linezolid. See Linezolid. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-16 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Mefloquine See Mefloquine. See Mefloquine. Posaconazole See Posaconazole. See Posaconazole. Quinine See Quinine. See Quinine. Sofosbuvir/Velpatasvir Sofosbuvir AUC ↓ 72% Velpatasvir AUC ↓ 82% Do not coadminister. TAF TAF Plus Rifampin • TAF AUC ↓ 56% • TFV AUC ↓ 53% • TFV-DP AUC ↓ 36% Intracellular TFV-DP concentration is 4.2-fold greater than with TDF alone. If coadministered, monitor for HIV and HBV treatment efficacy. Note: FDA labeling recommends not to coadminister. TDF TDF Plus Rifampin 600 mg Daily ↔ TFV No dosage adjustment necessary Voriconazole Voriconazole AUC ↓ 96% Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Rifapentinea Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Atovaquone See Atovaquone. See Atovaquone. Bedaquiline See Bedaquiline. See Bedaquiline. Caspofungin See Caspofungin. See Caspofungin. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Dapsone See Dapsone. See Dapsone. Doxycycline See Doxycycline. See Doxycycline. Erythromycin See Erythromycin. See Erythromycin. Fluconazole See Fluconazole. See Fluconazole. Glecaprevir/Pibrentasvir See Glecaprevir/Pibrentasvir. See Glecaprevir/Pibrentasvir. Isavuconazole See Isavuconazole. See Isavuconazole. Itraconazole See Itraconazole. See Itraconazole. Linezolid See Linezolid. See Linezolid. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-17 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Mefloquine See Mefloquine. See Mefloquine. Posaconazole See Posaconazole. See Posaconazole. Quinine See Quinine. See Quinine. TAF Daily and Weekly Rifapentine ↓ TAF, TFV, TFV-DP possible If coadministered, monitor for HIV and HBV treatment efficacy. Note: FDA labeling recommends not to coadminister. TDF ↔ TDF, TFV, TFV-DP expected No dosage adjustment necessary Sofosbuvir/Velpatasvir ↓ sofosbuvir, velpatasvir expected Do not coadminister. Voriconazole ↓ voriconazole expected Do not coadminister. Consider alternative antifungal and/or antimycobacterial agent(s). Sofosbuvir/ Velpatasvir Rifabutina See Rifabutin. See Rifabutin. Rifampina See Rifampin. See Rifampin. Rifapentinea See Rifapentine. See Rifapentine. TAF TFV AUC ↑ 52% (when RPV/TAF/FTC given with SOF/VEL/VOX) No dosage adjustment necessary TDF TFV AUC ↑ 35% to 40% (when given with EVG/c/FTC or RPV/FTC) TFV AUC ↑ 81% (when given with EFV/FTC and SOF/VEL) TFV AUC ↑ 39% (when given with DRV/r/FTC and SOF/VEL/VOX) Monitor for TDF toxicities. Consider TAF in place of TDF. Tenofovir Alafenamide Glecaprevir/Pibrentasvir See Glecaprevir/Pibrentasvir. See Glecaprevir/Pibrentasvir. Rifabutina See Rifabutin. See Rifabutin. Rifampina See Rifampin. See Rifampin. Rifapentinea See Rifapentine. See Rifapentine. Sofosbuvir/Velpatasvir See Sofosbuvir/Velpatasvir. See Sofosbuvir/Velpatasvir. Tenofovir Disoproxil Fumarate Rifabutina See Rifabutin. See Rifabutin. Rifampina See Rifampin. See Rifampin. Table 4. Significant Pharmacokinetic Interactions Between Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV HH-18 Primary Drug Interacting Agent Effect on Primary and/or Concomitant Drug Concentrations Recommendations Rifapentinea See Rifapentine. See Rifapentine. Glecaprevir/Pibrentasvir See Glecaprevir/Pibrentasvir. See Glecaprevir/Pibrentasvir. Sofosbuvir/Velpatasvir See Sofosbuvir/Velpatasvir. See Sofosbuvir/Velpatasvir. Voriconazole Artemether/Lumefantrine See Artemether/Lumefantrine. See Artemether/Lumefantrine. Bedaquiline See Bedaquiline. See Bedaquiline. Chloroquine See Chloroquine. See Chloroquine. Clarithromycin See Clarithromycin. See Clarithromycin. Erythromycin See Erythromycin. See Erythromycin. Mefloquine See Mefloquine. See Mefloquine. Quinine See Quinine. See Quinine. Rifabutina See Rifabutin. See Rifabutin. Rifampina See Rifampin. See Rifampin. Rifapentinea See Rifapentine. See Rifapentine. a Refer to the subsection Rifamycin-Related Induction Interactions in the Table 4 introduction above. Drugs marked with asterisk () are those which are known to have assays available (for clinical and/or research purposes) within the United States and typically in Europe. When TDM is appropriate, clinicians should contact their clinical laboratory to determine assay availability and turnaround time for their institution. Key to Symbols ↑ = increase ↓ = decrease ↔ = no substantial change Key: 14-OH = active metabolite of clarithromycin; AUC = area under the curve; Cmin = minimum concentration; Css = concentration at steady state; des-Rbt = desacetyl rifabutin; DHA = dihydroartemisinin; DRV/r = darunavir/ritonavir; EFV = efavirenz; EVG/c = elvitegravir/cobicistat; FDA = U.S. Food and Drug Administration; FTC = emtricitabine; HBV = hepatitis B virus; RPV = rilpivirine; SOF = sofosbuvir; t1/2 = half-life; TAF = tenofovir alafenamide; TDF = tenofovir disoproxil fumarate; TDM = therapeutic drug monitoring; TFV= tenofovir; TFV-DP = tenofovir diphosphate; VEL = velpatasvir; VOX = voxilaprevir Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-1 Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Updated: September 25, 2023 Reviewed: January 10, 2024 This table should not be considered a comprehensive list of all possible adverse reactions to each medication. For additional information, clinicians should consult other appropriate resources, such as the U.S. Food and Drug Administration prescribing information. For persons of childbearing potential, please refer to Table 7. Summary of Pre-Clinical and Human Data on, and Indications for, Opportunistic Infection Drugs During Pregnancy for information regarding adverse effect potential of these medications during pregnancy. Drug(s) Adverse Reactions Acyclovir • Crystalluria and nephrotoxicity secondary to obstructive urolithiasis, particularly after rapid high-dose IV infusion. Risk is increased with dehydration or pre-existing renal impairment. o Administer IV fluid hydration to reduce the risk for nephrotoxicity. • Neurotoxicity with high doses (agitation, confusion, hallucination, seizure, coma), especially in patients with renal impairment and/or older patients • Thrombophlebitis at peripheral IV infusion site • Nausea, vomiting, and headache Adefovir • Nephrotoxicity, especially in patients with underlying renal insufficiency, predisposing comorbidities, or taking concomitant nephrotoxic drugs • Nausea and asthenia Albendazole • Hepatotoxicity • Reversible alopecia • Nausea, vomiting, headache, and dizziness • Bone marrow suppression (i.e., pancytopenia, aplastic anemia, agranulocytosis, and leukopenia) (rare) o Patients with liver disease, including hepatic echinococcosis, appear to be at higher risk. Amikacin • Nephrotoxicity o Administer IV fluid hydration to reduce the risk for nephrotoxicity. • Ototoxicity, both hearing loss and vestibular toxicity, are possible. • Neuromuscular blockade, especially with myasthenia or Parkinson’s disease and rapid infusion of large doses (rare) Amphotericin B Deoxycholate and Lipid Formulations • Nephrotoxicity (lower incidence with liposomal formulations) o Administer IV fluid hydration to reduce the risk for nephrotoxicity. • Hypokalemia, hypomagnesemia, and hypocalcemia • Infusion-related reactions, including fever, chills, rigors, flank or back pain, and hypotension (lower incidence with liposomal formulations) • Thrombophlebitis Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-2 Drug(s) Adverse Reactions • Transaminase and bilirubin elevations • Headache, nausea, vomiting, and diarrhea • Heart failure (rarely reported) • Anemia (rare) Anidulafungin • Refer to the row on Echinocandins. Artemether/Lumefantrine • QTc prolongation • Fever, chills, fatigue, arthralgia, and myalgia • Headache, dizziness, asthenia, and insomnia • Nausea, vomiting, diarrhea, abdominal pain, and anorexia • Rash and pruritus • Delayed hemolytic anemia (rare) Artesunate • Acute renal failure requiring dialysis • Hemoglobinuria and jaundice • Post-treatment hemolysis that may require transfusion • QTc prolongation and bradycardia • Hypersensitivity reactions (anaphylaxis) • Dizziness, nausea, and vomiting Atovaquone • Hepatotoxicity • Rash, nausea, vomiting, and diarrhea • Fever, headache, and insomnia Atovaquone/Proguanil • Abdominal pain, nausea, vomiting, anorexia, diarrhea, headache, asthenia, dizziness, and rash • Reversible transaminase elevations Azithromycin • Ototoxicity with prolonged use • Hepatotoxicity • Hypersensitivity reactions • Nausea, vomiting, diarrhea, and abdominal pain • QTc prolongation Benznidazole • Photosensitivity and hypersensitivity reactions (including allergic dermatitis, TEN, and DRESS) • Paresthesia and peripheral neuropathy, headache, and insomnia • Bone marrow suppression • Embryo-fetal toxicity • Nausea, vomiting, abdominal pain, anorexia, and weight loss Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-3 Drug(s) Adverse Reactions Bedaquiline • QTc prolongation • Hepatotoxicity • Nausea, vomiting, anorexia, diarrhea, elevated amylase, arthralgia, headache, and skin rash Bezlotoxumab • Exacerbation of congestive heart failure • Nausea, pyrexia, and headache Brincidofovir • Elevations in hepatic transaminases and bilirubin • Nausea, vomiting, and diarrhea • Embryo-fetal toxicity, male infertility Caspofungin • Refer to the row on Echinocandins. Chloroquine and Hydroxychloroquine • Auditory and visual disturbances, including blurry vision. Retinal toxicity may occur with long-term use. • QTc prolongation • Cardiomyopathy • Bone marrow suppression and hemolysis • Neuropsychiatric changes, including extrapyramidal reactions, suicidal behavior, and convulsive seizures • Hypersensitivity reactions (including TEN, SJS, and EM) • Severe hypoglycemia which may require adjustment of antidiabetic medications • Photosensitivity, pruritus, skin pigmentation, and exacerbation of psoriasis • Headache, nausea, vomiting, diarrhea, anorexia, abdominal pain, and hepatitis • Neuromyopathy (may occur with long-term use) (rare) Cidofovir • Nephrotoxicity, proteinuria, azotemia, proximal tubular dysfunction (normoglycemic glycosuria, hypophosphatemia), and metabolic acidosis (including Fanconi’s syndrome) o Administer IV fluid hydration and oral probenecid to reduce the risk for nephrotoxicity. • Neutropenia and anemia • Ocular hypotony and anterior uveitis/iritis • Possibly carcinogenic and teratogenic; may cause hypospermia • Gastrointestinal intolerance and diarrhea • Asthenia, fever, headache, and alopecia • Side effects most likely related to co-administration with probenecid are rash, nausea, vomiting, anorexia, and gout exacerbation. Ciprofloxacin • Refer to the row on Fluoroquinolones. Clarithromycin • Hepatotoxicity • Ototoxicity, including reversible hearing loss and tinnitus, with high doses or prolonged use Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-4 Drug(s) Adverse Reactions • QTc prolongation • Increased risk of cardiac complications or death in patients with heart disease • Diarrhea • Headache, nausea, vomiting, diarrhea, abdominal cramps, and dysgeusia Clindamycin • Diarrhea, including C. difficile–associated diarrhea and colitis • Metallic taste (with IV infusion), thrombophlebitis, and arrhythmia with rapid IV infusion • Hypersensitivity reactions (including SJS and TEN) • Nausea, vomiting, abdominal pain, and abnormal liver function tests Clotrimazole (Troche) • Nausea, vomiting, anorexia, and metallic taste Cycloserine • Neuropsychiatric toxicities, including convulsions, psychosis, somnolence, confusion, inability to concentrate, hyperreflexia, headache, tremor, vertigo, paresis, dysarthria, depression (with suicidal ideation), peripheral neuropathy, and seizures (particularly with higher doses and in patients with history of chronic alcoholism) o Administer with pyridoxine. • Hypersensitivity reactions (including SJS), allergic dermatitis, and rash Dapsone • Methemoglobinemia, hemolytic anemia, neutropenia, and agranulocytosis o Do not use in patients with moderate to severe G6PD deficiency. • Sulfone syndrome (fever, exfoliative dermatitis, lymphadenopathy, hepatic necrosis, and hemolysis) • Phototoxicity and severe cutaneous reactions (including SJS and TEN) • Drug-induced lupus erythematosus • Hepatotoxicity and nephrotic syndrome • Peripheral neuropathy • Nausea and anorexia Doxycycline • Pill-induced esophagitis/esophageal ulceration • Intracranial hypertension • Photosensitivity and skin hyperpigmentation • Thrombophlebitis (with IV infusion) • Nausea and vomiting Echinocandins (Anidulafungin, Caspofungin, Micafungin) • Histamine-related infusion reactions (flushing, rash, pruritus, hypotension, and dyspnea) and thrombophlebitis • Hypersensitivity reactions (including anaphylaxis and anaphylactoid reaction) • Abnormal liver enzymes and hepatotoxicity • Hypokalemia • Embryo-fetal toxicity Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-5 Drug(s) Adverse Reactions • Diarrhea, nausea, vomiting, fever, and headache • Hemolysis (micafungin) (rare) Emtricitabine • Headache, nausea, and diarrhea • Skin hyperpigmentation and rash (palms and soles) Entecavir • Headache, fatigue, dizziness, and nausea Ethambutol • Optic neuritis (dose- and duration-dependent) and peripheral neuropathy • Headache, nausea, vomiting, anorexia, abdominal pain, and hyperuricemia/gout flare Ethionamide • Postural hypotension, hepatotoxicity, hypothyroidism (with or without goiter), and hypoglycemia • Dizziness, drowsiness, confusion, clumsiness, visual disturbances, and depression o Administer with pyridoxine. • Dose-dependent gastrointestinal side effects, including nausea, vomiting, anorexia, diarrhea, abdominal pain, and metallic taste • Photosensitivity and severe cutaneous reactions (including SJS, TEN, and DRESS) • Gynecomastia, acne, hair loss, and impotence Famciclovir • Nephrotoxicity (in patients with underlying renal disease) • Headache, nausea, vomiting, and diarrhea Fidaxomicin • Nausea, vomiting, and abdominal pain Flucytosine • Concentration-dependent (>100 mcg/mL) bone marrow suppression (anemia, neutropenia, agranulocytosis, and thrombocytopenia) • Hepatotoxicity • Diarrhea, nausea, vomiting, and headache • Rash, pruritus, and photosensitivity Fluconazole • Hepatotoxicity, nausea, vomiting, diarrhea, and abdominal pain • QTc prolongation • Reversible alopecia (with doses ≥400 mg/day for >2 months) Fluoroquinolones (ciprofloxacin, levofloxacin, moxifloxacin) • Restlessness, insomnia, nightmares, confusion, anxiety, paranoia, tremors, seizure, hallucinations, depression, suicidal thoughts, and attempted and completed suicide • Tendonitis and tendon rupture (associated with age over 60, concurrent corticosteroids, diabetes, and kidney, heart, and lung transplant) • Diarrhea including C. difficile–associated diarrhea and colitis • QTc prolongation • Photosensitivity/phototoxicity • Anemia, thrombocytopenia, and leukopenia Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-6 Drug(s) Adverse Reactions • Arthralgia and myalgia • Peripheral neuropathy and retinal detachment • Hyper- and hypoglycemia, including hypoglycemic coma • Nausea, diarrhea, bloating, headache, dizziness, and malaise • Vasculitis • Aortic dissection (rare) • Transaminase elevations and interstitial nephritis (rare) • Severe cutaneous reactions (including SJS and TEN) (rare) Foscarnet • Nephrotoxicity and electrolyte imbalances (e.g., hypocalcemia, hypomagnesemia, hypophosphatemia, hyperphosphatemia, hypokalemia) o Administer IV fluid hydration to reduce the risk for nephrotoxicity. • Paresthesia and seizure (associated with electrolyte imbalances) • Anemia • Nausea, vomiting, anorexia, and headache • Genital ulceration • Thrombophlebitis Ganciclovir • Neutropenia, thrombocytopenia, anemia, and pancytopenia • Carcinogenic and teratogenic potential and impaired fertility • Nephrotoxicity • Neuropathy • Thrombophlebitis Glecaprevir/Pibrentasvir • Risk of hepatitis B virus reactivation • Hepatic decompensation/failure in patients with advanced liver disease • Mild headache, fatigue, nausea, and diarrhea • Altered glucose tolerance in diabetic patients Interferon-Alfa and Peginterferon-Alfa • Neuropsychiatric effects (e.g., depression, suicidal ideation) • Neutropenia, anemia, and thrombocytopenia • Flu-like syndrome (e.g., fever, headache, fatigue, myalgia) • Hepatitis exacerbations, thyroid dysfunction, and alopecia • Nausea, anorexia, diarrhea, and weight loss • Development or exacerbation of autoimmune diseases and ocular effects (e.g., retinal hemorrhage, retinal artery or vein obstructions, and cotton wool spots) • Ischemic and hemorrhagic cerebrovascular events, cardiovascular and pulmonary effects, hyper- and hypoglycemia, diabetes, severe infection, and colitis Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-7 Drug(s) Adverse Reactions • Hypersensitivity reactions Isavuconazonium Sulfate (Isavuconazole) • Hepatotoxicity and cholelithiasis • Infusion-related reactions (hypotension, dyspnea, chills, dizziness, paresthesia, and hypoesthesia) • Hypersensitivity reactions (including SJS) • Embryo-fetal toxicity • Shortening of QT interval • Nausea, vomiting, diarrhea, headache, hypokalemia, dyspnea, and cough Isoniazid • Hepatotoxicity and asymptomatic elevation in aminotransferase enzymes • Peripheral neuropathy, paresthesia, seizures, and optic neuritis o Administer with pyridoxine • Nausea, diarrhea, and flushing • Arthralgia and lupus-like syndrome • Psychosis (rare) • Hypersensitivity reactions (including TEN and DRESS) (rare) Itraconazole • Congestive heart failure, edema, and hypokalemia • QTc prolongation • Hepatotoxicity • Hearing loss • Neuropathy • Gynecomastia • Nausea, vomiting, diarrhea, and abdominal pain Lamivudine • Nausea and vomiting Levofloxacin • Refer to the row on Fluoroquinolones. Linezolid • Anemia, neutropenia, and thrombocytopenia (especially with treatment lasting longer than 2–4 weeks and renal insufficiency) • Peripheral neuropathy and optic neuritis with long-term therapy • Nausea, vomiting, diarrhea, and headache • Serotonin syndrome (rare) • Seizure (in patients with a history of seizure or with risk factors for seizure) (rare) • Lactic acidosis, hypoglycemia, and hyponatremia (rare) Mefloquine • Depression, psychosis, anxiety, agitation, dizziness, headache, insomnia, and abnormal dreams • QTc prolongation and arrhythmias (extrasystole and sinus bradycardia) Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-8 Drug(s) Adverse Reactions • Agranulocytosis and aplastic anemia • Nausea, vomiting, diarrhea, and epigastric pain Micafungin • Refer to the row on Echinocandins. Miconazole Buccal Tablets • Dysgeusia, diarrhea, nausea, vomiting, upper abdominal pain, and headache • Local reactions (e.g., oral discomfort, burning, pain, tongue/mouth ulceration, gingival pruritus, swelling, and dry mouth) • Hypersensitivity reaction (may occur in patients with known hypersensitivity reaction to milk product concentrate) Miltefosine • Nephrotoxicity and elevated transaminases and bilirubin • Retinal degeneration • Leukocytosis and thrombocytopenia • Embryo-fetal toxicity and impaired fertility, scrotal pain, and impaired ejaculation • Nausea, vomiting, diarrhea, anorexia, headache, and motion sickness • Severe cutaneous reactions (including SJS) Moxifloxacin • Refer to the row on Fluoroquinolones. Nifurtimox • Patients with a history of brain injury, seizures, psychiatric disease, and serious behavioral alterations may experience worsening of their conditions. • Vomiting, abdominal pain, headache, decreased appetite, weight loss, nausea, pyrexia, rash, polyneuropathy, insomnia, dizziness, and vertigo • Carcinogenic and teratogenic potential and impaired fertility • Hypersensitivity reactions with hypotension, angioedema, dyspnea, pruritus, rash or other severe skin reactions Nitazoxanide • Nausea, vomiting, diarrhea, abdominal pain, headache, and chromaturia Nystatin (Oral Preparations) • Unpleasant taste, nausea, vomiting, anorexia, and diarrhea Paromomycin • Nausea, vomiting, abdominal cramps, anorexia, rash, and headache • Nephrotoxicity (rare) o Inflammatory bowel disease and renal insufficiency may increase risk. Penicillin G All Penicillin G Preparations • Hypersensitivity (immediate or delayed reactions, including anaphylaxis), bone marrow suppression, nausea, vomiting, diarrhea, and drug fever • Jarisch-Herxheimer reaction when used for syphilis (occurs most frequently in persons with early syphilis, high non-treponemal antibody titers, and prior penicillin treatment) Benzathine Penicillin G Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-9 Drug(s) Adverse Reactions • IM injection-site reactions (pain and erythema), procaine neuropsychiatric reactions (with high dose), and neurovascular damage (due to inadvertent intravascular instead of IM injection) Aqueous Crystalline Penicillin G (IV) • Thrombophlebitis • Neurotoxicity at high doses—especially in patients with renal dysfunction—and hyperkalemia or hypernatremia at high doses (depending on formulation) Pentamidine • Nephrotoxicity, infusion-related hypotension, and thrombophlebitis • QTc prolongation, arrhythmias (including Torsades de pointes), and electrolyte abnormalities • Hypoglycemia, hyperglycemia, and diabetes mellitus • Hepatotoxicity and GI intolerance • Leukopenia and thrombocytopenia • Embryotoxic • Rash • Pancreatitis (rare) Aerosolized Therapy • Bronchospasm, cough, dyspnea, tachypnea, and metallic taste Posaconazole • Hepatotoxicity, QTc prolongation, and hypokalemia • Pseudohyperaldosteronism (hypokalemia and hypertension) • Nausea, vomiting, diarrhea, abdominal pain, and headache IV Infusion • Thrombophlebitis, SBECD accumulation, and worsening renal function with IV formulation (especially in patients with eGFR <50 mL/min per package labeling, but observational studies with IV voriconazole suggest that this may not be a concern) Primaquine • Methemoglobinemia, hemolytic anemia (use with caution in patients with mild-moderate G6PD deficiency; do not use if severe G6PD deficiency), leukopenia, and neutropenia • QTc prolongation • Abdominal cramps, nausea, vomiting, and dizziness Pyrazinamide • Hepatotoxicity • Polyarthralgia and myalgia • Hyperuricemia/gout flare • Thrombocytopenia and sideroblastic anemia • Nausea, vomiting, flushing, rash, and photosensitivity Pyrimethamine • Neutropenia, thrombocytopenia, and megaloblastic anemia o Administer with leucovorin. Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-10 Drug(s) Adverse Reactions • Anorexia, vomiting, and rash Quinine • QTc prolongation and cardiac arrythmias • Cinchonism (tinnitus, vertigo, and blurred vision) • Hemolytic anemia (especially in patients with G6PD deficiency), thrombocytopenia, and agranulocytosis • Vision abnormalities (e.g., photophobia, altered color perception, and blindness) • Hypersensitivity reactions (including SJS and TEN) • Hypoglycemia • Headache, nausea, vomiting, and diarrhea Rifabutin • Uveitis (concentration-dependent) • Neutropenia and thrombocytopenia • Arthralgia • Hepatotoxicity • Rash • Nausea, vomiting, abdominal pain, diarrhea, and anorexia • Red-orange discoloration of body fluids Rifampin • Hepatotoxicity (cholestatic hepatitis) • Thrombocytopenia and hemolytic anemia • Renal failure • Hypersensitivity reactions with flu-like syndrome • Interstitial pulmonary disease • Nausea, vomiting, anorexia, abdominal pain, flatulence, diarrhea, headache, confusion, and flushing, rash • Red-orange discoloration of body fluids Rifapentine • Hepatotoxicity • Anemia, neutropenia, and lymphopenia • Hypersensitivity reactions • Arthralgia • Rash and pruritis • Nausea, vomiting, diarrhea, and anorexia • Red-orange discoloration of body fluids Sofosbuvir/Velpatasvir • Risk of hepatitis B virus reactivation • Headache, fatigue, and anemia (associated with ribavirin co-administration) • Altered glucose tolerance in diabetic patients Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-11 Drug(s) Adverse Reactions Streptomycin • Neurotoxicity including irreversible ototoxicity (both hearing loss and vestibular toxicity) • Nephrotoxicity • Neuromuscular blockade and respiratory paralysis (associated with rapid infusion of large aminoglycoside doses) Sulfadiazine • Severe cutaneous reactions (including SJS, EM, and TEN) and photosensitivity • Anemia, neutropenia, agranulocytosis, and thrombocytopenia • Crystalluria (nephrolithiasis, urolithiasis) and nephrotoxicity • Hepatotoxicity • Drug fever • Peripheral neuritis, tinnitus, vertigo, and insomnia • Nausea, vomiting, and headache Tafenoquine • Decreased hemoglobin and methemoglobinemia and hemolytic anemia o Do not use in patients with G6PD deficiency; may cause harm to fetuses and breastfeeding infants who are G6PD deficient. • Psychiatric adverse reactions (in patients with history of psychiatric illness) • Hypersensitivity reactions (angioedema and urticaria) • Visual disturbances • Dizziness, nausea, vomiting, and headache Tecovirimat • Headache, nausea, abdominal pain, and vomiting IV formulation • Infusion site pain, swelling, erythema, and extravasation • Contains hydroxypropyl-β-cyclodextrin, which may accumulate in patients with renal impairment and has the potential to cause renal toxicity Tenofovir disoproxil fumarate • Renal insufficiency and Fanconi syndrome (proximal renal tubulopathy with hypophosphatemia, hypouricemia, proteinuria, and normoglycemic glycosuria) • Decrease in bone mineral density • Nausea and vomiting Tenofovir alafenamide • Headache, abdominal pain, fatigue, and nausea • Lower incidence of renal or bone toxicities than with tenofovir disoproxil fumarate Trimethoprim-Sulfamethoxazole • Cutaneous reactions (in some cases SJS, EM, and TEN) and photosensitivity • Anemia, neutropenia, agranulocytosis, and thrombocytopenia • Hepatotoxicity • Dose-dependent increase in serum creatinine (without change in GFR), interstitial nephritis, crystalluria (in patients with inadequate hydration), and hyperkalemia (with high-dose TMP) Table 5. Serious and/or Common Adverse Reactions Associated with Systemically Administered Drugs Used to Treat or Prevent Opportunistic Infections Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV II-12 Drug(s) Adverse Reactions • Hypoglycemia and hyponatremia • Drug fever • Nausea and vomiting • Aseptic meningitis and pancreatitis (rare) Valacyclovir • Neurotoxicity (e.g., agitation, confusion, hallucination, seizure, coma) with high doses, especially in patients with renal impairment • Nephrotoxicity • Nausea, vomiting, abdominal pain, and headache Valganciclovir • Bone marrow suppression • Confusion, pyrexia, and tremor • Nephrotoxicity • Carcinogenic and teratogenic potential and impaired fertility • Nausea, vomiting, and diarrhea Voriconazole • Visual disturbances (e.g., abnormal vision, color vision change, and/or photophobia) • Optic neuritis (associated with >28 days treatment) • Headache, delirium, hallucination, peripheral neuropathy (rare), and encephalopathy (associated with trough >5.5 mcg/mL) • Hepatotoxicity • QTc prolongation • Photosensitivity • Voriconazole-associated cutaneous squamous cell carcinoma (with long-term use) • Fluorosis and periostitis with high dose and/or prolonged use • Fever, nausea, vomiting, chills, tachycardia, and peripheral edema • Embryo-fetal toxicity • Nail changes and alopecia (with long-term use) • SBECD accumulation with IV formulation and worsening renal function (especially in patients with eGFR <50 mL/min per package labeling, but observational studies suggest that this may not be a concern) Key: DRESS = drug reaction with eosinophilia and systemic symptoms; eGFR = estimated glomerular filtration rate; EM = erythema multiforme; G6PD = glucose-6-phosphate dehydrogenase; GFR = glomerular filtration rate; GI = gastrointestinal; IM = intramuscular; IV = intravenous; QTc = QT corrected for heart rate; SBECD = sulfobutylether cyclodextrin; SJS = Stevens-Johnson syndrome; TEN = toxic epidermal necrolysis; TMP = trimethoprim Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-1 Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections that Require Dosage Adjustment in Patients with Renal Insufficiency Updated: September 25, 2023 Reviewed: January 10, 2024 When renally cleared drugs are administered to patients with reduced renal function, drug accumulation leading to supratherapeutic concentrations and drug toxicities is a primary concern. However, clearance is only one of the pharmacokinetic parameters that affect a drug’s disposition. The volume of distribution of a drug also can be altered in patients with reduced renal function. Furthermore, some patients with HIV or diabetes mellitus can have reduced oral absorption of certain drugs. Therefore, although a drug may require a dose reduction in renal failure based on reduced clearance (i.e., increased concentrations), other factors—such as an increased volume of distribution or reduced oral absorption—may decrease concentrations. Therapeutic drug monitoring (TDM), if available and appropriate, may facilitate dose adjustments in these complicated patients. TDM allows the clinician to make informed, individualized decisions about dose adjustments that are more precise than standardized dose adjustments based on estimated creatinine clearance. Drugs that are marked with an asterisk () in the table below are known to have assays (for clinical and/or research purposes) available within the United States and typically in Europe as well. When TDM is appropriate, clinicians should contact their clinical laboratory to determine assay availability and turnaround time for their institution. Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose Acyclovir IV Dose Serious HSV • 5 mg/kg IV every 8 hours VZV Infections or HSV encephalitis • 10 mg/kg IV every 8 hours 26–50 100% of dose IV every 12 hours 10–25 100% of dose IV every 24 hours <10 50% of dose IV every 24 hours HD 50% of dose every 24 hours; administer dose after HD on days of dialysis. PO Dose for Herpes Zoster: 800 mg PO five times per day 10–25 800 mg PO every 8 hours <10 800 mg PO every 12 hours HD 800 mg PO every 12 hours; administer dose after HD on days of dialysis Adefovir 10 mg PO every 24 hours 30–49 10 mg PO every 48 hours 10–29 10 mg PO every 72 hours Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-2 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose HD 10 mg PO weekly; administer dose after HD Amikacin For mycobacterial infections IV 15 mg/kg per day or 25 mg/kg three times per week Use with caution in patients with renal insufficiency and family history of ototoxicity. 15 mg/kg two to three times per week Perform TDM to adjust dose, with target peak concentration 35–45 mcg/mL and trough concentration <4 mcg/mL. Administer dose after HD on days of dialysis. Amphotericin B 3–6 mg/kg IV per day (lipid formulation) or 0.7–1.0 mg/kg IV per day (amphotericin B deoxycholate) N/A No dosage adjustment necessary; consider alternative antifungals if renal insufficiency occurs during therapy despite adequate hydration. Cidofovir 5 mg/kg IV on Day 0, repeat 5 mg/kg IV dose on Day 7, then 5 mg/kg IV every 2 weeks Give each dose with probenecid and saline hydration (see Table 2 for dosing instructions). Pretreatment SCr >1.5 mg/dL or CrCl <55 mL/min or Proteinuria ≥100 mg/dL (≥2 +) Cidofovir is not recommended unless benefits outweigh risks. See “Pharmacokinetics of cidofovir in renal insufficiency and in continuous ambulatory peritoneal dialysis or high-flux hemodialysis” for recommendations on renal dose adjustments. If SCr increases by 0.3–0.4 mg/dL above baseline Decrease to 3 mg/kg IV per dose. If SCr increases >0.5 mg/dL above baseline or Proteinuria ≥3 + Discontinue therapy. Ciprofloxacin 500–750 mg PO every 12 hours or 400 mg IV every 8–12 hours 30–50 500–750 mg PO every 12 hours or 400 mg IV every 12 hours <30 250–500 mg PO every 24 hours Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-3 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose or 400 mg IV every 24 hours HD or PD 250–500 mg PO every 24 hours or 200–400 mg IV every 24 hours; administer after HD or PD on days of dialysis. Clarithromycin 500 mg PO every 12 hours 30–60 Usual dose unless used with an HIV PI or with COBI, then reduce dose by 50%. <30 250 mg PO twice daily or 500 mg PO once daily If used with an HIV PI or COBI, reduce dose by 75% (or consider using azithromycin as alternative). Cycloserine 10–15 mg/kg/day PO in two divided doses (maximum 1,000 mg/day); start at 250 mg once daily and increase dose per tolerability. Target peak concentration 20–35 mcg/mL 30–80 Usual dose; consider TDM and monitor for toxicities. <30 (not on HD) or HD 250 mg once daily or 500 mg three times per week Perform TDM and adjust dose accordingly. Monitor for toxicities. Use with caution in patients with ESRD who are not on dialysis. Emtricitabinea (FTC) One 200-mg capsule PO once daily or 240-mg solution PO once daily CrCl^ or eGFR# (mL/min) Oral Capsules Oral Solution 15–29 200 mg every 72 hours 80 mg every 24 hours <15 and not on HD 200 mg every 96 hours 60 mg every 24 hours HD (administer dose after HD on days of dialysis) 200 mg every 24 hours 240 mg every 24 hours Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-4 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose Emtricitabine/ Tenofovir Alafenamide (FTC/TAF) (FDC Trade Name: Descovy) Note: Please refer to product labels for dosing recommendations for other ARV FDC products containing FTC/TAF. One tablet (FTC 200 mg/TAF 25 mg) PO once daily <30 and not on HD Coformulated tablet is not recommended. HD One tablet daily. Administer dose after HD on days of dialysis. Emtricitabine/ Tenofovir Disoproxil Fumarate (FTC/TDF) (FDC Trade Name: Truvada) Note: Please refer to product labels for dosing recommendations for other ARV FDC products containing FTC/TDF. One (FTC 200 mg/TDF 300 mg) tablet PO daily 30–49 One tablet PO every 48 hours (monitor for worsening renal function or consider switching to TAF) <30 or HD Do not use coformulated tablet. Use formulation for each component drug and adjust dose according to recommendations for the individual drugs. Entecavir Usual Dose: 0.5 mg PO once daily For Treatment of 3TC-Refractory HBV or for Patients with Decompensated Liver Disease: 1 mg PO once daily CrCl^ or eGFR# (mL/min) Usual Renal Dose Adjustment 3TC-Refractory or Decompensated Liver Disease 30 to <50 • 0.25 mg PO every 24 hours, or • 0.5 mg PO every 48 hours • 0.5 mg PO every 24 hours, or • 1 mg PO every 48 hours 10 to <30 • 0.15 mg PO every 24 hours, or • 0.5 mg PO every 72 hours • 0.3 mg PO every 24 hours, or • 1 mg PO every 72 hours Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-5 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose <10 or HD or CAPD (administer after HD on days of dialysis) • 0.05 mg PO every 24 hours, or • 0.5 mg PO once every 7 days • 0.1 mg PO every 24 hours, or • 1 mg PO once every 7 days Ethambutol For MAI: 15 mg/kg PO daily For MTB: 15–25 mg/kg PO daily (See the Dosing Recommendations table in the Mycobacterium tuberculosis section for additional MTB dosing recommendations.) <30 or HD Usual dose PO three times weekly (in patients on HD, give dose after dialysis). PD Do not use in patients on PD. Consider alternative MAI or MTB treatment (e.g., moxifloxacin). Perform TDM to guide optimal dosing. Ethionamide 15–20 mg/kg PO daily (usually 250–500 mg PO once or twice daily) <30 or HD 250–500 mg PO once daily Consider TDM. Famciclovir For Herpes Zoster: 500 mg PO every 8 hours For HSV: 500 mg PO every 12 hours 40–59 500 mg PO every 12 hours 20–39 500 mg PO every 24 hours <20 250 mg PO every 24 hours HD 250 mg PO only on HD days, administer after HD Fluconazole 200–1,200 mg PO or IV every 24 hours (dose and route of administration depends on type of OI) ≤50 Administer 100% of the indication-specific initial dose, then adjust maintenance doses to 50% of dose every 24 hours. HD Administer 100% of the indication-specific initial dose, then adjust maintenance doses to full dose three times per week after HD. Flucytosine 25 mg/kg PO every 6 hours TDM is recommended for patients to guide optimal dosing (target peak serum concentration 2 hours after dose: 25-100 mcg/mL). If TDM is not possible, monitor CBC twice weekly. 21–40 25 mg/kg PO every 12 hours 10–20 25 mg/kg PO every 24 hours <10 25 mg/kg PO every 48 hours HD 25–50 mg/kg PO every 48–72 hours; administer dose after HD. Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-6 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose Foscarnet Induction Therapy for CMV Infection: 180 mg/kg/day IV in two divided doses Maintenance Therapy for CMV Infection or for Treatment of HSV Infections: 90–120 mg/kg IV once daily Dosage adjustment needed according to calculated CrCl/kg; consult product label for dosing table. Dosage adjustment needed according to calculated CrCl/kg; consult product label for dosing table. Ganciclovir Induction Therapy: 5 mg/kg IV every 12 hours 50–69 2.5 mg/kg IV every 12 hours 25–49 2.5 mg/kg IV every 24 hours 10–24 1.25 mg/kg IV every 24 hours <10 or HD 1.25 mg/kg IV three times per week; administer dose after HD. Maintenance Therapy: 5 mg/kg IV every 24 hours 50–69 2.5 mg/kg IV every 24 hours 25–49 1.25 mg/kg IV every 24 hours 10–24 0.625 mg/kg IV every 24 hours <10 or HD 0.625 mg/kg IV three times per week; administer dose after HD. Lamivudineb (3TC) 300 mg PO every 24 hours 15–29 150 mg PO once, then 100 mg PO every 24 hours 5–14 150 mg PO once, then 50 mg PO every 24 hours <5 or HD 50 mg PO once, then 25 mg PO every 24 hours; administer dose after HD on days of dialysis. Lamivudine/ Tenofovir Disoproxil Fumarate (3TC/TDF) (FDC Trade Names: Cimduo or Temixys) Note: Please refer to product information for dosing recommendations for other ARV FDC One (3TC 300 mg/TDF 300 mg) tablet PO every 24 hours <50 Coformulated tablet is not recommended. Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-7 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose products containing 3TC/TDF. Levofloxacin 500 mg (low dose) or 750– 1,000 mg (high dose) IV or PO daily CrCl^ or eGFR# (mL/min) Low Dose High Dose 20–49 500 mg once, then 250 mg every 24 hours, IV or PO 750 mg every 48 hours IV or PO <20 or CAPD or HD (administer dose after HD on days of dialysis) 500 mg once, then 250 mg every 48 hours, IV or PO Dose can be adjusted based on serum concentrations. 750 mg once, then 500 mg every 48 hours, IV or PO Paromomycin 500 mg PO every 6 hours <10 Minimal systemic absorption. No dosage adjustment necessary but monitor for worsening renal function and ototoxicity in patients with ESRD. Peginterferon Alfa-2a 180 mcg SQ once weekly <30 135 mcg SQ once weekly HD 135 mcg SQ once weekly May reduce to 90 mcg once weekly if severe adverse effects or laboratory abnormalities occur. Penicillin G (Potassium or Sodium) Neurosyphilis, Ocular Syphilis, or Otosyphilis • 3–4 million units IV every 4 hours, or • 18–24 million units IV daily as continuous infusion 10–50 2–3 million units every 4 hours or 12–18 million units as continuous infusion <10 2 million units every 4–6 hours, or 8–12 million units as continuous infusion HD or CAPD 2 million units every 4–6 hours, or 8 million units as continuous infusion Pentamidine 4 mg/kg IV every 24 hours May reduce dose to 3 mg/kg IV daily in the event of toxicities <10 4 mg/kg IV every 48 hours Posaconazole IV: 300 mg twice daily on Day 1; then 300 mg once daily Delayed-Release Tablet: 300 mg PO once daily <50 No dosage adjustment of oral dose in patients with renal insufficiency. Higher variability in serum concentrations observed in patients with CrCl <20 mL/min. Perform posaconazole TDM (target trough concentration at least >1.25 mcg/mL for treatment). Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-8 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose Oral Suspension: 400 mg PO twice daily IV posaconazole is not recommended by the manufacturer because of potential toxicity due to accumulation of SBCD (vehicle of IV product). However, an observational study did not find worsening in renal function in patients with CrCl <50 ml/min given SBCD. Switch patients with CrCl <50 mL/min to oral posaconazole when feasible. Pyrazinamide See the Mycobacterium tuberculosis section for weight-based dosing guidelines. <30 or HD 25–35 mg/kg/dose three times per week; administer dose after HD. Quinine Sulfate 650 mg salt (524 mg base) PO every 8 hours <10 or HD 650 mg once, then 325 mg PO every 12 hours Rifabutin 5 mg/kg PO daily (usually 300 mg PO daily) See the Mycobacterium tuberculosis section and Drug–Drug Interactions in the Adult and Adolescent Antiretroviral Guidelines for dosage adjustment based on interactions with ARVs. <30 If toxicity is suspected, consider 50% of dose once daily and perform rifabutin TDM. Sofosbuvir 400 mg PO daily <30 Not recommended. Up to 20-fold higher sofosbuvir metabolite observed in patients with this level of renal impairment. Streptomycin 15 mg/kg IM or IV every 24 hours or 25 mg/kg IM or IV three times per week Use with caution in patients with renal insufficiency. TDM is no longer available. Consider an alternative aminoglycoside, as clinically appropriate. If used: 15 mg/kg two to three times weekly. Administer dose after HD. Sulfadiazine 1,000–1,500 mg PO every 6 hours (1,500 mg every 6 hours for patients >60 kg) ≤ 50 No data. Use alternative anti-toxoplasma therapy. Tecovirimat IV: 35 to <120 kg: 200 mg every 12 hours 30–89 No dosage adjustment necessary Use with caution due to potential accumulation of hydroxypropyl-β-cyclodextrin. Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-9 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose ≥120 kg: 300 mg every 12 hours <30 Contraindicated due to potential accumulation of hydroxypropyl-β-cyclodextrin. Note: IV formulation may be considered in patients with CrCl <30 only if drug absorption via enteral administration is expected to be problematic based on an individual risk-benefit assessment in consultation with CDC. In these circumstances, use with caution and monitor renal function continuously. Switch to the oral formulation as soon as possible. PO: 40 to <120 kg: 600 mg every 12 hours ≥120 kg: 600 mg every 8 hours Any eGFR No dosage adjustment necessary Tenofovir Alafenamide (TAF) Note: Please refer to product labels for dosing recommendations for other ARV FDC products containing FTC/TAF. 25 mg PO daily <15 Not recommended <15 on HD No dosage adjustment required. Administer dose after HD on days of dialysis. Tenofovir Disoproxil Fumarate (TDF) Note: Please refer to product labels for dosing recommendations for other ARV FDC products containing TDF. 300 mg PO daily 30–49 300 mg PO every 48 hours (consider switching to TAF for treatment of HBV) 10–29 300 mg PO every 72–96 hours (consider switching to alternative agent for treatment of HBV) <10 and not on dialysis Not recommended HD 300 mg PO once weekly; administer dose after dialysis Trimethoprim / Sulfamethoxazole (TMP-SMX) For PCP Treatment • 5 mg/kg (of TMP component) IV every 6–8 hours, or 15–30 5 mg/kg (TMP) IV every 12 hours, or two TMP-SMX DS tablets PO every 12 hours <15 5 mg/kg (TMP) IV every 24 hours, or one TMP-SMX DS tablet PO every 12 hours (or two TMP-SMX DS tablets every 24 hours) Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-10 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose • Two TMP-SMX DS tablets PO every 8 hours HD 5 mg/kg/day (TMP) IV, or two TMP-SMX DS tablets PO daily; administer dose after HD on days of dialysis. Consider TDM to optimize therapy (target TMP concentrations: 5–8 mcg/mL). For PCP Prophylaxis • One TMP-SMX DS tablet PO daily, • One TMP-SMX DS tablet PO three times per week, or • One TMP-SMX SS tablet PO daily 15–30 Reduce dose by 50% (e.g., 1 SS tablet PO daily). <15 Reduce dose by 50% or use alternative agent. For Toxoplasmosis Encephalitis (TE) Treatment: 5 mg/kg (TMP component) IV or PO every 12 hours 15–30 5 mg/kg (TMP component) IV or PO every 24 hours <15 5 mg/kg (TMP component) IV or PO every 24 hours or use alternative agent For TE Chronic Maintenance Therapy • One TMP-SMX DS tablet twice daily, or • One TMP-SMX DS tablet daily 15–30 Reduce dose by 50%. <15 Reduce dose by 50% or use alternative agent. For Toxoplasmosis Primary Prophylaxis: One TMP-SMX DS tablet PO daily 15–30 Reduce dose by 50%. <15 Reduce dose by 50% or use alternative agent. Valacyclovir For Herpes Zoster: 1 g PO three times daily 30–49 1 g PO every 12 hours 10–29 1 g PO every 24 hours <10 500 mg PO every 24 hours HD 500 mg PO every 24 hours; administer dose after HD on days of dialysis. 30–49 No dosage adjustment 10–29 For Treatment: 1 g PO every 24 hours Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-11 Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose For Herpes Simplex Virus Treatment: 1 g PO twice daily For Herpes Simplex Chronic Suppressive Therapy: 500 mg PO twice daily For Suppressive Therapy: 500 mg PO every 24 hours <10 500 mg PO every 24 hours HD 500 mg PO every 24 hours; administer dose after HD on days of dialysis. Valganciclovir Induction Therapy: 900 mg PO twice daily Maintenance Therapy: 900 mg PO once daily CrCl^ or eGFR# (mL/min) Induction Maintenance 40–59 450 mg PO twice daily 450 mg PO daily 26–39 450 mg PO daily 450 mg PO every 48 hours 10–25 450 mg PO every 48 hours 450 mg PO twice weekly <10 and not on dialysis Not recommended Use IV ganciclovir. May consider: • 200 mg (oral powder for solution) PO three times per week If oral powder formulation is not available, consider: • 450 mg (tablet) PO three times weekly Not recommended Use IV ganciclovir. May consider: • 100 mg (oral powder for solution) PO three times per week If oral powder formulation is not available, consider: • 450 mg (tablet) PO twice weekly HD Not recommended Use IV ganciclovir. May consider: • 200 mg (oral powder for solution) PO three times per week after HD If oral powder formulation is not available, may consider: • 450 mg (tablet) PO three times per week after HD Not recommended Use IV ganciclovir. May consider: • 100 mg (oral powder for solution) PO three times per week after HD If oral powder formulation is not available, may consider: • 450 mg (tablet) PO twice per week after HD Table 6. Dosing Recommendations for Drugs Used to Treat or Prevent Opportunistic Infections That Require Dosage Adjustment in Patients with Renal Insufficiency Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV JJ-12 Drugs marked with asterisk () are those known to have assays available (for clinical and/or research purposes) within the United States and typically in Europe. When TDM is appropriate, clinicians should contact their clinical laboratory to determine assay availability and turnaround time for their institution. a The prescribing information for emtricitabine (Emtriva) recommends adjusting doses for patients with CrCl 30-49 and for patients on hemodialysis. However, the prescribing information for several FDC products that contain emtricitabine (including Descovy, Biktaryy, Genvoya, and Odefsey) recommends that the standard dose (emtricitabine 200 mg) can be given once daily in these patients (on days of hemodialysis, give after completion of dialysis). The recommendations in this table incorporate the dosing guidance from the FDC products. b The prescribing information for lamivudine (Epivir) recommends dosage adjustment from 300 mg once daily to 150 mg once daily for patients with CrCl 30–49 mL/min. However, the prescribing information for several FDC products that contain lamivudine (including Epzicom, Dovato, and Triumeq) recommends no dose adjustment for CrCl 30–49 mL/min. The recommendation in this table incorporates the dosing guidance from the FDC products. ^Creatinine Clearance Calculation Male: (140 −𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖𝑖𝑖 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦) × 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑡𝑡 𝑖𝑖𝑖𝑖 𝑘𝑘𝑘𝑘 72 × 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 Female: (140 −𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖𝑖𝑖 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦) × 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑡𝑡 𝑖𝑖𝑖𝑖 𝑘𝑘𝑘𝑘× 0.85 72 × 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 #When estimating kidney function to facilitate drug dosing in patients with renal insufficiency, please refer to the drug’s prescribing information and to the National Institute of Diabetes and Digestive and Kidney Diseases’ Determining Drug Dosing in Adults with Chronic Kidney Disease page for a discussion on using CrCl based on the Cockcroft-Gault equation versus eGFR. Key: 3TC = lamivudine; ARV = antiretroviral; CAPD = continuous ambulatory peritoneal dialysis; CBC = complete blood count; CMV = cytomegalovirus; COBI = cobicistat; CrCl = creatinine clearance; DS = double strength; eGFR = estimated glomerular filtration rate; ESRD = end-stage renal disease; FDC = fixed-dose combination; FTC = emtricitabine; HBV = hepatitis B virus; HD = hemodialysis; HSV = herpes simplex virus; IM = intramuscular; IV = intravenous; MAI = Mycobacterium avium intracellulare; MTB = Mycobacterium tuberculosis; N/A = not applicable; OI = opportunistic infection; PCP = Pneumocystis pneumonia; PD = peritoneal dialysis; PI = protease inhibitor; PO = orally; SCr = serum creatinine; SQ = subcutaneous; SBCD = sulfobutylether cyclodextrin; SS = single strength; TAF = tenofovir alafenamide; TDF = tenofovir disoproxil fumarate; TDM = therapeutic drug monitoring; TMP-SMX = trimethoprim-sulfamethoxazole; VZV = varicella zoster virus Drug(s) Usual Dose Dosage Adjustment in Renal Insufficiency CrCl^ or eGFR# (mL/min) Dose Voriconazole 6 mg/kg IV every 12 hours for two doses, then 4 mg/kg IV every 12 hours or 200–300 mg PO every 12 hours <50 IV voriconazole is not recommended by the manufacturer because of potential toxicity due to accumulation of SBCD (vehicle of IV product). An observational study did not find worsening in renal function in patients with CrCl <50 ml/min. Switch patients with CrCl <50 ml/min to oral voriconazole when feasible. No need for dosage adjustment when the oral dose is used. Perform TDM to adjust dose. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV KK-1 Appendix A. List of Abbreviations (Last updated May 7 , 2013; last reviewed January 10, 2024) Acronym/Abbreviation ABGs ACTG AFB AIN ALT anti-HBc anti-HBs ART ARV ASCCP ASC-H  ASC-US AST AUC BA BAL BID BIW CAP CAPD CD4 CDC CDI CES-D CFU CIA CIN Cmax Cmin CMV CNS CPE CrCl CSF CT Definition arterial blood gases AIDS Clinical Trials Group acid-fact bacilli anal intraepithelial neoplasia alanine aminotransferase hepatitis B core antibody hepatitis B surface antibody antiretroviral therapy antiretroviral American Society for Colposcopy and Cervical Pathology atypical squamous cells—cannot exclude high grade cervical squamous intraepithelial lesion atypical squamous cells of uncertain significance serum aspartate aminotransferase area under the curve bacillary angiomatosis bronchoalveolar lavage twice a day twice a week community-acquired pneumonia continuous ambulatory peritoneal dialysis CD4 T lymphocyte cell Centers for Disease Control and Prevention Clostridium difficile-associated infection Center for Epidemiologic Studies Depression Scale colony-forming unit chemiluminescence immunoassays cervical intraepithelial neoplasia maximum concentration minimum concentration cytomegalovirus central nervous system central nervous system penetration effectiveness creatinine clearance cerebrospinal fluid computed tomography Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV KK-2 CYP3A4 Cytochrome P450 3A4 DAAs direct acting antiviral agents DOT directly observed therapy DS double strength EDTA ethylenediaminetetraacetic acid EIAs enzyme immunoassays EM erythema multiforme FDA Food and Drug Administration FTA-ABS fluorescent treponemal antibody absorbed g gram G6PD Glucose-6-phosphate dehydrogenase GFR glomerular filtration rate GI gastrointestinal HAV hepatitis A virus HBV hepatitis B virus HCV hepatitis C virus HHV-8 human herpesvirus-8 HPA hypothalamic-pituitary-adrenal HPV human papillomavirus HSIL high grade cervical squamous intraepithelial lesion HSV herpes simplex virus HSV-1 herpes simplex virus 1 HSV-2 herpes simplex virus 2 ICP intracranial pressure ICU intensive care unit IFN interferon IgG immunoglobulin G IgM immunoglobulin M IGRA interferon-gamma release assays IM intramuscular IND investigational new drug IRIS immune reconstitution inflammatory syndrome IRU immune recovery uveitis IV intravenous IVIG intravenous immunoglobulin JCV JC virus KS Kaposi Sarcoma LEEP loop electrosurgical excision procedure LP lumbar puncture LSIL low grade squamous intraepithelial lesion Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV KK-3 LTBI latent tuberculosis infection MAC Mycobacterium avium complex MAI Mycobacterium avium intracellulare MCD multicentric Castleman’s disease MDR TB multi-drug-resistant tuberculosis mg milligram mmHg millimeters of mercury MSM men who have sex with men MTB Mycobacterium tuberculosis NAA nucleic acid amplification NNRTI non-nucleoside reverse transcriptase inhibitor NRTI nucleoside reverse transcriptase inhibitors NSAID non-steroidal anti-inflammatory drugs NVP nevirapine OI opportunistic infection PCP Pneumocystis pneumonia PCR polymerase chain reaction PEL primary effusion lymphoma PK pharmacokinetic PML progressive multifocal leukoencephalopathy PO orally PORN Progressive Outer Retinal Necrosis PPV polysaccharide vaccine PSI pneumonia severity index q(n)h every ”n” hours qAM every morning QID four times a day qPM every evening RPR rapid plasma reagin RVR rapid virological response SCr serum creatinine SJS Stevens-Johnson syndrome SLE systemic lupus erythematosus SQ subcutaneous SS single strength STD sexually transmitted disease SVR sustained virologic response TB tuberculosis TDM therapeutic drug monitoring TE Toxoplasma encephalitis Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV KK-4 TEN toxic epidermal necrolysis TID three times daily TIW three times weekly TP-PA T. pallidum particle agglutination TST tuberculin skin test ULN upper limit of normal VAIN vaginal intra-epithelial neoplasia VDRL Venereal Disease Research Laboratory VIII vestibulocochlear VIN vulvar intraepithelial neoplasia VZV varicella zoster virus WBC white blood cell WHO World Health Organization XDR TB extensively drug-resistant tuberculosis Abbreviation Drug Name 3TC lamivudine 5-FU fluorouracil ATV/r ritonavir-boosted atazanavir BCA bichloroacetic acid BOC boceprevir COBI cobicistat ddA-TP dideoxyadenosine triphosphate ddI didanosine DHA dihydroartemisinin EFV efavirenz EMB ethambutol EVG elvitegravir FTC emtricitabine INH isoniazid MVC maraviroc PCV13 13-valent pneumococcal conjugate vaccine PegIFN peginterferon alfa PI protease inhibitor PPV23 23-valent pneumococcal polysaccharides vaccine PZA pyrazinamide RAL raltegravir RBV ribavirin RFB rifabutin RIF rifampin Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents with HIV KK-5 RPT rifapentine SMX sulfamethoxazole TCA trichloroacetic acid TDF tenofovir disoproxil fumarate TMP trimethoprim TMP-SMX trimethoprim-sulfamethoxazole TVR telaprevir ZDV zidovudine Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-1 Appendix B. Panel Roster and Financial Disclosures Leadership Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Constance Benson University of California, San Diego School of Medicine Gilead Sciences Research Support (paid to institution) John Brooks Atlanta, GA None N/A Shireesha Dhanireddy University of Washington Medicine None N/A Henry Masur National Institutes of Health None N/A Alice Pau National Institutes of Health None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-2 Appendix B. Panel Roster and Financial Disclosures Section Review Group Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Lydia Aoun Barakat Yale University School of Medicine None N/A Rodrigo Burgos University of Illinois Chicago College of Pharmacy OptumRx Consultant Merck Janssen Vaccines & Prevention Moderna Research Support (paid to institution) Thomas Campbell University of Colorado School of Medicine None N/A Catherine Decker Walter Reed National Military Medical Center None N/A Ellen Kitchell The University of Texas Southwestern Medical Center None N/A Susana Lazarte The University of Texas Southwestern Medical Center Gilead Sciences Research Support (paid to institution) Paul Pham The Johns Hopkins University School of Medicine; Westview Urgent Care Medi Center Novo Nordisk Stockholder Gregory Robbins Massachusetts General Hospital Leonard-Meron Biosciences Seed Health/LUCA Biologics Teradyne Consultant Emergent BioSolutions Pfizer Research Support Anandi Sheth Emory University School of Medicine None N/A William Short Perelman School of Medicine at the University of Pennsylvania ViiV Healthcare Advisory Board Gilead Sciences Research Support Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-3 Appendix B. Panel Roster and Financial Disclosures Bacterial Enteric Infections Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Carolyn Alonso Harvard Medical School; Beth Israel Deaconess Medical Center ClinicalCare Honoraria Anna Bowen Centers for Disease Control and Prevention None N/A Paul Pham The Johns Hopkins University School of Medicine Novo Nordisk Stockholder Jennifer Spicer Emory University School of Medicine None N/A Brian Zanoni Emory University School of Medicine Accordant Health Services Consultant Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-4 Appendix B. Panel Roster and Financial Disclosures Bartonellosis Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Nesli Basgoz Harvard Medical School Allergen Equity Interest Carl Boodman University of Manitoba, Canada Research Foundation – Flanders, Fonds de recherche du Québec Research Support European Society of Clinical Microbiology and Infectious Diseases Research Support Clinical Investigator Program (University of Manitoba) Research Support European Union (doctoral mobility grant) Travel Support International Diagnostics Network/Global Health CPD Consultant James Kirby Harvard Medical School; Beth Israel Deaconess Medical Center None N/A Jane Koehler University of California, San Francisco School of Medicine None N/A Grace Marx Centers for Disease Control and Prevention None N/A Stacey Rose Baylor College of Medicine None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-5 Appendix B. Panel Roster and Financial Disclosures Candidiasis Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Melissa Johnson Duke University School of Medicine Scynexis Research Support Biomeme Patent Michail Lionakis National Institutes of Health None N/A Jeniel Nett University of Wisconsin– Madison School of Medicine and Public Health National Institutes of Health Research Support Burroughs Wellcome Fund Research Support Doris Duke Charitable Foundation Research Support Honoraria Jack Sobel Wayne State University School of Medicine Mycovia Pharmaceuticals Advisory Board Speakers Bureau Consultant Scynexis Advisory Board Speakers Bureau Consultant UpToDate Honoraria Author Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-6 Appendix B. Panel Roster and Financial Disclosures Community-Acquired Pneumonia Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Engi Attia None N/A Miwako Kobayashi Centers for Disease Control and Prevention None N/A Ionnis Konstantinidis University of Pittsburgh Medical Center None N/A Michael Niederman NewYork-Presbyterian/Weill Cornell Medical Center Merck & Co. Advisory Board Gilead Sciences Bayer IQVIA DSMB Chair/Member Maria Rodriguez-Barradas Michael E. DeBakey Department of Veterans Affairs Medical Center; Baylor College of Medicine None N/A Jerry Zifodya Tulane School of Medicine Firland Foundation Research Support Wetmore Foundation Research Support Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-7 Appendix B. Panel Roster and Financial Disclosures Cryptosporidiosis/Microsporidiosis Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Mahalia Desruisseaux Yale School of Medicine None N/A Timothy Hatlen University of California, Los Angeles David Geffen School of Medicine None N/A Michele Hlavsa Centers for Disease Control and Prevention None N/A Nagalingeswaran Kumarasamy The Warren Alpert Medical School of Brown University None N/A Honorine Ward Tufts University School of Medicine None N/A Louis Weiss Albert Einstein College of Medicine National Institutes of Health/National Institute of Allergy and Infectious Diseases Research Support Clinton White The University of Texas Medical Branch None N/A Lihua Xiao Centers for Disease Control and Prevention None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-8 Appendix B. Panel Roster and Financial Disclosures Geographic Opportunistic Infections Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Naomi Aronson Uniformed Services University of the Health Sciences, F. Edward Hébert School of Medicine Wellcome Trust Scientific Advisory Board Johanna Daily Albert Einstein College of Medicine, Weiler Hospital None N/A Mahalia Desruisseaux Yale School of Medicine None N/A Thuy Le Duke University School of Medicine Gilead Sciences Research Support (paid to institution) Rogelio López-Vélez Ramón y Cajal Health Research Institute, Ramón y Cajal University Hospital None N/A Rojelio Mejia Baylor College of Medicine Romark, L.C. Research Support (paid to institution) Edward Mitre Uniformed Services University of the Health Sciences, F. Edward Hébert School of Medicine None N/A Susan Montgomery Centers for Disease Control and Prevention None N/A Sunil Parikh Yale School of Public Health Medincell Scientific Advisory Board Kainomyx Consultant Adrienne Showler National Institute of Allergy and Infectious Diseases None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-9 Appendix B. Panel Roster and Financial Disclosures Hepatitis B Virus Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Debika Bhattacharya University of California, Los Angeles David Geffen School of Medicine Gilead Sciences Research Support (paid to institution) Claudia Hawkins Northwestern University Feinberg School of Medicine None N/A Min Kim Centers for Disease Control and Prevention None N/A Kristen Marks Weill Cornell Medicine Gilead Sciences Consultant Immorna DSMB member Novo Nordisk DSMB member Viiv Healthcare Research Support (paid to institution) Chloe Thio The Johns Hopkins University School of Medicine None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-10 Appendix B. Panel Roster and Financial Disclosures Hepatitis C Virus Member Institution Financial Disclosure Company Relationship Meena Bansal Icahn School of Medicine at Mount Sinai None N/A Greer Burkholder The University of Alabama at Birmingham Heersink School of Medicine Merck Foundation Cepheid Research Support Emily Cartwright Centers for Disease Control and Prevention None N/A Arthur Kim Harvard Medical School Kintor Pharmaceuticals Data Monitoring Committee Nina Kim University of Washington School of Medicine and School of Public Health Gilead Sciences (FOCUS Grant) Research Support (paid to institution) Kristen Marks Weill Cornell Medicine Gilead Sciences Consultant Immorna Data Safety Monitoring Board Member Novo Norodisk Data Safety Monitoring Board Member Viiv Research Support (paid to institution) Susanna Naggie Duke University School of Medicine Bristol Myers Squibb Adjudication Committee Pardes Biosciences, Inc. Consultant National Institutes of Health Research Support Vir Biotechnology Advisory Board Gilead Sciences Research Support Personal Health Insights, Inc. Data Safety Monitoring Board Chair/Member Research Support FHI 360 Event Adjudication Merceditas Villanueva Yale School of Medicine None N/A Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-11 Appendix B. Panel Roster and Financial Disclosures Herpes (HHV-8/CMV) Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Gary Holland David Geffen School of Medicine at the University of California, Los Angeles None N/A Christine Johnston University of Washington School of Medicine Gilead Sciences AbbVie Consultant Warren Phipps University of Washington School of Medicine None N/A Ramya Ramaswami National Institutes of Health Celgene/Bristol-Myers Squibb Cooperative Research and Development Agreement EMD Serono Merck CTI BioPharma Shannon Ross The University of Alabama at Birmingham Heersink School of Medicine None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-12 Appendix B. Panel Roster and Financial Disclosures Herpes (HSV/VZV) Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Gary Holland David Geffen School of Medicine at the University of California, Los Angeles None N/A Christine Johnston University of Washington School of Medicine Gilead Sciences AbbVie Consultant Andrew Karaba The Johns Hopkins University School of Medicine Hologic, Inc. Consultant Poonam Mathur University of Washington School of Medicine None N/A Shannon Ross The University of Alabama at Birmingham Heersink School of Medicine None N/A Sarah Schmalzle University of Maryland, Institute of Human Virology Thera Technologies Gilead Sciences Research Support (paid to institution) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-13 Appendix B. Panel Roster and Financial Disclosures Human Papillomavirus Member Institution Financial Disclosure Company Relationship Susan Cu-Uvin The Warren Alpert Medical School of Brown University AIDS Malignancy Consortium Data Safety Monitoring Board Chair/Member International Antiviral Society–USA Honoraria Speaker UpToDate Honoraria Author Mark Einstein Rutgers New Jersey Medical School AstraZeneca Inovio Pharmaceuticals Iovance Biotherapeutics Johnson & Johnson Pfizer VBL Therapeutics Research Support (paid to institution) BD Douglas Pharmaceuticals Inovio Pharmaceuticals Merck PapiVax PDS Biotechnology Consulting Fee (paid to institution) Lauri Markowitz Centers for Disease Control and Prevention None N/A L. Stewart Massad Washington University School of Medicine in St. Louis None N/A Anna-Barbara Moscicki David Geffen School of Medicine at the University of California, Los Angeles Merck Advisory Board Joel Palefsky University of California, San Francisco School of Medicine Merck Research Support (paid to institution) Elizabeth Stier Boston University Medical Campus None N/A John Weiser Centers for Disease Control and Prevention None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-14 Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Timothy Wilkin NewYork–Presbyterian Weill Cornell Medicine Merck Scientific Advisory Board Merck ViiV Healthcare Research Support (paid to institution) Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-15 Appendix B. Panel Roster and Financial Disclosures Immunizations Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Meagan Deming University of Maryland School of Medicine None N/A Shireesha Dhanireddy University of Washington School of Medicine None N/A Philip Peters Centers for Disease Control and Prevention None N/A Daniel Solomon Harvard Medical School None N/A Jennifer Whitaker Baylor College of Medicine None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-16 Appendix B. Panel Roster and Financial Disclosures Invasive Mycoses Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship John Baddley University of Maryland School of Medicine Synexis Research Support (paid to institution) David Boulware University of Minnesota Medical School Appili Therapeutics Matinas BioPharma Research Support (paid to institution) Marisa Miceli University of Michigan Medical School SCYNEXIS F2G Mayne Pharma Research Support (paid to institution) SCYNEXIS Data Safety Monitoring Board Astellas Pharma Consulting John Perfect Duke University School of Medicine Pfizer Advisory Board George R. Thompson University of California, Davis Medical Center Amplyx Pharmaceuticals Astellas Pharma Cidara Therapeutics F2G Mayne Pharma Scientific Advisory Board Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-17 Appendix B. Panel Roster and Financial Disclosures Mpox Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship John Brooks Atlanta, GA None N/A Chase Cannon University of Washington Roche Diagnostics Consultant Emily Heil University of Maryland School of Pharmacy Wolters Kluwer Consultant Jesse O’Shea Centers for Disease Control and Prevention None N/A Agam Rao Centers for Disease Control and Prevention None N/A Boghuma Kabisen Titanji Emory University School of Medicine Critica ICMEC Advisory Board GSK Mediq Honoraria Critica Consultant Jason Zucker Columbia University Vagelos College of Physicians and Surgeons None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-18 Appendix B. Panel Roster and Financial Disclosures Mycobacterium avium Complex Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Jacqueline Achkar Albert Einstein College of Medicine SD Biosensor Company paid license fees Albert Einstein College of Medicine Patent Inventor Constance Benson University of California, San Diego School of Medicine Gilead Sciences Research Support (paid to institution) Lauren Collins Emory University School of Medicine Timothy Hatlen Harbor-UCLA Medical Center Maura Manion National Institutes of Health None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-19 Appendix B. Panel Roster and Financial Disclosures Mycobacterium tuberculosis Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship James Brust Albert Einstein College of Medicine None N/A Kelly Dooley Vanderbilt University School of Medicine None N/A Neela Goswami Centers for Disease Control and Prevention None N/A Scott Heysell University of Virginia School of Medicine None N/A Jyoti Mathad NewYork-Presbyterian/Weill Cornell Medicine None N/A Graeme Meintjes University of Cape Town, South Africa, Faculty of Health Sciences Gilead Sciences Honoraria Otsuka Data and Safety Monitoring Board Sarita Shah Emory University School of Medicine None N/A Timothy Sterling Vanderbilt University Medical Center None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-20 Appendix B. Panel Roster and Financial Disclosures Pharmacology Member Institution Financial Disclosure Company Relationship Rodrigo Burgos University of Illinois Chicago, Retzky College of Pharmacy ViiV Healthcare, GSK Advisory Board Gilead Sciences Janssen Vaccines & Prevention Merck Shionogi, Inc. ViiV Healthcare, GSK Research Support OptumRx, Inc. Consultant Daniel Chastain The University of Georgia College of Pharmacy None N/A Jomy George National Institutes of Health None N/A Emily Heil University of Maryland School of Pharmacy Wolters Kluwer (Lexicomp) Consultant Rupali Jain University of Washington School of Pharmacy Wolters Kluwer Consultant Bernadette Jakeman The University of New Mexico School of Medicine American College of Clinical Pharmacy (Infectious Diseases Self-Assessment Program Chapter) ASHP Continuing Education CEimpact Education Pharmacy Times Continuing Education ViiV Healthcare, GSK Honoraria Merck Research Support Wolters Kluwer Consultant Safia Kuriakose National Institutes of Health None N/A Alice Pau National Institutes of Health None N/A Charles Peloquin University of Florida College of Pharmacy and Emerging Pathogens Institute Sun Pharmaceutical Industries Ltd. Consultant Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-21 Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Anthony Podany University of Nebraska Medical Center None N/A Katherine Yang University of California, San Francisco School of Pharmacy None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-22 Appendix B. Panel Roster and Financial Disclosures Progressive Multifocal Leukoencephalopathy Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Shruti Agnihotri The University of Alabama at Birmingham Heersink School of Medicine Moderna Pfizer Gilead Sciences Johnson & Johnson Equity Interest Paola Cinque San Raffaele Scientific Institute, Milan, Italy Pfizer Takeda Pharmaceuticals ShirePharma Polpharma Data and Safety Monitoring Board Cellevolve Sobi Advisory Board Excision BioTherapeutics Janssen Consultant David Clifford Washington University School of Medicine in St. Louis Wave Life Sciences Atara Biotherapeutics Cellevolve Takeda Pharmaceuticals Data and Safety Monitoring Board Arena Pharmaceuticals Roche Seagen (Seattle Genetics) Consultant National Institutes of Health Research Support Irene Cortese National Institutes of Health Nouscom PDCline Pharma Life Sciences Partners V Cv Equity Interest Jose M. Miro Hospital Clínic de Barcelona–IDIBAPS, University of Barcelona, Spain None N/A C. Sabrina Tan The University of Iowa Carver College of Medicine Cellevolve Advisory Board Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-23 Appendix B. Panel Roster and Financial Disclosures Pneumocystis Pneumonia Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Kristina Crothers University of Washington School of Medicine None N/A Jannik Helweg-Larsen Rigshospitalet, Copenhagen University, Denmark None N/A Aley Kalapila Emory University School of Medicine None N/A Joseph Kovacs National Institutes of Health Matinas BioPharma Research Support Merck Alison Morris University of Pittsburgh School of Medicine None N/A Sean Wasserman University of Cape Town, South Africa, Faculty of Health Sciences None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-24 Appendix B. Panel Roster and Financial Disclosures Pregnancy Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Jean Anderson The Johns Hopkins University School of Medicine DKBmed Research Support (paid to institution) Katherine Bunge UPMC Magee-Womens Hospital None N/A Karley Dutra Medical University of South Carolina None N/A Oluwatosin Goje Cleveland Clinic Lerner College of Medicine UpToDate Honoraria Topic Contributor Merck Honoraria Topic Contributor ClinicalKey Honoraria Evvy Advisory Board Scynexis Consultant Erica Hardy Warren Alpert Medical School of Brown University None N/A Sylvia LaCourse University of Washington School of Medicine and School of Public Health Merck Research Support (paid to institution) Gweneth Lazenby Medical University of South Carolina Sanaria Data and Safety Monitoring Board Anna Powell The Johns Hopkins University School of Medicine Cepheid Consultant UpToDate Honoraria Rodney Wright Albert Einstein College of Medicine None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-25 Appendix B. Panel Roster and Financial Disclosures Syphilis Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Laura Bachmann Centers for Disease Control and Prevention None N/A Khalil Ghanem The Johns Hopkins University School of Medicine None N/A Matthew Hamill The Johns Hopkins University School of Medicine Chembio Diagnostics, Inc. Honoraria Cepheid Chembio Diagnostics, Inc. Roche Diagnostics Other Edward W. Hook University of Alabama at Birmingham Marnix E. Heersink School of Medicine Visby Medical Scientific Advisory Board Arlene Sena University of North Carolina at Chapel Hill School of Medicine None N/A Irene Stafford The University of Texas Health Science Center at Houston, McGovern Medical School None N/A Susan Tuddenham The Johns Hopkins University School of Medicine None N/A Kimberly Workowski Emory University School of Medicine None N/A Guidelines for the Prevention and Treatment of Opportunistic Infections in Adults and Adolescents With HIV LL-26 Appendix B. Panel Roster and Financial Disclosures Toxoplasma gondii Section Group Lead Note: Members are required to update disclosures annually and to notify guideline staff of any relevant changes in status during the interim. Member Institution Financial Disclosure Company Relationship Sarita Boyd U.S. Food and Drug Administration None N/A Joseph Kovacs National Institutes of Health None N/A Janaki Kuruppu National Institutes of Health None N/A Leon Lai MedStar Washington Hospital Center None N/A Jose M. Miro Hospital Clínic de Barcelona– IDIBAPS, University of Barcelona, Spain None N/A Daniel Podzamczer Fight AIDS and Infectious Diseases Foundation, Hospital Germans Trias i Pujol, Badalona, Spain Gilead Sciences Consultant MSD Janssen ViiV Healthcare Bryan R. Smith National Institutes of Health None N/A
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https://math.stackexchange.com/questions/969345/how-to-solve-a-differential-equation-that-is-equal-to-a-constant
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Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more How to solve a differential equation that is equal to a constant? Ask Question Asked 10 years, 11 months ago Modified10 years, 11 months ago Viewed 25k times This question shows research effort; it is useful and clear 2 Save this question. Show activity on this post. How to solve a differential equation: d 2 u d x 2+u=k,d 2 u d x 2+u=k, where k k is some constant number? I know that if this was d 2 u d x 2+u=0 d 2 u d x 2+u=0, then an auxiliary equation: m 2+1=0 m 2+1=0 can be used where m=±i m=±i to which I think the solutions are: u u = A sin(t)+B cos(t)A sin⁡(t)+B cos⁡(t)? But what about if the zero is a constant? ordinary-differential-equations Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications edited Oct 11, 2014 at 21:33 Michael Hardy 1 asked Oct 11, 2014 at 21:30 GuestGuest 161 2 2 gold badges 2 2 silver badges 4 4 bronze badges Add a comment| 3 Answers 3 Sorted by: Reset to default This answer is useful 5 Save this answer. Show activity on this post. There are a number of different techniques for solving linear inhomogeneous differential equations. The simplest, which is very useful for simple right hand sides like this one, is called undetermined coefficients. Here you find the general solution to the homogeneous problem and then assume a simple form with undetermined coefficients for a particular solution. The most common case is that when the right hand side is a polynomial, you assume a solution in the form of a polynomial. In this case, you can assume a constant solution u≡c u≡c, because if u u is constant then d 2 u d x 2 d 2 u d x 2 is zero, and so your equation reduces to c=k c=k. Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Oct 11, 2014 at 21:35 IanIan 105k 5 5 gold badges 101 101 silver badges 171 171 bronze badges 3 I see. Please correct me if I didn't understand this right, but would the final solution to this problem (where it equals to a constant k) then be: u= u(homogeneous) + u(particular) = A sin(t)+B cos(t) + k?Guest –Guest 2014-10-11 21:39:47 +00:00 Commented Oct 11, 2014 at 21:39 @Guest That is correct.Ian –Ian 2014-10-11 21:40:46 +00:00 Commented Oct 11, 2014 at 21:40 Ok! Thank you so much!Guest –Guest 2014-10-11 21:41:31 +00:00 Commented Oct 11, 2014 at 21:41 Add a comment| This answer is useful 4 Save this answer. Show activity on this post. If you introduce u′≡u−k u′≡u−k, the equation reduces to d 2 u′d x 2+u′=0 d 2 u′d x 2+u′=0 Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications edited Oct 11, 2014 at 21:56 answered Oct 11, 2014 at 21:50 hickslebummbummhickslebummbumm 1,471 8 8 silver badges 11 11 bronze badges 1 Ok, I will try that also. Thanks!Guest –Guest 2014-10-11 21:58:25 +00:00 Commented Oct 11, 2014 at 21:58 Add a comment| This answer is useful 2 Save this answer. Show activity on this post. Notice that the solution of the differential equation with second member is the sum of the solution of the homogenous equation and a particular solution. For the given differential equation u=k u=k is an obvious particular solution so the general solution is u(x)=A sin x+B cos x+k u(x)=A sin⁡x+B cos⁡x+k Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Oct 11, 2014 at 21:41 user63181 user63181 2 Oh I see, yes, it would be A sin(x)+B cos(x) and not t, wouldn't it. My bad. Thank you!Guest –Guest 2014-10-11 21:43:47 +00:00 Commented Oct 11, 2014 at 21:43 You're welcome.user63181 –user63181 2014-10-11 21:45:59 +00:00 Commented Oct 11, 2014 at 21:45 Add a comment| You must log in to answer this question. 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https://chrisj.math.gatech.edu/18f/m1553/materials/08_29_web.pdf
(Reduced) Row Echelon Form Review from last time A matrix is in row echelon form if 1. All zero rows are at the bottom. 2. Each leading nonzero entry of a row is to the right of the leading entry of the row above. 3. Below a leading entry of a row, all entries are zero. A matrix is in reduced row echelon form if it is in row echelon form, and in addition, 4. The pivot in each nonzero row is equal to 1. 5. Each pivot is the only nonzero entry in its column. Row echelon form:     ⋆ ⋆ ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆ ⋆ 0 0 0 ⋆ ⋆ 0 0 0 0 0     Reduced row echelon form:     1 0 ⋆ 0 ⋆ 0 1 ⋆ 0 ⋆ 0 0 0 1 ⋆ 0 0 0 0 0     ⋆= pivots Row Reduction: Theorem Theorem Every matrix is row equivalent to one and only one matrix in reduced row echelon form. We’ll give an algorithm, called row reduction or Gaussian elimination, which demonstrates that every matrix is row equivalent to at least one matrix in reduced row echelon form. Note: Like echelon forms, the row reduction algorithm does not care if a column is augmented: ignore the vertical line when row reducing. The uniqueness statement is interesting—it means that, nomatter how you row reduce, you always get the same matrix in reduced row echelon form. (Assuming you only do the three legal row operations.) (And you don’t make any arithmetic errors.) Maybe you can figure out why it’s true! Row Reduction Algorithm Step 1a Swap the 1st row with a lower one so a leftmost nonzero entry is in 1st row (if necessary). Step 1b Scale 1st row so that its leading entry is equal to 1. Step 1c Use row replacement so all entries below this 1 are 0. Step 2a Swap the 2nd row with a lower one so that the leftmost nonzero entry is in 2nd row. Step 2b Scale 2nd row so that its leading entry is equal to 1. Step 2c Use row replacement so all entries below this 1 are 0. Step 3a Swap the 3rd row with a lower one so that the leftmost nonzero entry is in 3rd row. etc. Last Step Use row replacement to clear all entries above the pivots, starting with the last pivot (to make life easier). Example   0 −7 −4 2 2 4 6 12 3 1 −1 −2   [animated] Row Reduction Example   0 −7 −4 2 2 4 6 12 3 1 −1 −2   Step 1a: Row swap to make this nonzero. R1 ← →R2   2 4 6 12 0 −7 −4 2 3 1 −1 −2   Step 1b: Scale to make this 1. R1 = R1 ÷ 2   1 2 3 6 0 −7 −4 2 3 1 −1 −2   Step 1c: Subtract a multiple of the first row to clear this. R3 = R3 −3R1   1 2 3 6 0 −7 −4 2 0 −5 −10 −20   Optional: swap rows 2 and 3 to make Step 2b easier later on. R2 ← →R3   1 2 3 6 0 −5 −10 −20 0 −7 −4 2   Row Reduction Example, continued   1 2 3 6 0 −5 −10 −20 0 −7 −4 2   Step 2a: This is already nonzero. Step 2b: Scale to make this 1. (There are no fractions because of the optional step before.) R2 = R2 ÷ −5   1 2 3 6 0 1 2 4 0 −7 −4 2   Step 2c: Add 7 times the second row to clear this. R3 = R3 + 7R2   1 2 3 6 0 1 2 4 0 0 10 30   Note: Step 2 never messes up the first (nonzero) column of the matrix, because it looks like this:   1 ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆   “Active” row Row Reduction Example, continued   1 2 3 6 0 1 2 4 0 0 10 30   Step 3a: This is already nonzero. Step 3b: Scale to make this 1. R3 = R3 ÷ 10   1 2 3 6 0 1 2 4 0 0 1 3   Note: Step 3 never messes up the columns to the left. Note: The matrix is now in row echelon form!   1 2 3 6 0 1 2 4 0 0 1 3   Last step: Add multiples of the third row to clear these. R2 = R2 −2R3   1 2 3 6 0 1 0 −2 0 0 1 3   R1 = R1 −3R3   1 2 0 −3 0 1 0 −2 0 0 1 3   Last step: Add −2 times the third row to clear this. R1 = R1 −2R2   1 0 0 1 0 1 0 −2 0 0 1 3   Row Reduction Example, continued Success! The reduced row echelon form is   1 0 0 1 0 1 0 −2 0 0 1 3   = ⇒    x = 1 y = −2 z = 3 Recap     ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆     Get a 1 here     1 ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆     Clear down     1 ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆     Get a 1 here     1 ⋆ ⋆ ⋆ 0 1 ⋆ ⋆ 0 ⋆ ⋆ ⋆ 0 ⋆ ⋆ ⋆     Clear down     1 ⋆ ⋆ ⋆ 0 1 ⋆ ⋆ 0 0 0 ⋆ 0 0 0 ⋆     (maybe these are already zero)     1 ⋆ ⋆ ⋆ 0 1 ⋆ ⋆ 0 0 0 ⋆ 0 0 0 ⋆     Get a 1 here    1 ⋆ ⋆ ⋆ 0 1 ⋆ ⋆ 0 0 0 1 0 0 0 ⋆     Clear down     1 ⋆ ⋆ ⋆ 0 1 ⋆ ⋆ 0 0 0 1 0 0 0 0     Matrix is in REF     1 ⋆ ⋆ ⋆ 0 1 ⋆ ⋆ 0 0 0 1 0 0 0 0     Clear up     1 ⋆ ⋆ 0 0 1 ⋆ 0 0 0 0 1 0 0 0 0     Clear up     1 0 ⋆ 0 0 1 ⋆ 0 0 0 0 1 0 0 0 0     Matrix is in RREF Profit? Row Reduction Another example The linear system 2x + 10y = −1 3x + 15y = 2 gives rise to the matrix  2 10 −1 3 15 2  . Let’s row reduce it: [interactive row reducer]  2 10 −1 3 15 2  R1 = R1 ÷ 2  1 5 −1 2 3 15 2  (Step 1b) R2 = R2 −3R1  1 5 −1 2 0 0 7 2  (Step 1c) R2 = R2 × 2 7  1 5 −1 2 0 0 1  (Step 2b) R1 = R1 + 1 2 R2  1 5 0 0 0 1  (Step 2c) The row reduced matrix  1 5 0 0 0 1  corresponds to the inconsistent system x + 5y = 0 0 = 1. Inconsistent Matrices Question What does an augmented matrix in reduced row echelon form look like, if its system of linear equations is inconsistent? Answer:   1 0 ⋆ ⋆ 0 0 1 ⋆ ⋆ 0 0 0 0 0 1   An augmented matrix corresponds to an inconsistent system of equations if and only if the last (i.e., the augmented) column is a pivot column. Section 2.3 Parametric Form Another Example The linear system 2x + y + 12z = 1 x + 2y + 9z = −1 gives rise to the matrix  2 1 12 1 1 2 9 −1  . Let’s row reduce it: [interactive row reducer]  2 1 12 1 1 2 9 −1  R1 ← →R2  1 2 9 −1 2 1 12 1  (Optional) R2 = R2 −2R1  1 2 9 −1 0 −3 −6 3  (Step 1c) R2 = R2 ÷ −3  1 2 9 −1 0 1 2 −1  (Step 2b) R1 = R1 −2R2  1 0 5 1 0 1 2 −1  (Step 2c) The row reduced matrix  1 0 5 1 0 1 2 −1  corresponds to the linear system  x + 5z = 1 y + 2z = −1 Another Example Continued The system x + 5z = 1 y + 2z = −1 comes from a matrix in reduced row echelon form. Are we done? Is the system solved? Yes! Rewrite: x = 1 −5z y = −1 −2z For any value of z, there is exactly one value of x and y that makes the equations true. But z can be anything we want! So we have found the solution set: it is all values x, y, z where x = 1 −5z y = −1 −2z (z = z) for z any real number. This is called the parametric form for the solution. [interactive picture] For instance, (1, −1, 0) and (−4, −3, 1) are solutions. Free Variables Definition Consider a consistent linear system of equations in the variables x1, . . . , xn. Let A be a row echelon form of the matrix for this system. We say that xi is a free variable if its corresponding column in A is not a pivot column. 1. You can choose any value for the free variables in a (consistent) linear system. 2. Free variables come from columns without pivots in a matrix in row echelon form. Important In the previous example, z was free because the reduced row echelon form matrix was  1 0 5 4 0 1 2 −1  . In this matrix:  1 ⋆ 0 ⋆ ⋆ 0 0 1 ⋆ ⋆  the free variables are x2 and x4. (What about the last column?) One More Example The reduced row echelon form of the matrix for a linear system in x1, x2, x3, x4 is  1 0 0 3 2 0 0 1 4 −1  The free variables are x2 and x4: they are the ones whose columns are not pivot columns. This translates into the system of equations  x1 + 3x4 = 2 x3 + 4x4 = −1 = ⇒ x1 = 2 −3x4 x3 = −1 −4x4 . What happened to x2? What is it allowed to be? Anything! The general solution is (x1, x2, x3, x4) = (2 −3x4, x2, −1 −4x4, x4) for any values of x2 and x4. For instance, (2, 0, −1, 0) is a solution (x2 = x4 = 0), and (5, 1, 3, −1) is a solution (x2 = 1, x4 = −1). The boxed equation is called the parametric form of the general solution to the system of equations. It is obtained by moving all free variables to the right-hand side of the =. Yet Another Example The linear system x + y + z = 1 has matrix form 1 1 1 1  . This is in reduced row echelon form. The free variables are y and z. The parametric form of the general solution is x = 1 −y −z. Rearranging: (x, y, z) = (1 −y −z, y, z), where y and z are arbitrary real numbers. This was an example in the second lecture! [interactive] Trichotomy There are three possibilities for the reduced row echelon form of the augmented matrix of a linear system. 1. The last column is a pivot column. In this case, the system is inconsistent. There are zero solutions, i.e. the solution set is empty. Picture:   1 0 0 0 1 0 0 0 1   2. Every column except the last column is a pivot column. In this case, the system has a unique solution. Picture:   1 0 0 ⋆ 0 1 0 ⋆ 0 0 1 ⋆   3. The last column is not a pivot column, and some other column isn’t either. In this case, the system has infinitely many solutions, corresponding to the infinitely many possible values of the free variable(s). Picture:  1 ⋆ 0 ⋆ ⋆ 0 0 1 ⋆ ⋆  Summary ▶Row reduction is an algorithm for solving a system of linear equations represented by an augmented matrix. ▶The goal of row reduction is to put a matrix into (reduced) row echelon form, which is the “solved” version of the matrix. ▶An augmented matrix corresponds to an inconsistent system if and only if there is a pivot in the augmented column. ▶Columns without pivots in the RREF of a matrix correspond to free variables. You can assign any value you want to the free variables, and you get a unique solution. ▶A linear system has zero, one, or infinitely many solutions.
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https://math.stackexchange.com/questions/4816393/maximization-question-using-inequalities-cauchy-schwarz-am-gm
discrete mathematics - Maximization question using inequalities (Cauchy-Schwarz, AM-GM) - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community Mathematics helpchat Mathematics Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Maximization question using inequalities (Cauchy-Schwarz, AM-GM) Ask Question Asked 1 year, 10 months ago Modified1 year, 10 months ago Viewed 113 times This question shows research effort; it is useful and clear 0 Save this question. Show activity on this post. Consider this system of equations: a 2+b 2+c 2+d 2=14 3 a+2 b+c+d=14 a 2+b 2+c 2+d 2=14 3 a+2 b+c+d=14 I want to find the maximum value of d d given that a,b,c,d∈R a,b,c,d∈R. Here is some work I've done so far: By using the AM-GM inequality on the first equation, we have that a 2+b 2+c 2+d 2 4≥a 2 b 2 c 2 d 2−−−−−−−√4 a 2+b 2+c 2+d 2 4≥a 2 b 2 c 2 d 2 4, and so 14 4≥a b c d−−−−√14 4≥a b c d, and so a b c d≤49 4 a b c d≤49 4. By using the AM-GM inequality on the second equation, we have that 3 a+2 b+c+d 4≥6 a b c d−−−−−√4 3 a+2 b+c+d 4≥6 a b c d 4, and so 14 4≥6 a b c d−−−−−√4 14 4≥6 a b c d 4, and so 6 a b c d≤2401 16 6 a b c d≤2401 16, and so a b c d≤2401 96 a b c d≤2401 96. This doesn't give us any new information from the first bullet point. Then, I tried using the Cauchy-Schwarz Inequality. If we let x^=(a,b,c,d),y^=(3,2,1,1)x^=(a,b,c,d),y^=(3,2,1,1), then we have that x^⋅y^=3 a+2 b+c+d=14≤||x||||y||=a 2+b 2+c 2+d 2−−−−−−−−−−−−−−√3 2+2 2+1 2+1 2−−−−−−−−−−−−−−√=15(a 2+b 2+c 2+d 2)−−−−−−−−−−−−−−−−−√=15(14)−−−−−√=210−−−√x^⋅y^=3 a+2 b+c+d=14≤||x||||y||=a 2+b 2+c 2+d 2 3 2+2 2+1 2+1 2=15(a 2+b 2+c 2+d 2)=15(14)=210. However, we already know this anyways, as we are given that 3 a+2 b+c+d=14 3 a+2 b+c+d=14, and 14≤210−−−√14≤210 already. Can someone provide hints/a solution to this problem? discrete-mathematics inequality systems-of-equations cauchy-schwarz-inequality a.m.-g.m.-inequality Share Share a link to this question Copy linkCC BY-SA 4.0 Cite Follow Follow this question to receive notifications asked Nov 29, 2023 at 2:02 Christopher MillerChristopher Miller 668 3 3 silver badges 12 12 bronze badges Add a comment| 2 Answers 2 Sorted by: Reset to default This answer is useful 2 Save this answer. Show activity on this post. We can focus on a,b,c a,b,c to derive an inequality about d d. That is , (14−d)2=(3 a+2 b+c)2≤(3 2+2 2+1 2)(a 2+b 2+c 2)=14⋅(14−d 2).(14−d)2=(3 a+2 b+c)2≤(3 2+2 2+1 2)(a 2+b 2+c 2)=14⋅(14−d 2). Solve this inequality we have d≤28 15 d≤28 15, and the maximum can be achieved when the Cauchy-Schwarz Inequality takes "=""=" and the system of equations for a,b,c,d a,b,c,d hold, where (a,b,c,d)=(39/15,26/15,13/15,28/15)(a,b,c,d)=(39/15,26/15,13/15,28/15). Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Follow Follow this answer to receive notifications answered Nov 29, 2023 at 4:07 Shuai YangShuai Yang 71 5 5 bronze badges Add a comment| This answer is useful 2 Save this answer. Show activity on this post. Hint: Esp since you don't know when equality holds, your AM-GM approaches aren't likely to work. IE It seems very unlikely that the maximum is achieved when a=b=c=d a=b=c=d or 3 a=2 b=c=d 3 a=2 b=c=d. What I might believe is that 3 a=2 b=c 3 a=2 b=c or a=b=c a=b=c or a 3=b 2=c 1 a 3=b 2=c 1, and then d d is left to vary to maximize the leftover. Hint: Try to form an inequality involving d d only. Your third idea involving CS is a great start, how can we isolate out d d terms? (14−d)2=(3 a+2 b+c)2≤(a 2+b 2+c 2)(3 2+2 2+1 2)=(14−d 2)×14(14−d)2=(3 a+2 b+c)2≤(a 2+b 2+c 2)(3 2+2 2+1 2)=(14−d 2)×14 Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Follow Follow this answer to receive notifications answered Nov 29, 2023 at 3:21 Calvin LinCalvin Lin 77.6k 5 5 gold badges 86 86 silver badges 170 170 bronze badges Add a comment| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions discrete-mathematics inequality systems-of-equations cauchy-schwarz-inequality a.m.-g.m.-inequality See similar questions with these tags. 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https://pmc.ncbi.nlm.nih.gov/articles/PMC11469930/
Clinical Challenges and Surgical Interventions in Managing Neck Hematoma After Cervical Spine Fusion: A Case Report - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Advanced Search Journal List User Guide New Try this search in PMC Beta Search View on publisher site Download PDF Add to Collections Cite Permalink PERMALINK Copy As a library, NLM provides access to scientific literature. 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Learn more: PMC Disclaimer | PMC Copyright Notice Case Rep Surg . 2024 Oct 4;2024:3173782. doi: 10.1155/2024/3173782 Search in PMC Search in PubMed View in NLM Catalog Add to search Clinical Challenges and Surgical Interventions in Managing Neck Hematoma After Cervical Spine Fusion: A Case Report Parimal Rana Parimal Rana 1 Luminis Health Orthopedics at Anne Arundel Medical Center, 2000 Medical Parkway, Suite 503, Annapolis 21401, Maryland, USA Find articles by Parimal Rana 1, Justin Turcotte Justin Turcotte 1 Luminis Health Orthopedics at Anne Arundel Medical Center, 2000 Medical Parkway, Suite 503, Annapolis 21401, Maryland, USA Find articles by Justin Turcotte 1,✉, Sohail Zaidi Sohail Zaidi 1 Luminis Health Orthopedics at Anne Arundel Medical Center, 2000 Medical Parkway, Suite 503, Annapolis 21401, Maryland, USA Find articles by Sohail Zaidi 1 Author information Article notes Copyright and License information 1 Luminis Health Orthopedics at Anne Arundel Medical Center, 2000 Medical Parkway, Suite 503, Annapolis 21401, Maryland, USA Academic Editor: Jochen Tüttenberg ✉ Corresponding author. Received 2024 Apr 24; Revised 2024 Jul 26; Accepted 2024 Aug 24; Collection date 2024. Copyright © 2024 Parimal Rana et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. PMC Copyright notice PMCID: PMC11469930 PMID: 39398298 Abstract This case study discusses a 47-year-old Caucasian male with a past medical history of dyslipidemia, gastroesophageal reflux disease, previous cervical spine surgery, and anxiety who developed a neck hematoma postrevision of a C5–6 cervical spine fusion. Emergent neck exploration and evacuation of the hematoma were performed, and ventilation was restored. The patient was transferred to the intensive care unit and extubated on postoperative day 5 with a stable wound and no residual bleeding. At the 3-week follow-up appointment, the patient was noted to be doing well, with a chest radiograph showing no effusion or hematoma. This report elucidates the challenges posed by acute clinical symptoms and their correlation with the underlying cause, as well as the subsequent management and outcomes of a neck hematoma complication following cervical spine surgery. 1. Introduction Anterior cervical spine (ACS) surgery, a common procedure performed by orthopedics and neurosurgeons, typically yields favorable clinical outcomes [1, 2]. However, complications, particularly hematoma formation causing airway obstruction, remain a significant concern, with a reported incidence rate ranging from 0.2% to 1.9% [3–5]. These hematomas can be categorized into wound hematoma, spinal epidural hematoma, and retropharyngeal hematoma, with the latter posing a higher risk due to its potential to compromise the airway . In fact, postoperative cervical hematoma has been associated with a significant increase in mortality rates . Additionally, it is noteworthy that the prevalence of cardiac complications in ACS surgery is relatively low, with only 4 out of 1000 cases (0.004%) experiencing such issues . Therefore, surgical trauma–related complications, such as hemorrhage and hematoma formation, should not be overlooked or overshadowed by cardiac concerns. 2. Case Presentation 2.1. History The patient, a 47-year-old Caucasian male, had a pertinent medical history, including dyslipidemia, gastroesophageal reflux disease, and anxiety. He had previously undergone C5–6 anterior fusion in 2017 due to cervical spondylosis with radiculopathy, with subsequent axial spine discomfort. The decision was made to revise the surgery of the fusion with an additional extension to the C6–7 level, and the procedure was performed without intraoperative complications. Postoperatively, after approximately 4 h, the patient developed sudden-onset chest pain and diaphoresis while being prepared for discharge from the postanesthesia care unit. Suspecting cardiac ischemia, blood labs were drawn, and a chest radiograph was completed within the hour. However, the first physical exam of the neck was not completed until 2 h after symptom onset, which revealed a large neck hematoma. This prompted an urgent consultation by the floating anesthesia care team to protect the airway. The operating neurosurgeon was contacted, and cardiothoracic and vascular surgery were consulted in the operating room. Due to the elapsed time from the onset of symptoms to the evaluation of the neck swelling, a large hematoma continued to expand, compressing the patient's trachea and requiring emergent surgical intervention. 2.2. Physical Exam Upon examination, the patient presented with a seal-like cough, bilateral wheezing on lung auscultation, and a large swelling on the left side of the neck. Vital signs revealed elevated blood pressure (140/80 mmHg, subsequently raised to 190/135 mmHg), bradycardia (49 beats/min), normal respiratory rate (14 breaths/min), and oxygen saturation of 97%–100% on 2 L O 2. 2.3. Investigations Diagnostic evaluations included an EKG, a troponin assay, and a chest radiograph, all of which returned negative results for cardiac issues. Imaging revealed a wide mediastinum (Figure 1), prompting a CT with IV contrast. The CT scan demonstrated a large prevertebral soft tissue hematoma extending from C3 through the carina (Figure 2), accompanied by a rightward and anterior deviation of the airway. Additionally, a lobulated 9-mm hyperdense collection was identified along the anterior margin of the C7 vertebral body (Figure 3), suggesting active contrast extravasation within the prevertebral soft tissues immediately caudal to the C6−7 fusion construct in the surgical bed. A repeat chest radiograph confirmed the presence of a 10.3 cm mediastinum. Figure 1. Open in a new tab Initial cervical fusion postoperative chest radiograph. Figure 2. Open in a new tab CT image demonstrating a large prevertebral soft tissue hematoma extending from C3 through the carina. Figure 3. Open in a new tab CT image demonstrating hyperdense collection along the anterior margin of the C7 vertebral body. 2.4. Differential Diagnosis The alarming presentation of chest pain and diaphoresis led the medical team to consider cardiac ischemia as the primary diagnosis initially. However, subsequent evaluation, notably the chest radiograph, shifted the focus to the widening mediastinum, prompting consideration of various etiologies. Potential causes include thoracic aortic aneurysm or dissection, traumatic aortic rupture, cardiac tamponade, fractured ribs or thoracic vertebrae, mediastinitis, and pneumomediastinum. Though less likely due to the acute nature of this case, other differentials should include hilar lymphadenopathy (either infectious or malignant) and mediastinal masses such as lymphoma, seminoma, or thymoma. Each of these conditions necessitates careful consideration and diagnostic evaluation to identify the underlying pathology and guide appropriate management strategies accurately. However, it is crucial to prioritize the exploration of the most likely cause, such as in this case, where the patient had undergone neck surgery and likely had postoperative hemorrhage. 2.5. Management and Treatment At the onset of symptoms 4 h postoperative, the patient was initially worked up for cardiac ischemia. Cardiothoracic surgery was consulted, and the patient was evaluated approximately 2 h after the onset of symptom. Given the emergent nature of their findings, the patient was transferred to the operating room for exploration and evacuation of the hematoma by neurosurgery almost 3 h after the patient complained of chest pain. Despite endotracheal intubation, ventilation was unsuccessful. Bronchoscopy revealed compression of the trachea, prompting immediate action (Figure 4). The neck was prepared with betadine, and an emergency neck exploration was performed through the incision made earlier by the neurosurgery team. Upon opening the platysma, a significant amount of fresh blood and hematoma was encountered, necessitating urgent evacuation. With successful hematoma evacuation, ventilation was restored. Figure 4. Open in a new tab Bronchoscope image showing severe compression of the trachea before hematoma evacuation. On bronchoscopy, there was still posterior compression of the membranous distal airway and extensive mucosal edema. Utilizing the left cervical incision that was already made and the bronchoscope, neurosurgery, with the assistance of vascular surgery, bluntly dissected behind the airway and esophagus and directly onto the spine. The residual hematoma was bluntly loosened and evacuated. The remaining portion was explored, and some additional hematoma was carefully extracted. There was no vascular injury of a named vessel. Repeat bronchoscopy revealed some improvement in the distal airway patency, the remainder of which was likely related to the associated edema. Upper endoscopy was performed to ensure the esophageal mucosa was uninjured, and insufflated air under saline was used to confirm there was no extravasation of air. Once this was completed, hemostasis was confirmed, and the incision was closed with a drain. 2.6. Outcome and Follow-Up On postoperative day (POD) 1, a chest radiograph revealed persistent widening of the upper mediastinum, and the patient remained intubated and sedated for airway protection. The next day, there was a significant improvement in hematoma size. A neck CT scan showed adequate drainage of hematoma and minimal soft tissue swelling without significant airway compression. Cardiac labs and exams were all normal. Extubation was planned for the next day, pending approval from the intensive care unit team, along with antibiotic therapy and prophylactic deep vein thrombosis management. The patient was successfully extubated on POD 5 with a stable neck wound and no bleeding. No other complaints were reported, and the patient was agreeable to physical and occupational therapy. Prophylactic anticoagulation was restarted. The patient was discharged from the hospital on POD 7, indicating successful recovery and resolution of the acute complication. At the 3-week follow-up appointment, the patient was noted to be doing well, with a chest radiograph showing no effusion or hematoma. 3. Discussion Several risk factors contribute to the development of postoperative hematomas, including hypertension, smoking history, male sex, low BMI, long operative times, increased venous pressure, coagulopathy, multilevel surgery, and the invasiveness of the surgical procedure itself [6, 9]. The management of neck hematoma following cervical spine surgery necessitates proactive strategies for early recognition and intervention. Implementing protocols for rigorous postoperative monitoring is crucial, particularly for promptly identifying symptoms such as chest pain and respiratory distress indicative of hematoma formation. Equally vital is fostering a collaborative approach among surgical and critical care teams to ensure swift communication and coordinated responses to emergent situations. Continuous postoperative monitoring, including regular physical examinations and imaging studies, further enhances the ability to detect and manage complications effectively. These recommendations underscore the significance of timely intervention and multidisciplinary teamwork in optimizing patient outcomes. Algorithms for the diagnosis and treatment of neck hematoma following cervical spine surgery should consider various factors, including clinical presentation, radiological findings, and patient comorbidities . Signs such as worsening dyspnea, stridor, neck swelling, and neurological deficits typically occur within the first 6 h postoperative or up to 24 h and warrant urgent evaluation and intervention . Diagnostic imaging modalities such as CT with IV contrast play a crucial role in confirming the diagnosis and assessing the extent of hematoma. Given the potential for disastrous airway compromise, protecting the airway becomes paramount, and alternative airway access with cricothyroidotomy and/or immediate evacuation of obstructive hematomas should be considered if intubation becomes difficult . Therefore, having equipment such as a bronchoscope and a capable team available for immediate exploration is essential to facilitate prompt intervention and optimize patient outcomes. In a prior review of 785 anterior cervical discectomy and fusion procedures, nine cases (1.15%) of neck hematoma resulting in acute airway obstruction were observed. Notably, none of the nine patients had preoperative risk factors for hematoma; six of the nine patients developed a hematoma within 24 h of surgery . These findings highlight the importance of maintaining a high level of clinical suspicion for hematoma and acute airway obstruction during the early postoperative period. Airway compromise can evolve from subtle changes in voice quality and complaints of difficulty talking and breathing during the early period to dyspnea, stridor, and cyanosis during later stages . Critical airway compromise, consisting of the near or complete loss of airway patency, requires an emergent response progressing from bag-mask ventilation, to intubation, and surgical exploration and evacuation of the hematoma . In cases where the airway cannot be re-established by these means, establishment of a surgical airway by cricothyroidotomy is required . In this case, the decision to contact the primary neurosurgeon, along with cardiothoracic and vascular surgery consults, initiated a coordinated care approach aimed at addressing the emergent situation comprehensively. However, the initial focus on chest pain and cardiac ischemia led to a delay in accessing the operating room, potentially impacting the management of the hematoma. Had the neck examination been completed promptly by the primary surgeon, it is plausible that the hematoma might not have progressed to a stage necessitating the involvement of cardiothoracic and vascular surgery. This highlights the necessity of early physical examination for the evaluation of potential postoperative hematoma and for timely surgical intervention upon diagnosis. There are reported cases where hematomas mimic myocardial infarction, leading to the misdiagnosis and subsequent treatment of non-ST segment elevation myocardial infarctions, leading to detrimental consequences . This diagnostic challenge highlights the importance of maintaining a broad differential diagnosis but, more importantly, prompt recognition of hematoma-related symptoms and examination. Fortunately, in the current case, the delayed diagnosis of neck hematoma did not result in an adverse outcome, as the patient ultimately recovered uneventfully and made a full return to normal activities. Performing ACS surgeries in ambulatory surgical centers (ASCs) versus hospitals presents unique considerations regarding the management of complications, particularly hematoma formation. While ASCs offer advantages such as efficiency and cost-effectiveness [15, 16], they may lack the resources and infrastructure required to manage emergent situations such as hematoma-related airway compromise effectively . Patients undergoing ACS procedures in ASCs may face delays in accessing specialized care and interventions, potentially exacerbating the risk of adverse outcomes associated with hematoma formation . Therefore, careful patient selection, consideration of procedural complexity, and access to emergency care are essential when determining the appropriateness of ACS in ASCs, with a focus on ensuring timely access to comprehensive medical services and resources necessary for managing complications such as hematomas. Moreover, it is noteworthy that our case was managed in a hospital setting, which likely facilitated prompt access to specialized care and interventions, thus potentially avoiding additional delays compared to if the procedure had been performed at an ASC. In conclusion, neck hematoma following cervical spine surgery is a rare but potentially life-threatening complication that requires prompt recognition and intervention. While cardiac issues are a valid concern, especially given the patient's symptoms, the markedly lower prevalence of cardiac complications underscores the need for early consultation, vigilant monitoring for signs of hematoma formation, and adherence to a structured algorithm for triage and management to ensure timely intervention and favorable outcomes in these challenging cases. Data Availability Statement Patient identifiers were removed, and thus, consent was not required. Due to patient confidentiality, medical records cannot be made public for review. Conflicts of Interest The authors declare no conflicts of interest. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References 1.McCarthy M. H., Weiner J. A., Patel A. A. Strategies to Achieve Spinal Fusion in Multilevel Anterior Cervical Spine Surgery: An Overview. HSS Journal . 2020;16(2):155–161. doi: 10.1007/s11420-019-09738-3. 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Articles from Case Reports in Surgery are provided here courtesy of Wiley ACTIONS View on publisher site PDF (2.0 MB) Cite Collections Permalink PERMALINK Copy RESOURCES Similar articles Cited by other articles Links to NCBI Databases On this page Abstract 1. Introduction 2. Case Presentation 3. Discussion Data Availability Statement Conflicts of Interest Funding References Associated Data Cite Copy Download .nbib.nbib Format: Add to Collections Create a new collection Add to an existing collection Name your collection Choose a collection Unable to load your collection due to an error Please try again Add Cancel Follow NCBI NCBI on X (formerly known as Twitter)NCBI on FacebookNCBI on LinkedInNCBI on GitHubNCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter)NLM on FacebookNLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top
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https://artofproblemsolving.com/wiki/index.php/Permutation?srsltid=AfmBOoq4yLuRcMbSVcgsTRgCXfb51tUqu9BDO9bGbA2nIYFP_ZjUzAzd
Art of Problem Solving Permutation - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Permutation Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Permutation A permutation of a set of objects is any rearrangement (linear ordering) of the objects. There are (the factorial of ) permutations of a set with distinct objects. One can also consider permutations of infinite sets. In this case, a permutation of a set is simply a bijection between and itself. Contents [hide] 1 Video 2 Notations 3 The Symmetric Group 4 Picking Ordered Subsets of a Set 5 Related Videos 6 See also Video This video goes over what Permutations & Combinations are, their various types, and how to calculate each type! It serves as a great introductory video to combinations, permutations, and counting problems in general! Permutations & Combinations Video This video is a great introduction to permutations, combinations, and constructive counting: Notations A given permutation of a finite set can be denoted in a variety of ways. The most straightforward representation is simply to write down what the permutation looks like. For example, the permutations of the set are and . We often drop the brackets and commas, so the permutation would just be represented by . Another common notation is cycle notation. The Symmetric Group The set of all permutations of an -element set is denoted . In fact, forms a group, known as the Symmetric group, under the operation of permutation composition. A permutation in which no object remains in the same place it started is called a derangement. Picking Ordered Subsets of a Set An important question is how many ways to pick an -element subset of a set with elements, where order matters. To find how many ways we can do this, note that for the first of the elements, we have different objects we can choose from. For the second element, there are objects we can choose, for the third, and so on. In general, the number of ways to permute objects from a set of is given by . Related Videos Permutation Videos (Counting Permutations) (Permutations and Factorials) See also Combinations Combinatorics Derangement Retrieved from " Categories: Combinatorics Definition Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
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https://www.ck12.org/flexi/math-grade-7/applications-of-two-step-equations/
Applications of Two-Step Equations | Flexi Homework help & answers | CK-12 Foundation What are you looking for? Search Math Grade 6 Grade 7 Grade 8 Algebra 1 Geometry Algebra 2 PreCalculus Science Earth Science Life Science Physical Science Biology Chemistry Physics Social Studies Economics Geography Government Philosophy Sociology Subject Math Elementary Math Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Interactive Math 6 Math 7 Math 8 Algebra I Geometry Algebra II Conventional Math 6 Math 7 Math 8 Algebra I Geometry Algebra II Probability & Statistics Trigonometry Math Analysis Precalculus Calculus What's the difference? 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Learn. Interact. eXplore. CCSS Math Concepts and FlexBooks aligned to Common Core NGSS Concepts aligned to Next Generation Science Standards Certified Educator Stand out as an educator. Become CK-12 Certified. Webinars Live and archived sessions to learn about CK-12 Other Resources CK-12 Resources Concept Map Testimonials CK-12 Mission Meet the Team CK-12 Helpdesk FlexLets Know the essentials. Pick a Subject Donate Sign InSign Up All Subjects Math Grade 7 Applications of Two-Step Equations Applications of Two-Step Equations Solving Two-Step EquationsWriting Two-Step Inequalities Concept Summary: To solve two-step equations, use inverse operations (re verse PEMDAS) It is important to use the correct units when solving problems within a context. Ask your own question How to problem solve? How to solve word problems? If it takes a water pump 2.5 hours to empty a tank containing 60,000 gallons of water, how long does it take the same pump to empty a tank containing 108,000 gallons of water? A 10 ft chain weighs 45 lb and hangs from a ceiling. Find the work done (in ft-lb) in lifting the lower end of the chain to the ceiling so that it's level with the upper end. How many ft-lb? Two pipes can fill a tank in 10 hours and 15 hours, respectively. There is also a drain pipe that can empty the tank in 30 hours. If all three pipes are used simultaneously, how long will it take to fill the tank? He buys 4 bolts. The bolts cost $2 each. How much do the bolts cost in total? $ Jeff's friend George is a plumber. He has offered to fix the gas plumbing in the café for $20 an hour. Write the correct answers in the gaps. How much will it cost if it takes George: 4 hours? $ 6 hours? $ 8 hours? $___ An ad shows two printers for sale: a color one for $287.00 and a black-and-white one for $138.00. How much cheaper is the black-and-white printer? A washer and dryer cost a total of $1092. The cost of the washer is two times the cost of the dryer. Find the cost of each item. The question consists of a problem question followed by two statements I and II. Find out if the information given in the statement(s) is sufficient to solve the problem. Problem question: How long will it take for two pipes A and B to fill an empty cistern if they work alternately for an hour each? Statements: I) Working alone, Pipe A can fill the cistern in 40 hours. II) Pipe B is one-third as efficient as Pipe A. Options: Statement I alone is sufficient. Statement II alone is. Two cars A and B move along parallel paths from a common point in a given direction. If u and v are their speeds (u>v), then find the separation between them after time t. A. ut + vt B. 2ut + vt C. (u-v)t D. ut The difference in hours between full-timers and the part-timers who work 2 hours a day is 2 working hours. How many hours per day do full-timers work? The number of full-time hours is (enter your response here). Scientist are studying the temperature on a distant planet. Let Y represent the temperature in degrees Celsius. Let X represent the height above the surface in kilometers. Suppose that x and y are related by the equation y = -5x + 41. What is the temperature on the surface of the planet? Kamala is saving her allowance. She earns $25 per week for doing chores around the house. She starts with $40 in savings. Let n be the number of weeks that Kamala has been saving. True/False? A truck rental company rents a moving truck for one day by charging $20 plus $0.12 per mile. Write a linear equation that relates the cost​ C, in​ dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 120 ​miles? What is the cost if it is driven 379 ​miles? You are choosing between two different cell phone plans. The first plan charges a rate of 27 cents per minute. The second plan charges a monthly fee of $44.95 plus 12 cents per minute. Let t be the number of minutes you talk and C1 and C2 be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans. Solve for C1 and C2. Giuseppe buys supplies to make pizzas at a cost of $4.84. Operating expenses of the business are 111% of the cost, and the profit he makes is 171% of the cost. What is the regular selling price of each pizza? The regular selling price of each pizza is $___. Hoot for the Moon Auto Sales and Service has an end-of-season sale on the remaining SUVs in their lot. The original price of one of these SUVs was $67,998.00. The first discount is 12% and the second discount is 13%. Calculate the final price of the vehicle to the nearest cent. Options: A. $57,798.30 B. $52,059.27 C. $50,998.50 D. $59,838.24 E. $61,198.20 Author royalties and copyright fees cost the company an average of $5 per novel, and the monthly cost of operating and maintaining the online publishing service amounts to $700 per month. Express the monthly profit P as a function of the unit price p, P(p) = _. Hence, determine the unit price you should charge for a maximum monthly profit. (Round your answer to the nearest cent.) $ _. What is the resulting profit (or loss)? (Round your answer to the nearest cent.) $ ____. Shoot for the Moon Auto Sales and Service has an end-of-season sale on the remaining SUVs in their lot. The original price of one of these SUVs was $67,998.00. The first discount is 12%, and the second discount is 13%. Calculate the final price of the vehicle to the nearest cent. Options: A. $52,059.27, B. $50,998.50, C. $61,198.20, D. $57,798.30, E. $59,838.24 Out of his income of Rs. 55,000, Nandhu spent 18% on transportation and out of his remaining income he spent 40% on rent and saved the rest. The amount saved by Vinod is Rs. 940 more than that saved by Nandhu. If Vinod saved 70% of his income, then find the income of Vinod. Options: a. Rs 44,000 b. Rs 56,000 c. Rs 40,000 d. Rs 36,000 A hotel advertises vacation packages on its website, and it charges the same amount per night. The table shows the total cost of a stay for different numbers of nights. The table shows the following costs for a hotel stay: Two nights cost two hundred ten dollars, three nights cost three hundred fifteen dollars, and four nights cost four hundred twenty dollars. What is the unit rate per night? Enter the correct answer in the box. $ /night Mr. Pham is looking at renting a vacation home. He finds one that can be rented for $229 per night. In addition, there is a one-time cleaning fee of $89. Write an equation that shows how the cost of renting the house, y, depends on the number of nights, x. Do not include dollar signs in the equation. You are choosing between two different cell phone plans. The first plan charges a rate of 27 cents per minute. The second plan charges a monthly fee of $44.95 plus 12 cents per minute. Let t be the number of minutes you talk and C1 and C2 be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans. Milan will rent a car for the weekend. He can choose one of two plans. The first plan has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $65 and costs an additional $0.70 per mile driven. How many miles would Milan need to drive for the two plans to cost the same? Hector and his family are heading to Tiny Acres Mini-Golf. They plan to purchase the group package. With the group package, the cost per person is $2 less than the normal cost for an individual. There are 5 people in Hector's family. His mom called ahead and found that the total cost for the family will be $35. What is the normal cost for an individual? Jen plans to sell homemade candles online. She spent $44 on a melting pot, and she will spend $4 on wax and $2 on a jar for each candle she makes. She will sell her candles for $10 each. Which equation can you use to find c, the number of candles Jen must sell for her sales to equal her expenses? How many candles must Jen sell for her sales to equal her expenses? Fred teaches swimming at a local pool. He charges $60 per lesson. This month, he spent $114.50 on online advertisements and $45.50 on a website. The pool charges him $20 per lesson to use its facilities. Which equation can you use to find n, the number of lessons Fred must teach this month for the amount he brings in to equal the amount he spends? The function P(m) = 43 + 0.08m is used to determine the price, P(m), of your phone bill depending on the number of minutes, m, used. (a) What is the price for using 100 minutes? (b) Using the function P(m)=43+0.08m , how many minutes were used if the price of the bill is $49.00? The adventure club went on a hike to see a waterfall. To get to the hike, the club members took 10 cars and 4 vans. There were 2 people in each car and 14 people in each van. How many people went on the hike? Amanda and her best friend found some money buried in the field. They split the money evenly, each getting $24.28. How much money did they find? A rectangular room is 2 meters longer than it is wide, and its perimeter is 28 meters. Find the dimension of the room. The length is : meters and the width is meters. A rectangular room is 2 meters longer than it is wide, and its perimeter is 20 meters. Find the dimension of the room. The length is : meters and the width is meters. A rectangular room is 4 times as long as it is wide, and its perimeter is 40 meters. Find the dimension of the room. The length is : meters and the width is meters. A rectangular room is 4 times as long as it is wide, and its perimeter is 60 meters. Find the dimension of the room. The length is: meters and the width is: meters. A farmer has sheep and hens. Sheep and hens together have 39 heads and 140 legs together. How many sheep and hens are there? Question: Hector and his family are heading to Tiny Acres Mini-Golf. They plan to purchase the group package. With the group package, the cost per person is $2 less than the normal cost for an individual. There are 5 people in Hector's family. His mom called ahead and found that the total cost for the family will be $35. What is the normal cost for an individual? $ Getting trained and licensed involved a one-time cost of $437. Gas and insurance end up costing him $1 per kilometer. For his first delivery, Oscar will get paid $381 plus $5 per kilometer that he drives. If he drives a certain distance on this delivery, Oscar will break even, making back all the money he had to spend. How much would both the costs and the earnings be? What distance would he have to drive? A crayon company recently changed its labels. It currently has 623 crayons with the old label and 320 crayons with the new label. How many crayons does the company have in stock? Shoot for the Moon Auto Sales and Service has an end-of-season sale on the remaining SUVs in their lot. The original price of one of these SUVs was $67,998.00. The first discount is 12%, and the second discount is 13%. Calculate the final price of the vehicle to the nearest cent. Options: A. $52,059.27, B. $50,998.50, C. $61,198.20, D. $57,798.30, E. $59,838.24 If there are 3 fiction books and this is 5% of all books on the shelf, how many books are on the shelf in total? Author royalties and copyright fees cost the company an average of $5 per novel, and the monthly cost of operating and maintaining the online publishing service amounts to $700 per month. Express the monthly profit P as a function of the unit price p, P(p) = _. Hence, determine the unit price you should charge for a maximum monthly profit. (Round your answer to the nearest cent.) $ _. What is the resulting profit (or loss)? (Round your answer to the nearest cent.) $ ____. Out of his income of Rs. 55,000, Nandhu spent 18% on transportation and out of his remaining income he spent 40% on rent and saved the rest. The amount saved by Vinod is Rs. 940 more than that saved by Nandhu. If Vinod saved 70% of his income, then find the income of Vinod. Options: a. Rs 44,000 b. Rs 56,000 c. Rs 40,000 d. Rs 36,000 Mary's hourly wage is 3 1 half times greater than John's. John's and Dennis' hourly wages added together total $40.89 an hour. If Dennis earns one-half of John's rate, what is Mary's hourly wage? The owner of ProPhone has charted the company's marginal revenue and marginal cost for its latest line of smartphones, the Blazer. Use the chart to calculate the company's profit. What is the difference between marginal revenue and marginal cost? Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600, find the marked price. The taxi charges in a city comprise a fixed charge of Rs. 100 for 5 kms and Rs. 16 per km for every additional km. If the amount paid at the end of the trip was Rs. 740, find the distance traveled. The cost C (in dollars) of renting a paddle board for H (hours) is given by C = 25 + 7H. After how many hours is the cost $81? Which equation can you use to find d, the number of days the trip would need to last for the two options to cost the same? How many days would the trip need to last for the two options to cost the same? A truck rental company rents a moving truck for one day by charging $20 plus $0.12 per mile. Write a linear equation that relates the cost​ C, in​ dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 120 ​miles? What is the cost if it is driven 379 ​miles? Sheridan Service sells oil at a markup of 30​% of the selling price. Sheridan paid $ 0.97 per litre of oil. What is the selling price per litre? A hotel advertises vacation packages on its website, and it charges the same amount per night. The table shows the total cost of a stay for different numbers of nights. The table shows the following costs for a hotel stay: Two nights cost two hundred ten dollars, three nights cost three hundred fifteen dollars, and four nights cost four hundred twenty dollars. What is the unit rate per night? Enter the correct answer in the box. $ /night A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimensions of the room. The length is : meters and the width is meters Kaya rented a limousine for prom. There was a one-time charge of $100, plus an hourly rate of $45. Her total cost for the night was $437.50. How many hours did Kaya rent the limo for? Celia paid $15 to become a member at Planet Fitness. She then had to pay a monthly membership fee. If her total cost for 6 months was $183, how much was the monthly fee? Josie spent $3,000 to buy 3 sets of golf clubs. The sets all had the same price. How much did each set cost? Parkside High School was having a talent show to raise money. It was x dollars for adults and $8 for students. Stephanie’s family had 4 adults and 1 student. Her family paid $48 to see the show. How much money was it for each adult? Mr. Pham is looking at renting a vacation home. He finds one that can be rented for $229 per night. In addition, there is a one-time cleaning fee of $89. Write an equation that shows how the cost of renting the house, y, depends on the number of nights, x. Do not include dollar signs in the equation. You are choosing between two different cell phone plans. The first plan charges a rate of 27 cents per minute. The second plan charges a monthly fee of $44.95 plus 12 cents per minute. Let t be the number of minutes you talk and C1 and C2 be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans. A rectangular room is 3 meters longer than it is wide, and its perimeter is 22 meters. Find the dimension of the room? Milan will rent a car for the weekend. He can choose one of two plans. The first plan has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $65 and costs an additional $0.70 per mile driven. How many miles would Milan need to drive for the two plans to cost the same? Hector and his family are heading to Tiny Acres Mini-Golf. They plan to purchase the group package. With the group package, the cost per person is $2 less than the normal cost for an individual. There are 5 people in Hector's family. His mom called ahead and found that the total cost for the family will be $35. What is the normal cost for an individual? Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron? Jen plans to sell homemade candles online. She spent $44 on a melting pot, and she will spend $4 on wax and $2 on a jar for each candle she makes. She will sell her candles for $10 each. Which equation can you use to find c, the number of candles Jen must sell for her sales to equal her expenses? How many candles must Jen sell for her sales to equal her expenses? Fred teaches swimming at a local pool. He charges $60 per lesson. This month, he spent $114.50 on online advertisements and $45.50 on a website. The pool charges him $20 per lesson to use its facilities. Which equation can you use to find n, the number of lessons Fred must teach this month for the amount he brings in to equal the amount he spends? To take a taxi, it costs $3.00 plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi, which includes the $1 tip you left. How many miles did you travel? Allen has a business, mowing lawns for $20 per lawn and raking leaves for $0.75 per pile. His goal is to earn exactly $30 each time he mows lawns and rakes leaves. If X represents the number of piles of leaves, which equation models Allen's goal? A taxi service charges an initial $5 fee, plus $2 per mile driven. Write an equation to represent the situation. How much is the taxi service for 150 miles driven? Pierre is 3 years older than his brother, Claude. 1. Write an equation that represents how old Pierre is ( P ) when Claude is C years old.2. How old is Pierre when Claude is 17 years old? The function P(m) = 43 + 0.08m is used to determine the price, P(m), of your phone bill depending on the number of minutes, m, used. (a) What is the price for using 100 minutes? (b) Using the function P(m)=43+0.08m , how many minutes were used if the price of the bill is $49.00? The owner of ProPhone has charted the company's marginal revenue and marginal cost for its latest line of smartphones, the Blazer. Use the chart to calculate the company's profit. What is the difference? 75% OFF of the original price! The original price of a designer rug is $4,048. What is the sale price? Last spring, the average amount of rent paid for apartments in Clarksville was $1,780. This spring, it is 5% more. What is the current average? Scientist are studying the temperature on a distant planet. Let Y represent the temperature in degrees Celsius. Let X represent the height above the surface in kilometers. Suppose that x and y are related by the equation y = -5x + 41. What is the temperature on the surface of the planet? How to determine the capitalization rate? How to determine impulse? What are the applications of linear algebra? How would you approach solving problems involving age? How do you solve linear equations by substitution? How do you solve linear equation word problems? How do you solve age problems using ratios? How do you solve age problems in linear equations? How do you solve age problems in algebra? How do you calculate age in word problems? How do I solve age problems algebraically? How can algebra problems with two variables be solved? How can age problems be solved step-by-step? How can age problems be solved quickly? How can a linear equation in standard form be solved? Can we solve word problems on age without algebra? Why study linear algebra? How can age word problems be solved? Define Two-Step Equation. How to solve two-step equations? How to write a linear model from a word problem? How do you solve age math problems? How can you use simple equations in real life? CK-12 Foundation is a non-profit organization that provides free educational materials and resources. FLEXIAPPS ABOUT Our missionMeet the teamPartnersPressCareersSecurityBlogCK-12 usage mapTestimonials SUPPORT Certified Educator ProgramCK-12 trainersWebinarsCK-12 resourcesHelpContact us BYCK-12 Common Core MathK-12 FlexBooksCollege FlexBooksTools and apps CONNECT TikTokInstagramYouTubeTwitterMediumFacebookLinkedIn -75fd10bcd7 © CK-12 Foundation 2025 | FlexBook Platform®, FlexBook®, FlexLet® and FlexCard™ are registered trademarks of CK-12 Foundation. Terms of usePrivacyAttribution guide Curriculum Materials License Ask me anything! Student Sign Up Are you a teacher? Sign up here Sign in with Google Having issues? Click here Sign in with Microsoft Sign in with Apple or Sign up using email By signing up, I confirm that I have read and agree to the Terms of use and Privacy Policy Already have an account? Sign In No Results Found Your search did not match anything in . Got It
4020
https://www.rcog.org.uk/guidance/browse-all-guidance/green-top-guidelines/the-management-of-women-with-red-cell-antibodies-during-pregnancy-green-top-guideline-no-65/
Coronavirus Resources to inform and support clinicians We provide tailored benefits depending on your career stage The revenue we receive from membership fees supports our strategic objectives Membership fees and payment FAQs Answers to frequently asked questions The Management of Women with Red Cell Antibodies during Pregnancy (Green-top Guideline No. 65) Summary: This guideline provides guidance on the management of pregnant women with red cell antibodies predating the pregnancy or those developing antibodies during pregnancy. The guideline also includes the management of fetal anaemia caused by red cell antibodies, as well as the early management of the neonate at risk of anaemia and/or hyperbilirubinaemia. It does not address the management of the pregnant woman with anti-platelet antibodies or other autoimmune or alloimmune antibodies. COVID disclaimer: This guideline was developed as part of the regular programme of Green-top Guidelines, as outlined in our document Developing a Green-top Guideline: Guidance for developers (PDF), and prior to the emergence of COVID-19. Version history: This is the first edition of this guideline. Developer declaration of interests: Available on request. This page was last reviewed 28 May 2014.
4021
https://math.answers.com/algebra/How_do_you_know_whether_to_use_an_open_circle_or_a_closed_circle_when_graphing_an_inequality_and_why
0 Subjects>Math>Algebra How do you know whether to use an open circle or a closed circle when graphing an inequality and why? Anonymous ∙ 13y ago Updated: 4/28/2022 An open or closed circle are used to graph an inequality in one variable. An open circle is used if the value at the end point is excluded from the feasible region while a closed circle is used if the value at that point is within the accepted region. Wiki User ∙ 13y ago What else can I help you with? Trending Questions What is 1.6666667 in a fraction? How do you write 0.81 squared in standard form? Is transferred a verb? Is catch a verb or a noun? What is a math unit bar? Given the function Fx you can get a picture of the graph of its inverse F-1y by flipping the original graph of Fx over the line? What is the sum of 19? What shape has 4 equal sides no right angles? What is the algebraic equation for half a number plus 7? What is -8x times 7y? The sum of two thirds of a number and one fourth of the number exceeds five sixths of that number by two Find the number? How many solutions does 5(x - 2) 5x - 7 have? Explain about Cartesian coordinate system? What is the independent variable of a variable? Why do you have to take Algebra 2? When Albert Einstein get married? About how steep is the angle of the slope for Extreme Skiers? What is the maximum number of points at which two lines can intersect each other? What is the slope intercept form of 11x-8y equals 32? Solve for x and y 37x 43y 123 43x 37y 117? Resources Leaderboard All Tags Unanswered Top Categories Algebra Chemistry Biology World History English Language Arts Psychology Computer Science Economics Product Community Guidelines Honor Code Flashcard Maker Study Guides Math Solver FAQ Company About Us Contact Us Terms of Service Privacy Policy Disclaimer Cookie Policy IP Issues Copyright ©2025 Answers.com. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Answers.
4022
https://www.mathway.com/popular-problems/Precalculus/402083
Solve for ? cot(x) = square root of 3 | Mathway Enter a problem... [x] Precalculus Examples Popular Problems Precalculus Solve for ? cot(x) = square root of 3 Step 1 Take the inverse cotangent of both sides of the equation to extract from inside the cotangent. Step 2 Simplify the right side. Tap for more steps... Step 2.1 The exact value of is . Step 3 The cotangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant. Step 4 Simplify . Tap for more steps... Step 4.1 To write as a fraction with a common denominator, multiply by . Step 4.2 Combine fractions. Tap for more steps... Step 4.2.1 Combine and . Step 4.2.2 Combine the numerators over the common denominator. Step 4.3 Simplify the numerator. Tap for more steps... Step 4.3.1 Move to the left of . Step 4.3.2 Add and . Step 5 Find the period of . Tap for more steps... Step 5.1 The period of the function can be calculated using . Step 5.2 Replace with in the formula for period. Step 5.3 The absolute value is the distance between a number and zero. The distance between and is . Step 5.4 Divide by . Step 6 The period of the function is so values will repeat every radians in both directions. , for any integer Step 7 Consolidate the answers. , for any integer Please ensure that your password is at least 8 characters and contains each of the following: a number a letter a special character: @$#!%?&
4023
https://math.stackexchange.com/questions/1604846/finding-the-number-thats-less-than-90-of-result-set
data analysis - Finding the number that's less than 90% of result set - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Loading… Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products current community Mathematics helpchat Mathematics Meta your communities Sign up or log in to customize your list. more stack exchange communities company blog Log in Sign up Home Questions Unanswered AI Assist Labs Tags Chat Users Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Finding the number that's less than 90% of result set Ask Question Asked 9 years, 8 months ago Modified9 years, 8 months ago Viewed 91 times This question shows research effort; it is useful and clear 0 Save this question. Show activity on this post. Forgive if this sounds vague or poorly worded. I'm struggling to pinpoint the right terminology of what I'm looking to do. Hoping someone here can push me in the right direction. So I have a set of numbers. Say: 15,22,15,10,20,20,13,13,22,23,13,22,20,8 15,22,15,10,20,20,13,13,22,23,13,22,20,8 I'd like to know what would I need to do to calculate the number that is approximately Less Than or Equal to 90%90% of each these numbers as a whole (but not less than 90 90). Just playing around I know I'd want 10 (is Less Than or equal to 13 out of 14 numbers) but I'm not sure how to solidly calculate this. Any help would be great! =) data-analysis Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications edited Jan 8, 2016 at 20:58 user118494 6,095 5 5 gold badges 33 33 silver badges 81 81 bronze badges asked Jan 8, 2016 at 20:51 mBrice1024mBrice1024 133 1 1 silver badge 4 4 bronze badges Add a comment| 1 Answer 1 Sorted by: Reset to default This answer is useful 2 Save this answer. Show activity on this post. The number that is approximately less than or equal to 90% of each of your numbers is called the 10th percentile. Another phrasing is that any number that is greater than or equal to x% of your numbers is in the xth percentile. The best way to figure that number out is to list your numbers in order from least to greatest, and find the number in the list where 10% of the numbers are less than it (or 90% of the numbers are greater than it). Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Jan 8, 2016 at 20:56 Bob KruegerBob Krueger 6,619 2 2 gold badges 16 16 silver badges 29 29 bronze badges 1 Perfect! Percentile was the word I looking for. Thank you so much.mBrice1024 –mBrice1024 2016-01-08 21:35:02 +00:00 Commented Jan 8, 2016 at 21:35 Add a comment| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions data-analysis See similar questions with these tags. 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4024
https://www.youtube.com/watch?v=sL7nve5A2hM
Roots of Unity Filter on a CMIMC Problem Spec Z Earther 212 subscribers 5 likes Description 169 views Posted: 22 Apr 2021 This is a probability problem that showed up on the CMIMC (2020 Combo and CS round). I present a solution using a roots of unity filter. To see a derivation for the roots of unity filter formula, you can check The official solution uses a nice symmetry argument which you can search up, but this is a nice alternative solution. Feel free to comment with any questions, comments, or speakos (verbal typos). Transcript: okay so in this video i am going to present a solution to a problem that showed up on the cmimc and um it's sort of a counting combinatorial um probability question and um i'm going to present a solution to it using a generating function and a rotating filter so the problem is that you have cards laid on table number one through seven and um you have a sequence of shuffles and a shuffle is that you take one card that is not on the top so in this case it'll be anywhere from two to seven um so say you pick four and then put uh move four to the top and leave everything else unchanged so if you pick four then you go like four one two three five six seven and um so that's what we call a shuffle it's pretty bad if you ask me but that's what we're considering and we're asking after ten shuffles uh what is the probability that um top to bottom six ends up above of three um so the first thing that you might think about when you're starting off this problem is to instead of looking at ten different shuffles we'll just look at one shelf and see what happens so um if we do one shuffle then we can first try moving two to the top and so you see that the um relative positioning of three and six is unchanged so three is on top of six um or we can move three on top and three still on top of six or four on top four still on top of six oh sorry three still on top of six and if you move any card except for six uh three will still be on top of six however if you move six to the top they'll become like six one two three four five seven and so in that case um the six would be on top of three so what does that mean well we have six cards to choose from which are two through seven so there are six of them and um if we pick any five of them that aren't six so with the five six probability uh three is on top and um if we pick the six cards so that's a one six probability because there are six cards three to seven um then the six is on top of the three and so now um you say okay so that's one shuffle after one shuffle you have a one-sixth probability of six being on top um so what happens after two shuffles well um let's choose one of these so let's say that like we move four to the top so that's something like four one two three five six seven right and we can play the same sort of game and ask what happens if you move different cards to the top from this position um so we can choose to move say the two to the top that becomes two four one three five six seven or we can move like say the five to the top that's like five four one two three six seven and again if you move anything except for the six the three is still on top of the six right um because nothing here changes um unless you move the three flip top and which is still on top or if you move the six to the top and or space the six is on top of the 3. so here again with the 5 6 probability the 3 is on top and with a 1 6 probability a6 is on top and so here we took one particular case but you can easily convince yourself that the same sort of thing works with any sort of arrangement um after the first shuffle as long as it's not the six on top so with the other one six probability we already know what order it is because we move the six on the first shuffle set six one two three four five seven and so here again we can ask that is a two not a three um what happens if we move different cards here so we if we move the two then six on top of the three if we move the fourth sixes on top of the three um we can't move the six because the six is on top but we can see still that any one of the rest of these cards so one two four five or seven um if you move any of those five the relative position of six and three will remain the same um but if you move the three to the top and three will be on top of uh six so that will mean that with five six probability the six is on top and with one sixth probability b3 is on top so you notice that um these numbers one six and five six are coming up so you might wanna think well what happens with probability five six and what happens with probably one six right um so here um you can see that what happens is probably five six is that the um order between three and the six remains the same now you only care about the order between three and six and don't care about any of the other numbers so that's what you want to focus on and so here for example with the five six probability three started on top because three is on top of six obviously and three standing on top with five six here again three set on top of five six and change with a one six here three started on top it changes with uh one six probability becomes six on top and then six stays on top with probably five six and six switches to three on top with probably one sixth so how can you convince yourself that this is always the case well suppose like um one of the two uh three or six is on top then that means that the other one will be in one of the six lower cards and the only way to switch the position is to choose the lower of them and that's always possible because it's never on the it's never the top card because um it's on the bottom uh between three and six and so you can always choose like with one six probability of switch and with the five six probably stay on top um so you can work out a few more examples of that if you're not convinced but that means that we can rephrase the question of um after 10 shuffles where's the probability that the six is on top as saying this um so let's say that we take three shuffles right and so we start off with three on top so this is like the zero shuffle and then one two three let's say that we have a six on top three on top and then six on top so um we can choose some other things as well so for example we need three six six three or we can do like a three three three three a simple case and then we can look at how many switches do we have here here we have one switch two switch three switches here we have one switch uh not a switch two switches here we have no switches at all so it's pretty easy to see that if you have an even number of switches then you're gonna switch an even number of times between uh three and six and you're going to end up back at three however if you have an odd number of switches then you're gonna um switch an odd number of times between three and six and you're going to end up at six and that doesn't matter that we chose three you can also choose four it's the same sort of thing so for example um this one now has one two three switches so it's our number of switches so it doesn't have six this one has one two three switches so it also intended six this one has one switch which is odd so it also intended six and if this was like a three at the end it'd be easier switches and anyways um so now we can ask like let's say that we have ten right one two three four five six seven eight nine ten and to each of these we can either assign like switch not switch switch not switch switch switch not such switch switch not switch so for example this would be like three six six three three six three and so on and so uh for every sequence of like switch and not switch we can construct a sequence of whether three or six on top and we know that if the end number is six then we have an odd number of switches so what we want to ask is uh for each switch what is the problem uh for each like sequence of shuffles uh what's the probability that you have an odd number of switches and so how many ways are there to have for example um n switches out of um 10 uh total shuffles so every ten choose then and what are the probability that n of them are switches that would be 1 6 to probably n uh because each switch has to do probably 1 6 and you have 5 6 to the 10 minus n so that the rest of them are not so for example if you were to have six switches and four that horn switches you can have um ten to six possible ways to arrange those six switches and um each of those six you would have to have a one six probability that they do switch and each of the four it would have a five six probability that it doesn't and we want to take the sum of this overall and odd so that'd be like n equals one three five seven and nine okay so how can we possibly evaluate the sum it seems kind of messy well um notice here that we have ten choose and something to the power of n something to the power of 10 minus n so that should remind you of um the binomial uh series uh like 1 6 plus 5 6 to the n this will be the sum um from n equals 0 to 10 of 10 choose n 1 6 to the n 5 6 to 10 and so what we can do is uh well we want to sum over all the ones of these where n is odd and we can do that using a roots of unity filter by introducing an extra variable so what we'll do is we'll put in a little x here so it's 1 6 x plus 5 6 n and so that will just mean that um we instead of doing 1 6 to the power of n here we have x over 6 to the power of n or we can rewrite that as uh just being 1 6 the power of n times x to the power of n and so the advantage of doing this is that now we have a variable here and we have some coefficients of the variables so it's just like some sum a0 x 0 a1 x to the 1 plus so on and so forth and we want to sum over all the odd coefficients so a1 plus a3 plus a5 plus a7 plus a math and so if you watch my video on roots of immunity filter or if you just know about roots of beauty filter then you know that the formula to do that is let's say this is equal to f of x so since um we're taking the sum of k is congruent to 1 mod 2 of a sub k this will be equal to one half because uh we're taking mod 2 times the sum over the square roots of unity so it'll be x squared is equal to 1 or this is just x is equal to plus or minus 1 of f of x so what that means is that this sum over here um we're filtering out uh out of this all the ones which are a one mod two and that will be one half um of this sum of f of f one plus f of minus one uh times this actually no sorry uh this is times x inverse because you're taking all the numbers that are one mod two um it says zero two so if there's zero two you just have f of x but since one by two you have x inverse um so now let's evaluate this so that'll be one half times um well what's f of one that'll just be one sixth plus one fifth to the power of ten should be ten nine nine um and then x equals negative one that will be um x inverse so negative one inverse is negative one so i'll be minus five six minus one sixth power of m so i sort one six afterwards because it's one six times negative one and then you subtract that off why do i keep writing that it's ten um and so this will be this is just one so that's one to the power of ten um so that's just one and subtracting off one half times whatever this is so this will be 4 6 which is two-thirds this will be two-thirds to the power of ten and well that's just your answer because this is equal to this sum which we said was the sum that the the probability that you have an odd number of shuffles and the probability that you have an odd number of shuffles is the same probability that you end up with six on top and so just as a little sanity check you can see like uh this is slightly different than one half because um two-thirds is a number less than one so if you take a number less than one and raise it to a high power it's approximately zero and so this is like slightly different from one half which makes sense because you expect that the probability that you have a six on top of a three is approximately one half because like you have the probability that three is on top is also roughly the same probability um so yeah that's a nice solution to this problem which use uh generating functions to evaluate this really nasty sum um
4025
https://www.heart.org/en/professional/quality-improvement/ascvd
Skip to main content Atherosclerotic Cardiovascular Disease (ASCVD) Atherosclerotic cardiovascular disease, otherwise known as ASCVD, is caused by plaque buildup in arterial walls and refers to conditions that include: Coronary Heart Disease (CHD), such as myocardial infarction, angina, and coronary artery stenosis. Cerebrovascular disease, such as a transient ischemic attack, ischemic stroke, and carotid artery stenosis. Peripheral artery disease, such as claudication. Aortic atherosclerotic disease, such as abdominal aortic aneurysm and descending thoracic aneurysm. Currently, ASCVD- related conditions remain the leading cause of morbidity and mortality globally (source). As such, the American Heart Association is committed to promoting strategies that allow people to live longer, healthier lives. Learn more about ASCVD and how you can support our mission by exploring our links below. The resources in this toolkit have been created and assembled by the AHA, its volunteer medical professionals from across the country, and the hospitals participating in this initiative. The materials are for educational purposes only. The content provided in this toolkit does not constitute an endorsement or instruction by the American Heart Association or the American Stroke Association. Resources ## Resources for Health Care Professionals ## Professional Education Toolkit ## ASCVD Initiative
4026
https://ncse.ngo/marsupials
September 30, 2008 Marsupials The marsupial faunas of South America and Australia are at least as ecologically diverse as placental mammals worldwide (with some exceptions, see the discussion of developmental constraints in our response to chapter 8). The convergent evolution of Australian mammals and placentals found in comparable habitats elsewhere shows the power of evolution to adapt species to similar conditions. That they have similar adaptations to those found in placentals, but achieve such adaptations by different means, indicates how flexible evolutionary processes can be. Because of the ecological diversity of South American and Australian marsupials, and the biogeographic history which made such diversity possible, marsupials could serve as a useful exploration of the interplay of evolution and biogeography. Unfortunately, the discussion of marsupial biogeography in Explore Evolution is laughably bad: too brief to education, and so inaccurate as to be utterly useless. It begins with a mischaracterization of the evolution of marsupials: The first mammals with the marsupial's distinctive mode of reproduction arose on the ancient southern super-continent of Gondwanaland. Later, after this great land mass broke up into separate continents, the ancestors of marsupials were separated from other mammals and evolved in isolation on the new continents of Australia and South America. Explore Evolution, p. 75. This is a straw man. Textbooks and researchers in the field do not claim that marsupials originated in Australia or South America. The best evidence is that marsupials originated Asia, migrated to North America via a land bridge, and that the co-existed with placental mammals in the northern hemisphere for some time. Marsupials colonized first South America, and from there moved on to Antarctica and then Australia. The marsupial populations in Asia and North America went extinct, possibly as a result of competition with placental mammals among other factors, and the populations on southern continents remained in those safe havens. Explore Evolution's perfunctory and inaccurate coverage of this basic biogeography does students a disservice. Students cannot be guaranteed to have a background to know what Gondwanaland was, nor to appreciate that the supercontinent was already largely broken up by the time marsupials were crossing landbridges between the continents. If students do not have the background to appreciate the interplay of diversification and continental drift, the book's explanation will not help. Having created the straw man, Explore Evolution proceeds to knock it down: Critics of the marsupial argument insist that it, too, fails to establish Universal Common Descent or even the descent of all marsupials. At best, it shows that various groups of marsupials first originated in the same general area in the Southern Hemisphere and were then distributed more widely as the Southern continents separated from one another. But even this is questionable, some critics say. They point out that marsupials are not restricted to the southern continents of Australia and South America. Marsupials such as the opossum live in the northern hemisphere. And, in a recent development, paleontologists have unearthed the oldest marsupial fossil of all in China. Explore Evolution, p. 77-78. Marsupials exist in North America because of migration, a process described in this very chapter, but ignored now when the authors find it inconvenient. Around 3 million years ago, a combination of continental drift and the rising Andes brought South America into contact with North America. For the first time in 50 million years, North American species and South American species came into contact. Some marsupials (like the opossum) spread north. Some placentals from North American spread south. For reasons that scientists continue to investigate and discuss, the ability of North American placentals to persist and diversify in South America was much greater than the ability of South American marsupials to diversify in the north, or to outcompete the northern invaders (Stehli and Webb, eds. 1985. The Great American Biotic Interchange. Plenum Press: New York). Today, half of South American mammals are descended from North American ancestors. South American descendants represent no more than 20 percent of modern North American species, and most of those are in Central America, near the point of initial contact (Marshall, et al. 1982. "Mammalian evolution and the Great American Interchange," Science 215:1351-1357). This helps explain the confusion of the apparently biogeographically illiterate authors of Explore Evolution about why "marsupials such as the opossum live in the northern hemisphere." It is because of migration, a process they described as uncontroversial only a page earlier. It is not a mystery, and it is unclear why the authors would regard it as such. The claim that North American opossums are evidence against the common ancestry of marsupials bears striking similarities to a critique of biogeography by young earth creationist Kurt Wise: There are very few examples of macrobiogeographical evidences for macroevolution, and none of them is very strong. The best-known claim is the concentration of marsupials in Australia. But there are several reasons that marsupials in Australia are actually a poor example. First, all marsupials are not in Australia. The Virginia opossum of North America, for example, is a marsupial. It is thought to have come from South America, not Australia. Thus not all similar organisms are known from every continent. Third, marsupials are the oldest fossil mammals know from Africa, Antarctica and Australia in that order. The fossil record seems to show a migration of marsupials from somewhere around the intersection of the Eurasian and African continents and then a survival in only the continents farthest from their point of origin (South America and Australia). source Wise, Kurt (1994) "The Origins of Life's Major Groups," ch. 6 in J. P. Moreland (ed.) The Creation Hypothesis: Scientific Evidence for an Intelligent Designer, Intervarsity Press:Downers Grove, IL, p. 223). Wise's confusion over the status of the Virginia opossum perhaps reflects his confusion of the New World order Didelphimorphia commonly called opossums with the Australian order Diprotodontia some of which are commonly called possums (without the first "o"). The groups are morphologically and molecularly distinct, with well-established paleontological histories. If the opossum truly had roots in Australia, it would indeed be a biogeographic conundrum. In fact, the only close link between opossums and Australia is Wise's typo. Similar misunderstandings plague the discussion of the marsupial fossil record in Explore Evolution and its creationist source material. It is not surprising, the breathless tone of Explore Evolution notwithstanding, that "paleontologists have unearthed the oldest marsupial fossil of all in China." The authors wonder "If the ancestors of the marsupials originated in the Southern Hemisphere, why has the oldest known member of the group been discovered in the Norther Hemisphere?" The answer is simple: paleontologists do not claim that marsupials originated in the Southern hemisphere, only that they migrated there. Mammal Taxa: A phylogeny of fossil and extant mammalian taxa, combined with the known ages of fossils. The earliest fossils are found in Asia, with more modern fossils found in North America, and then spreading to South America and Australia. This pattern is consistent with known land connections between the continents at the times of apparent interchange. Zhe-Xi Luo, Qiang Ji, John R. Wible, Chong-Xi Yuan (2003) "An Early Cretaceous Tribosphenic Mammal and Metatherian Evolution", Science, 302(5652):1934-1940. Marsupials and placental mammals separated roughly 125 million years ago, according to the most recent fossil data. Several lines of evidence indicate that the marsupials originated in Asia, spread to North America over a land bridge, which can be seen in the figure. The ages and characteristics of fossils found in Europe, South America, Africa, Australia and Antarctica suggest that marsupials spread to Europe and South America from North America. South America, Africa, Australia and Antarctica still had linkages at that time, allowing species on the Southern continents to spread easily. Despite the feigned confusion of Explore Evolution's authors, the fossil record gives a very clear picture of the biogeographic history of marsupials, though there are many questions scientists continue to investigate. The earliest marsupial fossils (and the earliest placental fossils) are found in Asia. Fossilized marsupials are found in North America in rocks that are only a few million years younger than the Chinese fossils. During that period in geological history, plate tectonics had brought North America and Asia close enough together to forge a land bridge, allowing many species to migrate between those continents. Cretaceous Continents: Christopher Scotese's reconstruction of the continental arrangement 94 million years ago. The land bridge between North America and Asia is indicated at the upper left. The connection between North and South America is also visible. Africa is drifting away from other southern continents, but Australia, Antarctica and South America are linked. Africa split off from this southern supercontinent beginning around 140 million years ago. At that time, the southern continents were all connected, North America and Europe were still very close, and South America had not drifted far from North America, allowing dispersal during periods when ocean levels dropped. Marsupials related to North American species colonized Europe briefly, through a northern land bridge, and others colonized South America. Africa was in the process of separating from the supercontinent which also included Antarctica, Australia and South America, so the presence of marsupial fossils in Africa gives a good measure of how quickly they entered South America and dispersed across the supercontinent Gondwana. Fossilized marsupials in Antarctica also allow us to track their dispersal to Australia. This pattern is consistent with the fossil record of placental mammals, and with other lines of evidence (John P. Hunter and Christine M. Janis. 2006. "'Garden of Eden' or 'Fool s Paradise'? Phylogeny, dispersal, and the southern continent hypothesis of placental mammal origins," Paleobiology, 32(3):339 344). As the southern continents drifted apart as well, the marsupial faunas in each isolated continent followed a different path. As Antarctica drifted south towards its current polar position, it became colder and colder, ultimately driving its resident marsupials and palm trees extinct. South American and Australian marsupials produced diverse radiations which filled many of the same ecological niches occupied by placental mammals elsewhere. In the northern continents, which were periodically linked by land bridges, biotic interchanges resulted in periods of intense competition, which seem to have driven the native marsupials extinct. When South America drifted north again and connected with North America around 3 million years ago, the Great American Biotic Interchange had the same devastating effect that biotic interchanges had on other marsupial faunas. The same pattern of diversification and migration seen in marsupials can also be seen in other groups of plants and animals. That consistency between biogeographic and evolutionary patterns provides important evidence about the continuity of the processes driving the evolution and diversification of all life. This continuity is what would be expected of a pattern of common descent. The creationist orchard scheme gives us no reason to predict this pattern. Table of Contents Critique: Exploring "Explore Evolution" Preface Educational policy and terminology Santorum Amendment and UK National Curriculum Inquiry-based learning References Scientific controversy vs. social controversy "Controversy" over evolution Evolution, climate change, plate tectonics, and string theory "Key aspects" of evolution References Introduction Evolution Meanings of "evolution" Evolutionary mechanisms Universal Common Descent "Fundamentally new" organisms References Nature of Science "Historical science" vs. "experimental science" Evaluating the quality of a scientific explanation References Fossil Succession Other Errors in Chapter 3 Time Represented in Outcrops Geologic "Closeness" The Three Domains Weasel Words Phylogeny & the Nature of the Fossil Record Stability of Phyla Sudden taxonomic levels Fossil Preservation Absence of Fossil Evidence Punctuated Equilibrium Polyphyletic vs. Monophyletic Do scientists support polyphyletism? Evidence for Single Origin of Life Nature of Scientific Disagreement Malcolm Gordon The Cambrian Radiation Sudden Appearance? The Cambrian Radiation in the Geologic Record Creationist Statistics Soft-bodied fossils Cal Academy of Sciences display Transitional Fossils Transitional Fossils Are Not Rare Do animal forms change or stay the same? Darwin on Transitional Fossils The Sequence of Transitional Fossils Whale Evolution The Sizes of Transitional Fossils Anatomical Homology Misquoting Brian Goodwin David Wake Development Primer Homology via different genes or developmental pathways Non-homology via homologous genes Convergence Common function vs. common ancestry Vertebrate limbs Similarity of shape vs. similarity of form Convergence vs. natural selection Convergence and common descent Defining "homology" Homology and similarity Homologous structures, genes, and developmental pathways Circular definitions Molecular Homology Molecular Clocks Environmental Influences Molecular Clock Rates A Universal Tree of Life Do Different Genes Mean Different Phylogenetic Trees? Phylogenetic Trees and Molecular Family Histories The Last Universal Common Ancestor Malcolm Gordon References Evolving Codes and Novel Genes The Genetic Code ORFans Embryology References Philosophy Evolutionary Predictions of Common Ancestry Students as Jurors History of Embryology Darwin on Dissimilarities Ontogeny & Phylogeny Haeckel's Drawings Accuracy in embryo illustrations The Earliest Stages Sedgwick's Two Challenges Michael Richardson's photographs Biogeography Evolution on Islands The Breadth of Biogeography Island Diversity Marsupials "Lost" Genetic Information Fixity of species and common descent Fixity of Species Biogeographic predictability Doubting Common Ancestry Natural Selection Extrapolation Exrapolating microevolution to macroevolution Limits on Evolution Oscillations Experiments Biology Texts Modern Galapagos Finches Peppered Moths Kettlewell's Experiments Where Peppered Moths Rest Artificial and Natural Selection Artificial vs. Natural Selection Horses and Dogs Natural Selection & Mutation Morphology The Four-Winged Fly Survival "Hopeful Monsters" Hox & Development Modularity in Hox genes Body Plans Mutations & New Body Plans Developmental Controls Bacterial speciation DNA Information Other sources DNA and CD players "Genomic equivalence" Mutations Mutation Definition Protein Coding Normal Protein Mutation Accumulation Compensatory Mutations Pre-Existing Resistance Protein Changes Molecular "Machines" Claim about protein synthesis Claims about "cooption" Claims about evolution of flagella Claims about complexity of cells Natural Selection / Survival of the Fittest Tautology What Fossils Tell Us Transitional Forms Intermediates between modern forms Fossils of live birth Mammal eggs and reptile placentas Lungs Parabronchi Bird diaphragms Dinosaur diaphragms Hearts Mammalian hearts Crocodilian Hearts Dissent in Science Nature of Science Is this how science works? 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https://math.stackexchange.com/questions/2452900/on-the-recurrence-a-k1-fraca-kp-k1-frac1a-k-with-a-1-1-and
Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams On the recurrence $a_{k+1}=\frac{a_k}{p_{k+1}}+\frac{1}{a_k}$, with $a_1=1$ and being $p_k$ the $kth$ prime number Ask Question Asked Modified 7 years, 11 months ago Viewed 580 times 2 $\begingroup$ We denote for integers $n\geq 1$ the $nth$ prime number as $p_n$. And for integers $k\geq 1$, I consider this recurrence relation $$a_{k+1}=\frac{a_k}{p_{k+1}}+\frac{1}{a_k},\tag{1}$$ with $a_1$ defined to be equal to $1$. I've calculated some (few) terms of this sequence $a_k$. See here the first examples. Examples of computations of some terms of our sequence $ \left{ a_n\right}_{n=1} ^\infty$: 1) Since $a_1=1$ then $a_2=\frac{a_1}{p_2}+(a_1)^{-1}=\frac{1}{3}+\frac{1}{1}=\frac{4}{3}$. 2) Since the third prime number is $p_3=5$ one has $$a_3=\frac{a_2}{p_3}+\frac{1}{a_2}=\frac{4/3}{5}+\frac{3}{4}=\frac{61}{60}.$$ 3) Similarly $a_4=\frac{61}{7\cdot 60}+(60/61)^{-1}\approx 1.1288$. $\square$ Thus our sequence starts as $a_1=1,a_2\approx 1.3333, a_3\approx 1.0117, a_4\approx 1.1288$ and similarly we can calculate $a_5\approx 0.9664,a_6\approx 1.1091$ or $a_7\approx 0.9669$. To create this problem I was inspired in a recurrence that $\sqrt{2}$ solves as you can see from this WIkipedia, and now I am curious about how to check that the sequence in $(1)$ is convergent. Question. Please, can you prove that $\left{ a_n\right}_{n=1} ^\infty$ defined from $(1)$ is convergent? Many thanks. I know a a main tool in the theory of prime numbers is the Prime Number Theorem: $p_n\sim n\log n$ as $n\to\infty$. analysis limits convergence-divergence prime-numbers recurrence-relations Share asked Oct 1, 2017 at 14:17 user243301user243301 $\endgroup$ 12 1 $\begingroup$ have you tried to look for conditons under which $a_{k+1}>2$? $\endgroup$ dfnu – dfnu 2017-10-01 14:53:25 +00:00 Commented Oct 1, 2017 at 14:53 1 $\begingroup$ Sorry an error and the expression I could not edit of $\Delta_k = \frac{1}{a_k} - a_k\frac{p_{k+1}-1}{p_{k+1}}$ $\endgroup$ dfnu – dfnu 2017-10-01 19:02:54 +00:00 Commented Oct 1, 2017 at 19:02 1 $\begingroup$ I was able to show that both ${a_{2n}}$ and ${a_{2n+1}}$ converge. Also numerical computation with first 100k terms suggests that the error $|a_n - 1|$ decays at least as fast as $\mathcal{O}(1/\log n)$. $\endgroup$ Sangchul Lee – Sangchul Lee 2017-10-02 09:34:41 +00:00 Commented Oct 2, 2017 at 9:34 1 $\begingroup$ One could easily prove that if $a_k \leq 1+\epsilon$ for all $k \geq k_0$ then $a_k \geq 1-\epsilon$ for all $k \geq k_0$ and i proved that $a_k \leq 1.03$ for all $k \geq 20$ thus $0.97 \leq a_k \leq 1.03$ for all $k \geq 20$. $\endgroup$ user411780 – user411780 2017-10-02 20:25:21 +00:00 Commented Oct 2, 2017 at 20:25 1 $\begingroup$ Many thanks feel free to add you contribution as an answer. It enriches the post @Ahmad $\endgroup$ user243301 – user243301 2017-10-02 22:42:23 +00:00 Commented Oct 2, 2017 at 22:42 | Show 7 more comments 4 Answers 4 Reset to default 2 $\begingroup$ This partially answers the question by showing that both $(a_{2n})$ and $(a_{2n+1})$ converge. The proof may not be an easy path, and particularly the first section can be quite boring. You may focus on only color-boxed statements and skip the rest of the preliminary. 1. Preliminary Definition. For $p \geq 2$ we define $f_p : (0, \infty) \to (0, \infty)$ by $$f_p(x) = \frac{x}{p} + \frac{1}{x}$$ Also we set $g_{p,q} = f_q \circ f_p$ for $q \geq p \geq 2$. We would like to investigate these functions. Then it is immediate that the equation $f_p'(x) = 0$ has a unique zero $x = \sqrt{p}$ on $(0, \infty)$. Using this, we can solve $g_{p, q}'(x) = f_q'(f_p(x)) f_p'(x) = 0$. One zero comes from $f_p'(x) = 0$, yielding $x = \sqrt{p}$. There are two other zeros that come from $f_q'(f_p(x)) = 0$ or equivalently $f_p(x) = \sqrt{q}$. Solving this, we obtain two zeros $$ \bbox[#fff9e3,border:1px solid #ffeb8e,12px]{ \alpha_{p,q} := \frac{p\sqrt{q} - \sqrt{ p (pq - 4)} }{2} } \quad \text{and} \quad \beta_{p,q} := \frac{p\sqrt{q} + \sqrt{ p (pq - 4)} }{2} \tag{1} $$ As for the smaller zero, we have $\alpha_{p,q} = \frac{2}{\sqrt{q} + \sqrt{q - (4/p)}} < \frac{2}{\sqrt{q}} $ and hence it tends zero as $q \to \infty$. Similarly, we have $\beta_{p,q} \geq p\sqrt{q}/2 \geq \sqrt{p}$, where the last inequality follows from $q \geq p \geq 2$. Combining these observations, we obtain Lemma 1. $g_{p, q}$ is strictly increasing on $I_{p,q} := [\alpha_{p,q}, \sqrt{p}]$. Next we investigate the fixed point of $g_{p,q}$. By a brutal-force computation, we find that $g_{p,q}$ has the unique fixed point $$ \bbox[#fff9e3,border:1px solid #ffeb8e,12px]{ x_{p,q} := \sqrt{\frac{p}{\sqrt{pq} - 1}} } \tag{2}$$ on $(0, \infty)$. Moreover, since $g_{p,q}(\alpha_{p,q}) = \frac{2}{\sqrt{q}} > \alpha_{p,q}$ and $g_{p,q}(\sqrt{p}) = f_q(2/\sqrt{p}) \leq \sqrt{p}$, IVT tells that $x_{p,q} \in I_{p,q}$. So it follows that Lemma 2. We have (i) If $x \in [\alpha_{p,q}, x_{p,q})$, then $x < g_{p,q}(x) < x_{p,q}$. (ii) If $x \in (x_{p,q}, \sqrt{p}]$ then $x > g_{p,q}(x) > x_{p,q}$. This situation is summarized in the following graph: $\hspace{7em}$ We also need a bit technical observation. Lemma 3. Let $q' \geq p' \geq 2$ be such that $q' \geq q$. Then $g_{p,q}(I_{p,q}) \subseteq I_{p',q'}$. In order to prove this, it is enough to notice that $ \alpha_{p',q'} \leq \frac{2}{\sqrt{q'}} \leq \frac{2}{\sqrt{q}} = g_{p,q}(\alpha_{p,q}) $ and that $g_{p,q}(\sqrt{p}) = 2/\sqrt{p} \leq \sqrt{2} \leq \sqrt{p'}$. Finally we need an input from number theory. Let $p_n$ be the $n$-the smallest prime number. Then Lemma 4. $\lim_{n\to\infty} p_{n+1} / p_n = 1$. Proof. It is equivalent to saying that the prime gap satisfies $(p_{n+1} - p_n)/p_n \to 0$. See this for the reference. 2. Main proof Let $x_n = x_{p_n,p_{n+1}}$, where the right-hand side is the symbol defined as $\text{(2)}$. In a similar fasion, we write $g_n = g_{p_n,p_{n+1}}$ and $I_n = I_{p_n,p_{n+1}}$. Then by Lemma 3, we know that $g_n(I_n) \subseteq I_{n+2}$. Also we have $a_2 = \frac{4}{3} \in [2/\sqrt{5}, \sqrt{3}] = I_2$ and $a_3 = \frac{61}{60} \in [2/\sqrt{7}, \sqrt{5}] = I_3$. So by the induction together with the recurrence relation $a_{n+2} = g_n(a_n)$ tells that $a_n \in I_n$ for all $n \geq 2$. Now by Lemma 4, we know that $x_n \to 1$ as $n\to\infty$. So if we fix a sufficiently small $\epsilon > 0$, there exists $N = N(\epsilon) \geq 2$ such that $|x_n - 1| < \epsilon$ for all $n \geq N$. So by Lemma 1, If $a_n \leq 1-\epsilon$, then $a_n < x_n$ and hence $a_n < a_{n+2} < x_n < 1+\epsilon$. If $a_n \geq 1+\epsilon$, then $a_n > x_n$ and hence $a_n > a_{n+2} > x_n > 1-\epsilon$. Since $a_{n+2}$ always lies between $a_n$ and $x_n$, if $|a_n - 1| < \epsilon$ then $|a_{n+2} - 1| < \epsilon$ as well. Now let us fix $r \in {1,2}$. Then the above observation tells that we have the following trichotomy for the sequence $(a_{2n+r})_{n=0}^{\infty}$. Case 1. There exists $\epsilon > 0$ such that $a_{2n+r} \leq 1-\epsilon$ for all large $n$. In this case, the sequence is eventually monotone increasing and hence converges. Case 2. There exists $\epsilon > 0$ such that $a_{2n+r} \geq 1+\epsilon$ for all large $n$. By a similar reasoning, the sequence converges. Case 3. For all $\epsilon > 0$ we have $|a_{2n+r} - 1| < \epsilon$ for all large $n$. This immediately translates to the statement that $a_{2n+r}$ converges to $1$. Combining altogether, we have proved that Proposition. Both $(a_{2n})$ and $(a_{2n+1})$ converge. Remark. Calibrating the initial value, this proof should work for any sequence $(p_n)$ such that $p_n \geq 2$ and $p_n \nearrow \infty$ with $p_{n+1}/p_n \to 1$. I strongly suspect that we may find some sequence $(p_n)$ such that all these conditions are met but the limit of $(a_{2n})$ and $(a_{2n+1})$ do not coincide. (Geometric sequence might be such a candidate.) So we indeed need more input to settle down the issue of convergence of $(a_n)$. 3. Numerical computation Here is a computation of first $10^5$ terms using Mathematica: $\hspace{4em}$ Although it is not easy to read out the convergent bahavior, it seems that the error decays at least as fast as the speed of $1/\log n$. Scaling up the error by log factor indeed provides a better picture: $\hspace{8em}$ Share edited Oct 2, 2017 at 13:19 answered Oct 2, 2017 at 13:12 Sangchul LeeSangchul Lee 184k1717 gold badges300300 silver badges492492 bronze badges $\endgroup$ 3 $\begingroup$ very interesting. I'll read it carefully. Sorry for posting just a very partial disussion. I noticed your answer only after pasting mine. $\endgroup$ dfnu – dfnu 2017-10-02 13:52:15 +00:00 Commented Oct 2, 2017 at 13:52 $\begingroup$ @Matteo, There is absolutely no need for an apology! As the problem seems hard, we should appreciate any idea and input that we may come up with. Moreover I skimmed over your answer and got an impression that we are working based on almost the same idea. Even some estimations are quite close. It makes me believe that we are on track. :) $\endgroup$ Sangchul Lee – Sangchul Lee 2017-10-02 13:58:58 +00:00 Commented Oct 2, 2017 at 13:58 $\begingroup$ @Matteo here all contributions are welcome, and I am happy if you and Sangchul are working to help about this problem, it is a nice reference for all users. Many thanks to you and Sangchul. $\endgroup$ user243301 – user243301 2017-10-02 18:55:11 +00:00 Commented Oct 2, 2017 at 18:55 Add a comment | 1 $\begingroup$ Download Pari/GP and run this code N = 10^5; p = primes(N); a = vector(N); a=1.0; / 1.0 means float, with a = 1; instead the sequence of rationals is computed in closed form / for( k = 1, N-1, { a[k+1] = a[k]/p[k+1]+1/a[k];}); x = vector(N); for( k = 1, N, { x[k] = k;}); plothraw(x,a); Share answered Oct 1, 2017 at 19:21 reunsreuns 80.1k33 gold badges4848 silver badges138138 bronze badges $\endgroup$ 0 Add a comment | 0 $\begingroup$ The answer given in the meantime is very iteresting. However, as you suggested, I write my own results as answer instead of comment, even though I am far from a conclusion. I would start from an "easier" situation, with the sequence $$ a_{k+1} = \frac{a_k}{M} + \frac{1}{a_k},$$ with $M>2$. I now analyse the function $$y_M(x) = \frac{x}{M}+\frac{1}{x}$$ and interesect it with $y=x$ to look for the equilibrium point which occurs at $$x_C= \sqrt\frac{M}{M-1}.$$ The function reaches its minimum at $$x_m = \sqrt M.$$ If you take $x=f_M(x_c)=\frac{2\sqrt M}{M}$ and iterate the sequence once more, you get the point $$ f_M\left(\frac{2\sqrt M}{M}\right)=\sqrt M\left(\frac{2}{M^2}+\frac{1}{2}\right) =x_l $$ that, for $M>2$ is less then $\sqrt M$. As a consequence, once a value $$ \frac{2\sqrt{M}}{M} \leq a_k \leq \sqrt M\left(\frac{2}{M^2}+\frac{1}{2}\right)\tag{1}\label{eq:one} $$ is reached, the sequence values remain "trapped" in the range $$ \frac{2\sqrt{M}}{M} When the starting point $a_1$ is in the range $$f^{-1}_M(x_l)- If $a_1 > x_l$ then the sequence will first decrease monotonically until the range \eqref{eq:one} is reached; after that the it will behave as in 1. Finally, if $a_1 < f^{-1}_M(x_l)$, then from $a_2$ onwards, the sequence will behave as in 2. As I said, no conclusions here regarding your sequence, in which $M$ is a (growing) function of $k$. The consequences are, I believe: a. Affecting the ranges at each iteration. b. As $M$ increases, the sequences approaches the behavior of the sequence $a_k=\frac{1}{a_k}$, which of course does not converge. That is all for now. Share edited Oct 2, 2017 at 14:05 answered Oct 2, 2017 at 5:08 dfnudfnu 8,06011 gold badge1111 silver badges3131 bronze badges $\endgroup$ 1 $\begingroup$ Many thanks I am going to study yours and Sangchul's answer. $\endgroup$ user243301 – user243301 2017-10-02 18:58:36 +00:00 Commented Oct 2, 2017 at 18:58 Add a comment | 0 $\begingroup$ Assume that $1-\frac{1}{p_k} \geq a_k \geq 1-\frac{1}{k} \geq 0.8$,so $k \geq 5$. We will prove that $1-\frac{1}{p_{k+2}} \geq a_{k+2} \geq 1-\frac{1}{k+2}$. We need first to bound $a_{k+1}$ by upper and lower bound. $a_{k+1} = \frac{a_k}{p_{k+1}} +\frac{1}{a_k}$, so $\frac{d}{d a_k} (\frac{a_k}{p_{k+1}} +\frac{1}{a_k}) = \frac{1}{p_{k+1}}-\frac{1}{a_k^2} < 0$ since $1 \geq a_k \geq 0.8$ and $p_{k+1} \geq 13$, which means that an upper bound for $a_{k+1}$ is when $a_k = 1-\frac{1}{k}$ and lower bound is when $a_k = 1-\frac{1}{p_k}$. Substituting the values for $a_k = 1-\frac{1}{k} , 1-\frac{1}{p_k}$ in the equation $a_{k+1} = \frac{a_k}{p_{k+1}}+\frac{1}{a_k}$ gives the following upper and lower bound for $a_{k+1}$. $1+\frac{1}{p_k-1} +\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}} \leq a_{k+1} \leq 1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}$. The same idea to bound $a_{k+2} = \frac{a_{k+1}}{p_{k+2}} +\frac{1}{a_{k+1}}$ gives us the following upper and lower bound. $ \frac{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}}{p_{k+2}}+\frac{1}{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}} \leq a_{k+2} \leq \frac{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}}{p_{k+2}}+ \frac{1}{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}}$ Now we just need to prove that, $ \frac{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}}{p_{k+2}}+\frac{1}{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}} \geq 1-\frac{1}{k+2} $, and $\frac{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}}{p_{k+2}}+ \frac{1}{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}} \leq 1-\frac{1}{p_{k+2}} $ First, $\frac{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}}{p_{k+2}}+\frac{1}{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}-\frac{1}{k p_{k+1}}} \geq \frac{1+\frac{1}{k-1}}{p_{k+2}} +\frac{1}{1+\frac{1}{k-1}+\frac{1}{p_{k+1}}} \geq 1-\frac{1}{k+2}$ So $ \frac{1}{p_{k+2}}+\frac{1}{(k-1)p_{k+2}} +\frac{1}{\frac{k}{k-1}+\frac{1}{p_{k+1}}} \geq \frac{k+1}{k+2}$, multiply by $p_{k+2}$ to get $1+\frac{1}{k-1} +\frac{p_{k+2}}{\frac{k p_{k+1}+1}{(k-1)p_{k+1}}} \geq \frac{k+1}{k+2} p_{k+2}$, multiply by $(k-1)$, to get $ k-1+1 +\frac{p_{k+2}(k-1)(k-1)p_{k+1} }{k p_{k+1}+1} \geq \frac{(k+1)(k-1)}{k+2} p_{k+2} $ which is $ k +\frac{p_{k+2}(k-1)(k-1)p_{k+1} }{k p_{k+1}+1} \geq \frac{(k+1)(k-1)}{k+2} p_{k+2} $ multiply by $ (k+2)(k p_{k+1}+1)$, to get $k(k+2)(k p_{k+1}+1) + (k+2) p_{k+2} p_{k+1} (k-1)^2 \geq p_{k+2} (k^2-1) (k p_{k+1} +1) $, which is $k(k+2)(k p_{k+1} +1) \geq p_{k+2}((k^2-1) (k p_{k+1}+1)-p_{k+1}(k+2)(k-1)^2)$, which is $(k^2+2k)(k p_{k+1}+1) \geq p_{k+2}(2 k p_{k+1}-2p_{k+1}+k^2-1)$, We have that $k^2+2k \geq k^2$, so we arrive at $ k^2 (k p_{k+1} +1) \geq k^2 (k p_{k+1}) \geq p_{k+2}(2 k p_{k+1}+k^2) \geq p_{k+2}(2 k p_{k+1}-2p_{k+1}+k^2-1)$, which is $ k^3 p_{k+1} \geq p_{k+2}(2 k p_{k+1} +k^2)$ We know that $k^2 \leq k p_{k+1}$, so $k^3 p_{k+1} \geq p_{k+2}(2 k p_{k+1}+k p_{k+1}) \geq p_{k+2}(2 k p_{k+1} +k^2)$, which is $ k^3 p_{k+1} \geq 3 k p_{k+2} p_{k+1}$ , which is $k^3 \geq 3 p_{k+2}$, which is $ k^2 \geq 3p_{k+2}$ which is true for all $k \geq 12$. Second part, $\frac{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}}{p_{k+2}}+ \frac{1}{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}} \leq 1-\frac{1}{p_{k+2}} $, multiply by $p_{k+2}$, we get that $1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}+ \frac{p_{k+2}}{1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}} \leq p_{k+2}-1 $, multiply by $ 1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}$ to get that $ (1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}})^2+p_{k+2} \leq p_{k+2}(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}})-(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}})$ At least $p_{k+2} \geq p_k +6$ (Hint : no $3$ consecutive twin primes) and $p_{k+2} \geq p_{k+1}+2$, so $(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}})^2+(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}) \leq p_{k+2}(\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}) $ , by the idea above we get that $(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}})^2+(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}) \leq (\frac{p_k+6}{p_{k-1}}+\frac{p_{k+1}+2}{p_{k+1}}-\frac{p_{k+2}}{p_k p_{k+1}}) $, we get that $(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}})^2+(1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}}-\frac{1}{p_k p_{k+1}}) \leq (1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}})^2+1+\frac{1}{p_{k-1}}+\frac{1}{p_{k+1}} \leq (\frac{p_k+6}{p_{k-1}}+\frac{p_{k+1}+2}{p_{k+1}}-\frac{p_{k+2}}{p_k p_{k+1}}) $ Its easy to prove that $\frac{1}{p_{k}-1} +\frac{1}{p_{k+1}} \leq \frac{1}{p_k-1}+\frac{1}{p_k+2} \leq \frac{2}{p_k}$ for all $k \geq 3$. $(1+\frac{2}{p_k})^2+1+\frac{2}{p_k} \leq 1+\frac{7}{p_k-1}+1+\frac{2}{p_{k+1}}-\frac{p_{k+2}}{p_k p_{k+1}}$, which is $1+\frac{4}{p_k}+\frac{4}{p_k^2}+1+\frac{2}{p_k} \leq 1+\frac{7}{p_k}+1+\frac{2}{p_{k+1}} -\frac{p_{k+2}}{p_k p_{k+1}} \leq 1+\frac{7}{p_k-1}+1+\frac{2}{p_{k+1}} -\frac{p_{k+2}}{p_k p_{k+1}} $ Which is just $\frac{4}{p_k^2}+\frac{p_{k+2}}{p_k p_{k+1}} \leq \frac{1}{p_k}+\frac{2}{p_{k+1}}$ There is a prime between $[x,\frac{6}{5}x]$ for all $x \geq 25$,so $\frac{4}{p_k^2} +\frac{1.44p_k}{p_k^2} \leq \frac{1}{p_k}+\frac{2}{1.2p_k}$, which is $ \frac{4}{p_k^2} +\frac{1.44}{p_k} \leq \frac{8}{3p_k}$ which is true for all $k \geq 10$. Thus concluding the proof for all $k\geq 12$ but we need to check for small $k$, checking for small $k$ we get that its true for all $k\geq 19$ and $k$ is odd. And since $a_k$ for even $k$ converges according to $a_k$ for $k$ odd, then we can conclude that $\lim \limits_{k \to \infty} a_k =1$. Share answered Oct 16, 2017 at 7:46 user411780user411780 $\endgroup$ 3 $\begingroup$ it bugged me that such a beautiful question with no complete answer, so i was determined that first thing in the morning is sitting down and writing a proof for the question (actually not the first thing, first i listened to Firooz morning songs, but then right away i start solving the problem, i really enjoyed solving it. $\endgroup$ user411780 – user411780 2017-10-16 07:55:54 +00:00 Commented Oct 16, 2017 at 7:55 $\begingroup$ Many thanks, my skills in mathematics aren't the best thus I am going to need some days to read your proof. Many thanks for your attention and work. $\endgroup$ user243301 – user243301 2017-10-16 09:02:31 +00:00 Commented Oct 16, 2017 at 9:02 $\begingroup$ you are very welcome, you won't believe how much effort i put to the answer, i just could not agree that such amazing question with no full answer, i kept bugging me, until today :) $\endgroup$ user411780 – user411780 2017-10-16 18:51:29 +00:00 Commented Oct 16, 2017 at 18:51 Add a comment | You must log in to answer this question. Featured on Meta Introducing a new proactive anti-spam measure Spevacus has joined us as a Community Manager stackoverflow.ai - rebuilt for attribution Community Asks Sprint Announcement - September 2025 Related 0 How to prove a telescoping series converges ??? 0 Number of ways 1a,1b,5 can add up to n (with this being a permutation) Number of monomials in $a_n=a_{n-1}+(a_{n-2})^2$ with $a_1=a$, $a_2=b$ 2 Follow-up question on conditionally convergent series. 0 Trying to solve a simple-looking recurrence relation Consider the following recurrence, $a_n=\frac{4a_{n-1}^3+2a_{n-1}-a_{n-2}}{1+4a_{n-1}a_{n-2}}$ where $a_0=0, a_1=1$. Show every $a_n$ is an integer. Hot Network Questions Why is the definite article used in “Mi deporte favorito es el fútbol”? Passengers on a flight vote on the destination, "It's democracy!" "Unexpected"-type comic story. Aboard a space ark/colony ship. 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https://www.edraw.ai/feature/online-probability-tree-creator.html
Edraw.AI is not ready for mobile devices. Try our apps! Make diagrams: flowcharts, blueprints, UML, etc EdrawMax Make a mindmap, timelines, and more maps EdrawMind Online probability tree maker Map out your decisions and predict outcomes with ease using Edraw.AI’s probability tree maker. Real-time editing, robust security, and quick sharing; everything you need for informed decision-making! Get started, it's free! Analyze process outcomes and risks with our simple probability tree maker! Intuitive interface Our tree diagram maker is designed to make your work easier, faster, and more effective. On Edraw.AI, you can quickly design your decision paths, adjust details, and customize every element. Map out your decision paths and visualize potential outcomes in no time. Collaborate anytime, anywhere Team effort is the key to making wise decisions. Edraw.AI lets you and your team collaborate in real time, no matter where you are. Work together, share ideas, make instant edits, and leave feedback, all with a few clicks. Share and export with ease Once your probability tree is ready, sharing it with others is simple. Import or download your diagram in various formats like VSDX, CAD, Excel, and more. Alternatively, share it via email, generate a public link, or even post it on social media. Ideal tool for collaboration Efficiency Boost With multi-device support and access on the cloud, team members can access and edit files anytime, reducing repetitive tasks and significantly improving efficiency. All-in-one Solution Edraw.AI supports over 210 drawing types, from mind maps to flowcharts. This extensive range allows teams to create diverse visual content within a single platform. Enhanced Communication Visual diagrams simplify complex ideas, improving communication within teams and with external partners, making discussions and decision-making more efficient and clear. Seamless Collaboration It allows team members to co-edit and share diagrams in real-time, ensuring smooth workflow without the need for constant tool switching or delays. Get started. It's free! How to make a probability tree diagram with Edraw.AI? Empowering visual creativity with AIand templates. Get started, it's free! Edraw.AI Start for visual collaboration. Get unlimited access to40+ AI tools and premium templates. Start Online Free
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https://www.writing-world.com/rights/lynch.shtml
| | | | | --- --- | | Your Guide to a Successful Writing Career | | | HOME | CONTACT | ADVERTISE! | HELPFUL LINKS | ARTICLE INDEX Launching Your Writing Career Building Skills/Polishing Your Prose Queries, Submissions & Marketing | Business, Finance & Tax Issues Understanding Rights & Copyright | Coping with the Writing Life Time Management for Writers Ramblings on the Writing Life | Publishing Self-Publishing POD & E-Publishing Promoting Your Writing Blogs, Websites & Social Media Elements of Great Fiction Characters, Dialogue & Viewpoint Structure, Genres & Publishing Tips Mystery Romance SF/Fantasy Writing for Children | Successful Freelancing Tips Finding Nonfiction Markets Travel Writing & Photography Business & Technical Writing Writing for International Markets | Poetry & Greeting Cards Essays, Memoirs & Creative Nonfiction | | | | | | --- The Perfectly Acceptable Practice of Literary Theft: Plagiarism, Copyright, and the Eighteenth Century by Jack Lynch--- In the very first issue of Poor Richard's Almanac, late in 1732, the young Benjamin Franklin teased a rival publisher and editor, Titan Leeds, by predicting that his death would occur on October 17, 1733. Leeds was not amused, and published a petulant response in his American Almanack. In the next few issues Franklin maintained, with mock solemnity, that his prediction had in fact come true, even though Leeds kept on writing: "Whatever he may pretend, 'tis undoubtedly true that he is really defunct and dead." The humorless Leeds fumed at the treatment he got from the upstart almanac publisher, while Franklin's reputation was bolstered by his clever hoax. It was a witty satire, it was a daring stroke for an up-and-coming writer -- and it was stolen. The idea comes from Jonathan Swift, whose Bickerstaff Papers appeared in 1708 and 1709. There the fictional Isaac Bickerstaff taunted John Partridge, a quack and almanac-writer, by predicting his death and then pretending to disbelieve Partridge's protestations that he was still alive. Every element of Franklin's sham comes straight from Swift's essays of a quarter-century before, and yet Franklin nowhere credits his source. And though in this case he paraphrased Swift rather than quoting him directly, he often stole words as well as ideas, as when he filched from Rabelais, taking long passages from an English translation of Gargantua and Pantagruel in the Almanac for 1739. Franklin, in short, was a serial plagiarist. Is this some dirty secret from his past, which would have disqualified him from a position of responsibility had it come out during his lifetime? Hardly. When several historians were recently charged with plagiarizing passages in their works, the scandal occupied front pages and buzzed in faculty lounges for months. But when Franklin stole whole works, no one cared. Far from being a scandal, it was almost the norm. In England, Laurence Sterne stole long passages from Robert Burton's Anatomy of Melancholy as he worked on Tristram Shandy, and John Wesley brazenly incorporated much of Samuel Johnson's Taxation No Tyranny into his own Calm Address to Our American Colonies. On both sides of the Atlantic, newspapers and magazines routinely lifted articles from each other without credit or payment. When the Roman poet Martial accused a rival, Fidentinus, of stealing his verses, he called him a "kidnapper" -- in Latin, plagiarius. The term stuck. The Latin word made its way into English in 1601 when Ben Jonson described a literary thief as a plagiary, a word Jonson's near-namesake, Samuel Johnson, defined in his Dictionary of 1755 as "A thief in literature; one who steals the thoughts or writings of another" and "The crime of literary theft." But, odd though it may seem to us, plagiarism hasn't always been viewed as a crime. Many people throughout history didn't regard words or ideas as property at all, and saw nothing wrong with "borrowing" liberally from others. For centuries, writers (and painters and sculptors and composers) were actually encouraged to copy the masters as closely as possible. Some writers were blamed for being presumptuous enough to invent their own plots. The situations, characters, and ideas in the classics were, after all, the "publica materies," the common property, which the great Roman poet and critic Horace told young writers to pillage. So you'll find hardly any original plots in Shakespeare's thirty-seven or so plays: as Alexander Lindey put it in his study of plagiarism, Shakespeare "evinced a marked propensity for avoiding unnecessary invention." He routinely inserted speeches from history books and other plays into his own, and even in his least derivative work, The Tempest, you'll find long passages copied out of the French writer Montaigne. In the 18th century, writers were still expected to find their material in other writers. Alexander Pope described the plight of the poet who wants to be original by imitating Nature: "Nature and Homer were, he found, the same." We have no choice but to steal from the classics, said Pope, because "To copy Nature is to copy them." It was only during the 18th century that "originality" in the modern sense became an ideal. An important milestone is Edward Young's Conjectures Concerning Original Composition, which appeared in London in 1759. There Young celebrates novelty and attacks imitation: "Originals are, and ought to be, great Favourites, for they are great Benefactors; they extend the Republic of Letters, and add a new province to its dominion: Imitators only give us a sort of Duplicates of what we had, possibly much better, before." Good authors are original, bad authors copy, and copying is no better than "sordid Theft." It is, though, an odd sort of theft, because words and ideas are an odd sort of property. If I steal your wallet, your money is gone, but if I steal your words or ideas, you've lost nothing tangible. It's no coincidence that the law began thinking seriously about "intellectual property" -- the notion that you "own" your ideas -- right around the time poets and critics began to value originality. Although authors had been complaining about literary theft since ancient times, they had no recourse until 10 April 1710, when the world's first copyright act was passed in London: "An Act for the Encouragement of Learning, by Vesting the Copies of Printed Books in the Author's or Purchasers of Such Copies," known as the Statute of Anne. A copyright is just what the name suggests: the right to make copies of a work, whether whole or in part. Unauthorized copies of any sort were a problem, but the Statute of Anne wasn't actually aimed at plagiarists. The real target was literary pirates, who reprinted works with the author's name intact but without permission or payment. Technically, plagiarism is no crime. Plagiarism is an ethical matter, copyright is a legal matter, and not every case of plagiarism is against the law. But in practice, many plagiarists violate copyright statutes, since recent works -- usually the ones most worth stealing -- cannot legally be copied, whether by pirates or plagiarists. Paradoxically, the loudest objections to the Statute of Anne came from the booksellers and publishers. They insisted on an exclusive common-law right to print the books on their lists, a right that they said lasted forever. It took two thirds of a century for the courts to work out the real meaning of the Statute of Anne. The verdict finally came in a case called Donaldson v. Beckett, decided in the House of Lords in 1774. Publishers have no perpetual common-law copyright, said the Lords; the government gives authors the exclusive but limited right to copy their works. Authors can sell that right to publishers, but when that right expires, works can be copied freely by anyone. America inherited Britain's legal system and its ideas about intellectual property, and by the time the new nation began writing its own laws, copyright was a major concern. In May 1783, the Colonial Congress urged the states "to secure to the authors or publishers of any new books . . . the copy right of such books." Connecticut was the first to comply with "An Act for the Encouragement of Literature and Genius," and in the next three years, all but one of the original thirteen states passed copyright laws. But each law's scope was restricted to a single state: an author who wanted to protect his work had to register a dozen copyrights in a dozen states under a dozen sets of rules. Noah Webster complained bitterly about traveling up and down the country in the 1780s seeking protection for his American Speller. Writers pleaded that copyright should be a Federal issue. The framers of the U.S. Constitution paid attention. They took intellectual property so seriously that it might be called the first right to be protected by the Constitution. Before the ratification of the Bill of Rights, the Constitution contained the word "right" exactly once, in Article I, Section 8: the Congress has the authority "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." It wasn't long before Congress took up its Constitutional mandate. On April 15, 1789, David Ramsay of South Carolina, author of The History of the Revolution of South Carolina, petitioned Congress to protect that book and his next. The House voted to form a select committee, and Thomas Tudor Tucker of South Carolina, Alexander White of Virginia, and Benjamin Huntington of Connecticut met to consider a course of action. On April 20, Tucker reported on the need for a copyright law, and on June 23, Huntington introduced an eleven-page bill: H.R. 10, from the first session of the first Congress. Echoing the language of the Constitution, he called it "A bill to promote the progress of science and useful arts by securing to authors and inventors the exclusive right to their respective writings and inventions." Most of Huntington's bill was actually concerned with patents for inventions, not copyrights for books, but in the second Congressional session the two kinds of intellectual property were split into two bills. While the bills were being debated, President George Washington devoted part of his first State of the Union Address on 8 January 1790 to the topic: "There is nothing which can better deserve your patronage," he told the Congress, "than the promotion of science and literature. Knowledge is, in every country, the surest basis of public happiness." The Congress agreed, and the new bill, "A bill for the encouragement of learning, by securing the copies of maps, charts, books, and other writings, to the authors and proprietors of such copies, during the times therein mentioned," passed the House on 30 April and the Senate on 14 May. It was signed by Washington on 31 May 1790, and became America's first Federal copyright act. For the first time, authors and proprietors were given "the sole right and liberty of printing, reprinting, publishing and vending" their works. "The crime of literary theft" had actually become a crime, and the sort of pilfering that raised no eyebrows in Franklin's audience a half-century earlier was now a real breach of ethics. The story didn't end there. Over the next century, more than two hundred copyright bills were debated in Congress, twenty-five of which became law. At first copyright didn't extend to music or art; it didn't safeguard the right to make "derivative" works like translations or dramatizations; and it didn't respect international copyright conventions. British authors had no protection across the Atlantic, and unscrupulous American printers sometimes bribed their London counterparts to give them advance copies of English books. (Charles Dickens famously complained about the practice: in 1842 he called it "a horrible thing that scoundrel-booksellers should grow rich" from English works in American newspapers that "no honest man would admit . . . into his house, for a water-closet doormat.") America entered into a few international copyright treaties in the 19th century, but resisted joining the Berne Convention -- the modern international copyright system -- until 1988, fully 102 years after its founding. This brief history of the first copyright laws might help us to understand the proper function of intellectual property legislation today. Protecting the property rights of authors was only part of their intention: their more important job was protecting the public and promoting the public good. Plagiaries and pirates hurt the people they steal from, but they also hurt their audiences by selling them stolen goods and discouraging writers from sharing their thoughts. We can see this concern with the public in the Statute of Anne, which was devised "for the encouragement of learned men to compose and write useful books"; we can see it in the U.S. Constitution, which worked "To promote the Progress of Science and useful Arts." They promote this progress in two ways. First, by protecting creators they encourage them to create again. The government gives authors a short-term monopoly because the public will be better served when writers are rewarded. Second, and just as important, they make copyright of a limited duration, so that after the short-term monopoly expires, works enter the "public domain." They then become part of the "publica materies" Horace had written about two thousand years ago, the common stock from which everyone can draw. The Statute of Anne, remember, put an end to the supposed perpetual copyright the booksellers claimed for themselves. Samuel Johnson insisted that "reason and the interests of learning are against" unlimited copyright, "for were it to be perpetual, no book, however useful, could be universally diffused amongst mankind, should the proprietor take it into his head to restrain its circulation. For the good of the world, therefore, whatever valuable work has once been created by an author, and issued out by him, should be understood as no longer in his power, but as belonging to the publick." Fixed-term copyright ensures that works and ideas will eventually become the shared property of an entire culture. Anyone can quote from them without fear of prosecution, and publishers can compete to make them available at the lowest prices. Many have argued in recent years that our legislators have forgotten this lesson, and that copyright, which was invented specifically to take power away from the monopolist publishers and to give it for a fixed time to the authors, has instead begun to retard the progress of the useful arts. Most authors grant their copyrights to publishers in order to appear in print, and publishers and the media firms that own them are naturally eager to use the law to maximize their profits. Corporate interests have worked to increase the "limited Times" guaranteed in the Constitution to previously unimagined lengths, hardly distinguishable from the perpetual copyrights the 18-century booksellers urged. The first copyright laws protected a work for fourteen years from its publication. The current U.S. copyright law, by contrast, protects most works for the duration of the author's life plus another 70 years, meaning something published this year may be under monopoly control until the next century. Works published today by a young writer who enjoys a long life may not enter the public domain until 2150, when everyone now alive will be long dead. It is hard to argue that protecting the profits of an author's publisher's stockholders' great-grandchildren a century and a half into the future will encourage authors or increase the stock of ideas usable by the public. One valuable inheritance of our 18-century past is an admiration for originality, and with it a respect for others' intellectual property rights. We now see plagiarists as thieves, and punish them when they are caught. No modern author could expect the friendly reception Franklin got when he stole from other writers. But we should be careful not to go too far in the other direction by stifling the free exchange of ideas. The law protects us from unscrupulous writers, but we grant authors copyright protection only on the condition that their works will eventually serve the public good. Copyright © 2006 Jack Lynch This article originally appeared in Colonial Williamsburg. This article may not be reprinted without the author's written permission. --- Jack Lynch is an Associate Professor in the English department of the Newark campus of Rutgers University, specializing in the English literature of the 18th century. His books include a Anniversary Essays on Johnson's "Dictionary, an abridgement of f Johnson's Dictionary, and a forthcoming book on forgery, fakery, and fraud, provisionally called Deception and Detection in Eighteenth-Century Britain. Lynch is the host of the popular "Guide to Grammar and Style" website ( and is in the process of turning this site into a book. He also maintains several sites on 18th-century history and literature; for more information, visit his bio page at --- | | | | This free script provided by JavaScript Kit | | | | Becoming a successful writer isn't just about mastering great writing skills. It's also about overcoming the challenges and obstacles of the writing life: Rejection, fear of failure, lack of time, writer's block, the "Am I Really a Writer?" syndrome, and, of course, friends and family who just don't get it. Fortunately, you're not alone. We've all been there. So here's a handy "survival guide" that will bring you inspiration, motivation, support and good old-fashioned advice to help you through the tough times. Don't let those writing gremlins keep you from achieving your dreams! More from Moira Allen: | | | | | | Copyright © 2025 by Moira Allen. All rights reserved. All materials on this site are the property of their authors and may not be reprinted without the author's written permission, unless otherwise indicated. For more information please contact Moira Allen, Editor Please read our Privacy Statement. | | | |
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https://www.youtube.com/watch?v=vt6WjF1O_08
Autoionization of water | Acids and bases | AP Chemistry | Khan Academy Khan Academy 9040000 subscribers 385 likes Description 29817 views Posted: 31 Jul 2021 Keep going! Check out the next lesson and practice what you’re learning: In the autoionization of water, a proton is transferred from one water molecule to another to produce a hydronium ion (H₃O⁺) and a hydroxide ion (OH⁻). The equilibrium expression for this reaction is Kw = [H₃O⁺][OH⁻], where Kw is the autoionization constant for water. At 25°C, the value of Kw is 1.0 x 10⁻¹⁴. In pure water, the concentrations of H₃O⁺ and OH⁻ are equal, and the water is considered to be neutral. View more lessons or practice this subject at Khan Academy is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We offer quizzes, questions, instructional videos, and articles on a range of academic subjects, including math, biology, chemistry, physics, history, economics, finance, grammar, preschool learning, and more. We provide teachers with tools and data so they can help their students develop the skills, habits, and mindsets for success in school and beyond. Khan Academy has been translated into dozens of languages, and 15 million people around the globe learn on Khan Academy every month. As a 501(c)(3) nonprofit organization, we would love your help! Donate or volunteer today! Donate here: Volunteer here: 10 comments Transcript: the autoionization of water refers to the reaction of water molecules to form two ions the hydronium ion which is h3o plus and the hydroxide ion which is oh minus water can function as an acid or base and in this reaction one water molecule functions as a bronsted-lowry acid and donates a proton and another water molecule functions as a bronsted-lowry base and accepts a proton in the reaction the base takes an h plus ion from the acid and these two electrons are left behind on this oxygen adding an h plus to h2o gives the hydronium ion h3o plus and taking away an h plus from h2o gives the hydroxide ion o h minus we can write an equilibrium constant expression for this reaction so we would write the equilibrium constant k is equal to we would start with our products we'd have the concentration of hydronium ions and since we have a coefficient of one in front of hydronium and the balanced equation it'd be the concentration of hydronium ions raised to the first power times the concentration of hydroxide ions and once again there's a coefficient of one the balanced equation so it's the concentration of hydroxide ions raised to the first power for the reactants liquid water is left out of the equilibrium constant expression normally we would write k c where the c stands for concentration for the equilibrium constant since we're dealing with concentrations however this is a special equilibrium constant expression for the autoionization of water so instead of writing kc we're going to write kw where w stands for water kw is equal to 1.0 times 10 to the negative 14th at 25 degrees celsius and with such a low value for kw so this value is much less than one that tells us at equilibrium we have an extremely small concentration of hydronium and hydroxide ions so mostly we have h2o molecules at equilibrium let's go ahead and solve for the concentration of hydronium ions and hydroxide ions at equilibrium in the balanced equation there's a coefficient of one in front of both hydronium and hydroxide therefore at equilibrium these two concentrations are equal since we don't know what those concentrations are we're going to represent it by writing in here x so this would be x times x is equal to 1.0 times 10 to the negative 14. so we would have x squared is equal to 1.0 times 10 to the negative 14. and taking the square root of both sides we would find that x is equal to 1.0 times 10 to the negative seventh therefore if we had a sample of pure water at 25 degrees celsius the concentration of hydronium ions and the concentration of hydroxide ions would be equal to 1.0 times 10 to the negative seventh instead of using two water molecules to show the autoionization of water it's also possible to show it using only one water molecule so h2o could break up to form h plus and o h minus so h plus which is the hydrogen ion is sometimes used interchangeably with h3o plus which is the hydronium ion we've just seen that pure water has the concentration of hydronium ions equal to the concentration of hydroxide ions therefore pure water is a neutral substance and for any aqueous solution where the concentration of hydronium ion is equal to the concentration of hydroxide ion we would classify that as a neutral solution if an aqueous solution has a concentration of hydronium ions that's greater than the concentration of hydroxide ions we would classify the solution as an acidic solution and if an aqueous solution has a concentration of hydronium ions that's less than the concentration of hydroxide ions or you could say the concentration of hydroxide ions is greater than that of hydronium the solution would be considered a basic solution and the equation that we've already talked about the concentration of hydronium ions times the concentration of hydroxide ions is equal to kw which which is equal to 1.0 times 10 to the negative 14 at 25 degrees celsius this equation is true if you're dealing with an acidic solution a neutral solution or a basic solution and i'll call this equation the kw equation from now on let's say we have an aqueous solution and the concentration of hydronium ions in solution is equal to 4.0 times 10 to the negative 6 molar at 25 degrees celsius and our goal is to calculate the concentration of hydroxide ions in this solution at 25 degrees celsius to solve for the concentration of hydroxide ion we can use our kw equation so we need to plug in for the concentration of hydronium ion so that gives us 4.0 times 10 to the negative six times the concentration of hydroxide ion which we'll just go ahead and make x here and all that's equal to kw which is equal to 1.0 times 10 to the negative 14. solving for x we find that x is equal to 2.5 times 10 to the negative 9. and since x is equal to the concentration of hydroxide ion the concentration of hydroxide ion is equal to 2.5 times 10 to the negative ninth molar for this aqueous solution the concentration of hydronium ion is greater than the concentration of hydroxide ion therefore this is an acidic solution so let me go ahead and write that in here this is an acidic solution an equilibrium constant is only constant at a specific temperature for example at 25 degrees celsius kw is equal to 1.0 times 10 to the negative 14. but if you change the temperature you change the value for kw at 50 degrees celsius kw is equal to 5.5 times 10 to the negative 14th so an increase in temperature from 25 degrees celsius to 50 degrees celsius causes an increase in the value for kw so increase in temperature causes an increase in kw and we can use le chatelier's principle to predict if the autoionization of water is an endothermic reaction or an exothermic reaction an increase in kw means an increased concentration of hydronium ion and hydroxide ion at equilibrium therefore the net reaction must have gone to the right to increase the amount of our products and if we treat heat as a reactant and we increase the temperature it's as if we've increased the amount of one of our reactants therefore according to le chatelier's principle the net reaction is going to shift to the right to make more of the product since that's what we observe by increasing the value for kw we know that the autoionization of water is an endothermic reaction if we had put heat on the product side and treated this like an exothermic reaction we would have gotten a shift in the wrong direction we've got to shift back to the left so we know it's not exothermic finally let's calculate the concentration of hydronium ions and hydroxide ions in a sample of pure water at 50 degrees celsius we can still use the kw equation so kw is equal to the concentration of hydronium ions times the concentration of hydroxide ions however since the temperature is now 50 degrees celsius we can't use 1.0 times 10 to the negative 14 because that's the kw at 25 degrees celsius we need to use the kw at 50 degrees celsius which is 5.5 times 10 to the negative 14th for the autoionization of water the mole ratio of hydronium ion to hydroxide ion is one to one therefore the concentration of hydronium ion is equal to the concentration of hydroxide ion so when we plug in for hydronium if you say that concentration is x and the concentration of hydroxide would also be x so we have x times x is equal to kw which is equal to 5.5 times 10 to the negative 14. so x squared is equal to 5.5 times 10 to the negative 14th and to solve for x we simply take the square root of both sides so x is equal to 2.3 times 10 to the negative seventh so the concentration of hydronium ions is equal to the concentration of hydroxide ions which is 2.3 times 10 to the negative seventh molar notice that this is a higher concentration than we got at 25 degrees celsius which makes sense because the value for kw has increased however since the concentration of hydronium is still equal to the concentration of hydroxide ions pure water is still neutral
4031
http://clubztutoring.com/ed-resources/math/graphs-definitions-examples-6-7-2/
Graphs: Definitions and Examples Graphs: Definitions, Formulas, & Examples GET TUTORING NEAR ME! By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy Introduction Graphs are powerful data structures used to represent relationships between various entities. They are extensively used in computer science, mathematics, social sciences, and other fields. In this article, we will delve into the world of graphs, exploring their definitions, types, and real-life examples. We will also provide an FAQ section to address common queries, followed by a quiz to test your understanding of the topic. Definitions: Examples: FAQ: Quiz: Answers: Conclusion: Graphs are versatile and powerful data structures that help us understand and analyze relationships between entities. They find applications in various fields, from computer science to social sciences and beyond. Understanding the different types of graphs, their representations, and algorithms associated with them can greatly enhance problem-solving capabilities. Whether it’s modeling social networks, analyzing transportation systems, or optimizing resource allocation, graphs provide a valuable framework for visualizing and solving real-world problems. If you’re interested in online or in-person tutoring on this subject, please contact us and we would be happy to assist! We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson. Testimonials Club Z! has connected me with a tutor through their online platform! This was exactly the one-on-one attention I needed for my math exam. I was very pleased with the sessions and ClubZ’s online tutoring interface. My son was suffering from low confidence in his educational abilities. I was in need of help and quick. Club Z! assigned Charlotte (our tutor) and we love her! My son’s grades went from D’s to A’s and B’s. I’ve been using Club Z’s online classrooms to receive some help and tutoring for 2 of my college classes. I must say that I am very impressed by the functionality and ease of use of their online App. Working online with my tutor has been a piece of cake. Thanks Z. Jonathan is doing really well in all of his classes this semester, 5 A’s & 2 B’s (he has a computer essentials class instead of PLC). In his Algebra class that Nathan is helping him with he has an A+. Sarah is very positive, enthusiastic and encourages my daughter to do better each time she comes. My daughter’s grade has improved, we are very grateful for Sarah and that she is tutoring our daughter. Way to go ClubZ! Who We Are Study With Us Join the Club Subscribe to Our Newsletter Receive discounts, study tips, and more. Please leave this field empty. START TUTORING TODAY! Fill out the form above or give us a call at: 866-442-2582
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https://wmueller.com/precalculus/families/fundamental.html
The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra Theorem: A polynomial of degree n can have at most n distinct real roots. The usefuleness of the Fundamental Theorem comes from the limits that it sets. At most tells us to stop looking whenever we have found n roots of a polynomial of degree n . There are no more. For example, we may find – by trial and error, looking at the graph, or other means – that the polynomial P(x) = 2 x 3 + x 2 – x has three real roots: P(–1) = 0 P(0) = 0 P(1/2) = 0 . Since the polynomial has degree 3, we would be wasting our time looking for others. Having at most n roots, of course, is no guarantee that a polynomial will actually cross the x-axis this maximum number of allowable times. For example, the cubic polynomial P(x) = x 3 – x 2 + x – 1 has only one real root. (Can you find it?) The possible number of roots between 0 and n depends on how we count. If we count distinct roots (as we usually do), then: A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots. This is of little help, except to tell us that polynomials of odd degree must have at least one real root. If we count roots according to their multiplicity (see The Factor Theorem), then: A polynomial of degree n can have only an even number fewer than n real roots. Thus, when we count multiplicity, a cubic polynomial can have only three roots or one root; a quadratic polynomial can have only two roots or zero roots. This is useful to know when factoring a polynomial. The Fundamental Theorem, in its most general form (involving complex numbers), has a long history. Finding the roots of polynomials is an activity that has engaged mathematicians for many centuries.
4033
https://stackoverflow.com/questions/20269703/intersection-of-line-segment-and-convex-polygon
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Home Questions AI Assist Labs Tags Challenges Chat Articles Users Jobs Companies Collectives Communities for your favorite technologies. Explore all Collectives Teams Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Try Teams for freeExplore Teams 3. Teams 4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams Collectives™ on Stack Overflow Find centralized, trusted content and collaborate around the technologies you use most. Learn more about Collectives Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Hang on, you can't upvote just yet. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Intersection of line segment and convex polygon Ask Question Asked 11 years, 10 months ago Modified2 years, 5 months ago Viewed 5k times This question shows research effort; it is useful and clear 6 Save this question. Show activity on this post. Looking for a O(logn) algorithm to identify the line segments of the convex polygon which intersect with an extended line segment. It is known for sure that the line segment lies inside the convex polygon completely. Example: Input: ab /Line segment/ , {1,2,3,4,5,6} /Convex polygon vertices in CCW order alongwith their coordinates/ Output: 3-4,5-6 This can be done by getting the equation of all the lines and checking if they intersect but that would be O(n) as n lines need to be checked for intersection. I think it should be possible to use Binary search(because of the logn bound) to reduce the complexity but I can't understand on what to apply it. algorithm math graphics computational-geometry Share Share a link to this question Copy linkCC BY-SA 3.0 Improve this question Follow Follow this question to receive notifications edited Jun 20, 2020 at 9:12 CommunityBot 1 1 1 silver badge asked Nov 28, 2013 at 15:23 Sahil SareenSahil Sareen 1,834 3 3 gold badges 26 26 silver badges 40 40 bronze badges 8 Yes, binary search would do the trick here. And another hint - you can use that the cross (vector) product of the points of a polygon side, which is bellow the line are both negative(positive) and the points of a side which is above the line are both positive(negative). Hope that helps, and does not spoil it too bad.yasen –yasen 2013-11-28 16:04:13 +00:00 Commented Nov 28, 2013 at 16:04 On what do I apply Binary Search?Sahil Sareen –Sahil Sareen 2013-11-28 16:16:21 +00:00 Commented Nov 28, 2013 at 16:16 1 I have an idea, but there are some corner cases for it. I will try to define this idea completely and when I'm done I'll get back to you. (in short, you can use ternary search over the distance from the line, but in some cases you can lose solutions in that way)yasen –yasen 2013-11-28 16:59:24 +00:00 Commented Nov 28, 2013 at 16:59 An important question - how do you store the data about the polygon?Danstahr –Danstahr 2013-11-28 18:23:37 +00:00 Commented Nov 28, 2013 at 18:23 2 cs.princeton.edu/~chazelle/pubs/… Theorem 3 seems to solve the problem for dynamic polygons as well.ile –ile 2013-11-29 07:13:13 +00:00 Commented Nov 29, 2013 at 7:13 |Show 3 more comments 2 Answers 2 Sorted by: Reset to default This answer is useful 2 Save this answer. Show activity on this post. At first, you need to work with oriented polygon edges and store them in an array (or may be in another data structure, which allows direct access with time complexity not more than O(logN)). The linked list isn't good for this problem. Also you need to assign orientation to your extended segment - let's say it's oriented from A to B. Then it partitions the plane into two halfplanes - left and right. You choose your initial edge (with vertices 0 and 1) and then the middle edge (with vertices [n/2]-1 and [n/2]). There are two cases - the initial edge intersects the extended segment or it doesn't. I'll consider the first case here, leaving the second one to you. Also I'll assume the initial edge lies entirely in the right halfplane (the left plane case is symmetric). The middle edge partitions the polygon into two edge paths - I'll call them the first one (vertices from 0 to [n/2]) and second one (vertices from [n/2] to 0). Five cases are possible - the middle edge can: Lie entirely in the right halplane (the same as the initial edge) and follow the initial edge - then you recursively analyze the second path. Lie entirely in the right halplane (the same as the initial edge) and precede the initial edge - then you recursively analyze the first path. Lie entirely in the left halfplane (not the one where the initial edge is) - then you have to recursively analyze both paths. Intersect the extended segment going from right halfplane to the left halfplane - one intersection is found, and then you recursively analyze the second path. Intersect the extended segment going from left halfplane to the right halfplane - one intersection is found, then you recursively analyze the first path. So - the most "inconvenient" case is the (2) - you can't drop any paths in this case, but it looks like it can't be repeated for the whole polygon. Also you'll have to calculate relationship between oriented polygon edges - "follows/precedes". It can be done using the relative edge angle - the "following" edge must turn to the left relative to the "preceding" edge (because of convexity). Share Share a link to this answer Copy linkCC BY-SA 3.0 Improve this answer Follow Follow this answer to receive notifications edited Dec 7, 2013 at 0:31 answered Dec 6, 2013 at 21:08 HEKTOHEKTO 4,246 2 2 gold badges 32 32 silver badges 51 51 bronze badges Comments Add a comment This answer is useful 0 Save this answer. Show activity on this post. This answer was confusing so I wanted to provide some more detail in a different way. Lets assume you have your data in array P and you are checking against Line U. p_0 is the most left lowest point. I.e p_0.x < p_i.x and in ties ensure p_0.y < p_i.y. P is sorted in ccw like most ConvexHulls are. You also have p_m where m is the half way point i.e n/2 at first. We define L,M,H as our binary search indices with L = 0, M = n/2, H = n-1. I'm going to write recursion but you could unroll this. Base case: Is the "polygon" array has n<= 3 points. In this case just check every line in the triangle or line for intersection with U O(1). Recursive Step: Do L_m = Line(p_0, p_m) intersect with U to find p_I, O(1). If p_I is NULL we know that U is ccw or cw from L_m you can use a directed Orientation Test to find which in O(1). If its ccw, recurse with ConvexLineInt({p_0,p_m,...,p_h},U) else ConvexLineInt({p_0,p_l,...,p_m},U). If p_I exists it must occur among the line L_m i.e it is in a fully ordered set and we check these cases: L_m.0 <= p_I <= L_m.1 (in between) => return Line intersects p_I < L_m.0 i.e is to the left of the polygon. We calculate p_U which is U intersects with L_0= Line(p_0, p_l), O(1). If p_U is NULL that means the Line U is outside the polygon. This means U is ccw to L_0. Since p_U exists we can check Orient(L_m, p_U)=w this cannot be 0 since there is an intersection. If w > 0 the intersection is ccw i.e U can only be ccw to L_m and we can recurse as we did above on the "right" set. otherwise the point is below and U can only be cw to L_m recurse on the "left" set Notice we always keep p_0 its a pivot point for us. p_I > L_m.1 should be symmetric and I'll leave as an exercise Since every check is O(1) and we are dividing the set into two or so the run time is that of binary search i.e O(log n). Use Master's Theorem if you want to be formal. Hopefully this is helpful! Orient test: How to tell whether a point is to the right or left side of a line Finding an intersection of 2 lines: Share Share a link to this answer Copy linkCC BY-SA 4.0 Improve this answer Follow Follow this answer to receive notifications answered Apr 18, 2023 at 16:16 Luke QuinnLuke Quinn 1 Comments Add a comment Your Answer Thanks for contributing an answer to Stack Overflow! Please be sure to answer the question. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience. To learn more, see our tips on writing great answers. Draft saved Draft discarded Sign up or log in Sign up using Google Sign up using Email and Password Submit Post as a guest Name Email Required, but never shown Post Your Answer Discard By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions algorithm math graphics computational-geometry See similar questions with these tags. 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4034
https://www.cerritos.edu/dford/SitePages/Math_70_F13/Math70_F2013_Lecture-Sections7-2thru7-3.pdf
Chapter 7.2-7.3 Triangle Centers and Regular Polygon Properties Some triangle centers – (for a funny song, click on There are many types of triangle centers. Below are four common ones. There is a page for each one. Click on the link to probe deeper. These centers are POINTS OF CONCURRENCY of some “Special Lines” in the triangle. Incenter Located at intersection of the angle bisectors. Properties: The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides. See Incircle of a Triangle. Always inside the triangle The incenter is equidistant to the sides of the triangle See Triangle incenter definition and How to Construct the Incenter of a Triangle Circumcenter Located at intersection of the perpendicular bisectors of the sides . Properties: The circumcenter is the center of a circle circumscribed around the vertices of the triangle. The circumcenter is equidistant to the vertices of the triangle See Triangle circumcenter definition and How to Construct the Circumcenter of a Triangle Centroid Located at intersection of the medians Properties: The centroid is always inside the triangle. The centroid of a triangle is the point through which all the mass of a triangular plate seems to act. Also known as its 'center of gravity' , 'center of mass' , or barycenter. Each median divides the triangle into two smaller triangles of equal area. The centroid is exactly two-thirds the way along each median. Put another way, the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex. See Triangle centroid definition and Constructing the Centroid of a Triangle . Orthocenter Located at intersection of the altitudes See Triangle orthocenter definition and Constructing the Orthocenter of a Triangle . a 2a b 2b 2c c Chapter 7.2-7.3 Triangle Centers and Regular Polygon Properties Incenter of a regular polygon The point where the interior angle bisectors intersect. If you bisect the interior angles of a regular polygon, the bisectors will always converge at the same point - called the incenter of the polygon. The incenter is also the center of: 1. The incircle - the largest circle that will fit inside the polygon 2. The circumcircle - the circle that passes through every vertex. Radius of a regular polygon (also Circumradius) Definition: The distance from the center of a regular polygon to any vertex . The radius of a regular polygon is the distance from the center to any vertex. It will be the same for any vertex. The radius is also the radius of the polygon's circumcircle, which is the circle that passes through every vertex. In this role, it is sometimes called the circumradius. Irregular polygons are not usually thought of as having a center or radius. Chapter 7.2-7.3 Triangle Centers and Regular Polygon Properties Apothem of a Regular Polygon Definition: A line segment from the center of a regular polygon to the midpoint of a side. The apothem is also the radius of the incircle of the polygon. For a polygon of n sides, there are n possible apothems, all the same length of course. The word apothem can refer to the line itself, or the length of that line. So you can correctly say 'draw the apothem' and 'the apothem is 4cm'. For a regular hexagon, the apothem can be found given the length of a side because the central angle formed by the vertices of a hexagon is 60°. Because each angle is the same. the triangles formed are equalilateral triangles. Because the apothem is the perpendicular bisector of an equilateral triangle it forms 2 30-60-90 triangles. 2 3 s x  x s ½ s ½ s s Chapter 7.2-7.3 Triangle Centers and Regular Polygon Properties Incircle of a Polygon Definition: The largest circle the will fit inside a polygon that touches every side The incircle of a regular polygon is the largest circle that will fit inside the polygon and touch each side in just one place (see figure above) and so each of the sides is a tangent to the incircle. If the number of sides is 3, this is an equilateral triangle and its incircle is exactly the same as the one described in Incircle of a Triangle. The inradius of a regular polygon is exactly the same as its apothem. The formulas below are the same as for the apothem. Circumcircle of a Polygon Definition: The circle that passes through each vertex of the regular polygon. Also - circumscribed circle. For Regular Polygons The circumcircle of a regular polygon is the circle that passes through every vertex of the polygon. If the number of sides is 3, then the result is an equilateral triangle and its circumcircle is exactly the same as the one described in Circumcircle of a Triangle. Chapter 7.2-7.3 Triangle Centers and Regular Polygon Properties Finding the radius The radius of a regular polygon is the distance from the center to any vertex. It will be the same for any vertex. The radius is also the radius of the polygon's circumcircle, which is the circle that passes through every vertex. In this role, it is sometimes called the circumradius. Irregular polygons are not usually thought of as having a center or radius. Irregular Polygons Irregular polygons are not usually considered as having a circumcircle. If you draw a polygon at random, it is unlikely there will be a circle that passes through every vertex. Irregular quadrilaterals that have a circumcircle are called cyclic quadrilaterals. A convex quadrilateral is cyclic if and only if the four perpendicular bisectors to the sides are concurrent. This common point is the circumcenter, A convex quadrilateral ABCD is cyclic if and only if its opposite angles are supplementary
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Factoring Quadratic Equations when a ≠ 1 | | | --- | | Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 3, b = 7 and c = 4. | 3x2 + 7x + 4 = 0 | | Step 2: Multiple a · c and find the factors of the result, let's call this p. | a = 3, c = 4 3 · 4 = 12 = p | | Step 3: Determine the factor pairs of p that will add to b. 3.1: List the factor pairs of p. First ask yourself what are the factors pairs of p, ignoring the negative sign for now. 3.2: Determine the signs of the factors. If p is positive then both factors will be positive or both factors will be negative. If p is negative then one factor will be positive and the other negative. 3.3: Determine the factor pair that will add to give b. If both p and b are positive, both factors will be positive. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If p is positive and b is negative, both factors will be negative. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative. | 3.1: Factors pairs of 12: (1, 12);(2, 6);(3, 4) 3.2: p = 12, a positive number, therefore both factors will be positive or both factors will be negative. 3.3: b = 7, a positive number, therefore both factors will be positive. ( 1,12 ): 12+1=13≠ b ( 2,6 ): 2+6=8≠ b These pairs do not work. ( 3,4 ): 3+4=7= b This pair works!!! (3, 4) | | Step 4: Rewrite bx as a sum of two x-terms using the factor pair found in Step 3. | 3x2 + 3x + 4x + 4 = 0 | | Step 5: Group the terms for factoring. | (3x2 + 3x) + (4x + 4) = 0 | | Step 6: Factor the greatest common denominator from each group. | 3x(x + 1) + 4(x + 1) = 0 | | Step 7: Rewrite the equation as two polynomial factors. Notice that the parenthetical expression is the same for both groups. If this does not occur, regroup the terms and try again. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. | (3x + 4)(x + 1) = 0 | | Now that the equation has been factored, solve for x. | | | Step 8: Set each factor to zero and solve for x. | (3x + 4) = 0, or (x + 1) = 0 x=− 4 3 , or x = -1 | Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 3, b = 7 and c = 4. 3x2 + 7x + 4 = 0 Step 2: Multiple a · c and find the factors of the result, let's call this p. a = 3, c = 4 3 · 4 = 12 = p Step 3: Determine the factor pairs of p that will add to b. 3.1: List the factor pairs of p. First ask yourself what are the factors pairs of p, ignoring the negative sign for now. 3.2: Determine the signs of the factors. If p is positive then both factors will be positive or both factors will be negative. If p is negative then one factor will be positive and the other negative. 3.3: Determine the factor pair that will add to give b. If both p and b are positive, both factors will be positive. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If p is positive and b is negative, both factors will be negative. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative. 3.1: Factors pairs of 12: (1, 12);(2, 6);(3, 4) 3.2: p = 12, a positive number, therefore both factors will be positive or both factors will be negative. 3.3: b = 7, a positive number, therefore both factors will be positive. ( 1,12 ): 12+1=13≠ b ( 2,6 ): 2+6=8≠ b These pairs do not work. ( 3,4 ): 3+4=7= b This pair works!!! (3, 4) Step 4: Rewrite bx as a sum of two x-terms using the factor pair found in Step 3. 3x2 + 3x + 4x + 4 = 0 Step 5: Group the terms for factoring. (3x2 + 3x) + (4x + 4) = 0 Step 6: Factor the greatest common denominator from each group. 3x(x + 1) + 4(x + 1) = 0 Step 7: Rewrite the equation as two polynomial factors. Notice that the parenthetical expression is the same for both groups. If this does not occur, regroup the terms and try again. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. (3x + 4)(x + 1) = 0 Now that the equation has been factored, solve for x. Step 8: Set each factor to zero and solve for x. (3x + 4) = 0, or (x + 1) = 0 x=− 4 3 , or x = -1 | | | --- | | Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 4, b = -19 and c = 12. | 4x2 - 19x + 12 = 0 | | Step 2: Multiple a · c and find the factors of the result, let's call this p. | a = 4, c = 12 4 · 12 = 48 = p | | Step 3: Determine the factor pairs of p that will add to b. 3.1: List the factor pairs of p. First ask yourself what are the factors pairs of p, ignoring the negative sign for now. 3.2: Determine the signs of the factors. If p is positive then both factors will be positive or both factors will be negative. If p is negative then one factor will be positive and the other negative. 3.3: Determine the factor pair that will add to give b. If both p and b are positive, both factors will be positive. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If p is positive and b is negative, both factors will be negative. If p is negative andb is positive, the larger factor will be positive and the smaller will be negative. | 3.1: Factors pairs of 48: (1, 48);(2, 24);(3, 16);(4, 12);(6, 8) 3.2: p = 48, a positive number, therefore both factors will be positive or both factors will be negative. 3.3: b = -19, a negative number, therefore both factors will be negative. ( −1,−48 ): −1−48=−49≠ b ( −2,−24 ): −2−24=−26≠ b ( −4,−12 ): −4−12=−16≠ b ( −6,−8 ): −6−8=−14≠ b These pairs do not work. ( −3,−16 ): −3−16=−19= b This pair works!!! (-3, -16) | | Step 4: Rewrite bx as a sum of two x-terms using the factor pair found in Step 3. | 4x2 - 19x + 12 = 0 | | Step 5: Group the terms for factoring. | (4x2 -16x) + (-3x + 12) = 0 | | Step 6: Factor the greatest common denominator from each group. | 4x(x - 4) - 3(x - 4) = 0 | | Step 7: Rewrite the equation as two polynomial factors. Notice that the parenthetical expression is the same for both groups. If this does not occur, regroup the terms and try again. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. | (4x - 3)(x - 4) = 0 | | Now that the equation has been factored, solve for x. | | | Step 8: Set each factor to zero and solve for x. | (4x - 3) = 0, or (x - 4) = 0 x= 3 4 , or x = 4 | Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 4, b = -19 and c = 12. 4x2 - 19x + 12 = 0 Step 2: Multiple a · c and find the factors of the result, let's call this p. a = 4, c = 12 4 · 12 = 48 = p Step 3: Determine the factor pairs of p that will add to b. 3.1: List the factor pairs of p. First ask yourself what are the factors pairs of p, ignoring the negative sign for now. 3.2: Determine the signs of the factors. If p is positive then both factors will be positive or both factors will be negative. If p is negative then one factor will be positive and the other negative. 3.3: Determine the factor pair that will add to give b. If both p and b are positive, both factors will be positive. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If p is positive and b is negative, both factors will be negative. If p is negative andb is positive, the larger factor will be positive and the smaller will be negative. 3.1: Factors pairs of 48: (1, 48);(2, 24);(3, 16);(4, 12);(6, 8) 3.2: p = 48, a positive number, therefore both factors will be positive or both factors will be negative. 3.3: b = -19, a negative number, therefore both factors will be negative. ( −1,−48 ): −1−48=−49≠ b ( −2,−24 ): −2−24=−26≠ b ( −4,−12 ): −4−12=−16≠ b ( −6,−8 ): −6−8=−14≠ b These pairs do not work. ( −3,−16 ): −3−16=−19= b This pair works!!! (-3, -16) Step 4: Rewrite bx as a sum of two x-terms using the factor pair found in Step 3. 4x2 - 19x + 12 = 0 Step 5: Group the terms for factoring. (4x2 -16x) + (-3x + 12) = 0 Step 6: Factor the greatest common denominator from each group. 4x(x - 4) - 3(x - 4) = 0 Step 7: Rewrite the equation as two polynomial factors. Notice that the parenthetical expression is the same for both groups. If this does not occur, regroup the terms and try again. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. (4x - 3)(x - 4) = 0 Now that the equation has been factored, solve for x. Step 8: Set each factor to zero and solve for x. (4x - 3) = 0, or (x - 4) = 0 x= 3 4 , or x = 4 | | | --- | | Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 15, b = 24 and c = -12. | 15x2 + 24x - 12 = 0 | | Step 2: Multiple a · c and find the factors of the result, let's call this p. | a = 15, c = -12 15 · (-12) = -180 = p | | Step 3: Determine the factor pairs of p that will add to b. 3.1: List the factor pairs of p. First ask yourself what are the factors pairs of p, ignoring the negative sign for now. 3.2: Determine the signs of the factors. If p is positive then both factors will be positive or both factors will be negative. If p is negative then one factor will be positive and the other negative. 3.3: Determine the factor pair that will add to give b. If both p and b are positive, both factors will be positive. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If p is positive and b is negative, both factors will be negative. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative. | 3.1: Factors pairs of 180: (1,180);(2,90);(3,60);(4,45);(5,36);(6,30); (9,20);(10,18);(12,15) 3.2: p = -180, a negative number, therefore one factor will be positive and the other negative. 3.3: b = 24, a positive number, therefore the larger factor will be positive and the smaller will be negative. ( −1,−80 ): −1+180=179≠ b ( −2,−0 ): −2+90=88≠ b ( −3,60 ): −3+60=57≠ b ( −4,45 ): −4+45=41≠ b ( −5,−6 ): −5+36=31≠ b ( −9,20 ): −9+20=11≠ b ( −10,18 ): −1+18=8≠ b These pairs do not work. ( −6,−0 ): −6+30=24= b This pair works!!! (-6, 30) | | Step 4: Rewrite bx as a sum of two x-terms using the factor pair found in Step 3. | 15x2 + 24x - 12 = 0 | | Step 5: Group the terms for factoring. | Grouping 1: (15x2 -6x) + (30x - 12) = 0 OR Grouping 2: (15x2 + 30x) +(-6x + 12) = 0 | | Step 6: Factor the greatest common denominator from each group. | Grouping 1: 3x(5x - 2) + 6(5x - 2) = 0 OR Grouping 2: 15x(x + 2) - 6(x - 2) = 0 | | Step 7: Rewrite the equation as two polynomial factors. Notice that the parenthetical expression is the same for both groups. If this does not occur, regroup the terms and try again. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. | Grouping 1: (3x + 6)(5x - 2) = 0 Grouping 2: (15x - 6)(x + 2) = 0 | | Now that the equation has been factored, solve for x. | | | Step 8: Set each factor to zero and solve for x. | Grouping 1: (3x + 6) = 0, or (5x - 2) = 0 x=− 6 3 =−2 , or x= 2 5 Grouping 2: (15x - 6) = 0, or (x + 2) = 0 x= 6 15 = 2 5 , or x = -2 In either case the answer is the same. | Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 15, b = 24 and c = -12. 15x2 + 24x - 12 = 0 Step 2: Multiple a · c and find the factors of the result, let's call this p. a = 15, c = -12 15 · (-12) = -180 = p Step 3: Determine the factor pairs of p that will add to b. 3.1: List the factor pairs of p. First ask yourself what are the factors pairs of p, ignoring the negative sign for now. 3.2: Determine the signs of the factors. If p is positive then both factors will be positive or both factors will be negative. If p is negative then one factor will be positive and the other negative. 3.3: Determine the factor pair that will add to give b. If both p and b are positive, both factors will be positive. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If p is positive and b is negative, both factors will be negative. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative. 3.1: Factors pairs of 180: (1,180);(2,90);(3,60);(4,45);(5,36);(6,30); (9,20);(10,18);(12,15) 3.2: p = -180, a negative number, therefore one factor will be positive and the other negative. 3.3: b = 24, a positive number, therefore the larger factor will be positive and the smaller will be negative. ( −1,−80 ): −1+180=179≠ b ( −2,−0 ): −2+90=88≠ b ( −3,60 ): −3+60=57≠ b ( −4,45 ): −4+45=41≠ b ( −5,−6 ): −5+36=31≠ b ( −9,20 ): −9+20=11≠ b ( −10,18 ): −1+18=8≠ b These pairs do not work. ( −6,−0 ): −6+30=24= b This pair works!!! (-6, 30) Step 4: Rewrite bx as a sum of two x-terms using the factor pair found in Step 3. 15x2 + 24x - 12 = 0 Step 5: Group the terms for factoring. Grouping 1: (15x2 -6x) + (30x - 12) = 0 OR Grouping 2: (15x2 + 30x) +(-6x + 12) = 0 Step 6: Factor the greatest common denominator from each group. Grouping 1: 3x(5x - 2) + 6(5x - 2) = 0 OR Grouping 2: 15x(x + 2) - 6(x - 2) = 0 Step 7: Rewrite the equation as two polynomial factors. Notice that the parenthetical expression is the same for both groups. If this does not occur, regroup the terms and try again. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. Grouping 1: (3x + 6)(5x - 2) = 0 Grouping 2: (15x - 6)(x + 2) = 0 Now that the equation has been factored, solve for x. Step 8: Set each factor to zero and solve for x. Grouping 1: (3x + 6) = 0, or (5x - 2) = 0 x=− 6 3 =−2 , or x= 2 5 Grouping 2: (15x - 6) = 0, or (x + 2) = 0 x= 6 15 2 5 , or x = -2 In either case the answer is the same. | | | Related Links: Math algebra Quadratic Formula | To link to this Factoring Quadratic Equations when a ≠ 1 page, copy the following code to your site: More Topics Educational Videos © 2005-2020 Softschools.com
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Techniques for the interruption of tubal patency for female sterilisation - Lawrie, TA - 2016 | Cochrane Library Opens in a new window Opens an external website Opens an external website in a new window This website utilizes technologies such as cookies to enable essential site functionality, as well as for analytics, personalization, and targeted advertising. To learn more, view the following link: Privacy Policy Skip to Content Cookies Our site uses cookies to improve your experience. You can find out more about our use of cookies in About Cookies, including instructions on how to turn off cookies if you wish to do so. By continuing to browse this site you agree to us using cookies as described in About Cookies. I accept The Cochrane Library Trusted evidence. Informed decisions. Better health. 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December 28, 2016 Editorials Audio summaries Special Collections About this review Information Authors Version history Keywords (MeSH, PICOs) Related content Translation notes Request permissions Request data reuse Cochrane Database of Systematic reviewsReview - Intervention New search Techniques for the interruption of tubal patency for female sterilisation Theresa A Lawrie Regina Kulier Juan Manuel Nardin Authors' declarations of interest Version published: 05 August 2016 Version history Collapse all Expand all Abstract available in English Español فارسی ภาษาไทย Background This is an update of a review that was first published in 2002. Female sterilisation is the most popular contraceptive method worldwide. Several techniques exist for interrupting the patency of fallopian tubes, including cutting and tying the tubes, damaging the tube using electric current, applying clips or silicone rubber rings, and blocking the tubes with chemicals or tubal inserts. Objectives To compare the different tubal occlusion techniques in terms of major and minor morbidity, failure rates (pregnancies), technical failures and difficulties, and women's and surgeons' satisfaction. Search methods For the original review published in 2002 we searched MEDLINE and the Cochrane Central Register of Controlled Trials (CENTRAL). For this 2015 update, we searched POPLINE, LILACS, PubMed and CENTRAL on 23 July 2015. We used the related articles feature of PubMed and searched reference lists of newly identified trials. Selection criteria All randomized controlled trials (RCTs) comparing different techniques for tubal sterilisation, irrespective of the route of fallopian tube access or the method of anaesthesia. Data collection and analysis For the original review, two review authors independently selected studies, extracted data and assessed risk of bias. For this update, data extraction was performed by one author (TL) and checked by another (RK). We grouped trials according to the type of comparison evaluated. Results are reported as odds ratios (OR) or mean differences (MD) using fixed‐effect methods, unless heterogeneity was high, in which case we used random‐effects methods. Main results We included 19 RCTs involving 13,209 women. Most studies concerned interval sterilisation; three RCTs involving 1632 women, concerned postpartum sterilisation. Comparisons included tubal rings versus clips (six RCTs, 4232 women); partial salpingectomy versus electrocoagulation (three RCTs, 2019 women); tubal rings versus electrocoagulation (two RCTs, 599 women); partial salpingectomy versus clips (four RCTs, 3627 women); clips versus electrocoagulation (two RCTs, 206 women); and Hulka versus Filshie clips (two RCTs, 2326 women). RCTs of clips versus electrocoagulation contributed no data to the review. One year after sterilisation, failure rates were low (< 5/1000) for all methods.There were no deaths reported with any method, and major morbidity related to the occlusion technique was rare. Minor morbidity was higher with the tubal ring than the clip (Peto OR 2.15, 95% CI 1.22 to 3.78; participants = 842; studies = 2; I² = 0%; high‐quality evidence ), as were technical failures (Peto OR 3.93, 95% CI 2.43 to 6.35; participants = 3476; studies = 3; I² = 0%; high‐quality evidence). Major morbidity was significantly higher with the modified Pomeroy technique than electrocoagulation (Peto OR 2.87, 95% CI 1.13 to 7.25; participants = 1905; studies = 2; I² = 0%; low‐quality evidence ), as was postoperative pain (Peto OR 3.85, 95% CI 2.91 to 5.10; participants = 1905; studies = 2; I² = 0%; moderate‐quality evidence). When tubal rings were compared with electrocoagulation, postoperative pain was reported significantly more frequently for tubal rings (OR 3.40, 95% CI 1.17 to 9.84; participants = 596; studies = 2; I² = 87%; low‐quality evidence). When partial salpingectomy was compared with clips, there were no major morbidity events in either group (participants = 2198, studies = 1). The frequency of minor morbidity was low and not significantly different between groups (Peto OR 7.39, 95% CI 0.46 to 119.01; participants = 193; studies = 1, low‐quality evidence ). Although technical failure occurred more frequently with clips (Peto OR 0.18, 95% CI 0.08 to 0.40; participants = 2198; studies = 1; moderate‐quality evidence); operative time was shorter with clips than partial salpingectomy (MD 4.26 minutes, 95% CI 3.65 to 4.86; participants = 2223; studies = 2; I² = 0%; high‐quality evidence). We found little evidence concerning women's or surgeon's satisfaction. No RCTs compared tubal microinserts (hysteroscopic sterilisation) or chemical inserts (quinacrine) to other methods. Authors' conclusions Tubal sterilisation by partial salpingectomy, electrocoagulation, or using clips or rings, is a safe and effective method of contraception. Failure rates at 12 months post‐sterilisation and major morbidity are rare outcomes with any of these techniques. Minor complications and technical failures appear to be more common with rings than clips. Electrocoagulation may be associated with less postoperative pain than the modified Pomeroy or tubal ring methods. Further research should include RCTs (for effectiveness) and controlled observational studies (for adverse effects) on sterilisation by minimally‐invasive methods, i.e. tubal inserts and quinacrine. PICOs PICOs Population (5) Adult 19-44 years Not Pregnant Middle Aged 45-64 years Young Adult 19-24 years Adolescent 13-18 years Intervention (12) Tubal Occlusion Quinacrine Female Sterilization Bilateral Segmental Tubal Excision And Ligation By Endoscopy Fallopian Tube Ring Bilateral Tubal Ligation Surgical Department Fallopian Tube Occlusion Insert Endoscopic Bilateral Occlusion Of Fallopian Tubes Using Intrafallopian Implants Ligation Of Fallopian Tube Electrocoagulation Of Fallopian Tube Fallopian Tube Clip Comparison (2) Surgical Department Usual Care Outcome (12) Infection Postoperative Complication Intraoperative Complications Pain Blood Transfusion Revision Injury To Blood Vessel During Surgery Unplanned Pregnancy Injury Of Pelvic Organs Ectopic Pregnancy Readmission Intraoperative Death The PICO model is widely used and taught in evidence-based health care as a strategy for formulating questions and search strategies and for characterizing clinical studies or meta-analyses. PICO stands for four different potential components of a clinical question: Patient, Population or Problem; Intervention; Comparison; Outcome. See more on using PICO in the Cochrane Handbook. Plain language summary available in English Español فارسی Polski Русский ภาษาไทย A review of techniques for tubal sterilisation (blocking the fallopian tubes) Background This is an update of a Cochrane Review that was first published in 2002 and previously updated in 2011. Tubal sterilisation prevents pregnancy by stopping the woman's unfertilised eggs from passing through the fallopian tubes to be fertilised by sperm. Techniques to close the tubes include cutting and tying them (partial salpingectomy), blocking them mechanically by using clips or rings, or by applying electric current (electrocoagulation) to damage and block them, and blocking them by using chemicals or tubal inserts (inserted via the mouth of the womb) that cause tubal scarring. Methods We, the Cochrane researchers, wanted to compare the different techniques for tubal sterilisation in terms of: ‐ how unwell they made women feel in the short and long term, including pain experienced (major and minor morbidity); ‐ failure rates (pregnancies); ‐ technical failures and difficulties encountered during the sterilisation procedure; and ‐ women's and surgeons' satisfaction. We searched the medical literature up to 23 July 2015 for randomised controlled trials (RCTs) that compared any methods of closing the fallopian tubes; RCTs produce the most reliable results. Findings We included 19 RCTs involving 13,209 women of childbearing age. The trials compared: ‐ tubal rings versus clips (six RCTs, 4232 women); ‐ partial salpingectomy versus electrocoagulation (three RCTs, 2019 women); ‐ tubal rings versus electrocoagulation (two RCTs, 599 women); ‐ partial salpingectomy versus clips (four RCTs, 3827 women); ‐ clips versus electrocoagulation (two RCTs, 206 women); and ‐ two types of clips, i.e. Hulka clips versus Filshie clips (two RCTs, 2326 women). We found no RCTs that investigated sterilisation by chemicals or tubal inserts, so all the included studies involved an abdominal operation. There were no deaths reported with any method, and major and minor morbidity were rare. Pregnancy rates were less than 5/1000 procedures one year after surgery. Complicationrates (problems after surgery/minor morbidity) were very low for all methods compared. Minor complications, including pain, and technical failures were more common with rings than clips. Major morbidity and postoperative pain were more common with partial salpingectomy than with electrocoagulation. Postoperative pain was reported twice as often by women sterilised by tubal rings than those sterilised by electrocoagulation.Technical failures were more common with clips than cutting and tying techniques, but operating time was shorter for clips. We found little evidence concerning women's or surgeon's satisfaction. Conclusions Tubal sterilisation by cutting and tying the tubes, or using electric current, clips or rings, is an effective method of contraception with few problems. The choice of method will depend upon the surgeon's experience, availability of equipment, setting, and cost. More research is needed about methods for tubal sterilisation that do not require an abdominal operation. Visual summary Authors' conclusions Implications for practice Failure rates at 12 months post‐sterilisation and major morbidity were found to be rare outcomes with sterilisation by partial salpingectomy, electrocoagulation, clips, and tubal rings. Technical failures were more common with tubal rings compared with clips, and more common with clips compared with partial salpingectomy. The choice of the tubal occlusion technique should include consideration of the costs, equipment availability, the setting and the surgeon's experience. We were unable to draw any conclusions about the relative efficacy and safety of hysteroscopic sterilisation and more research is needed. Implications for research RCTs comparing hysteroscopic sterilisation methods, e.g. Essure®, with laparoscopic (and other) methods are needed. To assess adverse effects, controlled observational studies of sterilisation by minimally invasive methods would also be of value. Women's satisfaction, side‐effects, and cost are important outcomes for future RCTs. Women in their forties without hormonal treatment may experience more dysfunctional uterine bleeding, which is often treated with hormonally‐impregnated intrauterine systems (French 2004); studies evaluating differences in long‐term effectiveness and adverse effects between hysteroscopic sterilisation methods and IUSs, especially among women over 40 years of age, are therefore of interest. Given that quinacrine sterilisation is cheap, minimally invasive, and in use in some countries (Lippes 2015), a trial of quinacrine compared with hysteroscopic sterilisation would be very informative. Further comparative trials of abdominally accessed sterilisation methods are not considered to be a high priority for research. Summary of findings Open in table viewer Summary of findings for the main comparison.Summary of findings: ring versus clip Tubal ring compared with tubal clip for interval sterilisation Patient or population: women > 6 weeks postpartum requesting tubal sterilisation Settings: any Intervention: tubal ring Comparison: tubal clip OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ClipRing Major morbidity: totalLow risk populationOR 0.14 (0.00 to 7.05)545 (1)⊕⊕⊝⊝ low 1,2Only one event occurred in the clip group 4 per 1000 1 per 1000 (0 to 28) Minor morbidity: totalLow risk populationOR 2.15 (1.22 to 3.78)842 (2)⊕⊕⊕⊕ high 57 per 1000123 per 1000 (70 to 215) Minor morbidity: details ‐ procedure‐related injuriesLow risk populationOR 1.95 (1.36 to 2.78)3575 (3)⊕⊕⊕⊕ high 21 per 100041 per 1000 (29 to 58) Technical failuresLow risk populationOR 3.93 (2.43 to 6.35)3476 (3)⊕⊕⊕⊕ high 10 per 100039 per 1000 (24 to 63) Failure rate: details (12 to 24 months)Low risk populationOR 0.72 (0.33 to 1.57)3822 (4)⊕⊕⊕⊕ high 4 per 10003 per 1000 (1 to 6) Complaints: Postoperative pain (24 hours)Low risk populationOR 1.14 (0.88 to 1.48)922 (3)⊕⊕⊕⊕ high 477 per 1000544 per 1000 (420 to 706) The basis for the assumed risk is the median control group (clip) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. Open in table viewer Summary of findings 2.Summary of findings: modified Pomeroy partial salpingectomy versus electrocoagulation Modified Pomeroy partial salpingectomy compared with tubal electrocoagulation for interval sterilisation Patient or population: women > 6 weeks postpartum requesting tubal sterilisation Settings: any Intervention: modified Pomeroy partial salpingectomy Comparison: electrocoagulation OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ElectrocoagulationModified Pomeroy Major morbidity: totalLow risk populationOR 2.87 (1.13 to 7.25)1905 (2)⊕⊕⊝⊝ low 1,2 10 per 100029 per 1000 (11 to 73) Major morbidity: procedure‐related injuries requiring additional operation or blood transfusion10 per 100019 per 1000 (19 to 190)OR 1.90 (0.19 to 18.96)1905 (2)⊕⊕⊝⊝ low 1,2 Major morbidity: rehospitalisation as a consequence of the operation20 per 1000115 per 1000 (15 to 900)OR 5.74 (0.73 to 45.09)295 (1)⊕⊝⊝⊝ very low 1,2 Minor morbidity: totalLow risk populationOR 1.60 (1.10 to 2.33)1905 (2)⊕⊕⊝⊝ low 1,4The WHO study reported significantly more wound infections in the modified Pomeroy group, where participants underwent minilaparotomy, compared with the electrocoagulation group where laparoscopy was used) 38 per 100061 per 1000 (42 to 89) Minor morbidity: procedure‐related injuries with no additional operationLow risk populationOR 0.53 (0.06 to 5.11)1610 (1)⊕⊕⊕⊝ moderate 1 2 per 10001 per 1000 0 to 10) Failure rate: total (12 months)Low risk populationOR 4.47 (0.07 to 286.78)295 (1)⊕⊕⊝⊝ low 1,3 0.5 per 10002 per 1000 (0 to 143) Complaints ‐ postoperative pain (24 hours)Low risk populationOR 3.85 (2.91 to 5.10)1905 (2)⊕⊕⊕⊝ moderate 4 95 per 1000366 per 1000 (276 to 485) Complaints ‐ persistent pain at follow‐up visitLow risk populationOR 1.09 (0.88 to 1.47)1610 (1)⊕⊕⊕⊝ moderate 4 117 per 1000128 per 1000 (95 to 172) The basis for the assumed risk is the median control group (electrocoagulation) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to inconsistency. 3 Sparse data. 4 Downgraded due to indirectness (this effect may be due to the abdominal approach (minilaparotomy versus laparoscopy) rather than the tubal technique). Open in table viewer Summary of findings 3.Summary of findings: tubal ring versus electrocoagulation Tubal ring compared with electrocoagulation for interval sterilisation Patient or population: women > 6 weeks postpartum requesting tubal sterilisation Settings: any Intervention: tubal ring Comparison: electrocoagulation OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ElectrocoagulationRing Major morbidity: totalLow risk populationOR 0.14 0.00 to 7.01 596 (2)⊕⊕⊝⊝ low 1,2Unipolar electrocoagulation stated in one study and not specified in the other. Only one event reported in total 0.5 per 10000 per 1000 (0 to 4) Minor morbidity: totalLow risk populationOR 0.97 (0.50, 1.87)596 (2)⊕⊕⊕⊝ moderate 1 66 per 100064 per 1000 (33 to 123) Technical failures: totalLow risk populationOR 3.42 (0.59 to 19.81)596 (2)⊕⊕⊕⊝ moderate 1 3 per 100010 per 1000 (2 to 60) Failure rate: totalnot estimable not estimable Not estimable due to insufficient data 160 (1)‐No pregnancies reported in one study Complaints ‐ postoperative pain (24 hours)Low risk populationOR 3.40 (1.17 to 9.84)596 (2)⊕⊕⊝⊝ low 1,3 176 per 1000598 per 1000 (206 to 1000) Complaints ‐ persistent pain at follow‐up visitLow risk populationOR 1.22 (0.75 to 1.97)594 (2)⊕⊕⊕⊝ moderate 1 140 per 1000171 per 1000 (105 to 276) The basis for the assumed risk is the median control group (electrocoagulation) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. 3 Downgraded due to inconsistency. Open in table viewer Summary of findings 4.Summary of findings: partial salpingectomy versus clip Partial salpingectomy compared with tubal clips for tubal sterilisation Patient or population: women requesting postpartum or interval sterilisation Settings: any Intervention: partial salpingectomy Comparison: tubal clips OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ClipsPartial salpingectomy Major morbidity: totalLow risk populationnot estimable 2198 (1)‐No deaths or major morbidity events reported in one large trial 0 per 10000 per 1000 Minor morbidity: totalLow risk populationOR 7.39 (0.46 to 119.01)193 (1)⊕⊕⊝⊝ low 1,2 0.5 per 10004 per 1000 (0 to 60) Technical failuresLow risk populationOR 0.18 (0.08 to 0.40)2198 (1)⊕⊕⊕⊝ moderate 3 20 per 10004 per 1000 (2 to 8) Failure rate: total (12 months)Low risk populationOR 0.21, 95% CI 0.05 to 0.84 3537 (2)⊕⊕⊕⊝ moderate 4In this analysis, we grouped studies according to whether sterilisation was performed on a postpartum (1) or interval basis (1). Results were similar across these subgroups (Test for subgroup differences: P value 0.58, I² = 0%) 2 per 10000.4 per 1000 (0 to 2) Complaints (12 months)Low risk populationOR 1.30 (0.92 to 1.82)2137 (1)⊕⊕⊕⊝ moderate 1This single study reported data on 'chief complaints' at 3, 6, and 12 months and rates were similar between groups at all assessment points 59 per 1000 77 per 1000 (54 to 107) The basis for the assumed risk is the median control group (clips) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. 3 Downgraded due to indirectness (unclear whether silver clips and Filshie clips are similarly effective). 4 Downgraded due to risk of bias. Open in table viewer Summary of findings 5.Summary of findings: Hulka clip versus Filshie clip Hulka clips compared with Filshie clips for interval sterilisation Patient or population: women requesting sterilisation Settings: any Intervention: Hulka clips Comparison: Filshie clips OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk Filshie clipHulka clip Minor morbidity: totalLow risk populationOR 0.14 (0.00 to 7.32)197 (1)⊕⊕⊝⊝ low 1,2 10 per 10001 per 1000 (0 to 70) Minor morbidity: procedure‐related injuriesLow risk populationOR 1.55 (0.73 to 3.26)2322 (2)⊕⊕⊕⊝ moderate 1 10 per 100016 per 1000 (7 to 33) Technical failuresLow risk populationOR 1.04 (0.10 to 11.33)2325 (2)⊕⊕⊝⊝ low 1,3 7 per 10007 per 1000 (1 to 79) Failure rate: total (12 months)Low risk populationOR 6.20 (0.75 to 51.66)1441 (1)⊕⊕⊕⊝ moderate 1 1 per 10006 per 1000 (1 to 52) Complaints: postoperative pain (24 hours)Low risk populationOR 1.74 (0.99 to 3.03)197 (1)⊕⊕⊝⊝ low 1,4 45 per 100078 per 1000 (45 to 136) The basis for the assumed risk is the median control group (Filshie clips) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. 3 Downgraded due to inconsistency. 4 Downgraded due to risk of bias. Background This is an updated version of this review. The original version of the review was published in 2002 and the last update was published in The Cochrane Database of Systematic Reviews, Issue 2, 2011. Female sterilisation, also called tubal ligation or tubal occlusion, is the most widely used contraceptive method in the world. Globally, in 2011, sterilisation accounted for approximately 19% of all contraceptive methods used by women between the ages of 15 and 49 years who were married or in a union, with the highest prevalences occurring in developing region (21%), and the lowest prevalences occurring in the least developed countries (3%) (UN 2013). Female sterilisation is most prevalent in Latin America and the Carribean (26%) (UN 2013). Figures published by the United Nations Population Division estimate prevalence rates for various other countries as follows: India 35.8%, China 28.7%, North America 22%, South Africa 14.3%, Germany 8.3%, United Kingdom 8%, France 3.8%, and Nigeria 0.3% (UN 2013). The increased efficacy and acceptability of long‐acting reversible contraceptive methods (LARCs) has contributed in a trend towards declining sterilisation rates in some regions, e.g. the United Kingdom, in favour of LARCs. Description of the intervention Female sterilisation prevents pregnancy by occluding or disrupting tubal patency so that the ovum cannot reach the uterus. In the 1930s, Pomeroy made tubal sterilisation well known, however it was considered a major procedure (Bhiwandiwala 1980). From 1950 to 1982 voluntary sterilisation increased thirty‐fold worldwide, the increase partly being attributed to surgical innovations that made sterilisation a safe and effective outpatient procedure (Bhiwandiwala 1980). Sterilisation failures (pregnancies) in the first year post‐sterilisation of five per 1000 procedures are comparable with pregnancy rates for women using LARCs; however, tubal sterilisation appears to be a more effective contraceptive method over time (Peterson 2008). This is probably due to high continuation rates compared with LARCs. Sterilisation failures may result from conception occurring before the procedure (so‐called luteal phase pregnancy), incomplete tubal occlusion, or the formation of fistulas, and may occur several years after the procedure (Gupta 1980; Peterson 1996; Peterson 2008). Tubal sterilisation is traditionally achieved by an abdominal operation (either via laparotomy or laparoscopy). Tubal sterilisation techniques employed via the abdominal route include surgically cutting and tying the fallopian tubes (with or without a section of tube being removed), mechanically blocking the tubes using clips or rings, and electrically coagulating the tubes. Tubal sterilisation can also be achieved via the vaginal route by means of chemicals or mechanical tubal inserts that block the tubes by inducing a fibrotic reaction. Interventions such as hysterectomy or ovariectomy also lead to female sterility, but are not considered in this review as these operations are usually performed primarily for other medical reasons. Surgical methods There are a number of surgical techniques employed for interrupting tubal patency. Possibly the most common method of surgical sterilisation is a partial salpingectomy using the Pomeroy or 'modified' Pomeroy technique in which a chromic tie is placed around a loop of fallopian tube, and a 1 cm to 2 cm portion is then excised. The Parkland method involves separating a mid‐portion of the tube from mesosalpinx and twice ligating the tube; the intervening segment between the ties is then resected, achieving immediate separation of the tubal ends. Alternatively, the Irving method double ties and divides the tube, then buries the proximal stump of the tube into the myometrium through an incision in the posterior uterine wall near the utero‐tubal junction. The Uchida method involves infiltration of the serosa of the tube with a vasoconstricting solution with subsequent dissection of the subserosa and resection of a 2 cm portion of the muscular part of the tube; the proximal stump retracts into the mesosalpinx, which is closed, and the distal stump is exteriorised to the peritoneal cavity (Peterson 2008). Other methods and modifications include fimbriectomies and salpingectomies, e.g. Kroener, Madlener and Aldrich techniques. In a large, prospective cohort study (CREST) conducted in the United States between 1978 and 1992, interval (not within 42 days of pregnancy) and postpartum partial salpingectomy were associated with cumulative 10‐year probabilities of pregnancy of 20.1 per 1000 and 7.5 per 1000 procedures, respectively (Peterson 1996). Mechanical methods Bands or rings made of silicone and rubber (e.g. Yoon, Falope) are placed around a loop of fallopian tube, using a cone‐shaped applicator. When the ring is released onto the loop of tube, it contracts and constricts the base of the loop, thereby blocking the tube. The 2 cm to 3 cm loop undergoes necrosis and the healthy ends of the tube separate. Hinged clips (e.g. Filshie, Hulka) can also be used to block the fallopian tubes mechanically. Filshie clips are made of titanium and silicone rubber, while Hulka clips are made of plastic with a gold spring lock. Only a small portion of the tube is damaged when these devices are used (Chi 1994; Kaplan 1990; Lipscomb 1992), therefore their use might increase the chance of reversibility among women who experience regret (Hillis 1999). In the CREST study, tubal rings and clips were associated with cumulative 10‐year probabilities of pregnancy of 17.7 per 1000 and 36.5 per 1000 procedures, respectively (Peterson 1996). Electrical methods The standard laparoscopic technique for tubal occlusion by electrocoagulation originally used unipolar forceps, however, since the risk of burns to the bowel and other organs is decreased with the use of bipolar forceps, the latter are preferred (Kessel 1976). With bipolar coagulation, the tube is grasped with the forceps, and electrical current passes between the two ends of the forceps, damaging the tube. To achieve successful occlusion it is recommended that at least 3 cm of the isthmic portion of the tube is coagulated (Peterson 2008). Unipolar coagulation damages a wider segment of tube, which is often cut after coagulation. In the CREST study, unipolar and bipolar electrocoagulation were associated with cumulative 10‐year probabilities of pregnancy of 7.5 per 1000 and 24.7 per 1000 procedures, respectively (Peterson 1996). Chemical methods Licensed as an antimalarial and in use for more than 70 years, quinacrine's use in sterilisation in low‐ and middle‐income countries has been fraught with ethical issues (Bhattacharyya 2003). However, a report on 40,252 cases of quinacrine sterilisation (QS) from Chile, Indonesia, Pakistan, India, Egypt, Libya, Syria, China, Costa Rica and the USA concluded that this is a safe and effective method (IJOG 2003). The method, involving the interuterine device‐like insertion of quinacrine pellets trans‐cervically into the uterus, leads to chemical irritation and scarring of the fallopian tubes (Suhadi 1998). QS does not immediately result in sterilisation, which can take up to 12 weeks, and failure rates appear to vary depending on dosage and the number of insertions (Agoestina 2003). Two insertions one month apart seems to be the most common and effective method of QS, and results in reported gross pregnancy rates of 1.2% to 4.3% in 10 years (Lu 2003; Suhadi 2003). Tubal inserts Essure® inserts are 4 cm devices consisting of a stainless steel inner coil coated with PET (polyethylene tenephterate), and a nickel titanium outer coil. According to the manufacturer, approximately 750,000 women have undergone Essure® sterilisation to date (Bayer 2015). To achieve sterilisation, these inserts are introduced bilaterally into the proximal fallopian tubes via hysteroscopy and expand on insertion. The PET fibres induce a tissue response that causes fibrosis of the tubes (Valle 2001). Bilateral occlusion must be verified, usually by hysterosalpingogram (HSG), three months postinsertion (Veersema 2015). Although other inserts have been developed (Adiana, Ovabloc), Essure® is currently the only tubal insert on the market. Successful bilateral placement varies from between 80% to 99% of first attempts (Arjona 2008; Connor 2009; Cooper 2003; Duffy 2005; Panel 2010; Savage 2009; Shavell 2009), and placement failure has been attributed mainly to related to poor visualisation of the tubal ostia or tubal spasm/stenosis on hysteroscopy, and operator experience (Mino 2007). Sterilisation failures may be mainly attributed to misinterpretation of the HSG and non‐adherence to the follow‐up protocol (Veersema 2015), although evidence from controlled studies is lacking. Why it is important to do this review Contraception plays a vital role in reducing maternal morbidity and mortality, and the acceptability and satisfaction of women with contraceptive methods is increased when users are well‐informed (Blumenthal 2011). This review considers the different techniques for tubal interruption, regardless of the method used to access the fallopian tubes, and evaluates them for their safety and effectiveness. Previous versions of this review identified no eligible studies of chemical or hysteroscopic methods that could be included in the review. Given the evolving nature of sterilisation methods, and contraception in general, it is important that we keep this review updated. Objectives To compare the different tubal occlusion techniques in terms of major and minor morbidity, failure rates (pregnancies), technical failures and difficulties, and women's and surgeons' satisfaction. Methods Criteria for considering studies for this review Types of studies Randomised controlled trials (RCTs) comparing different occlusion techniques for tubal sterilisation. Quasi‐RCTs are excluded. Types of participants Women requesting tubal sterilisation. Types of interventions Interventions include interrupting tubal patency by partial salpingectomy, clips, silicone rings, electrocoagulation, chemicals and tubal inserts. Interventions may be performed as: postpartum sterilisation: sterilisation performed during caesarean section or within 42 days of delivery (it is usually performed during the first 48 to 72 hours postpartum); postabortion sterilisation: sterilisation performed immediately after termination of pregnancy; or interval sterilisation: sterilisation performed at least six weeks after delivery. Types of outcome measures Primary outcomes Failure rate (yearly incidence of unintended pregnancy) including extrauterine pregnancy. Operative mortality, major and minor morbidity (procedure‐related intestinal, vascular or bladder injuries, injury to other pelvic organ, blood transfusion, re‐admission). Failure of technical approach (e.g. clip converted to partial salpingectomy). Other outcomes included: operative time; changes in menstrual bleeding pattern; postoperative pain: pain scores or use of analgesics; postoperative complications: wound infection, reoperation, urinary tract infection, pelvic inflammatory disease; length of hospital stay; difficulty of procedure; persistent pain; women's satisfaction; surgeons' satisfaction. Definitions Postoperative pain: defined whenever possible as localised physical suffering related to the tubal occlusion technique. Postoperative complication: any disease or condition developed as a direct consequence of the procedure. Changes in menstrual pattern: any changes in frequency or quantity of menstrual bleeding. Major morbidity: any morbidity occurring as a result of the intervention that lead to an additional intervention (e.g. additional surgical procedure, blood transfusion) or to re‐admission. Minor morbidity: any morbidity occurring as a result of the intervention and which does not lead to major additional interventions. Technical failure or failure of technical approach: failure to apply the intended method with the consequent need to switch to another technique. Technical difficulties: any difficulty in applying the selected method and which does not lead to change to another procedure. Search methods for identification of studies For the original review, the Cochrane Central Register of Controlled Trials (CENTRAL) and MEDLINE were searched; the electronic search strategy included the following terms: (tubal OR female OR contracep) AND (sterilis OR steriliz OR laparo OR culdoscopy OR colpotomy OR Filshie OR Hulka OR Yoon OR Pomeroy OR Irving OR Parkland OR (Rocket and Clips) OR (tubal and ring) OR (silastic and ring) OR (Quinacrine AND tubal) OR (chemical AND instillation AND tubal)). For the 2010 and 2015 updates, PubMed, POPLINE and LILACS were also searched and the following search strategy was used: PubMed: sterilisation, tubal AND (technique OR method OR methods OR methodology OR procedure) AND clinical trial. POPLINE: (female sterilisation/female sterilisation/((tubal & (ligat/occlud/occlus)) & female)) & clinical trial. LILACS: sterilisation, tubal or esterilizacion tubaria or esterilizacao tubaria [Words] AND method OR metodo OR methods OR metodos OR technique OR techniques OR technica OR technicas OR procedure OR procedures OR procedimiento. Searches were conducted by Carol Manion of FHI 360 (formerly Family Health International). In addition, we searched reference lists of identified trials and used the 'related articles' feature of PubMed to search for other possible trials. Data collection and analysis Selection of studies For the original 2002 review, two reviewers (RK, JMN) selected the trials for inclusion (Nardin 2002; Nardin 2003). For the update, TL and RK sifted the searches and selected trials. Data extraction and management For this update, we designed a Microsoft Excel® spreadsheet based on a Microsoft Word® form that was previously designed and used for this review. Data extraction for the original review was performed by RK and JMN. For the updates, this was performed by TL and checked by RK. TL entered data into Review Manager software and RK checked them (RevMan 2014). In addition to outcome data, we also extracted information about the following: setting (country, level of the healthcare institution, year); details of surgery: type of surgical procedure, type of anaesthesia, timing of procedure (postpartum, interval, postabortion); interventions compared; types and numbers of participants; risk of bias criteria including, method of randomisation, concealment of allocation, loss to follow‐up and postrandomisation exclusions. Whenever possible, we extracted outcome data according to 'intention to treat'. Assessment of risk of bias in included studies The 2002 and 2010 versions of this review utilised older Cochrane methodology for assessing risk of bias that involved an A, B, C system of assessing bias and excluded studies with poor allocation concealment (Appendix 1). For this updated review we reviewed previous exclusions and, where possible, updated the 'Risk of bias' assessment of previously included studies. For this version of the review (and future versions), risk of bias has been assessed according to the following criteria: 1. Random sequence generation (checking for possible selection bias) For each study we assessed the method used to generate the allocation sequence as: low risk of bias (any truly random process, e.g. random‐number table; computer random‐number generator); high risk of bias (any non‐random process, e.g. odd or even date of birth; hospital or clinic record number); though quasi‐randomised studies are not eligible for inclusion in the review; unclear risk of bias (if the process of sequence generation was not described). 2. Allocation concealment (checking for possible selection bias) For each included study, we assessed the method used to conceal allocation to interventions prior to assignment and assessed whether intervention allocation could have been foreseen in advance of, or during recruitment, or changed after assignment. We assessed the methods as: low risk of bias (e.g. telephone or central randomisation; consecutively numbered sealed opaque envelopes); high risk of bias (open random allocation; unsealed or non‐opaque envelopes, alternation; date of birth); unclear risk of bias (if the process of was not described). 3. Blinding of participants, personnel and outcome assessors (checking for possible performance and detection bias) For each included study, we assessed the methods used, if any, to blind study participants, personnel and outcome assessors from knowledge of which intervention a participant received. We considered that studies were at low risk of bias if they were blinded. We assessed the methods as: low, high or unclear risk of bias for participants; low, high or unclear risk of bias for personnel; low, high or unclear risk of bias for outcome assessors. 4. Incomplete outcome data (checking for possible attrition bias due to the amount, nature and handling of incomplete outcome data) We assessed the completeness of data including attrition and exclusions from the analyses. We recorded whether attrition and exclusions were reported and the numbers included in the analysis at each stage (compared with the total randomized participants), reasons for attrition or exclusion where reported, and whether missing data were balanced across groups or were related to outcomes. We assessed methods as: low risk of bias (e.g. no missing outcome data; missing outcome data balanced across groups); high risk of bias (e.g. numbers or reasons for missing data imbalanced across groups; ‘as treated’ analysis done with substantial departure of intervention received from that assigned at randomisation); unclear risk of bias (e.g. withdrawals not stated, denominators not given). 5. Selective reporting (checking for reporting bias) We assessed the possibility of selective outcome reporting bias as: low risk of bias (where it was clear that all of the study’s pre‐specified outcomes and all expected outcomes of interest to the review have been reported); high risk of bias (where not all the study’s pre‐specified outcomes have been reported; one or more reported primary outcomes were not pre‐specified; outcomes of interest were reported incompletely and so could not be used; study failed to include results of a key outcome that would have been expected to have been reported); unclear risk of bias. 6. Other bias (checking for bias due to problems not covered by 1 to 5 above) We assessed whether there were other possible sources of bias, for example, imbalances in important baseline characteristics, and judged these to be at low, high or unclear risk. 7. Overall risk of bias We made explicit judgements about whether studies were at high risk of bias, according to the criteria given in the Cochrane Handbook for Systematic Reviews of Interventions (Higgins 2011). With reference to points 1 to 6 above, we attempted to assess the likely magnitude and direction of the bias and whether we considered it likely to impact on the findings. We explored the impact of the level of bias through undertaking sensitivity analyses ‐ seeSensitivity analysis. Measures of treatment effect Dichotomous data For dichotomous data, we used summary odds ratios (OR) with 95% confidence intervals (CI). Continuous data We used the mean difference (MD) with 95% CIs if outcomes were measured in the same way between trials, which was the case for this version of the review. Had they not been measured in the same way, we would have used the standardised mean difference (SMD), provided pooling these data was considered meaningful. Unit of analysis issues We did not anticipate unit of analysis issues. Dealing with missing data For included studies, we noted levels of attrition. We did not impute data. For all outcomes, as far as possible, we performed analyses on an intention‐to‐treat basis, that is, we attempted to include all participants randomized to each group in the analyses. The denominator for each outcome in each trial was the number randomized minus any participants whose outcomes were known to be missing. Assessment of heterogeneity We assessed statistical heterogeneity in each meta‐analysis using the Tau², I² and Chi² statistics. We regarded heterogeneity as substantial if I² was greater than 30% and, either Tau² was greater than zero, or there was a low P value (less than 0.10) in the Chi² test for heterogeneity. Assessment of reporting biases There were insufficient studies to assess publication bias using funnel plots; however, in future versions, this may be possible if there are 10 or more studies in a meta‐analysis. Data synthesis We carried out statistical analysis using Review Manager software (RevMan 2014). We used fixed‐effect methods to produce an overall summary of effect if heterogeneity was low (I² < 30%), otherwise we used random‐effects methods. The random‐effects summary was treated as the average of the range of possible treatment effects. Quality of evidence The quality of the evidence was assessed using the GRADE approach for the following key outcomes (GRADE 2014): failure rate (yearly incidence of unintended pregnancy); major morbidity; minor morbidity; failure of technical approach; postoperative pain. We considered evidence from RCTs to be high quality in the first instance, and downgraded the evidence quality for imprecision, inconsistency, indirectness, risk of bias, and publication bias when present. We also downgraded for sparse data when few events occurred (equivalent to downgrading twice for imprecision). Sensitivity analysis If there were sufficient trials, we carried out sensitivity analyses to explore the effect of trial quality by excluding studies at high risk of bias from the analyses in order to assess whether this made any difference to the overall results. Results Description of studies Results of the search We included nine RCTs in the original 2002 review, and 12 trials in the 2011 version. For this latest review, we ran the searches on 23 July 2015, which produced a list of 62 references. After screening these references for title and abstract, we identified three eligible studies; two of which we included (Qui 2011; Rodriguez 2013), and one that we excluded (Chapa 2015). We also identified two additional studies that we included using the 'related articles' feature of PubMed (Dominik 2000; Siegle 2005). We reviewed all previously excluded RCTs according to our updated methodology, and included three that had previously been excluded due to risk of bias concerns, bringing the total number of included RCTs in the review to 19. Included studies Trials evaluated the following comparisons. Sterilisation (interval) using tubal ring compared with tubal clip: six trials, including a total of 4232 women (Aranda 1985; Argueta 1980; Geirsson 1985; Pymar 2004; Sokal 2000; Stovall 1991). Sterilisation (interval) with partial salpingectomy (modified Pomeroy technique) compared with electrocoagulation: three trials, including 2019 women (Siegle 2005; Sitompul 1984; WHO 1982). Sterilisation (interval) using tubal ring compared with electrocoagulation: two trials, including a total of 599 women (Aranda 1976; Koetsawang 1978). Postpartum sterilisation by partial salpingectomy (Pomeroy and Modified Pomeroy techniques) compared with Filshie clip: three trials, including 1629 women (Kohaut 2004; Rodriguez 2013; Yan 1990). Interval or postabortion sterilisation by partial salpingectomy (modified Uchida technique) compared with silver clip: one trial, including 2198 women (Qui 2011). Interval sterilisation by Hulka clip compared with Filshie clip: two trials, including 2326 women (Dominik 2000; Toplis 1988). Interval sterilisation by clip compared to electrocoagulation: two trials, including 206 women (Gentile 2006; Goynumer 2009). Electrocoagulation was specified as unipolar in Koetsawang 1978, and bipolar in Gentile 2006, Goynumer 2009 and Siegle 2005, but type was not specified in three other trials that used electrocoagulation. Design and settings Most of the studies were single‐centre RCTs, with six exceptions: WHO 1982 involved eight centres, four in industrialised countries and four in non‐industrialised countries; Aranda 1976 was conducted in three low‐ and middle‐income country centres (Costa Rica, El Salvador, Egypt); Qui 2011 was conducted in 20 clinics in China; Rodriguez 2013 was conducted in centres in Thailand, Taiwan, Panama and the Phillipines; Sokal 2000 was conducted in centres in Panama, Peru, Kenya, Brazil, Mexico, Indonesia,Thailand and the Dominican Republic; and Dominik 2000 was conducted in centres in Malaysia, Panama, the Dominican Republic, Mexico, Venezuela, Guatamala, and Haiti. Surgical approach Access to the abdomen was achieved by different approaches. Ten studies used laparoscopy (Aranda 1976; Argueta 1980; Geirsson 1985; Gentile 2006; Goynumer 2009; Koetsawang 1978; Pymar 2004; Siegle 2005; Stovall 1991; Toplis 1988); three used laparotomy (Aranda 1985; Qui 2011; Yan 1990); two used minilaparotomy (Kohaut 2004; Rodriguez 2013); three used minilaparotomy or laparoscopy (Dominik 2000; Sokal 2000; WHO 1982), and one study compared three different approaches to enter the abdominal cavity (Sitompul 1984). Procedures were performed by experienced surgeons in five trials (Dominik 2000; Sitompul 1984; Sokal 2000; Toplis 1988; WHO 1982), and by trainee third year residents in two trials (Siegle 2005; Stovall 1991); in the remainder, the surgeon's experience was not explicitly stated. The type of anaesthesia used varied among participating institutions according to institutional standards or at the surgeons' discretion for certain multicentre studies (Rodriguez 2013; Sokal 2000; WHO 1982). For other studies, procedures were performed under general anaesthesia (Geirsson 1985; Goynumer 2009; Siegle 2005), local anaesthesia (Aranda 1976; Argueta 1980; Koetsawang 1978; Qui 2011; Sitompul 1984) epidural anaesthesia (Yan 1990), general or local (Aranda 1985), general or spinal (Kohaut 2004), or was not clearly stated (Dominik 2000; Gentile 2006; Pymar 2004; Stovall 1991; Toplis 1988). Participants and outcomes 1. Tubal ring versus clip trials Aranda 1985 randomized 663 women to tubal ring or Rocket clip. Women had similar socio‐demographic characteristics, and a similar percentage of interval and post‐spontaneous abortion procedures (about 55% and 45% respectively) was performed in each group. Main outcomes were major and minor morbidity, technical failures and difficulties, failure rates and complaints. Argueta 1980 randomized 299 women to interval sterilisation by tubal ring or spring‐loaded clip. Selected socio‐demographic characteristics of the subjects were similar in both groups. Main outcomes were operative morbidity, technical failures and difficulties, failure rates, and complaints. A total of 114 women were lost to follow‐up at 24 months; 54 from the clip group (36% of group) and 60 from the ring group (40% of group). Stovall 1991 randomized 365 women to interval sterilisation by tubal ring (189 women) or the spring‐loaded clip (176 women). All women had urine tests for human chorionic gonadotropin (hCG) 72 hours before their planned surgical procedure. Both groups had similar socio‐demographic characteristics. The primary outcome was failure rate. An average of 16 months (range, 6 to 24 months) of follow‐up was reported. Chromopertubation was performed on all the women after application of the occluding devicesand confirmed successful tubal occlusion in all women. Geirsson 1985 randomized 79 women to interval sterilisation by tubal ring or Filshie clip. Mean age and parity were similar between the two groups. Primary outcomes were postoperative pain and analgesic requirements. Pymar 2004 included 40 women who had a Filshie clip and a ring applied to opposite tubes. The side of application and type of device was randomized. Pain during the first 24 hours postoperatively was the primary outcome based on evidence that women can discriminate between pain on each side of the abdomen. The method of anaesthesia was not stated. Sokal 2000 randomized 2746 women to a Filshie clip (1381 women) or tubal ring (1365 women). The report combined data from two studies, one utilising a minilaparotomy approach, the other utilising laparoscopy. Outcomes evaluated included pregnancy, adverse events, hospital admissions, and further surgery with follow‐up conducted at one, six, and 12 months. 2. Partial salpingectomy versus electrocoagulation Sitompul 1984 randomized 300 women to interval sterilisation in three groups (100 each for minilaparotomy, laparoscopy and culdoscopy). The modified Pomeroy technique was performed for all women in the minilaparotomy and the culdoscopy group, while electrocoagulation was the sterilisation method used in the laparoscopy group. Outcomes included operative time, hospitalisation, postoperative complications, and failure rates. WHO 1982 randomized 1827 women to interval sterilisation by Pomeroy partial salpingectomy via minilaparotomy (912 women) or electrocoagulation via laparoscopy (915 women). Main outcomes were major and minor morbidity, technical failures, and postoperative complaints. Siegle 2005 randomized 109 women to interval partial salpingectomy (Pomeroy) or bipolar electrocoagulation. The primary outcome was postoperative pain up to two weeks after surgery. There was little usable data from this study. 3. Tubal ring versus electrocoagulation In Aranda 1976, 299 women who were at least six weeks postpartum were randomly assigned to electrocoagulation or tubal ring groups via laparoscopy (interval sterilisation). Women in the two groups were similar with respect to socio‐demographic characteristics. Outcomes included surgical and early postoperative complications, and complaints. Koetsawang 1978 randomized 300 women in equal numbers to electrocoagulation (unipolar) or the tubal ring. All operations were performed on an outpatient basis for women who had not recently been pregnant (interval sterilisation). The two groups had similar socio‐economic characteristics. All women completed the six month follow‐up. Outcomes included operative morbidity, technical failures and difficulties, failure rates, operative time, and complaints. 4. Postpartum partial salpingectomy versus clip Yan 1990 randomized 200 women postpartum: 100 to Pomeroy partial salpingectomy and 100 to Filshie clip, and followed them up for 24 months after sterilisation. Socio‐demographic characteristics (age, total live births and previous contraceptive use) were reported to be similar between groups. Rodriguez 2013 randomized 1400 postpartum women to partial salpingectomy or Filshie clip. All women had undergone a vaginal delivery. Follow‐up was performed at one, six, 12, and 24 months following sterilisation. This report includes the 200 particpants in Yan 1990 (but reports fewer outcomes). Kohaut 2004 randomized 32 women to postpartum or intraoperative (after caesarean section) sterilisation by the Filshie clip or the Pomeroy method. Main outcomes concerned the ease of procedure and the surgeons' satisfaction. There was little usable data from this study. 5. Interval partial salpingectomy versus clip Qui 2011 randomized 2198 women to partial salpingectomy (Uchida technique) or silver clips. The participants were mostly more than six weeks postpartum (interval sterilisation), with less than 2% being postabortion. Approximately 63% of sterilisations were performed in lactating women in whom menses had not resumed. Outcomes were pregnancy rates, morbidity, operative time, and women's satisfaction. Women were followed up at one week, and three, six, and 12 months following sterilisation. 6. Comparison of different clip methods for interval sterilisation Toplis 1988 randomized 200 women to Filshie clip or Hulka clip (spring‐loaded clip). Main outcomes were operative morbidity, operative time, and complaints. Dominik 2000 reported the combined results of two multicentre RCTs comparing Filshie and Hulka clips, one using a minilaparotomy approach (878 women), the other using a laparoscopic approach (1248 women). Outcomes were failure rates, technical failure and difficulties, and morbidity. 7. Clips versus electrocoagulation Gentile 2006 randomized 118 women to Hulka clips or bipolar electrocautery for interval sterilisation and conducted a series of urine and serum oestradiol and progesterone tests for two years poststerilisation. Unpublished data on secondary outcomes, including women's satisfaction, were not available. Goynumer 2009 randomized 88 women to a mechanical clip or bipolar electrocoagulation for interval sterilisation. Outcomes were ovarian reserve indicators (hormones and ovarian volume). These two trials contributed no data that could be used in the review analyses. Risk of bias in included studies The risk of bias of included studies is summarised in Figure 1. Most studies were older studies with an unclear risk of bias as information about study methods was often missing from trial reports. Randomisation and allocation concealment was inadequately described in 50% of the studies. Blinding of the outcome assessor was described in nine studies (Aranda 1976; Aranda 1985; Argueta 1980; Gentile 2006; Koetsawang 1978; Pymar 2004; Rodriguez 2013; Sokal 2000; Yan 1990). Open in figure viewer Figure 1 Risk of bias summary: review authors' judgements about each risk of bias item for each included study. Attrition bias was serious in two studies: in Geirsson 1985, nine women were excluded post‐procedure "due to intra‐operative difficulties" that were not described in detail, while in Aranda 1985, 30 cases of technical failure (5% of total) were excluded from the analyses. It was not clear from which groups these women came, and we were unable to include these data on technical failures in the review. Postrandomisation exclusions due to protocol violations occurred with similar frequency in the WHO 1982 trial (about 12% in the Pomeroy group and about 10% in the electrocoagulation group); however, there were also important differences in baseline characteristics and methods of accessing the tubes between arms of this trial, which may have had an impact on the results. We took the assessment of risk of bias into consideration when grading the quality of the evidence. For more details, see Characteristics of included studies. Effects of interventions See: Summary of findings for the main comparison Summary of findings: ring versus clip; Summary of findings 2 Summary of findings: modified Pomeroy partial salpingectomy versus electrocoagulation; Summary of findings 3 Summary of findings: tubal ring versus electrocoagulation; Summary of findings 4 Summary of findings: partial salpingectomy versus clip; Summary of findings 5 Summary of findings: Hulka clip versus Filshie clip 1. Tubal ring versus clip Six trials evaluated this comparison for interval sterilisation. Only one trial reported major morbidity (one event in the clip arm; Peto OR 0.14, 95% CI 0.00 to 7.05; participants = 545; studies = 1; Analysis 1.1) and no deaths were reported in any of the trials. Overall minor morbidity was more frequent in the ring group (Peto OR 2.15, 95% CI 1.22 to 3.78; participants = 842; studies = 2; I² = 0%; Analysis 1.2) and there were more procedure‐related injuries in the ring group compared with the clip group (Peto OR 1.95, 95% CI 1.36 to 2.78; participants = 3575; studies = 3; I² = 0%; Analysis 1.3.1). Failure of technical approach occurred more often in the ring group (Peto OR 3.93, 95% CI 2.43 to 6.35; participants = 3476; studies = 3; I² = 0%; Analysis 1.4). Technical difficulties were not very different between tubal ring and clip groups (Peto OR 1.13, 95% CI 0.87 to 1.46; participants = 3590; studies = 3; I² = 28%; Analysis 1.5). There was no clear difference in failure (pregnancy) rates between the tubal ring and clip groups (Peto OR 0.72, 95% CI 0.33 to 1.57; participants = 3822; studies = 4; I² = 0%; Analysis 1.6). Follow‐up in these studies was between 12 and 24 months. There were no clear differences in postoperative pain complaints (Peto OR 1.14, 95% CI 0.88 to 1.48; participants = 922; studies = 3; I² = 0%; Analysis 1.10.1) or analgesic use; however, one study reported more complaints of cramping pain during the first week after surgery with the tubal ring compared with the clip (Peto OR 5.24, 95% CI 1.52 to 18.00; participants = 70; studies = 1; Analysis 1.10.3). There was no difference in the frequency of menstrual irregularities between groups (Peto OR 1.61, 95% CI 0.75 to 3.49; participants = 612; studies = 2; I² = 0%; Analysis 1.11). 2. Modified Pomeroy partial salpingectomy versus electrocoagulation Three trials evaluated this comparison for interval sterilisation. There were no cases of operative mortality in the one study that reported this outcome (WHO 1982). Major morbidity was more frequent in the Pomeroy group than the electrocoagulation group (Peto OR 2.87, 95% CI 1.13 to 7.25; participants = 1905; studies = 2; I² = 0%; Analysis 2.2); with one case of a burn to the small bowel reported in the electrocoagulation group. Minor morbidity was also more frequent in the Pomeroy group (Peto OR 1.60, 95% CI 1.10 to 2.33; participants = 1905; studies = 2; I² = 0%; Analysis 2.4), mainly due to wound infections. There were no data on technical failures and difficulties. One pregnancy was reported (in the Pomeroy group) in the only trial that reported this outcome (Sitompul 1984; Peto OR 4.47, 95% CI 0.07 to 286.78; participants = 295; studies = 1; Analysis 2.6). This intrauterine pregnancy occurred between one and two years of follow‐up (Analysis 2.7). There was no clear difference in the proportion of women hospitalised for more than 24 hours (OR 0.48, 95% CI 0.08 to 2.74; participants = 108; studies = 1; Analysis 2.8). More women in the Pomeroy group reported postoperative abdominal pain (Peto OR 3.85, 95% CI 2.91 to 5.10; participants = 1905; studies = 2; I² = 0%; Analysis 2.9). Single studies found no clear difference in rates of analgesic use (Peto OR 2.05, 95% CI 0.40 to 10.56; participants = 109; studies = 1; Analysis 2.9.2), or rates of persistent pain at follow‐up visit between the groups (Peto OR 1.09, 95% CI 0.81 to 1.47; participants = 1610; studies = 1; Analysis 2.9.3). 3. Tubal ring versus electrocoagulation Two trials evaluated this comparison for laparoscopic interval sterilisation (Aranda 1976; Koetsawang 1978). Electrocoagulation was unipolar in Koetsawang 1978 and not specified in Aranda 1976. No deaths were reported. Major morbidity was not significantly different between the groups, with only Aranda 1976 reporting an adverse event due to a burn of the small intestine in the electrocoagulation group (Peto OR 0.14, 95% CI 0.00 to 7.01; participants = 596; studies = 2; I² = 0%; Analysis 3.1 and Analysis 3.2). There were no clear differences in minor morbidity (Peto OR 0.97, 95% CI 0.50 to 1.87; participants = 596; studies = 2; I² = 0%; Analysis 3.3), technical failures (Peto OR 3.42, 95% CI 0.59 to 19.81; participants = 596; studies = 2; I² = 0%; Analysis 3.5) or technical difficulties (Peto OR 0.14, 95% CI 0.01 to 1.33; participants = 298; studies = 1; Analysis 3.6) between the groups. No pregnancies were reported. More women in the ring group reported postoperative abdominal pain (OR 3.40, 95% CI 1.17 to 9.84; participants = 596; studies = 2; I² = 87%; Analysis 3.9). There was no difference between groups in either operative time (Analysis 1.8) or menstrual irregularities (Analysis 1.11). 4. Partial salpingectomy versus clip Four trials evaluated this comparison, three used the modified Pomeroy technique for partial salpingectomy (Kohaut 2004; Rodriguez 2013; Yan 1990) versus titanium (Filshie) clips, one using the modified Uchida technique for interval sterilisation versus silver clips (Qui 2011). Two studies contributed little data (Kohaut 2004; Rodriguez 2013). Yan 1990 was one of the study centres included in Rodriguez 2013 and reported more outcomes than Rodriguez 2013. There were no cases of operative mortality or major morbidity in the only study that reported these outcomes (Qui 2011; Analysis 4.1 and Analysis 4.2). Minor morbidity was not significantly different between treatment groups (Peto OR 7.39, 95% CI 0.46 to 119.01; participants = 193; studies = 1; Analysis 4.3). Technical failures were more common in the clip group (Peto OR 0.18, 95% CI 0.08 to 0.40; participants = 2198; studies = 1; Analysis 4.5), but not technical difficulties (Peto OR 0.97, 95% CI 0.42 to 2.24; participants = 2198; studies = 1; Analysis 4.6). Pregnancies by 12 months occurred more frequently in the clip group (OR 0.21, 95% CI 0.05 to 0.84; participants = 3537; studies = 2; I 2 = 0%; Analysis 4.7). Operative time was longer for partial salpingectomy procedures than for clips (MD 4.26, 95% CI 3.65 to 4.86; participants = 2223; studies = 2; I² = 0%; Analysis 4.8). Neither patient complaints (Peto OR 1.30, 95% CI 0.92 to 1.82; participants = 2137; studies = 1; Analysis 4.9) nor menstrual irregularities were significantly different between groups (OR 1.43, 95% CI 0.73 to 2.79; participants = 2283; studies = 2; I² = 49%; Analysis 4.10). Patient complaints were reported by Qui 2011 at three, six, and 12 months and rates were similar at all assessment points. Women's satisfaction, reported in this study favoured the partial salpingectomy group (Peto OR 1.27, 95% CI 0.99 to 1.64; participants = 2110; studies = 1; Analysis 4.11); authors of this Chinese trial linked this to historical preferences. 5. Filshie clip versus Hulka clip Two trials evaluated this comparison (Dominik 2000; Toplis 1988). There was no clear difference in minor morbidity overall (Peto OR 0.14, 95% CI 0.00 to 7.32; participants = 197; studies = 1; Analysis 5.1), or in procedure‐related injuries (OR 1.57, 95% CI 0.73 to 3.36; participants = 2322; studies = 2; I² = 0%; Analysis 5.2.1), urogenital tract infections (OR 2.40, 95% CI 0.62 to 9.30; participants = 1910; studies = 1; Analysis 5.2.2), or minor wound complications (OR 0.86, 95% CI 0.63 to 1.17; participants = 1910; studies = 1; Analysis 5.2.3). There was no clear difference in technical failures (OR 1.04, 95% CI 0.10 to 11.33; participants = 2325; studies = 2; I² = 55%; Analysis 5.3); however, technical difficulties occurred more frequently with the Hulka clip (Peto OR 1.51, 95% CI 1.09 to 2.10; participants = 2323; studies = 2; I² = 0%; Analysis 5.4). There was no clear difference between groups in the failure rate at one year poststerilisation (OR 6.20, 95% CI 0.75 to 51.66; participants = 1441; studies = 1; Analysis 5.5). Cumulative two‐year failures rates in the largest study, Dominik 2000, were 11.7 and 28.1 pregnancies per 1000 procedures for Filshie and Hulka clips, respectively. Discussion Summary of main results Altogether we included 19 RCTs involving 13,209 women requesting sterilisation. Sterilisation was performed on an interval basis in most trials, apart from three RCTs of postpartum sterilisation involving 1632 women. RCTs compared tubal rings versus clips (six RCTs, 4232 women), partial salpingectomy versus electrocoagulation (three RCTs, 2019 women), tubal rings versus electrocoagulation (two RCTs, 599 women), partial salpingectomy versus clips (four RCTs, 3627 women), clips versus electrocoagulation (two RCTs, 206 women) and Hulka versus Filshie clips (2 RCTs, 2326 women). The RCTs of clips versus electrocoagulation contributed no data to analyses. Studies of postpartum sterilisation compared partial salpingectomy with clips. No RCTs compared tubal inserts (hysteroscopic sterilisation) to other methods. The main findings are summarised in summary of findings Table for the main comparison, summary of findings Table 2; summary of findings Table 3; summary of findings Table 4; and summary of findings Table 5. One year after sterilisation, failure rates were comparable for tubal rings and clips (high‐quality evidence), partial salpingectomy and clips (high‐quality evidence), and for partial salpingectomy and electrocoagulation (low‐quality evidence). Estimates of failure rates for these methods were less than five pregnancies per 1000 procedures in the first year post‐sterilisation, and longer‐term pregnancy rates were generally not reported. No deaths were reported as a results of the procedures in any of the studies. Major morbidity was rare with 22 events reported in three trials (Aranda 1976; Aranda 1985; WHO 1982), 17 events occurred with partial salpingectomy, four with electrocoagulation, and one with a clip procedure. Minor morbidity occurred twice as often with tubal rings than with tubal clips (high‐quality evidence) and technical failures were also significantly more common with rings than clips (high‐quality evidence). There was no significant difference in postoperative pain between these groups (see summary of findings Table for the main comparison). Major and minor morbidity occurred more frequently with partial salpingectomy than with electrocoagulation for interval sterilisation (low‐ to moderate‐quality evidence; summary of findings Table 2). Postoperative pain (up to 24 hours) was also significantly more common in the partial salpingectomy group than with electrocoagulation (moderate‐quality evidence). There was no significant difference in major or minor morbidity when tubal rings were compared with electrocoagulation for interval sterilisation (low‐ to moderate‐quality evidence; summary of findings Table 3). Evidence relating to technical failures was of a low quality for this comparison. Significantly more women undergoing sterilisation by tubal ring complained of postoperative pain in the first 24 hours compared with those in the electrocoagulation group (low‐quality evidence); however, this difference did not persist to the follow‐up visit. For partial salpingectomy versus tubal clips, one large study reported no major morbidity with either method (summary of findings Table 4). We found limited data on minor morbidity suggesting that there may be little difference between groups (low‐quality evidence). Evidence suggested that technical failures were more frequent with clip sterilisation (moderate‐quality evidence). There was no significant difference in patients' complaints at follow‐up in the one large study that reported this outcome (moderate‐quality evidence). Pooled data from two studies indicated that operative time was shorter on average with the clip technique than with partial salpingectomy (high‐quality evidence). Hulka and Filshie clips were comparable in most outcomes for which there were data (summary of findings Table 5), except that technical difficulties occurred more frequently in the Hulka clip group (moderate‐quality evidence). We found little evidence about women's and surgeons' satisfaction for any of the comparisons. Overall completeness and applicability of evidence We found a fairly substantial body of evidence indicating that various established techniques for interrupting tubal patency, including partial salpingectomy, electrocoagulation, and use of tubal clips and rings, are safe and effective methods. As studies utilising electrocoagulation did not always state whether unipolar or bipolar coagulation was used, we were unable to draw differential conclusions regarding these methods; however, major morbidity attributed to electrocoagulation in the included studies was very low. We found no RCTs that compared sterilisation by tubal inserts (hysteroscopic sterilisation) with other methods, so more evidence on the safety and efficacy of this relatively new method is needed. The short duration of follow‐up in the RCTs included in this review, which was usually one or two years, limits the evidence on failure (pregnancy) rates. In addition, failure rates were possibly underestimated due to high losses to follow‐up in those RCTs that reported a two‐year follow‐up.Thus, data on longer‐term failure rates may best be derived from the CREST study (Peterson 1996). Cumulative evidence from this prospective cohort study found that the 10‐year probability of pregnancy was highest after clip sterilisation (36.5/1000 procedures) and lowest for postpartum partial salpingectomy (7.5/1000) and unipolar coagulation (7.5/1000). Tubal ring was the most common sterilisation technique in the CREST cohort and was associated with a 10‐year probability of pregnancy of 17.7/1000 procedures. The one‐year and 10‐year probabilities of pregnancy with any procedure was 5.5 /1000 and 18.5/1000 procedures, respectively. Younger women (18 to 27 years) undergoing sterilisation by bipolar coagulation were at greatest risk of sterilisation failure within ten years of the procedure (54.3/1000 procedures). We did not try to determine the relative effects of different types of anaesthetic methods (local, spinal, general anaesthesia and other) on women's sterilisation experience, including postoperative pain, and this could be the subject of a separate review. Quality of the evidence We graded the quality of the main findings of the review using the GRADE (Grading of Recommendations Assessment, Development and Evaluation) approach. The quality of the evidence relating to tubal rings versus clips was mainly high. For the evidence related to partial salpingectomy compared with electrocoagulation, we downgraded the evidence quality to low or moderate due to imprecision or indirectness, as the findings may have been due to the access approach rather than the tubal occlusion technique (partial salpingectomy was mainly performed via minilaparotomy, whereas electrocoagulation was performed via laparoscopy). We downgraded the quality of the evidence relating to tubal rings versus electrocoagulation for most outcomes, most frequently due to imprecision of the effect. We graded the evidence relating to partial salpingectomy versus tubal clips mainly as moderate due to imprecision or risk of bias. Evidence on minor morbidity for this comparison was very sparse and imprecise, hence we downgraded it to low quality evidence. For the comparison of Filshie and Hulka clips, evidence was mainly of a low to moderate quality due to imprecision, with or without other factors. Potential biases in the review process The original review was performed in 2002 using old Cochrane methods for classifying studies and assessing risk of bias. For this update, we revised the methodology to conform with current Cochrane methods for 'Risk of bias' assessment, resulting in the inclusion of three RCTs that had been excluded from previous versions of the review. Two of these studies contributed little (Geirsson 1985), or no (Goynumer 2009), data. In addition, we identified two RCTs using the related articles feature of PubMed, which should have been included in earlier versions of the review (Dominik 2000; Siegle 2005). Due to resource constraints we did not re‐extract the missing risk of bias details from previously included studies for this update. For the comparison 'partial salpingectomy versus clips', we pooled data from two RCTs that used different methods for partial salpingectomy (modified Pomeroy and Uchida methods) and different clip methods (titanium and silver clips; see Included studies) and performed subgroup analysis to compare these findings. The test for subgroup differences indicated no difference, however, these subgroup analyses were not pre‐specified in the protocol. This subgrouping also served to distinguish between studies according to the timing of the procedure, i.e. postpartum and interval sterilisation, which similarly indicated no significant difference in findings according to the procedure timing. Although we noted when studies were at moderate or high risk of bias for specific outcomes, we did not perform sensitivity analysis, because few studies contributed to most analyses; however, we downgraded results accordingly in the 'Summary of findings' tables. We found no RCTs comparing types of tubal inserts or comparing tubal inserts with other methods of interrupting tubal patency; however, we found one RCT comparing two methods of accessing the fallopian tubes (vaginoscopy compared with hysteroscopy) to insert Essure inserts (Chapa 2015). Studies comparing methods of accessing the tubes are not included in this review. Abdominal approaches (minilaparotomy versus laparoscopy) for female sterilisation are the subject of a separate Cochrane review (Kulier 2004) and, similarly, studies comparing methods of vaginal approaches to hysteroscopic sterisation should be considered in a separate Cochrane review. Agreements and disagreements with other studies or reviews Data from newly included studies support the previous findings of this review, that tubal sterilisation by most established methods is an effective and safe procedure. Evidence relating to postoperative pain was limited in our review; however, for the comparison of partial salpingectomy versus electrocoagulation, and tubal rings versus electrocoagulation, moderate‐quality evidence indicated that there was less postoperative pain with electrocoagulation. A recent review of RCTs of local anaesthesia to reduce postoperative pain following interval laparoscopic sterilisation found that the intraoperative application of local anaesthetic to the tubes significantly reduced postoperative pain for ring and clip sterilisation (Harrison 2014). In addition, a protocol for a Cochrane Review to evaluate the effectiveness of interventions for pain relief in women undergoing postpartum mini‐laparotomy tubal sterilisation has recently been published (Lumbiganon 2015). This review should help further towards improving the experience of women requesting this popular form of contraception. We found no RCTs of hysteroscopic sterilisation compared with other methods of sterilisation. Hysteroscopic sterilisation with tubal inserts has several advantages over older techniques in that the procedure avoids the peritoneal cavity, requires no incisions, usually requires no anaesthesia, may be well tolerated, and is usually performed as an outpatient procedure (Peterson 2008). In the USA, hysteroscopic sterilisation with Essure® is reported to be rapidly replacing laparoscopic sterilisation and is potentially associated with lower cost (Connor 2009; Kraemer 2009). User satisfaction rates are reported to be high (Arjona 2008; Chudnoff 2015; Connor 2009; Sinha 2007), however, placement failure rates vary and long‐term efficacy has still to be established. Two systematic reviews of non‐randomised studies were unable to calculate the cumulative probability of pregnancy with Essure® due to limitations in available data (Cleary 2013; la Chapelle 2015). One found 'fair‐quality evidence' that pregnancy was rare in women with documented bilateral tubal occlusion at three months after the procedure (Cleary 2013); the other reported a cumulative three‐year probability of pregnancy with Adiana (no longer available) of 16/1000 procedures (la Chapelle 2015). Gariepy 2014 used an evidence‐based Markov model to estimate the relative probability of pregnancy over 10 years following sterilisation with three methods ‐ Essure®, the silicone ring, and bipolar coagulation ‐ and estimated pregnancy probabilities of 96, 24 and 30 per 1000 women, respectively, with the highest risk of pregnancy after Essure® sterilisation occurring in the first year post‐procedure (57 per 1000 women). This estimate considered the complete clinical pathways of the procedures, taking into account uncertainties regarding placement success, hysterosalpingogram (HSG) follow‐up, and successful tubal occlusion, and therefore possibly reflects the 'real‐life' situation. Other recent reports of Essure® sterilisation include a prospective study that reported no pregnancies in 449 women with successful bilateral placement and confirmed occlusion who completed the five‐year follow‐up (71% of cohort; Chudnoff 2015), and a retrospective cohort study of 109,277 women who underwent sterilisation by Essure® (39,169 women) or laparoscopic tubal ligation procedures (70,108 women) in France between 2006 and 2010 reporting pregnancy rates of 0.36% and 0.45%, respectively (Fernandez 2014). More data are needed on the short‐ and long‐term side‐effects of hysteroscopic sterilisation relative to other methods. In Chudnoff 2015, intermenstrual bleeding occurred among 23.6% of women during the first three months postprocedure, 20% of women (74/386) reported heavier menses at the five‐year follow‐up visit; 5.3% (25/473) experienced recurrent pelvic pain, and 15 women underwent hysterectomy during the five‐year follow‐up period (apparently only two were possibly attributable to Essure®). Ouzounelli 2015 conducted a review of hysteroscopic sterilisation compared with laparoscopic tubal ligation and found that both had low rates of complications, although complications related to Essure® procedures were "more likely to be minor in nature". Another review concluded that "the incidence and severity of complications with hysteroscopic sterilisation has not been adequately studied and remains unclear" (la Chapelle 2015). A review by Cooper 2010 found that the vaginoscopic approach (whereby hysteroscopy is performed without a vaginal speculum or cervical instruments to grasp the cervix) may be associated with less pain than traditional hysteroscopic sterilisation techniques with no difference in the number of failed procedures. One of the obvious limitations of hysteroscopic sterilisation at present is the delay in achieving its occlusive effect and the need for confirmatory testing at three months. A new iteration of the Essure® insert designed to achieve immediate tubal occlusion appears to show promise in this regard, and may reduce pre‐HSG pregnancies (Thiel 2014). A search of clinical trial registries at the time of writing (31 July 2015) found no registered or ongoing RCTs comparing hysteroscopic methods with more widely used methods. No RCTs investigating the safety and effectiveness of quinacrine sterilisation, which is used unlicensed in some regions, have been conducted or registered. Due to its low cost, easy application, apparent safety, and comparable effectiveness, a call has been made recently for the use of quinacrine in low‐ and middle‐income countries to be reconsidered (Lippes 2015). Concerns about the mutagenicity of quinacrine have not been supported by epidemiological evidence from extensive human studies (Lippes 2015), with at least two large studies finding no association between quinacrine sterilisation (QS) and the risk of gynaecological cancer (Sokal 2010a; Sokal 2010b). Furthermore, studies conducted in China and Iran have reported that QS is more acceptable to women than surgical sterilisation (Lu 2003; Soroodi‐Moghaddam 2003). A large, well‐conducted RCT of this inexpensive, minimally‐invasive method could be important. Figures and Tables - Figure 1 Risk of bias summary: review authors' judgements about each risk of bias item for each included study. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.1 Comparison 1 Tubal ring versus clip, Outcome 1 Major morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.2 Comparison 1 Tubal ring versus clip, Outcome 2 Minor morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.3 Comparison 1 Tubal ring versus clip, Outcome 3 Minor morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.4 Comparison 1 Tubal ring versus clip, Outcome 4 Technical failures. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.5 Comparison 1 Tubal ring versus clip, Outcome 5 Technical difficulties. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.6 Comparison 1 Tubal ring versus clip, Outcome 6 Failure rate: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.7 Comparison 1 Tubal ring versus clip, Outcome 7 Failure rate: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.8 Comparison 1 Tubal ring versus clip, Outcome 8 Operative time. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.9 Comparison 1 Tubal ring versus clip, Outcome 9 Hospital stay > 24 h. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.10 Comparison 1 Tubal ring versus clip, Outcome 10 Complaints. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 1.11 Comparison 1 Tubal ring versus clip, Outcome 11 Menstrual irregularities. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.1 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 1 Operative mortality. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.2 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 2 Major morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.3 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 3 Major morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.4 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 4 Minor morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.5 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 5 Minor morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.6 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 6 Failure rate: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.7 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 7 Failure rate: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.8 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 8 Hospital stay more 24 h. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 2.9 Comparison 2 Partial salpingectomy (modified Pomeroy) versus electrocoagulation, Outcome 9 Complaints. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.1 Comparison 3 Tubal ring versus electrocoagulation, Outcome 1 Major morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.2 Comparison 3 Tubal ring versus electrocoagulation, Outcome 2 Major morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.3 Comparison 3 Tubal ring versus electrocoagulation, Outcome 3 Minor morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.4 Comparison 3 Tubal ring versus electrocoagulation, Outcome 4 Minor morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.5 Comparison 3 Tubal ring versus electrocoagulation, Outcome 5 Technical failures: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.6 Comparison 3 Tubal ring versus electrocoagulation, Outcome 6 Technical difficulties. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.7 Comparison 3 Tubal ring versus electrocoagulation, Outcome 7 Failure rate: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.8 Comparison 3 Tubal ring versus electrocoagulation, Outcome 8 Operative time. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.9 Comparison 3 Tubal ring versus electrocoagulation, Outcome 9 Complaints. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 3.10 Comparison 3 Tubal ring versus electrocoagulation, Outcome 10 Menstrual irregularities. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.1 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 1 Operative mortality. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.2 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 2 Major morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.3 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 3 Minor morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.4 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 4 Minor morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.5 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 5 Technical failures. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.6 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 6 Technical difficulties. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.7 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 7 Failure rate (12 months) : total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.8 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 8 Operative time. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.9 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 9 All complaints. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.10 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 10 Menstrual irregularities. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 4.11 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 11 Women's satisfaction. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Study.. Kohaut 2004 Seven out of 10 surgeons performing a total of 29 sterilisations preferred the Filshie clip method to the Pomeroy method. Figures and Tables - Analysis 4.12 Comparison 4 Partial salpingectomy (PS) versus clip, Outcome 12 Surgeon's satisfaction. Navigate to figure in review Figures and Tables - Analysis 5.1 Comparison 5 Hulka versus Filshie clip, Outcome 1 Minor morbidity: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 5.2 Comparison 5 Hulka versus Filshie clip, Outcome 2 Minor morbidity: details. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 5.3 Comparison 5 Hulka versus Filshie clip, Outcome 3 Technical failures. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 5.4 Comparison 5 Hulka versus Filshie clip, Outcome 4 Technical difficulties. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 5.5 Comparison 5 Hulka versus Filshie clip, Outcome 5 Failure rate: total. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 5.6 Comparison 5 Hulka versus Filshie clip, Outcome 6 Operative time. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Figures and Tables - Analysis 5.7 Comparison 5 Hulka versus Filshie clip, Outcome 7 Complaints. Using systematic reviews (free)Navigate to figure in reviewPrint figureOpen in new tab Summary of findings for the main comparison.Summary of findings: ring versus clip Tubal ring compared with tubal clip for interval sterilisation Patient or population: women > 6 weeks postpartum requesting tubal sterilisation Settings: any Intervention: tubal ring Comparison: tubal clip OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ClipRing Major morbidity: totalLow risk populationOR 0.14 (0.00 to 7.05)545 (1)⊕⊕⊝⊝ low 1,2Only one event occurred in the clip group 4 per 1000 1 per 1000 (0 to 28) Minor morbidity: totalLow risk populationOR 2.15 (1.22 to 3.78)842 (2)⊕⊕⊕⊕ high 57 per 1000123 per 1000 (70 to 215) Minor morbidity: details ‐ procedure‐related injuriesLow risk populationOR 1.95 (1.36 to 2.78)3575 (3)⊕⊕⊕⊕ high 21 per 100041 per 1000 (29 to 58) Technical failuresLow risk populationOR 3.93 (2.43 to 6.35)3476 (3)⊕⊕⊕⊕ high 10 per 100039 per 1000 (24 to 63) Failure rate: details (12 to 24 months)Low risk populationOR 0.72 (0.33 to 1.57)3822 (4)⊕⊕⊕⊕ high 4 per 10003 per 1000 (1 to 6) Complaints: Postoperative pain (24 hours)Low risk populationOR 1.14 (0.88 to 1.48)922 (3)⊕⊕⊕⊕ high 477 per 1000544 per 1000 (420 to 706) The basis for the assumed risk is the median control group (clip) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. Figures and Tables - Summary of findings for the main comparison.Summary of findings: ring versus clip Navigate to table in review Summary of findings 2.Summary of findings: modified Pomeroy partial salpingectomy versus electrocoagulation Modified Pomeroy partial salpingectomy compared with tubal electrocoagulation for interval sterilisation Patient or population: women > 6 weeks postpartum requesting tubal sterilisation Settings: any Intervention: modified Pomeroy partial salpingectomy Comparison: electrocoagulation OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ElectrocoagulationModified Pomeroy Major morbidity: totalLow risk populationOR 2.87 (1.13 to 7.25)1905 (2)⊕⊕⊝⊝ low 1,2 10 per 100029 per 1000 (11 to 73) Major morbidity: procedure‐related injuries requiring additional operation or blood transfusion10 per 100019 per 1000 (19 to 190)OR 1.90 (0.19 to 18.96)1905 (2)⊕⊕⊝⊝ low 1,2 Major morbidity: rehospitalisation as a consequence of the operation20 per 1000115 per 1000 (15 to 900)OR 5.74 (0.73 to 45.09)295 (1)⊕⊝⊝⊝ very low 1,2 Minor morbidity: totalLow risk populationOR 1.60 (1.10 to 2.33)1905 (2)⊕⊕⊝⊝ low 1,4The WHO study reported significantly more wound infections in the modified Pomeroy group, where participants underwent minilaparotomy, compared with the electrocoagulation group where laparoscopy was used) 38 per 100061 per 1000 (42 to 89) Minor morbidity: procedure‐related injuries with no additional operationLow risk populationOR 0.53 (0.06 to 5.11)1610 (1)⊕⊕⊕⊝ moderate 1 2 per 10001 per 1000 0 to 10) Failure rate: total (12 months)Low risk populationOR 4.47 (0.07 to 286.78)295 (1)⊕⊕⊝⊝ low 1,3 0.5 per 10002 per 1000 (0 to 143) Complaints ‐ postoperative pain (24 hours)Low risk populationOR 3.85 (2.91 to 5.10)1905 (2)⊕⊕⊕⊝ moderate 4 95 per 1000366 per 1000 (276 to 485) Complaints ‐ persistent pain at follow‐up visitLow risk populationOR 1.09 (0.88 to 1.47)1610 (1)⊕⊕⊕⊝ moderate 4 117 per 1000128 per 1000 (95 to 172) The basis for the assumed risk is the median control group (electrocoagulation) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to inconsistency. 3 Sparse data. 4 Downgraded due to indirectness (this effect may be due to the abdominal approach (minilaparotomy versus laparoscopy) rather than the tubal technique). Figures and Tables - Summary of findings 2.Summary of findings: modified Pomeroy partial salpingectomy versus electrocoagulation Navigate to table in review Summary of findings 3.Summary of findings: tubal ring versus electrocoagulation Tubal ring compared with electrocoagulation for interval sterilisation Patient or population: women > 6 weeks postpartum requesting tubal sterilisation Settings: any Intervention: tubal ring Comparison: electrocoagulation OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ElectrocoagulationRing Major morbidity: totalLow risk populationOR 0.14 0.00 to 7.01 596 (2)⊕⊕⊝⊝ low 1,2Unipolar electrocoagulation stated in one study and not specified in the other. Only one event reported in total 0.5 per 10000 per 1000 (0 to 4) Minor morbidity: totalLow risk populationOR 0.97 (0.50, 1.87)596 (2)⊕⊕⊕⊝ moderate 1 66 per 100064 per 1000 (33 to 123) Technical failures: totalLow risk populationOR 3.42 (0.59 to 19.81)596 (2)⊕⊕⊕⊝ moderate 1 3 per 100010 per 1000 (2 to 60) Failure rate: totalnot estimable not estimable Not estimable due to insufficient data 160 (1)‐No pregnancies reported in one study Complaints ‐ postoperative pain (24 hours)Low risk populationOR 3.40 (1.17 to 9.84)596 (2)⊕⊕⊝⊝ low 1,3 176 per 1000598 per 1000 (206 to 1000) Complaints ‐ persistent pain at follow‐up visitLow risk populationOR 1.22 (0.75 to 1.97)594 (2)⊕⊕⊕⊝ moderate 1 140 per 1000171 per 1000 (105 to 276) The basis for the assumed risk is the median control group (electrocoagulation) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. 3 Downgraded due to inconsistency. Figures and Tables - Summary of findings 3.Summary of findings: tubal ring versus electrocoagulation Navigate to table in review Summary of findings 4.Summary of findings: partial salpingectomy versus clip Partial salpingectomy compared with tubal clips for tubal sterilisation Patient or population: women requesting postpartum or interval sterilisation Settings: any Intervention: partial salpingectomy Comparison: tubal clips OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk ClipsPartial salpingectomy Major morbidity: totalLow risk populationnot estimable 2198 (1)‐No deaths or major morbidity events reported in one large trial 0 per 10000 per 1000 Minor morbidity: totalLow risk populationOR 7.39 (0.46 to 119.01)193 (1)⊕⊕⊝⊝ low 1,2 0.5 per 10004 per 1000 (0 to 60) Technical failuresLow risk populationOR 0.18 (0.08 to 0.40)2198 (1)⊕⊕⊕⊝ moderate 3 20 per 10004 per 1000 (2 to 8) Failure rate: total (12 months)Low risk populationOR 0.21, 95% CI 0.05 to 0.84 3537 (2)⊕⊕⊕⊝ moderate 4In this analysis, we grouped studies according to whether sterilisation was performed on a postpartum (1) or interval basis (1). Results were similar across these subgroups (Test for subgroup differences: P value 0.58, I² = 0%) 2 per 10000.4 per 1000 (0 to 2) Complaints (12 months)Low risk populationOR 1.30 (0.92 to 1.82)2137 (1)⊕⊕⊕⊝ moderate 1This single study reported data on 'chief complaints' at 3, 6, and 12 months and rates were similar between groups at all assessment points 59 per 1000 77 per 1000 (54 to 107) The basis for the assumed risk is the median control group (clips) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. 3 Downgraded due to indirectness (unclear whether silver clips and Filshie clips are similarly effective). 4 Downgraded due to risk of bias. Figures and Tables - Summary of findings 4.Summary of findings: partial salpingectomy versus clip Navigate to table in review Summary of findings 5.Summary of findings: Hulka clip versus Filshie clip Hulka clips compared with Filshie clips for interval sterilisation Patient or population: women requesting sterilisation Settings: any Intervention: Hulka clips Comparison: Filshie clips OutcomesIllustrative comparative risks (95% CI)Relative effect (95% CI)No of participants (studies)Quality of the evidence (GRADE)Comments Assumed riskCorresponding risk Filshie clipHulka clip Minor morbidity: totalLow risk populationOR 0.14 (0.00 to 7.32)197 (1)⊕⊕⊝⊝ low 1,2 10 per 10001 per 1000 (0 to 70) Minor morbidity: procedure‐related injuriesLow risk populationOR 1.55 (0.73 to 3.26)2322 (2)⊕⊕⊕⊝ moderate 1 10 per 100016 per 1000 (7 to 33) Technical failuresLow risk populationOR 1.04 (0.10 to 11.33)2325 (2)⊕⊕⊝⊝ low 1,3 7 per 10007 per 1000 (1 to 79) Failure rate: total (12 months)Low risk populationOR 6.20 (0.75 to 51.66)1441 (1)⊕⊕⊕⊝ moderate 1 1 per 10006 per 1000 (1 to 52) Complaints: postoperative pain (24 hours)Low risk populationOR 1.74 (0.99 to 3.03)197 (1)⊕⊕⊝⊝ low 1,4 45 per 100078 per 1000 (45 to 136) The basis for the assumed risk is the median control group (Filshie clips) risk across studies. The corresponding risk (and its 95% confidence interval) is based on the assumed risk in the comparison group and the relative effect of the intervention (and its 95% CI). CI: confidence interval; OR: odds ratio GRADE Working Group grades of evidence High quality: Further research is very unlikely to change our confidence in the estimate of effect. Moderate quality: Further research is likely to have an important impact on our confidence in the estimate of effect and may change the estimate. Low quality: Further research is very likely to have an important impact on our confidence in the estimate of effect and is likely to change the estimate. Very low quality: We are very uncertain about the estimate. 1 Downgraded due to imprecision. 2 Downgraded due to sparse data. 3 Downgraded due to inconsistency. 4 Downgraded due to risk of bias. Figures and Tables - Summary of findings 5.Summary of findings: Hulka clip versus Filshie clip Navigate to table in review Comparison 1.Tubal ring versus clip Outcome or subgroup title No. of studies No. of participants Statistical method Effect size 1 Major morbidity: total Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 1.1 Procedure‐related injuries requiring additional operation or blood transfusion 1 545 Peto Odds Ratio (Peto, Fixed, 95% CI)0.14 [0.00, 7.05] 2 Minor morbidity: total Show forest plot2 842 Peto Odds Ratio (Peto, Fixed, 95% CI)2.15 [1.22, 3.78] 3 Minor morbidity: details Show forest plot3 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 3.1 Procedure related injuries with no additional operation 3 3575 Peto Odds Ratio (Peto, Fixed, 95% CI)1.95 [1.36, 2.78] 3.2 Urogenital infections 3 3145 Peto Odds Ratio (Peto, Fixed, 95% CI)1.88 [0.83, 4.28] 3.3 Wound infection 3 3144 Peto Odds Ratio (Peto, Fixed, 95% CI)1.17 [0.73, 1.87] 3.4 Postoperative temperature > 38 °C without hospitalisation 1 296 Peto Odds Ratio (Peto, Fixed, 95% CI)7.49 [0.15, 377.52] 4 Technical failures Show forest plot3 3476 Peto Odds Ratio (Peto, Fixed, 95% CI)3.93 [2.43, 6.35] 5 Technical difficulties Show forest plot3 3590 Peto Odds Ratio (Peto, Fixed, 95% CI)1.13 [0.87, 1.46] 6 Failure rate: total Show forest plot4 3822 Peto Odds Ratio (Peto, Fixed, 95% CI)0.72 [0.33, 1.57] 7 Failure rate: details Show forest plot2 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 7.1 Failure rate ≤ 1 year, total 2 2629 Peto Odds Ratio (Peto, Fixed, 95% CI)0.85 [0.23, 3.14] 7.2 Failure rate ≤ 1 year, extrauterine pregnancy 1 2202 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 7.3 Failure rate > 1 year, extrauterine pregnancy 1 427 Peto Odds Ratio (Peto, Fixed, 95% CI)8.11 [0.16, 410.33] 8 Operative time Show forest plot1 297 Mean Difference (IV, Fixed, 95% CI)0.0 [0.0, 0.0] 9 Hospital stay > 24 h Show forest plot1 Odds Ratio (M‐H, Fixed, 95% CI)Totals not selected 10 Complaints Show forest plot4 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 10.1 Postoperative pain < 24 h 3 922 Peto Odds Ratio (Peto, Fixed, 95% CI)1.14 [0.88, 1.48] 10.2 Postoperative analgesic use 1 70 Peto Odds Ratio (Peto, Fixed, 95% CI)0.70 [0.28, 1.79] 10.3 Cramping pain during first week after surgery 1 70 Peto Odds Ratio (Peto, Fixed, 95% CI)5.24 [1.52, 18.00] 11 Menstrual irregularities Show forest plot2 612 Peto Odds Ratio (Peto, Fixed, 95% CI)1.61 [0.75, 3.49] Figures and Tables - Comparison 1.Tubal ring versus clip Navigate to table in review Comparison 2.Partial salpingectomy (modified Pomeroy) versus electrocoagulation Outcome or subgroup title No. of studies No. of participants Statistical method Effect size 1 Operative mortality Show forest plot1 1610 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 2 Major morbidity: total Show forest plot2 1905 Peto Odds Ratio (Peto, Fixed, 95% CI)2.87 [1.13, 7.25] 3 Major morbidity: details Show forest plot2 Odds Ratio (M‐H, Random, 95% CI)Subtotals only 3.1 Procedure‐related injuries requiring additional operation or blood transfusion 2 1905 Odds Ratio (M‐H, Random, 95% CI)1.90 [0.19, 18.96] 3.2 Rehospitalisation as a consequence of operation 1 295 Odds Ratio (M‐H, Random, 95% CI)5.74 [0.73, 45.09] 4 Minor morbidity: total Show forest plot2 1905 Peto Odds Ratio (Peto, Fixed, 95% CI)1.60 [1.10, 2.33] 5 Minor morbidity: details Show forest plot2 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 5.1 Procedure‐related injuries with no additional operation 1 1610 Peto Odds Ratio (Peto, Fixed, 95% CI)0.53 [0.06, 5.11] 5.2 Urogenital infections 1 1610 Peto Odds Ratio (Peto, Fixed, 95% CI)0.81 [0.43, 1.50] 5.3 Wound infection 1 1610 Peto Odds Ratio (Peto, Fixed, 95% CI)2.49 [1.54, 4.04] 5.4 Postoperative temperature > 38 °C without hospitalisation 1 295 Peto Odds Ratio (Peto, Fixed, 95% CI)1.45 [0.18, 11.77] 6 Failure rate: total Show forest plot1 295 Peto Odds Ratio (Peto, Fixed, 95% CI)4.47 [0.07, 286.78] 6.1 Failure rate, total 1 295 Peto Odds Ratio (Peto, Fixed, 95% CI)4.47 [0.07, 286.78] 7 Failure rate: details Show forest plot1 295 Peto Odds Ratio (Peto, Fixed, 95% CI)4.47 [0.07, 286.78] 7.1 Failure rate > 1 year, total 1 295 Peto Odds Ratio (Peto, Fixed, 95% CI)4.47 [0.07, 286.78] 8 Hospital stay more 24 h Show forest plot1 108 Odds Ratio (M‐H, Fixed, 95% CI)0.48 [0.08, 2.74] 9 Complaints Show forest plot3 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 9.1 Postoperative pain < 24 h 2 1905 Peto Odds Ratio (Peto, Fixed, 95% CI)3.85 [2.91, 5.10] 9.2 Postoperative analgesic use 1 109 Peto Odds Ratio (Peto, Fixed, 95% CI)2.05 [0.40, 10.56] 9.3 Persistent pain at follow‐up visit 1 1610 Peto Odds Ratio (Peto, Fixed, 95% CI)1.09 [0.81, 1.47] Figures and Tables - Comparison 2.Partial salpingectomy (modified Pomeroy) versus electrocoagulation Navigate to table in review Comparison 3.Tubal ring versus electrocoagulation Outcome or subgroup title No. of studies No. of participants Statistical method Effect size 1 Major morbidity: total Show forest plot2 596 Peto Odds Ratio (Peto, Fixed, 95% CI)0.14 [0.00, 7.01] 2 Major morbidity: details Show forest plot1 298 Peto Odds Ratio (Peto, Fixed, 95% CI)0.14 [0.00, 7.01] 2.1 Procedure‐related injuries requiring additional operation or blood transfusion 1 298 Peto Odds Ratio (Peto, Fixed, 95% CI)0.14 [0.00, 7.01] 3 Minor morbidity: total Show forest plot2 596 Peto Odds Ratio (Peto, Fixed, 95% CI)0.97 [0.50, 1.87] 4 Minor morbidity: details Show forest plot2 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 4.1 Procedure‐related injuries with no additional operation 2 596 Peto Odds Ratio (Peto, Fixed, 95% CI)0.76 [0.17, 3.38] 4.2 Urogenital infections 1 296 Peto Odds Ratio (Peto, Fixed, 95% CI)1.03 [0.14, 7.37] 4.3 Wound infection 1 296 Peto Odds Ratio (Peto, Fixed, 95% CI)0.93 [0.38, 2.25] 4.4 Postoperative temperature > 38 °C without hospitalisation 2 594 Peto Odds Ratio (Peto, Fixed, 95% CI)1.37 [0.31, 6.06] 5 Technical failures: total Show forest plot2 596 Peto Odds Ratio (Peto, Fixed, 95% CI)3.42 [0.59, 19.81] 6 Technical difficulties Show forest plot1 298 Peto Odds Ratio (Peto, Fixed, 95% CI)0.14 [0.01, 1.33] 7 Failure rate: total Show forest plot1 160 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 7.1 Failure rate, total 1 160 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 8 Operative time Show forest plot1 298 Mean Difference (IV, Fixed, 95% CI)0.0 [0.0, 0.0] 9 Complaints Show forest plot2 Odds Ratio (M‐H, Random, 95% CI)Subtotals only 9.1 Postoperative pain < 24 h 2 596 Odds Ratio (M‐H, Random, 95% CI)3.40 [1.17, 9.84] 9.2 Postoperative analgesic use 1 298 Odds Ratio (M‐H, Random, 95% CI)2.51 [1.00, 6.30] 9.3 Persistent pain at follow‐up visit 2 594 Odds Ratio (M‐H, Random, 95% CI)1.22 [0.75, 1.97] 10 Menstrual irregularities Show forest plot1 296 Peto Odds Ratio (Peto, Fixed, 95% CI)0.90 [0.56, 1.45] Figures and Tables - Comparison 3.Tubal ring versus electrocoagulation Navigate to table in review Comparison 4.Partial salpingectomy (PS) versus clip Outcome or subgroup title No. of studies No. of participants Statistical method Effect size 1 Operative mortality Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 1.1 Uchida vs silver clip 1 2198 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 2 Major morbidity: total Show forest plot1 2198 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 2.1 Uchida vs silver clip 1 2198 Peto Odds Ratio (Peto, Fixed, 95% CI)0.0 [0.0, 0.0] 3 Minor morbidity: total Show forest plot1 193 Peto Odds Ratio (Peto, Fixed, 95% CI)7.39 [0.46, 119.01] 4 Minor morbidity: details Show forest plot1 193 Peto Odds Ratio (Peto, Fixed, 95% CI)7.39 [0.46, 119.01] 4.1 Procedure related injuries with no additional operation 1 193 Peto Odds Ratio (Peto, Fixed, 95% CI)7.39 [0.46, 119.01] 5 Technical failures Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 5.1 Uchida vs silver clip 1 2198 Peto Odds Ratio (Peto, Fixed, 95% CI)0.18 [0.08, 0.40] 6 Technical difficulties Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 6.1 Uchida vs silver clip 1 2198 Peto Odds Ratio (Peto, Fixed, 95% CI)0.97 [0.42, 2.24] 7 Failure rate (12 months) : total Show forest plot2 3537 Odds Ratio (M‐H, Random, 95% CI)0.21 [0.05, 0.84] 7.1 Pomeroy vs Filshie 1 1400 Odds Ratio (M‐H, Random, 95% CI)0.22 [0.05, 1.02] 7.2 Uchida vs silver clip 1 2137 Odds Ratio (M‐H, Random, 95% CI)0.19 [0.01, 3.95] 8 Operative time Show forest plot2 2223 Mean Difference (IV, Fixed, 95% CI)4.26 [3.65, 4.86] 8.1 Pomeroy vs Filshie 1 25 Mean Difference (IV, Fixed, 95% CI)6.70 [0.77, 12.63] 8.2 Uchida vs silver clip 1 2198 Mean Difference (IV, Fixed, 95% CI)4.23 [3.62, 4.84] 9 All complaints Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 9.1 Uchida vs silver clip 1 2137 Peto Odds Ratio (Peto, Fixed, 95% CI)1.30 [0.92, 1.82] 10 Menstrual irregularities Show forest plot2 2283 Odds Ratio (M‐H, Random, 95% CI)1.43 [0.73, 2.79] 10.1 Pomeroy vs Filshie 1 146 Odds Ratio (M‐H, Random, 95% CI)2.49 [0.88, 7.05] 10.2 Uchida vs silver clip 1 2137 Odds Ratio (M‐H, Random, 95% CI)1.16 [0.90, 1.49] 11 Women's satisfaction Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 11.1 Uchida vs silver clip 1 2110 Peto Odds Ratio (Peto, Fixed, 95% CI)1.27 [0.99, 1.64] 12 Surgeon's satisfaction Show forest plotOther data No numeric data Figures and Tables - Comparison 4.Partial salpingectomy (PS) versus clip Navigate to table in review Comparison 5.Hulka versus Filshie clip Outcome or subgroup title No. of studies No. of participants Statistical method Effect size 1 Minor morbidity: total Show forest plot1 197 Peto Odds Ratio (Peto, Fixed, 95% CI)0.14 [0.00, 7.32] 2 Minor morbidity: details Show forest plot2 Odds Ratio (M‐H, Random, 95% CI)Subtotals only 2.1 Procedure‐related injuries with no additional operation 2 2322 Odds Ratio (M‐H, Random, 95% CI)1.57 [0.73, 3.36] 2.2 Urogenital infection 1 1910 Odds Ratio (M‐H, Random, 95% CI)2.40 [0.62, 9.30] 2.3 Wound complications 1 1910 Odds Ratio (M‐H, Random, 95% CI)0.86 [0.63, 1.17] 3 Technical failures Show forest plot2 2325 Odds Ratio (M‐H, Random, 95% CI)1.04 [0.10, 11.33] 4 Technical difficulties Show forest plot2 2323 Peto Odds Ratio (Peto, Fixed, 95% CI)1.51 [1.09, 2.10] 5 Failure rate: total Show forest plot1 1441 Odds Ratio (M‐H, Fixed, 95% CI)6.20 [0.75, 51.66] 6 Operative time Show forest plot1 197 Mean Difference (IV, Fixed, 95% CI)0.70 [‐0.04, 1.44] 7 Complaints Show forest plot1 Peto Odds Ratio (Peto, Fixed, 95% CI)Subtotals only 7.1 Postoperative pain < 24 h 1 197 Peto Odds Ratio (Peto, Fixed, 95% CI)1.74 [0.99, 3.03] Figures and Tables - 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https://math.stackexchange.com/questions/4187473/shortest-distance-between-two-points-in-an-n-dimensional-isometric-triangular
Skip to main content Shortest distance between two points in an n-dimensional isometric (triangular) lattice Ask Question Asked Modified 2 years, 9 months ago Viewed 364 times This question shows research effort; it is useful and clear 2 Save this question. Show activity on this post. Consider this isometric lattice. This example is two dimensional and of size (6,5). Now, the goal is to compute the shortest distance between any two points on the grid given the coordinates for two points. However, a line cannot directly be drawn from the first point to the second - a "connection" between the two points must happen only through points in the grid, and points in the grid can only be connected to one of their six directly adjacent neighbors. For example, the shortest distances between points (0,4) and (0,1), (1,2) and (3,2), (2,4) and (4,1), (5,4) and (5,1) are 3, 2, 4, 3, as shown in this image. For two dimensions, I've been able to come up with the following equation to compute the distance between any two points: distance=max(0,|Δx|−⌊|Δy|2⌋)+|Δy| where Δx=x2−x1 and Δy=y2−y1 given that the two points under consideration have the coordinates (x1,y1) and (x2,y2). Now, I was only able to figure it out for two dimensions, simply because it was possible for me to draw the grid, visualize, and test combinations - I'm still not even sure if it works in all cases. I have been unable to figure out how to expand this to 3 dimensions, which is a formula that I need. Perhaps a general formula for an n dimensional lattice may also be interesting. I'm blindly speculating here, but by mindlessly following a similar pattern you'd perhaps get this for three dimensions: distance=max(0,|Δx|−⌊|Δy|2⌋−⌊|Δz|2⌋)+max(0,|Δy|−⌊|Δz|2⌋)+|Δz| Did I get it right? It is important to note that when expanding to other dimensions, the quantized nature of the distances must be preserved, i.e., the lattice must be extended in a manner that ensures that distances between any two adjacent points is always equal to the distance between (0,0) and (0,1) (hence a triangular lattice). Similarly, the distance between any two points can only be an integer multiple of the distance between (0,0) and (0,1). Insight would be much appreciated. Thank you very much and I hope you have nice day! geometry triangles integer-lattices network Share CC BY-SA 4.0 Follow this question to receive notifications edited Jul 1, 2021 at 5:01 Claudia Kincaid asked Jul 1, 2021 at 4:00 Claudia KincaidClaudia Kincaid 2133 bronze badges Add a comment | 2 Answers 2 Reset to default This answer is useful 1 Save this answer. Show activity on this post. Your formula for two dimensions doesn't work consistently. I have come across this post while researching a similar problem, so for the sake of posterity I would like to add to WimC's answer by noting that one can simply convert from nonlinear coordinates to linear coordinates temporarily and then perform the mentioned calculations. Assuming one can come up with a conversion function of course. The transformation for the nonlinear coordinates in the given example would be (x,y)⟶(x−⌊y2⌋,y), after which the formula given by WimC works just fine. (This probably could've been a comment, but I don't have the reputation for that.) Share CC BY-SA 4.0 Follow this answer to receive notifications answered Oct 29, 2022 at 11:23 fsocfsoc 1111 bronze badge Add a comment | This answer is useful 0 Save this answer. Show activity on this post. An n-dimensional grid L can be created by taking L={x∈Zn+1∣x1+…+xn+1=0}. The offset between two neighbours in the grid is then ej−ek for j≠k in {1,…,n+1} (so any point with exactly one coordinate 1, one coordinate −1 and all others zero). The distance between a point x∈L and the origin is then the sum of its positive coordinates: d(x,0)=∑{xj∣xj>0}. The distance between two points x,y∈L is the distance of x−y to the origin: d(x,y)=d(x−y,0). The coordinates in your picture are unusual because they are not linear. This makes it a bit harder to express distances. In more natural, linear, coordinates, the point (1,2) in the picture would have coordinates (0,2) since it is twice the point (0,1), etc. For the case n=2, a point expressed in such linear coordinates (x,y) can be mapped to the point (x,y,−x−y)∈L. Let’s do one of your examples. The points (2,4) and (4,1) in your picture have linear coordinates (0,4) and (4,1) respectively. The distance between (0,4) and (4,1) is d((0,4,−4),(4,1,−5))=d((−4,3,1),0)=3+1=4. Share CC BY-SA 4.0 Follow this answer to receive notifications edited Jul 1, 2021 at 5:37 answered Jul 1, 2021 at 5:10 WimCWimC 33.4k22 gold badges5252 silver badges9898 bronze badges 2 Thank you for generously taking the time to reply! The reason for the strange coordinate system is because of the fact that I wanted the lattice to have a somewhat rectangle-like shape rather than a parallelogram. While mathematically it is less natural and more complex, using my coordinate system in the particular application I'm interested in provides simplicity. If I were to use linear coordinates, my lattice have the final shape of a parallelogram, and I'd need to create two triangular exclusion zones to get a rectangle, which makes things more complex for my end use case. – Claudia Kincaid Commented Jul 1, 2021 at 6:02 The reason I simply didn't just use a square lattice when I'm clearly interested in a final rectangular shape was because the isometric one offers 50% more adjacent equidistant nodes. – Claudia Kincaid Commented Jul 1, 2021 at 6:03 Add a comment | You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions geometry triangles integer-lattices network See similar questions with these tags. 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https://www.sparkl.me/learn/ib/physics-hl/rotational-kinetic-energy/revision-notes/1631
Past Papers Log In Past Papers Courses Collegeboard AP IB DP Cambridge IGCSE AS & A Level IB MYP 1-3 IB MYP 4-5 All Topics physics-hl | ib The Particulate Nature of Matter 1.1.1 Heat and temperature 1.1.2 Specific heat capacity and latent heat 1.1.3 Methods of heat transfer (conduction, convection, radiation) 1.1.4 Thermal expansion 1.2.1 Earth's energy balance 1.2.2 Greenhouse gases and their role 1.2.3 Impact of human activity on the greenhouse effect 1.3.1 Ideal gas law (PV = nRT) 1.3.2 Boyle’s law, Charles’s law, Avogadro’s law 1.3.3 Real gases and deviations from ideal gas behaviour 1.4.1 Laws of thermodynamics 1.4.2 Heat engines and efficiency 1.4.3 Entropy and spontaneous processes 1.5.1 Electric charge and current 1.5.2 Ohm’s law and resistivity 1.5.3 Kirchhoff’s laws 1.5.4 Power dissipation in resistors Wave Behaviour 2.1.1 Types of waves: Transverse and longitudinal 2.1.2 Properties of waves (amplitude, frequency, wavelength, speed) 2.1.3 Wave equations 2.2.1 Reflection, refraction, diffraction, and interference 2.2.2 Doppler effect 2.2.3 Standing waves and resonance 2.3.1 Displacement, velocity, and acceleration in SHM 2.3.2 Energy in SHM 2.3.3 Pendulum and spring systems Nuclear and Quantum Physics 3.1.1 Quantum theory and uncertainty principle 3.1.2 Wave-particle duality 3.1.3 Photoelectric effect 3.2.1 Types of radiation: Alpha, beta, gamma 3.2.2 Half-life and decay constant 3.2.3 Radioactive decay and applications 3.3.1 Nuclear fission process 3.3.2 Chain reaction and critical mass 3.3.3 Applications of nuclear fission (nuclear reactors) 3.4.1 Nuclear fusion and energy production in stars 3.4.2 Stellar nucleosynthesis 3.4.3 Life cycle of stars 3.5.1 Atomic models (Bohr, quantum model) 3.5.2 Electron configuration and energy levels 3.5.3 Isotopes and atomic mass Space, Time, and Motion 4.1.1 Scalars and vectors 4.1.2 Displacement, velocity, and acceleration 4.1.3 Equations of motion (constant acceleration) 4.1.4 Graphical analysis of motion 4.2.1 Newton’s laws of motion 4.2.2 Force, mass, and acceleration 4.2.3 Momentum and impulse 4.2.4 Conservation of momentum 4.2.5 Collisions and explosions 4.3.1 Work done by a force 4.3.2 Kinetic and potential energy 4.3.3 Conservation of mechanical energy 4.3.4 Power and efficiency 4.4.1 Torque and rotational motion 4.4.2 Moment of inertia and angular acceleration 4.4.3 Rotational kinetic energy 4.4.4 Angular momentum and its conservation 4.5.1 Frames of reference 4.5.2 Lorentz transformation equations 4.5.3 Time dilation and length contraction 4.5.4 Mass-energy equivalence (E = mc²) Fields 5.1.1 Gravitational force and field strength 5.1.2 Gravitational potential energy 5.1.3 Kepler's laws and orbital mechanics 5.2.1 Electric fields and potentials 5.2.2 Magnetic fields and forces 5.2.3 Coulomb's law and Gauss’s law 5.2.4 Applications in motors and electromagnets 5.3.1 Charge in magnetic fields 5.3.2 Cyclotron and magnetic force on a current 5.3.3 Magnetic flux and induction 5.4.1 Faraday’s law of electromagnetic induction 5.4.2 Lenz's law and applications 5.4.3 Transformers and power transmission Experimental Programme (Internal Assessment) 6.1.1 Laboratory techniques and safety protocols 6.1.2 Data collection, analysis, and uncertainty in measurements 6.1.3 Writing scientific reports and conclusions 6.2.1 Collaborative research and experimental work 6.2.2 Communicating scientific findings with others 6.2.3 Working within interdisciplinary teams 6.3.1 Developing research questions and hypotheses 6.3.2 Designing experiments and gathering data 6.3.3 Data analysis and interpretation of results Rotational kinetic energy Topic 2/3 Revision Notes Flashcards Past Paper Analysis Questions Videos Your Flashcards are Ready! 15 Flashcards in this deck. or How would you like to practise? Choose Difficulty Level. Choose Easy, Medium or Hard to match questions to your skill level. Choose Learning Method. Choose Easy, Medium or Hard to match questions to your skill level. 3 Still Learning I know 12 Previous Next Rotational Kinetic Energy Introduction Rotational kinetic energy is a fundamental concept in rigid body mechanics, pivotal in understanding the motion of rotating objects. For IB Physics HL students, grasping rotational kinetic energy is essential for analyzing various physical systems, from everyday machinery to complex astrophysical phenomena. This article delves into the intricacies of rotational kinetic energy, providing a comprehensive exploration tailored to the IB curriculum. Key Concepts Definition of Rotational Kinetic Energy Rotational kinetic energy is the energy possessed by an object due to its rotation about an axis. Unlike translational kinetic energy, which depends on the linear motion of an object, rotational kinetic energy is associated with rotational motion. The total kinetic energy of a rotating object is given by: $$ K = \frac{1}{2} I \omega^2 $$ where: - ( K ) is the rotational kinetic energy, - ( I ) is the moment of inertia, - ( \omega ) is the angular velocity. Moment of Inertia The moment of inertia (( I )) quantifies an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. For various shapes, the moment of inertia is calculated differently. For example: - Solid Cylinder: ( I = \frac{1}{2} m r^2 ) - Hollow Cylinder: ( I = m r^2 ) - Solid Sphere: ( I = \frac{2}{5} m r^2 ) Understanding the moment of inertia is crucial for accurately determining the rotational kinetic energy of different objects. Angular Velocity Angular velocity (( \omega )) measures how quickly an object rotates around an axis, expressed in radians per second (rad/s). It relates to the linear velocity (( v )) at a point on the object through the equation: $$ v = r \omega $$ where ( r ) is the radius from the axis of rotation to the point of interest. Angular velocity plays a pivotal role in calculating both rotational kinetic energy and torque. Energy Conservation in Rotational Motion In isolated systems where no external torques act, the total mechanical energy (sum of translational and rotational kinetic energy) remains conserved. This principle allows us to solve complex problems involving rotating objects by equating initial and final energies. For example, when a rotating wheel slows down due to friction, the loss in rotational kinetic energy is converted into thermal energy, assuming no other forms of energy are involved. Work-Energy Principle in Rotation The work done by a torque (( \tau )) in rotating an object through an angle (( \theta )) is given by: $$ W = \tau \theta $$ This work results in a change in the object's rotational kinetic energy: $$ \Delta K = \frac{1}{2} I \omega_f^2 - \frac{1}{2} I \omega_i^2 $$ where ( \omega_i ) and ( \omega_f ) are the initial and final angular velocities, respectively. This relationship is analogous to the translational work-energy theorem. Rotational Dynamics Rotational dynamics involves the study of forces and torques that cause rotational motion. Newton's second law for rotation states: $$ \tau = I \alpha $$ where ( \alpha ) is the angular acceleration. This equation links the applied torque to the resulting change in rotational motion, allowing for the analysis of systems undergoing rotational acceleration. Rotational Power Power in rotational systems measures how quickly work is done by a torque. It is defined as: $$ P = \tau \omega $$ where ( P ) is power, ( \tau ) is torque, and ( \omega ) is angular velocity. Rotational power is essential in understanding the efficiency and performance of engines and other mechanical systems. Examples and Applications Understanding rotational kinetic energy is vital in various real-world applications: - Automobiles: The rotational kinetic energy of wheels affects acceleration and fuel efficiency. - Sports: Athletes utilize rotational motion in activities like gymnastics and figure skating. - Astrophysics: The rotation of celestial bodies influences their formation and behavior. - Engineering: Designing machinery requires precise calculations of rotational energies to ensure safety and functionality. Equilibrium in Rotational Systems Rotational equilibrium occurs when the sum of torques acting on a system is zero, resulting in no angular acceleration. This condition is crucial for static structures like bridges and buildings, ensuring they remain stable under various forces. Rotational Inertia vs. Mass While mass quantifies an object's resistance to linear acceleration, rotational inertia (moment of inertia) measures resistance to angular acceleration. The two concepts are analogous but applied to different types of motion. Understanding this distinction is essential for solving problems involving both translational and rotational dynamics. Units of Measurement Rotational kinetic energy is measured in joules (J), consistent with other forms of energy. Angular velocity is measured in radians per second (rad/s), and moment of inertia is measured in kilogram square meters (kg.m²). Dimensional Analysis Performing dimensional analysis ensures the correctness of equations involving rotational kinetic energy. For instance: $$ \text{Dimensions of } K = \frac{1}{2} I \omega^2 = \frac{1}{2} \left( \text{kg.m}^2 \right) \left( \frac{\text{rad}}{\text{s}} \right)^2 = \text{kg.m}^2/\text{s}^2 $$ Since 1 joule = 1 kg.m²/s², the dimensions confirm that the equation correctly represents energy. Rotational Kinetic Energy in Different Frames of Reference Analyzing rotational kinetic energy can vary depending on the chosen frame of reference. In an inertial frame, calculations are straightforward, but in a non-inertial frame, additional fictitious forces and torques must be considered. Understanding these variations is crucial for accurately describing rotational systems in different contexts. Impact of Radius on Rotational Kinetic Energy The radius of rotation significantly influences the rotational kinetic energy. Larger radii increase the moment of inertia, thereby increasing the energy required for a given angular velocity. This principle is evident in systems like flywheels, where a larger radius enhances energy storage capabilities. Rotational Kinetic Energy in Composite Bodies For bodies composed of multiple interconnected parts, the total rotational kinetic energy is the sum of the kinetic energies of each part. Calculating this requires determining the moment of inertia for each component and summing their contributions: $$ K_{\text{total}} = \sum \frac{1}{2} I_i \omega_i^2 $$ where ( I_i ) and ( \omega_i ) are the moment of inertia and angular velocity of each component, respectively. Rotational Energy Transfer Energy can be transferred between translational and rotational forms. For example, when a rolling object accelerates, part of the energy goes into rotational kinetic energy. Understanding this transfer is essential for comprehensively analyzing motion in systems where both types of kinetic energy are present. Practical Calculation Examples Consider a solid disk of mass ( m ) and radius ( r ) rotating with angular velocity ( \omega ). Its rotational kinetic energy is: $$ K = \frac{1}{2} I \omega^2 = \frac{1}{2} \left( \frac{1}{2} m r^2 \right) \omega^2 = \frac{1}{4} m r^2 \omega^2 $$ If ( m = 2 ) kg, ( r = 0.5 ) m, and ( \omega = 10 ) rad/s, then: $$ K = \frac{1}{4} \times 2 \times (0.5)^2 \times 10^2 = \frac{1}{4} \times 2 \times 0.25 \times 100 = 12.5 \text{ J} $$ This example illustrates the step-by-step calculation of rotational kinetic energy using the provided formula. Advanced Concepts Mathematical Derivation of Rotational Kinetic Energy To derive the expression for rotational kinetic energy, consider an object rotating about a fixed axis. Each infinitesimal mass element ( dm ) at a distance ( r ) from the axis has a tangential velocity ( v = r \omega ). The kinetic energy of this mass element is: $$ dK = \frac{1}{2} dm \, v^2 = \frac{1}{2} dm \, (r \omega)^2 = \frac{1}{2} \omega^2 r^2 dm $$ Integrating over the entire mass ( M ) of the object: $$ K = \frac{1}{2} \omega^2 \int r^2 dm = \frac{1}{2} I \omega^2 $$ where ( I = \int r^2 dm ) is the moment of inertia. This derivation connects the microscopic velocities of mass elements to the macroscopic concept of rotational kinetic energy. Rotational Inertia Tensor For objects rotating in three dimensions, the moment of inertia generalizes to the inertia tensor, a 3x3 matrix that encapsulates the distribution of mass relative to all three principal axes. The inertia tensor ( \mathbf{I} ) allows for the calculation of rotational kinetic energy in more complex rotational motions: $$ K = \frac{1}{2} \boldsymbol{\omega}^T \mathbf{I} \boldsymbol{\omega} $$ where ( \boldsymbol{\omega} ) is the angular velocity vector. This tensorial approach is essential for analyzing rotational dynamics in objects with non-symmetric mass distributions. Euler's Equations of Motion Euler's equations describe the rotation of a rigid body in the absence of external torques. They are expressed as: $$ \begin{aligned} I_1 \frac{d \omega_1}{dt} + (I_3 - I_2) \omega_2 \omega_3 &= 0 \ I_2 \frac{d \omega_2}{dt} + (I_1 - I_3) \omega_3 \omega_1 &= 0 \ I_3 \frac{d \omega_3}{dt} + (I_2 - I_1) \omega_1 \omega_2 &= 0 \end{aligned} $$ where ( I_1, I_2, I_3 ) are the principal moments of inertia, and ( \omega_1, \omega_2, \omega_3 ) are the components of angular velocity. These equations are fundamental in understanding the rotational stability and dynamics of rigid bodies. Gyroscopic Precession Gyroscopic precession occurs when a spinning object experiences an external torque, causing the axis of rotation to change direction. The rate of precession (( \Omega )) for a gyroscope is given by: $$ \Omega = \frac{\tau}{I \omega} $$ where ( \tau ) is the applied torque, ( I ) is the moment of inertia, and ( \omega ) is the angular velocity. This phenomenon is crucial in applications like navigation instruments and stability mechanisms in vehicles. Energy in Rotating Frames Analyzing rotational kinetic energy in a rotating reference frame involves additional considerations, such as fictitious forces (e.g., Coriolis and centrifugal forces). The effective kinetic energy in such frames includes contributions from these pseudo-forces, complicating the energy calculations. Understanding energy transformations in rotating frames is essential for advanced studies in dynamics and relativity. Rotational Energy in Non-Rigid Bodies While rigid body mechanics assumes objects do not deform during rotation, real-world objects often experience slight deformations. These deformations can lead to energy dissipation through internal friction and heat generation. Analyzing rotational energy in non-rigid bodies requires considering these energy loss mechanisms, which are vital in engineering applications to prevent wear and tear. Quantum Mechanical Perspective At the quantum level, rotational kinetic energy plays a role in molecular and atomic structures. Molecules possess quantized rotational states, and transitions between these states involve discrete changes in rotational energy. Understanding rotational kinetic energy in quantum mechanics is fundamental for fields like spectroscopy and quantum chemistry. Rotational Brownian Motion Rotational Brownian motion refers to the random rotational movements of particles suspended in a fluid due to collisions with molecules. This concept is significant in understanding diffusion processes, colloidal stability, and the behavior of microscopic particles in various mediums. Application in Rotational Dynamics of Celestial Bodies The rotational kinetic energy of celestial bodies, such as planets and stars, influences their formation, stability, and evolution. Differential rotation in stars can lead to magnetic field generation through dynamo processes, while planetary rotation affects climate and atmospheric dynamics. Advanced Problem-Solving Techniques Solving complex problems in rotational kinetic energy often requires integrating multiple concepts: - Torque and Angular Momentum: Relating applied torques to changes in angular momentum. - Energy Conservation: Applying conservation principles to systems exchanging energy forms. - Inertia Tensor Calculations: Computing rotational kinetic energy for non-symmetric objects. - Precession and Nutation: Analyzing the motion of spinning objects under external influences. For instance, calculating the rotational kinetic energy of a spinning top undergoing precession involves understanding both angular momentum and torque interactions. Interdisciplinary Connections Rotational kinetic energy intersects with various disciplines: - Engineering: Designing rotating machinery, turbines, and flywheels. - Biology: Studying the rotational movements in biological systems, such as bacterial flagella. - Medicine: Understanding rotational dynamics in biomechanics and medical devices. - Environmental Science: Analyzing the rotation of Earth and its impact on climate systems. These interdisciplinary connections highlight the broad applicability and significance of rotational kinetic energy beyond traditional physics. Energy Storage Applications Rotational kinetic energy is harnessed in energy storage systems like flywheels, which store energy by maintaining rotational motion. These systems offer advantages in rapid energy release and high power density, making them suitable for applications in renewable energy integration, uninterruptible power supplies, and transportation. Rotational Energy Dissipation Mechanisms Dissipation of rotational kinetic energy occurs through various mechanisms: - Friction: Between moving parts or with the surrounding medium. - Air Resistance: Causing drag on rotating objects. - Internal Material Friction: Leading to heat generation within the object. - Electromagnetic Induction: In systems like electric motors, where energy is converted to other forms. Understanding these dissipation mechanisms is crucial for improving the efficiency and longevity of rotating systems. Rotational Dynamics in Robotics In robotics, controlling rotational kinetic energy is essential for maneuvering and performing precise tasks. Robotic joints and actuators rely on accurate calculations of rotational energy to ensure stability and responsiveness. Advanced control algorithms often integrate rotational dynamics to optimize robot performance. Impact of Rotational Speed on Kinetic Energy The relationship between rotational speed and kinetic energy is quadratic, meaning that doubling the angular velocity increases the rotational kinetic energy by a factor of four. This sensitivity necessitates careful consideration in applications where rotational speeds can vary widely, such as in turbines and engines. Thermodynamic Implications Rotational kinetic energy interacts with thermodynamic systems, particularly in energy conversion processes. For example, in heat engines, mechanical work often involves converting thermal energy into rotational motion. Analyzing these interactions requires an understanding of both thermodynamics and rotational dynamics. Rotational Vibrations Rotational vibrations involve oscillations in the rotational motion of an object. These vibrations can impact the stability and integrity of mechanical systems, necessitating analysis and control in engineering applications to prevent resonant conditions and material fatigue. Nonlinear Rotational Systems Nonlinearities in rotational systems arise when the relationships between torque, angular velocity, and angular acceleration are not directly proportional. Such complexities require advanced mathematical techniques to model and solve, often involving numerical methods and computational simulations. Advanced Computational Methods Modern computational tools facilitate the analysis of rotational kinetic energy in complex systems. Techniques like finite element analysis (FEA) and computational fluid dynamics (CFD) enable precise modeling of rotating objects under various conditions, enhancing our ability to predict and optimize rotational behavior. Comparison Table | | | | --- | Aspect | Rotational Kinetic Energy | Translational Kinetic Energy | | Definition | Energy due to an object's rotation about an axis. | Energy due to an object's linear motion. | | Formula | $K = \frac{1}{2} I \omega^2$ | $K = \frac{1}{2} m v^2$ | | Depends On | Moment of inertia and angular velocity. | Mass and linear velocity. | | Units | Joules (J) | Joules (J) | | Application Example | Spinning wheel, rotating flywheel. | Moving car, flying airplane. | | Energy Distribution | Distributed based on mass distribution relative to the axis. | Distributed based on mass and velocity. | Summary and Key Takeaways Rotational kinetic energy is crucial for understanding the motion of rotating objects. The moment of inertia and angular velocity are key determinants of rotational kinetic energy. Advanced concepts include the inertia tensor, Euler's equations, and gyroscopic precession. Applications span across engineering, astrophysics, biology, and more. Rotational and translational kinetic energies have analogous but distinct characteristics. Coming Soon! Examiner Tip Tips To remember the formula for rotational kinetic energy, think of the translational version and replace mass with moment of inertia and velocity with angular velocity: ( \frac{1}{2} I \omega^2 ). When solving problems, always double-check your units to ensure consistency. Visualize the mass distribution relative to the axis to accurately determine the moment of inertia. Practice by calculating rotational kinetic energy for different shapes to reinforce your understanding. Did You Know Did You Know Did you know that the conservation of rotational kinetic energy plays a crucial role in the stability of spinning satellites? Additionally, athletes in sports like diving and gymnastics use rotational kinetic energy to control their spins and flips. Surprisingly, gyroscopes, which rely on rotational kinetic energy, are fundamental components in modern navigation systems, ensuring accurate orientation for everything from smartphones to spacecraft. Common Mistakes Common Mistakes One common mistake is confusing rotational kinetic energy with translational kinetic energy. For example, students might incorrectly use ( \frac{1}{2} m v^2 ) instead of ( \frac{1}{2} I \omega^2 ) for rotating objects. Another frequent error is neglecting the distribution of mass when calculating the moment of inertia, leading to inaccurate energy assessments. Additionally, overlooking the units of angular velocity can result in incorrect calculations of kinetic energy. FAQ What is rotational kinetic energy? Rotational kinetic energy is the energy an object possesses due to its rotation around an axis, calculated using the moment of inertia and angular velocity. How does moment of inertia affect rotational kinetic energy? A higher moment of inertia increases the rotational kinetic energy for a given angular velocity, indicating greater resistance to changes in rotational motion. Can rotational kinetic energy be converted to other forms of energy? Yes, rotational kinetic energy can be transformed into thermal energy through friction, or into electrical energy in generators. What is the relationship between angular velocity and rotational kinetic energy? Rotational kinetic energy increases with the square of the angular velocity, meaning that doubling the angular velocity quadruples the kinetic energy. How is rotational kinetic energy applied in everyday machinery? In everyday machinery, rotational kinetic energy is utilized in components like flywheels to store energy, in motors to perform work, and in wheels to facilitate motion. The Particulate Nature of Matter 1.1.1 Heat and temperature 1.1.2 Specific heat capacity and latent heat 1.1.3 Methods of heat transfer (conduction, convection, radiation) 1.1.4 Thermal expansion 1.2.1 Earth's energy balance 1.2.2 Greenhouse gases and their role 1.2.3 Impact of human activity on the greenhouse effect 1.3.1 Ideal gas law (PV = nRT) 1.3.2 Boyle’s law, Charles’s law, Avogadro’s law 1.3.3 Real gases and deviations from ideal gas behaviour 1.4.1 Laws of thermodynamics 1.4.2 Heat engines and efficiency 1.4.3 Entropy and spontaneous processes 1.5.1 Electric charge and current 1.5.2 Ohm’s law and resistivity 1.5.3 Kirchhoff’s laws 1.5.4 Power dissipation in resistors Wave Behaviour 2.1.1 Types of waves: Transverse and longitudinal 2.1.2 Properties of waves (amplitude, frequency, wavelength, speed) 2.1.3 Wave equations 2.2.1 Reflection, refraction, diffraction, and interference 2.2.2 Doppler effect 2.2.3 Standing waves and resonance 2.3.1 Displacement, velocity, and acceleration in SHM 2.3.2 Energy in SHM 2.3.3 Pendulum and spring systems Nuclear and Quantum Physics 3.1.1 Quantum theory and uncertainty principle 3.1.2 Wave-particle duality 3.1.3 Photoelectric effect 3.2.1 Types of radiation: Alpha, beta, gamma 3.2.2 Half-life and decay constant 3.2.3 Radioactive decay and applications 3.3.1 Nuclear fission process 3.3.2 Chain reaction and critical mass 3.3.3 Applications of nuclear fission (nuclear reactors) 3.4.1 Nuclear fusion and energy production in stars 3.4.2 Stellar nucleosynthesis 3.4.3 Life cycle of stars 3.5.1 Atomic models (Bohr, quantum model) 3.5.2 Electron configuration and energy levels 3.5.3 Isotopes and atomic mass Space, Time, and Motion 4.1.1 Scalars and vectors 4.1.2 Displacement, velocity, and acceleration 4.1.3 Equations of motion (constant acceleration) 4.1.4 Graphical analysis of motion 4.2.1 Newton’s laws of motion 4.2.2 Force, mass, and acceleration 4.2.3 Momentum and impulse 4.2.4 Conservation of momentum 4.2.5 Collisions and explosions 4.3.1 Work done by a force 4.3.2 Kinetic and potential energy 4.3.3 Conservation of mechanical energy 4.3.4 Power and efficiency 4.4.1 Torque and rotational motion 4.4.2 Moment of inertia and angular acceleration 4.4.3 Rotational kinetic energy 4.4.4 Angular momentum and its conservation 4.5.1 Frames of reference 4.5.2 Lorentz transformation equations 4.5.3 Time dilation and length contraction 4.5.4 Mass-energy equivalence (E = mc²) Fields 5.1.1 Gravitational force and field strength 5.1.2 Gravitational potential energy 5.1.3 Kepler's laws and orbital mechanics 5.2.1 Electric fields and potentials 5.2.2 Magnetic fields and forces 5.2.3 Coulomb's law and Gauss’s law 5.2.4 Applications in motors and electromagnets 5.3.1 Charge in magnetic fields 5.3.2 Cyclotron and magnetic force on a current 5.3.3 Magnetic flux and induction 5.4.1 Faraday’s law of electromagnetic induction 5.4.2 Lenz's law and applications 5.4.3 Transformers and power transmission Experimental Programme (Internal Assessment) 6.1.1 Laboratory techniques and safety protocols 6.1.2 Data collection, analysis, and uncertainty in measurements 6.1.3 Writing scientific reports and conclusions 6.2.1 Collaborative research and experimental work 6.2.2 Communicating scientific findings with others 6.2.3 Working within interdisciplinary teams 6.3.1 Developing research questions and hypotheses 6.3.2 Designing experiments and gathering data 6.3.3 Data analysis and interpretation of results Get PDF PDF Share Explore How would you like to practise? 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https://www.quora.com/How-do-I-solve-the-equation-cos-x-cos-2x-for-all-values-of-x-E-0-2pi
How to solve the equation cos x=cos 2x for all values of x E [0,2pi] - Quora Something went wrong. Wait a moment and try again. Try again Skip to content Skip to search Sign In Mathematics Cos Function Trigonometric Identities Solving Equations Cosine (math function) Trigonometry Functions Trigonometric Geometry Doing Mathematics Trigonometric Analysis 5 How do I solve the equation cos x=cos 2x for all values of x E [0,2pi]? All related (38) Sort Recommended Peter Weusten B.Sc in Mathematics&Statistics (academic discipline), University of Canterbury (Graduated 1976) · Author has 181 answers and 118.4K answer views ·4y You will need to use the identity cos2x = 2 (cos x)^2 -1 cos x=cos 2x 2 (cos x)^2 -cos x -1 = 0 factorise (2 cos x +1)(cos x -1)=0 either cos x = -1/2 or cos x =1 Continue Reading You will need to use the identity cos2x = 2 (cos x)^2 -1 cos x=cos 2x 2 (cos x)^2 -cos x -1 = 0 factorise (2 cos x +1)(cos x -1)=0 either cos x = -1/2 or cos x =1 Upvote · Related questions More answers below Can you integrate ∫π 0 e e e cos(x)cos(sin(x))cos(sin(sin(x))e cos(x))cos(sin(sin(sin(x))e cos(x))e e cos(x)cos(sin(x)))d x∫0 π e e e cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x))e cos⁡(x))cos⁡(sin⁡(sin⁡(sin⁡(x))e cos⁡(x))e e cos⁡(x)cos⁡(sin⁡(x)))d x? What is the solution to the equation (sin x) /x=cos x? How can I solve the equation x-cos (x)=0? What are all possible values of cos(x) if cos(2x) =2cos(x)? How do I solve this equation? Sin(2x) / 1-cos(2x) = 1 Enrico Gregorio Associate professor in Algebra · Author has 18.4K answers and 16M answer views ·4y Two angles have the same cosine if and only if either they differ by integral multiples of 2 π 2 π or their sum is an integral multiple of 2 π 2 π. In brief, but less accurately, cos α=cos β cos⁡α=cos⁡β if and only if β=±α+2 k π β=±α+2 k π. In your case we get either 2 x=x+2 k π 2 x=x+2 k π or 2 x+x=2 k π 2 x+x=2 k π With the limitation on the solutions, the first case yields 0 0 and 2 π 2 π; the second case yields 0,2 π/3,4 π/3,2 π 0,2 π/3,4 π/3,2 π Upvote · 9 1 Assistant Bot · Sep 5 Solve cos x = cos 2x on [0, 2π]. Use the double-angle identity cos 2x = 2 cos^2 x − 1. Then cos x = 2 cos^2 x − 1 0 = 2 cos^2 x − cos x − 1. Let u = cos x. Solve 2u^2 − u − 1 = 0: u = [1 ± √(1 + 8)]/(4) = [1 ± 3]/4, so u = 1 or u = −1/2. Now find x in [0, 2π] with cos x = 1 or cos x = −1/2. cos x = 1 ⇒ x = 0 (only solution in [0,2π]). cos x = −1/2 ⇒ x = 2π/3 and x = 4π/3. Thus the solutions on [0, 2π] are x = 0, 2π/3, 4π/3. Upvote · Pramodkumar Tandon Retired as Prof. & Head at Institute of Engineering and Rural Technology (1965–present) · Author has 2.1K answers and 1.2M answer views ·4y cos x = cos 2x => cosx = 2 cos²x - 1 => 2 cos²x - cosx - 1 = 0 =>2 cos²x - 2 cosx + cosx - 1 = 0 => 2 cosx ( cosx - 1 ) + ( cosx - 1 ) => ( 2 cosx + 1 ) ( cosx - 1 ) = 0 => cosx = - 1/2, cosx = 1 Hence within 0 to ( 2 π ) range x = 2π/3 , 4 π/3, 0 =>x = 0, 2π/3 , 4 π/3 ………… Answer Upvote · 9 2 9 1 Related questions Can you integrate ∫π 0 e e e cos(x)cos(sin(x))cos(sin(sin(x))e cos(x))cos(sin(sin(sin(x))e cos(x))e e cos(x)cos(sin(x)))d x∫0 π e e e cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x))e cos⁡(x))cos⁡(sin⁡(sin⁡(sin⁡(x))e cos⁡(x))e e cos⁡(x)cos⁡(sin⁡(x)))d x? What is the solution to the equation (sin x) /x=cos x? How can I solve the equation x-cos (x)=0? What are all possible values of cos(x) if cos(2x) =2cos(x)? How do I solve this equation? Sin(2x) / 1-cos(2x) = 1 The equation √(3) sin(x) + cos(x) = 4 has how many solutions? How do I solve this equation cos 2x = sin (2x-30°)? How do you solve cos(2x) +cos(x) =0? What are the solutions to the equation x = cos(x)? What is the value of x in the following equation: tan(x)-cos(x) /1= 1.50? What is the answer for cos(2x) tan(x) =0? How do you solve the equation cos 2x = √\2? How do I find all the values of x in between the range [0,2π] for the equation 2 sin (4x) - 3 cos (4x) =0? What is cos(X) =0 over the interval [0,2pi]? How do I solve the equation cos(x π)−x π sin(x π)=0 cos⁡(x π)−x π sin⁡(x π)=0 for x x? -2pi<x<2pi Related questions Can you integrate ∫π 0 e e e cos(x)cos(sin(x))cos(sin(sin(x))e cos(x))cos(sin(sin(sin(x))e cos(x))e e cos(x)cos(sin(x)))d x∫0 π e e e cos⁡(x)cos⁡(sin⁡(x))cos⁡(sin⁡(sin⁡(x))e cos⁡(x))cos⁡(sin⁡(sin⁡(sin⁡(x))e cos⁡(x))e e cos⁡(x)cos⁡(sin⁡(x)))d x? What is the solution to the equation (sin x) /x=cos x? How can I solve the equation x-cos (x)=0? What are all possible values of cos(x) if cos(2x) =2cos(x)? How do I solve this equation? Sin(2x) / 1-cos(2x) = 1 The equation √(3) sin(x) + cos(x) = 4 has how many solutions? How do I solve this equation cos 2x = sin (2x-30°)? How do you solve cos(2x) +cos(x) =0? What are the solutions to the equation x = cos(x)? What is the value of x in the following equation: tan(x)-cos(x) /1= 1.50? About · Careers · Privacy · Terms · Contact · Languages · Your Ad Choices · Press · © Quora, Inc. 2025
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https://evolution.berkeley.edu/mutations-are-random/
Skip to primary navigation Skip to footer About Image & Use Policy Translations Glossary SUPPORT UE UC MUSEUM OF PALEONTOLOGY UC Berkeley Understanding Evolution Your one-stop source for information on evolution Understanding Evolution Home → Mutations are random ES en Español Mutations are random The mechanisms of evolution — like natural selection and genetic drift — work with the random variation generated by mutation. Factors in the environment are thought to influence the rate of mutation but are not generally thought to influence the direction of mutation. For example, exposure to harmful chemicals may increase the mutation rate, but will not cause more mutations that make the organism resistant to those chemicals. In this respect, mutations are random — whether a particular mutation happens or not is generally unrelated to how useful that mutation would be. In the U.S., where people use shampoos with particular chemicals in order to kill lice, we have a lot of lice that are resistant to the chemicals in those shampoos. There are two possible explanations for this: Scientists generally think that the first explanation is the right one and that directed mutations, the second possible explanation, is not correct. Researchers have performed many experiments in this area. Though results can be interpreted in several ways, none unambiguously support directed mutation. Nevertheless, scientists are still doing research that provides evidence relevant to this issue. In addition, experiments have made it clear that many mutations are in fact “random,” and did not occur because the organism was placed in a situation where the mutation would be useful. For example, if you expose bacteria to an antibiotic, you will likely observe an increased prevalence of antibiotic resistance. In 1952, Esther and Joshua Lederberg determined that many of these mutations for antibiotic resistance existed in the population even before the population was exposed to the antibiotic — and that exposure to the antibiotic did not cause those new resistant mutants to appear. More Details Evo Examples Teaching Resources Read more about how mutations factored into the history of evolutionary thought Learn more about mutation in context: Evolution at the scene of the crime, a news brief with discussion questions. A chink in HIV's evolutionary armor, a news brief with discussion questions. Find lessons, activities, videos, and articles that focus on mutation. Footer Connect Subscribe to our newsletter Teach Teaching resource database Correcting misconceptions Conceptual framework and NGSS alignment Image and use policy Learn Evo 101 Evo in the News The Tree Room Browse learning resources Glossary We use cookies to see how our website is performing. We do not collect or store your personal information, and we do not track your preferences or activity on this site.
4041
https://billthelizard.blogspot.com/2009/06/casting-out-nines.html
Bill the Lizard: Casting Out Nines Loading [MathJax]/extensions/MathMenu.js skip to main | skip to sidebar Bill the Lizard "The time has come," the Walrus said, "To talk of many things..." Saturday, June 13, 2009 Casting Out Nines You may already be familiar with the divisibility rule that says a number is evenly divisible by 9 if and only if the sum of its digits is also divisible by 9. For example, I know 3,645 is divisible by 9 without dividing because its digits add up to 18, which I remember from elementary school to be 2 9. This is an interesting rule because it leads to a recursive property of divisibility by 9. Notice that the digits of 18 in the preceding example also add up to 9. If we have a larger number like 13,286,025,801 we can repeatedly apply the same rule until we get down to one digit. Only if that single digit is a 9 is the original number (and every digital sum in between) divisible by 9. For example, the sum of the digits of 13,286,025,801 is: 1 + 3 + 2 + 8 + 6+ 0 + 2 + 5 + 8 + 0 + 1 = 36 and the sum of the digits of 36 is: 3 + 6 = 9 This process of repeatedly summing the digits of a number until you're left with a single digit is called finding the number's digital root. If the digital root of a number is 9, then that number is divisible by 9. For small numbers like the ones above it's easy to just do long division to see if a number is evenly divisible by 9, but for extremely large numbers with hundreds of digits, division can be quite time consuming. For example, can you tell me if 153,441,702,921,204,324,780,111,405,711, 801,641,412,504,117,621,135,207,441,603, 126,450,890,010,720,810,243,171,423,583, 110,999,306,450,902,232,414,027,522,126, 087,102,603,909,333,306,252,412,702,011 is divisible by 9? You might be awhile if you try to solve this using long division. I can tell you that this number is divisible by 9, but before you add up all the digits, let me show you a shortcut called "casting out nines." Let's first try it out on the following example, which is a little bit more manageable 1,729,254,036 Start off adding from the left as normal, and for each digit you add, keep a running total. 1 + 7 = 8 8 + 2 = 10 When you reach a total greater than 9, as I have here after the third digit, "cast out" a 9 from the total by simply subtracting 9 from it. In this case our running total of 10 becomes 1. 1 + 9 = 10 (-9 = 1) 1 + 2 = 3 3 + 5 = 8 8 + 4 = 12 (-9 = 3) 3 + 0 = 3 3 + 3 = 6 6 + 6 = 12 (-9 = 3) If the final total isn't 9 (or 0 after casting out that final 9) then the number is not divisible by 9. Since we were left with a remainder of 3, we now know that 1,729,254,036 is not divisible by 9. An even quicker method of casting out nines is by grouping the digits that add up to 9 and eliminating them. The sum 1 + 7 + 2 + 9 + 2 + 5 + 4 + 0 + 3 + 6 is much easier to reduce if you group it by digits that add up to 9. 1 + (7 + 2) + (9) + 2 + (5 + 4) + 0 + (3 + 6) You can cast out these nines at this step before you do any addition at all. 1 + (0) + (0) + 2 + (0) + 0 + (0) 1 + 2 = 3 You can repeat the grouping and casting process as many times as you need before summing the remaining digits. Now that you know these shortcuts, take a closer look at that monstrous 150-digit number that I showed you earlier. Using the grouping and casting method it shouldn't take more than a moment to reduce even that large a number to see that it is divisible by 9. Why does the divisibility test even work? To understand why the test for divisibility by 9 works, we need to use a few properties of congruences. Let's start with the fact that 10 ≡ 1 (mod 9) which in English says that 10 is congruent to 1 modulus 9, or in plain English that 10 and 1 both leave the same remainder (sometimes called the residue) when divided by 9. (In fact, if the right-hand side of the congruence, in this case 1, is less than the modulus, then the right-hand side is the remainder when the left-hand side is divided by the modulus.) In general, b ≡ c (mod n) says that the difference between b and c is evenly divisible by n. One algebraic property of congruences says that we can raise both sides of the congruence to the same power and the modulus will stay the same (this can be more generally stated as P(a) ≡ P(b) (mod n), where P(x) is any polynomial). Using this property we can say that 10 2 ≡ 1 2 (mod 9) or 100 ≡ 1 (mod 9) You can substitute any non-negative whole exponent you like. 10 0 ≡ 1 0 (mod 9) 10 1 ≡ 1 1 (mod 9) 10 2 ≡ 1 2 (mod 9) 10 3 ≡ 1 3 (mod 9) ... 10 n ≡ 1 n (mod 9) So 10 raised to any natural exponent will leave a remainder of 1 when divided by 9. 10 n ≡ 1 (mod 9) This should be intuitively obvious when you consider that 10 3 - 1 = 1,000 - 1 = 999 is evenly divisible by 9 10 4 - 1 = 10,000 - 1 = 9,999 is evenly divisible by 9 10 5 - 1 = 100,000 - 1 = 99,999 is evenly divisible by 9 ... Another property of congruences says that we can multiply both sides by the same number and the congruence remains unchanged. So starting back at 10 ≡ 1 (mod 9) we can multiply both sides by any number and still have a valid congruence. 10 2 ≡ 1 2 (mod 9) 20 ≡ 2 (mod 9) 10 5 ≡ 1 5 (mod 9) 50 ≡ 5 (mod 9) 10 8 ≡ 1 8 (mod 9) 80 ≡ 8 (mod 9) Starting from the following statements (that we showed to be true above) 1000 ≡ 1 (mod 9) 100 ≡ 1 (mod 9) 10 ≡ 1 (mod 9) 1 ≡ 1 (mod 9) we can multiply both sides of each congruence by any number we like. 1000 3 ≡ 1 3 (mod 9) 100 6 ≡ 1 6 (mod 9) 10 4 ≡ 1 4 (mod 9) 1 5 ≡ 1 5 (mod 9) is the same as 3000 ≡ 3 (mod 9) 600 ≡ 6 (mod 9) 40 ≡ 4 (mod 9) 5 ≡ 5 (mod 9) We can add congruences together as long as they have the same modulus. Adding the four congruences above we get 3000 + 600 + 40 + 5 ≡ 3 + 6 + 4 + 5 (mod 9) or 3645 ≡ 3 + 6 + 4 + 5 (mod 9) Doesn't that look like it says that 3645 is congruent to the sum of its own digits modulo 9? Yes, in fact, it does. I deliberately chose the numbers 3, 6, 4, and 5 so that we would arrive back at a familiar example (from the first paragraph of this post), but I could have chosen any digits I wanted. This relationship holds true for any natural number. If s is the sum of the digits of n, then n is congruent to s modulo 9. n ≡ s (mod 9) But we're only really concerned with the cases where the sum of the digits is evenly divisible by 9. Another way of stating this is s ≡ 0 (mod 9) This brings us to the last algebraic property of congruences that we need to use (I promise, this is the last one). Remember that the transitive property of regular arithmetic says that if a = b and b = c, then a = c. The transitive property of congruences is similar. It says that if a ≡ b (mod n) and b ≡ c (mod n) then a ≡ c (mod n) This is simply saying that if a and b leave the same remainder when divided by n, and b and c leave the same remainder when divided by n, then a and c must also leave the same remainder when divided by n. For a concrete example, consider that 32 ≡ 18 (mod 7) and 18 ≡ 11 (mod 7) so that 32 ≡ 11 (mod 7) (They all leave a remainder of 4.) Since we've already shown that in the general case n ≡ s (mod 9) and we know that in the particular cases we're concerned with that the sum of the digits is evenly divisible by 9, or s ≡ 0 (mod 9) we can say that in those cases n ≡ 0 (mod 9) This means that in those cases where the sum of the digits of n is divisible by 9, the number n itself is also divisible by 9. Precisely what we set out to prove. Posted by Bill the Lizard on 6/13/2009 Labels: math, numbers Share:Email ThisBlogThis!Share to XShare to FacebookShare to Pinterest 3 comments: Unknown said... Interesting, I wonder if I will ever meed to divide a huge number by nine. 6/22/2009 Bill the Lizard said... Sam152, Please note that this post only shows you how to tell if a number is divisible by nine. Maybe my next insanely long and boring post will show you how to actually divide. ;) 6/22/2009 Derek said... What most people miss is the computers don't track numbers in base 10, but in base 16. That allows us to test for division of 3 & 5. 7/29/2009 Post a Comment Newer PostOlder PostHome Subscribe to: Post Comments (Atom) Other places to find me... Mastodon Github Kaggle Stack Overflow Google Play Good Reads Subscribe to this blog via RSS. 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4042
https://arxiv.org/pdf/2203.06675
Clumsy Packing of Polyominoes in Finite Space Emma Miller, Moravian University Mitchel O’Connor, Whitman College Nathan Shank, Moravian University March 15, 2022 1 Introduction In 1971, Sands proposed the following problem: Given an n × n checker-board, what is the minimum number of dominoes we can place on the board, assuming each domino covers exactly two adjacent squares, so that no addi-tional domino can fit? In other words, what is the maximum number of 1 × 1‘holes’ that can be created? In 1988, Gy´ arf´ as, Lehel, and Tuza called this type of packing a clumsy packing which requires the density of packed poly-ominoes to be as small as possible relative to the size of the board. They were able to generate results for general board sizes with dominoes, which are 1 ×2rectangular polyominoes. Goddard considered clumsy packing density for hooks (3 squares in the shape of an L), m × m squares , and 1 × m longs on infinite board. More recently, Walzer (, ) considered other clumsy packing of the infinite plane for more complicated polyominoes. Tiling and packing of polyominoes has particular importance for topology and geometry with applications in physics and chemistry. In this paper, we consider a clumsy packing of polyominoes on a finite space. The polyominoes we consider are rectangular , L, T , and plus poly-ominoes. If a polyomino is made of n squares, we consider packing on a n × n board. This finite packing gives configurations and densities that are different than the previous results because of the edge effect that we have on a finite board. Clumsy packing on finite boards has applications in prod-1 arXiv:2203.06675v1 [math.CO] 13 Mar 2022 uct design related to filling a finite space using the least amount of material possible. 2 Background and Definitions We will assume throughout that a, b , and n are positive integers. We will be packing our polyominoes on a square grid of size n × n where n is the size of the polyomino. We will adapt more of our notation and definitions from chapter 14 of , however, to help with notation and terminology, we will make the following definitions: 2.1 The Board The board will be a square n × n grid where we place our polyominoes. So, an 8 × 8 board can be visualized as a checkerboard. A 1 × 1 closed square on our grid whose sides are parallel to the coordinate axes and corners are at integer coordinates will be called a cell and we will denote the cell in column i and row j by Ci,j . For 1 ≤ i, j ≤ n define Xi = {Ci,j : 1 ≤ j ≤ n} and Yj = {Ci,j : 1 ≤ i ≤ n}. We will refer to Xi as column i and Yj as row j. We will use the convention that X1 is the leftmost column, Xn is the rightmost column, Y1 is the top row, and Yn is the bottom row. Thus, cell C1,1 is the cell in the first column and first row which would be the upper left cell of the grid. The square n × n grid will be called the board, B, so that B = {Ci,j : 1 ≤ i ≤ n and 1 ≤ j ≤ n where i, j ∈ Z}. 2.2 General Polyominoes A polyomino , P, is a a finite set of cells. The number of cells in a polyomino will be the size of the polyomino and will be denoted |P| . Note that two polyominoes are considered disjoint if they do not have any cells in common, but visually they may share edges or corners. Polyominoes will be located on board based on an anchor which will be a specific cell that uniquely deter-mines the location of the polyomino on the board. Informally, for example, for a L polyomino (definition 3.7) we will define the anchor as the cell located on the intersection of the horizontal and vertical legs. For integers c and d a shift of a polyomino P by ( c, d ) is a polyomino P1 so that P1 = {Cx+c,y +d : Cx,y ∈ P} . Thus P1 is a shift of P c units 2horizontally and d units vertically. We will use the notation P1 = P + ( c, d )to represent a shift by ( c, d ). For certain polyominoes, we will consider a clockwise rotation of our poly-omino by an integer multiple of 90 ◦. For any integer m, if P is a polyomino then PRm is a rotation of P by ( m · 90) ◦ clockwise. This idea will be made more formal for each individual polyomino. Note that a rotation or shift may produce a polyomino which is no longer on the board. We will not be considering reflections of polyominoes in this paper which could be of particular importance for L polyominoes. We will be working with two different types of packings, free and fixed. For fixed packing , we will not be allowed to rotate the polyomino, we will only be allowed to shift the polyomino. In free packing , we will be allowed to rotate and shift the polyomino. Definition 2.1. We will call two polyominoes P1 and P2 fixed equivalent if there is an integer pair ( c, d ) so that P2 = P1 + ( c, d ). We will denote fixed equivalent polyominoes by P1 ≈ P 2.Thus, two polyominoes are fixed equivalent if we can shift one polyomino by ( c, d ) to equal the other polyomino. For free equivalent polyominoes, we are allowed to rotate and shift the polyominoes. Definition 2.2. We will call two polyominoes P1 and P2 free equivalent if there is a non-negative integer m and and integers pair ( c, d ) so that P2 = P1Rm + ( c, d ). We will denote free equivalent polyominoes by P1 ∼ P 2.Our objective is to pack as few copies of our polyomino on the board so that we can not include another polyomino. To do so, we need to define how polyominoes fit onto a board and what makes a valid arrangement. Definition 2.3. Given a board B and a set of polyominoes P = {P 1, . . . Pk},we say P is a valid arrangement if ⋃ki=1 Pi ⊆ B and if Pi ∩ P j = ∅ for all 1 ≤ i < j ≤ k. Otherwise, we call P an invalid arrangement. Therefore a valid arrangment simply means the the set of polyominoes is pairwise disjoint and fits onto the board. The following definitions are for free polyominoes and can easily be ex-tended to fixed polyominoes. 3Definition 2.4. A set of polyominoes composed of polyominoes which are free equivalent polyominoes to P will be called a free polyomino set of P. Definition 2.5. A free polyomino set of P, denoted P, is a free packing of P on a board B if P is a valid arrangement such that for any free equivalent polyomino P∗ ∼ P we have that P∗ ∪ P is an invalid arrangement. Thus, we can think of a free packing as a maximal set of P.So for a set of polyominoes to be a free packing, they must be a valid packing and they must be maximal in the sense that no additional polyomino can be placed onto the board without overlapping an already placed poly-omino. The number of polyominoes in the set is the free packing number of the set. Definition 2.6. Given a free packing of P, denoted P, the size of P is the free packing number of P. We will denote this by pn f ree (P). Definition 2.7. The clumsy free packing number of P, denoted cp f ree (P) is the minimum free packing number over all free polyomino sets of P.The clumsy free packing number is the minimum of all of the possible free packing numbers for a particular polyomino. In essence, the clumsy free packing number is the minimum of the maximals. Any set of polyominoes which attains this minimum will be called a clumsy free packing. Definition 2.8. A clumsy free packing of P is a free polyomino set of P,denoted P, whose free packing number is the clumsy free packing number of P. Thus pn f ree (P) = cp f ree (P). Unless otherwise specified, we will always consider packing (free or fixed) of a polyomino P on a n × n board B where n = |P| . 3 Results This section will consist of subsection for rectangular polyominoes, L poly-ominoes, T polyominoes, and plus polyominoes. In each section, we will define the polyomino and consider fixed and free packing. 43.1 Rectangular Polyominoes Rectangular polyominoes are a popular polyomino to study. The classic domino is a rectangular polyomino. Some packing problems have been stud-ied for dominoes and straights, which are 1 × m rectangular polyominoes. Definition 3.1. The rectangular polyomino , Ra,b , is the polyomino consisting of all cells Ci,j where 1 ≤ i ≤ a and 1 ≤ j ≤ b. Thus Ra,b , is a rectangular polyomino of size ab .To know the location of a rectangular polyomino, we need to define the anchor. Definition 3.2. Given a rectangular polyomino, Ra,b , with a, b > 1, we will define the anchor of the polyomino to be the cell Cb a 2c,bb 2c .Notice that if a = b = 1 then R1,1 is just an individual cell which is a trivial case since cp f ix (R1,1) = cp f ree (R1,1) = 1 . Straight polyominoes are a special case of rectangular polyominoes. We will use straight vertical and straight horizontal polyominoes for our clumsy free packing. Definition 3.3. For n > 1, the straight vertical polyomino , SV n, is the rectangular polyomino R1,n . We will define the anchor as C1,b n 2c . Definition 3.4. For n > 1, the straight horizontal polyomino , SH n, is the rectangular polyomino Rn, 1. We will define the anchor as Cb n 2c,1 The following theorem finds the clumsy packing number for fixed and free straight polyominoes. Theorem 3.5. For any n ≥ 1, cp f ree (SV n) = cp f ree (SH n) = cp f ix (SV n) = cp f ix (SH n) = n. Proof. Fixed Case: We will only consider straight vertical polyominoes, SV n. Notice that any polyomino P1 ≈ SV n (fixed equivalent) will consist of cells from only one column Xi. So a valid arrangement of 1 < m < n polyominoes fixed equivalent to SV n will have n − m empty columns, which is not a fixed packing. Therefore the clumsy packing number must be at least n, but it clearly can not be greater than n since there are only n2 cells in the board. Thus cp f ix (SV n) = n.5Free Case: Notice that any rotation of a straight polyomino will result in a straight polyomino. Also, any valid arrangement on a n × n board cannot contain a straight vertical polyomino and a straight horizontal polyomino as they cannot be disjoint. Therefore cp f ree (SV n) = cp f ix (SV n). An identical argument can be made for SH n using rows. The following theorem finds the clumsy fixed packing number for rectan-gular polyominoes of size at least 2 × 2. Theorem 3.6. For any rectangular polyomino, Ra,b with a, b ≥ 2, the clumsy fixed packing is cp f ix (Ra,b ) = ⌈ab −a+1 2a−1 ⌉ ⌈ ab −b+1 2b−1 ⌉.Proof. Notice that n = ab . In order to find the clumsy fixed packing num-ber for rectangular polyominoes, we will first show that there exists a fixed packing of a set of Ra,b , P, so that pn f ixed (P) = ⌈ab −a+1 2a−1 ⌉ ⌈ ab −b+1 2b−1 ⌉ . Consider tiling the board by having b − 1 empty rows, Y1 through Yb−1,and a − 1 empty columns, X1 through Xa−1. Then have a horizontal tiling of polyominoes with a − 1 empty column between each polyomino and b − 1empty rows between each horizontal tiling. We may need to add an additional column of polyominoes so that the number of empty columns to the right of the board is less than or equal to a − 1. Similarly, we may need to add an additional row of polyominoes so that the number of empty rows at the bottom of the board is less than or equal to b − 1. See Figure 1. The number of polyominoes placed along a non-empty row will be ⌈ab −(a−1) 2a−1 ⌉ .The number of polyominoes placed along a non-empty column will be ⌈ab −(b−1) 2b−1 ⌉ .So the total number of polyominoes in this particular tiling will be ⌈ab −a+1 2a−1 ⌉ ⌈ ab −b+1 2b−1 ⌉.Therefore cp f ix (Ra,b ) ≤ pn f ixed (P) = ⌈ab − a + 1 2a − 1 ⌉ ⌈ ab − b + 1 2b − 1 ⌉ . Now we will show that this is also a lower bound for cp f ix (Ra,b ) and we will do this based on the parity of a and b. Even/Odd Case : Assume we have a clumsy fixed packing of Ra,b , where a, b ≥ 2 and a = 2 k and b = 2 l + 1 for non-negative integers k and l.It is easy to see that there must be an anchor in the top 3 l + 1 rows and the bottom most 3 l + 1 rows and every 4 l + 1 rows in between. Similarly, 6Figure 1: This figure depicts a general example of a clumsy fixed packing of some Ra,b . The shaded areas are the polyominoes. The hatched region represents the area that may or may not include an additional row or column of polyominoes. there also must be an anchor in the leftmost 3 k − 1 column the rightmost 3k columns and every 4 k − 1 columns in between. Note that every region of 4l + 1 rows and 4 k − 1 columns must contain an anchor. Otherwise, in any region of such size without an anchor, we can fit an additional polyomino fixed equivalent to Ra,b . This is demonstrated in Figure 2 across the top edge of the board. Therefore, there are 2 + ⌊ab −2(3 l+1) 4l+1 ⌋ = 2 + ⌊ab −(3 b−1) 2b−1 ⌋ pairwise disjoint sets of rows, each of which must contain an anchor in each of the 2 + ⌊ab −(3 k−1+3 k)4k−1 ⌋ = 2 + ⌊ab −(3 a−1) 2a−1 ⌋ pairwise disjoint sets of columns. This leaves us with a total of ⌊ 2 + ab −(3 b−1) 2b−1 ⌋ ⌊ 2 + ab −(3 a−1) 2a−1 ⌋ disjoint regions on the board each of which must contain an anchor. (Note that if ab −2(3 l+1) 4l+1 < 0, then the top 3 l + 1 rows and bottom 3 l + 1 7Figure 2: Even by Odd Case: This shows that a (4 k − 1) × (3 l + 1) rectan-gular region along the top of the board must contain an anchor which are represented by the black cells. If not, there is a (2 k) × (2 l + 1) region which can contain another polyomino. rows are not disjoint and therefore we can place one anchor which will be in the top most 3 l + 1 rows and the bottom 3 l + 1 rows. Also, notice that since a ≥ 2 we know ab ≥ 2l + 1 which implies ab −2(3 l+1) 4l+1 ≥ − 1. Similarly for columns.) This shows that for the even/odd case we have cp f ix (Ra,b ) ≥ ⌊ 2 + ab − (3 b − 1) 2b − 1 ⌋ ⌊ 2 + ab − (3 a − 1) 2a − 1 ⌋ . Even/Even Case : Assume a, b ≥ 2 and a = 2 k and b = 2 l. Following similar logic as above, we can see there must be an anchor in the top 3 l − 1rows, bottom 3 l rows, and every 4 l − 1 rows in between. There also must be an anchor in the leftmost 3 k − 1 columns, the rightmost 3 k columns, and every 4 k − 1 columns in between. Note that every region of 4 k − 1 columns and 4 l − 1 rows must contain an anchor. Therefore, there are 2 + ⌊ab −(3 l−1) −3l 4l−1 ⌋ = 2 + ⌊ab −(3 b−1) 2b−1 ⌋ pairwise dis-joint sets of rows, each of which must contain an anchor in each of the 2 + ⌊ab −3k−(3 k−1) 4k−1 ⌋ = 2 + ⌊ab −(3 a−1) 2a−1 ⌋ pairwise disjoint sets of columns. This leaves us with a total of ⌊ 2 + ab −(3 b−1) 2b−1 ⌋ ⌊ 2 + ab −(3 a−1) 2a−1 ⌋ disjoint regions on the board each of which must contain an anchor. Notice this is the same as in the even/odd case. 8Odd/Odd Case : Assume a, b ≥ 2 and a = 2 k + 1 and b = 2 l + 1. Following the similar logic as above, we can see there must be an anchor in the top 3 l + 1 rows, bottom 3 l + 1 rows, and every 4 l + 1 rows in between. There also must be an anchor in the leftmost 3 k + 1 columns, the rightmost 3k + 1 columns, and every 4 k + 1 columns in between. Note that every region of 4 k + 1 columns and 4 l + 1 rows must contain an anchor. Therefore, there are 2 + ⌊ab −(3 l+1) −(3 l+1) 4l+1 ⌋ = 2 + ⌊ab −(3 b−1) 2b−1 ⌋ pairwise dis-joint sets of rows, each of which must contain an anchor in each of the 2 + ⌊ab −(3 k+1) −(3 k+1) 4k+1 ⌋ = 2 + ⌊ab −(3 a−1) 2a−1 ⌋ pairwise disjoint sets of columns. This leaves us with a total of ⌊ 2 + ab −(3 b−1) 2b−1 ⌋ ⌊ 2 + ab −(3 a−1) 2a−1 ⌋ disjoint regions on the board each of which must contain an anchor. Notice this is the same as in the previous two cases. Since all three cases give the same inequality, we will now proceed inde-pendent of the parity of a and b.Now we need to show the equality of our upper and lower bound on the fixed clumsy packing number. To accomplish this, we call upon a well known equality for floor and ceiling functions: ⌈ TB ⌉ = ⌊T + B − 1 B ⌋ . From this we can easily show that, ⌈ TB ⌉ = ⌊T − 1 − BB ⌋ 2 . With this we are able to see ⌈ab − a + 1 2a − 1 ⌉ = ⌊(ab − a + 1) − 1 − (2 a − 1) 2a − 1 ⌋ 2 = ⌊ab − (3 a − 1) 2a − 1 ⌋ 2 and similarly ⌈ab − b + 1 2b − 1 ⌉ = ⌊ab − (3 b − 1) 2b − 1 ⌋ 2 . 9Thus we are able to justify that cp f ix (Ra,b ) ≥ ⌈ab − a + 1 2a − 1 ⌉ ⌈ ab − b + 1 2b − 1 ⌉ . The clumsy free packing for general rectangular polyominoes turned out to be more difficult because of the edge effects. We pose this as an open question in Section 4. 3.2 L Polyominoes As noted in the introduction, previous work has been completed for hooks which is a special case of a L polyomino. Definition 3.7. An L polyomino , La,b , is a polyomino where 0 < a ≤ b such that La,b = {Ci, 1 : 1 ≤ i ≤ a + 1 } ∪ { C1,j : 1 < j ≤ b + 1 }. The |La,b | = a + b + 1. We will define the anchor of the polyomino to be the cell C1,1.Thus, L polyominoes have legs of length a + 1 and b + 1 and have size a + b + 1. We will define LR a,b , LR 2 a,b , and LR 3 a,b to be a 90 ◦, 180 ◦, and 270 ◦ clock-wise rotation of La,b respectively. So we have: • LR a,b = {Ci, 1 : 1 ≤ i ≤ b + 1 } ∪ { Cb+1 ,j : 1 ≤ j ≤ a + 1 } which will have anchor at cell Cb+1 ,1, • LR 2 a,b = {Ci,b +1 : 1 ≤ i ≤ a + 1 } ∪ { Ca+1 ,j : 1 ≤ j ≤ b + 1 } which will have anchor at cell Ca+1 ,b +1 , and • LR 3 a,b = {Ci,a +1 : 1 ≤ i ≤ b + 1 } ∪ { C1,j : 1 ≤ j ≤ a + 1 } which will have anchor at cell C1,a +1 . An example of an L polyomino rotated is provided in Figure 3. For simplicity, we will use La,b , LR a,b , etc. to describe the size and orien-tation of the polyomino and use the anchor to describe its location which is just a shift of La,b , LR a,b , etc.. The packing of L polyominoes may seem straight forward, but there are some intricacies we must consider. The case where a = b is a special case as seen in Theorem 3.8 for clumsy fixed packing and Theorem 3.10 for clumsy free packing. 10 Figure 3: This figure demonstrates L1,2, LR 1,2, LR 21,2, and LR 31,2. The shaded cell is the anchor. Theorem 3.8. For a L polyomino, La,a , cp f ix (La,a ) = 1 .Proof. Place the L polyomino so that the anchor is on the cell Ca+1 ,1 as seen in Figure 4. Notice that if we want to include another L polyomino, we must have the anchor in the first a rows and a columns. However, we must have at least a + 1 consecutive empty horizontal cells which does not happen in the first a rows. Figure 4: This figures shows the size of the empty regions after placing the anchor of La,a in Ca+1 ,1.A general formula for cp f ix (La,b ) is conjectured in section 4. Notice that cp f ix (La,b ) could be small, as in the case when a = b. However when a and b are dramatically different, for example a = 1 and b >> a , then every set of 11 three adjacent columns must contain an anchor. So our clumsy fixed packing number is at least b b 3 c.Now we turn our attention to free packing. We provide bounds for La,b as well as show that cp f ree (La,a ) = 2 . Lemma 3.9. For a L polyomino, La,b , cp f ree (La,b ) ≥ 2. Proof. It suffices to show that there does not exist a clumsy packing of size 1. Assume by contradiction, there exist two positive integers a and b so that cp f ree (La,b ) = 1. Without loss of generality, we will use La,b without any rotations. Assume the anchor is on cell Cx,y . If y > 1 and x > 1 then we can fit another La,b with anchor at cell Cx−1,y −1. Assume y = 1. We can fit an LR 2 a,b with anchor at cell Cx+a,b +2 . A similar argument holds for x = 1 . See Figure 5 for an example. Figure 5: If y = 1, then we can fit LR 2 a,b with anchor at cell Cx+a,b +2 . Theorem 3.10. For a L polyomino, La,a , cp f ree (La,a ) = 2 . Proof. By Lemma 3.9, cp f ree (La,a ) ≥ 2. Consider placing a L polyomino La,a , call it L1, with anchor at cell Ca+1 ,a +1 . Place another L polyomino La,a ,call it L2, with anchor at cell Ca, 1. Notice to the left of L1 and L2 there are at most a empty columns which is not enough for another L polyomino. 12 Similarly, notice to the right of the L1 and L2, there are at most a empty rows which is not enough for another L polyomino. As seen in Figure 6. Figure 6: Free packing showing cp f ree (La,a ) = 2. For a general L polyomino, the maximum number of free L polyominoes we need is 5. This is shown in the following theorem. Theorem 3.11. For a L polyomino, La,b , 2 ≤ cp f ree (La,b ) ≤ 5.Proof. By Lemma 3.9, 2 ≤ cp f ree (La,b ). A valid arrangement of five L poly-ominoes can always be constructed in the manner shown in Figure 7, where the four L polyominoes on the left are embedded into a square of sizelength b + 2. Thus, there can not be another L polyomino in the center of these four L polyominoes. The bottom most a − 1 rows and right most a − 1 columns will be empty. However, placing a LR 2 a,b with anchor at Ca+b+1 ,b +3 will create a free packing since a ≤ b. Therefore, 2 ≤ cp f ree (La,b ) ≤ 5. With these bounds, we know the clumsy free packing number is often less than the upper bound. For example, consider a = 3 , b = 6 and n = 10 . We 13 Figure 7: General pattern to show cp f ree (La,b ) ≤ 5. can place three copies L3,6 with anchor at C2,1, C 3,4, and C7,4. This creates a free packing of L3,6 whose packing number is 3. A similar arrangement can be made to find a free packing of L2,7 whose packing number is 4. We conjecture that these are the clumsy free packing numbers for L3,6 and L2,7 respectively. Corollary 3.12. For a L polyomino, L1,b , 2 ≤ cp f ree (L1,b ) ≤ 4. Proof. Note that if a = b = 1 then cp f ree (L1,1) = 2 via Theorem 3.10. Given 1 6 = b, a free packing of four L polyominoes can always be constructed in the manner shown in Figure 8, which has at most b consecutive empty horizontal cells and b consecutive empty vertical cells. Therefore, 2 ≤ cp f ree (L1,b ) ≤ 4. 3.3 T Polyominoes A T polyomino is a natural extension of the L polyomino. Definition 3.13. A T polyomino , Ta,b , is a polyomino such that Ta,b = {Ci, 1 :1 ≤ i ≤ 2a + 1 } ∪ { (a + 1 , j ) : 2 ≤ j ≤ b + 1 }. Notice |Ta,b | = 2 a + b + 1 . We will define the anchor of the polyomino to be the cell Ca+1 ,1.We will define T R a,b , T R 2 a,b , and T R 3 a,b to be a 90 ◦, 180 ◦, and 270 ◦ clock-wise rotation of Ta,b respectively. So we have: • T R a,b = {Cb+1 ,i : 1 ≤ i ≤ 2a + 1 and ( j, a + 1) : 1 ≤ j ≤ b} which will have anchor at cell Cb+1 ,a +1 ,14 Figure 8: Shows cp f ree (L1,b ) ≤ 4. • T R 2 a,b = {Ci,b +1 : 1 ≤ i ≤ 2a + 1 and ( a + 1 , j ) : 1 ≤ j ≤ b} which will have anchor at cell Ca+1 ,b +1 , and • T R 3 a,b = {C1,i : 1 ≤ i ≤ 2a + 1 and ( j, a + 1) : 2 ≤ j ≤ b + 1 } which will have anchor at cell C1,a +1 . As before, we will use Ta,b , T R a,b , etc. to describe the size and orientation of the polyomino and use the anchor to describe its location which is just a shift of Ta,b , T R a,b , etc.. To proceed, we will consider two cases for fixed T polyominoes. The first case, b ≤ 2a implies that the T polyomino is as wide or wider than it is tall. The second case, b ≥ 2a + 1 implies that the T polyomino is taller than it is wide. Theorem 3.14. For a T polyomino, Ta,b , if b ≤ 2a then cp f ix (Ta,b ) = ⌈2a + 1 2b + 1 ⌉ . Proof. Place T polyominoes, Ta,b , with anchors Cb b 2 c+a+1 ,y , where y = b + 1 mod 2 b + 1. In addition, if n mod 2 b + 1 ≥ b + 1, add another T polyomino with center Cb b 2 c+a+1 ,n −(b+1) . Note that this will put T polyominoes, centered horizontally, so that the centers have exactly 2 b rows between them, with the exception being at the bottom of the board where the centers may have less than 2 b rows between them. If there are at least 2 b + 1 rows below 15 the bottom most anchor, then we include another T polyomino with anchor Cb b 2 c+a+1 ,n −(b+1) . See Figure 9. Figure 9: Pattern for cp f ix (Ta,b ) when b ≤ 2a.Notice that there is no anchor in the top b rows, and then every 2 b+1 rows thereafter will contain an anchor. If there are at least 2 b+1 empty rows at the bottom of the board, we include another T polyomino. Therefore, the number of polyominoes that we now have in our arrangement is ⌈ n−b 2b+1 ⌉ = ⌈2a+1 2b+1 ⌉. This shows cp f ix (Ta,b ) ≤ ⌈2a + 1 2b + 1 ⌉ . To show this is optimal, notice that we must have an anchor in the top b + 1 rows, Otherwise we can include another T polyomino with an anchor in the top row. Next, notice that for every 2 b + 1 rows thereafter, we must have an anchor. If not, we will have at least b + 1 consecutive empty rows. Therefore, the number of T polyominoes must be at least cp f ix (Ta,b ) ≥ ⌊n − (b + 1) 2b + 1 ⌋ 1 = ⌈ n − b 2b + 1 ⌉ . 16 The last equality follows since if x and y are positive integers then ⌊xy ⌋ = ⌈x−y+1 y ⌉ . Theorem 3.15. For a fixed T polyomino, Ta,b , if b > 2a, then cp f ix (Ta,b ) = ⌈ b + 1 2a + 1 ⌉ . Proof. The proof here is similar to the proof of Theorem 3.14 above, but consider anchors in columns rather than rows. For free T polyominoes, we can find an exact value when a = b and bounds for Ta,b . Theorem 3.16. For a free T polyomino, Ta,b , if a = b, then cp f ree (Ta,a ) = 2 . Proof. Assume a = b. Consider placing a T polyomino with anchor Ca+1 ,a +1 and another T R polyomino with anchor C2a+2 ,2a+1 . See Figure 10 Notice that this creates three pairwise disjoint regions which can not contain another T polyomino. Therefore cp f ree (Ta,a ) ≤ 2. Assume by way of contradiction that cp f ree (Ta,a ) = 1. Assume, without loss of generality, a single T polyomino, unrotated, is placed on the board so that column n is empty. Notice that the anchor must be in the first a+1 rows and the first 2 a columns. We can always place another T R polyomino with anchor Cn, 2a+1 since column n was empty and there are at least a columns between the anchors. Note that column 1 or column n must be empty and if column 1 is empty, the argument is similar. Therefore cp f ree (Ta,a ) ≥ 2 which completes the proof. Theorem 3.17. For a free T polyomino, Ta,b , 2 ≤ cp f ree (Ta,b ) ≤ 4.Proof. Assume by way of contradiction that cp f ree (Ta,b ) = 1 . Since Xn or X1 must be empty, we will assume without loss of generality a single T polyomino, unrotated, is placed on the board with anchor Cx,y , so that Xn is empty. If Yn is empty, then we can place a T R 2 polyomino on the board with anchor Cx+1 ,n . Therefore, the T polyomino must intersect Yn so therefore 17 Figure 10: Shows cp f ree (Ta,a ) = 2. the anchor must be on row y = 2 a + 1. Since Xn is empty, we can place a T R polyomino with anchor Cn,a +1 . This implies cp f ree (Ta,b ) ≥ 2. Let c = min {a, b }. Consider placing the following four T polyominoes on the board: Ta,b with anchor Ca+1 ,c , T R a,b with anchor Cn−c+1 ,a +1 , T R 2 a,b with anchor Cn−a,n −c+1 , and T R 3 a,b with anchor Cc,n −a.Case 1: Assume a < b . Note that T and T R will always be adjacent. This is because T would occupy cells {Cx,y : 1 ≤ x ≤ 2a + 1 , y = a} and T R would occupy cells {Cx,y : a + 2 ≤ x ≤ n − a, y = a + 1 }. This implies that the four polyominoes will create five disjoint empty regions, four along the outside of the board and one on the interior of the board. The empty interior region will be a square with side length b − 1 and therefore we can not fit another T polyomino in the region. Each empty region on the outside of the board will be subsets of a a × n rectangle and therefore can not fit another T polyomino. Thus, we have a clumsy packing with four T polyominoes. See Figure 11. Case 2: Assume b ≤ a. Note that T and T R will always be adjacent. This is because T would occupy cells {Cx,y : 1 ≤ x ≤ 2a + 1 , y = b} and T R would occupy cells {Cx,y : x = n − c + 1 = 2 a + 2 , 1 ≤ y ≤ 2a + 1 }This implies that the four poloyominoes will create five disjoint empty regions, four along the outside of the board and one on the interior of the board. The empty interior region will be a subset of a square with side length n − 2b = 2 a + 1 − b ≤ 2a and therefore we can not fit another T polyomino in the region. Each empty region on the outside of the board will be subsets of a ( b − 1) × 2a + 1 18 Figure 11: Pattern for cp f ree (Ta,b ) when a < b .rectangle and therefore can not fit another T polyomino. Thus, we have a clumsy packing with four T polyominoes. See Figure 12. Figure 12: Pattern for cp f ree (Ta,b ) when b ≤ a.Note that these are not always optimal packing. For example, Theorems 3.16 shows that cp f ree (Ta,a ) = 2. Also, consider a = 4 and b = 3. This can be packed using only three T4,3 polyominoes, specifically two T4,3 polyomino with centers C5,4 and C5,9 as well as T R 4,3 with center C10 ,8. See the Figure 13 for more details. 19 Figure 13: Shows cp f ree (T4,3) ≤ 3. 3.4 Plus Polyominoes Our last polyomino is a plus polyomino. Definition 3.18. A plus polyomino , Pa, is a polyomino such that Pa = {Ci,a +1 : 1 ≤ i ≤ 2a + 1 } ∪ { Ca+1 ,j : 1 ≤ j ≤ 2a + 1 }. The |Pa| = 4 a + 1. We will define the anchor of the polyomino to be the cell Ca+1 ,a +1 .A plus polyomino when rotated by an integer multiple of 90 deg remains the same polyomino. Thus a free, and fixed, polyominoes are indistinguish-able. Therefore we will use cp (Pa) to denote the clumsy packing number since cp f ix (Pa) = cp f ree (Pa) Theorem 3.19. For a plus polyomino, Pa, cp (Pa) = 1 . Proof. Let Pa denote a plus polyomino. Note that no polyomino can have an anchor in the leftmost a columns, rightmost a columns, top a rows, or the bottom a rows. Place the polyomino Pa on the board with anchor at cell C2a+1 ,2a+1 and call this polyomino P . To place another plus polyomino anchor at the board we must have at least 2 a + 1 consecutive empty cells in a single column. This only happens in the leftmost a columns and the rightmost a columns which can not contain an anchor. Therefore cp (Pa) = 1. 20 4 Open Conjectures and Questions The area of packing polyominoes still has a lot of work. Although infinite spaces have been considered, there are a lot of applications for finite packing which makes this a worthwhile problem to pursue. In the future, in addition to looking into different types of polyominoes and different sized finite boards, we propose some of the following questions and conjectures. Some of these may be much easier than others. 4.1 Rectangular Polyominoes Question 4.1. For a free rectangular polyomino, Ra,b , when a 6 = b and a or b 6 = 1, what is the cp f ree (Ra,b )? This is particularly interesting considering that a horizontal tiling of R3,6 shows cp f ree (R3,6) ≤ cp f ix (R3,6) ≤ 8 and we think this is an equality. However, a similar horizontal tiling would imply cp f ree (R3,9) ≤ cp f ix (R3,9) ≤ 10 but we have constructed a different tiling so that cp f ree (R3,9) ≤ 9 which keeps 7 × 8 rectangular regions empty in the four corners. 4.2 L Polyominoes Conjecture 4.2. For a fixed L polyomino, La,b , if b < a , then cp f ix (La,b ) ≤ ⌊ n (a+2) 2+a ⌋ (a + 1) + ⌈n− ⌈n (a+1) 2+a ⌉ (( a+1) 2)−aa+1 ⌉ . Question 4.3. For a free L polyomino, La,b , under what conditions do a and b need to be for cp f ree (La,b ) = 2, cp f ree (La,b ) = 3, cp f ree (La,b ) = 4, and cp f ree (La,b ) = 5? 4.3 T Polyominoes Question 4.4. For a free T polyomino, Ta,b , under what conditions do a and b need to be for cp f ree (Ta,b ) = 2, cp f ree (Ta,b ) = 3, and cp f ree (Ta,b ) = 4? Question 4.5. If T polyominoes, Ta,b has an addition parameter, c, such that Ta,b,c = {(i, 1) : 1 ≤ i ≤ a + b + 1 } ∪ { (a + 1 , j ) : 2 ≤ j ≤ c + 1 }, how would the cp f ree (Ta,b,c ) and cp f ix (Ta,b,c ) be affected? 21 4.4 Plus Polyominoes Question 4.6. If plus polyominoes, Pa, have three addition variables, b, c and d, such that Pa,b,c,d = {(i, a + 1) : 1 ≤ i ≤ 2a + 1 } ∪ { (a + 1 , j ) : 1 ≤ j ≤ 2a + 1 } ∪ { (i, 0) : −a ≤ i ≤ b; (0 , j ) : (0 , j ) : −d ≤ j ≤ c}, how would the cp (Pa,b,c,d ) be affected? References W. Goddard. Mistilings with dominoes. Discrete Math. , 137(1-3):361– 365, 1995. J. Goodman, J. O’Rourke, and C. T´ oth. Handbook of Discrete and Com-putation Geometry . CRC Press, 3 edition, 2017. A. Gy´ arf´ as, J. Lehel, and Z. Tuza. Clumsy packing of dominoes. Discrete Math. , 71(1):33–46, 1988. B. Sands. The Gunport Problem. Math. Mag. , 44(4):193–196, 1971. S. Walzer. Clumsy packings in the grid. Karlsruhe Institute of Technology, Institute for Algebra and Geometry Institute of Theoretical Informatics ,Bachelor’s Thesis, 2012. S. Walzer, M. Axenovich, and T. Ueckerdt. Packing polyominoes clumsily. Computational Geometry , 47(1):52–60, 2014. 22
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Solved: Simplify the radical. sqrt(99) 3sqrt(11) 11sqrt(3) 9sqrt(11) 11sqrt(9) [Math] Drag Image or Click Here to upload Command+to paste Upgrade Sign in Homework Homework Assignment Solver Assignment Calculator Calculator Resources Resources Blog Blog App App Gauth Unlimited answers Gauth AI Pro Start Free Trial Homework Helper Study Resources Math Arithmetic Questions Question Simplify the radical. sqrt(99) 3sqrt(11) 11sqrt(3) 9sqrt(11) 11sqrt(9) Gauth AI Solution 100%(5 rated) Answer The answer is 3\sqrt {11} Explanation Simplify the radical To simplify $$\sqrt{99}$$99​, find the prime factorization of 99. $$99 = 9 \times 11 = 3^{2} \times 11$$99=9×11=3 2×11 2. Rewrite the radical using the factorization $$\sqrt{99} = \sqrt{3^{2} \times 11}$$99​=3 2×11​ 3. Apply the product rule for radicals $$\sqrt{3^{2} \times 11} = \sqrt{3^{2}} \times \sqrt{11}$$3 2×11​=3 2​×11​ 4. Simplify the perfect square $$\sqrt{3^{2}} \times \sqrt{11} = 3\sqrt{11}$$3 2​×11​=3 11​ Helpful Not Helpful Explain Simplify this solution Gauth AI Pro Back-to-School 3 Day Free Trial Limited offer! Enjoy unlimited answers for free. Join Gauth PLUS for $0 Previous questionNext question Related SIMPLIFYING RADICALS Simplify the radical betow square root of -24= square root of 94% (16 rated) Simplify square root of -25 93% (367 rated) Simplify the radical. - square root of 9 100% (9 rated) Simplified Radical square root of square 100% (5 rated) Simplify the radical. square root of 16a2b3=square 100% (10 rated) Simplify the radical. square root of 145 97% (440 rated) Simplify the radical Simplify the radical square root of -72 square root of -80 100% (3 rated) Simplify the radical: square root of 4a2 100% (9 rated) Simplifying Radicals a radical square root of this is 100% (1 rated) Which equation represents a circle with center -5,-6 and radius of 5? x+52+y+62= square root of 5 x+52+y+62=25 x+52+y+62=5 x-52+y-62=25 75% (4 rated) Gauth it, Ace it! contact@gauthmath.com Company About UsExpertsWriting Examples Legal Honor CodePrivacy PolicyTerms of Service Download App
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https://www.youtube.com/watch?v=V-yJfiQTbwk
Dot Product and the Parallelogram Law in High Dimension Mike, the Mathematician 19000 subscribers 14 likes Description 185 views Posted: 19 Jun 2024 We introduce the dot product of two vectors in n dimensional Euclidean space. This will give us a method of extending the geometric notions from two and three dimensional space to the higher dimensional setting. We use properties of dot products to generalize the parallelogram law for vectors in n dimensional space. mikethemathematician, #mikedabkowski, #profdabkowski 4 comments Transcript: hello students in this video we'll discuss the dot product on high dimensional uding spaces let's let X and Y be vectors in RN and we're going to write them as row vectors then Define an operation called the dotproduct which we've seen from Cal 3 and we're later going to call this the inner product we do an arbitrary Vector spaces that support the structure by X doy is equal to well X and Y are in RN so they have components X1 through xn y1 through YN I'm going to multiply the first components add that to the multiplication the second components all the way down to the m of the last components over there okay so easy enough it's an algebraic calculation what are the sort of the basic algebraic properties of this operation well the basic properties of the following so there's some trivial properties to prove properties okay so the properties are as follows number one is that it's commutative is that x.y is equal to y.x that's trivial two is that X do y + Z is equal to X doy + y do Z again that's also from distributivity and then three is it homogene homogeneity is that Lambda X for any Lambda scalar doy is the same as x. Lambda Y and that's the same as Lambda time x doy right so these are the typical algebraic properties of the product of the operation of course there's also geometric properties right so the geometric properties stem from the fact that inner products give rise to Norms right so these are the geometric properties so dot products give rise to Norms okay and in more general settings every time you have an inner product space that will give you a norm space but vice versa right a norm space will generate an inner product space if and only if there's some sort of parallelogram identity so we'll see that in further videos okay and so what's the definition of a norm so I'm going to define the norm of x to be the square root of x dox and of course X dox is not negative because X dox will be X12 + X2 2 plus xn^ 2 so this breaks perfect sense over here right and so now of course what are the properties of this Norms so the properties of this Norms are as follows so one is that the norm of X is always greater than or equal to zero and it's equal to zero if and only if x is the zero Vector itself okay two is that it's homogene homogeneous name if I have Lambda X then this will be absolute value Lambda Norm X okay and finally three is we're going to have this triangle in equality over here right so the triangle these are basically the only two properties essentially that we're going to need right but we have this triangle equality as well x + y we'll have to prove this of course less or equal to X plus that's the triangle in equality so these are the geometric properties of norms right okay and as an immediate consequence of this what what can we say we can say let's do some examples of this over here so here's a example let's consider the norm of x + yty squ well this of course will give us some good application of doing foiling Properties or these distributed properties okay so we can do by property number two I can sort I can foil this out and I can sort of change the order so this will be what this will be x.x which is Norm of x squar plus what plus 2 x doy plus Norm of Y quantity squar over here and so now of course so that gives me one calculation I can symmetrize this let me look at this expression over here xus y^ 2ar just as some basic properties of computing with inner products this is going to be x + y x - y excuse me so that's an xus y so let's kill it kill it over there x - y x - y okay and by similar reasoning what is this over here this is just going to be the norm of X squar and then - 2 x.y and then plus the norm of y^ s because the negative negative is going to cancel out like that and so these two relationships together by the Symmetry gives me the following so if I add these equations together over here I get what we get Norm of x + y^ 2 plus Norm of xus y^ 2ar is equal to two Norms of X plus two Norms of y^2 right and this relationship over here is called the parallelogram identity this is the parallelogram identity and why is it called the parallelogram identity well let's think about what happens we know this Norm is sort of a measure of length right so this is an idea of length right so in other words this is sort of like the length of the vector X right at least in uclean space is certainly the length of the vector X and of course we can see this is the parallelogram because if I draw a parallelogram so if I have a vector X over here from Cal 3 if that's my Vector X over here and that's my Vector y over here then this is another copy of the vector Y and that's another copy of the vector X over here and of course this Vector over here is what that Vector over there is the vector X Plus y and this Vector over here on the opposite diagonal if I go from here to here what's that going to be well this Vector plus X is going to have to give me y so this going to be y - x that's going to be y - x or x - y right and so of course we know for a parallelogram that the sum of the square of the diagonals so I know that for a parallelogram diagonal 1^ 2 plus diagonal 2^ 2 is equal to twice length 1 s length 1 S Plus length 2 s that's true from ukan so we called this corresponding identity over here the parallelogram identity for Norms thank you very much
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http://images.pcmac.org/SiSFiles/Schools/TN/AlcoaCitySchools/AlcoaHigh/Uploads/DocumentsSubCategories/Documents/Incline%20Plane%20Worksheet.pdf
Name: ______ Date: ___ Simple Machines: Lesson 2, Tools and Equipment, Part I – Inclined Plane Worksheet 1 Tools and Equipment, Part I Activity – Inclined Plane Worksheet Instructions/Questions A Measure the length and height of Inclined Plane 1: Length: ___ (m) Height: __ (m) 1. What is the mechanical advantage based on these measurements? _ 2. What was the required force to raise the object? Without the inclined plane: (Output force) _ (g) With the inclined plane: (Input force) _ (g) 3. What is the mechanical advantage based on these measurements? __ Name: ______ Date: ___ Simple Machines: Lesson 2, Tools and Equipment, Part I – Inclined Plane Worksheet 2 B Measure the length and height of Inclined Plane 2: Length: __ (m) Height: __ (m) 1. What is the mechanical advantage based on these measurements? __ 2. What was the required force to raise the object? Without the inclined plane: (Output force) _ (g) With the inclined plane: (Input force) _ (g) 3. What is the mechanical advantage based on these measurements? __ C Measure the length and height of Inclined Plane 3: Length: __ (m) Height: __ (m) 1. What is the mechanical advantage based on these measurements? __ 2. What was the required force to raise the object? Without the inclined plane: (Output force) _ (g) With the inclined plane: (Input force) _ (g) 3. What is the mechanical advantage based on these measurements? __ D Measure the length and height of Inclined Plane 4: Length: __ (m) Height: __ (m) 1. What is the mechanical advantage based on these measurements? __ 2. What was the required force to raise the object? Without the inclined plane: (Output force) _ (g) With the inclined plane: (Input force) ___ (g) 3. What is the mechanical advantage based on these measurements? ______
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https://online.stat.psu.edu/stat501/lesson/2/2.4
2.4 - Sums of Squares (continued) | STAT 501 Skip to main content ENROLL Search Search STAT 501Regression Methods User Preferences Font size Font family A A Mode Cards Reset Content Preview Arcu felis bibendum ut tristique et egestas quis: Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris Duis aute irure dolor in reprehenderit in voluptate Excepteur sint occaecat cupidatat non proident Lorem ipsum dolor sit amet, consectetur adipisicing elit. Odit molestiae mollitia laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio voluptates consectetur nulla eveniet iure vitae quibusdam? Excepturi aliquam in iure, repellat, fugiat illum voluptate repellendus blanditiis veritatis ducimus ad ipsa quisquam, commodi vel necessitatibus, harum quos a dignissimos. Close Save changes Keyboard Shortcuts Help F1 or ?Previous Page← + CTRL (Windows) ← + ⌘ (Mac) Next Page→ + CTRL (Windows) → + ⌘ (Mac) Search Site CTRL + SHIFT + F (Windows) ⌘ + ⇧ + F (Mac) Close Message ESC Breadcrumb Home 2 2.4 2.4 - Sums of Squares (continued) Investigating Height and GPA Data Section Now, let's do a similar analysis to investigate the research question, "Is there a (linear) relationship between height and grade point average?"(Height and GPA data) Review the following scatterplot and estimated regression line. What does the plot suggest for answering the above research question? In this case, it appears as if there is almost no relationship whatsoever. The estimated slope is almost 0. Again, we can answer the research question using the P-value of the t-test for: testing the null hypothesis H 0:β 1=0 against the alternative hypothesis H A:β 1≠0. As the Minitab output below suggests, the P-value of the t-test for "height" is 0.761. There is not enough statistical evidence to conclude that the slope is not 0. We conclude that there is no linear relationship between height and grade point average. The Minitab output also shows the analysis of variable table for this data set. Again, the P-value associated with the analysis of variance F-test, 0.761, appears to be the same as the P-value, 0.761, for the t-test for the slope. The F-test similarly tells us that there is insufficient statistical evidence to conclude that there is a linear relationship between height and grade point average. Analysis of Variance | Source | DF | Adj SS | Adj MS | F-Value | P-Value | --- --- --- | | Constant | 1 | 0.0276 | 0.0276 | 0.09 | 0.761 | | Residual Error | 33 | 9.7055 | 0.2941 | | | | Total | 34 | 9.7331 | | | | Model Summary S = 0.5423 R-Sq = 0.3% R-Sq (adj) = 0.0% Coefficients | Predictor | Coef | SE Coef | T-Value | P-Value | --- --- | Constant | 3.410 | 1.435 | 2.38 | 0.023 | | height | -0.00656 | 0.02143 | -0.31 | 0.761 | Regression Equation gpa = 3.14 -0.0066 height The scatter plot of grade point average and height appear below, now adorned with the three labels: y i denotes the observed grade point average for student i y^i is the estimated regression line (solid line) and therefore denotes the estimated grade point average for the height of student i y¯ represents the "no relationship" line (dashed line) between height and grade point average. It is simply the average grade point average of the sample. For this data set, note that the estimated regression line and the "no relationship" line are very close together. Let's see how the sums of squares summarize this point. ∑i=1 n(y^i−y¯)2=0.0276 ∑i=1 n(y i−y^i)2=9.7055 ∑i=1 n(y i−y¯)2=9.7331 The "total sum of squares," which again quantifies how much the observed grade point averages vary if you don't take into account height, is ∑i=1 n(y i−y¯)2=9.7331. The "regression sum of squares," which again quantifies how far the estimated regression line is from the no relationship line, is ∑i=1 n(y^i−y¯)2=0.0276. The "error sum of squares," which again quantifies how much the data points vary around the estimated regression line, is ∑i=1 n(y i−y^i)2=9.7055. In short, we have illustrated that the total variation in the observed grade point averages y (9.7331) is the sum of two parts — variation "due to" height (0.0276) and variation due to random error (9.7055). Unlike the last example, most of the variation in the observed grade point averages is just due to random error. It appears as if very little of the variation can be attributed to the predictor height. Try It! Sums of Squares Section Some researchers at UCLA conducted a study on cyanotic heart disease in children. They measured the age at which the child spoke his or her first word (x, in months) and the Gesell adaptive score (y) on a sample of 21 children. Upon analyzing the resulting data, they obtained the following analysis of variance table: Analysis of Variance | Source | DF | Adj SS | Adj MS | F-Value | P-Value | --- --- --- | | Constant | 1 | 1604.08 | 1604.08 | 13.20 | 0.002 | | Residual Error | 19 | 2308.59 | 121.50 | | | | Total | 20 | 3912.67 | | | | Which number quantifies how much the observed scores vary if you don't take into account the age at which the child first spoke? Answer Analysis of Variance | Source | DF | Adj SS | Adj MS | F-Value | P-Value | --- --- --- | | Constant | 1 | 1604.08 | 1604.08 | 13.20 | 0.002 | | Residual Error | 19 | 2308.59 | 121.50 | | | | Total | 20 | 3912.67 | | | | Which number quantifies how far the estimated regression line is from the "no trend" line? Answer Analysis of Variance | Source | DF | Adj SS | Adj MS | F-Value | P-Value | --- --- --- | | Constant | 1 | 1604.08 | 1604.08 | 13.20 | 0.002 | | Residual Error | 19 | 2308.59 | 121.50 | | | | Total | 20 | 3912.67 | | | | Which number quantifies how much the scores vary around the estimated regression line? Answer Analysis of Variance | Source | DF | Adj SS | Adj MS | F-Value | P-Value | --- --- --- | | Constant | 1 | 1604.08 | 1604.08 | 13.20 | 0.002 | | Residual Error | 19 | 2308.59 | 121.50 | | | | Total | 20 | 3912.67 | | | | «Previous 2.3 - Sums of Squares Next 2.5 - Analysis of Variance: The Basic Idea» Lesson Lesson 1: Simple Linear Regression 1.1 - What is Simple Linear Regression? 1.2 - What is the "Best Fitting Line"? 1.3 - The Simple Linear Regression Model 1.4 - What is The Common Error Variance? 1.5 - The Coefficient of Determination, R 2 1.6 - (Pearson) Correlation Coefficient, r 1.7 - Some Examples 1.8 - R 2 Cautions 1.9 - Hypothesis Test for the Population Correlation Coefficient 1.10 - Further Examples Software Help 1 Minitab Help 1: Simple Linear Regression R Help 1: Simple Linear Regression Lesson 2: SLR Model Evaluation 2.1 - Inference for the Population Intercept and Slope 2.2 - Another Example of Slope Inference 2.3 - Sums of Squares 2.4 - Sums of Squares (continued) 2.5 - Analysis of Variance: The Basic Idea 2.6 - The Analysis of Variance (ANOVA) table and the F-test 2.7 - Example: Are Men Getting Faster? 2.8 - Equivalent linear relationship tests 2.9 - Notation for the Lack of Fit test 2.10 - Decomposing the Error 2.11 - The Lack of Fit F-test 2.12 - Further Examples Software Help 2 Minitab Help 2: SLR Model Evaluation R Help 2: SLR Model Evaluation Lesson 3: SLR Estimation & Prediction 3.1 - The Research Questions 3.2 - Confidence Interval for the Mean Response 3.3 - Prediction Interval for a New Response 3.4 - Further Example Software Help 3 Minitab Help 3: SLR Estimation & Prediction R Help 3: SLR Estimation & Prediction Lesson 4: SLR Model Assumptions 4.1 - Background 4.2 - Residuals vs. Fits Plot 4.3 - Residuals vs. Predictor Plot 4.4 - Identifying Specific Problems Using Residual Plots 4.5 - Residuals vs. Order Plot 4.6 - Normal Probability Plot of Residuals 4.6.1 - Normal Probability Plots Versus Histograms 4.7 - Assessing Linearity by Visual Inspection 4.8 - Further Examples Software Help 4 Minitab Help 4: SLR Model Assumptions R Help 4: SLR Model Assumptions Lesson 5: Multiple Linear Regression 5.1 - Example on IQ and Physical Characteristics 5.2 - Example on Underground Air Quality 5.3 - The Multiple Linear Regression Model 5.4 - A Matrix Formulation of the Multiple Regression Model 5.5 - Further Examples Software Help 5 Minitab Help 5: Multiple Linear Regression R Help 5: Multiple Linear Regression Lesson 6: MLR Model Evaluation 6.1 - Three Types of Hypotheses 6.2 - The General Linear F-Test 6.3 - Sequential (or Extra) Sums of Squares 6.4 - The Hypothesis Tests for the Slopes 6.5 - Partial R-squared 6.6 - Lack of Fit Testing in the Multiple Regression Setting 6.7 - Further Examples Software Help 6 Minitab Help 6: MLR Model Evaluation R Help 6: MLR Model Evaluation Lesson 7: MLR Estimation, Prediction & Model Assumptions 7.1 - Confidence Interval for the Mean Response 7.2 - Prediction Interval for a New Response 7.3 - MLR Model Assumptions 7.4 - Assessing the Model Assumptions 7.5 - Tests for Error Normality 7.6 - Tests for Constant Error Variance 7.7 - Data Transformations Software Help 7 Minitab Help 7: MLR Estimation, Prediction & Model Assumptions R Help 7: MLR Estimation, Prediction & Model Assumptions Lesson 8: Categorical Predictors 8.1 - Example on Birth Weight and Smoking 8.2 - The Basics 8.3 - Two Separate Advantages 8.4 - Coding Qualitative Variables 8.5 - Additive Effects 8.6 - Interaction Effects 8.7 - Leaving an Important Interaction Out of a Model 8.8 - Piecewise Linear Regression Models 8.9 - Further Examples 8.10 - Summary Software Help 8 Minitab Help 8: Categorical Predictors R Help 8: Categorical Predictors Lesson 9: Data Transformations 9.1 - Log-transforming Only the Predictor for SLR 9.2 - Log-transforming Only the Response for SLR 9.3 - Log-transforming Both the Predictor and Response 9.4 - Other Data Transformations 9.5 - More on Transformations 9.6 - Interactions Between Quantitative Predictors 9.7 - Polynomial Regression 9.8 - Polynomial Regression Examples Software Help 9 Minitab Help 9: Data Transformations R Help 9: Data Transformations Lesson 10: Model Building 10.1 - What if the Regression Equation Contains "Wrong" Predictors? 10.2 - Stepwise Regression 10.3 - Best Subsets Regression, Adjusted R-Sq, Mallows Cp 10.4 - Some Examples 10.5 - Information Criteria and PRESS 10.6 - Cross-validation 10.7 - One Model Building Strategy 10.8 - Another Model Building Strategy 10.9 - Further Examples Software Help 10 Minitab Help 10: Model Building R Help 10: Model Building Lesson 11: Influential Points 11.1 - Distinction Between Outliers & High Leverage Observations 11.2 - Using Leverages to Help Identify Extreme x Values 11.3 - Identifying Outliers (Unusual y Values) 11.4 - Deleted Residuals 11.5 - Identifying Influential Data Points 11.6 - Further Examples 11.7 - A Strategy for Dealing with Problematic Data Points 11.8 - Summary Software Help 11 Minitab Help 11: Influential Points R Help 11: Influential Points Lesson 12: Multicollinearity & Other Regression Pitfalls 12.1 - What is Multicollinearity? 12.2 - Uncorrelated Predictors 12.3 - Highly Correlated Predictors 12.4 - Detecting Multicollinearity Using Variance Inflation Factors 12.5 - Reducing Data-based Multicollinearity 12.6 - Reducing Structural Multicollinearity 12.7 - Further Example 12.8 - Extrapolation 12.9 - Other Regression Pitfalls Software Help 12 Minitab Help 12: Multicollinearity R Help 12: Multicollinearity Lesson 13: Weighted Least Squares & Logistic Regressions 13.1 - Weighted Least Squares 13.1.1 - Weighted Least Squares Examples 13.2 - Logistic Regression 13.2.1 - Further Logistic Regression Examples Software Help 13 Minitab Help 13: Weighted Least Squares & Logistic Regressions R Help 13: Weighted Least Squares & Logistic Regressions Optional Content Topic 1: Robust Regression T.1.1 - Robust Regression Methods T1.1.1 - Robust Regression Examples T.1.2 - Resistant Regression Methods T.1.3 - Regression Depth Topic 2: Time Series & Autocorrelation T.2.1 - Autoregressive Models T.2.2 - Regression with Autoregressive Errors T.2.3 - Testing and Remedial Measures for Autocorrelation T.2.4 - Examples of Applying Cochrane-Orcutt Procedure T.2.5 - Advanced Methods T.2.5.1 - ARIMA Models T.2.5.4 - Generalized Least Squares T.2.5.2 - Exponential Smoothing T.2.5.3 - Spectral Analysis Software Help: Time & Series Autocorrelation Minitab Help: Time Series & Autocorrelation R Help: Time Series & Autocorrelation Topic 3: Poisson & Nonlinear Regression T.3.1 - Poisson Regression T.3.2 - Polytomous Regression T.3.3 - Generalized Linear Models T.3.4 - Nonlinear Regression T.3.5 - Exponential Regression Example T.3.6 - Population Growth Example Software Help: Poisson & Nonlinear Regression Minitab Help: Poisson & Nonlinear Regression R Help: Poisson & Nonlinear Regression Resource Menu Notation Used in this Course Common Procedures in Minitab Calculate a T-Interval for a Population Mean Code Numeric to Numeric Data Code a Text Variable into a Numeric Variable Conduct Best Subsets Regression Conduct Regression Error Normality Tests Conduct Stepwise Regression Conduct a Lack of Fit Test Conducting a Hypothesis Test for the Population Correlation Coefficient P Create Interaction Variables Create Residual Plots Create a Basic Scatter Plot Create a Fitted Line Plot Create a Fitted Line Plot with Confidence and Prediction Bands Create a Simple Matrix of Scatter Plots Creating a Correlation Matrix Display Data Find a Confidence Interval and a Prediction Interval for the Response Find a t Critical Value Find a t-based P-value Find an F Critical Value Find an F-based P-value Generate Random Normally Distributed Data Obtain a Sample Correlation Perform a Basic Regression Analysis Perform a Linear Regression Analysis Perform a t-test for a Population Mean µ Randomly Sample Data with Replacement from Columns Split the Worksheet Based on the Value of a Variable Store Residuals, Leverages, and Influence Measures × Save changes Close OPEN.ED@PSU Except where otherwise noted, content on this site is licensed under a CC BY-NC 4.0 license. 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https://math.stackexchange.com/questions/2969528/probability-for-choosing-couples-in-a-party
combinatorics - probability for choosing couples in a party - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 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Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more probability for choosing couples in a party Ask Question Asked 6 years, 11 months ago Modified6 years, 11 months ago Viewed 153 times This question shows research effort; it is useful and clear 0 Save this question. Show activity on this post. there are N couples in a party. 2 K people from the party are invited to play a game (2 K≤N). What is the probability that out of the 2 K people that were invited to play the game: A. exactly K couples were invited to play B. exactly o n e couple was invited to play this is what I did: first I calculated the Omega: there is no order (it doesn't matter if one couple was chosen before the other) and after we chose a couple we can't choose them again, so: |Ω|=N!(N−2 K)! now we can look at a couple as an individual- so I have to chose K couples from N couples, so: P(A)=|A||Ω|=N!(N−K)!N!(N−2 K)!=(N−2 K)!(N−K)! Am I right? for B I am a little confused. I know I need to choose one couple so: (N 1) , but now I'm not sure how to continue. Thank you! probability combinatorics Share Share a link to this question Copy linkCC BY-SA 4.0 Cite Follow Follow this question to receive notifications asked Oct 24, 2018 at 18:30 rose12rose12 377 1 1 silver badge 9 9 bronze badges Add a comment| 1 Answer 1 Sorted by: Reset to default This answer is useful 1 Save this answer. Show activity on this post. There are N couples at a party, from which 2 K people are selected to play a game. What is the probability that out of the 2 K people invited to play the game, exactly K couples were selected? The sample space consists of all subsets of 2 K people that can be selected from the 2 N people at the party. Hence, |Ω|=(2 N 2 K)=(2 N)!(2 K)!(2 N−2 K)! In your sample space, you counted ordered selections of 2 K people from the N couples at the party. While you could use ordered selections if you also use ordered selections for the favorable cases, you should have selected 2 K people from the 2 N people at the party. Observe that if exactly K couples are selected, then all 2 K of the people selected to play the game must be members of those K couples. Hence, the number of favorable cases is the number of ways we can select exactly K of the N couples at the party, which is (N K) Hence, Pr(exactly K couples are selected)=(N K)(2 N 2 K) There are N couples at a party, from which 2 K people are selected to play a game. What is the probability that out of the 2 K people invited to play the game, exactly one couples was selected? Strategy: Use the same sample space as above. For the favorable cases: Select from which of the N couples both members will be invited to play the game. That leaves you with 2 K−2 people to select to play the game, each of whom must come from a separate couple. From the remaining N−1 couples, select 2 K−2 couples from which a representative may be selected (here we use the fact that 2 K≤N). Choose a representative from each of those 2 K−2 couples. Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Follow Follow this answer to receive notifications answered Oct 24, 2018 at 21:32 N. F. TaussigN. F. Taussig 79.3k 14 14 gold badges 62 62 silver badges 77 77 bronze badges 0 Add a comment| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions probability combinatorics See similar questions with these tags. 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https://ocw.mit.edu/courses/5-111-principles-of-chemical-science-fall-2008/b1fcec8b1170537bf27a3ac6b7c1abcb_5-111F08-L19.pdf
MIT OpenCourseWare 5.111 Principles of Chemical Science, Fall 2008 Please use the following citation format: Catherine Drennan and Elizabeth Vogel Taylor, 5.111 Principles of Chemical Science, Fall 2008. (Massachusetts Institute of Technology: MIT OpenCourseWare). (accessed MM DD, YYYY). License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: MIT OpenCourseWare 5.111 Principles of Chemical Science, Fall 2008 Transcript – Lecture 19 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: We're pretty much ready to get started. Let's settle down and take a look at the clicker question. So take 10 more seconds. Very good. Most people had this right, and the trick here is just to think about the sign of delta g, whether it's negative and positive, and think about the equation and the influence of temperature on that equation. So whether it's going to make delta s a bigger factor or a smaller factor and how that will play out. So you can look at the equation and figure out what the signs have to be and then the influence of temperature. All right, so let's move to the first slide that I have today, which is welcome to the middle of the semester. So I'm Kathy Drennan and this is lecture 19 of 36, which means that you are halfway through the course. And so what you heard on Monday before the exam was about thermodynamics, and if you don't have all your delta g's and delta h's and if you don't have entropy full in mind, that's OK, we are not really leaving thermodynamics, we're going into chemical equilibrium, which is all about thermodynamics. So you're going to hear a lot more about delta g, delta h, temperature, and about our friend, entropy as we go along in the second half. So it's the middle of the semester. That means that you've had two of the sort of four hour exams -- remember the fourth hour exam is actually combined with the final exam. So the final exam is 200 points of cumulative material, and 100 points of new material, so you've done two now of those four sort of hour exams. Just to remind you of some of the topics you have seen and the topics coming ahead, this is on the syllabus, and we're actually where we're supposed to be on the syllabus, so if you want to take a look at that ever to see where we're going, we're actually on track. So the first half of the course are a lot of basic principles, and we're moving today into chemical equilibrium, so a lot more delta g's, delta h's coming on. And then we're going to move into acid base, which is acid base equilibrium. So we're not going to be leaving equilibrium or thermodynamics. Then we're going to go into oxidation reduction, which is also about equilibrium, and then transition metals, and end with kenetics. And so, these altogether represent the fundamentals needed for the study of biochemistry, organic chemistry, any kind of chemistry, biology, the life sciences, many things -- so you're getting all the fundamental principles of chemistry in this class. So along those lines, I just thought I would share something that happened to me on Wednesday when I was riding the T, the Silver Line, in particular. So I don't know if any of you have had this kind of experience yet where you're on public transportation and someone next to you says, "So, are you a student?" Maybe you have a notebook out or a book out or something. And you say, "Yes," and they said, "Oh, what are you studying?" And then you say "Well, you know, chemistry, math, physics." And they're like "Oh." And then they go busy themselves doing something else. Or they tell you "I didn't really like those subjects in school." And then they stop talking to you. So how many people have had that experience so far, that you scare the person next to you by what you study? OK, a few people. If I ask that question four years from now, I think it'll be like half the class, eight years from now it'll be everybody. So this is kind of common. But what happened to me on the Silver Line was actually pretty exciting, because I've had that other experience many times. So, I was wearing my keys around my neck, because women's professional clothes, no pockets, with a little MIT cord, and the person next to be on the Silver Line said "So, do you go to the Georgia Tech of the east?" And I said "Well, I am a professor at MIT." And he said "Well, I'm a mechanical engineer and I went to Georgia Tech." And so he said, "So, what do you teach?" I said, "Chemistry." And he said, "Chemistry -- I really wish I had paid more attention in chemistry." I said, "Well, what do you do now?" And he said "Well, I work for the army, and I'm part of a team that has mechanical engineers, electrical engineers, and chemists, and we're trying to figure out ways to detect explosives." So I said, "Oh, well have you heard of the head of the Chemistry Department at MIT, Tim Swager who works in the area, and he said, "Yes," he knew the name. And so he said that one of his porblems on the team, and in talking to the chemist, his chemistry language is not really good enough, and so he was really struggling, and that the best results of this team effort would be if everyone could really talk to each other. So he wished that he had paid more attention in his chemistry class. And so I, of course, my connection with chemistry was by wanting to understand biology, but for everyone it might be a little bit different. So, as I mentioned in the beginning of the class, one challenge that you have this semester is figure out what your connection to chemistry is. What are you going to use chemistry for? How does this fit into what you want to do? And maybe for some of you, you're not going to know that yet. Hopefully it won't take till you have a job doing something to realize that you're lacking something in your education. And so, probably if you stay in science and engineering, need chemistry, good to learn it all now. And from exam 2, we see that you are learning it now and that's really great. So, some day maybe someone in this room will be involved in national security, and if you're not a chemist, you'll be able to talk to the chemists and make really good progress toward that work. So, chemistry -- it's important in medicine, national security, the economy, energy initiatives, a lot of the big things going on now. It's a fundamental, and you will get in this course, the fundamentals. So if you have any good tea or bus or airplane conversations, let me know -- I'll catalog those for future reference. It's always a touch of how what we do here connects with the real world. All right, so we're not going far from thermodynamics, we're going into chemical equilibrium. And we're going to be talking a lot about delta g. So if delta g is not your friend yet, don't worry, you can still bond with delta g. All right, so chemical reactions, chemical reactions can go into a state of equilibrium. And it's a dynamic equilibrium, the reaction is still happening, but if a reaction is an equilibrium, the rate of the forward reaction will equal the rate of the reverse reaction, so there'll be no net change in composition. So let's take a look at an example. So let's look at a reaction in which we have nitrogen gas, and we have hydrogen gas, and they are reacting to form ammonia. Suppose we just start with nitrogen gas and hydrogen gas and we don't have any ammonia left. So if we consider concentrations versus time. So say we start with, we have some nitrogen gas, some concentration of nitrogen gas. As it reacts with hydrogen, the concentration will decrease and then level off. We'll start with some amount of hydrogen gas, and its concentration will also decrease and level off. And in the beginning we won't have any of the product, any of the ammonia, so its concentration will increase and then level off. So when these reactions level off, you're reaching equilibrium. The reaction is still happening, but the rate of the forward reaction is equal to the rate of the reverse reaction, so there's no net change. So the concentrations are staying the same, but there's still -- the reaction is still going forward. So let's think about the case when we have pure reactants when we haven't formed enough products yet to reach equilibrium. So if we have pure reactants, the reaction is going to be spontaneous in the forward direction. So we'll have a reaction that is spontaneous in the forward direction. And what will that mean about our friend delta g? Is it going to be greater or less than zero? So it'll be less than zero -- so delta g or the forward reaction will be less than zero. So when delta g is negative, the reaction is spontaneous in the forward direction. So what about when you have pure products, then the reaction should be spontaneous in the reverse direction. So you have spontaneous in the reverse direction, and what does that mean about the sign of delta g? Greater or less than zero? Greater, so it'll be positive. So, we can think about that in terms of a plot. We can think about free energy versus the progress of the reaction. So, the progress of the reaction is going this direction as you go along. So in the beginning if you have pure reactants, delta g is going to be less than zero. And you're going to proceed along in the forward direction spontaneously. If, on the other hand you have pure products, delta g will be positive, so you'll be spontaneous in the reverse direction, and the reaction will go in the reverse direction until what happens? Till you reach equilibrium. And what would delta g be at equilibrium? Zero. So you see, there is a great relationship between delta g and equilibrium, so we have not left delta g behind. So, delta g is going to change as the components of the reaction change. As you have more products or more reactants, you're going to have a different delta g. So let's look at some equations. So delta g is the change in free energy, the difference in free energy, at some point in the reaction at any time with amount of composition. We also have delta g nought, which talks about delta g under particular conditions, so it's sort of the standard free energy. We have a term called q, which is the reaction quotient, which tells you about products and reactants. We have our friend r, which is the gas constant, and this depends on temperature. So temperature is a term involved here. So the delta g at any point in the reaction is going to depend on the delta g nought for that reaction, and the reaction quotient, products and reactants, and we'll define this in a minute, and then the temperature as well. So we need to know more about what q is, what this reaction quotient is. So this slide looks a little bit scary, but it's going to be fine, because a lot of the terms are going to cancel out. So we're going to talk about q, this reaction quotient, and we're going to have different types of problems -- some where we're talking about gases, and others we're talking about solutions. So you can see two different kinds of q's, one that depends on partial pressure of the gas, and another that depends on concentration. So here is our equation again that we just saw -- delta g equals delta g nought plus r t natural log of q, and here we've expanded the term for q. So p to the sub x is the partial pressure of a particular gas, and so in this equation, we have a plus b going to c plus d, the top of the line or the products. So we have the partial pressure of gas c, and this is over a reference, partial pressure, raised to the power c, the coefficient, and then also we have d, the partial pressure of gas d, over a reference raised to the small letter d. On the bottom of the terms for the reactants, partial pressure of gas a over a reference raised to the coefficient a, partial pressure of gas b over the reference raised to the coefficient b. Now what's great is that the partial pressure is one bar, and so that basically cancels out as far as we're concerned. And so the term for q is much simplified. You won't see problems that have the reference in them, so you can just think about q in terms of products over reactants. And you just have to remember that the coefficients in the reactions do matter. If you're talking about solutions, the only difference is that we'll be talking about molar, so we have one molar, so the reference term here also cancels out. When you see something in brackets, like c in brackets, here that telling you it's a concentration term. So here, q is the concentration of c raised to its coefficiency. The concentration of d raised to its coefficient d over reactants. Concentration of a to a, concentration of b raised to b. So the thing in x indicates it's a concentration term. So q is just products over reactants, considering the stoichiometry of the particular reaction. So what about the equilibrium constant k? So at equilibrium you told me that delta g equals zero, and at equilibrium q, the reaction quotient equals k, the equilibrium constant. So we can consider that in terms of this expression, if we're talking about this expression at equilibrium, delta g is going to equal zero. And so, we just set this whole term equal to zero. We can rearrange the equation bringing delta g nought to the other side. And so we have delta g at nought equals minus r t natural log of K, because at equilibrium, k is equal to q. So now we have another term to solve for delta g, and an equation that relates delta g nought to be equilibrium constant k. So k, the equilibrium's constant has the same form as q, but we're only talking about the concentrations or the partial pressures of things at equilibrium. So it's the same, it's product over reactants, same expressions as q, but in the corner you say at equilibrium. So you're only talking about the concentrations of things at equilibrium if you're solving for k. If you're solving for q, it's the concentration or the partial pressure at any time in that particular reaction. Important thing, products over reactants. All right, so, we can rewrite the equation one more way. So I just told you that delta g nought is equal to minus r t natural log of K. So we can substitute into the expression minus r t natural log of k, and now we can rearrange this equation. And so, if we rearrange it, we have delta g, the delta g at any particular point in the reaction equals r t natural log of q over k. And this equation is helpful for people if they're thinking about what is the equilibrium constant, what concentrations do I have now -- we're not at equilibrium, what concentrations do I have now, what is q now in the reaction, how does that compare to k? And when you know what those values are, you'll know something about the direction of the reaction because you'll know if delta g is positive or negative. It'll to be spontaneous in the forward direction or in the reverse direction. So this is a handy equation for thinking about the relationship q k delta g. So let's think about that relationship for a minute. If q is less than k, what is the sign of delta g? So it would be negative, which means the forward direction of the reaction will occur. So if you think about it, you can think about in terms of products and reactants. So at equilibrium then, if q is less than k at equilibrium, there are more products than there are right now, so you need to make more products. So you would have delta g would be negative, you'll see that mathematically, and you can think about it in terms of whether you're going to make more products or less products. If q is greater than k, what is delta g? So it would be positive and the reverse direction would occur. So you think that at q, if it's larger than k, it has more products in its terms, and at equilibrium there are less products, so you need to go in a direction that will get rid of some of those products so you'll reach equilibrium again. So this equation is very helpful in thinking about the direction of the reaction -- which direction will it be spontaneous. So let's look at an example. K is given in this example, and then we have a bunch of partial pressures. And we're asked which direction the reaction will go. So what do I need to do to answer this question, what do I need to calculate? So if I'm given k, and a bunch of partial pressures, what do I first need to calculate? Q, right. So let's calculate q. So q, we're going to talk about products over reactants, so we're going to talk about be partial pressure of the ammonia, and there are two of them being formed. Our reactants, we want to talk about the partial pressure of the nitrogen, and the partial pressure of the hydrogen gas, and again include the stoichiometry, so we have three there. So now I can plug in my values, so I'm told I have 1 . 1 bar, and down here I have 5 . 5 and 2 . 2 to the 3, again, considering the stoichiometry. And if you do the math, you get 2 . 1 times 10 to the minus 2. That's your q value. Now given your k value, which the problem states, and this q value, let's do a clicker question, tell me which direction the reaction will go. All right, 10 seconds. So, 77%, pretty good. So, q is greater than k here. And if q is greater than k, what will be true about delta g? I have another clicker question for that -- yell out the answer. What is it? Positive, right. So you're going to shift towards reactants, so you're going to go in the reverse direction. So you think about whether there are more products or less products at equilibrium, and so there are more products, so we have to think about which direction it'll go, and here, ammonium will dissociate until equilibrium is reached again. OK. So let's think more about what k is going to tell us. So k tells us about the mixture of products and reactants at equilibrium, whether we can expect low or high concentration of reactants at equilibrium. So let's look at another example. So when you have k that's greater than one, so more products than reactants at equilibrium, you can think about this in terms of higher products at equilibrium. When you have k less than one, we're going to have lower products. So again, think about k in terms of products over reactants at equilibrium. So if k is greater than one, there are more products than reactants. If it's less than one, there will be less reactants than products. So let's look at an example of that. Let's look at when k is greater than one. And I have the equation up there and I'll write it here as well. So we have 2 n o 2, and two double arrows, and n 2 o 4. So we have a k value here of 6 . 84, so that's greater than one value. So let's think about this reaction. So over here instead of concentration, we're going to talk about partial pressure because we're talking about gas, and we have time. So initially we have a reactant. And the reactant starts at some concentration and decreases and then reaches a straight line, so reaches equilibrium. So we have our reactant here. Originally we have no product, and so product is going to go up and be formed and then it's going to level off as you reach equilibrium. So initially, what is true about q and k? So with no products, what is true about q and k? Q is less than k. And so what's true about delta g? Less than zero, it'll be negative, so it'll be spontaneous in the forward direction. So you're going to be spontaneous in the forward direction and you're going to make your product. So now let's calculate what the concentrations are going to be at equilibrium. So initially, so you have your initial pressure for the reaction, 2 n o 2 going to n 2 o 2, and our initial concentrations are given as one bar, and we have no product. Now we talk about the change as we go toward equilibrium, how much does the reactant change? What do I write here? What change? Minus x minus something x? Minus 2 x. So again, we're considering the stoichiometry, and what's over here? So just plus x, and then at equilibrium we now have 1 minus 2 x and x. So we're talking about equilibrium concentrations, so we're talking about k, so k equals 6 . 84, which is going to be equal to the partial pressure of the product over the partial pressure of the reactant squared. So it's going to be equal to x over 1 minus 2 x squared. So x, if you calculate it out, should equal point 381 bar. And then if we do 1 minus 2 times 0.381 bar, we get . 238 bar. So if we go back over here, our products at equilibrium -- oh, I guess I should write what -- so x is our product and this is our reactant. So the product we have . 381, and our reactant at equilibrium is going to be 0.238 bar. So we have more product than reactant at equilibrium, which is consistent with the value of k being greater than one. So, when you know something about the equilibrium constant, you know something about the reaction and whether you would expect more products or reactants at equilibrium. So again, you can think about this in terms of q and k. All right, so now we are going to go toward our next clicker question. So if we can rewrite the expression for delta g equals minus r t natural log of k, and express it in terms of k, and now we can think about then what is that relationship. If you have a large value for k, what do you expect to be true about delta g nought? All right, let's give that 10 seconds. OK, why don't you discuss for a minute with your friends whether you agree with that 78% or not. All right, now we're going to re-poll, so click in again. Now give the right answer. Interesting. It actually usually goes the other direction, that after there's a discussion, more people come to the same conclusion. So I guess it's a matter of if the professor asks that, you assume that that must have been the wrong answer. Was that people's logic? So what are the points of doing this, and we're going to actually do this kind of thing a few more times in class, is that collectively, and I was actually just at an education meeting about science down at the Howard Hughes Medical Institute, that statistics show that if you have a group where everyone in the group has the wrong answer and they're allowed to discuss it, there's a good chance they'll come up with the right answer. So that it's not just about one person in the group having the right answer, convincing everyone else that they're right, that the act of discussing often leads to new answers. So now that you know that it's not a trick on my part to tell you you got it wrong, we'll see next time whether this, in fact, holds, that the act of discussing helps give the right answer. Anyway, so if k is large, it is true that delta g nought would tend to be negative and more -- it would be negative and more on the large side. So one can think about if there's more products over reactants, that's going to indicate something about the delta g nought for the reaction, and the k -- the k, if it's greater than 1, if it's a big number, then there are more products than reactants, and delta g nought would be negative and would tend to be a large number. All right, so this is more actually kind of simple bookkeeping involved that if you know steps in the reactions and you know equilibrium constants, you can calculate an overall equilibrium constant for that reaction. So you can write a reaction as the sum of different components. And so up here, we are going to try to add these first two equations to get this net equation. So we have 2 gas p 3 c l 2 going to 2 p l c 3, and that's equilibrium 1. And so then in the next reaction, some of that is being consumed reacting with another c l 2, giving you p c l 5, and the net reaction we're interested in has 2 p 5 c l 2's going to 2 p c l 5. All right, what do I have to do before I can add these together effectively and have things cancel out? I need to multiply what? Second equation by 2, yeah. So to get that to work I would need to have 2's there, then this is going to cancel out and these will add up, so we have 5 and then we have two of the main products. So if I do that, and I have the equilibrium constant for one and for two, how am I going to get equilibrium constant for three? I'm going to multiply k 1 by k 2 and k 2. So I'm going to have to multiply k 2 in there twice, because there's two of those -- we'd multiply that up. So if you have different parts of reactions and you can sum them together, then you can multiply out the individual k's to get the new value of k. So that's something that's just useful that you'll run into in doing these types of problems. All right. Now we're going to think about how equilibriums respond to stress. And I always feel like I need to pause. MIT students, you guys are some of the smartest, most talented scientists in the world. I don't know if you fully appreciate how smart you all are. But this concept is tough for MIT students. So Le Chatelier's principle says that a system in equilibrium that is subjected to with stress tends to react in such a way to minimize that stress. I have advisees coming to my office saying, "I'm double-majoring in this and that and I'm taking five classes and I have UROP and I have this lab exercise -- I don't know what's going on, so I've been thinking a lot about it and I think I should add a third major." Le Chatelier would be very unhappy with that. Le Chatelier would say that the appropriate response is to drop one of the majors, to minimize the stress. So in doing these problems, what I want to encourage you to do is think the opposite of what you would do. Minimize the stress. If you think about that you'll be all set. All right. So Le Chatelier's principle actually is very useful. If you think about minimizing the stress, you'll be able to predict the direction that the reaction will shift. So the reaction's going to shift in a way to minimize the stress, so you can predict it. If you're thinking along these lines, you say, oh, that system was stressed, and then you can think about how that reaction or that system is going to respond. So let's give some examples. So, we have a system in equilibrium -- we started out, we had our nitrogen and our hydrogen and we had no product. We reacted the hydrogen and the nitrogen, their forming products, and eventually they reach equilibrium, their delta g equals zero there's still the reaction going on, but there's no net change. All right, now the system is going to be stressed. So we're going to add more of a reactant. How will the system react to minimize that stress? What is it going to do? It now has too much of one of the reactants. You'll form more products, and that's going to use up some of your other reactant, which will go down, and you're going to form more product until equilibrium is reached again. And one thing that I'll mention that the ratio has to be the same. The equilibrium constant is a constant given the same temperature, but you're not necessarily always going to have the same concentrations, but you should have the same ratios, the same value of k. All right, so what about if you add more product, what's going to happen? What direction will the reaction shift? Right, it's going to shift toward the reactants, so you're going to make more of each of the two reactants until again, you find your equilibrium again. And then the reaction's still going but there's no net change anymore. All right, so let's think about this -- let's think about this in terms of the math as well. If you want to stick with the math, that's OK, you can think about calculating delta g's here. So if you're a system in equilibrium and you add more hydrogen, the system will respond to minimize that increase. So it's going to make more product that will minimize the increase, it shifts to the right. And this can be explained in terms of q and k. So, you can think about, again, do you have more products now or did you have more products at equilibrium, and if you're adding more reactants, momentarily q will become less than k. And so, you would get a negative delta g, which would make it spontaneous in the forward direction. So some people like to think about this in terms of delta g equals r t natural log of q over k. So you think about if q is less than k, what sign you have for delta g, and that's tells you whether the reaction is spontaneous in the forward or the reverse direction. And let me just give you one hint for taking exams in this unit. That use of the arrow is really good, or saying "toward product" or "reactant." I can't tell you how many people write -- know what the answer is and write left when mean right, or write right when they mean left. But if you draw an arrow you never really get it wrong, and when you say products or reactants it's a lot harder to make that mistake. So if you're not good with right or left, which let me tell you a large fraction of people are not, hedge your bets, you can write everything, more products, arrows, and then write if you want, then you're pretty sure that you have it all in there. OK. So again, we can explain this in terms of q or k. All right. So let's just quickly talk about adding more products. We did this already. If more products are added. then q is going to be greater than k momentarily, and you would shift toward reactants, shift toward the left, and again, we saw that down there. So tell me a final clicker question and then we're done. What happens if you remove products and why? OK, 10 seconds. See if we can get in the 90's. No, no 90's today, we'll have to do it next time, but we got 73 right. So we're going to make more products as well.
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https://www.youtube.com/watch?v=BTdOVFEWaqU
Knights and Knaves Problems CSCI 2824 284 subscribers 303 likes Description 25094 views Posted: 20 Jan 2019 This is a tutorial teaching students how to solve knights and knaves problems using propositional statements and truth tables. This video was filmed for CSCI 2824 at the University of Colorado Boulder in the Spring 2019 semester. 23 comments Transcript: hello and welcome to a tutorial for CSCI 2824 discrete structures in the past few weeks you've been going over propositions compound propositions propositional statements and truth tables Knights names problems are a really great way to cement all of these subjects in your mind for this reason we're going to go over an example Knights neighs problem now suppose were given the following there are two people a and B a says at least one of us is a knave B is silent to go about solving this problem we first want to make some propositional statements in order to do that we're going to actually have to make some propositional variables first we can say let's P equal a is the night and let Q equal B is a nice using these variables we can determine what a is saying by saying at least one of us is a knave this is actually the statement A or B is a knave because we set it up so that both P and Q are a tonight and B's a night we're going to use not P or not Q for this statement so a says not P or not Q our second step is going to be making a truth table in order to do that I've first set up P and Q I like to set up so that P is true true false false and Q is true false true false after that you're going to want to set up the different parts of the propositional statement so we've set up not P here and not Q here together these will form not P or not Q in order to solve a nights in eighth problem we're going to use the biconditional where we use what a said an a is P and we're going to compare it now we're going fill out the truth table so first not P we know that not is going to be the opposite and so we get false false true true the same goes for not Q so we get false true false true now we look at not P or not Q for or we remember that only one has to be true in order for the entire statement to be true here we have false and false so that's going to give us false now we have false and true that will give us true true and false will give us true and true and true will give us true now for the biconditional we remember that this is true whenever one in whenever is two truths or two falses we also want to make sure that we're looking at p and the statement not P or not Q so we pretty much have to ignore these three here here we see it true and a false that gives us a false here we have a true and a true that gives us a true here we have a false and a true now go is a fault and here we have a false and a true that will also give us a false you'll notice here there's actually only one column or one row that is a true for the biconditional statement and that is this calll row here in this row we see that P is true and Q is false we can go back up to the statements that we said above if P is true this means a in the night and if Q is false this means that B is a nays now in some of these nights and 8th problems you'll have examples where both a and B are saying something let's use the same problem but suppose the B had also said a is a knave the steps here look very similar again we're going to make some propositional statements we have P saying a denied P being a denied Q being B's night and a Seng not P or not Q but what we also want to add in now is B says not P so by saying a is a knave B is saying P is not a knight now we go and we make a truth table I've set the truth table just the same way we did just a couple seconds ago and I filled it out fully however you're going to notice two extra rows here this row is a Q if and only if not P so this is essentially checking what be said here I've just simplified it to be the and so well we're actually gonna be comparing there is P if and only if not P or not Q and Q if and only if not P so let's solve the rest of the table here again we're looking at Q if and only if not P so we only want to be looking at Q and not P we have a true and a false that gives us a false it falls in a false that gives us a true true and true that gives us true and then false and true that gives us false now we do the and operation so we have a false and a false that's gonna be false we have a true and a true that will be true false and a true that's false and a false and false which is false again we notice that only one row is going to have a true for this and of the by conditionals we'll find that this actually gives us the same result so we see that a is a night and B is a knave which makes sense because we're working off of the same problem so this is an example of how you can go over nights and nays problem again this is a really great way to cement your skills in propositional statements compound propositions and truth tables so it's highly recommended that you do as many of these example problems as you can until you really feel comfortable with the subjects thanks so much for watching
4051
https://kids.britannica.com/students/article/hake/274730
hake - Students | Britannica Kids | Homework Help Articles AnimalsArts and LiteratureEarth and GeographyHistoryLife ProcessesLiving Things (Other)Philosophy and ReligionPlantsScience and MathematicsSocietySports and RecreationTechnology Images & Video AnimalsArts and LiteratureEarth and GeographyHistoryLife ProcessesLiving Things (Other)Philosophy and ReligionPlantsScience and MathematicsSocietySports and RecreationTechnology BiographiesDictionaryCompare CountriesWorld AtlasPodcast Switch Level KidsStudentsScholars About Us students Kids Students Scholars Fundamentals NEW 7-day free trial Search Login ArticlesFeatured Article alphabet All Categories Animals Arts and Literature Earth and Geography History Life Processes Living Things (Other) Philosophy and Religion Plants Science and Mathematics Society Sports and Recreation Technology Images & VideosFeatured Media calendar All Categories Animals Arts and Literature Earth and Geography History Life Processes Living Things (Other) Philosophy and Religion Plants Science and Mathematics Society Sports and Recreation Technology Biographies Dictionary Compare Countries World Atlas Podcast × hake View article for: Kids Students Scholars Article Images & Videos Related Subscriber features Print (Subscriber Feature) Email (Subscriber Feature) Cite (Subscriber Feature) Translate (Subscriber Feature) Listen (Subscriber Feature) × Related resources for this article Articles Primary Sources & E-Books Websites View search results for: Search Painting by Jean Helmer Fish of the hake family, Merlucciidae, are found in many parts of the world. Hakes and their relatives have two dorsal fins and a long ventral fin. On the top of the head is a V-shaped ridge. Most hakes are slate gray above and white or silver below and on the sides of the head. The white hake (Urophycis tenuis) is actually a member of the cod family, Gadidae. It is a major food fish in the New England states. It grows to a length of about 50 inches (127 centimeters) and may weigh as much as 40 pounds (18 kilograms). The smaller red, or squirrel, hake (U. chuss) is closely related. True hakes include the silver hake, also called whiting, of the Atlantic coast, and the Pacific hake (Merluccius productus) of the West coast. × It’s here: the NEW Britannica Kids website! We’ve been busy, working hard to bring you new features and an updated design. We hope you and your family enjoy the NEW Britannica Kids. Take a minute to check out all the enhancements! The same safe and trusted content for explorers of all ages. Accessible across all of today's devices: phones, tablets, and desktops. Improved homework resources designed to support a variety of curriculum subjects and standards. A new, third level of content, designed specially to meet the advanced needs of the sophisticated scholar. And so much more! Want to see it in action? Take a tour Start a free trial Subscribe now! × E-mail To Recipients Please enter a valid email address. To share with more than one person, separate addresses with a comma From Sender Name Please enter your name. Sender Email Please enter a valid email address. Cancel Submit Translate this page Choose a language from the menu above to view a computer-translated version of this page. Please note: Text within images is not translated, some features may not work properly after translation, and the translation may not accurately convey the intended meaning. Britannica does not review the converted text. After translating an article, all tools except font up/font down will be disabled. To re-enable the tools or to convert back to English, click "view original" on the Google Translate toolbar. About Us Contact Us Privacy Notice Terms of Use Diversity Privacy settings ©2025 Encyclopædia Britannica, Inc. By continuing to use this site, you consent to the terms of our cookie policy, which can be found in our Privacy Notice. ×
4052
https://www.houseofmath.com/encyclopedia/statistics-and-probability/probability-and-combinatorics/combinatorics/permutations-ordered-sampling-without-replacement
Numbers and Quantities Algebra Geometry Statistics and Probability Functions Proofs Encyclopedia>Statistics and Probability>Probability and Combinatorics>Combinatorics>Permutations (Ordered Sampling Without Replacement) Permutations (Ordered Sampling Without Replacement) An ordered set is a set where the order of the elements matter. Without replacement means that you can’t pick the same element more than once. Theory Permutations When you draw elements from a set of elements, you call the number of possible orders the permutations. | | | | Note! The order of the drawn elements matters! Example 1 15 teams are joining a relay race. 1. : How many different ways can the teams place first through third? 2. : Messi, Bale and Ronaldo each run for their team. What’s the probability that Bale’s team wins, Messi’s team comes in second, and Ronaldo’s team comes in third? 1. : Since it matters whether you come in first, second or third place, the order matters. That means you can think of the different ways to distribute the places as permutations. The calculation becomes | | | | That means there are 2730 different ways to fill the three first places when there are 15 teams. 2. : Since the placement is decided, “Bale, Messi and Ronaldo” is one event out of the possible options. You calculate and get: Example 2 You’re electing 4 students for the student council from a group of 31 people: One president, one vice president, one secretary and one treasurer. 1. : How many different councils can there be, when you take who gets which position into account? 2. : Al Gore is in the group. What is the probability that he is elected to the student council? 1. : Since it matters who has the different positions, you can think of this as a case where the order matters. That means each possible student council is a permutation. There are 31 students that can be chosen for president, 30 for vice president, and so on. Because you pick 4 council members out of the group, you find the number of different councils like this: | | | | That means you can elect different student councils. 2. : Al Gore is one of the 31 students, so if you assume that there’s an equal possibility for everyone to be elected, you calculate that: Previous entry How Factorials Work Want to know more?Sign UpIt's free! Next entry Combinations (Unordered Sampling Without Replacement)
4053
https://artofproblemsolving.com/wiki/index.php/Circumcenter?srsltid=AfmBOopxOJG7YLyih-gi1D8UPtVYwbbla_uzdrJwG26USijPJjP57Poj
Art of Problem Solving Circumcenter - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki Circumcenter Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search Circumcenter The circumcenter is the center of the circumcircle of a polygon. Only certain polygons can be circumscribed by a circle: all nondegeneratetriangles have a circumcircle whose circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle. Quadrilaterals which have circumcircles are called cyclic quadrilaterals. Also, every regular polygon is cyclic. Proof that the perpendicular bisectors of a triangle are concurrent First Proof We consider a nondegenerate triangle . Since the triangle is nondegenerate, and lie on different lines and so their perpendicular bisectors are not parallel and thus intersect. Let be the intersection of these perpendicular bisectors. Since lies on the perpendicular bisector of , it is equidistant from and ; likewise, it is equidistant from and . Hence is equidistant from and ; hence also lies on the perpendicular bisector of (and is the circumcenter). Second Proof We start with a diagram: One of the most common techniques for proving the concurrency of lines is Ceva's Theorem. However, there aren't any cevians in the diagram which would be needed for a direct application of Ceva's Theorem. Thus, we look for a way to make some by drawing in helpful lines. Drawing in and (i.e. the medial triangle of ) does the trick. By SAS Similarity. Thus making . Since and making an altitude of . Likewise, and are also altitudes. Thus, the problem is reduced to proving that the altitudes of a triangle are concurrent. This can be done using Ceva's Theorem. It is worth noting that the existence of the circumcenter is a much more fundamentally important theorem than it might seem, since it implies that three points determine a circle. This article is a stub. Help us out by expanding it. Retrieved from " Categories: Geometry Stubs Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
4054
https://download.itp3.uni-stuttgart.de/aqt2425/aqt2425_problemset-13.pdf
ADVANCED QUANTUM THEORY Problem Set 13 Prof. Dr. Hans-Peter Büchler January 22nd, 2025 Institute for Theoretical Physics III, University of Stuttgart WS 2024/25 Problem 13.1: Relativistic corrections for the hydrogen atom [ Written | 4 (+1 bonus) pt(s) ] ID: ex_relativistic_corrections_hydrogen:aqt2425 Learning objective In this problem, you examine the relativistic corrections to the hydrogen atom and derive the energy levels including relativistic effects like spin-orbit coupling and quantum fluctuations in the electron’s position. These effects give rise to the fine structure of the hydrogen energy levels and can also be derived directly from the Dirac equation. We examine the corrections after an expansion of the relativistic theory in powers of v/c for a single hydrogen atom. The expansion reads H = mc2 + p2 2m + V (r) | {z } H0 − p4 8m3c2 | {z } Hkin + 1 2m2c2 1 r dV (r) dr L · S | {z } HSO + ¯ h2 8m2c2∆V (r) | {z } HD + . . . , (1) where H0 is the Hamiltonian of the non-relativistic hydrogen atom with eigenstates |n, l, ml⟩and V (r) = −e2/r is the Coulomb potential. The first term is given by the rest mass of the electron and plays no role in the dynamics. a) We start with the relativistic correction of the kinetic energy Hkin. Calculate the energy correc-1pt(s) tions in first order perturbation theory. Hints: • Rewrite the kinetic energy in the form Hkin = − 1 2mc2  H2 0 + e2H0 1 r + e2 1 rH0 + e4 1 r2  . (2) • Note, that despite the degenracy of the states |n, l, ml⟩, the perturbation Hkin can be treated by non-degenerate perturbation theory. Why? • Show that the occurring matrix elements ⟨r−s⟩nl can be written in the form r−s nl = Z ∞ 0 dr r2−s |Rnl(r)|2 . (3) • Convince yourself that the following identities hold true by either calculating the integrals explicitly for 1s and 2p or doing subtask (e). r−1 nl = 1 a0 1 n2 , (4a) r−2 nl = 2 a2 0 1 (1 + 2l) 1 n3 . (4b) Problem Set Version: 1.0 | aqt2425 Page 1 of 2 ADVANCED QUANTUM THEORY Problem Set 13 b) The term HSO is known as spin-orbit coupling. What are the good quantum numbers for this 1pt(s) Hamiltonian? Derive the first order corrections due to this term. Hints: Use r−3 nl = 4 a3 0 1 n3 2(2l −1)! (2l + 2)! for 1 ≤l ≤n −1. (5) c) Calculate the energy corrections for the Darwin term HD. 1pt(s) d) After having taken into account all the corrections to the lowest order, write down the energy 1pt(s) E = E0 +Ekin +ESO +ED as a function of α = e2/¯ hc and the rest energy mc2 for the considered energy levels and show, that the total correction is independent of l and ml. Determine the corrections for the 1s, 2s and 2p orbitals explicitly and sketch how the energy levels change when taking into account more and more corrections. (Start with the unperturbed energy E0, then add the kinetic energy correction Ekin, then the spin-orbit coupling ESO and finally the Darwin term ED). ∗e) Derive the relations in equations 4 and 5. +1pt(s) Hints: • Bring the integrals to the form Z ∞ 0 dx xα+1−se−xLα k(x)Lα k(x) (6) • Replace one Laguerre polynomial by Lα k(x) = x−αex k! dk dxk  e−xxk+α (7) and one by Lα k(x) = k X j=0 k + α k −j (−x)j j! (8) • You should now arrive at integrals of the form Z ∞ 0 dx xj+1−s dk dxk  e−xxk+α , (9) with s = 1, 2, 3. The integral can be solved using integration by parts and Z ∞ 0 dx xme−x = m!. (10) Problem Set Version: 1.0 | aqt2425 Page 2 of 2
4055
https://www.nagwa.com/en/videos/620127160192/
Question Video: Solving Trigonometric Equations by Squaring | Nagwa Question Video: Solving Trigonometric Equations by Squaring | Nagwa Sign Up Sign In English English العربية English English العربية My Wallet Sign Up Sign In My Classes My Messages My Reports My Wallet My Classes My Messages My Reports Question Video: Solving Trigonometric Equations by Squaring Mathematics • First Year of Secondary School By first squaring both sides, or otherwise, solve the equation 4 sin 𝜃 − 4 cos 𝜃 = √3, where 0° < 𝜃 ⩽ 360°. Be careful to remove any extraneous solutions. Give your answers to two decimal places. Pause Play % buffered 00:00 00:00 0:00 Unmute Mute Disable captions Enable captions Settings Captions English Quality 0 Speed Normal Captions Go back to previous menu Disabled English EN Quality Go back to previous menu Speed Go back to previous menu 0.5×0.75×Normal 1.25×1.5×1.75×2× Exit fullscreen Enter fullscreen Play 06:47 Video Transcript By first squaring both sides, or otherwise, solve the equation four sin 𝜃 minus four cos 𝜃 is equal to the square root of three, where 𝜃 is greater than zero degrees and less than or equal to 360 degrees. Be careful to remove any extraneous solutions. Give your answers to two decimal places. The question advises that we approach the problem by first squaring both sides of the equation. Doing so, we obtain four sin 𝜃 minus four cos 𝜃 all squared is equal to root three squared. Distributing the parentheses and then collecting like terms on the left-hand side gives us 16 sin squared 𝜃 minus 32 sin 𝜃 cos 𝜃 plus 16 cos squared 𝜃. On the right-hand side, root three squared is equal to three. Next, we recall the Pythagorean identity, which states that sin squared 𝜃 plus cos squared 𝜃 is equal to one. Simplifying the left-hand side further gives us 16 multiplied by sin squared 𝜃 plus cos squared 𝜃 minus 32 sin 𝜃 cos 𝜃. Replacing sin squared 𝜃 plus cos squared 𝜃 with one gives us the equation 16 minus 32 sin 𝜃 cos 𝜃 equals three. Subtracting 16 from both sides of this equation gives us negative 32 sin 𝜃 cos 𝜃 is equal to negative 13. We can then divide through by negative 32 such that sin 𝜃 cos 𝜃 equals 13 over 32. We now have two equations in the two variables sin 𝜃 and cos 𝜃. This means that the system of equations can be solved simultaneously. Adding four cos 𝜃 to both sides of our original equation, we have four sin 𝜃 is equal to root three plus four cos 𝜃. Dividing both sides of this equation by four, we have sin 𝜃 is equal to root three plus four cos 𝜃 all divided by four. After clearing some space, we will now consider how we can solve these two simultaneous equations. We will begin by substituting the expression for sin 𝜃 in equation two into equation one. This gives us root three plus four cos 𝜃 over four multiplied by cos 𝜃 is equal to 13 over 32. We can simplify this equation by firstly distributing the parentheses. We can then multiply through by 32, giving us eight root three cos 𝜃 plus 32 cos squared 𝜃 equals 13. Finally, subtracting 13 from both sides of this equation, we have the quadratic equation in terms of cos 𝜃 as shown. This can be solved using the quadratic formula, where 𝑎 is 32, 𝑏 is eight root three, and 𝑐 is negative 13. Substituting in these values and then simplifying gives us cos of 𝜃 is equal to negative three plus or minus the square root of 29 all divided by eight. Taking the inverse cosine of both sides with positive root 29 gives us 𝜃 is equal to 62.829 and so on. To two decimal places, this is equal to 62.83 degrees. Taking the inverse cosine of our equation with negative root 29 gives us 𝜃 is equal to 152.829 and so on. This rounds to 152.83 degrees to two decimal places. We were asked to give all solutions that are greater than or equal to zero degrees and less than or equal to 360 degrees. We therefore need to consider the symmetry of the cosine function such that the cos of 𝜃 is equal to the cos of 360 degrees minus 𝜃. Subtracting each of our values from 360 degrees gives us further solutions 297.17 degrees and 207.17 degrees to two decimal places. We have therefore found four possible solutions to the given equation. However, we were reminded in the question to remove any extraneous solutions, these extra solutions that were created when we squared our original equation. We need to substitute each of our four solutions into the initial equation to check they are valid. The initial equation was four sin 𝜃 minus four cos 𝜃 equals root three. Substituting 𝜃 equals 62.83 into the left side of our equation gives us an answer of root three. This means that this is a valid solution. However, when we substitute 𝜃 is equal to 152.83 degrees into the left-hand side of our equation, we do not get root three. This means that this is not a valid solution. Repeating this process for 207.17 degrees and 297.17 degrees, we see that 207.17 is a valid solution, whereas the fourth answer of 297.17 is not. We can therefore conclude that there are two solutions that satisfy the equation in the given interval of 𝜃, which are 62.83 and 207.17 degrees. Lesson Menu Lesson Lesson Plan Lesson Presentation Lesson Video Lesson Explainer Lesson Playlist Join Nagwa Classes Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher! Interactive Sessions Chat & Messaging Realistic Exam Questions Nagwa is an educational technology startup aiming to help teachers teach and students learn. 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4056
https://www.youtube.com/watch?v=nNw48yWDEOk
Matrices Quick Tip for Rotating and Reflecting Mario's Math Tutoring 458000 subscribers 2151 likes Description 129662 views Posted: 28 May 2016 Quick tips for remembering the matrices that rotate and reflect in this free math video tutorial by Mario's Math Tutoring. We go through reflecting over the x-axis, y-axis, y=x, Rotation 90, Rotation 180, and Rotation 270. Timestamps: 00:00 Intro 0:24 Technique for Remembering the Rotation Matrices 0:53 Definition of the Identity Matrix 1:19 Rotation 90 Degrees 1:49 Rotation 180 Degrees 2:12 Rotation 270 Degrees 2:25 Reflection Over x Axis 2:40 Reflection Over y Axis 2:55 Reflection Over Line y=x 3:07 Reflecting (3,1) Over y=x Related Videos: Coordinate Rules for Rotating and Reflecting (Not Matrices) My Video Playlist of More Matrices Videos Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below) ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) 175 comments Transcript: Intro taking a look at are these two points here. Point number one and point number two. Point number one is one zero and point number two is 01. And if we make a matrix like this 1 0 0 1 this is point number one and this is point number two. So they're the coordinates are written vertically. Okay as you can see here 1 0 and 0 1. And if you notice this is the identity matrix. The identity matrix Technique for Remembering the Rotation Matrices means that if you multiply this times another matrix, okay, it's going to give that matrix back. So, it's just like multiplying by the number one. Anything times one gives you itself back. Same thing with the identity matrix. And what we're going to do now is we're going to look at how does this matrix change as you rotate 90°, 180, 270, and if you reflect over the x-axis, y-axis, or the line y equals x. And it's very easy. All you do is pay attention to these two points. If we want to remember the matrix that rotates 90°, we look at what Definition of the Identity Matrix happens to point 1 and two when we rotate 90. So if we rotate 90, okay, look at what happens. Point 1 0 moves to 01. So what I'm going to do is I'm going to replace 0.1 here with its new coordinates 01. Point number two, 01 is going to move to this point over here, which is - 1 0. So this matrix is going to be the matrix we want if we want to Rotation 90 Degrees rotate 90°. Okay, let's look at 180. So if we rotate 180, this point is going to move half a rotation over to here, which is going to put us at -10. Whereas point number two is going to rotate all the way down to here and that's coordinate is going to be 01. So by multiplying by this matrix, uh you're going to be able to rotate, you know, pre-image to its image 180°. If you rotate 270, this point here is going to rotate 3/4 of a Rotation 180 Degrees turn. It's going to end up at 01. And this point 01 is going to rotate 3/4 of a turn. It'll be at 1 0. Now, if you reflect over the x-axis, we're folding it over the x-axis, the mirror image. This point is actually on the line of reflection, so it's going to stay right where it's at 1 0. Whereas this point is going to reflect down there at 01. So, Rotation 270 Degrees you with me so far? If we reflect over the y ais, this point's going to reflect over here. It's going to be at zero. Oops, I'm sorry. Negative 1 0. And then this point is on the line of reflection. So, it's going to stay where it's at at Reflection Over x Axis 01. And then the line y equals x. That's this 45° line here. This point is going to be where 2 is. 2 is going to be where 0.1 is. They're actually going to interchange positions. So, that's going to be 01 and 1 0. And just to give you a Reflection Over y Axis quick example like say for example you just want to take a point uh 31 like this and you want to uh you know reflect it over the line y=x. Well all you would have to do is multiply this matrix times Reflection Over Line y=x the point 31 and you multiply rows times columns. So that gives you what? 0 3 is 0. 1 1 is 1. And we add those together. And then second row first Reflecting (3,1) Over y=x column you get three plus 0 which is three.
4057
https://www.studocu.com/en-gb/document/the-skinners-school/mathematics/1hnov2022ms-maths-mark-scheme-2022/82389982
Mark Scheme for Pearson Edexcel GCSE Maths (1MA1) Nov 2022 1H - Studocu Skip to document Teachers University High School Discovery Sign in Welcome to Studocu Sign in to access study resources Sign in Register Guest user Add your university or school 0 followers 0 Uploads 0 upvotes New Home My Library AI Notes Ask AI AI Quiz Chats Recent You don't have any recent items yet. My Library Modules You don't have any modules yet. Add Modules Books You don't have any books yet. Studylists You don't have any Studylists yet. Create a Studylist Home My Library Discovery Discovery Universities High Schools High School Levels Teaching resources Lesson plan generator Test generator Live quiz generator Ask AI Mark Scheme for Pearson Edexcel GCSE Maths (1MA1) Nov 2022 1H maths mark scheme 2022 Original title: 1hnov2022ms - maths mark scheme 2022 Subject Mathematics 999+documents Degree • Grade GCSE • Year 2 School The Skinners' School Academic year:2021/2022 Uploaded by: Nathan The Skinners' School 0 followers 2 Uploads44 upvotes Follow Recommended for you 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics Practice materials 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics Practice materials 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics Practice materials 100% (15) 40 2024 Edexcel IGCSE Maths Paper 2H: Predicted Topics Overview Mathematics Practice materials 100% (13) 24 Walking Talking Mock Exam Set 4 - Autumn 2018 (GCSE Maths 1MA1/2H)Mathematics Practice materials 100% (9) Comments Please sign in or register to post comments. Report Document Students also viewed Edexcel Predicted Paper 2H - June 2023 Exam Prep Guide Test 1 - Easy Practice Tests for Maths Students (Grades 6/7) GCSE Higher Revision Question Booklet Answers GCSE 3D Trigonometry Exam Practice Questions (N22127A01220) 8300 GCSE Mathematics Higher Tier Paper 1H Non-Calculator Shadow Paper GCSE Chemistry 1107 Titrations 3 Practice Problems and Solutions Related documents GCSE Maths Paper 2 Practice (Calculator) - Complete Solutions Vectors Questions - MME GCSE Venn Diagrams Practice Questions - 5-VDIAG-1-9 Practice Tests Set 21 - Paper 1H Mark Scheme Analysis GCSE Edexcel Maths Revision Guide for Grade 9 Success GCSE MATHS Aiming for Grade 3 REVISION BOOKLET with Answers Preview text Mark Scheme (Results) November 2022 Pearson Edexcel GCSE In Mathematics (1MA1) Higher (Non-Calculator) Paper 1H Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awarding body. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at edexcel or btec.co. Alternatively, you can get in touch with us using the details on our contact us page at edexcel/contactus. Pearson: helping people progress, everywhere Pearson aspires to be the world’s leading learning company. Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We’ve been involved in education for over 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: pearson/uk November 2022 Question Paper Log Number P Publications Code 1MA1_1H_2211_MS All the material in this publication is copyright © Pearson Education Ltd 2021 7 Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question or its context. (eg an incorrectly cancelled fraction when the unsimplified fraction would gain full marks). It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect (eg. incorrect algebraic simplification). 8 Probability Probability answers must be given as a fraction, percentage or decimal. If a candidate gives a decimal equivalent to a probability, this should be written to at least 2 decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer. 9 Linear equations Unless indicated otherwise in the mark scheme, full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously identified in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded (embedded answers). 10 Range of answers Unless otherwise stated, when an answer is given as a range (eg 3 – 4) then this is inclusive of the end points (eg 3, 4) and all numbers within the range 11 Number in brackets after a calculation Where there is a number in brackets after a calculation eg 2 × 6 (=12) then the mark can be awarded either for the correct method, implied by the calculation or for the correct answer to the calculation. 12 Use of inverted commas Some numbers in the mark scheme will appear inside inverted commas eg “12” × 50 ; the number in inverted commas cannot be any number – it must come from a correct method or process but the candidate may make an arithmetic error in their working. 13 Word in square brackets Where a word is used in square brackets eg [area] × 1 : the value used for [area] does not have to come from a correct method or process but is the value that the candidate believes is the area. If there are any constraints on the value that can be used, details will be given in the mark scheme. 14 Misread If a candidate misreads a number from the question. eg uses 252 instead of 255; method or process marks may be awarded provided the question has not been simplified. Examiners should send any instance of a suspected misread to review. Guidance on the use of abbreviations within this mark scheme M method mark awarded for a correct method or partial method P process mark awarded for a correct process as part of a problem solving question A accuracy mark (awarded after a correct method or process; if no method or process is seen then full marks for the question are implied but see individual mark schemes for more details) C communication mark awarded for a fully correct statement(s) with no contradiction or ambiguity B unconditional accuracy mark (no method needed) oe or equivalent cao correct answer only ft follow through (when appropriate as per mark scheme) sc special case dep dependent (on a previous mark) indep independent awrt answer which rounds to isw ignore subsequent working Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 3 26 M1 for the start of a method of simplification, eg 2 −5+8 (= 23 ) or 2 −5× 2 (= 2 −10) or 28 × 2 (= 216 ) A1 cao SC B1 for answer of 64 or 8 2 or 4 3 if M0 scored. 4 0 M1 for digits 128 or for correct placement of the decimal point following one arithmetical error, eg 32 × 4 = 138 with an answer of 0. A1 for 0 or 1 × 10 − 3 5 7500 M1 for method to find expected number of model B, eg 15 80 × 40000 oe or 15 "23 + 15 + 30 + 12" × 40000 oe A1 cao Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 6 (a)(i) 2 : 6 : 5 P1 for process to compare ratios, eg a : b = 2 : 6 or b : c = 3 : 2. Could use 3 or any common multiple of 3 and 6 A1 for 2 : 6 : 5 oe (ii) 2 13 M1 for process to find fraction, eg [2 + 6 + 5] or for a a + b +c A1 for 2 13 oe or ft (a)(i) (b) 1 : 10 P1 for process to express all numbers in terms of one number, eg p = 5 × 2m (= 10m) or m = 2 n or for 2m = 5 p or for assigning values in the ratio given, eg m = 1, n = 2, p = 10 or for n : m : p = 2 : 1 : 10 oe or 10 : 1 oe A1 for 1 : 10 oe Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 10 (a) 1 16 M1 for method to find probability of getting a score of 5, eg 10 6 + 8 + 9 + 7 + 10 (= 10 40 ) oe A1 for 1 16 oe Accept any equivalent fraction, decimal form 0(25) or 0, percentage form 6(.25)% or 6% Ignore subsequent incorrect attempts to write the correct answer in a different form. (b) 15 M1 for method to find the proportion of 1s, eg 6 40 oe A1 cao 11 Enlargement scale factor 1 3 centre (0, 2) B for enlargement scale factor 1 3 centre (0, 2) No marks if more than one transformation is given (B1 for any 2 aspects) 12 x = 3, y = –2 M1 for a correct method to eliminate either variable or rearrangement of one equation leading to substitution (condone one arithmetic error) Trial and improvement methods score 0 marks unless both x and y are correct A1 for either correct value of x or correct value of y M1 (dep M1) for a correct substitution of found value into one of the equations or a correct method leading to the second value (condone one arithmetic error) A1 x = 3, y = – Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 13 t = 20 p = 4, 50 M1 for method to find a missing value of p, eg 100 25 oe (= 4) or 100 2 oe (= 50) or for p 100 t = Marks for 4 or 50 can only be awarded if in correct cell of table or unambiguous in working M1 for method to find the missing value of t, eg 100 ÷ 5 1 (= 20) or for finding both missing values of p Mark for 20 can only be awarded if in correct cell of table or unambiguous in working A1 cao 14 Histogram drawn B3 for fully correct histogram, eg relative heights 1, 5, 6, 1 Frequency densities are 1, 5, 6, 1. (B2 for 3 correct bars or for frequency ÷ class interval for at least 3 frequencies and 2 correct bars of different widths) (B1 for 2 correct bars of different widths or for frequency ÷ class interval for at least 3 frequencies) 15 40 P1 for a start to the process, eg 2 18 360 x × × π× (= 4π) oe or 4 2 18 π × π× (= 360 x ) oe Any arrangement equivalent to this equation acceptable P1 for a complete process to find x, eg 4 360 36 π π × oe A1 cao Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 17 81 M1 for showing the cube root of 8 = 2 and the cube root of 27 = 3 or an intention to find the cube root and raise to power 4 eg 4 3 8 27     or 4 3 8 27       or 2 4 3     A1 cao Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 18 Result shown M1 for angle OBC = 90 or for method to find angle OBA or angle OAB, eg 180 2 − xoe or for angle ABC = 90 – angle OBA, eg angle ABC = 90 – y or marks point on circumference and draws triangle using A and B and point marked Angles must be clearly labelled on the diagram or otherwise identified. Correct method can be implied from angles on the diagram if no ambiguity or contradiction. M1 for method to find angle ABC, eg 90 – “ 180 2 − x” oe or for x = 180 – 2 × angle OBA, eg x = 180 – 2y or for angle at circumference = 1 2 x C1 for correct algebra leading to angle ABC = 1 2 x and one circle theorem relevant to their method, eg The tangent to a circle is perpendicular to the radius OR for x = 180 – 2y and angle ABC = 90 – y and one circle theorem relevant to their method, eg The tangent to a circle is perpendicular to the radius OR for angle ABC = 1 2 x and one circle theorem relevant to their method, eg The angle at the centre of a circle is twice the angle at the circumference or Alternate segment theorem Underlined words need to be shown; reasons need to be linked to their method. Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 20 110 P1 for process to find a probability of 2 cards of different colours, eg 3 7 11 10 × or 3 1 11 10 × or 7 3 11 10 × or 7 1 11 10 × or 1 3 11 10 × or 1 7 11 10 × oe or 3 8 11 10 × oe or 7 4 11 10 × oe or 1 10 11 10 × oe May see fraction with denominator 110 P1 for a complete process, eg 3 7 11 10 × + 3 1 11 10 × + 7 3 11 10 × + 7 1 11 10 × + 1 3 11 10 × + 1 7 11 10 × oe or 3 8 7 4 1 10 11 10 11 10 11 10 × + × + × oe A1 for 62 110 oe OR Accept equivalent fraction, decimal form 0(36...) or percentage form 56(.36...)% P1 for process to find a probability of 2 cards of the same colour, eg 3 2 11 10 × or 7 6 11 10 × or 1 0 11 10 × oe P1 for a complete process, eg 1 – 3 2 11 10 × – 7 6 11 10 × (– 1 0 11 10 × ) oe A1 for 62 110 oe SC B1 for answer of 62 121 (replacement) Accept equivalent fraction, decimal form 0(36...) or percentage form 56(.36...)% Paper: 1MA1/1H Question Answer Mark Mark scheme Additional guidance 21 (180, – 1) B1 for 180(o) B1 for – SC B1 if B0 scored for answer of (–1, 180) 22 214 B1 for sin 30 = 0. P1 for use of the sine rule with values substituted, eg 6 10. sin ABC sin 30 = oe P1 for (sin ABC =) 6 sin 30 10. × oe or for a complete process to find sin ABC, eg (sin ABC =) 6 10. × oe Answer of 3. 10. or 6. 21. gets 3 marks Where is their value of sin A1 for 65 214 oe eg 325 1070 Answer must be in the form m n where m and n are integers Question 9(b) -3 -2 -1 0 1 2 3 x - - - - - - - - - - - - - Modifications to the mark scheme for Modified Large Print (MLP) papers: 1MA1 1H Only mark scheme amendments are shown where the enlargement or modification of the paper requires a change in the mark scheme. Notes apply to both MLP papers and Braille papers unless otherwise stated. The following tolerances should be accepted on marking MLP papers, unless otherwise stated below: Angles: ±5º Measurements of length: ±5 mm Mark Scheme for Pearson Edexcel GCSE Maths (1MA1) Nov 2022 1H Download Download AI Tools Ask AI Multiple Choice Flashcards Quiz Video Audio Lesson 5 0 Save Mark Scheme for Pearson Edexcel GCSE Maths (1MA1) Nov 2022 1H Subject: Mathematics 999+documents Degree • Grade: GCSE • Year 2 Info More info Download Download AI Tools Ask AI Multiple Choice Flashcards Quiz Video Audio Lesson 5 0 Save Mark Scheme (Res ults) November 202 2 Pearson Edexcel GCSE In Mathematics (1MA1) Higher (Non-Calculator) Paper 1H Edexcel and BT EC Qualificati ons Edexcel a nd BTEC q ualifications are awa rded by Pearson, the UK’s largest a warding body. We provide a wide ra nge of qualificatio ns including academic, vocatio nal, occupational and specific programmes for employers. For furthe r information visit our qualific ations websi tes at www.edexcel.co m or www.btec.co.uk. Alternatively, you can get in touch with us using the details on o ur contact us page at www.edex cel.com/contactus. Pearson: helpi ng peop le progress, e verywhere Pearson aspi res to b e the world’s leading l earning co mpany. Our aim is t o help ev eryone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever t hey are in the world. We’ve been involved i n educati on for over 1 50 years, and by working across 70 count ries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achiev ement through innovation i n education. Find out more about how we can help you and yo ur students at: www.pearson.co m/uk November 202 2 Question Pape r Log Nu mber P6872 1 Publications Code 1MA 1_1H_2211_M S All the mat erial in this p ublication is c opyright © Pearson Educati on Ltd 2021 General ma rking guidance These notes offer gener al guidan ce, but the spe cific notes f or examiners app ertaining t o individual q uestions take precedence. 1 All candid ates must rec eive the sam e treatment. Examiners mu st mark t he last cand idate in exa ctly the s ame way as th ey mark the first. Where some judgement is required, mark sch emes will p rovide th e principl es by which marks will be award ed; exempl ification/in dicative content will n ot be exhaustive. Wh en examine rs are in doubt rega rding the app lication of the mark scheme to a candidate’s response, the response shou ld be sent to review. 2 All the ma rks on the m ark scheme a re designe d to be awarded; ma rk schem es should be appl ied positivel y. Examin ers should als o be prepared to award zero marks if the cand i date’s respons e is n ot worthy of credit acc ording to t he mark s cheme.If there is a w rong answer (or no an swer) indi cated on th e answer line alway s check t he wo rking in t he body of the script (an d on an y diagr ams), and a ward any marks approp riate from the mark scheme. Questions whe re working is not required: I n general, the correct a nswer should be given fu ll marks. Questions th at specifically requi re working: In general, cand idates who do not show w orking on t his type of question wil l get no marks – full d etails will be gi ven in th e mark scheme for each indivi dual qu estion. 3 Crossed out work This should be mark ed unless the candidate h as replaced it w ith an alternative resp onse. 4 Choice of m ethod If there i s a choic e of m ethods shown, mark the method that l eads to th e answe r given on th e answe r line. If no answer appears on the answer line, mark b oth methods then a ward the lower numbe r of marks. 5 Incorrect met hod If it is clear fr om the working that the “corr ect” answer has be en obtained from incor rect working, award 0 marks. Send the response to review for your Team Leader to check. 6 Follow throug h marks Follow throug h marks whi ch involve a single stage cal culation can be awarded wi thout wor king as you can check th e answer, but if ambiguous d o not awa rd. Follow throug h marks w hich involve m ore than one sta ge of calcula tion can only be award ed on sigh t of the relevan t working, e ven if i t appears obvious that t here is only one way y ou could g et the answer g iven. Too long to read on your phone? Save to read later on your computer Save to a Studylist 7 Ignoring subsequ e nt work It is app ropriate to ig nore subsequ ent work wh en the additional wo rk does n ot change the answe r in a way that is i nappropriat e fo r the question or its context. (eg an incor rectly cancell ed fraction when the unsimp lified fraction wou ld gain full marks). It is not app ropriate t o ignore subs equent wo rk when the ad ditional work essent ially makes the answer in correct (eg. incorrec t algebrai c simplification). 8 Probability Probability answe rs must be given as a fraction, percentage or decima l. If a can didate gi ves a decimal equ ivalent to a probability, th is should be written to at least 2 decimal plac es (unless t enths). Incorrect notati on should lose the accu racy mar ks, but b e awarded any implied meth od marks. If a probabil ity fraction is given then c ancelled incorrectly, ign ore the incorrectly canc elled answer. 9 Linear equ ations Unless indicat ed otherwise in t he mark schem e, full marks can be gained if t he solution alone is given on the ans wer line, or othe rwise unambigu ously identified i n working (with out contradiction elsewhere). Where the cor rect solution only is shown su bstituted, but not identified as the solutio n, the accura cy mark is lost but an y method ma rks can b e awarded (em bedded answe rs). 10 Range of answers Unless otherwi se stated, wh en an answer is given as a range (eg 3.5 –4.2) then this is inclusi ve of the end p oints (eg 3.5, 4.2) and all numbers wi thin the ran ge 11 Number in brackets a fter a calcu lation Where there is a numb er in brackets after a calc ulation eg 2 × 6 (=12) th en the mark can be awarded eit her for the correct meth od, implied by th e calculation or for the correct ans wer to the calculati on. 12 Use of inve rted comm as Some numb ers in th e mark scheme will appear in side inv erted commas eg “12” × 50 ; t he number in inverted commas cannot be an y number – it must come from a correct method or process but th e candidate may make an a rithmetic error in their w orking. 13 W ord in square brack ets Where a wo rd is us ed in square bra ckets eg [a rea] × 1.5 : the val ue used f or [area] do es not have to come from a correct method o r process but i s the val ue that the candidate b elieves is the area. If th ere are an y constraint s on the valu e that can be used, detail s will be given in the mark sc heme. 14 Misread If a candi date misreads a number from t he questi on. eg uses 252 i nstead of 25 5; method or process ma rks may b e awarded p rovid ed the questi on has not been simpli fied. Examine rs should send any instance of a susp ected misread to revi ew. Guidance on the use of abbreviation s with in this mark sc heme M method mark award ed for a correct method or partial method P process mark award ed for a correct pro cess as part of a problem solvin g question A accuracy mar k (award ed after a correct method o r process; if no method o r proces s is seen then full marks f or the question ar e implied but see in dividual mark s chemes for m ore details) C communication ma rk a warded for a fully corre ct statement(s) wit h no c ontradiction or ambiguity B unconditional accuracy mark (no meth od needed) oe or equivalent cao correct answe r only ft follow through(wh en appropriat e as per mark scheme) sc special case dep dependent (on a pre vious mark) indep independent awrt answer which round s to isw ignore subs equent work ing Paper: 1MA1/1 H Question Answer Mark Mark scheme Additional guidan ce 1 2² × 5 ³ M1 for a complete meth od to find prim e factors, could be s hown on a complete factor tree w ith no more than one e rror or by division by prime factors with no mo re than one error Condone the inclusion of 1 for the method marks M1 for complete facto risation, eg 2, 2, 5, 5, 5 Could be shown on a f ully correct facto r tree A1 for 2² × 5³ 2 (a) 17 3 20 M1 for finding two fractions with a correc t common denominator (multip le of 20), with at leas t one correct corresponding numerat or, eg 12 20 , 5 20 or 32 20 , 45 20 May be from 3 5 and 1 4 or from 8 5 and 9 4 A1 for 17 3 20 or an equivalen t mixed number SC B1 for an answer o f 3.85 if M0 scored (b) shown M1 for 8 1 3 6 × oe or 4 6 9 1 × oe or 8 9 3 4 × oe A1 for unsimplified frac tion which could lead to 4 9 , eg 8 18 or for 4 1 3 3 × or 24 6 9÷ or for unsimplified frac tion which could lead to 2 2 3 , eg 24 9 or for unsimplified frac tion which could lead to 6, eg 72 12 Document continues below Discover more from: Mathematics GCSEYear 2 999+documents Go to course 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics Practice materials 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics Practice materials 100% (18) 92 GCSE Math Revision Booklet: Aiming for Grade 5 Solutions Mathematics Class notes 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics Practice materials 100% (15) 40 2024 Edexcel IGCSE Maths Paper 2H: Predicted Topics Overview Mathematics Practice materials 100% (13) 13 2406 9MA0-01 Pure Mathematics 1 June 2024 Shadow Paper MS Guide Mathematics Summaries 100% (11) Discover more from: MathematicsGCSEYear 2 999+documents Go to course 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics 100% (18) 92 GCSE Math Revision Booklet: Aiming for Grade 5 Solutions Mathematics 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics 100% (15) 40 2024 Edexcel IGCSE Maths Paper 2H: Predicted Topics Overview Mathematics 100% (13) 13 2406 9MA0-01 Pure Mathematics 1 June 2024 Shadow Paper MS Guide Mathematics 100% (11) Paper: 1MA1/1 H Question Answer Mark Mark scheme Additional guidan ce 3 6 2 M1 for the start of a method of simplification, eg 2−5+8(= 2 3) or 2−5×2(= 2−10) or 2 8×2(= 2 16) A1 cao SC B1 for answer of 64 or 8 2 or 4 3 if M0 scored. 4 0.00128 M1 for digits 128 or for correct placemen t of the decimal point following one arithmet ical error, eg 32 × 4 = 138 wit h an answer of 0.00138 A1 for 0.00128 or 3 1.28 10 − × 5 7500 M1 for method to find e xpected number of model B, eg 15 80 × 40000 oe or 15 "23 15 30 12"+++ × 40000 oe A1 cao 1 out of 24 Share Download Download More from:Mathematics More from: Mathematics GCSEYear 2 999+documents Go to course 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics Practice materials 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics Practice materials 100% (18) 92 GCSE Math Revision Booklet: Aiming for Grade 5 Solutions Mathematics Class notes 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics Practice materials 100% (15) More from: MathematicsGCSEYear 2 999+documents Go to course 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics 100% (18) 92 GCSE Math Revision Booklet: Aiming for Grade 5 Solutions Mathematics 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics 100% (15) 40 2024 Edexcel IGCSE Maths Paper 2H: Predicted Topics Overview Mathematics 100% (13) 13 2406 9MA0-01 Pure Mathematics 1 June 2024 Shadow Paper MS Guide Mathematics 100% (11) Recommended for you 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics Practice materials 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics Practice materials 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics Practice materials 100% (15) 40 2024 Edexcel IGCSE Maths Paper 2H: Predicted Topics Overview Mathematics Practice materials 100% (13) 28 1MA1/1H Maths Worked Answers 2022 - Higher Tier Exam Solutions Mathematics 98% (45) 22 Math GCSE Paper 3H - November 2022 Solutions and Explanations Mathematics 100% (18) 16 Set 21 - Paper 2H-3H Practice Tests Mark Scheme Mathematics 100% (15) 40 2024 Edexcel IGCSE Maths Paper 2H: Predicted Topics Overview Mathematics 100% (13) 24 Walking Talking Mock Exam Set 4 - Autumn 2018 (GCSE Maths 1MA1/2H) Mathematics 100% (9) 72 GCSE Chemistry AQA (Grade 9-1) - 10-Minute Tests Overview Mathematics 100% (9) Students also viewed Edexcel Predicted Paper 2H - June 2023 Exam Prep Guide Test 1 - Easy Practice Tests for Maths Students (Grades 6/7) GCSE Higher Revision Question Booklet Answers GCSE 3D Trigonometry Exam Practice Questions (N22127A01220) 8300 GCSE Mathematics Higher Tier Paper 1H Non-Calculator Shadow Paper GCSE Chemistry 1107 Titrations 3 Practice Problems and Solutions Related documents GCSE Maths Paper 2 Practice (Calculator) - Complete Solutions Vectors Questions - MME GCSE Venn Diagrams Practice Questions - 5-VDIAG-1-9 Practice Tests Set 21 - Paper 1H Mark Scheme Analysis GCSE Edexcel Maths Revision Guide for Grade 9 Success GCSE MATHS Aiming for Grade 3 REVISION BOOKLET with Answers Get homework AI help with the Studocu App Open the App English Great Britain Company About us Studocu Premium Academic Integrity Jobs Blog Dutch Website Study Tools All Tools Ask AI AI Notes AI Quiz Generator Notes to Quiz Videos Notes to Audio Infographic Generator Contact & Help F.A.Q. 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https://www.youtube.com/watch?v=2IFItASxDVo
Algorithm for mentally computing binomial expansion coefficients | Algebra II | Khan Academy Khan Academy 9090000 subscribers 423 likes Description 125861 views Posted: 27 Mar 2014 Watch the next lesson: Missed the previous lesson? Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Algebra II channel: Subscribe to Khan Academy: 33 comments Transcript: Voiceover:What I want to show you in this video is what could be described as, I guess, a trick for finding binomial expansions, especially binomial expansions where the exponent is fairly large. But what I want you to do after this video is think about how this connects to the binomial theorem and how it connects to Pascal's Triangle. Now let me show you the trick. I'm going to take (X+Y)^7. That's going to have eight terms. How do I know that? Well (X+Y)^1 has two terms, it's a binomial. (X+Y)^2 has three terms. (X+Y)^3 has four terms. So this is going to have eight terms. Let me just create little buckets for each of the terms. This is the bucket, these aren't the coefficients these are just the buckets. 1st term, 2nd term, 3rd term, 4th term, 5th term, 6th term, 7th term, and 8th term. Now lets write out the actual X's and Y's. The first term, we're going to start with X^7. Then each term after that our degree or our power on the X goes down by one. So you go X^6, X^5, X^4, X^3, X^2, X^1, we could just write that as X, and this is going to be X^0, which is just going to be one. Now lets think about Y. This is going to start at Y^0, which is just one so I'm not going to write it, Then it's going to be Y^1, Y^2, Y^3, Y^4, Y^5, Y^6, and then Y^7 and you can verify you got it right because for each term, the exponents should add up to seven. You see that even here. This is X^1 times Y^6. Those add up to be seven. Now, lets get to the interesting part, which is actually calculating the coefficient. And the algorithm is for each term right over here, so lets just start, we know the coefficient right over here is going to be one. Actually, let me write that down. The coefficient over here is going to be one. So for each term, the coefficient right over here, I'm going to try to color-code it so we can see it, the coefficient is going to be the exponent of the previous term, so the exponent of the previous term in this case is the seven, the exponent of the previous term, times the coefficient of the previous term, divided by which term that actually was, so divided by the term. That was the 1st term, so now the coefficient on the 2nd term is seven times one divided by seven, which is going to be equal to seven. Now what about this one? We use the exact same process. The exact same process. It is going to be the exponent on the X term, I guess you could say the exponent on X, I guess we could go with. The exponent on the X, which is six, times the coefficient of the previous term, so times seven, so we're taking the X power times the coefficient of the previous term, so times seven. So the X part of the previous term, times the coefficient of the previous term, divided by the actual, I guess you could say, index of the previous term, so divided by two. So what is that going to be? So this is the equivalent to three times seven, so this is going to be equal to 21. And now lets go to this term, exact same idea. Go to the previous term, what's our exponent on X? It is five. Lets multiply it times the coefficient, so lets multiply it times 21, and then lets divide it by which term that is, so that was the 3rd term. So this is going to be, lets see, five times 21 over three is seven, so this is going to be 35, five times seven. And we can keep going, or we can recognize that there's a symmetry here. If this is one, then the last term is also going to be one. If the second term is seven, then the second-to-last term is seven. If the third term is 21, then the third term to the last is 21. And then if the 4th term is 35, then the fourth from the last is 35. And just like that, we have figured out the expansion of (X+Y)^7. Pretty neat, in my mind.
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https://www.cureus.com/articles/357219-sjogrens-syndrome-presenting-with-proximal-myopathy-due-to-osteomalacia-complicating-renal-tubular-acidosis-a-case-report.pdf?email=
Review began 04/01/2025 Review ended 04/11/2025 Published 04/13/2025 © Copyright 2025 Islam et al. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. DOI: 10.7759/cureus.82206 Sjogren’s Syndrome Presenting With Proximal Myopathy Due to Osteomalacia Complicating Renal Tubular Acidosis: A Case Report Mohammad Syedul Islam , Quazi Mamtaz Uddin Ahmed , Farzana Ahmed , Md Ashraf Uddin , Naznin Naher Department of Internal Medicine, Bangabandhu Sheikh Mujib Medical University, Dhaka, BGD 2. Department of Pediatrics, Marks Medical College and Hospital, Dhaka, BGD Corresponding author: Naznin Naher, nazninnaher05@gmail.com Abstract Primary Sjögren’s syndrome (pSS) is typically associated with dryness of the eyes and mouth, but it can also involve other organs, including the lungs, kidneys, nervous system, and joints. Among its less common manifestations is distal renal tubular acidosis (dRTA), which can lead to metabolic acidosis, hypokalemia, and bone-related complications due to chronic acid-base imbalance. We report the case of a 42-year-old woman with a four-year history of recurrent hypokalemic quadriparesis, who recently developed progressive difficulty walking over the past two months, severely limiting her mobility. Laboratory investigations revealed a normal anion gap metabolic acidosis and elevated urine pH, consistent with dRTA. Further evaluation confirmed a diagnosis of pSS with objective evidence of glandular involvement. Imaging and biochemical findings supported the presence of osteomalacia secondary to dRTA. This case highlights a rare and often overlooked complication of pSS. Timely diagnosis and appropriate management are crucial to preventing long-term disability and improving patient outcomes. Categories: Internal Medicine, Rheumatology, Allergy/Immunology Keywords: distal renal tubular acidosis, fracture neck of femur, osteoporosis, proximal myopathy, recurrent hypokalemic quadriparesis Introduction Primary Sjögren’s syndrome (pSS) is a chronic autoimmune disorder marked by lymphocytic infiltration of exocrine glands, resulting in persistent inflammation and hallmark symptoms such as dry eyes and dry mouth . Beyond the exocrine glands, mucosal dryness can extend to other surfaces, including the airways, gastrointestinal tract, and vagina, contributing to the broader clinical picture of sicca syndrome. pSS is also known for its potential to affect multiple organ systems, with extraglandular manifestations classified as either nonvisceral (musculoskeletal and cutaneous) or visceral (neurological, renal, hematological, pulmonary, gastrointestinal, and cardiovascular). Systemic involvement occurs through two main mechanisms: periepithelial infiltration and extraepithelial immune complex-mediated damage . Among the visceral manifestations, renal involvement most commonly presents as tubulointerstitial nephritis (TIN), caused by lymphocytic infiltration of the renal interstitium, which leads to tubular dysfunction . A key clinical consequence of TIN is renal tubular acidosis (RTA), with distal RTA (dRTA) being the most frequently observed subtype, occurring in up to 20% of pSS patients . dRTA is characterized by defective hydrogen ion secretion in the distal tubules, resulting in non-anion gap metabolic acidosis (NAGMA), persistently high urinary pH (>5.5), and hypokalemia. These disturbances can lead to muscle weakness, nephrocalcinosis, nephrolithiasis, and metabolic bone diseases such as osteomalacia and osteoporosis. A classic manifestation of hypokalemic paralysis involves the acute onset of symmetrical, ascending proximal muscle weakness accompanied by reduced deep tendon reflexes, typically without any alteration in consciousness. Although osteomalacia is rarely the initial presentation of pSS, it can emerge as a long-term complication of chronic dRTA in affected individuals . Case Presentation A 42-year-old woman presented with a history of five similar episodes of flaccid quadriparesis over the last four years. Each episode had a sudden onset, was unrelated to carbohydrate-rich meals or physical exertion, and resolved completely after potassium supplementation. More recently, she had developed progressive difficulty in rising from a seated position and performing overhead activities over the preceding six months. Additionally, she reported groin pain and increasing difficulty walking over the last two months. She denied any associated symptoms, such as fever, joint swelling or pain, dry eyes or mouth, skin rashes, Raynaud’s phenomenon, or muscle pain. A detailed clinical history was obtained to identify any potential 1 1 2 1 1 Open Access Case Report How to cite this article Islam, Mamtaz Uddin Ahmed Q, Ahmed F, et al. (April 13, 2025) Sjogren’s Syndrome Presenting With Proximal Myopathy Due to Osteomalacia Complicating Renal Tubular Acidosis: A Case Report. Cureus 17(4): e82206. DOI 10.7759/cureus.82206 contributing factors. She had no history suggestive of malabsorption, thyroid dysfunction, prolonged steroid use, alcohol or tobacco use, or self-induced vomiting. However, she did report an unintended weight loss of approximately 7 kg over the last six months. On general examination, the patient appeared mildly anemic, with no signs of thyroid enlargement or lymphadenopathy. Neurological assessment revealed reduced muscle strength - Medical Research Council grade 3 out of 5 in proximal muscles and 4 out of 5 in distal muscles - in all four limbs, while all sensory modalities were preserved. Additionally, hip joint movement was restricted bilaterally. Initial laboratory workup showed normocytic, normochromic anemia on CBC. Serum potassium was significantly low at 2.1 mmol/L. Arterial blood gas analysis revealed normal anion gap metabolic acidosis, with a bicarbonate level of 13.5 mmol/L and a positive urinary anion gap - findings consistent with a diagnosis of dRTA (Table 1). Investigation Result Reference range CBC Hb 9.3 gm/dl 11.20-15.70 gm/dl MCV 97.8 fl 76-96 fl MCH 29.3 pg 27-32 pg RBC 3.17 million/dl 4.04-6.12 million/dl Serum electrolytes Sodium 144 mmol/L 135-145 mmol/L Potassium 2.1 mmol/L 3.5-5.0 mmol/L Chloride 123 mmol/L 95-105 mmol/L Bicarbonate 13.5 mmol/L 12-22 mmol/L Anion gap 9.6 mmol/L 8-16 mmol/L ABG pH 7.25 7.35-7.45 pCO ₂ 30.8 mmHg 38-42 mmHg HCO ₃⁻ 13.5 mmol/L 22-28 mmol/L Urine pH 7.25 7.35-7.45 Urine electrolytes Sodium 40 mmol/L 40-220 mmol/L Potassium 20 mmol/L 25-125 mmol/L Chloride 44 mmol/L 14-150 mmol/L TABLE 1: Laboratory investigations showing severe hypokalemic, hyperchloremic metabolic acidosis, along with elevated urinary pH and a positive urine anion gap, consistent with a diagnosis of dRTA ABG: arterial blood gas; dRTA: distal renal tubular acidosis; Hb: hemoglobin; MCH: mean corpuscular hemoglobin; MCV: mean corpuscular volume The patient underwent a comprehensive evaluation to identify potential causes of dRTA, including a detailed drug history and autoimmune screening. Serological analysis revealed positive antinuclear antibody (ANA), anti-SSA/Ro, and anti-SSB/La antibodies. Other autoimmune markers, including anti-dsDNA, anti-Smith antibody, and rheumatoid factor, were negative (Table 2). Objective evidence of glandular involvement was demonstrated by markedly reduced unstimulated salivary flow and Schirmer’s test results (3 mm in both eyes within five minutes) (Table 2). Additionally, salivary gland ultrasonography showed characteristic features consistent with Sjögren’s syndrome. 2025 Islam et al. Cureus 17(4): e82206. DOI 10.7759/cureus.82206 2of 6 Investigation Result Reference range ANA screening Positive (>400) <40 AU/mL Anti-Ro/SS-A Positive (>400) 0-40.0 AU/mL Anti-La/SS-B Positive (>195) 0-40.0 AU/mL Unstimulated salivary flow 0.056 ml/min <0.1 ml/min considered salivary gland hypofunction Schirmer’s test Rt eye 3 mm in five minutes; Lt eye 3 mm in five minutes <5 mm in five minutes in at least one eye is considered dry eye Anti-ds-DNA Negative 10-15 IU/mL RA Negative 0-20 IU/mL TABLE 2: Laboratory findings indicative of pSS ANA: antinuclear antibody; anti-SSA/Ro: anti-Sjögren’s syndrome-related antigen A; anti-SSB/La: anti-Sjögren’s syndrome-related antigen B; pSS: primary Sjögren’s syndrome; RA: rheumatoid arthritis As the patient developed proximal myopathy, further investigations were conducted to rule out alternative etiologies. Laboratory tests revealed hypocalcemia (serum calcium 8.0 mg/dL), hypophosphatemia (serum phosphate 1.5 mg/dL), and elevated alkaline phosphatase (203 U/L). Additionally, 25-hydroxy vitamin D was markedly low at 10.3 ng/mL, confirming vitamin D deficiency. Bone mineral density assessments showed osteopenia in the lumbar spine and both femoral necks (Table 3). These findings were consistent with osteomalacia. Serum creatine phosphokinase and thyroid-stimulating hormone levels were within normal ranges (Table 3). Investigation Result Reference range CPK Negative 30-135 U/L S. TSH 1.84 mIU/L 0.7-1.3 mg/dl S. calcium 8.0 mg/dl 8.5-10.2 mg/dl S. inorganic phosphate 1.5 mg/dl 2.4-5.1 mg/dl S. magnesium 2.1 mg/dl 1.82-2.30 mg/dl S. ALP 203 U/L 40-150 U/L PTH 113.5 pg/ml 10-65 pg/ml S. inorganic phosphate 1.5 mg/dl 2.4-5.1 mg/dl Vitamin D level 10.3 ng/ml <20 ng/ml DEXA scan Lumbar first to fourth vertebrae: T score -2.0, Z score -1.6; right femoral neck: T score -1.8, left femoral neck: T score -1.2 TABLE 3: Biochemical and imaging findings indicative of osteomalacia and osteopenia ALP: alkaline phosphatase; CPK: creatinine phosphokinase; DEXA: dual-energy X-ray absorptiometry; PTH: parathyroid hormone; TSH: thyroid- stimulating hormone A plain radiograph of the pelvis revealed bilateral old femoral neck fractures (Figure 1), indicative of bone complications associated with chronic dRTA. 2025 Islam et al. Cureus 17(4): e82206. DOI 10.7759/cureus.82206 3 of 6FIGURE 1: Plain X-ray of the pelvis and femur (AP view): (A) Preservation of the normal Shenton’s line with no significant findings. (B) Bilateral shortening of the femoral necks, reduced joint space, and disruption of Shenton’s line, indicative of old femoral neck fractures in a 42-year-old woman The patient was started on potassium chloride syrup, 30 mL daily in three divided doses, providing a total of 40 mEq/day, along with sodium bicarbonate (500 mg), two tablets four times a day, delivering 12 mEq of bicarbonate with each 1000 mg dose. She was also prescribed weekly cholecalciferol for eight weeks and calcium supplementation. After one week of inpatient treatment, the patient showed significant improvement, with her potassium levels stabilizing between 3 and 3.5 mEq/L and experiencing minimal symptoms. She was discharged with instructions for close follow-up and scheduled for outpatient reevaluation. Additionally, she was referred to orthopedics for the management of her old femoral fractures. Discussion Sjögren’s syndrome is an autoimmune disorder characterized by lymphocytic infiltration and inflammation of the exocrine glands, resulting in decreased glandular secretion. This typically manifests as dry eyes and dry mouth. The estimated prevalence of Sjögren’s syndrome is 10.3 per 10,000 people, with a notably higher occurrence in females, at a male-to-female ratio of 1:16. Extraglandular manifestations are observed in about one-third of cases, and renal involvement is reported in 4.9% of patients . While glandular involvement usually precedes extraglandular symptoms, in some cases, the latter may present first. Diagnosing Sjögren’s syndrome can be particularly challenging when extraglandular symptoms appear initially . Sjögren’s syndrome is classified into two forms: primary and secondary. pSS occurs as an independent condition, whereas secondary Sjögren’s syndrome develops in the context of other rheumatologic diseases, such as systemic lupus erythematosus, rheumatoid arthritis, or scleroderma . The diagnosis of pSS is confirmed when a patient meets four out of six classification criteria, which include histopathological findings or the presence of autoantibodies. Alternatively, a diagnosis can be made if the patient fulfills three out of four objective criteria . Our patient meets three out of four objective criteria. Renal involvement, an extraglandular manifestation of Sjögren’s syndrome, affects less than 10% of cases. RTA is seen in 4.5-9% of patients, typically in middle-aged individuals, with only two-thirds of these patients being symptomatic. In pSS, kidney involvement is primarily due to TIN, with glomerular disease being less common . Renal involvement in Sjögren’s syndrome can be classified into two types: peri- epithelial, caused by lymphocytic infiltration, and extra-epithelial, due to immune complex deposition. Peri- epithelial lesions affect the proximal tubules, intercalated cells, or the loop of Henle . pSS can affect the entire nephron, leading to both proximal and dRTA. The most common clinical features of dRTA include NAGMA, alkaline urine, and hypokalemia. In this patient, the combination of NAGMA, hypokalemia, elevated urine pH, and a positive urine anion gap supports a diagnosis of dRTA with predominant renal potassium loss . Distal RTA, often asymptomatic, is a frequent manifestation of Sjögren’s syndrome that remains undiagnosed in many cases. Hypokalemia is the most common electrolyte disturbance associated with dRTA, occurring in approximately 28-53% of patients. Notably, hypokalemia can precede the classic glandular symptoms of Sjögren’s syndrome, potentially facilitating an earlier diagnosis. 2025 Islam et al. Cureus 17(4): e82206. DOI 10.7759/cureus.82206 4of 6 In some cases, hypokalemic paralysis serves as the initial presentation, affecting around 7% of patients . Distal RTA is characterized by defective hydrogen ion (H ⁺) secretion in the distal nephron, impairing urinary acid excretion and reducing ammonium (NH₄ ⁺) excretion. To maintain electroneutrality, there is an increase in distal potassium excretion, leading to hypokalemia. Severe hypokalemia (<2.5 mmol/L) can cause acute flaccid paralysis, ranging from mild muscle weakness to profound paralysis . Metabolic bone disease and osteomalacia due to dRTA in Sjögren’s syndrome have been previously documented. In distal RTA, chronic acidosis combined with hypophosphatemia contributes to bone demineralization . Chronic metabolic acidosis suppresses both bone formation and resorption, leading to reduced bone mass. This abnormal bone remodeling is characterized by low-turnover bone disease with defective mineralization. Prolonged metabolic acidosis can impair osteoblast function and disrupt bone matrix mineralization, contributing to osteomalacia. Additionally, coexisting vitamin D deficiency may further exacerbate bone loss . In our patient, clinical and biochemical findings were consistent with osteomalacia. The treatment approach for Sjögren’s syndrome varies depending on the presenting symptoms and the presence of extraglandular manifestations. Hydroxychloroquine is the first-line treatment for systemic manifestations of Sjögren’s syndrome, including arthralgia, arthritis, and fatigue. For patients with severe systemic involvement, corticosteroids are the mainstay of therapy, often combined with immunosuppressive agents. While pSS generally follows a benign course, certain features such as vasculitis, glandular enlargement, low complement levels, and cryoglobulinemia are linked to a higher risk of severe complications, including non-Hodgkin lymphoma. The management of dRTA primarily focuses on supportive care, including potassium and bicarbonate supplementation, while monitoring for complications such as nephrolithiasis. Early diagnosis and long-term alkali treatment are crucial for preventing both acute hypokalemia and long-term complications like osteomalacia, kidney stones, and progression to chronic kidney disease . Conclusions This case underscores the importance of considering pSS in middle-aged women presenting with recurrent hypokalemic quadriparesis, even in the absence of classic sicca symptoms. Hypokalemia may serve as an indicator of underlying renal involvement, particularly dRTA, which can lead to complications such as osteomalacia and osteoporosis. Early diagnosis and appropriate management are crucial to prevent long- term morbidity and improve patient outcomes. Additional Information Author Contributions All authors have reviewed the final version to be published and agreed to be accountable for all aspects of the work. Concept and design: Naznin Naher, Quazi Mamtaz Uddin Ahmed, Farzana Ahmed Drafting of the manuscript: Naznin Naher, Md Ashraf Uddin, Mohammad Syedul Islam Critical review of the manuscript for important intellectual content: Naznin Naher, Quazi Mamtaz Uddin Ahmed, Farzana Ahmed, Mohammad Syedul Islam Acquisition, analysis, or interpretation of data: Md Ashraf Uddin, Quazi Mamtaz Uddin Ahmed, Mohammad Syedul Islam Supervision: Quazi Mamtaz Uddin Ahmed, Mohammad Syedul Islam Disclosures Human subjects: Consent for treatment and open access publication was obtained or waived by all participants in this study. Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: All authors have declared that no financial support was received from any organization for the submitted work. Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work. References 1.Ho K, Dokouhaki P, McIsaac M, Prasad B: Renal tubular acidosis as the initial presentation of Sjögren's 2025 Islam et al. Cureus 17(4): e82206. DOI 10.7759/cureus.82206 5of 6 syndrome . BMJ Case Rep. 2019, 12: 10.1136/bcr-2019-230402 Boussetta N, Salah HM, Metoui L, et al.: Osteomalacia revealing primary Sjögren’s syndrome in a Tunisian woman with distal renal tubular acidosis . Egypt Rheumatol. 2016, 39:131-3. 10.1016/j.ejr.2016.08.003 Hamada S, Takata T, Yamada K, et al.: Renal tubular acidosis without interstitial nephritis in Sjögren's syndrome: a case report and review of the literature . BMC Nephrol. 2023, 24:237. 10.1186/s12882-023- 03290-3 Louis-Jean S, Ching PR, Wallingford A: Distal renal tubular acidosis in Sjögren’s syndrome: a case report . Cureus. 2020, 12:e10962. 10.7759/cureus.10962 Furqan S, Banu S, Ram N: Osteoporosis complicating renal tubular acidosis in association with Sjogren’s syndrome . Cureus. 2021, 13:e18373. 10.7759/cureus.18373 Fayyaz A, Kurien BT, Scofield RH: Autoantibodies in Sjögren's Syndrome . Rheum Dis Clin North Am. 2016, 42:419-34. 10.1016/j.rdc.2016.03.002 Maciel G, Crowson CS, Matteson EL, Cornec D: Prevalence of primary Sjögren’s syndrome in a US population-based cohort . Arthritis Care Res (Hoboken). 2017, 69:1612-6. 10.1002/acr.23173 Vitali C, Bombardieri S, Jonsson R, et al.: Classification criteria for Sjögren's syndrome: a revised version of the European criteria proposed by the American-European Consensus Group . Ann Rheum Dis. 2002, 61:554- 10.1136/ard.61.6.554 Romão VC, Talarico R, Scirè CA, et al.: Sjögren's syndrome: state of the art on clinical practice guidelines . RMD Open. 2018, 4:e000789. 10.1136/rmdopen-2018-000789 10 . Vasquez-Rios G, Westrich DJ Jr, Philip I, Edwards JC, Shieh S: Distal renal tubular acidosis and severe hypokalemia: a case report and review of the literature . J Med Case Rep. 2019, 13:103. 10.1186/s13256-019- 2056-1 11 . Palmer BF, Kelepouris E, Clegg DJ: Renal tubular acidosis and management strategies: a narrative review . Adv Ther. 2021, 38:949-68. 10.1007/s12325-020-01587-5 12 . Laxmi Supriya Y, Nalam R, Lagishetty SP, Meka P, Rangari G: A case report of recurrent hypokalemic quadriparesis in the setting of distal renal tubular acidosis preceding typical sicca symptoms in primary Sjögren’s syndrome . Cureus. 2024, 16:e70185. 10.7759/cureus.70185 13 . Abdulla MC, Zuhara S, Parambil AA, Ram N: Pathological fracture in Sjögren's syndrome due to distal renal tubular acidosis . Int J Rheum Dis. 2017, 20:2162-4. 10.1111/1756-185X.13193 14 . Disthabanchong S, Domrongkitchaiporn S, Sirikulchayanonta V, Stitchantrakul W, Karnsombut P, Rajatanavin R: Alteration of noncollagenous bone matrix proteins in distal renal tubular acidosis . Bone. 2004, 35:604-13. 10.1016/j.bone.2004.04.028 15 . Stefanski AL, Tomiak C, Pleyer U, Dietrich T, Burmester GR, Dörner T: The diagnosis and treatment of Sjögren’s syndrome . Dtsch Arztebl Int. 2017, 114:354-61. 10.3238/arztebl.2017.0354 2025 Islam et al. Cureus 17(4): e82206. 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https://www.themathdoctors.org/domain-and-range-of-a-radical-function/
Domain and Range of a Radical Function – The Math Doctors Typesetting math: 100% Skip to content Main Menu Home Ask a Question Blog FAQ About The Math Doctors Contact Search Search for: Domain and Range of a Radical Function February 26, 2021 February 25, 2021 / Algebra, NQOTW / Functions / By Dave Peterson (A new question of the week) We’ve looked at domain and range problems before, but some have more interesting details than others. Here is a superficially basic radical function (and the answer is extremely easy when you just use a graphing tool), which raised some interesting issues while solving it algebraically. Domain and range: basic approaches This question came from repeat “patient” Mubashshir in mid-January: What is the domain and range of the function? f(x) = 2x/√(4x-x²) The function, written out nicely, is f(x)=2 x 4 x−x 2−−−−−−√ A bare question like this, with no indication of what particular help is needed, calls for some questioning before we can decide what most needs to be said. We need to know what tools the student has in his tool kit, and what difficulties he’s faced in using (or just choosing) them. Doctor Rick answered, mixing that request for information with a variety of suggestions: Hi, Mubashshir. As we have said before, we want you to show whatever work you have done, and tell us what you have been learning, so that we can see where you need help and what methods are available to you. Finding thedomainof a function is generally a straight-forward task: you just look for values of x for which the function cannot be evaluated. There are two particularly common reasons that an algebraic expression cannot be evaluated: either the denominator is zero, or there is a negative number under a square root. If you have been able to do this part of the problem, I’d like to see your answer; if you haven’t, please show me your work, so I can see how far you got and where you had difficulty. For discussions of domain (and other issues we’ll be dealing with here), see this post: Domain, Range, and Quadratic Inequalities Finding the rangeof a function is often much harder, and a variety of methods might be needed, depending on the function. One common technique is to find the inverse of the function; the range of a function is the domain of its inverse, and as I said, finding the domain is relatively easy. However, finding the inverse in this case is a bit more difficult, because it involves squaring both sides of an equation, and this can introduce extraneous solutions. For more on range (including a radical function somewhat like ours here), see Finding the Range of a Function For examples of extraneous solutions and what to do about them, see Extraneous Solutions: Causes and Cures If you know calculus, you could try finding the derivative of the function. This can then be used to find relative minima and maxima of the function; and that’s a big help in finding the range. But again, there is one complication in this case (I won’t even get into that if you don’t know calculus yet). Please show me your work, using these suggestions if they help, and tell me something about what you have learned. Then we can have further discussion about how to solve this challenging problem. We’ll take a look at calculus when we look at the graph, and we’ll see what complicates it a little. Looking for the inverse Mubashshir replied, choosing the inverse function route: I don’t know calculus. y = f(x) = 2x/√(4x–x²) → 4x²+x²y² = 4xy² I can’t do more. Doctor Rick answered, I didn’t think it too likely that you knew calculus, though one of your past questions was on a topic somewhat related to calculus (sums of series). So we will put that tool aside. You didn’t say how you did on finding the domain, but you showed some initial work on my first suggestion for finding the range. As a first step to inverting the function, you wrote y = 2x/√(4x–x 2) 4x 2+ x 2 y 2= 4xy 2 Presumably what he has done here is to multiply both sides by the denominator, and square both sides: y=2 x 4 x−x 2−−−−−−√y 4 x−x 2−−−−−−√=2 x(y 4 x−x 2−−−−−−√)2=(2 x)2 y 2(4 x−x 2)=4 x 2 4 x y 2−x 2 y 2=4 x 2 4 x y 2=x 2 y 2+4 x 2 That’s good so far. Our goal here is to solve for x in terms of y, which will be (almost) the inverse function, x = f–1(y). So we’d like next to isolate x on one side — but we can’t really do that, because there are terms in both x and x 2. One thing wecoulddo is to think of the equation above as a quadratic equation in x, treating y (for now) as just a number. If we did that, we’d write it as (y 2+4)x 2−4 x y 2=0 and factor it: x((y 2+4)x−4 y 2)=0 so that either x=0 or (y 2+4)x−4 y 2=0 which leads to x=4 y 2 y 2+4 Or … we could notice that all the terms have a factor of x, so we can divide the equation through by x. The only problem with this is that we have to remember x can’t be 0 when we divide by it. So we consider the case x = 0 first, and we see that when x = 0, y = f(x) cannot be evaluated (so 0 is not part of the domain of f). When x ≠ 0, we do the division and get 4x + xy 2= 4y 2 which is easy to solve for x. When you have done that, the domain of this (inverse) function will be the set of values of y for which the function f–1(y) can be evaluated. Again, we find that x=4 y 2 y 2+4 Incidentally, you may be confused by the fact that he didn’t interchange x and y as is often taught, at least in American schools, as the first step in inverting a function. For a discussion of this, see How to Find an Inverse Function: Conflicting Approaches We generally defer to the method a student is using, to avoid confusing them; but in this case, as I state there, this is my preferred approach. Now we have an inverse function (x as a function of y); what is its domain (possible values of y)? I mentioned before that there is an issue yet to be resolved, because you obtained your equation by squaring, and this means that our new function is not exactly the inverse of f. But I’ll leave it here for now, to see what you can do with it, since I’m not even sure whether you want to continue working on the problem at all. If you do, please show me all the work you can do (even if you think it’s wrong — that would still show me important things). Since the denominator is always positive, the domain of the inverse as we see it so far would be all real numbers. Finding the domain We’ll be coming back to that soon; but for the moment, Mubashshir answered by showing work for the domain of the given function: f(x) ∈ R, 4x – x² > 0 x² – 4x < 0 Domain = (0,4) Here he is looking at the radicand in the denominator of our function f(x)=2 x 4 x−x 2√, which has to be non-negative in order to take the root (as a real number), and non-zero in order to divide by it. Such a polynomial inequality can be solved in several ways (which are discussed in one of the blog posts mentioned above). One way is just to sketch the graph of 4 x−x 2: This is positive between 0 and 4. Finding the range Next, he returned to the range, deriving the inverse again and looking at its domain: y = 2x/√(4x–x²) 4x + xy² = 4y² x = 4y²/(4 + y²) x ∈ R, 4 + y² ≠ 0 It’s not possible. Range= {x ∈ R: x > 0}. [f(x) is always larger than 0] If I’m not right, please tell me. What is “not possible” is for the denominator to be zero, so that the inverse is defined for all values of y … so then, what is that next line saying? Doctor Rick answered, You correctly found the domain to be (0, 4). The quantity under the square root, 4x – x 2, must be non-negative, yielding 0 ≤ x ≤ 4; but also the denominator, which is the square root of that quantity, cannot be zero, removing 0 and 4 from the domain. Good work on that part! Then, On the range, you did correctly what I suggested, and you found no values of y that could not be in the domain of x =4y²/(4+y²). But you didn’t stop there and assert that the range is all real numbers! You stated that f(x) is always greater than 0, so the range is y > 0. That is correct, but I am left wondering how you drew that conclusion. Could you explain your reasoning? This is the tricky part of the problem, so I don’t want to miss the opportunity for us to learn something from it. Some subtleties of the range After a brief side discussion, Doctor Rick repeated: I asked you why you said that Range = {x ∈ R: x >0}. [f(x) is always larger than 0] Even if you can’t explain very clearly, you must have had some reason for thinking that. I can think of some possibilities, but I want to hear it from you! Whatever you can say about this will be a basis for further discussion. Mubashshir replied, x = 4y²/(4 + y²) x ∈ R, iff 4 + y² ≠ 0 So, y² ≠ –4, it’s not possible. For this reason the range would be all real numbers. But we will not get any negative numbers or 0 for the values which are included as domain. The set of the values of y are range. So, the range can’t be less than 0. So, I said the range is (0,∞). Now Doctor Rick could say more: Thanks, Mubashshir. That is what I was looking for — and it is pretty much what I would have guessed. We had seen that the domain of the function x = 4y²/(4 + y²) (which would be the range of f(x) if this function were truly f-1(y) ) is all real numbers. However, I suppose you noticed that with f(x) = 2x/√(4x – x 2) when x is in (0, 4), the numerator is positive and the denominator is also positive, so f(x) must be positive. Thus the range of f must be the positive numbersorsome subset of the positive numbers. This is what Mubashshir had explicitly said. But that is not quite enough: The only thing we haven’t established for certain is thatallpositive numbers are in the range. There are things we can say that are more or less in the realm of calculus, but that should at least make sense without a study of calculus. For instance, f(x) iscontinuousfor x in (0, 4): that is, there is no sharp break in the graph of f(x). That’s because the numerator 2x is continuous (its graph is a straight line), and the denominator√(4x–x 2) is also continuous (its graph is a semicircle), and the denominator is not zero between x = 0 and x = 4 (though it is zero at both those end points). We can also consider thelimits of f(x) as x gets very close to 0 on the one hand, or very close to 4 on the other. It’s easy to see that for x very close to 4, the numerator is close to 8 while the denominator is a small positive number – getting even smaller as x gets closer to 4. And a fraction whose denominator is very close to zero has a very large value. As x approaches zero, though, it’s harder to be sure without formal calculus concepts. Here is what the denominator, 4 x−x 2−−−−−−√, looks like (the semicircle): As x approaches 4, the fraction 2 x 4 x−x 2√ approaches “8/0”, that is, it becomes infinitely large; so we know that there is no upper bound. But as x approaches 0, the fraction approaches “0/0”, which is indeterminate: We can’t determine what it does without more advanced methods. In particular (keep your eyes closed if you don’t want any calculus), we find that lim x→0 2 x 4 x−x 2−−−−−−√=lim x→0 2 x x−−√4−x−−−−−√=lim x→0 2 x−−√4−x−−−−−√=0 4=0 Another approach, probably more fruitful for you, is to consider what went wrong as we tried to find the inverse of f. As I mentioned, the problem was that we squared both sides. The work, again, was y = 2x/√(4x – x 2), 0 < x < 4 y 2= 4x 2/(4x – x 2) (squaring both sides) 4x 2+ x 2 y 2= 4xy 2 4x + xy 2= 4y 2 (dividing by x, which cannot be 0) x = 4y 2/(4 + y 2) From step 2 on, negative values for y are allowed. In fact, for any positive value of y, its negative will also work. Thus, x as a function of y is an “even” function – its graph is symmetric in the x axis – because replacing y by –y does not change the function. This, again, is not the actual inverse. Going backward now, I conclude that foranypair (x, y) that satisfies , the pair (x, -y) also satisfies , but we only want to keep the pair withpositivey. Therefore I conclude that the range of is (0, ∞). (One other thing I forgot to say: since we know x cannot be 0, y also cannot be 0; without this, I would have concluded that the range of is [0, ∞).) You can graph and to see more clearly what’s going on. So what do the graphs say? That was the end of the discussion. Let’s take a look at the graph of our function (equation : As we’ve seen, the domain is (0,4), and the range is (0,∞). And here is the graph of the equation 4 x 2+x 2 y 2=4 x y 2 (equation 3), or x=4 y 2 4+y 2 (equation ): Observe that this equation includes the origin (because we are no longer dividing), and is symmetrical (because we don’t take the square root); and that here y is not a function of x. Now, what would happen if we used calculus to find the domain? We’d first look for local maxima or minima by finding the derivative: f(x)=2 x(4 x−x 2)1/2 f′(x)=2(4 x−x 2)1/2−2 x(4−2 x)1 2(4 x−x 2)−1/2 4 x−x 2=2(4 x−x 2)−x(4−2 x)(4 x−x 2)3/2=8 x−2 x 2−4 x+2 x 2(4 x−x 2)3/2=4 x(4 x−x 2)3/2 At first glance, this will be zero only at x=0; but it is actually indeterminate there. If we use the same trick we used above to find the limit, we find lim x→0 4 x(4 x−x 2)3/2=lim x→0 4 x x 3/2(4−x)3/2=lim x→0 4 x 1/2(4−x)3/2=∞ The same, more simply, is true of the limit of the derivative at 4. Also, we can observe that the derivative is always positive, so the function is monotonically increasing. This agrees with our graph, and indicates that there is no minimum, and that the limits of the function determine the range. Post navigation ← Previous Post Next Post → Leave a Comment Cancel Reply Your email address will not be published.Required fields are marked Type here.. Name Email Website Δ This site uses Akismet to reduce spam. 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Home 2. Campus Bookshelves 3. SUNY Schenectady County Community College 4. Discrete Structures 5. 4: Mathematical Induction (with Sequences) 6. Supplementary Notes: Sequences, Definitions 7. Supplementary Notes: Sequences, Arithmetic and Geometric 8. Supplementary Notes: Recurrence Relations Expand/collapse global location Supplementary Notes: Recurrence Relations Last updated Aug 3, 2023 Save as PDF Supplementary Notes: Sequences, Arithmetic and Geometric 5: Set Theory Page ID 137024 ( \newcommand{\kernel}{\mathrm{null}\,}) Table of contents 1. The Characteristic Root Technique Investigate! Consider the recurrence relation a n=5⁢a n−1−6⁢a n−2. 1. What sequence do you get if the initial conditions are a 0=1,a 1=2? Give a closed formula for this sequence. 2. What sequence do you get if the initial conditions are a 0=1,a 1=3? Give a closed formula. 3. What if a 0=2 and a 1=5? Find a closed formula. We have seen that it is often easier to find recursive definitions than closed formulas. Lucky for us, there are a few techniques for converting recursive definitions to closed formulas. Doing so is called solving a recurrence relation. Recall that the recurrence relation is a recursive definition without the initial conditions. For example, the recurrence relation for the Fibonacci sequence is F n=F n−1+F n−2. (This, together with the initial conditions F 0=0 and F 1=1 give the entire recursive definition for the sequence.) Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.1 Find a recurrence relation and initial conditions for 1,5,17,53,161,485…. Solution Finding the recurrence relation would be easier if we had some context for the problem (like the Tower of Hanoi, for example). Alas, we have only the sequence. Remember, the recurrence relation tells you how to get from previous terms to future terms. What is going on here? We could look at the differences between terms: 4,12,36,108,…. Notice that these are growing by a factor of 3. Is the original sequence as well? 1⋅3=3,5⋅3=15,17⋅3=51 and so on. It appears that we always end up with 2 less than the next term. Aha! So a n=3⁢a n−1+2 is our recurrence relation and the initial condition is a 0=1. We are going to try to solve these recurrence relations. By this we mean something very similar to solving differential equations: we want to find a function of n (a closed formula) which satisfies the recurrence relation, as well as the initial condition. 2 Recurrence relations are sometimes called difference equations since they can describe the difference between terms and this highlights the relation to differential equations further. Just like for differential equations, finding a solution might be tricky, but checking that the solution is correct is easy. Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.2 Check that a n=2 n+1 is a solution to the recurrence relation a n=2⁢a n−1−1 with a 1=3. Solution First, it is easy to check the initial condition: a 1 should be 2 1+1 according to our closed formula. Indeed, 2 1+1=3, which is what we want. To check that our proposed solution satisfies the recurrence relation, try plugging it in. 2⁢a n−1−1=2⁢(2 n−1+1)−1=2 n+2−1=2 n+1=a n. That's what our recurrence relation says! We have a solution. Sometimes we can be clever and solve a recurrence relation by inspection. We generate the sequence using the recurrence relation and keep track of what we are doing so that we can see how to jump to finding just the a n term. Here are two examples of how you might do that. Telescoping refers to the phenomenon when many terms in a large sum cancel out - so the sum “telescopes.” For example: (2−1)+(3−2)+(4−3)+⋯+(100−99)+(101−100)=−1+101 because every third term looks like: 2+−2=0, and then 3+−3=0 and so on. We can use this behavior to solve recurrence relations. Here is an example. Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.3 Solve the recurrence relation a n=a n−1+n with initial term a 0=4. Solution To get a feel for the recurrence relation, write out the first few terms of the sequence: 4,5,7,10,14,19,…. Look at the difference between terms. a 1−a 0=1 and a 2−a 1=2 and so on. The key thing here is that the difference between terms is n. We can write this explicitly: a n−a n−1=n. Of course, we could have arrived at this conclusion directly from the recurrence relation by subtracting a n−1 from both sides. Now use this equation over and over again, changing n each time: a 1−a 0=1 a 2−a 1=2 a 3−a 2=3⋮⋮a n−a n−1=n. Add all these equations together. On the right-hand side, we get the sum 1+2+3+⋯+n. We already know this can be simplified to n⁢(n+1)2. What happens on the left-hand side? We get (a 1−a 0)+(a 2−a 1)+(a 3−a 2)+⋯(a n−1−a n−2)+(a n−a n−1). This sum telescopes. We are left with only the −a 0 from the first equation and the a n from the last equation. Putting this all together we have −a 0+a n=n⁢(n+1)2 or a n=n⁢(n+1)2+a 0. But we know that a 0=4. So the solution to the recurrence relation, subject to the initial condition is a n=n⁢(n+1)2+4. (Now that we know that, we should notice that the sequence is the result of adding 4 to each of the triangular numbers.) The above example shows a way to solve recurrence relations of the form a n=a n−1+f⁡(n) where ∑k=1 n f⁡(k) has a known closed formula. If you rewrite the recurrence relation as a n−a n−1=f⁡(n), and then add up all the different equations with n ranging between 1 and n, the left-hand side will always give you a n−a 0. The right-hand side will be ∑k=1 n f⁡(k), which is why we need to know the closed formula for that sum. However, telescoping will not help us with a recursion such as a n=3⁢a n−1+2 since the left-hand side will not telescope. You will have −3⁢a n−1's but only one a n−1. However, we can still be clever if we use iteration. We have already seen an example of iteration when we found the closed formula for arithmetic and geometric sequences. The idea is, we iterate the process of finding the next term, starting with the known initial condition, up until we have a n. Then we simplify. In the arithmetic sequence example, we simplified by multiplying d by the number of times we add it to a when we get to a n, to get from a n=a+d+d+d+⋯+d to a n=a+d⁢n. To see how this works, let's go through the same example we used for telescoping, but this time use iteration. Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.4 Use iteration to solve the recurrence relation a n=a n−1+n with a 0=4. Answer Again, start by writing down the recurrence relation when n=1. This time, don't subtract the a n−1 terms to the other side: a 1=a 0+1. Now a 2=a 1+2, but we know what a 1 is. By substitution, we get a 2=(a 0+1)+2. Now go to a 3=a 2+3, using our known value of a 2: a 3=((a 0+1)+2)+3. We notice a pattern. Each time, we take the previous term and add the current index. So a n=((((a 0+1)+2)+3)+⋯+n−1)+n. Regrouping terms, we notice that a n is just a 0 plus the sum of the integers from 1 to n. So, since a 0=4, a n=4+n⁢(n+1)2. Of course in this case we still needed to know formula for the sum of 1,…,n. Let's try iteration with a sequence for which telescoping doesn't work. Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.5 Solve the recurrence relation a n=3⁢a n−1+2 subject to a 0=1. Answer Again, we iterate the recurrence relation, building up to the index n. a 1=3⁢a 0+2 a 2=3⁢(a 1)+2=3⁢(3⁢a 0+2)+2 a 3=3⁢[a 2]+2=3⁢[3⁢(3⁢a 0+2)+2]+2⋮⋮⋮a n=3⁢(a n−1)+2=3⁢(3⁢(3⁢(3⋯(3⁢a 0+2)+2)+2)⋯+2)+2. It is difficult to see what is happening here because we have to distribute all those 3's. Let's try again, this time simplifying a bit as we go. a 1=3⁢a 0+2 a 2=3⁢(a 1)+2=3⁢(3⁢a 0+2)+2=3 2⁢a 0+2⋅3+2 a 3=3⁢[a 2]+2=3⁢[3 2⁢a 0+2⋅3+2]+2=3 3⁢a 0+2⋅3 2+2⋅3+2⋮⋮⋮a n=3⁢(a n−1)+2=3⁢(3 n−1⁢a 0+2⋅3 n−2+⋯+2)+2=3 n⁢a 0+2⋅3 n−1+2⋅3 n−2+⋯+2⋅3+2. Now we simplify. a 0=1, so we have 3 n+⟨stuff⟩. Note that all the other terms have a 2 in them. In fact, we have a geometric sum with first term 2 and common ratio 3. We have seen how to simplify 2+2⋅3+2⋅3 2+⋯+2⋅3 n−1. We get 2−2⋅3 n−2 which simplifies to 3 n−1. Putting this together with the first 3 n term gives our closed formula: a n=2⋅3 n−1. Iteration can be messy, but when the recurrence relation only refers to one previous term (and maybe some function of n) it can work well. However, trying to iterate a recurrence relation such as a n=2⁢a n−1+3⁢a n−2 will be way too complicated. We would need to keep track of two sets of previous terms, each of which were expressed by two previous terms, and so on. The length of the formula would grow exponentially (double each time, in fact). Luckily there happens to be a method for solving recurrence relations which works very well on relations like this. The Characteristic Root Technique Suppose we want to solve a recurrence relation expressed as a combination of the two previous terms, such as a n=a n−1+6⁢a n−2. In other words, we want to find a function of n which satisfies a n−a n−1−6⁢a n−2=0. Now iteration is too complicated, but think just for a second what would happen if we did iterate. In each step, we would, among other things, multiply a previous iteration by 6. So our closed formula would include 6 multiplied some number of times. Thus it is reasonable to guess the solution will contain parts that look geometric. Perhaps the solution will take the form r n for some constant r. The nice thing is, we know how to check whether a formula is actually a solution to a recurrence relation: plug it in. What happens if we plug in r n into the recursion above? We get r n−r n−1−6⁢r n−2=0. Now solve for r: r n−2⁢(r 2−r−6)=0, so by factoring, r=−2 or r=3 (or r=0, although this does not help us). This tells us that a n=(−2)n is a solution to the recurrence relation, as is a n=3 n. Which one is correct? They both are, unless we specify initial conditions. Notice we could also have a n=(−2)n+3 n. Or a n=7⁢(−2)n+4⋅3 n. In fact, for any a and b,a n=a⁢(−2)n+b⁢3 n is a solution (try plugging this into the recurrence relation). To find the values of a and b, use the initial conditions. This points us in the direction of a more general technique for solving recurrence relations. Notice we will always be able to factor out the r n−2 as we did above. So we really only care about the other part. We call this other part the characteristic equation for the recurrence relation. We are interested in finding the roots of the characteristic equation, which are called (surprise) the characteristic roots. Characteristic Roots Given a recurrence relation a n+α⁢a n−1+β⁢a n−2=0, the characteristic polynomial is x 2+α⁢x+β giving the characteristic equation: x 2+α⁢x+β=0. If r 1 and r 2 are two distinct roots of the characteristic polynomial (i.e, solutions to the characteristic equation), then the solution to the recurrence relation is a n=a⁢r 1 n+b⁢r 2 n, where a and b are constants determined by the initial conditions. Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.6 Solve the recurrence relation a n=7⁢a n−1−10⁢a n−2 with a 0=2 and a 1=3. Solution Rewrite the recurrence relation a n−7⁢a n−1+10⁢a n−2=0. Now form the characteristic equation: x 2−7⁢x+10=0 and solve for x: (x−2)⁢(x−5)=0 so x=2 and x=5 are the characteristic roots. We therefore know that the solution to the recurrence relation will have the form a n=a⁢2 n+b⁢5 n. To find a and b, plug in n=0 and n=1 to get a system of two equations with two unknowns: 2=a⁢2 0+b⁢5 0=a+b 3=a⁢2 1+b⁢5 1=2⁢a+5⁢b Solving this system gives a=7 3 and b=−1 3 so the solution to the recurrence relation is a n=7 3⁢2 n−1 3⁢5 n. Perhaps the most famous recurrence relation is F n=F n−1+F n−2, which together with the initial conditions F 0=0 and F 1=1 defines the Fibonacci sequence. But notice that this is precisely the type of recurrence relation on which we can use the characteristic root technique. When you do, the only thing that changes is that the characteristic equation does not factor, so you need to use the quadratic formula to find the characteristic roots. In fact, doing so gives the third most famous irrational number, φ, the golden ratio. Before leaving the characteristic root technique, we should think about what might happen when you solve the characteristic equation. We have an example above in which the characteristic polynomial has two distinct roots. These roots can be integers, or perhaps irrational numbers (requiring the quadratic formula to find them). In these cases, we know what the solution to the recurrence relation looks like. However, it is possible for the characteristic polynomial to only have one root. This can happen if the characteristic polynomial factors as (x−r)2. It is still the case that r n would be a solution to the recurrence relation, but we won't be able to find solutions for all initial conditions using the general form a n=a⁢r 1 n+b⁢r 2 n, since we can't distinguish between r 1 n and r 2 n. We are in luck though: Characteristic Root Technique for Repeated Roots Suppose the recurrence relation a n=α⁢a n−1+β⁢a n−2 has a characteristic polynomial with only one root r. Then the solution to the recurrence relation is a n=a⁢r n+b⁢n⁢r n where a and b are constants determined by the initial conditions. Notice the extra n in b⁢n⁢r n. This allows us to solve for the constants a and b from the initial conditions. Example S⁢u⁢p⁢p⁢l⁢e⁢m⁢e⁢n⁢t⁢a⁢r⁢y⁢N⁢o⁢t⁢e⁢s.7 Solve the recurrence relation a n=6⁢a n−1−9⁢a n−2 with initial conditions a 0=1 and a 1=4. Answer The characteristic polynomial is x 2−6⁢x+9. We solve the characteristic equation x 2−6⁢x+9=0 by factoring: (x−3)2=0 so x=3 is the only characteristic root. Therefore we know that the solution to the recurrence relation has the form a n=a⁢3 n+b⁢n⁢3 n for some constants a and b. Now use the initial conditions: a 0=1=a⁢3 0+b⋅0⋅3 0=a a 1=4=a⋅3+b⋅1⋅3=3⁢a+3⁢b. Since a=1, we find that b=1 3. Therefore the solution to the recurrence relation is a n=3 n+1 3⁢n⁢3 n. Although we will not consider examples more complicated than these, this characteristic root technique can be applied to much more complicated recurrence relations. For example, a n=2⁢a n−1+a n−2−3⁢a n−3 has characteristic polynomial x 3−2⁢x 2−x+3. Assuming you see how to factor such a degree 3 (or more) polynomial you can easily find the characteristic roots and as such solve the recurrence relation (the solution would look like a n=a⁢r 1 n+b⁢r 2 n+c⁢r 3 n if there were 3 distinct roots). It is also possible to solve recurrence relations of the form a n=α⁢a n−1+β⁢a n−2+C for some constant C. It is also possible (and acceptable) for the characteristic roots to be complex numbers. Supplementary Notes: Recurrence Relations is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. Back to top Supplementary Notes: Sequences, Arithmetic and Geometric 5: Set Theory Was this article helpful? Yes No Recommended articles 4.1: The Principle of Mathematical InductionIn this section, we will learn a new proof technique, called mathematical induction, that is often used to prove statements of the form (∀n∈N)(P(n)) 4.2: Other Forms of Mathematical Induction 4.3: Induction and RecursionIn a proof by mathematical induction, we “start with a first step” and then prove that we can always go from one step to the next step. We can use thi... 4.S: Mathematical Induction (Summary) Supplementary Notes: Sequences, DefinitionsThese sections are from the text "Discrete Math" by Oscar Levin. Readers who have not seen sequences for a while, might want to refer to these supple... Article typeSection or Page Tags This page has no tags. © Copyright 2025 Mathematics LibreTexts Powered by CXone Expert ® ? 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Revision Notes - Calculating consumer and producer surplus | Supply and Demand | Microeconomics | Collegeboard AP | Sparkl Courses Past Papers Log InSign Up Past Papers Courses Collegeboard AP IB DP Cambridge IGCSE AS & A Level IB MYP 1-3 IB MYP 4-5 All Topics microeconomics | collegeboard-ap 1.Supply and Demand 1.1 Price Elasticity of Demand 1.1.1 Total revenue test 1.1.2 Elastic, inelastic and unit elastic demand 1.1.3 Determinants of price elasticity: Substitutability, proportion of income 1.2 Price Elasticity of Supply 1.2.1 Factors influencing elasticity: Availability of inputs, production time 1.2.2 Comparison of short-run and long-run elasticity 1.3 Other Elasticities 1.3.1 Cross-price elasticity: Substitutes and complements 1.3.2 Income elasticity: Normal and inferior goods 1.4 Market Equilibrium and Consumer and Producer Surplus 1.4.1 Equilibrium price and quantity determination 1.4.2 Calculating consumer and producer surplus 1.4.3 Welfare economics: Maximizing total surplus 1.5 Market Disequilibrium and Changes in Equilibrium 1.5.1 Effects of shifts in supply and demand 1.5.2 Price floors (e.g. minimum wage) and price ceilings (e.g. rent control) 1.6 Effects of Government Intervention in Markets 1.6.1 Taxes: Impact on consumers, producers and deadweight loss 1.6.2 Subsidies: Benefits and inefficiencies 1.6.3 Quantity controls (e.g. quotas) 1.7 International Trade and Public Policy 1.7.1 Effects of imports and exports on domestic markets 1.7.2 Tariffs and quotas: Costs and benefits 1.7.3 Free trade vs. protectionism 1.8 Demand 1.8.1 Law of demand and reasons for downward slope 1.8.2 Determinants of demand: Income, tastes, prices of related goods 1.8.3 Normal vs. inferior goods 1.9 Supply 1.9.1 Law of supply and reasons for upward slope 1.9.2 Determinants of supply: Input costs, technology, expectations 1.9.3 Short-run vs. long-run adjustments 2.Imperfect Competition 2.1 Oligopoly and Game Theory 2.1.1 Collusion and cartels: Benefits and challenges 2.1.2 Characteristics of oligopolies: Few large firms, barriers to entry 2.1.3 Strategic behavior: Nash equilibrium and dominant strategies 2.2 Introduction to Imperfectly Competitive Markets 2.2.1 Comparison of market structures: Monopoly, oligopoly, monopolistic competition 2.2.2 Causes and implications of market power 2.3 Monopoly 2.3.1 Sources of monopoly power 2.3.2 Price-setting behavior and inefficiency 2.3.3 Graphical representation of monopoly pricing 2.4 Price Discrimination 2.4.1 Conditions for price discrimination 2.4.2 Examples of first, second, and third-degree price discrimination 2.5 Monopolistic Competition 2.5.1 Characteristics: Product differentiation and many sellers 2.5.2 Short-run profit and long-run equilibrium 2.5.3 Excess capacity and inefficiency 3.Factor Markets 3.1 Introduction to Factor Markets 3.1.1 Derived demand: Factors of production 3.1.2 Marginal product of labor (MPL) and capital 3.1.3 Value of marginal product (VMP) 3.2 Changes in Factor Demand and Supply 3.2.1 Determinants of factor demand: Productivity, prices of goods 3.2.2 Determinants of factor supply: Population, preferences 3.3 Profit-Maximizing Behavior in Factor Markets 3.3.1 Marginal revenue product (MRP) = Marginal resource cost (MRC) 3.3.2 Hiring decisions in competitive and imperfect markets 3.4 Monopsonistic Markets 3.4.1 Characteristics of monopsony 3.4.2 Wage determination and inefficiency 4.Market Failure and the Role of Government 4.1 Socially Efficient and Inefficient Market Outcomes 4.1.1 Allocative efficiency: Marginal benefit equals marginal cost 4.1.2 Causes of market failures: Externalities, public goods 4.2 Externalities 4.2.1 Positive externalities: Subsidies and government intervention 4.2.2 Negative externalities: Taxes, regulations, and tradable permits 4.2.3 Graphical analysis of externalities 4.3 Public and Private Goods 4.3.1 Characteristics: Excludability and rivalry 4.3.2 Free-rider problem and under-provision of public goods 4.4 Government Intervention in Different Market Structures 4.4.1 Regulation of monopolies: Price caps and subsidies 4.4.2 Antitrust policies: Promoting competition 4.5 Inequality 4.5.1 Measurement of income inequality: Lorenz curve and Gini coefficient 4.5.2 Causes of inequality: Education, skills, inheritance 4.5.3 Government redistribution policies 5.Production, Cost and the Perfect Competition Model 5.1 The Production Function 5.1.1 Relationship between inputs and outputs 5.1.2 Short-run vs. long-run production 5.1.3 Law of diminishing marginal returns 5.2 Short-Run Production Costs 5.2.1 Fixed variable and total costs 5.2.2 Marginal cost (MC), average total cost (ATC), and average variable cost (AVC) 5.2.3 Cost curves and their relationships 5.3 Long-Run Production Costs 5.3.1 Economies of scale, diseconomies of scale, and constant returns 5.3.2 Long-run average cost curve (LRAC) 5.4 Types of Profit 5.4.1 Accounting profit vs. economic profit 5.4.2 Normal profit and its role in resource allocation 5.5 Profit Maximization 5.5.1 MC = MR rule for maximizing profit 5.5.2 Loss minimization in the short run 5.6 Firms’ Short-Run Decisions 5.6.1 Shutdown decision: Comparing price to AVC 5.6.2 Sunk costs and decision-making 5.7 Perfect Competition 5.7.1 Characteristics of perfect competition 5.7.2 Short-run vs. long-run equilibrium 5.7.3 Efficiency of perfectly competitive markets 6.Basic Economic Concepts 6.1 Scarcity 6.1.1 Definition and examples of scarcity 6.1.2 Unlimited wants vs. limited resources 6.1.3 Implications for individuals and societies 6.2 Resource Allocation and Economic Systems 6.2.1 Types of systems: Command, market and mixed economies 6.2.2 How different systems address fundamental economic questions 6.2.3 Examples of real-world economies 6.3 Production Possibilities Curve (PPC) 6.3.1 Trade-offs and opportunity cost 6.3.2 Efficiency, inefficiency and unattainable points 6.3.3 Economic growth and shifts in the PPC 6.4 Comparative Advantage and Trade 6.4.1 Difference between absolute and comparative advantage 6.4.2 Specialization and mutual gains from trade 6.4.3 Calculation of opportunity costs 6.5 Cost-Benefit Analysis 6.5.1 Rational decision-making using marginal analysis 6.5.2 Marginal benefits vs. marginal costs 6.5.3 Applications to individual and business decisions 6.6 Marginal Analysis and Consumer Choice 6.6.1 Marginal utility and diminishing marginal returns 6.6.2 Optimal allocation of resources 6.6.3 Budget constraints and consumer equilibrium Show Collegeboard AP Economics Microeconomics Supply and Demand Market Equilibrium and Consumer and Producer Surplus Calculating consumer and producer surplus Revision Notes Calculating consumer and producer surplus Topic 2/3 Revision NotesFlashcardsPast Paper AnalysisQuestionsVideos Your Flashcards are Ready! 15 Flashcards in this deck. Start Start or Create your own deck How would you like to practise? Choose Difficulty Level. Choose Easy, Medium or Hard to match questions to your skill level. [x] Easy - [x] Medium - [x] Hard Choose Learning Method. Choose Easy, Medium or Hard to match questions to your skill level. [x] Flashcards Game Mode Continue Shuffle 3 Still Learning I know 12 Previous Next Shuffle Calculating Consumer and Producer Surplus Introduction Understanding consumer and producer surplus is fundamental in microeconomics, particularly within the study of market equilibrium. These concepts measure the benefits consumers and producers receive from market transactions beyond their respective costs and prices. This article delves into the intricacies of calculating consumer and producer surplus, providing essential insights for students preparing for the Collegeboard AP Microeconomics exam. Key Concepts Understanding Consumer Surplus Consumer surplus represents the difference between what consumers are willing to pay for a good or service and what they actually pay. It measures the net benefit consumers receive from participating in the market. The concept is pivotal in assessing consumer welfare and market efficiency. To calculate consumer surplus, one must understand the demand curve, which illustrates the relationship between the price of a good and the quantity demanded. The area below the demand curve and above the market price up to the equilibrium quantity represents the consumer surplus. The formula for consumer surplus is: Consumer Surplus=1 2×Base×Height \text{Consumer Surplus} = \frac{1}{2} \times \text{Base} \times \text{Height} Consumer Surplus=2 1​×Base×Height where the base is the equilibrium quantity, and the height is the difference between the maximum price consumers are willing to pay and the equilibrium price. For example, if consumers are willing to pay a maximum of 50 f o r a p r o d u c t,b u t t h e m a r k e t p r i c e i s 50 for a product, but the market price is 50 f or a p ro d u c t,b u tt h e ma r k e tp r i ce i s 30, and the equilibrium quantity is 100 units, the consumer surplus would be: Consumer Surplus=1 2×100×(50−30)=1000 \text{Consumer Surplus} = \frac{1}{2} \times 100 \times (50 - 30) = 1000 Consumer Surplus=2 1​×100×(50−30)=1000 Understanding Producer Surplus Producer surplus is the difference between the market price and the minimum price at which producers are willing to sell a good or service. It assesses the benefit producers receive from selling at a higher price than the minimum they would accept. The producer surplus is graphically represented by the area above the supply curve and below the market price up to the equilibrium quantity. This area quantifies the additional benefit producers gain from selling at the market price. The formula for producer surplus mirrors that of consumer surplus: Producer Surplus=1 2×Base×Height \text{Producer Surplus} = \frac{1}{2} \times \text{Base} \times \text{Height} Producer Surplus=2 1​×Base×Height where the base is again the equilibrium quantity, and the height is the difference between the equilibrium price and the minimum acceptable price (often the marginal cost). For instance, if the equilibrium price is 30,b u t t h e m i n i m u m p r i c e p r o d u c e r s a r e w i l l i n g t o a c c e p t i s 30, but the minimum price producers are willing to accept is 30,b u tt h e minim u m p r i ce p ro d u cers a re w i ll in g t o a cce pt i s 20, and the equilibrium quantity is 100 units, the producer surplus would be: Producer Surplus=1 2×100×(30−20)=500 \text{Producer Surplus} = \frac{1}{2} \times 100 \times (30 - 20) = 500 Producer Surplus=2 1​×100×(30−20)=500 Market Equilibrium and Surplus Market equilibrium occurs where the quantity demanded equals the quantity supplied. At this point, the consumer and producer surplus are maximized, indicating an efficient allocation of resources. Any deviation from equilibrium, such as through price controls, taxes, or subsidies, can alter these surpluses. For example, imposing a price ceiling below the equilibrium price can increase consumer surplus for some consumers but decrease it overall by causing shortages. Conversely, a price floor above equilibrium can increase producer surplus for some producers but lead to excess supply. Graphical Representation Both consumer and producer surplus can be visualized using supply and demand graphs. The demand curve typically slopes downward, reflecting the inverse relationship between price and quantity demanded, while the supply curve slopes upward. In the graph: The area above the equilibrium price and below the demand curve represents the consumer surplus. The area below the equilibrium price and above the supply curve represents the producer surplus. Total Surplus=Consumer Surplus+Producer Surplus \text{Total Surplus} = \text{Consumer Surplus} + \text{Producer Surplus} Total Surplus=Consumer Surplus+Producer Surplus Maximizing total surplus is a key objective in achieving allocative efficiency in markets. Calculating Surplus with Linear Demand and Supply Curves When dealing with linear demand and supply curves, specific equations can simplify the calculation of consumer and producer surplus. Suppose the demand curve is given by: P=a−b Q P = a - bQ P=a−b Q and the supply curve is: P=c+d Q P = c + dQ P=c+d Q where a a a, b b b, c c c, and d d d are constants, P P P is price, and Q Q Q is quantity. To find the equilibrium, set the demand and supply equations equal to each other: a−b Q=c+d Q a - bQ = c + dQ a−b Q=c+d Q Solving for Q Q Q: Q=a−c b+d Q = \frac{a - c}{b + d} Q=b+d a−c​ Substituting Q Q Q back into either equation yields the equilibrium price P P P. Once equilibrium price and quantity are determined, consumer and producer surplus can be calculated as areas of triangles: Consumer Surplus=1 2×Q×(a−P) \text{Consumer Surplus} = \frac{1}{2} \times Q \times (a - P) Consumer Surplus=2 1​×Q×(a−P)Producer Surplus=1 2×Q×(P−c) \text{Producer Surplus} = \frac{1}{2} \times Q \times (P - c) Producer Surplus=2 1​×Q×(P−c) Example: Suppose the demand equation is P=100−2 Q P = 100 - 2Q P=100−2 Q and the supply equation is P=20+Q P = 20 + Q P=20+Q. Find the consumer and producer surplus. First, find equilibrium Q Q Q: 100−2 Q=20+Q 80=3 Q Q=80 3≈26.67 100 - 2Q = 20 + Q \ 80 = 3Q \ Q = \frac{80}{3} \approx 26.67 100−2 Q=20+Q 80=3 Q Q=3 80​≈26.67 Equilibrium P P P: P=100−2×26.67=46.66 P = 100 - 2 \times 26.67 = 46.66 P=100−2×26.67=46.66 Then, Consumer Surplus=1 2×26.67×(100−46.66)≈1 2×26.67×53.34≈712.45 \text{Consumer Surplus} = \frac{1}{2} \times 26.67 \times (100 - 46.66) \approx \frac{1}{2} \times 26.67 \times 53.34 \approx 712.45 Consumer Surplus=2 1​×26.67×(100−46.66)≈2 1​×26.67×53.34≈712.45 Producer Surplus=1 2×26.67×(46.66−20)≈1 2×26.67×26.66≈355.60 \text{Producer Surplus} = \frac{1}{2} \times 26.67 \times (46.66 - 20) \approx \frac{1}{2} \times 26.67 \times 26.66 \approx 355.60 Producer Surplus=2 1​×26.67×(46.66−20)≈2 1​×26.67×26.66≈355.60 Impact of Taxes and Subsidies on Surplus Taxes and subsidies can significantly affect consumer and producer surplus by altering the effective prices paid and received in the market. When a tax is imposed, it typically causes the supply curve to shift upward by the amount of the tax. This results in a higher equilibrium price for consumers and a lower price received by producers, thereby reducing both consumer and producer surplus. Additionally, the tax revenue can be viewed as a portion of the surplus transferred to the government. Conversely, a subsidy shifts the supply curve downward, effectively lowering the cost for producers. This leads to a lower price for consumers and a higher price received by producers, increasing producer surplus while slightly affecting consumer surplus. The subsidy can be seen as an injection of surplus into the market by the government. Deadweight Loss and Surplus Deadweight loss represents the loss of total surplus due to market inefficiencies, such as those caused by taxes, subsidies, or price controls. It is the reduction in the sum of consumer and producer surplus that results when the market is not in equilibrium. For instance, a tax can create deadweight loss by preventing some mutually beneficial trades from occurring, thereby reducing overall economic welfare. Graphically, deadweight loss is represented by the area of the triangle between the demand and supply curves, delineated by the quantity changes resulting from the tax or subsidy. Minimizing deadweight loss is essential for achieving efficient market outcomes and maximizing total surplus. Elasticity and Its Effect on Surplus The elasticity of demand and supply affects the distribution of surplus between consumers and producers, as well as the magnitude of deadweight loss. Elastic Demand: When demand is elastic, consumers are sensitive to price changes. A tax will lead to a significant reduction in quantity demanded, increasing deadweight loss. Inelastic Demand: When demand is inelastic, consumers are less responsive to price changes. A tax imposed on goods with inelastic demand will cause a smaller reduction in quantity demanded, resulting in less deadweight loss. Elastic Supply: When supply is elastic, producers can easily adjust their production levels in response to price changes. A tax on elastic supply goods will lead to a larger decrease in quantity supplied, increasing deadweight loss. Inelastic Supply: When supply is inelastic, producers cannot easily alter their production in response to price changes. A tax on inelastic supply goods results in a smaller decrease in quantity supplied, reducing deadweight loss. Understanding elasticity helps in predicting the impact of taxes and subsidies on consumer and producer surplus. Applications of Consumer and Producer Surplus Consumer and producer surplus are not only theoretical constructs but have practical applications in various economic policies and business strategies. Policy Analysis: Governments use surplus analysis to assess the welfare implications of policies like taxes, subsidies, and regulations. Cost-Benefit Analysis: Businesses and policymakers employ surplus measures to evaluate the benefits and costs of projects and initiatives. Market Efficiency: Surplus metrics help in determining whether markets are operating efficiently or if there are distortions that need correction. Pricing Strategies: Firms analyze producer surplus to set prices that optimize profits while remaining competitive. Challenges in Calculating Surplus Accurately calculating consumer and producer surplus can be challenging due to several factors: Non-Linear Curves: Real-world demand and supply curves often deviate from linearity, complicating surplus calculations. Dynamic Markets: Markets are constantly changing, with shifts in demand and supply affecting surplus over time. Data Availability: Precise data on consumer and producer valuations can be difficult to obtain, leading to estimation errors. External Factors: Externalities and market imperfections can distort surplus measures, making them less reliable indicators of welfare. Comparison Table AspectConsumer SurplusProducer Surplus DefinitionDifference between what consumers are willing to pay and what they actually pay.Difference between the market price and the minimum price producers are willing to accept. Graphical RepresentationArea below the demand curve and above the equilibrium price.Area above the supply curve and below the equilibrium price. Formula1 2×Q×(P max−P equilibrium) \frac{1}{2} \times Q \times (P_{\text{max}} - P_{\text{equilibrium}}) 2 1​×Q×(P max​−P equilibrium​)1 2×Q×(P equilibrium−P min) \frac{1}{2} \times Q \times (P_{\text{equilibrium}} - P_{\text{min}}) 2 1​×Q×(P equilibrium​−P min​) Impact of TaxesGenerally decreases due to higher prices.Generally decreases due to lower net prices. Policy ImplicationsUsed to assess consumer welfare and the impact of price controls.Used to evaluate producer benefits and the effects of market interventions. Summary and Key Takeaways Consumer surplus measures the additional benefit consumers receive when paying less than their maximum willingness to pay. Producer surplus quantifies the extra profit producers earn by selling above their minimum acceptable price. Both surpluses are integral to understanding market efficiency and the impact of economic policies. Taxes and subsidies can significantly alter consumer and producer surplus, often leading to deadweight loss. Elasticity plays a crucial role in determining how surpluses are affected by market changes. Coming Soon! Examiner Tip Tips To excel in calculating surpluses on the AP exam, always sketch a clear supply and demand graph first. Remember the triangle area formula: 1 2×Base×Height \frac{1}{2} \times \text{Base} \times \text{Height} 2 1​×Base×Height. Use the mnemonic "SUPPLY Surplus on Producers" to differentiate between consumer and producer surplus. Practice with multiple examples to solidify your understanding and ensure accuracy under exam conditions. Did You Know Did You Know Did you know that the concept of consumer and producer surplus was first introduced by the economist Alfred Marshall in the late 19th century? Additionally, during the 2008 financial crisis, governments worldwide analyzed these surpluses to implement effective stimulus packages. Understanding these surpluses helps in evaluating the true impact of economic events and policies on different market participants. Common Mistakes Common Mistakes Students often confuse the definitions of consumer and producer surplus. For example, mistakenly calculating producer surplus using the demand curve instead of the supply curve leads to incorrect results. Another common error is misapplying the surplus formulas by not correctly identifying the base and height of the triangles. Ensuring that the equilibrium price and quantity are accurately determined before calculations can help avoid these mistakes. FAQ What is consumer surplus? Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay, representing their net benefit. How is producer surplus calculated? Producer surplus is calculated using the formula 1 2×Q×(P equilibrium−P min) \frac{1}{2} \times Q \times (P_{\text{equilibrium}} - P_{\text{min}}) 2 1​×Q×(P equilibrium​−P min​), where Q Q Q is the equilibrium quantity. What factors affect consumer and producer surplus? Factors include market price changes, taxes, subsidies, and the elasticity of demand and supply, all of which can shift the supply and demand curves. What is deadweight loss? Deadweight loss is the loss of total surplus that occurs when a market is not in equilibrium due to inefficiencies like taxes or subsidies. How do taxes impact consumer and producer surplus? Taxes generally decrease both consumer and producer surplus by raising prices for consumers and lowering net prices for producers, also creating deadweight loss. Why is understanding surplus important for the AP exam? Understanding consumer and producer surplus is crucial for analyzing market efficiency, the effects of policies, and answering related AP Microeconomics questions accurately. 1.Supply and Demand 1.1 Price Elasticity of Demand 1.1.1 Total revenue test 1.1.2 Elastic, inelastic and unit elastic demand 1.1.3 Determinants of price elasticity: Substitutability, proportion of income 1.2 Price Elasticity of Supply 1.2.1 Factors influencing elasticity: Availability of inputs, production time 1.2.2 Comparison of short-run and long-run elasticity 1.3 Other Elasticities 1.3.1 Cross-price elasticity: Substitutes and complements 1.3.2 Income elasticity: Normal and inferior goods 1.4 Market Equilibrium and Consumer and Producer Surplus 1.4.1 Equilibrium price and quantity determination 1.4.2 Calculating consumer and producer surplus 1.4.3 Welfare economics: Maximizing total surplus 1.5 Market Disequilibrium and Changes in Equilibrium 1.5.1 Effects of shifts in supply and demand 1.5.2 Price floors (e.g. minimum wage) and price ceilings (e.g. rent control) 1.6 Effects of Government Intervention in Markets 1.6.1 Taxes: Impact on consumers, producers and deadweight loss 1.6.2 Subsidies: Benefits and inefficiencies 1.6.3 Quantity controls (e.g. quotas) 1.7 International Trade and Public Policy 1.7.1 Effects of imports and exports on domestic markets 1.7.2 Tariffs and quotas: Costs and benefits 1.7.3 Free trade vs. protectionism 1.8 Demand 1.8.1 Law of demand and reasons for downward slope 1.8.2 Determinants of demand: Income, tastes, prices of related goods 1.8.3 Normal vs. inferior goods 1.9 Supply 1.9.1 Law of supply and reasons for upward slope 1.9.2 Determinants of supply: Input costs, technology, expectations 1.9.3 Short-run vs. long-run adjustments 2.Imperfect Competition 2.1 Oligopoly and Game Theory 2.1.1 Collusion and cartels: Benefits and challenges 2.1.2 Characteristics of oligopolies: Few large firms, barriers to entry 2.1.3 Strategic behavior: Nash equilibrium and dominant strategies 2.2 Introduction to Imperfectly Competitive Markets 2.2.1 Comparison of market structures: Monopoly, oligopoly, monopolistic competition 2.2.2 Causes and implications of market power 2.3 Monopoly 2.3.1 Sources of monopoly power 2.3.2 Price-setting behavior and inefficiency 2.3.3 Graphical representation of monopoly pricing 2.4 Price Discrimination 2.4.1 Conditions for price discrimination 2.4.2 Examples of first, second, and third-degree price discrimination 2.5 Monopolistic Competition 2.5.1 Characteristics: Product differentiation and many sellers 2.5.2 Short-run profit and long-run equilibrium 2.5.3 Excess capacity and inefficiency 3.Factor Markets 3.1 Introduction to Factor Markets 3.1.1 Derived demand: Factors of production 3.1.2 Marginal product of labor (MPL) and capital 3.1.3 Value of marginal product (VMP) 3.2 Changes in Factor Demand and Supply 3.2.1 Determinants of factor demand: Productivity, prices of goods 3.2.2 Determinants of factor supply: Population, preferences 3.3 Profit-Maximizing Behavior in Factor Markets 3.3.1 Marginal revenue product (MRP) = Marginal resource cost (MRC) 3.3.2 Hiring decisions in competitive and imperfect markets 3.4 Monopsonistic Markets 3.4.1 Characteristics of monopsony 3.4.2 Wage determination and inefficiency 4.Market Failure and the Role of Government 4.1 Socially Efficient and Inefficient Market Outcomes 4.1.1 Allocative efficiency: Marginal benefit equals marginal cost 4.1.2 Causes of market failures: Externalities, public goods 4.2 Externalities 4.2.1 Positive externalities: Subsidies and government intervention 4.2.2 Negative externalities: Taxes, regulations, and tradable permits 4.2.3 Graphical analysis of externalities 4.3 Public and Private Goods 4.3.1 Characteristics: Excludability and rivalry 4.3.2 Free-rider problem and under-provision of public goods 4.4 Government Intervention in Different Market Structures 4.4.1 Regulation of monopolies: Price caps and subsidies 4.4.2 Antitrust policies: Promoting competition 4.5 Inequality 4.5.1 Measurement of income inequality: Lorenz curve and Gini coefficient 4.5.2 Causes of inequality: Education, skills, inheritance 4.5.3 Government redistribution policies 5.Production, Cost and the Perfect Competition Model 5.1 The Production Function 5.1.1 Relationship between inputs and outputs 5.1.2 Short-run vs. long-run production 5.1.3 Law of diminishing marginal returns 5.2 Short-Run Production Costs 5.2.1 Fixed variable and total costs 5.2.2 Marginal cost (MC), average total cost (ATC), and average variable cost (AVC) 5.2.3 Cost curves and their relationships 5.3 Long-Run Production Costs 5.3.1 Economies of scale, diseconomies of scale, and constant returns 5.3.2 Long-run average cost curve (LRAC) 5.4 Types of Profit 5.4.1 Accounting profit vs. economic profit 5.4.2 Normal profit and its role in resource allocation 5.5 Profit Maximization 5.5.1 MC = MR rule for maximizing profit 5.5.2 Loss minimization in the short run 5.6 Firms’ Short-Run Decisions 5.6.1 Shutdown decision: Comparing price to AVC 5.6.2 Sunk costs and decision-making 5.7 Perfect Competition 5.7.1 Characteristics of perfect competition 5.7.2 Short-run vs. long-run equilibrium 5.7.3 Efficiency of perfectly competitive markets 6.Basic Economic Concepts 6.1 Scarcity 6.1.1 Definition and examples of scarcity 6.1.2 Unlimited wants vs. limited resources 6.1.3 Implications for individuals and societies 6.2 Resource Allocation and Economic Systems 6.2.1 Types of systems: Command, market and mixed economies 6.2.2 How different systems address fundamental economic questions 6.2.3 Examples of real-world economies 6.3 Production Possibilities Curve (PPC) 6.3.1 Trade-offs and opportunity cost 6.3.2 Efficiency, inefficiency and unattainable points 6.3.3 Economic growth and shifts in the PPC 6.4 Comparative Advantage and Trade 6.4.1 Difference between absolute and comparative advantage 6.4.2 Specialization and mutual gains from trade 6.4.3 Calculation of opportunity costs 6.5 Cost-Benefit Analysis 6.5.1 Rational decision-making using marginal analysis 6.5.2 Marginal benefits vs. marginal costs 6.5.3 Applications to individual and business decisions 6.6 Marginal Analysis and Consumer Choice 6.6.1 Marginal utility and diminishing marginal returns 6.6.2 Optimal allocation of resources 6.6.3 Budget constraints and consumer equilibrium Get PDF PDF Share Explore How would you like to practise? 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https://medium.com/@ashwinpalo/how-to-calculate-thermal-efficiency-of-rankine-cycle-37a7dbcadc12
Sitemap Open in app Sign in Sign in How to Calculate Thermal Efficiency of Rankine Cycle Ashwin Palo | Performance Marketer 5 min readNov 23, 2018 Rankine Cycle: Before calculating Thermal Efficiency of Rankine cycle, let’s understand about Rankine Cycle. Rankine cycle is a theoretical cycle in which heat energy converts into work. Rankine Cycle is developed by William John Macquorn Rankine in the 19th century. It has been widely used across all kinds of steam engines. Roles 1–2: Work Done by Turbine 2–3: Heat Rejection in Cooling Tower 3–4: Pump 4–1: Heat Addition in Boiler Working Fluid in Rankine Cycle is water. Water goes through the following process in the Cycle. C-D, D-F, F-G, G-C are the defining process in Rankine Cycle. C-D Process: This is an isentropic process, where water is pumped from low pressure to high pressure with a Centrifugal Pump. This is a process where there is no change in entropy and water remains in liquid phase only. D-F Process: It happens inside a boiler. Water changes its phase from liquid to steam. F-G Process: The process occurs in Steam Turbine. The steam from the boiler enters the turbine and undergoes an isentropic-expansion process. The energy stored in water vapor converts to kinetic energy in the turbine. G-C Process: It is an Isobaric Compression process and happens in a Condenser. The phase change of the working fluid happens here from steam to water. Calculation of Thermal Efficiency of Rankine Cycle: Thermal Efficiency of Rankine Cycle: The thermal efficiency of the Rankine cycle is the ratio between the work produced by the steam turbine that has been reduced by the pump work, with the incoming heat energy from the boiler. The heat energy from the fuel is transferred to the working fluid i.e. water. The calorific value absorbed by water vapor can be calculated using the following formula: Qin = m (hF — hD) The superheated steam produced by the boiler then goes to the steam turbine. Heat energy from water vapor is then converted into kinetic energy, shown by the F-G line in the image above. The reduction of the enthalpy can be used to calculate the magnitude of the motion energy produced by the steam turbine using the following formula: Wout = m (hF — hG) The steam coming out from the steam turbine enters the condenser to be condensed back into liquid phase. Here the heat energy not converted into kinetic energy, because the energy is used to convert the water into steam (latent heat). The decreases of the enthalpy (G-C line) can be used to calculate the thermal energy of condensed water using the following formula: Qout = m (hG — hC) In the next process, the condensate water is pumped to the boiler to increase its pressure. Shown by the C-D line, water does not experience much increase in enthalpy. This means that the energy given to the air is not too significant. Incoming energy values can be calculated using the following formula: Win = m (hD — hC) So now we can calculate the thermal efficiency by using the formula below: Get Ashwin Palo | Performance Marketer’s stories in your inbox Join Medium for free to get updates from this writer. Thermal Efficiency = [(Work Output — Work input)/Heat entered into the system] Rankine cycle efficiency formula Thermal Efficiency = [(Work Output — Work input)/Heat entered into the system] Rankine Cycle Efficiency Rankine Cycle Efficiency = [m (hF — hG) — m (hD — hC) ] / [m (hF — hD)] Lets solve a Rankine Cycle Efficiency Problem 1. Identify Key Parameters: Turbine Inlet Temperature (T1): The temperature of the steam entering the turbine. Condenser Temperature (T2): The temperature of the steam exiting the turbine and entering the condenser. Boiler Pressure (P1): The pressure of the steam generated in the boiler. Condenser Pressure (P2): The pressure of the steam after condensation. 2. Determine Enthalpy Values: Use a steam table or online calculator to find the enthalpy values (h1, h2, h3, and h4) corresponding to the given temperatures and pressures at each stage of the cycle: h1: Enthalpy of steam at turbine inlet (P1, T1) h2: Enthalpy of steam at turbine outlet (P2, T2) h3: Enthalpy of water at condenser outlet (P2) h4: Enthalpy of water at boiler inlet (P1) 3. Calculate Net Work Output: Net work output (W_net) is the difference between the work done by the turbine and the work required by the pump: W_net = (h1 — h2) — (h4 — h3) 4. Calculate Heat Input: Heat input (Q_in) is the energy added to the water in the boiler to generate steam: Q_in = h1 — h4 5. Calculate Efficiency: Rankine cycle efficiency (η_Rankine) is the ratio of net work output to heat input: η_Rankine = W_net / Q_in = (h1 — h2 — h4 + h3) / (h1 — h4) 6. Express as a Percentage: Multiply the result by 100 to express efficiency as a percentage. Example: Assuming T1 = 500°C, T2 = 30°C, P1 = 10 MPa, and P2 = 0.1 MPa, and using typical steam table values: h1 = 3375 kJ/kg h2 = 2510 kJ/kg h3 = 125 kJ/kg h4 = 125 kJ/kg Efficiency = [(3375–2510–125 + 125) / (3375–125)] 100 = 25.54% Additional Notes: Actual efficiency values for real-world power plants are often lower due to irreversible losses and inefficiencies in components. Increasing the temperature and pressure at the turbine inlet, lowering the condenser pressure, or using superheated steam can all improve efficiency. The rankine cycle is the fundamental thermodynamic cycle for most steam power plants, including those used for electricity generation. 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https://www.keyence.it/ss/products/measure-sys/measurement-selection/environment/thermal-expansion.jsp
Temperatura e misurazione Dato che il volume di un oggetto cambia a causa della dilatazione termica, con le fluttuazioni di temperatura cambia la sua lunghezza. Pertanto, anche se due oggetti hanno le stesse caratteristiche, le lunghezze possono variare a seconda della temperatura al momento della misurazione. Il tasso di dilatazione termica varia anche a seconda del materiale, come indicato nella tabella seguente. Esempi di materiali e coefficienti di dilatazione termica | | | --- | | Materiale | Coefficiente di dilatazione termica × 10-6 | | Alluminio | 23 | | Ottone | 17,5 | | Polietilene | 100 - 200 | Quando si misura la lunghezza di un oggetto, è necessario considerare le condizioni della temperatura. L'Organizzazione internazionale per la normazione (ISO) ha stabilito che la temperatura di riferimento per la misurazione è di 20°C. Quando il target da misurare viene da un luogo con una temperatura diversa, in genere occorre lasciargli almeno un'ora di tempo perché si adatti alla nuova temperatura. Inoltre, se la temperatura al momento della misurazione non è di 20°C, è necessario calcolare l'errore ed effettuare le correzioni corrispondenti. La dilatazione termica non interessa solo il target da misurare. Si verifica anche nello strumento di misurazione. Pertanto, è necessario mantenere la temperatura di riferimento sia per il target da misurare che per lo strumento di misurazione. INDICE "Robusto e resistente ai cambiamenti ambientali" Sistema di misurazione dimensionale tramite immagini Serie IM-8000 Misurare automaticamente un pezzo con la semplice pressione di un pulsante. +39-02-668-8220 Home Gamma di prodotti KEYENCE ITALIA S.p.A. Codice fiscale e partita IVA 03932910965 Copyright (C) 2025 KEYENCE CORPORATION. All Rights Reserved.
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https://math.stackexchange.com/questions/823129/the-coordinate-axes-has-minimum-area
optimization - the coordinate axes has minimum area - Mathematics Stack Exchange Join Mathematics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 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Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more the coordinate axes has minimum area Ask Question Asked 11 years, 3 months ago Modified4 years, 7 months ago Viewed 2k times This question shows research effort; it is useful and clear 0 Save this question. Show activity on this post. How can i find the point in the first quadrant on the parabola y=4−x 2 y=4−x 2 such that the triangle tangent to the parabola at the point and the coordinate axes has minimum area. Some help to interpret the equation so minimize in this exercise i stuck i know how to calculate minima but i can't fin the equation to minimize. I tried but y=4−x 2 y=4−x 2 and the tangent is the derivative then i have d y/d x=−2 x d y/d x=−2 x and i stuck here.Thanx for you hints and help. optimization Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Follow Follow this question to receive notifications asked Jun 6, 2014 at 17:59 Rosa Maria Gtz.Rosa Maria Gtz. 3,886 3 3 gold badges 29 29 silver badges 57 57 bronze badges 1 You might want to rephrase the question to say, "...such that the right triangle in the first quadrant formed by the coordinate axes and the tangent line to the parabola" or something similar.heropup –heropup 2014-06-06 18:05:03 +00:00 Commented Jun 6, 2014 at 18:05 Add a comment| 3 Answers 3 Sorted by: Reset to default This answer is useful 1 Save this answer. Show activity on this post. ANSWER; At the point (a,b), using the equation of the parabola b=4−a 2 b=4−a 2 The equation of the tangent line is then y−b=−2 a(x−a)y−b=−2 a(x−a) y=b−2 a x+2 a 2 y=b−2 a x+2 a 2 Substituting the value of b from the first equation, y=4−a 2−2 a x+2 a 2=4+a 2−2 a x y=4−a 2−2 a x+2 a 2=4+a 2−2 a x For the point in X-axis,say (x 1,0)(x 1,0), 0=4+a 2−2 a x 1 0=4+a 2−2 a x 1 x 1=4+a 2 2 a x 1=4+a 2 2 a For the point in Y-axis, say (0,y 1)(0,y 1) y 1=4+a 2 y 1=4+a 2 Area of the triangle =1 2 x 1 y 1=1 2 x 1 y 1 Substituting the value of x 1,y 1 x 1,y 1 in terms of a A=(4+a 2)2 4 a A=(4+a 2)2 4 a Now set d A d a=0 d A d a=0 If you take the derivative using quotient rule, you get a=2 3–√a=2 3 and b=8 3 b=8 3 Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications edited Jun 6, 2014 at 18:37 answered Jun 6, 2014 at 18:30 Satish RamanathanSatish Ramanathan 12.5k 3 3 gold badges 20 20 silver badges 29 29 bronze badges 2 the area is A=(4+a 2)2 4 a A=(4+a 2)2 4 a ?Rosa Maria Gtz. –Rosa Maria Gtz. 2014-06-06 18:34:18 +00:00 Commented Jun 6, 2014 at 18:34 You are right. I will edit it Satish Ramanathan –Satish Ramanathan 2014-06-06 18:37:01 +00:00 Commented Jun 6, 2014 at 18:37 Add a comment| This answer is useful 1 Save this answer. Show activity on this post. So you calculated the derivative, which means you know the slope of the tangent line for some general x x-value. For a given point (x 0,y 0)(x 0,y 0) on this parabola (so in particular, y 0=4−x 2 0 y 0=4−x 0 2), what is the equation of the tangent line to this point? Next, given the equation of the tangent line, where does it intersect the x x- and y y-axes? This will give you the length of the two legs of the right triangle enclosed by the tangent line. Finally, what is the area of such a triangle as a function of the x x-coordinate of the point (x 0,y 0)(x 0,y 0)? How can you minimize this area? Share Share a link to this answer Copy linkCC BY-SA 3.0 Cite Follow Follow this answer to receive notifications answered Jun 6, 2014 at 18:08 heropupheropup 145k 15 15 gold badges 114 114 silver badges 201 201 bronze badges Add a comment| This answer is useful 0 Save this answer. Show activity on this post. Using similar triangles, it can be proven that the area of the triangle is twice the product x y x y where y=f(x)y=f(x). Maximizing x y x y will give you your answer. A=x y=x(4−x 2)=4 x−x 3 A=x y=x(4−x 2)=4 x−x 3 A′=0=4−3 x 2 A′=0=4−3 x 2 So x=2 3√x=2 3 Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Follow Follow this answer to receive notifications edited Mar 1, 2021 at 15:16 answered Oct 17, 2018 at 21:07 TurlocTheRedTurlocTheRed 6,586 1 1 gold badge 11 11 silver badges 17 17 bronze badges 4 How do you prove, "The area of the triangle is twice the product x y x y where y=f(x)y=f(x)?Kartal Tabak –Kartal Tabak 2021-02-06 21:02:47 +00:00 Commented Feb 6, 2021 at 21:02 I asked a separate question: math.stackexchange.com/questions/4015520/….Kartal Tabak –Kartal Tabak 2021-02-06 21:34:38 +00:00 Commented Feb 6, 2021 at 21:34 This answer has a correct calculation but a wrong explanation. You don't want to minimize x y.x y. You want to maximize x y.x y. It does happen to be true that once you find the maximum value of x y,x y, the area under the triangle tangent to the curve at (x,y)(x,y) will be 2 x y.2 x y. But at every other point on the curve the area of the triangle will be more than twice the product of the coordinates at the tangent point.David K –David K 2021-02-07 02:55:04 +00:00 Commented Feb 7, 2021 at 2:55 @KartalTabak, have something here: math.stackexchange.com/questions/4015695/…TurlocTheRed –TurlocTheRed 2021-03-03 17:17:00 +00:00 Commented Mar 3, 2021 at 17:17 Add a comment| You must log in to answer this question. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions optimization See similar questions with these tags. Featured on Meta Introducing a new proactive anti-spam measure Spevacus has joined us as a Community Manager stackoverflow.ai - rebuilt for attribution Community Asks Sprint Announcement - September 2025 Report this ad Linked 4The area between coordinate axes and tangent to f(x)f(x) is 2 x f(x)2 x f(x). Is this correct? 2A simple method to calculate minimal area enclosed between a tangent to f(x)f(x) and coordinate axes Related 0Find f with A plane curve whose equation is y−f(x)=0 y−f(x)=0 passes through the origin. 1Optimization problem? 1Maximisation: Half circle area inscribed within isoceles triangle? 1Find a tangent line through y=1−x 2 y=1−x 2 such that the triangle it forms has minimum area. 4Right triangle minimum area problem without calculus 0Finding area of largest rectangle between the axes and a line 2A simple method to calculate minimal area enclosed between a tangent to f(x)f(x) and coordinate axes 2Smallest possible area for triangle 1Maximizing area of a triangle from a parabola equation 0Maximum area of triangle Hot Network Questions Why do universities push for high impact journal publications? 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https://artofproblemsolving.com/wiki/index.php/1966_IMO_Problems/Problem_3?srsltid=AfmBOopPuFtYoHB6sZLg0AQwZT8mnywLLJSaMrUbC-soVAcBiQXJFylw
Art of Problem Solving 1966 IMO Problems/Problem 3 - AoPS Wiki Art of Problem Solving AoPS Online Math texts, online classes, and more for students in grades 5-12. Visit AoPS Online ‚ Books for Grades 5-12Online Courses Beast Academy Engaging math books and online learning for students ages 6-13. Visit Beast Academy ‚ Books for Ages 6-13Beast Academy Online AoPS Academy Small live classes for advanced math and language arts learners in grades 2-12. Visit AoPS Academy ‚ Find a Physical CampusVisit the Virtual Campus Sign In Register online school Class ScheduleRecommendationsOlympiad CoursesFree Sessions books tore AoPS CurriculumBeast AcademyOnline BooksRecommendationsOther Books & GearAll ProductsGift Certificates community ForumsContestsSearchHelp resources math training & toolsAlcumusVideosFor the Win!MATHCOUNTS TrainerAoPS Practice ContestsAoPS WikiLaTeX TeXeRMIT PRIMES/CrowdMathKeep LearningAll Ten contests on aopsPractice Math ContestsUSABO newsAoPS BlogWebinars view all 0 Sign In Register AoPS Wiki ResourcesAops Wiki 1966 IMO Problems/Problem 3 Page ArticleDiscussionView sourceHistory Toolbox Recent changesRandom pageHelpWhat links hereSpecial pages Search 1966 IMO Problems/Problem 3 Contents [hide] 1 Problem 2 Solution 3 Remarks (added by pf02, September 2024) 4 Solution 2 5 See Also Problem Prove that the sum of the distances of the vertices of a regular tetrahedron from the center of its circumscribed sphere is less than the sum of the distances of these vertices from any other point in space. Solution We will need the following lemma to solve this problem: Let be a regular tetrahedron, and a point inside it. Let be the distances from to the faces , and . Then, is constant, independent of . We will compute the volume of in terms of the areas of the faces and the distances from the point to the faces: because the areas of the four triangles are equal. ( stands for the area of .) Then This value is constant, so the proof of the lemma is complete. Let our tetrahedron be , and the center of its circumscribed sphere be . Construct a new regular tetrahedron, , such that the centers of the faces of this tetrahedron are at , , , and . For any point in , with equality only occurring when , , , and are perpendicular to the faces of , meaning that . This completes the proof. ~mathboy100 Remarks (added by pf02, September 2024) The text of the Lemma needed a little improvement, which I did. The Solution above is not complete. It considered only points inside the tetrahedron, but the problem specifically said "any other point in space". I will give another solution below, in which I will also fill in the gap of the solution above, mentioned in the preceding paragraph. Solution 2 We will first prove the problem in the 2-dimensional case. We do this to convey the idea of the proof, and because we will use this in one spot in proving the 3-dimensional case. So let us prove that: The sum of the distances of the vertices of an equilateral triangle from the center of its circumscribed circle is less than the sum of the distances of these vertices from any other point in the plane. We will do the proof in three steps: We will show that if is in one of the exterior regions, then there is a point on the boundary of the triangle (a vertex, or on a side), such that . Then we will show that if is on the boundary, then . For the final step, we will show that if is a point of minimum for inside the triangle, then the extensions of are perpendicular to the opposite sides . This implies that . If the point is outside the triangle, it can be in one of six regions as seen in the pictures below. If is in a region delimited by extensions of two sides of the triangle, as in the picture on the left, we notice that by taking , (because and as sides in an obtuse triangles, and similarly ). If is in a region delimited by a segment which is a side of the triangle and by the extensions of two sides, as in the picture on the right, take the foot of the perpendicular from to . Then (because the triangle is obtuse, and because the triangles are right triangles). Now assume that . A direct, simple computation shows that (indeed, if we take the side of the triangle to be , then , and ). Now assume that is on . If is not the midpoint of , let be the midpoint. Then (because and ). A direct, simple computation shows that (indeed, if we take the side of the triangle to be , and ). Assume that is inside the triangle . In this case, we make a proof by contradiction. We will show that if is a point where is minimum, then the extensions of are perpendicular to the opposite sides . (This statement implies that .) If this were not true, at least one of would be false. We can assume that is not perpendicular to . Then draw the ellipse with focal points which goes through . Now consider the point on the ellipse such that . Because of the properties of the ellipse, , and because of the definition of the ellipse . We conclude that , which contradicts the assumption that was such that was minimum. This proves the 2-dimensional case. NOTE: a very picky reader might object that the proof used that a minimum of exists, and is achieved at a point inside the triangle. This can be justified simply by noting that and quoting the theorem from calculus (or is it topology?) which says that a continuous function on a closed, bounded set has a minimum, and there is a point where the minimum is achieved. Because of the arguments in the proof, this point can not be on the boundary of the triangle, so it is inside. Now we will give the proof in the 3-dimensional case. We will do the proof in three steps. It is extremely similar to the proof in the 2-dimensional case, we just need to go from 2D to 3D, so I will skip some details. We will show that if is in one of the exterior regions, then there is a point on the boundary of the tetrahedron (a vertex, or on a edge, or on a side, such that . Then we will show that if is on the boundary, then . For the final step, consider the plane going through the edge perpendicular to the edge , the plane going through perpendicular to , the plane going through perpendicular to , etc. There are six such planes, and they all contain , the center of the circumscribed sphere. We will show that if is a point of minimum for inside the tetrahedron, then is in each of the six planes described above. This implies that . Let be in one of the exterior regions. Assume is in a prism shaped region delimited by extensions of three sides meeting in a vertex (there are 4 of them). Assume it is at vertex , the sides being the extensions of planes . Then take . We have because of obtuse triangles formed with . Now assume is in one of the wedge shaped regions, formed by an edge and the extensions of two sides going through them. (there are six such regions.) Assume this is the line and the extensions of . Then take to be the foot of the perpendicular from to . Again, we have the desired inequality because formed some right and obtuse triangles. Now assume is in the truncated prism region delimited by a side and the extensions of the faces going through the edges of this side. (There are four such regions.) Assume this is the side , and extensions of the sides . Then take to be the foot of the perpendicular from to the plane . Again, we have the desired inequality because of right and obtuse triangles formed by . Assume . If we take the edge of the tetrahedron to be , a direct computation gives us that , and . Assume is on . If is not the midpoint of , take to be the midpoint of . Then because of right triangles formed by . And, if we take the edge of the tetrahedron to be , a direct computation yields that , which is bigger than . Assume is on . If is not the circumcenter of then take to be the circumcenter. We have because . We also have because we proved the 2-dimensional analogue of the problem. And, if we take the edge of the tetrahedron to be , we have , which is bigger than . NOTE: In the above paragraph, we used that the similar result is true in the 2-dimensional case, with an equilateral triangle instead of a regular tetrahedron. NOTE: This part of the proof concludes filling in the gap in the first "Solution", written above. (A reader may complain that the proof in Solution 2 is very long (compared to the first "Solution"), but the first "Solution" should have done this too, one way or another.) Now consider the six planes going through one edge, perpendicular to the opposite edge. They intersect at the circumcenter of the tetrahedron. Assume is a point in the interior of the tetrahedron where achieves its minimum value. Then is in each of the six plane. Prove this statement by contradiction. Assume that there is a plane among the six, so that is not on it. Assume the plane is the one going through , perpendicular to . To make it more explicit, this is the plane going through , where is the midpoint of . Consider the ellipsoid with focal points going through . This can be obtained as the set of points in space so that . It can also be obtained as the surface obtained when we form the ellipse with focal points in the plane (as the set of points so that ), and we rotate this ellipse from the plane around its axis . Let be the foot of the perpendicular from to the plane . We have because . We also have because is in the interior of the ellipsoid. (Indeed, the intersection of the plane and the ellipsoid is the circle generated by rotating the ends of the small axis of the ellipse in the plane . Since the point is not on the plane CDE, it must be on a smaller circle, so its projection to the plane will be inside.) This concludes the proof of the problem. [Solution by pf02, September 2024] See Also 1966 IMO (Problems) • Resources Preceded by Problem 21•2•3•4•5•6Followed by Problem 4 All IMO Problems and Solutions Retrieved from " Categories: Olympiad Geometry Problems 3D Geometry Problems Art of Problem Solving is an ACS WASC Accredited School aops programs AoPS Online Beast Academy AoPS Academy About About AoPS Our Team Our History Jobs AoPS Blog Site Info Terms Privacy Contact Us follow us Subscribe for news and updates © 2025 AoPS Incorporated © 2025 Art of Problem Solving About Us•Contact Us•Terms•Privacy Copyright © 2025 Art of Problem Solving Something appears to not have loaded correctly. Click to refresh.
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https://wiki.sei.cmu.edu/confluence/display/java/MET07-J.+Never+declare+a+class+method+that+hides+a+method+declared+in+a+superclass+or+superinterface
MET07-J. Never declare a class method that hides a method declared in a superclass or superinterface - SEI CERT Oracle Coding Standard for Java - Confluence Skip to main content assistive.skiplink.to.breadcrumbs assistive.skiplink.to.header.menu assistive.skiplink.to.action.menu assistive.skiplink.to.quick.search Skip to sidebar")Skip to main contentSkip to breadcrumbsSkip to searchLog in Confluence Spaces Hit enter to search Help Online Help Keyboard Shortcuts") Feed Builder What’s new Available Gadgets About Confluence Log in SEI CERT Oracle Coding Standard for Java Pages Boards Space shortcuts Dashboard Secure Coding Home Android C C++ Java Perl Page tree MET00-J. Validate method arguments MET01-J. Never use assertions to validate method arguments MET02-J. Do not use deprecated or obsolete classes or methods MET03-J. Methods that perform a security check must be declared private or final MET04-J. Do not increase the accessibility of overridden or hidden methods MET05-J. Ensure that constructors do not call overridable methods MET06-J. Do not invoke overridable methods in clone() MET07-J. Never declare a class method that hides a method declared in a superclass or superinterface MET08-J. Preserve the equality contract when overriding the equals() method MET09-J. Classes that define an equals() method must also define a hashCode() method MET10-J. Follow the general contract when implementing the compareTo() method MET11-J. Ensure that keys used in comparison operations are immutable MET12-J. Do not use finalizers MET13-J. Do not assume that reassigning method arguments modifies the calling environment Rule 50. Android (DRD) Browse pages Configure Space tools Overview Content Tools Browse pages A t tachments (0)") Page History Page Information Resolved comments (0) View in Hierarchy View Source Export to PDF Export to Word Pages … SEI CERT Oracle Coding Standard for Java 2 Rules Rule 06. Methods (MET) Jira links MET07-J. Never declare a class method that hides a method declared in a superclass or superinterface Created by Dhruv Mohindra, last modified by David Svoboda on Aug 06, 2025 When a class declares a static method m, the declaration of m hides any method m', where the signature of m is a subsignature of the signature of m' and the declaration of m' is both in the superclasses and superinterfaces of the declaring class and also would otherwise be accessible to code in the declaring class (The Java Language Specification, §8.4.8.2 "Hiding (by Class Methods)" [JLS 2015]). An instance method defined in a subclass overrides another instance method in the superclass when both have the same name, number and type of parameters, and return type. Hiding and overriding differ in the determination of which method is invoked from a call site. For overriding, the method invoked is determined at runtime on the basis of the specific object instance in hand. For hiding, the method invoked is determined at compile time on the basis of the specific qualified name or method invocation expression used at the call site. Although the Java language provides unambiguous rules for determining which method is invoked, the results of these rules are often unexpected. Additionally, programmers sometimes expect method overriding in cases where the language provides method hiding. Consequently, programs must never declare a class method that hides a method declared in a superclass or superinterface. Noncompliant Code Example In this noncompliant code example, the programmer hides the static method rather than overriding it. Consequently, the code invokes the displayAccountStatus() method of the superclass, causing it to printAccount details for admin despite being instructed to chooseuser rather thanadmin. ? class``GrantAccess { `publicstaticvoiddisplayAccountStatus() {` `System.out.println("Account details for admin: XX"`); ``} } class``GrantUserAccess``extends``GrantAccess { `publicstaticvoiddisplayAccountStatus() {` `System.out.println("Account details for user: XX"`); ``} } public``class``StatMethod { `publicstaticvoidchoose(String username) {` `GrantAccess admin =new`GrantAccess(); `GrantAccess user =new`GrantUserAccess(); `if(username.equals("admin")) {` ``admin.displayAccountStatus(); `}else`{ ``user.displayAccountStatus(); ``} ``} `publicstaticvoidmain(String[] args) {` `choose("user"`); ``} } Compliant Solution In this compliant solution, the programmer declares the displayAccountStatus() methods as instance methods by removing the static keyword. Consequently, the dynamic dispatch at the call sites produces the expected result. The @Override annotation indicates intentional overriding of the parent method. ? class``GrantAccess { `publicvoid`displayAccountStatus() { `System.out.print("Account details for admin: XX"`); ``} } class``GrantUserAccess``extends``GrantAccess { ``@Override `publicvoid`displayAccountStatus() { `System.out.print("Account details for user: XX"`); ``} } public``class``StatMethod { `publicstaticvoidchoose(String username) {` `GrantAccess admin =new`GrantAccess(); `GrantAccess user =new`GrantUserAccess(); `if(username.equals("admin")) {` ``admin.displayAccountStatus(); `}else`{ ``user.displayAccountStatus(); ``} ``} `publicstaticvoidmain(String[] args) {` `choose("user"`); ``} } The methods inherited from the superclass can also be overloaded in a subclass. Overloaded methods are new methods unique to the subclass and neither hide nor override the superclass method [Java Tutorials]. Technically, a private method cannot be hidden or overridden. There is no requirement that private methods with the same signature in the subclass and the superclass bear any relationship in terms of having the same return type or throws clause, the necessary conditions for hiding [JLS 2015]. Consequently, hiding cannot occur when private methods have different return types or throws clauses. Exceptions MET07-J-EX0: Occasionally, an API provides hidden methods. Invoking those methods is not a violation of this rule provided that all invocations of hidden methods use qualified names or method invocation expressions that explicitly indicate which specific method is invoked. If the displayAccountStatus() were a hidden method, for example, the following implementation of the choose() method would be an acceptable alternative: ? public``static``void``choose(String username) { `if(username.equals("admin")) {` ``GrantAccess.displayAccountStatus(); `}else`{ ``GrantUserAccess.displayAccountStatus(); ``} } Risk Assessment Confusing overriding and hiding can produce unexpected results. | Rule | Severity | Likelihood | Detectable | Repairable | Priority | Level | --- --- --- | Rule | Severity | Likelihood | Detectable | Repairable | Priority | Level | | MET07-J | Low | Unlikely | Yes | No | P2 | L3 | Automated Detection Automated detection of violations of this rule is straightforward. Automated determination of cases in which method hiding is unavoidable is infeasible. However, determining whether all invocations of hiding or hidden methods explicitly indicate which specific method is invoked is straightforward. | Tool | Version | Checker | Description | --- --- | | Tool | Version | Checker | Description | | Parasoft Jtest | 2024.2 | CERT.MET07.AHSM | Do not hide inherited "static" member methods | Bibliography [Bloch 2005]Puzzle 48, "All I Get Is Static" [Java Tutorials]Overriding and Hiding Methods [JLS 2015]§8.4.8.2, "Hiding (by Class Methods)" met android-applicable android exportable-c++ rule 11 Comments David Svoboda Could use more NCCE/CCE pairs. One should demonstrate a private method being hidden (not overridden) by an identical method in a subclass. Permalink Aug 19, 2008 1. Dhruv Mohindra While it is certainly permissible to have a private method as hidden in a subclass, would it result in any vulnerability? For one, main() or anyone who instantiates the objects would not be able to invoke either methods as they would be invisible. If it does result in some unexpected behavior, I can add it as a separate example. Thanks. Permalink Dec 20, 2008 1. Thomas Hawtin The overridden method must also be accessible to the override method. Private methods are never overriden even using nested classes. This is different from C++, where private "template functions" can be overriden. Default access (package-private) methods may not be overriden by classes outside of the package. Exception specifications are not considered by the verifier, unlike javac. Permalink Dec 21, 2008 1. Dhruv Mohindra I agree. According to JLS section 8.4.6.3 (Requirements in Overriding and Hiding) - "Note that a private method cannot be hidden or overridden in the technical sense of those terms. This means that a subclass can declare a method with the same signature as a private method in one of its superclasses, and there is no requirement that the return type or throws clause of such a method bear any relationship to those of the private method in the superclass." So technically the subclass method has no relationship with the superclass method and thus it is not the case of "hiding" either. Permalink Dec 21, 2008 David Svoboda The NCCE/CS pair seems to be indicating that static functions in derived classes hide, rather than override, static functions in base classes. I'll grant that private methods cannot be hidden or overridden. However, I still wish this rec had more NCCE/CS pairs to demonstrate overriding vs. hiding. Is there any other way to hide base methods in Java? C++ has the rec VOID OOP02-CPP. Do not hide inherited non-virtual member functions. Since Java lacks 'non-virtual' members, this would not make a good Java rule. Permalink Feb 08, 2010 1. Dhruv Mohindra In addition, hiding is allowed for variables but this guideline talks about overriding vs hiding so it won't fit. Currently, I am unaware of other examples. I took a peek at the C++ rule and it seems to be suggesting that hiding should be avoided as it causes confusion (our friendly programmer expected overriding to occur). IIRC, hiding methods is usually not considered too sinful (@Override before an overridden method should also help clarify the intent), though hiding fields is not recommended. Permalink Mar 15, 2009 Dean Sutherland Reworded to make the rule normative. We now say "don't do it", but permit a limited exception for the few cases where hiding is required. Furthermore, all but the "hiding is required" part appear easy to check in a tool. Permalink Apr 08, 2011 1. Yitzhak Mandelbaum I find the exception somewhat confusing. It relates to client behavior, but the rule relates to API-developer behavior. Permalink Jan 18, 2012 DEEPAK KUMAR GUPTA A static method (class method) cannot be overridden in Java but if a static method defined in the parent class is redefined in a child class, the child class's method hides the method defined in the parent class. This mechanism is calledmethod hiding in Javaorfunction hiding. Permalink May 07, 2019 Ioannis Kostaras Even though this rule seems a good catch, nowadays IDEs provide hints that static methods and attributes should be called by the class and not by an instance, i.e. if (username.equals("admin")) { GrantAccess.displayAccountStatus();} else { GrantUserAccess.displayAccountStatus();} as static methods and attributes belong to the class not to an instance. Permalink Jan 16, 2020 1. David Svoboda You might have an espacially vigilant IDE, but we have to assume that some people have nothing more than their compiler and a bare-bones text editor, which will not catch such errors. 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https://www.shopify.com/retail/product-pricing-for-wholesale-and-retail
How to Calculate Wholesale Pricing: Profit Margin & Formulas (2025) - Shopify Skip to Content Log in Start for free Start for free Blog Menu Search Type something you're looking for Overview Manage Inventory Open Store Latest More Profitability Payments & Checkout Merchandising & Store Layout Store Management Marketing See All topics Start for free Solutions Start Start your business. Build your brand Create your website. Online store editor Customize your store. Store themes Find business apps. Shopify app store Own your site domain. Domains & hosting Explore free business tools. Tools to run your business Sell Sell your products. Sell online or in person Check out customers. World-class checkout Sell online. Grow your business online Sell across channels. Reach millions of shoppers and boost sales Sell in person. Point of Sale (POS) Sell globally. International sales Sell wholesale & direct. Business-to-business (B2B) Accept online payments. 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Start free trialTalk to sales blog|Profitability How to Calculate Wholesale Pricing: Profit Margin & Formulas (2025) Learn how to calculate wholesale pricing and steps you can take to create successful pricing strategies for your wholesale products. by Alexis Damen Published on May 8, 2025 On this page On this page What is wholesale pricing? How to calculate wholesale prices Wholesale pricing methods Tips to set wholesale prices How to calculate wholesale prices FAQ Unify online and in-person sales today. For free. Talk to sales Starting a wholesale business is a great way to move lots of products with little effort, at least theoretically. But wholesale pricing is a huge obstacle you’ll need to overcome. If the price is too high, you lose potential customers. If the price is too low, you’ll have little or no profit left to reinvest in your business. Every retailer, at one time or another, has wrangled with the issue of product pricing, especially those who sell products wholesale. If you’ve struggled with this question lately, you’re not alone. In this guide, learn how to calculate wholesale pricing and some steps you can take to create successful pricing strategies for your product. Click here to start selling with Shopify What is wholesale pricing? Wholesale pricing is what you charge retailers who buy products in large volumes. Product prices are cheaper than retail because wholesalers rely on economies of scale to make money. The goal of wholesale pricing is to earn a profit by selling goods at a higher price than what they cost to make. For example, if it costs you $5 in labor and materials to make one product, you may set a wholesale price of $10, which gives you a $5 per unit gross profit. Wholesale vs. retail pricing Wholesale and retail are two fundamentally different processes. Wholesale involves moving goods from manufacturing to distribution, and retail involves acquiring and selling goods to customers. Producers or distributors charge retailers wholesale prices. Then, the retailer charges consumers for that same product at a higher price—the retail price. In retail, profit margins are typically higher, though it usually takes more work and money to make a sale. Comparatively, wholesale might have smaller profit margins, but you’re selling bulk quantities—so it’s less effort to sell 100 units wholesale than to sell 100 units direct-to-consumer. But it’s also less profitable. Save wholesale price lists in the same platform that powers your DTC business with Shopify. How to calculate wholesale price 1. Research your market Before you set any product prices, determine your market segment and where you fit in. For example, are you a discount brand, a contemporary brand, or a designer brand? This also determines how your audience perceives you. Similarly, if your target customers are more budget-conscious or looking for a high-quality, high-end product, consider these factors when conducting market research. Most customers expect to pay a premium for higher-quality products. If a lower price point is your competitive advantage against other wholesalers, keep that in mind while researching. Be cognizant of your break-even point. Use the break-even point formula to calculate this number. Tip:Retail pricing analytics let you settle on an optimal product price that maximizes profits while remaining competitive in the market. Shopify gives you these tools with native analytics. View inventory, customer, and order data from everywhere you sell—all in one place. 2. Calculate your production costs Cost of goods manufactured (COGM) is the total cost of making or purchasing a product, including materials, labor, and any additional costs necessary to get the goods into inventory and ready to sell, like shipping and handling. A product’s COGM can be determined with the following calculation: Total Material Cost + Total Labor Cost + Additional Costs and Overhead = Cost of Goods Manufactured 3. Set your profit margin Your target profit margin will help you determine how to price your product objectively. If you’re unsure how to do this, you can use Shopify’s wholesale price calculator. Play around with the numbers to see different scenarios. When you sell wholesale, you’re likely selling a higher quantity in each order, which allows you to sell the products at a lower price. Aim for between 15% and 50% profit margin for each product to ensure you make money after accounting for expenses. Calculate your wholesale profit margin with Shopify’s free calculator. 4. Consider additional costs While you might make $2 profit per item, it might cost you more than $2 in overhead to sell that item—in which case you’ll need to adjust your wholesale pricing to make more profit. To factor these additional costs into your wholesale price calculation, you’ll need to know your costs of goods sold (COGS) and your overhead costs. These include rent, customer acquisition costs (CAC), utilities, and fees to run your online store. Calculate your cost of goods sold and the sum of any overhead costs. Once you have those two numbers, combine them to create your cost price for the wholesale price formula. 5. Use the wholesale pricing formula Profit margin is a retailer's gross profit when an item is sold. The higher this is, the better—but wholesalers have a shorter ceiling to add profit. They make their money by selling cheaper products in bulk. When setting your wholesale price, first multiply your cost of goods by two. This will ensure your wholesale profit margin is at least 50%. B2B customers that buy your wholesale products will add their markup when selling them through retail. Apparel retail brands, for example, typically aim for a 30% to 50% wholesale profit margin, while direct-to-consumer retailers aim for a profit margin of 55% to 65%. Wholesale pricing methods and examples Many different wholesale pricing strategies are available, but don’t fret—it’s not helpful to learn all of them if you’re new to selling wholesale. Instead, here are a few simple and easy-to-use methods you can use today. Keystone pricing method The Keystone pricing method is fairly straightforward. It involves setting the retail price of a product at double the wholesale price—essentially, the retail price is 100% markup over the wholesale cost. Here’s the formula to calculate wholesale prices: Wholesale Price = Retail Price / 2 This is arguably the most straightforward wholesale pricing approach you can take. It’s simple retail math and doesn’t depend on any advanced calculations. However, Keystone pricing doesn’t account for factors like competition, demand, or perceived value. This approach may not always provide enough profit margin to cover operating expenses and generate profits. You also need to know the end retail price before you can set the wholesale price, which limits your buyers to how they can price your products for their customers. Absorption pricing method Absorption pricing refers to factoring in all the associated costs, including fixed costs and profit margins, when determining your price. It’s called “absorption” because all the costs are consumed in the product’s final price. The formula for absorption wholesale pricing is as follows: Wholesale Price = Cost Price + Profit Margin This wholesale strategy is easy to use and requires no training or complicated formulas. Your profits are almost guaranteed. If you can account for all expenses, you’ll likely turn a good profit. However, pricing gaps are frequent. The formula also doesn’t consider any competitor’s pricing or value perception. You could charge too much, sending potential buyers to other providers. Differentiated pricing method Differentiated pricing is a wholesale pricing method that optimizes return on investment (ROI) by calculating the demand for a product. In this case, different buyers pay different prices for the same product in different situations. It’s based on the idea that buyer acceptance determines the price on any given market condition. Also known as demand pricing, you can sell seasonal items at a higher price than the average market value during peak seasons. For example, the price of bathing suits can rise quickly at the beginning of the summer season, and then come back down after the demand drops. This also applies to areas with less competition where customers typically buy products at a higher price, such as a beach resort or an airport. The differentiated wholesale pricing method can deliver maximum ROI. It takes advantage of market scenarios in real time, keeps you competitive, and allows you to gain data on buyers. Plus, when there’s higher demand for a product, buyers are often willing to pay a premium, which means more profit for you. However, there’s a fine line between maximizing profit and overcharging wholesale customers. If you’re perceived as opportunistic or people get the sense you’re price gouging them, it’ll hurt your brand’s reputation. You don’t want to be associated with this kind of greed because buyers won’t return. 💡Tip:Analyze customer behavior by unifying what you’ve already collected into a single unified commerce platform. Shopify is the only platform to natively build POS, ecommerce, and B2B on the same platform, giving you a centralized business “brain” to make smarter pricing decisions based on data—not guesswork. Use Shopify Analytics to view sales, inventory, and customer data from everywhere you sell. Tips to set wholesale prices Set a manufacturer's suggested retail price A suggested retail price (SRP), also known as a manufacturer’s suggested retail price (MSRP), is the price a manufacturer or wholesaler recommends retailers set for their product. It prevents resellers from undercutting you or your other retail partners. Calculate your recommended retail price using this formula formula: Wholesale Price / (1 - Markup Percentage) = Retail Price Research your market to see how other comparable brands or retailers set their prices. Then, you can work backward to see if your target retail price is feasible based on the costs you incur to produce your products. For example, if your target retail price is $60 and you want to give your wholesalers a 55% retail margin and yourself a 50% wholesale margin, you can use this pricing formula to work backward and calculate the wholesale price: $60 (Retail Price) x (1 - 0.55) = $27 (Wholesale Price) Consider a dual pricing strategy A dual pricing strategy means you’ll create an external retail price for your products listed on your website that your direct customers see, and a separate wholesale price you share with B2B customers. It ensures that you’ll still profit regardless of where you sell. Here’s where the formulas come in handy. You can do the math to determine your margins and set wholesale and suggested retail prices for your products. For example, if you design and manufacture swimsuits and sell them via wholesale and retail, you’ll need to look at the following numbers: COGS: $15 to make one swimsuit Wholesale price: $30 SRP: $75 Then, you’ll be able to calculate your wholesale and retail margin percentages: Your wholesale margin: 50% Wholesale Margin = $30 Wholesale - $15 COG / $30 Wholesale The retailer’s margin when they use your SRP: 60% Retail Margin = $75 Retail - $30 Wholesale / $75 Retail Your retail margin when you sell DTC: 80% Retail Margin = $75 Retail - $15 COG / $75 Retail With the above wholesale and retail pricing strategy, you’re making a gross profit margin of 50% on your wholesale orders and 80% on DTC orders. 💡 Pro tip:Shopify merchants can create a B2B storefront from the same commerce platform that powers their ecommerce store and retail stores. Unify your inventory, customer, and order data to get one single source of truth—no matter where you’re selling (and who to). Unify your wholesale and retail operations to reduce costs New research shows retailers using unified commerce platforms see 22% lower total cost of ownership and more efficient inventory management across sales channels. Learn how connecting your wholesale and retail operations can improve your bottom line. Get the report Think about sales volumes When setting your wholesale prices, consider how much your retailer customers order. Lower wholesale prices for bulk orders can incentivize large customers. On the other hand, if you anticipate smaller order volumes, you may need to adjust your wholesale prices to maintain profitability. Strategically align your pricing with expected sales volumes to balance competitive pricing and sustainable profit margins. Minimum order quantities come into use if you need to sell a specific number of products to turn a profit. That might mean a minimum order quantity of 50 units—wholesalers must exceed this threshold to place an order. 💡Tip:Use Shopify’s B2B commerce functionality to set MOQs for wholesale customers who self-serve through your online storefront. Review wholesale prices regularly New competitors, cost-effective suppliers, and fluctuations in customer demand can all impact your wholesale pricing strategy. That’s why it’s important to regularly audit and review your wholesale prices to ensure profitability and maintain a competitive edge. Remember to consider the cost of everything that goes into your products, as production costs can also change on a regular basis. Manage wholesale pricing with Shopify Now that you better understand the formulas used to calculate product pricing, it’s time to build your own wholesale pricing strategy. Use the formulas above to create a costing chart you can plug numbers into each time you need to define pricing for a new product. You’ll be able to calculate financial metrics like the cost of goods, wholesale price, wholesale margin, retail price, and retail margin. Shopify’s unified commerce platform makes selling wholesale and DTC from the same operating system easier than ever. Create a password-protected storefront to show your wholesale price lists for approved B2B buyers through their account login, using the same inventory data that powers your DTC storefront. “On Shopify Plus, our team has the liberty and the space to build relationships with customers, instead of just transacting with them,” says Nicolas Lukac, director of emerging channels at Brooklinen. “We spend more time understanding our customers and less on manual inputs. This allows us to provide exceptional experiences for our DTC, B2B customers and retail customers alike.” Instant demo: See Shopify POS in action Discover how Shopify POS helps you manage in-store and online sales from one powerful platform. Watch now Read more 20 Best Mobile Retail Apps to Seamlessly Run Your Store What is an EPOS System and How Does it Work? How to Build a Brand Story for Your Retail Store in 2024 What Is Inventory Management? How to Manage and Improve Stock Flow Pop-Up Shop Ideas: 19 Examples from Real-World Retailers How to Build Your Own Homemade Business With Craft Kits The Future of Payments: How Credit Card Processing Works How to Calculate Retail Conversion Rate: +7 Tips How Retailers Can Create and Execute a Wholesale Strategy Vision Board for Business: Use This Creative Tool to Accomplish Your New Year’s Resolutions How to calculate wholesale price FAQ What is the formula for wholesale price? Here’s the easiest formula to calculate wholesale prices: Wholesale price = Cost of goods + Desired wholesale margin. What is the wholesale price method? The wholesale price method takes your break-even point into account. Add up your total costs and business expenses, and multiply this figure by your desired profit margin to calculate wholesale prices. What is a good wholesale profit margin? A good wholesale profit margin is anywhere from 15% to 50%. Retailers tend to add their markup (between 35% and 65%) when reselling wholesale items to their customers. What is the best pricing strategy for wholesalers? The Keystone method is the simplest pricing strategy for wholesalers. It sets the wholesale price as 50% of the retail price. What is the difference between wholesale and retail price? Retailers set retail pricing and is the final selling price for customers. Wholesale prices are typically much lower than retail prices because retailers are offered a discount in exchange for agreeing to purchase a large amount of product. by Alexis Damen Published on May 8, 2025 Share article Facebook Twitter LinkedIn by Alexis Damen Published on May 8, 2025 Grow your retail business Get exclusive behind-the-scenes merchant stories, industry trends, and tips for creating standout brick-and-mortar experiences. Enter email Subscribe Subscribe No charge. Unsubscribe anytime. popular posts Open a Retail StoreGoogle Trends Products: Trending Products To Sell in 2024ProfitabilityHow to Price Wholesale & Retail Products (2024)Inventory ManagementWhat Is a SKU Number? How To Use Stock Keeping UnitsOpen a Retail StoreHow To Make Soap: Step-By-Step Guide on Making and Selling Soap (2024) The point of sale for every sale. Explore Shopify POS popular posts Payments & CheckoutCash on Delivery: What Is It and How Does It Work?Clicks to BricksPop-Up Shop Ideas: 15 Examples of Successful Shops (2024)Inventory ManagementInventory Management: Everything You Need to Know (2024)Merchandising & Store LayoutImpulse Buying: Why We Do It & 9 Ways to Encourage It popular posts Open a Retail Store Google Trends Products: Trending Products To Sell in 2024 2023-03-01 Profitability How to Price Wholesale & Retail Products (2024) 2022-03-16 Inventory Management What Is a SKU Number? How To Use Stock Keeping Units 2023-12-01 Open a Retail Store How To Make Soap: Step-By-Step Guide on Making and Selling Soap (2024) 2023-11-28 Payments & Checkout Cash on Delivery: What Is It and How Does It Work? 2023-10-27 Clicks to Bricks Pop-Up Shop Ideas: 15 Examples of Successful Shops (2024) 2023-07-27 Inventory Management Inventory Management: Everything You Need to Know (2024) 2023-12-04 Merchandising & Store Layout Impulse Buying: Why We Do It & 9 Ways to Encourage It 2023-01-10 Grow your retail business Get exclusive behind-the-scenes merchant stories, industry trends, and tips for creating standout brick-and-mortar experiences. Email here Subscribe Subscribe No charge. Unsubscribe anytime. Sell anywhere with Shopify Learn on the go. Try Shopify for free, and explore all the tools you need to start, run, and grow your business. 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https://www.boredteachers.com/post/riddles-for-students
We value your privacy This website or its third-party tools process personal data. You can opt out of the sale of your personal information by clicking on the “Do Not Sell or Share My Personal Information” link. Skip to main content Classroom Ideas Mar 27 10 minutes read Classroom Ideas 100 Riddles for the Classroom Your Students Will Love! by Sara Ipatenco Riddles are a great way to add some laughter and humor to your school day, but riddles can serve an ever bigger purpose. When students hear riddles, they will begin to make associations, link what they are learning in the classroom, and come to conclusions about things they already know. For example, a riddle about the moon might connect something your students are learning about in science class. Even if your riddles aren’t educational, the simple experience of laughter will increase joy in the classroom, and joyful students are more likely to enjoy school and become deeply engaged in their learning. Here are 100 riddles for students to help get you started! What has a face, but can’t smile. Answer: A clock. There is only one word spelled wrong in the dictionary. What is it? Answer: W-R-O-N-G. I can fill up a room, but take no space. What am I? Answer: Light. What is a bunny’s favorite kind of music? Answer: Hip hop music. What kind of room has no doors or windows? Answer: A mushroom. What can you catch, but not throw? Answer: A cold. What begins with T, finishes with T, and has T in it? Answer: A teapot. What goes up, but never comes back down? Answer: Your age. What is brown, has a head, and tails, but no legs? Answer: A penny. What room do ghosts avoid? Answer: The living room. What belongs to you, but other people use more? Answer: Your name. What gets wetter the more it dries? Answer: A towel. What is bright orange with a green top and sounds like a parrot? Answer: A carrot. What two things can you never eat for breakfast? Answer: Lunch and dinner. You buy me to eat, but you never eat me. What am I? Answer: A fork. The more you take, the more you leave behind. What am I? Answer: Footprints. What kind of tree can you carry in your hand? Answer: A palm. What has four legs but can’t walk? Answer: A table. How many months have 28 days? Answer: All of them! What is full of holes but still holds water? Answer: A sponge. What has an eye but can’t see anything? Answer: A needle. What has a key, but can’t open a locked door? Answer: A monkey. What do dogs have that no other animal has? Answer: Puppies. What must be broken before you can use it? Answer: An egg. I am full of keys but I can’t open any doors. What am I? Answer: A piano. What kind of coat can only be put on wet? Answer: A coat of paint. The more you take away, the bigger it gets. What is it? Answer: A hole. What follows you everywhere but can’t be caught? Answer: Your shadow. What goes up and down but never moves? Answer: A flight of stairs. I have no eyes, ears, or legs, but I can help you move earth. What am I? Answer: An earthworm. What is as big as an elephant but weighs nothing? Answer: An elephant’s shadow. When does Friday come before Thursday? Answer: In the dictionary. If an electric train is going south, what direction is the smoke going? Answer: There is no smoke – it’s an electric train. Why do lions eat raw meat? Answer: Because they don’t know how to cook. How can a pants pocket be empty but still have something in it? Answer: If it has a hole in it. Why are teddy bears never hungry? Answer: Because they are already stuffed. Why is the Mississippi such an unusual river? Answer: Because it has four “i’s” and can’t even see. What bank never has any money? Answer: A riverbank. Why isn’t your nose 12 inches long? Answer: Because then it would be a foot. What kind of cup can’t hold anything to drink? Answer: A cupcake. What goes through towns and over hills but never moves? Answer: A road. What type of house weighs the least? Answer: A lighthouse. What has a lot of teeth but can’t chew a thing? Answer: A comb. What is the best place to grow a garden in school? Answer: In kindergarten. Why did the boy bury is flashlight? Answer: Because the batteries died. What building in a town has the most stories? Answer: The library. What falls in winter but never gets hurt? Answer: The snow. What kind of shower doesn’t need water? Answer: A baby shower. What has ears but cannot hear? Answer: A field of corn. A girl fell off a 25-foot ladder but didn’t get hurt. How? Answer: She fell off the bottom rung. I have no legs so I never walk, but I always run. What am I? Answer: A river. I am as light as a feather but even the strongest man can’t hold me for more than a minute. What am I? Answer: Breath. I am not alive, but I can still die. What am I? Answer: A battery. I will always come but never arrive today. What am I? Answer: Tomorrow. What can you easily break without touching it? Answer: A promise. What is the hardest part about skydiving? Answer: The ground. A king, a queen, and two twins are in a room. How are there no adults? Answer: They are beds. Every time you stand up you lose it. What is it? Answer: Your lap. I am bought by the yard but worn by the foot. What am I? Answer: Carpet. What kind of flower does everyone wear on their face? Answer: Tulips. What can travel the world while staying in the corner? Answer: A stamp. I’m tall when I’m young and short when I’m old. What am I? Answer: A candle. If everything in a one-story house is yellow, what color are the stairs? Answer: There are no stairs in a one-story house. I shave every day but my beard stays the same. How? Answer: I’m the barber. What can’t talk but will reply when spoken to? Answer: An echo. The more of me there is the less you can see. What am I? Answer: The dark. What is black when it’s clean and white when it’s dirty? Answer: A chalkboard. What has a lot of eyes but can’t see? Answer: A potato. What has a lot of needles but can’t sew? Answer: A Christmas tree. What has one head, one foot, and four legs? Answer: A bed. What kind of band can’t play music? Answer: A rubber band. What has a lot of words but never speaks? Answer: A book. What runs around your backyard but never moves? Answer: The fence. What has a thumb and four fingers but isn’t a hand? Answer: A glove. What always tastes better than it smells? Answer: Your tongue. What has four wheels and flies? Answer: A trash truck. You see me once in June, twice in November, and not at all in May. What am I? Answer: the letter E. A dog crossed a river without a bridge or a boat, but didn’t get wet. How? Answer: The river was frozen. What has lakes with no water, mountains with no stones, and cities with no buildings? Answer: A map. What do dogs and trees have in common? Answer: Bark. I can travel up to 100 miles an hour but never leave the room. What am I? Answer: A sneeze. I am always running but I never get tired. What am I? Answer: The refrigerator. I have seven rings that you can’t wear on your fingers. What am I? Answer: Saturn. I can be 100 yards long but you can hold me in your hand. What am I? Answer: A ball of yarn. What is really easy to get into but really hard to get out of? Answer: Trouble. What can be full without eating a thing? Answer: The moon. What can you taste everyday but never eat? Answer: Toothpaste. A boy throws a ball as far as he can and it comes back to him without anyone touching it. How? Answer: He throws the ball straight up. What five letter gets shorter when you add two letters to it? Answer: Short. If a rooster is sitting on top of a barn and lays an egg, which way will it roll off? Answer: Roosters don’t lay eggs! Which weighs more: a pound of bricks or a pound of feathers? Answer: They both weight a pound. I am an odd number, but if you take away a letter I am even. What number am I? Answer: Seven. Where is the ocean the deepest? Answer: On the bottom. What word has 26 letters but only three syllables? Answer: Alphabet. Grandpa went for a walk in the rain with no umbrella but his hair didn’t get wet. How is that possible? Answer: Grandpa is bald. I am always in front of you and never behind you. What am I? Answer: The future. What starts with P, ends with E, and has over a thousand letters in it? Answer: The post office. What do you find at the end of the rainbow? Answer: The letter W. What has a tongue but cannot talk? Answer: A shoe. I can run even though I have no legs. What am I? Answer: Your nose. A riddle a day will keep your classroom joyful and ready to learn new things! Enjoy watching your students figure out these riddles and enjoy their laughter when they do. Have some riddles you want to share with other educators? Come join the comversation in the Empowered Teachers community! 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https://eyewiki.org/Gonioscopy
Please note: This website includes an accessibility system. Press Control-F11 to adjust the website to people with visual disabilities who are using a screen reader; Press Control-F10 to open an accessibility menu. Popup heading Create account Log in Page Discussion View form View source View history Gonioscopy From EyeWiki Jump to:navigation, search All content on Eyewiki is protected by copyright law and the Terms of Service. This content may not be reproduced, copied, or put into any artificial intelligence program, including large language and generative AI models, without permission from the Academy. Article initiated by: Michael D. Greenwood, MD, Shipra Gupta, MD All contributors: Michael D. Greenwood, MD, Ahmad A. Aref, MD, MBA, Carla J. Siegfried, MD, Koushik Tripathy, MD (AIIMS), Dr John Davis Akkara (MBBS, MS, FAEH, FMRF, FAICO), Leonard K. Seibold, MD, Anne Strong Caldwell Assigned editor: Leonard K. Seibold, MD Review: Assigned status Update Pending by Leonard K. Seibold, MD on October 4, 2024. | | | add | | Contributing Editors: | add | Contents 1 History 2 How to Perform Gonioscopy 3 Lenses 3.1 Direct gonioscopy 3.2 Indirect gonioscopy 4 Procedure 4.1 Indirect Gonioscopy 4.2 Dynamic Gonioscopy 4.3 Direct Gonioscopy 4.4 Anatomical Structures of the Normal Angle 4.4.1 Schwalbe’s Line 4.4.2 Trabecular Meshwork 4.4.3 Schlemm’s Canal 4.4.4 Scleral Spur 4.4.5 Ciliary Muscle Band 4.4.6 Iris Root and Iris 4.5 Grading Systems 4.5.1 Scheie 4.5.2 Shaffer 4.5.3 Spaeth 4.5.3.1 Iris Insertion 4.5.3.2 Iris Angularity 4.5.3.3 Iris Configuration 4.5.3.4 Pigmentation 4.5.4 Becker 4.5.5 Shaffer-Kanski 4.5.6 Van Herick 5 Documentation 6 Other Uses of Gonioscopy 7 References History Gonioscopy was first described in the early 1900s. The Greek ophthalmologist, Alexios Trantas, used the word “gonioscopy”, with the Greek root “gonia” meaning “angle” and “skopein” to “observe.” He described the anterior chamber angle using a direct ophthalmoscope and simultaneous digital pressure on the limbal region. Years later Maximilian Salzmann was the first to use a contact lens and indirect gonioscopy for examination of the angle. Today, both are regarded as the “fathers of gonioscopy”. Today, gonioscopy is a critical exam technique used for visualizing the anterior chamber angle. Due to total internal reflectivity at the tear-air interface, the angle cannot be seen without a gonioscopy lens. Use of a contact gonioscopy lens allows light to pass through the tear-air interface and bounce off a mirror to the examiners eye. Visualization of the anterior chamber angle provides the clinician with critical diagnostic exam findings. There are many great resources available for learning gonioscopy. The website is a recommended starting point with excellent videos and narration. Today, there are many applications for gonioscopy. With the advent of Micro-invasive Glaucoma Surgeries (MIGS), intraoperative gonioscopy is required to visualize the angle and preoperative gonioscopy in the clinic is critical to identifying appropriate candidates for these procedures. Further, it is the standard of care to perform gonioscopy on every new glaucoma patient or glaucoma suspect to establish the status of the angle. Due to the discomfort of the exam, gonioscopy often needs to be performed during exams under anesthesia in children. How to Perform Gonioscopy Gonioscopy is usually performed at the slit lamp and requires application of a gonio lens to the surface of the eye. The eye should be numbed prior to beginning the examination. Prior to placing the lens on the eye, fill the concave aspect of the lens with a methylcellulose solution. Special care should be taken to avoid introducing bubbles into the fluid. To apply the lens to the eye, while the patient is looking up, the examiner should place the inferior aspect of the edge onto the inferior sclera. The patient should then be instructed to look forward, and the gonio lens should be tipped forward, making contact and a seal with the cornea. Gonioscopy should be performed in a relatively dark room. A brightly lit room will constrict the pupil, opening the angle, and possibly missing iridotrabecular contact (ITC) and apposition. Likewise, a shorter and less bright slit beam should also be used. Care should be taken to maintain only a light pressure on the lens as too much pressure versus slight pulling on the lens may cause artificial compression or expansion of the angle. Lenses Gonioscopy is required to visualize the chamber angle because under normal conditions light from the angle structures undergoes total internal reflection at the tear-air interface. To overcome this, a lens must be placed against the eye. Depending on the type of lens used, the angle can be examined either directly or indirectly. Direct gonioscopy Allows for direct visualization of the chamber angle. Examples of direct gonio lenses include Koeppe, Barkan, Wurst, Swan-Jacob, or Richardson lenses. During direct gonioscopy, the viewer has an erect view of the angle structures. Direct gonioscopy is most easily performed with the patient supine and in the operating room for an exam under anesthesia or a MIGS procedure. Indirect gonioscopy Examples of indirect gonioscopy lenses include the Posner, Sussman, Zeiss, and Goldmann lenses. These are more commonly used in the clinic setting. The viewer in indirect gonioscopy will have an inverted and slightly foreshortened image of the opposite angle because the light from the angle is reflected off a mirror and directed towards the viewer. The Posner, Sussman, and Zeiss lenses have a smaller area of contact than the Goldmann-type lenses. This allows the examiner to apply pressure to the cornea, which may cause Descemet’s membrane folds, and falsely open the angle. The examiner can also deepen the angle, which is discussed more below in the dynamic gonioscopy section. The Goldmann lens does not allow for this indentation because of the size of the lens. Procedure Indirect Gonioscopy As with any procedure, the patient and the examiner must be positioned in a comfortable fashion. A drop of topical anesthetic should be applied to the conjunctiva of both eyes. If using the Goldmann lens, contact gel is placed in the concave part of the lens. If using a Posner or similar type lens, a drop of artificial tears can be placed on the concave surface. The patient is then asked to open both eyes and look upwards. The examiner can then pull down slightly on the lower lid and places the lens on the surface of the eye. The patient is then asked to look straight ahead. Most examiners choose to start with the inferior angle as it is usually a bit more open, and the pigmentation of the trabecular meshwork is slightly more prominent, allowing for easier identification of the angle structures. Continue identifying all angle structures in all 4 quadrants, and then repeat with the other eye. Dynamic Gonioscopy In eyes with a closed angle, one must distinguish between an anatomically closed angle with iridotrabecular contact (ITC, apposition) and peripheral anterior synechiae (PAS). To perform dynamic or compression gonioscopy, you will need to be using either the Posner, Sussman, or Zeiss style lens. The patient is positioned as noted above. Gentle pressure is placed on the cornea, and aqueous humor is forced into the chamber angle. If there is ITC or apposition, the angle will open and the structures should become more visible. If PAS is present, the angle will stay the same in the affected areas. Examine all areas of the angle and repeat on the other eye. Direct Gonioscopy Direct gonioscopy is most easily performed with the patient in a supine position. It is commonly used in the operating room for examination of the eyes of infants under anesthesia. It is essential for performing goniotomies or other angle-based surgeries, including MIGS. It can be performed using a direct goniolens and either a binocular microscope or a slit-pen light. Examples of direct goniolenses include Koeppe, Barkan, Wurst, Swan-Jacob, or Richardson lenses. The lens is positioned after saline or viscoelastic is placed on the eye, which can act as a coupling device. The lens provides direct visualization of the chamber angle (ie, light reflected directly from the chamber angle is visualized) in an erect position. Anatomical Structures of the Normal Angle The most important part of gonioscopy is identification of the anatomical landmarks. There are many normal variations that one must be aware of. We will discuss these below, moving from most anterior to posterior. Schwalbe’s Line Schwalbe’s line is a condensation of collagen tissue and interfaces with the edge of Descemet’s membrane. Schwalbe’s line is an important landmark to identify because normal vessels and tissue will not cross it. Neovascularization or PAS may pass Schwalbe’s line anteriorly. A prominent Schwalbe’s line is also called a “posterior embryotoxon” and can be found in normal individuals. There is no increased risk of glaucoma in these eyes. Figure 1: Gonioscopy view of anterior chamber angle demonstrating a Sampaolesi line (arrow). Photo courtesty: Monica Ertel, MD, PHD. A Sampaolesi line is a defined as an abundance of pigment at Schwalbe's line. This is commonly seen in pigment dispersion syndrome or pseudoexfoliation (Figure 1). An important technique in identifying Schwalbe’s line is the corneal light wedge, which allows the observer to determine the exact junction of the cornea and trabecular meshwork. To perform this technique, the examiner must use a narrow slit beam. They will see 2 reflections, one on the external surface of the cornea and the other on the internal surface indicating the corneal epithelium and endothelium, respectively. Schwalbe’s line can be found where the 2 reflections intersect. Trabecular Meshwork The trabecular meshwork is an important pigmented landmark for diagnostic purposes, incisional surgery, and laser surgery. The amount of pigmentation may vary from person to person, and even from quadrant to quadrant. The amount of pigmentation should be included in the grading of an angle. Schlemm’s Canal Schlemm’s canal drains the aqueous humor after passing through the trabecular meshwork. It is only visible when there is blood in the canal. It is an important structure as many surgical procedures target this area, especially many of the new MIGS devices. Scleral Spur The scleral spur is comprised of a ridge of collagen tissue and appears white on gonioscopy. Identifying this structure helps to differentiate open angles from closed angles. It is possible for the scleral spur to be covered by small sharp-ended iris processes that reach up to the trabecular meshwork. They do not cross the trabecular meshwork and have no pathologic consequence. Ciliary Muscle Band The anterior ciliary body band can be seen in eyes with deeper angles. It represents the longitudinal fibers of the ciliary muscle. This is the site of nonconventional or suprachoroidal outflow and is also a landmark for newer surgical procedures. Iris Root and Iris The insertion of the iris is an important part of the classification of angle anatomy. The configuration of the peripheral iris is also important to note when studying angle structures. Pathology that exists in this part of the angle includes ITC or apposition and PAS, which should be noted. Figure 2: Gonioscopic view of superior angle with Trabeculectomy ostium and Peripheral iridectomy visible Grading Systems Gonioscopy grading systems were established to provide a standardized description of the anatomy of the anterior chamber angle. There are many grading systems used today. Scheie The Scheie system is based upon visibility of the anatomical structures of the angle. They are graded Wide followed by I through IV, with Wide being open with all structures visible, and IV being closed with no visible structures. See Table 1 for an in-depth description of the Scheie system. Table 1. The Scheie Classification System | Grade | Visibility | Interpretation | | Wide | Wide | Open, all structures visible | | I | Slightly Narrowed | Ciliary body visible, but recess obscured by the last roll of the iris | | II | Apex not visible | Ciliary body not visible | | III | Posterior half of trabecular meshwork not visible | Ciliary body, scleral spur, and posterior half of the trabecular meshwork not visible | | IV | None of the angle structures visible | Cliary body, scleral spur, and trabecular meshwok not visible | Shaffer The Shaffer system is based on angularity. It follows a numbers-based grading system using degrees of angularity. See Table 2 for detailed description of the Shaffer classification system. Table 2. The Shaffer Classification System | Angular Grade | Width (in degrees) | Grade | Clinical Interpretation | | Wide Open Angle | 45-35 | 4 | Angle closure impossible in both Grades 3 and 4 | | 35-20 | 3 | | Narrow Angle | 20 | 2 | Angle closure possible | | Narrow Angle, extreme | 10 or less | 1 | Angle closure probable, eventually | | Narrow Angle, slit | Critically narrowed angle, quite possibly against the trabecular meshwork beyond Schwalbe’s line - | | Narrow angle, partial or complete closure | 0 | 0 | Angle closed in part or all of circumference | Spaeth The Spaeth system is much more complex and describes each detail of the anatomic angle. This system describes the iris insertion, angularity, configuration, and pigmentation of the posterior trabecular meshwork. We will illustrate this detailed description below. Iris Insertion Designated by letter A-E. A is anterior to Schwalbe’s line, B is between Schwalbe’s and the scleral spur, C is at the scleral spur, D is deep, E is extremely deep. Iris Angularity The angle of the iris is defined as the angle between two lines. The first line is parallel to the trabecular meshwork and the second a tangent to the anterior iris surface approximately 1/3 of the distance from the most peripheral portion of the iris. It is usually noted between 10 and 40 degrees. Iris Configuration This is named for the configuration or shape of the iris as it runs from the papillary margin to the insertion. S is for steep, B for bowing anteriorly, P for plateau, R or F for regular or flat, respectively, and C for concave posteriorly. Pigmentation This is graded on a 0 to 4 scale noting the amount of pigmentation in the posterior trabecular meshwork. The Spaeth system also considers dynamic or compressive gonioscopy. If a letter is in parentheses, this means it is the originally viewed insertion prior to compression. It is then followed by a letter without parentheses, which denotes the insertion after compression. An example is (B)D30P1. This is an angle that is thought to have an iris insertion between Schwalbe’s line and the scleral spur. After compression, it is noted that the insertion is deep, with an angle of 30 degrees and a plateau configuration with grade 1 pigmentation of the trabecular meshwork. Becker The Becker classification focuses on the amount of trabecular meshwork present and the distance between the scleral spur and the insertion of the iris. Numbers (0-3) are used to describe how much trabecular meshwork is present. Letters (A-C) are used to describe the level of iris insertion. Table 3 shows the details of this system. Table 3. The Becker Classification System | | 0 | 1 | 2 | 3 | | 0 | Angle closed | Small trabecular zone, iris insertion not visible | Average width of trabecular zone, iris insertion not visible | Broad trabecular zone, iris insertion not visible | | 1 | | Small trabecular zone, iris insertion anteriorly | Average width of trabecular zone, iris insertion anteriorly | Broad trabecular zone, iris insertion anteriorly | | 2 | | Small trabecular zone, iris insertion in the middle | Average width of trabecular zone, iris insertion in the middle | Broad trabecular zone, iris insertion in the middle | | 3 | | Small trabecular zone, iris insertion posteriorly | Average width of trabecular zone, iris insertion posteriorly | Broad trabecular zone, iris insertion posteriorly | Shaffer-Kanski This system is based on the width of the angle as previously described in the Shaffer system and the risk of angle closure. See Table 4. | Grade Angle (°) | Visiblity of structures | Risk of angle closure | --- | 0 | 0 No structures visible | Closed angle | | 1 | 10 Schwalbe’s line, possibly anterior trabecular meshwork visible | Closure possible | | 2 | 20 Schwalbe’s line and trabecular meshwork visible | Narrow, closure unlikely | | 3 | 20-35 Schwalbe’s line, trabecular meshwork and scleral spur visible | Closure impossible | | 4 | 35-45 All structures visible from Schwalbe’s line to ciliary band | Closure impossible | Table 4. The Shaffer-Kanski classification system Van Herick This is a non-gonioscopic grading system. It uses an estimation of the peripheral anterior chamber depth. It is done at the slit lamp and is most helpful before dilation. A thin slit beam is angled approximately 60 degrees and aimed at the cornea peripherally near the limbus. The corneal thickness is compared to the anterior chamber depth. The ratio is then used to provide information on the width of the chamber angle. Because it is done without gonioscopy, no angle structures can be identified. As such, this should not replace gonioscopy. See Table 5 and Figure 3. Figure 3: Van Herick grading system | Grade Cornea: | Peripheral anterior chamber ratio | Risk of angle closure Angle (°) | --- | 4 | 1:1 or higher | Very unlikely or impossible 35-40 | | 3 | 1:1/2 | Unlikely or improbable 20-35 | | 2 | 1:1/4 | Possible 20 | | 1 | 1:<1/4 | Likely or probably 10 | | 0 | No anterior chamber slit visible | Closed 0 | Table 5. Van Herick classification system Documentation Proper documentation is important to monitor patients over time. Both written documentation and drawings are acceptable ways of communicating findings. One can use any of the above mentioned classification systems or any drawing tool that is available in your charting system. Other Uses of Gonioscopy As discussed above, gonioscopy is extremely useful in determining how open or narrow an angle is and the possibility of it becoming closed. There are also many other indications and uses for gonioscopy. Knowing the anatomy described above will help with identifying any pathology that may be present. Peripheral anterior synechiae (PAS) can be confused with iris processes, however, PAS are pathologic and represent adhesions between the iris and the trabecular meshwork. Indentation or dynamic gonioscopy can be used to differentiate the two; with PAS, the angle will not open when pressure is applied to the lens where with iris processes, the angle opens. The formation of peripheral anterior synechiae and the identification of this is extremely important. Depending on the severity, this can decide a treatment approach or indication for a peripheral laser iridotomy. Plateau iris occurs in the setting of an anteriorly placed ciliary body resulting in the iris blocking, or partially blocking, the trabecular meshwork. On gonioscopy, two “humps” are typically seen. The outer hump represents the ciliary body pushing up against the iris while the inner hump represents the lens pushing against the iris. On slit lamp exam, the patient will often have a normal angle as well as a flat iris. Plateau iris configuration and plateau iris syndrome are further explained in the eyewiki plateau iris article. Blood in Schlemm’s canal can be seen in patients with increased episcleral venous pressure such as carotid cavernous fistulas. It can also be present with hypotony. Neovascularization may be noted in patients with uncontrolled diabetes or a history of retinal vein occlusions or ocular ischemic syndrome. There are other conditions that may cause neovascularization as well. Other findings that can be visible with gonioscopy include hyphemas, microhyphemas, foreign bodies, iris or uveal tumors, and iridodialysis or other damage to angle structures. The importance of gonioscopy cannot be understated and should be used routinely for evaluation and diagnosis of many different ophthalmologic conditions. It is a valuable skill that should be used by all ophthalmologists, not just glaucoma specialists. References ↑ Faschinger C, Hommer A. Gonioscopy. Springer-Verlag Berlin Heidelberg; 2012. ↑ Wallace L M Alward MD RALM. A Brief History of Gonioscopy. Published 2017. Accessed2022. ↑ Wallace L M Alward MD RALM. Techniques of Slit-Lamp Gonioscopy. Published 2017. Accessed2022. ↑ Alward, WLM, Longmuir, RA. American Academy of Ophthalmology. Gonioscopic Grading Systems. Color Atlas of Gonioscopy. Accessed October 07, 2021. Retrieved from " The Academy uses cookies to analyze performance and provide relevant personalized content to users of our website. Categories: Articles Glaucoma
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https://www.quora.com/Why-does-palladium-absorb-and-store-so-much-hydrogen
Something went wrong. Wait a moment and try again. Storage Capacity Palladium (metal) Materials Science and Eng... Hydrogen Gas Properties of Substances Chemical Elements Material Physics 5 Why does palladium absorb and store so much hydrogen? Ram Gopal Pareek Worked at Bharat Heavy Electricals Limited, Haridwar (1972–2008) · Author has 5.2K answers and 689.6K answer views · 4y Absorbing Hydrogen Turns Palladium Into A Quasi Liquid Palladium can absorb vast quantities of hydrogen but materials scientists have now discovered that this process has an extraordinary effect on the m Here’s a curious experiment involving palladium, the rare silvery metal well known for its ability to absorb hydrogen. When it is saturated, the ratio of hydrogen to palladium can be as high 0.6, which is why the metal is used to filter and even store hydrogen. It’s easy to imagine that the movement of hydrogen atoms in and out of the metallic lattice has little effect on the material. But that t Absorbing Hydrogen Turns Palladium Into A Quasi Liquid Palladium can absorb vast quantities of hydrogen but materials scientists have now discovered that this process has an extraordinary effect on the m Here’s a curious experiment involving palladium, the rare silvery metal well known for its ability to absorb hydrogen. When it is saturated, the ratio of hydrogen to palladium can be as high 0.6, which is why the metal is used to filter and even store hydrogen. It’s easy to imagine that the movement of hydrogen atoms in and out of the metallic lattice has little effect on the material. But that turns out to be wrong, as Akio Kawasaki at the University of Tokyo and friends discovered when they decided to test the idea. Materials scientists have known for some time that palladium expands when it absorbs hydrogen and shrinks during desorption. What they hadn’t known until now is the toll that this process takes on the metal. Kawasaki and co attached a rectangular plate of palladium about the size of of stick of gum to the side of a chamber so that it stuck out horizontally. They then heated it to 150 degrees C and hung the weight of an apple on the end of plate. Finally, they pumped hydrogen into the chamber and waited while the metal absorbed it. To their surprise, the palladium immediately drooped under the weight and continued to droop as the hydrogen was pumped out of the chamber and the gas was desorbed. (In contrast, when they hung the plate vertically with the weight hanging beneath, there was almost no stretching at all.) There’s no escaping the conclusion that hydrogen somehow robs palladium of its strength but in a very specific way. That’s a somewhat unexpected result but one that Kawasaki and co think they can explain. In its pure state, the palladium lattice has a face centre cubic structure but this has to change to allow so much hydrogen on board. Materials scientists know that when this a happens, it can adopt two other structures known as alpha and beta phases as well as a mixture of these phases. Kawasaki’s conclusion is that during this change, the metal atoms are neither held in a rigid solid structure nor able to move in an entirely random way either. This makes it a little like a liquid. In fact, physicists call this type of material a quasi-liquid. So what they have is a material that they can change into a quasi-liquid at will. That should peak the interest of materials scientists. The next stage will be to study the change using various techniques such as x-ray diffraction and perhaps NMR which should reveal what happens to a substance as it morphs from a solid to a quasi-liquid. Promoted by Coverage.com Johnny M Master's Degree from Harvard University (Graduated 2011) · Updated Sep 9 Does switching car insurance really save you money, or is that just marketing hype? 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No phone tag. No junk emails. Just a better deal in less time than it takes to make coffee. Here’s the link to two comparison sites - the one I used and an alternative that I also tested. If it’s been a while since you’ve checked your rate, do it. You might be surprised at how much you’re overpaying. Related questions Why does palladium absorb so much hydrogen? Why does palladium absorb pure hydrogen not impure hydrogen? Why is palladium (d-block) a good adsorber of hydrogen? Why does nickel, palladium, and platinum adsorb hydrogen so efficiently? What is the absorption of hydrogen by palladium called? Joe Webster Chief Technical Officer at Stabilization Technologies LLC (2000–present) · Author has 1.9K answers and 2.3M answer views · 4y Originally Answered: Why does palladium absorb so much hydrogen? · When it is saturated, the ratio of hydrogen to palladium can be as high 0.6, which is why the metal is used to filter and even store hydrogen. Materials scientists have known for some time that palladium expands when it absorbs hydrogen and shrinks during desorption.. There’s no escaping the fact that hydrogen somehow robs palladium of its strength but in a very specific way. In its pure state, the palladium lattice has a face centre cubic structure but this has to change to allow so much hydrogen on board. Materials scientists know that when this a happens, it can adopt two other structures k When it is saturated, the ratio of hydrogen to palladium can be as high 0.6, which is why the metal is used to filter and even store hydrogen. Materials scientists have known for some time that palladium expands when it absorbs hydrogen and shrinks during desorption.. There’s no escaping the fact that hydrogen somehow robs palladium of its strength but in a very specific way. In its pure state, the palladium lattice has a face centre cubic structure but this has to change to allow so much hydrogen on board. Materials scientists know that when this a happens, it can adopt two other structures known as alpha and beta phases as well as a mixture of these phases, during this change, the metal atoms are neither held in a rigid solid structure nor able to move in an entirely random way either. This makes it a little like a liquid. In fact, physicists call this type of material a quasi-liquid. Rodney Price Have a periodic table on my dining room wall. · Upvoted by Jerome Zoeller , Ph.D. Chemistry, The University of Texas at Austin (1968) · Author has 4.2K answers and 13.9M answer views · 4y Originally Answered: Why does palladium absorb so much hydrogen? · I’ve upvoted Joe Webster's answer to Why does palladium absorb so much hydrogen? to which I’d add the phase diagrams : x=0.5 means one H atom for every two Pd atoms. It can go over 1:1 : The palladium atoms seem to stay in a face-centred cubic structure through out the first phase diagram. Sadly no one seems to have explained why palladium absorbs more hydrogen than other metals. Maybe it’s because it has 10 outer d shell electrons. I’ve upvoted Joe Webster's answer to Why does palladium absorb so much hydrogen? to which I’d add the phase diagrams : x=0.5 means one H atom for every two Pd atoms. It can go over 1:1 : The palladium atoms seem to stay in a face-centred cubic structure through out the first phase diagram. Sadly no one seems to have explained why palladium absorbs more hydrogen than other metals. Maybe it’s because it has 10 outer d shell electrons. David Kahana Worked at Brookhaven National Laboratory · Author has 9.2K answers and 23.5M answer views · 5y Well, it has been known for a long time that palladium happens to form a hydride very easily, at varying concentrations. It is an extended alloy of palladium and hydrogen. The process is also pretty easily reversible. It is energetically favorable even at room temperature and pressure, for hydrogen molecules to become dissociated at the surface of a palladium lattice and to diffuse into the lattice as individual hydrogen atoms. Palladium has a face centered cubic lattice with a lattice constant of about 390 pm. At low concentrations of hydrogen the lattice simply expands a bit, as hydrogen is a Well, it has been known for a long time that palladium happens to form a hydride very easily, at varying concentrations. It is an extended alloy of palladium and hydrogen. The process is also pretty easily reversible. It is energetically favorable even at room temperature and pressure, for hydrogen molecules to become dissociated at the surface of a palladium lattice and to diffuse into the lattice as individual hydrogen atoms. Palladium has a face centered cubic lattice with a lattice constant of about 390 pm. At low concentrations of hydrogen the lattice simply expands a bit, as hydrogen is added, but at higher concentrations than about 2% hydrogen/palladium there is a sudden phase transition in which the whole lattice expands, so that the lattice constant is larger, on the order of 400 pm. At such densities there is room for the hydrogen atoms to fill the octahedral vacancies in the face centered cubic lattice. Expanding the lattice of course costs a bit of energy, but the modification in the overall electronic structure by the binding to the hydrogens is enough to win out, so in a sense a huge molecule of hydrogen and palladium can be formed. Absorption of hydrogen gas can proceed at room temperature and standard pressure until a concentration of about 70% hydrogen/palladium is reached. However, absorption happens much more quickly if the palladium is first heated, causing the lattice to expand, and the palladium is then placed in a hydrogen atmosphere. I have heard this process described, to manufacture a target for testing an erroneous measurement of so-called cluster fusion, by saturating a palladium lattice with deuterons. The experiment was actually detecting fusion, and there were real neutrons observed. However it turned out that the beam from the Cockcroft-Walton device that the chemists at BNL were using to experiment with cluster fusion, using clusters of a thousand or so heavy water molecules incident on such a deuterium saturated palladium target, was contaminated with trace amounts of oxygen, and the oxygen was energetic enough to hit deuterons in the lattice and then cause knock on fusion of deuterons, which explained the entire result. The energetics were many orders of magnitude off if you considered just the heavy water droplets being accelerated in the beam impacting on the palladium hydride. With heated palladium the absorption of the hydrogen is virtually instantaneous and pretty spectacular. The change in mass of the palladium metal can then be very easily measured after it is cooled down, and you can see directly that on the order of one hydrogen is present in each octahedral vacancy. This phenomenon alone, that the absorption process is much more rapid at temperature, when the lattice has expanded somewhat, but not that much, indicates to me that the whole process of absorption is very dependent on the surface physics. It is at the surface of the palladium that the necessary dissociation of H2 takes place. Sponsored by Grubhub For Merchants Ready to expand your customer reach? With millions of customers, Grubhub is the platform to grow your business. Related questions What is the purpose of using palladium to store hydrogen? How much amount of hydrogen can one gram of palladium store? For what purpose do we absorb hydrogen at palladium? Is helium as mobile as hydrogen within palladium? Does the form of palladium crystal or metallurgy make a difference to hydrogen vs helium absorption? Why is platinum or palladium not used in hydrogenation? Assistant Bot · 1y Palladium (Pd) is known for its exceptional ability to absorb and store hydrogen due to several key factors: Crystal Structure : Palladium has a face-centered cubic (FCC) crystal structure, which provides ample interstitial sites for hydrogen atoms to occupy. This structure allows hydrogen molecules to dissociate into atoms and fit into the spaces between palladium atoms. High Solubility : Palladium exhibits a high solubility for hydrogen, meaning it can dissolve a large amount of hydrogen gas. This solubility increases with temperature and pressure, allowing palladium to absorb significant quanti Palladium (Pd) is known for its exceptional ability to absorb and store hydrogen due to several key factors: Crystal Structure : Palladium has a face-centered cubic (FCC) crystal structure, which provides ample interstitial sites for hydrogen atoms to occupy. This structure allows hydrogen molecules to dissociate into atoms and fit into the spaces between palladium atoms. High Solubility : Palladium exhibits a high solubility for hydrogen, meaning it can dissolve a large amount of hydrogen gas. This solubility increases with temperature and pressure, allowing palladium to absorb significant quantities of hydrogen. Chemical Interaction : The interaction between hydrogen and palladium is favorable. Hydrogen can form weak bonds with palladium, allowing for the reversible absorption and desorption of hydrogen. This property is crucial for applications such as hydrogen storage and purification. Hydride Formation : Palladium can form palladium hydride (PdH), a compound where hydrogen is integrated into the palladium lattice. This hydride formation is a key aspect of its ability to store hydrogen efficiently. Catalytic Properties : Palladium is also a highly effective catalyst for hydrogenation reactions. Its catalytic properties facilitate the dissociation of hydrogen molecules, making it easier for hydrogen to be absorbed into the metal. Overall, these factors combine to make palladium one of the most effective materials for hydrogen storage and absorption, leading to its use in various applications, including fuel cells, hydrogen sensors, and catalytic converters. David Goodman Lives in Canada · Author has 1.9K answers and 14.9M answer views · 4y Originally Answered: Why does palladium absorb so much hydrogen? · Why does palladium absorb so much hydrogen? Thank you for the request to answer your question Jim. It is mainly to do with Palladium’s electron configuration and the electromagnetic properties of multiple palladium atoms in the lattice the element normally forms when it is gathered together as a purified metal. When hydrogen (H2) interacts with a Palladium lattice, there is a catalytic between the electron configurations of the two elements, where the H2 splits into 2 separate hydrogen atoms which are now small enough to penetrate deeper into the palladium lattice through the spaces between atoms Why does palladium absorb so much hydrogen? Thank you for the request to answer your question Jim. It is mainly to do with Palladium’s electron configuration and the electromagnetic properties of multiple palladium atoms in the lattice the element normally forms when it is gathered together as a purified metal. When hydrogen (H2) interacts with a Palladium lattice, there is a catalytic between the electron configurations of the two elements, where the H2 splits into 2 separate hydrogen atoms which are now small enough to penetrate deeper into the palladium lattice through the spaces between atoms of the Pd lattice. This property of Palladium allows it to absorb plenty of hydrogen even though the palladium appears to be a solid block of metal. For this reason Palladium is a candidate for Hydrogen storage systems, and was thought by some as a method for pressing hydrogen isotopes together during the cold fusion claims of the late 1980’s/early 90’s. Ron Morel B.S. in Chemistry, United States Air Force Academy (Graduated 1979) · Author has 13.9K answers and 2.7M answer views · 4y Originally Answered: Why does palladium absorb so much hydrogen? · Interesting thing about hydrogen, when it “loses” its electron into a metallic matrix, just as all metals do, all that is left is a naked proton with none of those pesky electron orbitals to take up room. The tiny protons can then occupy most any spaces in the metallic lattice. Palladium is said to form a hydride very easily, but there is a phase transition as the hydrogen concentration increases. See Related Question in Quora: Why does palladium absorb and store so much hydrogen? Sponsored by Grammarly Is your writing working as hard as your ideas? Grammarly’s AI brings research, clarity, and structure—so your writing gets sharper with every step. Naraina Group of Institution Lives in Naraina Group of Institutions (2000–present) · Author has 523 answers and 414.5K answer views · 3y Originally Answered: Why does palladium absorb so much hydrogen? · In its pure state, the palladium lattice has a face centre cubic structure but this has to change to allow so much hydrogen on board. Materials scientists know that when this a happens, it can adopt two other structures known as alpha and beta phases as well as a mixture of these phases. Simon Griffin Researcher & Educator · Author has 1.2K answers and 962.6K answer views · 5y This is a nice article that’s helpful here. A remarkable metal! Absorbing Hydrogen Turns Palladium Into A Quasi Liquid and this goes a little further Why gold-palladium alloys are better than palladium for hydrogen storage (which refers to the paper by Namba et al. 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MATHEMATICS Statistical Honours at St. Xavier's College, Ranchi (2021–2024) · Author has 693 answers and 2.5M answer views · 3y Originally Answered: Why does palladium absorb so much hydrogen? · Hye, Firstly palladium has FCC which is face centered cubic, it's a body type Or you can say structure. You will come acros in solid state about this. Palladium has large surface area ,which allow H to get absorbed. Also, Hydrogen is absorbed by palladium can be used further for some experiments like cold fusion , filtering of gases and many more. So palladium also used as hydrogen storage. Allen W. McDonnell Alternate Historian (2010–present) · Author has 1.9K answers and 2.6M answer views · 4y Is helium as mobile as hydrogen within palladium? Does the form of palladium crystal or metallurgy make a difference to hydrogen vs helium absorption? No not at all mobile in Palladium. The main method for filtering Helium-3 away from Hydrogen-3 is by using a thin layer of Palladium. Hydrogen will migrate right through the Palladium under moderate pressure while the Helium will be prevented from crossing the barrier. When Hydrogen-3 aka Tritium decays the resulting material is Helium-3. Hydrogen-3 is useful for many things from glow in the dark instruments dials to fusion fuel for high energy physics experiments or fusion boosted bombs. Helium-3 on the other hand has a tendency to absorb free neutrons which causes a loss of power in fusion e No not at all mobile in Palladium. The main method for filtering Helium-3 away from Hydrogen-3 is by using a thin layer of Palladium. Hydrogen will migrate right through the Palladium under moderate pressure while the Helium will be prevented from crossing the barrier. When Hydrogen-3 aka Tritium decays the resulting material is Helium-3. Hydrogen-3 is useful for many things from glow in the dark instruments dials to fusion fuel for high energy physics experiments or fusion boosted bombs. Helium-3 on the other hand has a tendency to absorb free neutrons which causes a loss of power in fusion explosive devices and this also makes it less desirable in many high energy physics experiments. R S Nagi Have been teaching Chemistry for JEE & NEET for two decades. · Author has 227 answers and 1.1M answer views · 8y Related Why does palladium absorb pure hydrogen not impure hydrogen? Palladium does not absorb Hydrogen instead it adsorbs hydrogen. Adsorption is a provess of attracting and retaining molecules of the gas generally on surface. It is of two types viz physical and chemical. Chemical adsorption is specific. That means only a specific gas would adsorb on a given surface. There are a sort of chemical bonds formed between gas molecules and metal called surface bonds. Now we know that only Hydrogen would form surface bonds with Palladium and impurities would not. Hence pure Hydrogen is adsorbed on palladium. Huge amount of Hydrogen gas is adsorbed in this manner and is kn Palladium does not absorb Hydrogen instead it adsorbs hydrogen. Adsorption is a provess of attracting and retaining molecules of the gas generally on surface. It is of two types viz physical and chemical. Chemical adsorption is specific. That means only a specific gas would adsorb on a given surface. There are a sort of chemical bonds formed between gas molecules and metal called surface bonds. Now we know that only Hydrogen would form surface bonds with Palladium and impurities would not. Hence pure Hydrogen is adsorbed on palladium. Huge amount of Hydrogen gas is adsorbed in this manner and is known as occluded Hydrogen. It is one of the ways to store Hydrogen gas. Hope this helps! Related questions Why does palladium absorb so much hydrogen? Why does palladium absorb pure hydrogen not impure hydrogen? Why is palladium (d-block) a good adsorber of hydrogen? Why does nickel, palladium, and platinum adsorb hydrogen so efficiently? What is the absorption of hydrogen by palladium called? What is the purpose of using palladium to store hydrogen? How much amount of hydrogen can one gram of palladium store? For what purpose do we absorb hydrogen at palladium? Is helium as mobile as hydrogen within palladium? Does the form of palladium crystal or metallurgy make a difference to hydrogen vs helium absorption? Why is platinum or palladium not used in hydrogenation? Why is a palladium hydrogen electrode used instead of platinum? What is the maximum amount of hydrogen that palladium can store? How much palladium is used for hydrogen extraction? Can platinum and palladium be used to store hydrogen? Is hydrogen adsorbed or absorbed by platinum and palladium? Related questions Why does palladium absorb so much hydrogen? Why does palladium absorb pure hydrogen not impure hydrogen? Why is palladium (d-block) a good adsorber of hydrogen? Why does nickel, palladium, and platinum adsorb hydrogen so efficiently? What is the absorption of hydrogen by palladium called? What is the purpose of using palladium to store hydrogen? How much amount of hydrogen can one gram of palladium store? For what purpose do we absorb hydrogen at palladium? Is helium as mobile as hydrogen within palladium? Does the form of palladium crystal or metallurgy make a difference to hydrogen vs helium absorption? Why is platinum or palladium not used in hydrogenation? About · Careers · Privacy · Terms · Contact · Languages · Your Ad Choices · Press · © Quora, Inc. 2025
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MATERIALS Patty paper Half Turns and Quarter Turns Rotations of Figures on the Coordinate Plane 5 Lesson Overview Students use patty paper to explore rotations of various figures on a coordinate plane. They then generalize about the effects of rotating a figure on its coordinates. Students verify that two figures are congruent by describing a sequence of rigid motions that map one figure onto another. Grade 8 Two-Dimensional Shapes (10) The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:  (A) generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane.  (C) explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 908, 1808, 2708, and 3608 as applied to two-dimensional shapes on a coordinate plane using an algebraic representation. ELPS 1.A, 1.C, 1.D, 1.E, 1.G, 2.C, 2.D, 2.G, 2.H, 2.I, 3.A, 3.B, 3.C, 3.D, 3.F, 4.A, 4.B, 4.C, 4.D, 4.G, 4.K, 5.E Essential Ideas • A rotation is a transformation that turns a figure clockwise or counterclockwise about a fixed point for a given angle and a given direction. • An angle of rotation is the amount of clockwise or counterclockwise rotation about a fixed point. • The point of rotation can be a point on the figure, in the figure, or outside the figure. LESSON 5: Half Turns and Quarter Turns • 67A ©2020 Carnegie Learning, Inc. Created on behalf of the Texas Education Agency. This work is subject to a CC BY-NC 4.0 license. 67B • TOPIC 1: Rigid Motion Transformations Lesson Structure and Pacing: 2 Days Day 1 Engage Getting Started: Jigsaw Transformations Students are presented with a jigsaw puzzle that has two pieces missing. Students match each missing piece to the open spot of the puzzle and describe the sequence of translations, reflections, and rotations that would move the puzzle piece presented to the matching open spot of the puzzle. Develop Activity 5.1: Modeling Rotations on the Coordinate Plane Students copy figures and the coordinates of their vertices onto patty paper. They perform rotations of 90° counterclockwise, 90° clockwise, 180°, 270° clockwise, and 360° about the origin. Students record the coordinates of the original (pre-image) and rotated (image) figures. They explore how the rotations affect the coordinates of the pre-image to create the image. Students end the activity by making conjectures about the effects of rotations on an arbitrary ordered pair (x, y). Day 2 Activity 5.2: Rotating Any Points on the Coordinate Plane A point with the coordinates (x, y) is located in the first quadrant. Students perform rotations of 90° counterclockwise, 90° clockwise, and 180° using the origin as the point of rotation and record the coordinates of the images. Next, students begin with a triangle in Quadrant I and perform rotations of 90° clockwise, 90° counterclockwise, 180°, 270° clockwise, and 360°. Lastly, they are given the coordinates of the vertices of a triangle, and without graphing they determine the coordinates of images resulting from different rotations. Activity 5.3: Verifying Congruence Using Rigid Motions Students examine the change in x- and y-coordinates to determine the congruence of geometric figures. They decide if a sequence of transformations can be used to prove the congruence of figures shown on a graph and then describe that sequence of rigid motions. Demonstrate Talk the Talk: Just the Coordinates Students verify the congruence of pairs of figures, given only the coordinates of the pre-images and images. LESSON 5: Half Turns and Quarter Turns • 67C Getting Started: Jigsaw Transformations Facilitation Notes In this activity, students are presented with a jigsaw puzzle that has two pieces missing. Students match each missing piece to the open spot of the puzzle and describe the sequence of translations, reflections, and rotations that would move the puzzle piece presented to the matching open spot of the puzzle. Note that the transformations students list in this activity can be described informally—a reference to a line of reflection or center of rotation is not needed. You might want to discuss the difference between a horizontal flip and a vertical flip of a puzzle piece. Have students work with a partner or in a group to complete Questions 1 and 2. Share responses as a class. Questions to ask • Which rigid motion transformation will move the puzzle piece from its initial position to an open position on the puzzle board? • Is there more than one rigid motion transformation or series of transformations that will work? • Does the order of the transformations make a difference? • Are the translations used to move the puzzle piece into position horizontal, vertical, or both? • If a reflection is used to move the puzzle piece into position, where is the location of the line of reflection? • If a rotation is used to move the puzzle piece into position, where is the location of the center of rotation? Differentiation strategy To scaffold support, suggest that students copy one or both of the puzzle pieces onto patty paper. They can then use the patty paper to perform the transformations necessary to fit the pieces into the puzzle. Summary Rigid motion transformations such as reflections, rotations, and translations can be used to describe and solve real-world situations. ENGAGE 67D • TOPIC 1: Rigid Motion Transformations Activity 5.1 Modeling Rotations on the Coordinate Plane Facilitation Notes In this activity, students copy figures and the coordinates of their vertices onto patty paper. They perform rotations of 90° counterclockwise, 90° clockwise, 180°, 270° clockwise, and 360° about the origin. Students record the coordinates of the original (pre-image) and rotated (image) figures. They explore how the rotations affect the coordinates of the pre-image to create the image. Students end the activity by making conjectures about the effects of rotations on an arbitrary ordered pair (x, y). Have students work with a partner or in a group to complete Questions 1 through 6. Share responses as a class. Questions to ask • Why is a rotation of 180° considered a half turn? • Is the figure rotated 180° clockwise about the origin or 180° counterclockwise about the origin? How do you know? • What is the difference between rotating the figure 180° clockwise about the origin and rotating the figure 180° counterclockwise about the origin? • Is there any relationship between the x-coordinate of the pre-image and the x-coordinate of the image? Is this true for all vertices? • Is there any relationship between the y-coordinate of the pre-image and the y-coordinate of the image? Is this true for all vertices? • Could this image have also been created by a translation? Explain. • Could this image have also been created by a reflection? Explain. • Why is a rotation of 90° considered a quarter turn? • What is the difference between rotating the figure 90° clockwise about the origin and rotating the figure 90° counterclockwise about the origin? • How are the coordinate changes evident in the position of the diagram? • What quadrant(s) do you conjecture the image will lie in? • How will the orientation of the image compare to the pre-image? DEVELOP LESSON 5: Half Turns and Quarter Turns • 67E • What is the same about rotating a figure 90° counterclockwise about the origin and rotating a figure 270° about the origin? • What do you notice about rotating a figure 360° about the origin? • Can you think of any real-world examples of a 360° rotation? Differentiation strategy To extend the activity, have students (1) rotate the figure 90° clockwise about the origin, (2) reflect the figure across the x-axis, (3) reflect the figure across the y-axis, and (4) reflect the figure first across the x-axis and then across the y-axis. Compare these images with the two completed in the activity. Summary A point (x, y) rotated 180° about the origin becomes the point (2x, 2y), and when it is rotated 90° counterclockwise about the origin becomes the point (2y, x). A point (x, y) rotated 270° clockwise about the origin becomes the point (2y, x). A point rotated 360° about the origin becomes the point (x, y). Activity 5.2 Rotating Any Points on the Coordinate Plane Facilitation Notes A point with the coordinates (x, y) is located in the first quadrant. Students perform rotations of 90° counterclockwise, 90° clockwise, and 180° using the origin as the point of rotation and record the coordinates of the images in terms of x and y. Next, students begin with a triangle in Quadrant I and perform rotations of 90° clockwise, 90° counterclockwise, 180°, 270° clockwise, and 360°. Lastly, they are given the coordinates of the vertices of a triangle, and without graphing they determine the coordinates of images resulting from different rotations. Have students work with a partner or in a group to complete Question 1. Share responses as a class. Questions to ask • When the figure was rotated 90° counterclockwise about the origin, did the rotation change the x-coordinate of each vertex? • When the figure was rotated 90° counterclockwise about the origin, did the rotation change the y-coordinate of each vertex? 67F • TOPIC 1: Rigid Motion Transformations • Which coordinate in every point of the pre-image changed as a result of the 90° counterclockwise rotation about the origin? • When the figure was rotated 90° clockwise about the origin, did the rotation change the x-coordinate of each vertex? • When the figure was rotated 90° clockwise about the origin, did the rotation change the y-coordinate of each vertex? • Does a 180° clockwise rotation about the origin bring about the same results as a 180° counterclockwise rotation about the origin? • What rotations cause a switch between the x-coordinates and y-coordinates? Why do you think that is the case? • If a rotation causes a switch in the x-coordinates and y-coordinates as well as a sign change, does it matter what order those changes are made? Explain. Have students work with a partner or in a group to complete Questions 2 through 4. Share responses as a class. Questions to ask • If the point (x, y) is rotated 90° counterclockwise about the origin, how does the x-coordinate change? • If the point (x, y) is rotated 90° counterclockwise about the origin, how does the y-coordinate change? • If the point (x, y) is rotated 90° clockwise about the origin, how does the x-coordinate change? • If the point (x, y) is rotated 90° clockwise about the origin, how does the y-coordinate change? • If the point (x, y) is rotated 180° about the origin, how does the x-coordinate change? • If the point (x, y) is rotated 180° about the origin, how does the y-coordinate change? • If the rotation of a point (x, y) about the origin results in the point (2x, y), what do you know about the rotation? • If the rotation of a point (x, y) about the origin results in the point (2y, x), what do you know about the rotation? • If the rotation of a point (x, y) about the origin results in the point (2x, 2y), what do you know about the rotation? • If the rotation of a point (x, y) about the origin results in the point (y, 2x), what do you know about the rotation? • If the point (x, y) is rotated 270° about the origin, how does the x-coordinate change? • If the point (x, y) is rotated 270° about the origin, how does the y-coordinate change? LESSON 5: Half Turns and Quarter Turns • 67G • If the point (x, y) is rotated 360° about the origin, how does the x-coordinate change? • If the point (x, y) is rotated 360° about the origin, how does the y-coordinate change? Note that when students rotate the original triangle 270° about the origin, the coordinates are the same as the 90° counterclockwise rotation. When they rotate the original triangle 360° about the origin, the coordinates are the same as the original triangle. Differentiation strategies To scaffold support when students must consider rotations without graphing: • Allow them to graph the vertices. • Refer them to the general form at the start of the activity to make a connection to their work and the general form. Summary A point (x, y) when rotated 90° counterclockwise becomes the point (2y, x), when rotated 90° clockwise becomes the point (y, 2x), and when rotated 180° becomes the point (2x, 2y). Activity 5.3 Verifying Congruence Using Rigid Motions Facilitation Notes In this activity, students examine the change in x- and y-coordinates to determine the congruence of geometric figures. They decide if a sequence of transformations can be used to prove the congruence of figures shown on a graph and then describe that sequence of rigid motions. Have students work with a partner or in a group to complete Questions 1 through 4. Share responses as a class. Differentiation strategies To scaffold support, • Suggest that students use patty paper to determine the required transformations. • Ask students if the orientation of the figure remained the same, and if so, suggest they use translations (even if other rigid motions may work as well). Questions to ask 67H • TOPIC 1: Rigid Motion Transformations • Is a translation involved in this situation? How do you know? • Is a rotation involved in this situation? How do you know? • Is a reflection involved in this situation? How do you know? • What is another set of rigid motions that would create the same image? • What is the x-coordinate of each point in the pre-image? What is the x-coordinate of each point in the image? • Is the relationship between the x-coordinate of each point in the pre-image and its corresponding x-coordinate in the image the same for all pairs of corresponding points? • What is the y-coordinate of each point in the pre-image? What is the y-coordinate of each point in the image? • Is the relationship between the y-coordinate of each point in the pre-image and its corresponding y-coordinate in the image the same for all pairs of corresponding points? • How can you check if you are correct? Summary Two figures are congruent if the same sequence of reflections, rotations, and translations moves all the points of one figure to all the points of the other figure. Talk the Talk: Just the Coordinates Facilitation Notes In this activity, students use the coordinates of the pre-image and image to describe the rigid motion transformations associated with two congruent geometric figures. Have students work with a partner or in a group to complete Questions 1 and 2. Share responses as a class. Differentiation strategy To assist all students, suggest they use graphs and patty paper and/ or tables to visualize these problems. Questions to ask • What do you know to be true about the coordinates of points that have undergone a vertical translation? • What do you know to be true about the coordinates of points that have undergone a horizontal translation? • What do you know to be true about the coordinates of points that have undergone a reflection across the x-axis? DEMONSTRATE LESSON 5: Half Turns and Quarter Turns • 67I • What do you know to be true about the coordinates of points that have undergone a reflection across the y-axis? • What do you know to be true about the coordinates of points that have undergone a 90° counterclockwise rotation about the origin? • What do you know to be true about the coordinates of points that have undergone a 90° clockwise rotation about the origin? • What do you know to be true about the coordinates of points that have undergone a 180° rotation about the origin? • What is another set of rigid motion transformations to create this same image? Summary Rigid motion transformations can be used to verify the congruence of geometric figures. NOTES 67J • TOPIC 1: Rigid Motion Transformations LESSON 5: Half Turns and Quarter Turns • 67 Warm Up Answers 1. 2. 3. ELL Tip Before beginning the lesson, remind students of the difference between clockwise and counterclockwise. Ask students to discuss the two words with one another and have them write down a few pieces of information about each word. Write the two words on the board, and have students come to the board and write down their pieces of information, not duplicating the information written previously. LESSON 5: Half Turns and Quarter Turns • 67 LEARNING GOALS • Rotate geometric figures on the coordinate plane 90°, 180°, 270°, and 360°. • Identify and describe the effect of geometric rotations of 90°, 180°, 270°, and 360° on two-dimensional figures using coordinates. • Identify congruent figures by obtaining one figure from another using a sequence of translations, reflections, and rotations. You have learned to model rigid motions, such as translations, rotations, and reflections. How can you model and describe these transformations on the coordinate plane? WARM UP 1. Redraw each given figure as described. a. so that it is turned 180° Before: After: b. so that it is turned 90° counterclockwise Before: After: c. so that it is turned 90° clockwise Before: After: Half Turns and Quarter Turns Rotations of Figures on the Coordinate Plane 5 G8_M01_T01_L05_Student Lesson.indd 67 G8_M01_T01_L05_Student Lesson.indd 67 02/12/22 7:45 AM 02/12/22 7:45 AM 68 • TOPIC 1: Rigid Motion Transformations Answers 1. Piece B. Sample explanations include: reflect horizontally then reflect vertically, or rotate 180°, translate 2. Piece A. Sample explanations include: rotate 90° clockwise, reflect vertically, translate 68 • TOPIC 1: Rigid Motion Transformations Getting Started Jigsaw Transformations There are just two pieces left to complete this jigsaw puzzle. A 1 2 B 1. Which puzzle piece fills the missing spot at 1? Describe the translations, reflections, and rotations needed to move the piece into the spot. 2. Which puzzle piece fills the missing spot at 2? Describe the translations, reflections, and rotations needed to move the piece into the spot. G8_M01_T01_L05_Student Lesson.indd 68 G8_M01_T01_L05_Student Lesson.indd 68 02/12/22 7:45 AM 02/12/22 7:45 AM LESSON 5: Half Turns and Quarter Turns • 69 Answers 1a, b. Check students’ work. 1c. x A‘ J‘ y –6 –8 0 –2 2 4 6 8 –4 –6 –8 2 4 6 8 B‘ C‘ D‘ E‘ F‘ G‘ H‘ K‘ Coordinates of Pre-Image Coordinates of Image A (2, 1) A’ (−2, −1) B (2, 3) B’ (−2, −3) C (4, 5) C’ (−4, −5) D (2, 5) D’ (−2, −5) E (2, 6) E’ (−2, −6) F (5, 6) F’ (−5, −6) G (5, 5) G’ (−5, −5) H (4, 2) H’ (−4, −2) J (5, 2) J’ (−5, −2) K (5, 1) K’ (−5, −1) 1d.  The coordinates are the same values with opposite signs. This is because the image is oriented the same way, but moved from Quadrant I to Quadrant III. LESSON 5: Half Turns and Quarter Turns • 69 In this activity, you will investigate rotating pre-images to understand how the rotation affects the coordinates of the image. 1. Rotate the figure 180° about the origin. a. Place patty paper on the coordinate plane, trace the figure, and copy the labels for the vertices on the patty paper. b. Mark the origin, (0, 0), as the center of rotation. Trace a ray from the origin on the x-axis. This ray will track the angle of rotation. c. Rotate the figure 180° about the center of rotation. Then, identify the coordinates of the rotated figure and draw the rotated figure on the coordinate plane. Finally, complete the table with the coordinates of the rotated figure. d. Compare the coordinates of the rotated figure with the coordinates of the original figure. How are the values of the coordinates the same? How are they different? Explain your reasoning. Modeling Rotations on the Coordinate Plane ACTIVITY 5.1 x 8 6 2 4 6 8 10 –2 –2 4 2 –4 –4 –6 –6 –8 –8 –10 y 10 –10 0 A B C D E F G H J K Coordinates of Pre-Image Coordinates of Image A (2, 1) B (2, 3) C (4, 5) D (2, 5) E (2, 6) F (5, 6) G (5, 5) H (4, 2) J (5, 2) K (5, 1) G8_M01_T01_L05_Student Lesson.indd 69 G8_M01_T01_L05_Student Lesson.indd 69 02/12/22 7:46 AM 02/12/22 7:46 AM 70 • TOPIC 1: Rigid Motion Transformations Answers 2a. Check students’ work. 2b. x y –6 –8 0 –2 2 4 8 –4 –6 –8 –4 2 4 6 8 A’ C’ D’ B’ NOTES 70 • TOPIC 1: Rigid Motion Transformations Now, let’s investigate rotating a figure 90° about the origin. 2. Consider the parallelogram shown on the coordinate plane. x 8 6 2 4 6 8 10 –2 –2 4 2 0 –4 –4 –6 –6 –8 –8 –10 y 10 –10 A B C D a. Place patty paper on the coordinate plane, trace the parallelogram, and then copy the labels for the vertices. b. Rotate the figure 90° counterclockwise about the origin. Then, identify the coordinates of the rotated figure and draw the rotated figure on the coordinate plane. G8_M01_T01_L05_Student Lesson.indd 70 G8_M01_T01_L05_Student Lesson.indd 70 02/12/22 7:46 AM 02/12/22 7:46 AM LESSON 5: Half Turns and Quarter Turns • 71 Answers 2c. Coordinates of Pre-Image Coordinates of Image (3, 0) (0, 3) (2, 4) (−4, 2) (−1, 6) (−6, −1) (0, 2) (−2, 0) 2d.  The x-coordinates of the pre-image became the y-coordinates of the image, and the opposites of the y-coordinates of the pre-image became the x-coordinates of the image. 3. Answers will vary. LESSON 5: Half Turns and Quarter Turns • 71 c. Complete the table with the coordinates of the pre-image and the image. Coordinates of Pre-Image Coordinates of Image d. Compare the coordinates of the image with the coordinates of the pre-image. How are the values of the coordinates the same? How are they different? Explain your reasoning. 3. Make conjectures about how a counterclockwise 90° rotation and a 180° rotation affect the coordinates of any point (x, y). G8_M01_T01_L05_Student Lesson.indd 71 G8_M01_T01_L05_Student Lesson.indd 71 02/12/22 7:46 AM 02/12/22 7:46 AM 72 • TOPIC 1: Rigid Motion Transformations Answers 4. Answers will vary. 72 • TOPIC 1: Rigid Motion Transformations You can use steps to help you rotate geometric objects on the coordinate plane. Let’s rotate a point 90° counterclockwise about the origin. Step 1: Draw a “hook” from the origin to point A, using the coordinates and horizontal and vertical line segments as shown. Step 2: Rotate the “hook” 90° counterclockwise as shown. Point A’ is located at (21, 2). Point A has been rotated 90° counterclockwise about the origin. 4. What do you notice about the coordinates of the rotated point? How does this compare with your conjecture? x 4 5 3 1 2 3 4 5 –1 –1 2 1 –2 –2 –3 –3 –4 –5 –4 –5 y 0 E A’ (–1, 2) A (2, 1) G8_M01_T01_L05_Student Lesson.indd 72 G8_M01_T01_L05_Student Lesson.indd 72 02/12/22 7:46 AM 02/12/22 7:46 AM LESSON 5: Half Turns and Quarter Turns • 73 Answers 5a. Check students’ work. 5b. x y –6 –8 0 –2 2 4 6 8 –4 –6 –8 –4 –2 2 4 6 8 P' R' S' Q' LESSON 5: Half Turns and Quarter Turns • 73 Now let’s investigate rotating figures more than 180° about the origin. 5. Consider the parallelogram shown on the coordinate plane. x y –6 –8 0 –2 2 4 6 8 –4 –6 –8 –4 –2 2 4 6 8 P Q S R a. Place patty paper on the coordinate plane, trace the parallelogram, and then copy the labels for the vertices. b. Rotate the figure 270° clockwise about the origin. Then, identify the coordinates of the rotated figure and draw the rotated figure on the coordinate plane. G8_M01_T01_L05_Student Lesson.indd 73 G8_M01_T01_L05_Student Lesson.indd 73 02/12/22 7:46 AM 02/12/22 7:46 AM 74 • TOPIC 1: Rigid Motion Transformations Answers 5c. Coordinates of Pre-Image Coordinates of Image P(3, 4) P9(24, 3) Q(7, 4) Q9(24, 7) R(3, 2) R9(22, 3) S(7, 2) S9(22, 7) 5d.  The x-coordinates of the pre-image became the y-coordinates of the image, and the opposites of the y-coordinates of the pre-image became the x-coordinates of the image. 74 • TOPIC 1: Rigid Motion Transformations c. Complete the table with the coordinates of the pre-image and the image. Coordinates of Pre-Image Coordinates of Image d. Compare the coordinates of the image with the coordinates of the pre-image. How are the values of the coordinates the same? How are they different? Explain your reasoning. 6. Consider the triangle shown on the coordinate plane. x y –6 –8 0 –2 2 4 6 8 –4 –6 –8 –4 –2 2 4 6 8 L N M G8_M01_T01_L05_Student Lesson.indd 74 G8_M01_T01_L05_Student Lesson.indd 74 02/12/22 7:46 AM 02/12/22 7:46 AM LESSON 5: Half Turns and Quarter Turns • 75 Answers 6a. Check students’ work. 6b. x y –6 –8 0 –2 2 4 6 8 –4 –6 –8 –4 –2 2 4 6 8 L' N' M' LESSON 5: Half Turns and Quarter Turns • 75 a. Place patty paper on the coordinate plane, trace the triangle, and then copy the labels for the vertices. b. Rotate the figure 360° about the origin. Then, identify the coordinates of the rotated figure and draw the rotated figure on the coordinate plane. G8_M01_T01_L05_Student Lesson.indd 75 G8_M01_T01_L05_Student Lesson.indd 75 02/12/22 7:46 AM 02/12/22 7:46 AM 76 • TOPIC 1: Rigid Motion Transformations Answers 6c. Coordinates of Pre-Image Coordinates of Image L(26, 4) L9(26, 4) M(21, 6) M9(21, 6) N(23, 3) N9(23, 3) 6d.  The coordinates are exactly the same because the triangle has made a full rotation or complete turn about the origin. 76 • TOPIC 1: Rigid Motion Transformations c. Complete the table with the coordinates of the pre-image and the image. Coordinates of Pre-Image Coordinates of Image d. Compare the coordinates of the image with the coordinates of the pre-image. How are the values of the coordinates the same? How are they different? Explain your reasoning. G8_M01_T01_L05_Student Lesson.indd 76 G8_M01_T01_L05_Student Lesson.indd 76 02/12/22 7:46 AM 02/12/22 7:46 AM LESSON 5: Half Turns and Quarter Turns • 77 Answers 1. x y (–y, x) (y, –x) (–x, –y) (x, y) Rotation About the Origin 90° Counter-clockwise Rotation About the Origin 90° Clockwise Rotation About the Origin 180° (–y, x) (y, –x) (–x, –y) LESSON 5: Half Turns and Quarter Turns • 77 Consider the point (x, y) located anywhere in the first quadrant. x y (x, y) 1. Use the origin, (0, 0), as the point of rotation. Rotate the point (x, y) as described in the table and plot and label the new point. Then record the coordinates of each rotated point in terms of x and y. Original Point Rotation About the Origin 90° Counterclockwise Rotation About the Origin 90° Clockwise Rotation About the Origin 180° (x, y) Rotating Any Points on the Coordinate Plane ACTIVITY 5.2 If your point was at (5, 0), and you rotated it 90°, where would it end up? What about if it was at (5, 1)? G8_M01_T01_L05_Student Lesson.indd 77 G8_M01_T01_L05_Student Lesson.indd 77 02/12/22 7:46 AM 02/12/22 7:46 AM 78 • TOPIC 1: Rigid Motion Transformations Answers 2. x 2 2 4 6 8 10 4 6 8 –2 –10 –8 –6 –4 –2 –4 –6 –8 y 10 –10 0 (3, 4) (–9, 4) (–1, 6) (–4, 3) B’’’ C’‘’ A’‘’ A’’ B’’ C’’ A A’ B’ C’ (6,1) (–6, –1) (–3, –4) (9, –4) (1, –6) (4, –3) (–4, –9) (4, 9) C B  Check students’ graphs.The 270º clockwise rotation is congruent to the 90º counterclockwise rotation. The 360º rotation is the same as the original triangle. 3a.  The triangle that has been rotated 270° clockwise about the origin has the same coordinates as the triangle that has been rotated 90° counterclockwise about the origin. Triangle A””B””C”” is congruent to triangle A’B’C’ 3b.  The triangle that has been rotated 360° about the origin has the same coordinates as the original triangle. The original triangle completed one full rotation. Triangle A’””B’””C’”” is congruent to triangle ABC. Rotation About the Origin 90° Counterclockwise Rotation About the Origin 90° Clockwise Rotation About the Origin 180° Rotation About the Origin 270° Clockwise Rotation About the Origin 360° ∆A9B9C9 ∆A0B0C0 ∆A09B09C09 ∆A00B00C00 ∆A009B009C009 A’ (–4, 3) A” (4, –3) A”’ (–3, –4) A”’’ (–4, 3) A”’’’ (3, 4) B’ (–1, 6) B” (1, –6) B”’ (–6, –1) B”’’ (–1, 6) B”’’’ (6, 1) C’ (–9, 4) C” (9, –4) C”’ (–4, –9) C”’’ (–9, 4) C”’’’ (4, 9) 78 • TOPIC 1: Rigid Motion Transformations 2. Graph ∆ABC by plotting the points A (3, 4), B (6, 1), and C (4, 9). x 8 6 2 0 4 6 8 10 –2 –2 4 2 –4 –4 –6 –6 –8 –8 –10 y 10 –10 Use the origin, (0, 0), as the point of rotation. Rotate ∆ABC as described in the table, graph and label the new triangle. Then record the coordinates of the vertices of each triangle in the table. Original Triangle Rotation About the Origin 90° Counterclock-wise Rotation About the Origin 90° Clockwise Rotation About the Origin 180° Rotation About the Origin 270° Clockwise Rotation About the Origin 360° ∆ABC ∆A9B9C9 ∆A0B0C0 ∆A09B09C09 ∆A00B00C00 ∆A009B009C009 A (3, 4) B (6, 1) C (4, 9) 3. Consider your table. a. What do you notice about the coordinates of the triangle that has been rotated 270° clockwise about the origin? What conjecture can you make about these two triangles? b. What do you notice about the coordinates of the triangle that has been rotated 360° about the origin? What conjecture can you make about these two triangles? G8_M01_T01_L05_Student Lesson.indd 78 G8_M01_T01_L05_Student Lesson.indd 78 02/12/22 7:46 AM 02/12/22 7:46 AM LESSON 5: Half Turns and Quarter Turns • 79 Answers 4a.  The coordinates of the vertices of Triangle D’E’F’ are D’ (−10, −7), E’ (−5, −5), and F’ (8, −1). 4b.  The coordinates of the vertices of the image were determined by writing the opposite of the y-coordinates, and then switching the x- and y-coordinates. 4c.  The coordinates of the vertices of Triangle D”E”F” are D” (10, 7), E” (5, 5), and F” (−8, 1). NOTES LESSON 5: Half Turns and Quarter Turns • 79 Let’s consider rotations of a different triangle without graphing. 4. The vertices of ∆DEF are D (27, 10), E (25, 5), and F (21, 28). a. If ∆DEF is rotated 90° counterclockwise about the origin, what are the coordinates of the vertices of the image? Name the rotated triangle. b. How did you determine the coordinates of the image without graphing the triangle? c. If ∆DEF is rotated 90° clockwise about the origin, what are the coordinates of the vertices of the image? Name the rotated triangle. G8_M01_T01_L05_Student Lesson.indd 79 G8_M01_T01_L05_Student Lesson.indd 79 02/12/22 7:46 AM 02/12/22 7:46 AM 80 • TOPIC 1: Rigid Motion Transformations Answers 4d.  The coordinates of the vertices of the image were determined by writing the opposite of the x-coordinates, and then switching the x- and y-coordinates. 4e.  The coordinates of the vertices of Triangle D’”E”’F”’ are D’” (7, −10), E”’ (5, −5), and F”’ (1, 8). 4f.  The coordinates of the vertices of the image were determined by writing the opposite of each of the x-coordinates and the opposite of each of the y-coordinates. 80 • TOPIC 1: Rigid Motion Transformations d. How did you determine the coordinates of the image without graphing the triangle? e. If ∆DEF is rotated 180° about the origin, what are the coordinates of the vertices of the image? Name the rotated triangle. f. How did you determine the coordinates of the image without graphing the triangle? NOTES G8_M01_T01_L05_Student Lesson.indd 80 G8_M01_T01_L05_Student Lesson.indd 80 02/12/22 7:46 AM 02/12/22 7:46 AM LESSON 5: Half Turns and Quarter Turns • 81 Answers 1.  Sample answer. The figures are congruent by a 90° counterclockwise rotation about the origin, and a translation up 1 unit. 2.  Sample answer. The figures are congruent by a translation of 1 unit to the left and a translation of 6 units down. LESSON 5: Half Turns and Quarter Turns • 81 Verifying Congruence Using Rigid Motions ACTIVITY 5.3 Describe a sequence of rigid motions that can be used to verify that the shaded pre-image is congruent to the image. 1. x 8 6 0 4 2 6 8 10 –2 –2 4 2 –4 –4 –6 –6 –8 –8 –10 y 10 –10 2. x 8 6 2 0 4 6 8 10 –2 –2 4 2 –4 –4 –6 –6 –8 –8 –10 y 10 –10 G8_M01_T01_L05_Student Lesson.indd 81 G8_M01_T01_L05_Student Lesson.indd 81 02/12/22 7:46 AM 02/12/22 7:46 AM 82 • TOPIC 1: Rigid Motion Transformations Answers 3.  Sample answer. The figures are congruent by a translation left 5 units and up 5 units. 4. Sample answer. The figures are congruent by a reflection across the y-axis, a translation down two units and a translation to the right one unit. 82 • TOPIC 1: Rigid Motion Transformations 3. x 8 6 2 0 4 6 8 10 –2 –2 4 2 –4 –4 –6 –6 –8 –8 –10 y 10 –10 4. x 8 6 2 0 4 6 8 10 –2 –2 4 2 –4 –6 –6 –8 –8 –10 y 10 –10 –4 G8_M01_T01_L05_Student Lesson.indd 82 G8_M01_T01_L05_Student Lesson.indd 82 02/12/22 7:47 AM 02/12/22 7:47 AM LESSON 5: Half Turns and Quarter Turns • 83 Answers 1. Sample answer. Rotate the figure counterclockwise 90° about the origin, translate the figure down 5 units and to the right 4 units. 2. Sample answer. Rotate the figure 180° about the origin. Then translate the figure to the right 3 units and down 2 units. NOTES LESSON 5: Half Turns and Quarter Turns • 83 TALK the TALK Just the Coordinates Using what you know about rigid motions, verify that the figures represented by the coordinates are congruent. Describe the sequence of rigid motions to explain your reasoning. 1. △QRS has coordinates Q (1, 21), R (3, 22), and S (2, 23). △Q9R9S9 has coordinates Q9 (5, 24), R9 (6, 22), and S9 (7, 23). 2. Rectangle MNPQ has coordinates M (3, 22), N (5, 22), P (5, 26), and Q (3, 26). Rectangle M9N9P9Q9 has coordinates M9 (0, 0), N9 (−2, 0), P9 (22, 4), and Q9 (0, 4). G8_M01_T01_L05_Student Lesson.indd 83 G8_M01_T01_L05_Student Lesson.indd 83 02/12/22 7:47 AM 02/12/22 7:47 AM
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https://www.nature.com/articles/s41396-023-01393-1
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View all journals Search Log in Explore content RSS feed Cooperative antibiotic resistance facilitates horizontal gene transfer Download PDF Download PDF Article Open access Published: Cooperative antibiotic resistance facilitates horizontal gene transfer Qinqin Wang1, Shaodong Wei2, Ana Filipa Silva1 & €¦ Jonas Stenløkke Madsen ORCID: orcid.org/0000-0003-4830-17961 The ISME Journal volume 17, pages 846€“854 (2023)Cite this article 7965 Accesses 24 Altmetric Metrics details Subjects Antibiotics Bacterial evolution Abstract The rise of β-lactam resistance among pathogenic bacteria, due to the horizontal transfer of plasmid-encoded β-lactamases, is a current global health crisis. Importantly, β-lactam hydrolyzation by β-lactamases, not only protects the producing cells but also sensitive neighboring cells cooperatively. Yet, how such cooperative traits affect plasmid transmission and maintenance is currently poorly understood. Here we experimentally show that KPC-2 β-lactamase expression and extracellular activity were higher when encoded on plasmids compared with the chromosome, resulting in the elevated rescue of sensitive non-producers. This facilitated efficient plasmid transfer to the rescued non-producers and expanded the potential plasmid recipient pool and the probability of plasmid transfer to new genotypes. Social conversion of non-producers by conjugation was efficient yet not absolute. Non-cooperative plasmids, not encoding KPC-2, were moderately more competitive than cooperative plasmids when β-lactam antibiotics were absent. However, in the presence of a β-lactam antibiotic, strains with non-cooperative plasmids were efficiently outcompeted. Moreover, plasmid-free non-producers were more competitive than non-producers imposed with the metabolic burden of a plasmid. Our results suggest that cooperative antibiotic resistance especially promotes the fitness of replicons that transfer horizontally such as conjugative plasmids. Similar content being viewed by others Cooperative resistance varies among β-lactamases in E. coli, with some enabling cross-protection and sustained extracellular activity Article Open access 01 July 2025 Plasmid-mediated phenotypic noise leads to transient antibiotic resistance in bacteria Article Open access 23 March 2024 Plasmids do not consistently stabilize cooperation across bacteria but may promote broad pathogen host-range Article 08 November 2021 Introduction Cooperation between microorganisms is often facilitated by the production and secretion of extracellular products, which function as a group resource that persists in the environment and serves as public goods , such as β-lactamases , siderophores , and quorum-sensing autoinducers . Cooperators that produce public goods generally bear a metabolic burden associated with synthesizing and releasing the public goods, while neighboring non-producers, also termed non-cooperators, can benefit from the public goods produced by cooperators, yet do not pay the cost to produce them. Cooperation is therefore vulnerable against non-cooperators as they can outcompete producers, which can lead to the downfall of the cooperative phenotype. This is known as the public goods dilemma . Although the public goods dilemma represents a significant barrier to cooperative behaviors, cooperation is promoted and maintained through diverse properties and phenotypes that safeguard the costly public goods. This, for example, is done by facilitating selection towards kin in accordance with Hamilton€™s theories on inclusive fitness . An example is growth in biofilms, where the matrix provides structure, which increases the genetic relatedness of neighbors. Another example is metabolic prudence, here public goods are regulated and only secreted when the cost of their production and impact on individual fitness is low. Horizontal gene transfer (HGT) has been proposed to act as a mechanism that can stabilize public goods cooperation by converting non-cooperative cells into cooperators [7, 8]. This is an appealing postulate because HGT is rampant among bacteria, especially when mediated by mobile genetic elements such as conjugative plasmids. Plasmids are DNA elements that replicate extra-chromosomally within bacterial genomes. They typically transfer horizontally by means of conjugation but can also do so by transformation, transduction, or through extracellular vesicles. Plasmids are infamous for spreading genes involved in virulence , ecological interaction , and are the main mechanism for the spread of antimicrobial resistance (AMR) [11,12,13]. Moreover, a prevalence of predicted public goods genes has been shown to be carried by plasmids of several different bacterial taxa, for example, the Enterobacteriaceae family that includes Escherichia coli . AMR is a rising global and critical public health concern and up to 10 million yearly deaths have been predicted to be associated with AMR by 2050 . Especially a growing number of carbapenemase-producing Enterobacteriaceae cause increased treatment times and mortality rates . Carbapenems are one of the most potent β-lactams for treating bacterial infections, especially infections with Enterobacteriaceae that produce extended-spectrum β-lactamases [18 - producing Enterobacteriaceae. Drugs 2003;63:353€“65.")], and carbapenem-resistant bacteria are thus a critical problem . The escalating global antibiotic resistance crisis is largely due to the spread of plasmid-borne antibiotic resistance genes including β-lactamases . Furthermore, β-lactamases have been shown to be public good antibiotic resistances that do not only protect the producer, but also the neighboring susceptible bacteria [2, 22, 23]. Yet, the interconnection between β-lactamases as public goods and their transfer by conjugative plasmids have not been disclosed. Here, we studied this interconnection using KPC-2 (Klebsiella pneumoniae carbapenemase-2), a carbapenemase that spreads horizontally through mobile genetic elements and mainly via plasmids [24,25,26]. KPC β-lactamases are the main cause of β-lactam resistance among bacteria belonging to Enterobacteriaceae, which not only act against carbapenems but also cephalosporins . Thus, the horizontal spread of blaKPC genes is an important cause of multidrug-resistant Gram-negative pathogens [28, 29]. The interconnection between HGT and public goods has previously been investigated by researchers mainly by computational approaches [7, 30,31,32], and a smaller number of in vitro studies have been done, for example, the work by Dimitriu et al. , where the quorum-sensing autoinducer C4-HSL was used as a model public good to investigate the role of HGT in promoting cooperation. In contrast, here we specifically studied how wild-type public goods production, in the form of antibiotic resistance, affects transmission and maintenance of conjugative plasmids in vitro in mixed bacterial populations. Results An experimental model of cooperative antibiotic resistance We first designed an experimental model based on E. coli. Our assumption was that the KPC-2 β-lactamase would act as a public good in the presence of the β-lactam imipenem. E. coli MG1655 was complemented with sfGFP (green fluorescence) and blaKPC-2 expressed from its wild-type promoter, either in (i) the chromosome; (ii) a conjugative plasmid (pKJK5); or (iii) a non-conjugative mutant of the plasmid (pKJK5NC). This way three distinct β-lactamase producers were constructed, referred to as the chromosomal producer (Pchr), the conjugative plasmid producer (Pconj), and the non-conjugative plasmid producer (Pnon-conj). An otherwise isogenic non-producer E. coli MG1655 (N) tagged with mCherry (red fluorescence) was also constructed. In experiments with conjugative plasmids, we distinguish between the original non-producer population (N), which may also include transconjugants (T), and the remaining non-producer population (Nrem) which are non-producers that have not acquired the plasmid. The minimal inhibitory concentrations (MIC) of imipenem and tetracycline were tested for all strains (Table S1) and their growth was compared (Fig. S1, n€‰=€‰6). Co-cultures of a producer (either Pchr, Pconj, or Pnon-conj) and N were grown as colonies on agar medium for up to six days with or without antibiotics (120% above-MIC levels of N). The different populations in the communities were monitored by flow cytometry and fluorescent stereo microscopy (Fig. S2). This setup was chosen as it previously has been shown that growing co-cultures of β-lactamase producers and non-producers in colonies on agar plates favor the rescue of non-producers when compared with growth in broth media [23, 33]. Plasmid-encoded KPC-2 elevates both intracellular and extracellular β-lactamase activity and enhances the rescue of non-producers Plasmids are often present in their bacterial hosts in multiple copies and the wild-type plasmid pKJK5 used here has a copy number of 5€“7 per cell [34, 35]. Plasmids that encode AMRs may, as an effect of higher copy numbers, increase the MIC of their host compared with the same AMR encoded as a single copy in the chromosome [36, 37]. Since higher expression of plasmid-encoded AMRs is a strongly selected trait during bacterial AMR evolution , we hypothesized that the multi-copy nature of plasmids would promote the protective effect of β-lactamase producers on non-producers as more β-lactamases are expressed to hydrolyze extracellular antibiotic. We quantified the total β-lactamase activity of the different strains in broth cultures (Fig. 1A, n€‰=€‰9). The plasmid-carrying strains (Pconj and Pnon-conj) had similar but higher β-lactamase activities than Pchr and N, both extracellularly and intracellularly (adjusted p value (padj) < 0.001, Table S2). The intracellular β-lactamase activities of all producers were higher than that of the extracellular activities (padj€‰<€‰0.001, Table S2). Next, we evaluated how copy number (plasmid vs. chromosome) and β-lactamase activity affects the putative cooperative sharing of β-lactam resistance, by quantifying non-producer survival in co-cultures with producers in the presence of imipenem. Producers (Pchr, Pconj, or Pnon-conj) and non-producers (N) were co-cultured at an initial ratio of 1:1 and followed for six days, either with or without imipenem (0.6€‰µg/ml IMP or AB-free) (Fig. S3). Looking at the fluorescence patterns of the colony images (Fig. 1B€“D, Fig. S3) it was seen that distinct populations radiate outwards, over time, from the central mixing zone where the droplets initially were placed on the agar medium. In experiments without the conjugative plasmids, the radiating patches consisted of specific populations (green producers or red non-producers) suggesting that intermixing was minor. In contrast, in experiments with Pconj radiating patches with cells that were both green and red (depicted as yellow) were observed, implying that most non-producers had become transconjugants. Furthermore, the colony images revealed that the width of the radially expanding N populations in co-cultures with Pnon-conj was wider than in those with Pchr. This supports a higher expression of β-lactamases by Pnon-conj compared with Pchr, and long-range cooperative resistance at a global scale . Cells were also enumerated by flow cytometry (Fig. 1E and Fig. S4A, n€‰=€‰6) which showed that all β-lactamase producers protected the non-producers in the presence of above-MIC levels of IMP. This demonstrated that KPC-2 is a public good, though the extent of protection was different. After one day of co-cultivation in the presence of IMP, the average relative proportion of N in Pnon-conj co-cultures was higher (36.1%) than those in Pchr (16.4%, padj€‰<€‰0.001, Table S2) and N in Pconj co-cultures (20.5%, padj€‰<€‰0.001, Table S2). During the following five days, the differences in the relative proportion of N across groups remained similar (padj€‰<€‰0.001, pairwise comparison, Tabel S2). The β-lactamase activity of Pchr and Pnon-conj and the relative proportion of protected N (ρ€‰=€‰0.87, p€‰<€‰0.001), respectively, was positively correlated. In parallel experiments without imipenem (AB-free), the relative proportion of N in Pnon-conj co-cultures was higher than those in Pchr co-cultures (padj€‰<€‰0.001, Table S2). This implies that it was more costly to maintain the plasmid and express the β-lactamase from plasmid replicons compared with the chromosome. Moreover, the proportion of N stayed closer to 50% in Pchr co-cultures (on average 56.5% over six days), suggesting that the fitness of Pchr was more similar to N, and a relatively low cost of chromosomal blaKPC-2 expression. HGT may facilitate the stable acquisition of cooperative genes , but plasmid carriage can also impose a fitness burden on the host. Hence, the effect of plasmid acquisition in Pconj co-cultures was investigated. The flow cytometry data (Fig. 1E and Fig. S4A) showed that in the Pconj co-cultures, most of the N population was noticeably efficiently converted into transconjugants. This supported that the yellow radiating patches of the colony images of Pconj co-cultures (Fig. 1B€“E, Fig. S3) were indeed cells that are fluorescing both green and red. In the absence of IMP (AB-free), N made up a smaller proportion when co-cultured with Pconj compared with Pnon-conj (Fig. 1E). This effect was also observed when IMP was present (Fig. 1E). Pnon-conj and Pconj had similar β-lactamase activities, both extracellular and intracellular (Fig. 1A, padj > 0.05, Table S2), but the proportion of N was lower in Pconj co-cultures because conjugation converted part of the N population into producers (T). Public good resistance increases the probability of plasmid transfer to distinct genotypes We compared conjugation when exposed to antibiotics that are evaded by either public good resistance vs. private good resistance. Besides blaKPC-2, pKJK5 and pKJK5NC also encode resistance towards tetracycline which, is mediated by an efflux pump and can thus be considered a private good resistance, as it solely protects the producer cells. Co-culture experiments with N and Pnon-conj or Pconj were performed in the presence of IMP, tetracycline (TET, 7€‰µg/ml), or without antibiotics (AB-free). Besides experiments initiated at producer to non-producer ratios of 1:1, experiments with initial ratios of 1:100 and 100:1 were also conducted (Fig. 2A, Fig. S3 and Fig. S5€“7, n€‰=€‰6). In the presence of IMP we observed that N survived at all initial ratios and the proportions of N were significantly higher than zero (padj€‰<€‰0.001, one-sample one-sided t-test, Table S2), confirming the protective effect of KPC-2. Relative to co-cultures with Pnon-conj, the proportion of surviving N (including both Nrem and T) in Pconj co-cultures was lower when the initial ratio of producer to non-producer was 1:1 and 100:1, both with and without IMP. In AB-free co-cultures part of the N population were T, which were less fit than Nrem as also seen for N in Pnon-conj co-cultures. N were relatively frequent in Pnon-conj co-cultures when IMP was present, but in Pconj co-cultures conjugation efficiently converted the N population into producing transconjugants (T) (Fig. S8, n€‰=€‰6). Moreover, when the initial ratio of producers was low (1:100 ratio) and IMP was present, fewer N received the plasmid leading to a similar proportion of N in both co-cultures with Pconj and Pnon-conj (Fig. 2A, AB-free). Conversely, at the 1:100 ratio, the proportion of N in IMP co-cultures with Pconj was higher than in Pnon-conj (Fig. 2A, IMP). Unlike co-cultures with IMP, when treated with TET, N did not grow in any of the Pnon-conj co-cultures (Fig. 2A and Fig. S8A) showing that the tetracycline resistance was indeed a private good. In Pconj co-cultures with TET, no N was detected when the initial producer ratio was high (100:1). Only a few N grew at ratios 1:100 and 1:1 and these were all transconjugants (Fig. S8B). We noted that successful transconjugant proliferation post conjugation (days two to six) was very rare. Colony images further demonstrate that no N were observed when selecting with TET and very few T were detected (Fig. 2B and Fig. S7). In communities with many different genotypes, the success of a plasmid may increase with the number of genotypes it associates with €“ essentially by €œhedging its bets€. To access the potential of conjugation to unique genotypes under the selection of IMP and TET, we enumerated individual transfer events based on the colony images acquired by fluorescent microscopy (Fig. 2C, n€‰=€‰10) . Each transconjugant lineage that radiated out as a patch (depicted as yellow) in the colonies was considered a hypothetical unique genotype that originated from a single parent cell. By enumerating these manually, it was found that a higher number of distinct genotypes received the plasmid when few donors/producers were present (1:100 or 1:1), compared with when many were present (100:1). Also, more unique genotypes were converted when treated with IMP compared with TET (Fig. 2B). These results support that public good resistance provides more potential recipients for conjugal transfer while also facilitating social conversion of non-cooperators. Efficient social conversion by plasmid conjugation To delineate the dynamics of social conversion by plasmid conjugation, we compared the relative difference between N abundances in co-cultures with IMP and those without (Fig. 3A, n€‰=€‰6) after one day of cultivation. In co-cultures where conjugation could not occur (Pchr and Pnon-conj), the relative difference of N abundances (proportion of N in co-cultures with IMP compared to those without) was highest when the initial ratio of N was low (ratio 100:1) (Fig. 3A). It gradually decreased when the initial ratio of N increased to 1:1 and 1:100 (slopes > 0, padj€‰=€‰0.002, linear regression, Table S2). In contrast, this relationship was reversed for Pconj co-cultures due to the conversion of N by conjugation (Fig. 3A). The relative difference of the N population (N[Pconj]) was significantly higher when fewer Pconj were initially present (slopes < 0, padj€‰=€‰0.008, linear regression, Table S2), because the relative number of T gradually increased as the initial proportion of Pconj decreased (Fig. S9, n€‰=€‰6). Another interconnection was found when comparing conjugation efficiencies (i.e., conversion efficiency) and transconjugant abundances in co-cultures exposed to IMP, TET and without antibiotics. The conjugation efficiency (Fig. 3B, n€‰=€‰6) was defined as the ratio of transconjugants divided by all surviving N (all possible recipients). When the initial producer to non-producer ratio was 1:100, the conjugation efficiency in AB-free co-cultures was lower than co-cultures with IMP, which in turn was lower than those with TET. TET co-cultures had a conjugation efficiency of 1 because all surviving N were transconjugants. At the 1:1 ratio, the conjugation efficiency in AB-free co-cultures was higher than at the 1:100 ratio and slightly lower compared to co-cultures with IMP, which were lower than TET. When the ratio was 100:1, all N from the IMP and AB-free co-cultures were transconjugants (T, conjugation efficiency of 1), and no N (Nrem nor T) were observed when with TET. Overall, the conjugation efficiency in IMP and AB-free co-cultures increased with the initial proportion of producers. In contrast, when comparing transconjugant abundances (i.e., convert abundances) (Fig. 3C, n€‰=€‰6) the opposite trend was observed. Despite low conjugation efficiencies in AB-free co-cultures, the abundance of T was higher compared to IMP and TET regardless of initial ratios (padj€‰<€‰0.001, two-sided t-test, Table S2). The lowest transconjugant abundances were found among co-cultures exposed to TET and overall T was more abundant when the abundance of N was higher. Collectively, the presence of antibiotics decreased transconjugant abundance, especially under TET treatment (Fig. 3C). Social conversion by conjugation and chromosomal association are both successful strategies for the impediment of non-cooperators The efficiencies at which non-cooperators were impeded by each of the three different types of cooperative antibiotic resistance producers was evaluated. As shown above (Fig. 3A), the ratio between public goods producers and non-cooperators strongly affects the fitness of non-cooperators. Therefore, in line with previous studies [43, 44], to constitute this effect the co-cultures initiated at the three different ratios (1:100, 1:1, and 100:1) were considered as €œsubpopulations€ within a €œglobal population€. The average of total cell numbers over time were attained for the subpopulations and by summing up the averages of the subpopulations over time, both for those with and without IMP, the cell numbers of global populations were calculated (Fig. S10 and Table S3, n€‰=€‰6). When treated with IMP after one day, fewer cells were found in the global populations with Pnon-conj than those of Pchr (padj€‰<€‰0.001). This was a consequence of higher levels of public goods utilization by non-producers and the burden of plasmid carriage in Pnon-conj global populations (Fig. 4A and Table S4). Similar trends were observed until day three and six. The total cell numbers in the global populations with Pconj after one day of IMP treatment, were lower than those of Pchr (padj€‰<€‰0.001), and more similar to Pnon-conj, but higher (padj€‰=€‰0.795). The difference in total cell numbers between global populations with Pconj and Pnon-conj became more pronounced from day one to day three and more so until day six, and those with Pconj gradually became comparable to those with Pchr. Yet, in global populations exposed to IMP, while fewer producers (including T) were observed in Pconj compared to Pchr, fewer non-cooperators were also present in Pconj. In comparison, public goods utilization by non-producers was evidently more pronounced in the global populations with Pnon-conj exposed to IMP than in those with Pconj and Pchr, where the numbers of producers and non-cooperators were comparable. As expected, when no antibiotics were present the numbers of both total cells and non-producers were higher overall in all global populations. On day one in the global populations with Pchr not exposed to antibiotics, the ratio between non-producers and producers was close to 1:1 but slightly more non-producers were present. This seemed to be a stable trend also seen from day one until day three and six. In global populations with Pnon-conj, non-producers outnumbered producers. Additionally, in contrast to global populations with Pchr or Pnon-conj, more producers (including T) were observed than non-producers in global populations with Pconj (day one, padj€‰<€‰0.001). The total number of producers in Pconj were also higher compared to Pchr (day one, padj€‰<€‰0.001). Overall, producers outcompeted non-producers globally when in the presence of IMP. However, when IMP wasn€™t present non-producers were more abundant but at varying levels. The level at which bacteria are exposed to antibiotics in hosts or other environments often fluctuates over time . Therefore, we evaluated how many times an IMP treated global population would have to mix, with global populations that had not been exposed to antibiotics, before the total number of non-producers would surpass the number of producers. This was done by adding the total average cell numbers from the IMP treated global populations with averages from n (1 to 20) AB-free global populations (Fig. 4B). We found that any mixing of an IMP treated global population with Pnon-conj, with those without IMP, will result in producers being outcompeted regardless of how many. This contrasts with results for the global populations with Pchr and Pconj. For Pchr the non-producers became the majority when one IMP exposed global population was mixed with seventeen global populations not exposed to IMP. This didn€™t seem to be the case for global populations with Pconj, as the intermixing events kept increasing the proportion of producers due to conjugation. While simplistic, this illustrates that both chromosomal and conjugative plasmid association of blaKPC-2 can impede non-cooperators globally (Fig. 4B). Non-cooperative plasmids can intrude but are unlikely to persist in populations if periodically exposed to β-lactam antibiotics The above data, based on co-cultures with Pchr, Pconj, or Pnon-conj and N (Fig.1E, AB-free), suggested that expressing the KPC-2 β-lactamase on its own did not impose much of a fitness burden but carrying a conjugative plasmid did. Yet, conversion by conjugation helped impede non-cooperators, especially when producers were few (Figs. 3 and 4, 1:100). This could imply that a plasmid without the β-lactamase gene (non-cooperative plasmid) could potentially outcompete a producer plasmid (cooperative plasmid). To assess the invasion potential of a non-cooperative plasmid, a non-producer strain with a non-cooperative plasmid (Nconj n-coop) was designed. The non-cooperative plasmid was similar to that of Pconj but did not encode KPC-2. Nconj n-coop was co-cultured with N and Pconj at an initial ratio of 1:1:1 (Fig. 5, n€‰=€‰10). After one day of co-cultivation, without antibiotics, the vast majority of cells (99.6%) carried one of the two plasmids. Just under half carried the cooperative plasmid (43.9%) and just over half the non-cooperative plasmid (55.5%) (Fig. 5A, AB-free). This slight difference was observed among the transconjugants during the first two days. Hereafter, the proportion of the transconjugants that carried the two plasmids became similar (Fig. 5B). Very few cells carried both the non-cooperative and cooperative plasmid, likely due to interference by incompatibility or surface exclusion (0.18% in IMP and 0.43% in AB-free on day one). Although a minor fraction, some N (0.42% on day one) did not acquire any of the plasmids and their numbers increased gradually during the six days (1.15% on day six). Correspondingly, in the presence of IMP, most cells ended up carrying plasmids (Fig. 5A), of which the vast majority was the cooperative plasmid (84.64% on day one). The non-cooperative plasmid was present at relatively higher proportions on day one (15.16%) and then dropped continuously until the end of the experiment at day six (slope€‰=€‰ˆ’2.208, padj€‰<€‰0.001, linear regression). This trend was different from what was observed in co-cultures without a non-cooperative plasmid where the proportion of rescued Nori remained relatively constant after the first couple of days (Fig. 1E, IMP). This implies that the fitness of transconjugants with the non-cooperative plasmid was lower than non-producers without a plasmid (20€“40% in Fig. 1E; IMP; 0€“20% in Fig. 5B, IMP). To not cooperate was thus a less viable strategy for strains with a non-producer plasmid, compared to not cooperating without a plasmid. A statistical comparison of the averaged proportions of the strains, with or without IMP, after one to six days of co-cultivation, is shown in Table S2. Pconj, Nconj n-coop, and N were also co-cultured at an initial ratio of 2:1:1, so that the producer to non-producer ratio would be 1:1 (Fig. S11, n€‰=€‰6). As expected, the proportion of cells with the cooperative plasmid was higher than those with the non-cooperative plasmid when IMP was present (Fig. S11, IMP). The same trend was observed in co-cultures without antibiotics (Fig. S11, AB-free). In the presence of IMP, the proportion of non-cooperative plasmids kept decreasing during the six days (slope€‰=€‰ˆ’2.074, padj€‰<€‰0.001, linear regression). By direct comparison with the co-culture data initiated at 1:1 ratio of Pconj and N (Fig. S12, n€‰=€‰6), the proportion of non-producers (including Nconj n-coop) was consistently lower in Pconj and N co-cultures compared to the co-cultures with the non-cooperative plasmid. This shows that the non-cooperative plasmid initially hindered the invasion and spread of the cooperative plasmid (especially on day one and two), but this effect was no longer detected after day three. Discussion Here, we find that KPC-2 β-lactamases are public goods with extracellular activity that can rescue sensitive non-producers when exposed to above-MIC concentrations of the β-lactam imipenem (Fig. 1, Fig. S3 and Figs. 5€“7). Due to the higher copy number of plasmids compared to chromosomes, increased expression levels resulted in higher β-lactamase activity and thus improved rescue of non-producers in co-cultures (Fig. 1). Moreover, rescuing non-producers by public good antibiotic resistance advanced the presence of KPC-2 encoding conjugative plasmids in the community, as the plasmids efficiently transferred to the rescued non-producers. This way, compared to private good tetracycline resistance, plasmids encoding cooperative resistance expanded the potential recipient pool by increasing the number of transconjugants (transconjugant abundance) and the probability of plasmid transfer to new genotypes. Conversely, private good resistance ensured the highest conjugation efficiency as only donors and transconjugants survived (Figs. 2, 3, and Fig. S8). The experiments were conducted on solid agar medium in line with, and to further extend previous work on cooperative antibiotic resistance [2, 23, 46]. In colonies grown on agar medium, susceptible cells have been shown to be more likely to survive during social protection by β-lactamase producers . For other public goods, the spatial structure has been shown to be an important factor that can exclude non-cooperators due to limited dispersion [1, 47, 48]. Rather than having to reduce the overall β-lactam concentration in a liquid medium, enabling the rescue of non-producers, rescue is likely more efficient in colonies, because β-lactams mainly are hydrolyzed locally spatially creating a steep gradient of β-lactams. Moreover, bacterial colonies on agar medium create a structured environment that resembles bacterial biofilms . When public goods were readily available, non-cooperators thrived and social conversion by conjugation became less pronounced (Fig. 3A). This was likely because a large number of public good producers increase the relative fitness of the non-cooperators . However, when fewer public good producers, which were also plasmid donors, were present social conversion by conjugation was relatively more pronounced, while the fitness of non-cooperators was at its lowest. These data highlight an interconnection between the potential of public good exploitation and the efficiency of social conversion by conjugation (Fig. 3A), and the conjugation efficiencies and transconjugant abundances illustrated an important difference in the transfer dynamics of plasmids when encoding private versus public good antibiotic resistances (Fig. 3B). In the case of private antibiotic resistance, N were competitive if producers were not the majority. However, because only a few of the potential recipients received the plasmid, the actual number of conjugation events was always low for the private antibiotic resistance. This disclosed that cooperative and private antibiotic resistance, respectively, advanced transconjugant abundance and conjugation efficiency. We noted that conjugation led to social conversion during antibiotic selection especially when donors/producers initially were rare. This is consistent with previous findings that HGT can enhance inclusive fitness benefits by increasing the relatedness of neighboring cells in a structured environment when public goods production is low . Also, conjugative transfer has been reported to contribute to the initial invasion of cooperative genes [50, 51]. Here we found that non-cooperative plasmids, that did not encode KPC-2, were only slightly more competitive than cooperative plasmids when no antibiotics were present. However, when imipenem was present the non-cooperative plasmids were efficiently outcompeted and the non-producers that persisted over time were those without the non-cooperative plasmid. We observed that competition among non-cooperators that were protected by cooperators disfavors non-cooperative plasmids, thus, they could intrude but were unlikely to persist. The positive relationship between the number of blaKPC-2 copies and the rescue of non-producers shown here, implies that the association of public goods specifically elevates the fitness of the replicon it is encoded on: (i) When encoded in a conjugative plasmid, blaKPC-2 advanced its presence in the community by also rescuing a relatively large number of potential recipients, which subsequently resulted in them acquiring the plasmid. (ii) In contrast, when encoded in the chromosome the metabolic burden of KPC-2 was minimal, and relatively fewer non-producers were rescued. This meant that chromosomally encoded KPC-2 was more privatized and the competitiveness of the associated replicon, the chromosome, was thus also improved. Nonetheless, the expression of chromosomal blaKPC-2 did lead to some rescue of non-producers and thus supported the survival of competing non-cooperative cells. In contrast, the N populations in co-cultures with Pconj were kept at bay due to the fitness cost imposed on them when transconjugants acquired the plasmid via conjugation (Fig. 1E). So, while the burden of carrying plasmids may weaken the competitiveness of the transconjugant producers (Fig. S10), the conjugative conversion will enhance the competitiveness of the original producer population as a similar burden is transferred to transconjugants (Fig. 3). The results thus suggest that public goods antibiotic resistance especially promotes the fitness of replicons that can transfer horizontally. Correspondingly, most β-lactamase genes, including blaKPC-2, predominantly are found encoded on plasmids [24, 25, 52,53,54,55,56]. At lower concentrations of imipenem, the rescue of non-producers increased (Fig. S13, n€‰=€‰4), and at below-MIC concentrations, a threshold should exist where the fitness of non-producers becomes equal to and subsequently higher than the producers. At this threshold or at lower concentrations, producers may be outcompeted and the cooperative phenotype lost . Nonetheless, our data suggest that social conversion by conjugation will reduce the risk that this occurs, and that utilization of public goods by non-cooperators is less pronounced when blaKPC-2 is expressed from chromosomes compared to non-conjugative plasmids (Fig. 4). It has been stated that the existence of conjugative plasmids is paradoxical . This is because (i) conjugation rates often are too low to solely maintain plasmids in a population, and (ii) accessory genes, such as those coding for antibiotic resistance, are less energetically costly when encoded on the chromosome versus conjugative plasmids, as experimentally verified in this study. Various factors and mechanisms are known to help maintain plasmids in their host population including toxin-antitoxins and partitioning systems . Furthermore, co-evolution between plasmid and chromosome can reduce the energetic burden the plasmid inflicts , for example, the amelioration of plasmid fitness costs due to compensatory mutations . Intriguingly, as shown here, an advantage of carrying a conjugative plasmid is that the plasmid and the cost it imposes can be transferred to other bacteria, hereby enabling the donor to compete more efficiently in the absence of plasmid-specific selection. This suggests that hosts that have co-adapted with a plasmid may be more competitive than transconjugants of strains where co-adaptation has not taken place. Recently it was discussed and argued that cooperative enforcement likely is an important mechanism facilitating the evolution of egalitarian cooperation . While cooperative conversion by HGT is a distinctive mechanism of safeguarding cooperation, the overall result€”that non-cooperators are forced to cooperate€”is conceptually similar to cooperative enforcement. In line with this, cooperative conversion by HGT may play a role in facilitating the evolution of egalitarian cooperation amongst bacteria. Materials and methods Bacterial strains and plasmids The background of all producer and non-producer strains used in this study was E. coli MG1655. A full list of strains and plasmids can be found in Table S5, and genome engineering was performed as described in €œSupplementary Materials and Methods€. All strains were cultured in standard Luria-Bertani (LB, VWR International, Germany) medium at 30€‰°C or 37€‰°C as specified. When needed, appropriate antibiotics (Sigma-Aldrich, USA) were used at the following concentrations: ampicillin (AMP), 100€‰µg/ml; imipenem (IMP), 4€‰µg/ml; tetracycline (TET), 15€‰µg/ml; and kanamycin (KAN), 50€‰µg/ml. β-lactamase activity assay A colorimetric assay based on the hydrolysis of nitrocefin was used to determine the total intracellular and extracellular β-lactamase activity in LB broth cultures (grown for 24€‰h) . 500€‰µl of 24-h-grown LB broth culture was centrifuged at 3000€‰Ã—€‰g for 15€‰min, and the obtained supernatant was used to measure the activity of extracellular β-lactamases. To measure intracellular activity, the pellet was resuspended in 500€‰µl PBS containing 1€‰mg/ml lysozyme and 2€‰mM EDTA, and then incubated at 37€‰°C for 1€‰h. Thereafter, 2€‰µl of sample was mixed with 198€‰µl PBS containing 20€‰µg nitrocefin in a 96-well plate, and placed in a spectrophotometer to detect and record the OD490 value every 5€‰min. All measurements were repeated three times. Flow cytometry Bacterial cells were counted on a BD FACSAria Illu (BD Biosciences, USA) flow cytometer, the related technical settings are outlined in €œSupplementary materials and methods€, and the gating strategy was adapted from our previous study . Briefly, a 488€‰nm excitation laser and the FITC (530/30€‰nm band-pass filter) detector were used to detect GFP, a 405€‰nm excitation laser and the DAPI (450/40€‰nm band-pass filter) detector were used to detect mTagBFP2, and a 561€‰nm excitation laser and the (PE)-Texas Red (610/20€‰nm band-pass filter) detector were used to detect mCherry. Data in Fig. 1E were analyzed using FlowJo software (Tree Star Inc., USA). Microscopy Fluorescent microscopy images were obtained with a Leica Stereo M205FA microscope (Germany). A GFP2 filter (excitation filter was 480/40, emission filter was 510LP) was used to excite sfGFP, and a DsRED filter (excitation filter was 546/10, emission filter was 600/40) was used to excite mCherry. 2560 × 1920 pixels of scan area were acquired with a 0.5x objective during laser irradiation. The images were processed using the ImageJ software . Statistical analysis A detailed summary of performed statistical analysis is shown in Table S2. Briefly, the mean value of β-lactamase activity, protection efficiency, and cell number were compared with either analysis of variance (ANOVA) followed by post-hoc Tukey€™s test, Welch€™s t-tests, or linear regression followed by R package €œemmeans€ . p values were adjusted (padj) by Tukey€™s test or Benjamini-Hochberg method. To compare the global populations depicted in Fig. 4, values from different days were averaged and then summed across ratios, eventually tested with ANOVA followed by Tukey€™s test. Correlations between β-lactamase activity and N proportions in Fig. 1 were determined using Spearman€™s rank-order correlation coefficient (function €œrcorr€ in R package €œHmisc€). The growth curves were analyzed with the R package Growthcurver . Significance was assumed when p or padj were 0.05 or below. Data availability Source data are provided with this paper. References Smith P, Schuster M. Public goods and cheating in microbes. Curr Biol. 2019;29:R442€“7. Article CAS PubMed Google Scholar 2. Medaney F, Dimitriu T, Ellis RJ, Raymond B. Live to cheat another day: bacterial dormancy facilitates the social exploitation of β-lactamases. ISME J. 2016;10:778€“87. Article CAS PubMed Google Scholar 3. Buckling A, Harrison F, Vos M, Brockhurst MA, Gardner A, West SA, et al. Siderophore-mediated cooperation and virulence in Pseudomonas aeruginosa. FEMS Microbiol Ecol. 2007;62:135€“41. Article CAS PubMed Google Scholar 4. Williams P, Winzer K, Chan WC, Cámara M. 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Thanks to Qiqi Fu for helping guide the use of FlowJo. We thank the Lundbeck Foundation for supporting this study (JSM, R250-2017-1392) and the China Scholarship Council for funding QW. AFS would like to thank European Union€™s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement (No. 794315) for the support. Funding This work is supported by the Lundbeck Foundation (JSM, R250-2017-1392) and the Marie Sklodowska-Curie grant agreement (No. 794315). Author information Authors and Affiliations Department of Biology, University of Copenhagen, 2100, Copenhagen, Denmark Qinqin Wang, Ana Filipa Silva & Jonas Stenløkke Madsen 2. National Food Institute, Technical University of Denmark, 2800, Lyngby, Denmark Shaodong Wei Authors Qinqin Wang View author publications Search author on:PubMed Google Scholar 2. Shaodong Wei View author publications Search author on:PubMed Google Scholar 3. Ana Filipa Silva View author publications Search author on:PubMed Google Scholar 4. Jonas Stenløkke Madsen View author publications Search author on:PubMed Google Scholar Contributions JSM and QW designed and carried out the study. SW and QW contributed to the plotting and statistical analysis. JSM and QW contributed to the concept and interpretation of the data. QW drafted the manuscript. SW, AFS, and JSM contributed to the manuscript preparation. Corresponding author Correspondence to Jonas Stenløkke Madsen. Ethics declarations Competing interests The authors declare no competing interests. Additional information Publisher€™s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary information Supplementary material Supplementary Table 2 Supplementary Table 4 Rights and permissions Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article€™s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article€™s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit Reprints and permissions About this article Cite this article Wang, Q., Wei, S., Silva, A.F. et al. Cooperative antibiotic resistance facilitates horizontal gene transfer. ISME J 17, 846€“854 (2023). Download citation Received: Revised: Accepted: Published: Issue Date: DOI: Share this article Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. 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https://es.quora.com/Cu%C3%A1l-es-el-valor-de-la-gravedad-en-el-sol
¿Cuál es el valor de la gravedad en el sol? - Quora Algo ha fallado. Espera un momento y vuelve a intentarlo. Intentarlo de nuevo Omitir e ir al contenido Omitir e ir la búsqueda Iniciar sesión Ciencias Gravedad Física El sol Astronomía Ciencias físicas Ciencias Naturales Astrofísica Astrofísicos 5 ¿Cuál es el valor de la gravedad en el sol? Todas las relacionadas (33) Ordenar Recomendado Juan Manuel Canó Serrano Grado en Ingeniería en Sistemas de Telecomunicacion, Universidad Politécnica de Madrid (Graduado en el 2020) ·4 años Sabemos que la fuerza con la que se atraen dos cuerpos, según la Ley de Gravitación Universal de Isaac Newton es: F = G • (m1•m2)/r^2 Siendo G la constante de gravitación universal, m1 y m2 las masas de los cuerpos que se atraen y r la distancia entre ambos. Como sabemos también, gracias a la segunda ley de Newton, una fuerza es igual a la masa de un cuerpo por su aceleración: F = m•a Si comparamos ambas ecuaciones, y considerando m1 = m, obtenemos que: a = g = G m2/r^2 siendo m2 la masa del sol y r su radio o distancia al centro mas la altura a la que este el otro cuerpo. Deduzco que quieres saber el Seguir leyendo Sabemos que la fuerza con la que se atraen dos cuerpos, según la Ley de Gravitación Universal de Isaac Newton es: F = G • (m1•m2)/r^2 Siendo G la constante de gravitación universal, m1 y m2 las masas de los cuerpos que se atraen y r la distancia entre ambos. Como sabemos también, gracias a la segunda ley de Newton, una fuerza es igual a la masa de un cuerpo por su aceleración: F = m•a Si comparamos ambas ecuaciones, y considerando m1 = m, obtenemos que: a = g = G m2/r^2 siendo m2 la masa del sol y r su radio o distancia al centro mas la altura a la que este el otro cuerpo. Deduzco que quieres saber el valor de la gravedad en su superficie, y por lo que se estima, la masa del sol es aproximadamente 1,989 × 10^30 kg, y su radio 696.340 km. Sabemos también que G es 6.67x10-11 kg-1m3s-2. Sustituyendo, obtenemos que la gravedad en la superficie es 273,60 m/s^2 aproximadamente. Como dato, tu peso allí (si no nos calcináramos, claro) sería casi 28 veces tu peso en la tierra. Si en la tierra pesas 60 kg, allí pesarías aproximadamente 1680 kg. Espero haberte ayudado. Un saludo. Votar positivo · 9 2 Preguntas relacionadas Más respuestas a continuación ¿Desde qué altura algo puede caer a la Tierra atraído por la gravedad? ¿Cómo es posible tener gravedad cero en el centro de la tierra? ¿Qué pasó con la gravedad del sol? ¿Cuál podría ser el origen de la gravedad? ¿A qué altura se hace cero la gravedad de la Tierra? ¿Cómo es el valor de la gravedad 9,81? Manny August FitzStephen Bono Ingeniero de Minas - ETS Minas - Madrid · El autor tiene 3,4 K respuestas y 8,2 M visitas a sus respuestas ·6 años Respondido inicialmente: ¿Cuál es la gravedad que hay en el Sol? · La gravedad del Sol, cuenta con unos 274 m/s², esto significa que es casi 28 veces más la gravedad de la Tierra que es tan solo de 9,8 m/s². Votar positivo · 9 7 Isaac A. Ruiz P. ∞🖤∞ ·Traductor/a · Actualizado el 1 año Relacionada Si el sol es sólo Hidrógeno y Helio (sin objetos sólidos como tierra o rocas), ¿Por qué su gravedad es tan extrema? La masa determina la gravedad… La masa determina la gravedad. Correcto, al menos en los sistemas Newtonianos. Un sistema solar es lo suficientemente pequeño como para que se pueda aplicar la gravedad Newtoniana. El Hidrógeno y el Helio tienen masa. No mucha masa, un metro cúbico de Hidrógeno tiene significativamente menos masa que un metro cúbico de Iridio, pero aún así, tiene masa. Ahora bien, el Sol es inimaginablemente enorme. Mira esta comparación: ¿Ves el pequeño punto gris a la izquierda de la fila inferior? No, no el azul, ése es Urano; Me refiero al punto gris debajo de él. Ésa es la Tierra. La Tierra es más densa que el Seguir leyendo La masa determina la gravedad. Correcto, al menos en los sistemas Newtonianos. Un sistema solar es lo suficientemente pequeño como para que se pueda aplicar la gravedad Newtoniana. El Hidrógeno y el Helio tienen masa. No mucha masa, un metro cúbico de Hidrógeno tiene significativamente menos masa que un metro cúbico de Iridio, pero aún así, tiene masa. Ahora bien, el Sol es inimaginablemente enorme. Mira esta comparación: ¿Ves el pequeño punto gris a la izquierda de la fila inferior? No, no el azul, ése es Urano; Me refiero al punto gris debajo de él. Ésa es la Tierra. La Tierra es más densa que el Sol, pero el Sol es tan grande que su masa es unas 333,000 veces la de nuestro planeta natal. El Hidrógeno y el Helio tienen poca masa… Pero el Sol contiene una cantidad ENORME de ambos, que hace que los componentes “más pesados” de la tierra sean irrelevantes. Votar positivo · 1,1 K 1,1 K 99 28 99 19 Gabriel Sandoval Trabaja en Self-Employed · El autor tiene 124 respuestas y 413 K visitas a sus respuestas ·6 años Relacionada Si el sol tiene aproximadamente 333.000 veces la masa de la tierra, ¿por qué solo tiene aproximadamente 28 veces su gravedad? ¿Cómo mides la gravedad? Un cuerpo de masa m m será atraído por un astro de masa M M a una distancia r r con una fuerza de G M⋅m r 2 G M⋅m r 2, o lo que es lo mismo, el primer cuerpo está bajo la influencia de un campo de magnitud G⋅M r 2 G⋅M r 2 en dirección al centro de masa del astro, donde r r es la distancia al centro de masa del astro. Si estás a la misma distancia del sol que de la tierra, el sol te atraerá con una fuerza gravitatoria 3330.000 veces mayor que lo que te atrae la tierra. Pero si estás en la superficie del sol, estás mucho más lejos del centro del sol que si estás en la supe Seguir leyendo ¿Cómo mides la gravedad? Un cuerpo de masa m m será atraído por un astro de masa M M a una distancia r r con una fuerza de G M⋅m r 2 G M⋅m r 2, o lo que es lo mismo, el primer cuerpo está bajo la influencia de un campo de magnitud G⋅M r 2 G⋅M r 2 en dirección al centro de masa del astro, donde r r es la distancia al centro de masa del astro. Si estás a la misma distancia del sol que de la tierra, el sol te atraerá con una fuerza gravitatoria 3330.000 veces mayor que lo que te atrae la tierra. Pero si estás en la superficie del sol, estás mucho más lejos del centro del sol que si estás en la superficie de la tierra del centro de la tierra. En ambos casos el r r de la ecuación será el radio del respectivo astro. La masa solar es 333.000 veces mayor que la tierra, y el radio es 109 veces mayor: si g tierra=G M tierra R 2 tierra g tierra=G M tierra R tierra 2, y g sol=G M sol R 2 sol g sol=G M sol R sol 2 y M sol=333 000⋅M tierra M sol=333 000⋅M tierra y R sol=109˙M tierra R sol=109 M˙tierra, reemplazamos: g sol=G M sol R 2 sol=G 333 000⋅M tierra(109⋅R tierra)2=333 000 110 2 G M tierra R 2 tierra=333 000 11 900 g tierra g sol=G M sol R sol 2=G 333 000⋅M tierra(109⋅R tierra)2=333 000 110 2 G M tierra R tierra 2=333 000 11 900 g tierra Donde 333.000÷11.900 = 28. Votar positivo · 9 3 Preguntas relacionadas Más respuestas a continuación ¿Qué sucedería si el valor de la gravedad fuera mayor? ¿Cuál es el efecto de la gravedad en el tiempo? ¿Cuál es el valor numérico de la gravedad en la tierra? ¿Cuál es la diferencia entre la gravedad según Newton y la gravedad según Einstein? ¿Por qué no sube la gravedad? Nazir Haffar El autor tiene 30,9 K respuestas y 75,8 M visitas a sus respuestas ·1 año Relacionada ¿Hasta que confines llega la gravedad del sol.? Empecemos por el principio. La gravedad del Sol, cuenta con unos 274 m/s², esto significa que es casi 28 veces más la gravedad de la Tierra que es tan solo de 9,8 m/s². Los límites no están bien definidos. O mejor dicho, pueden definirse de varias formas. Allá donde el viento solar cede al medio interestelar, allá donde orbitan los últimos objetos, allá donde la gravedad del Sol deja de ser dominante. Cada uno de estos límites nos muestra un sistema solar distinto. Si partimos desde el Sol y nos vamos alejando, en cualquier dirección, iremos pasando por diferentes regiones. Primero el cinturón d Seguir leyendo Empecemos por el principio. La gravedad del Sol, cuenta con unos 274 m/s², esto significa que es casi 28 veces más la gravedad de la Tierra que es tan solo de 9,8 m/s². Los límites no están bien definidos. O mejor dicho, pueden definirse de varias formas. Allá donde el viento solar cede al medio interestelar, allá donde orbitan los últimos objetos, allá donde la gravedad del Sol deja de ser dominante. Cada uno de estos límites nos muestra un sistema solar distinto. Si partimos desde el Sol y nos vamos alejando, en cualquier dirección, iremos pasando por diferentes regiones. Primero el cinturón de asteroides, más tarde el cinturón de Kuiper. Tal vez nos crucemos algún planeta en el camino, aunque dadas las escalas del sistema solar, es improbable. Si seguimos alejándonos abandonaremos la heliosfera. Mucho más allá cruzaríamos la conocida como nube de Oort , hasta que llegara un punto en el que entráramos en otro sistema solar, dominado por alguna de las estrellas más cercanas al Sol. Sin embargo, ¿en qué momento exacto habríamos abandonado el sistema solar? Pues no lo sabemos. O, visto de otro modo, existen diferentes definiciones de qué constituye abandonar el sistema solar. Una de ellas sería a partir de la heliopausa, la región donde termina la heliosfera. Esta sería la región en la que el viento solar es capaz de sobreponerse al medio interestelar. Imaginemos este medio interestelar como una nube de gas muy difusa que llena toda la galaxia, o al menos la región en la que se encuentra el Sol. Esta nube tenderá a expandirse y a ocupar cada rincón, a menos que algo se lo impida. En las cercanías de una estrella, el viento solar podrá ejercer suficiente presión como para mantener a raya a dicha nube de gas, creando una cubierta alrededor de la estrella. La heliopausa no es completamente esférica, la heliopausa se sitúa a una distancia entre 80 y 100 unidades astronómicas en la dirección de movimiento del Sol y a unas 200 unidades astronómicas en la dirección contraria, siendo una unidad astronómica la distancia media entre la Tierra y el Sol. Límite del Sistema Solar (Imagen Muy Interesante.com.) Votar positivo · 99 61 9 1 Santi Serradell Ha estudiado Facultad de Física en la Universidad de Barcelona (Graduado en el 1999) · El autor tiene 196 respuestas y 93,8 K visitas a sus respuestas ·Actualizado el 1 año Relacionada ¿Por qué el Sol no puede atraer la Tierra y todos los demás planetas hacia él por su gravedad? Vamos a ver la tierra nunca caerá sobre el sol porque se mantiene en la orbita donde la fuerza centrifuga de su rotación al sol, se iguala a la fuerza de atracción del sol. El sol tiene una rotación del 24,5 dias y la tierra da una vuelta al sol cada 365 dias con lo cual la rotación del sol es mas rápida, con lo cual las mareas solares aceleran la tierra y cada vez estamos y estaremos un poco mas lejos del sol. Lo mismo sucede con la luna que también esta dando vueltas en una posición de equilibrio entre la gravedad terrestre y su fuerza centrifuga que la mantiene en la orbita pero como la tier Seguir leyendo Vamos a ver la tierra nunca caerá sobre el sol porque se mantiene en la orbita donde la fuerza centrifuga de su rotación al sol, se iguala a la fuerza de atracción del sol. El sol tiene una rotación del 24,5 dias y la tierra da una vuelta al sol cada 365 dias con lo cual la rotación del sol es mas rápida, con lo cual las mareas solares aceleran la tierra y cada vez estamos y estaremos un poco mas lejos del sol. Lo mismo sucede con la luna que también esta dando vueltas en una posición de equilibrio entre la gravedad terrestre y su fuerza centrifuga que la mantiene en la orbita pero como la tierra gira cada 24 horas y el periodo lunar de translación es de 29,5 dias también nos encontramos con lo mismo. Las mareas terrestre aceleran a la Luna que cada vez esta mas lejos de nosotros. La luna tiene un movimiento de rotación que coincide con el de traslación (Por eso vemos siempre la misma cara). Eso es debido a que las mareas terrestre sobre la luna la han detenido haciendo que el movimiento de traslación coincidan con el de rotación. La Luna por otro lado provoca que los dias sean mas largos porque a medida que la luna se aleja frena la rotación de la tierra y cuando se formo la luna los dias terrestres duraban 18 horas y nos ha ido frenado hasta tener las 24 horas que tenemos ahora. Bueno no se si me explicado bien pero es asi. Votar positivo · 99 35 9 7 Javier Garcia-Julve Vivió en Google · El autor tiene 554 respuestas y 530,6 K visitas a sus respuestas ·Actualizado el 4 años Relacionada Si la gravedad del Sol mantiene los planetas en órbita, ¿qué evita que sean absorbidos por la misma gravedad? Gran oportunidad para insistir en la importancia de pensar con propiedad. Esta pregunta me recuerda lo que cuentan que dijo un instructor del ejército: "Los cuerpos caen por la cción de la gravedad. Y si no existiera la gravedad, caerían por su propio peso". Si la he comprendido, debería decir algo así como, "¿por qué la atracción gravitatoria del Sol mantiene a los planetas en sus órbitas, en lugar de hacerlos caer?" Está incorrectamente planteada. Consecuentemente, las respuestas que la asumen como cierta no puede ser adecuadas. Primero, en física todos los conceptos debe estar bien definidos—l Seguir leyendo Gran oportunidad para insistir en la importancia de pensar con propiedad. Esta pregunta me recuerda lo que cuentan que dijo un instructor del ejército: "Los cuerpos caen por la cción de la gravedad. Y si no existiera la gravedad, caerían por su propio peso". Si la he comprendido, debería decir algo así como, "¿por qué la atracción gravitatoria del Sol mantiene a los planetas en sus órbitas, en lugar de hacerlos caer?" Está incorrectamente planteada. Consecuentemente, las respuestas que la asumen como cierta no puede ser adecuadas. Primero, en física todos los conceptos debe estar bien definidos—lo cual es parte de pensar con propiedad—, pero aquí no sabemos lo que significa ‘absorber’ por gravedad. Supongo que se refiere a que los planetas terminaran cayendo al sol. Y podría obviar la respuesta diciendo que por la misma razón que no caen a la tierra los satélites artificiales. Segundo—y lo realmente importante—que el sol mantiene a los planetas en órbita no es más cierto que decir que los planetas mantienen al sol en su sitio. Y ninguna de las dos afirmaciones es cierta. El enfoque intuitivo analítico nos hace pensar en un modelo con el sol estático en el centro, por atracción gravitatoria haciendo a los planetas moverse en las órbitas que observamos. En realidad se trata de un sistema de interacción gravitatoria, en la que ninguno de los componentes tiene una actuación privilegiada. El hecho es que si el sol atrae a los planetas, también los planetas atrae al sol. Lo expreso en modo condicional porque eso es una suposición que el propio Newton consideraba ridícula. No voy a entrar en ello, pero hay documentos en los que manifiesta su secretas reservas sobre la atracción universal. Lo que sí que conoce todo el mundo es su advertencia “et hypoteses non fingo" que, en su contexto, creo puede traducirse libremente como que “esto es solo una hipótesis, no quiero decir que sea real”. Es simplemente que encaja con los hechos. Más en consonancia con los hechos está el enfoque holístico que considerar el sistema solar como un campo gravitatorio en el que se plantea un problema de cálculo diferencial de N cuerpos. Problema de los n cuerpos - Wikipedia, la enciclopedia libre Ese problema se simplifica enormemente si se toma al sol como centro de masas del sistema, dado que su masa pesante es incomparablemente mayor que la de los planetas—como la de la tierra y los satélites artificiales, o el núcleo atómico y los electrones—los cuales se moverán respecto a él como muestra esta ilustración para dos cuerpos Orbit5.gif Pero, insisto, no es que la gravedad del sol mantenga a los planetas en sus órbitas. Todos se mueven formando parte del mismo sistema, también el sol. Así, en rigor, la respuesta sería, porque así lo determina la ecuación de campo gravitatorio relativista para ese sistema. Ecuaciones del campo de Einstein - Wikipedia, la enciclopedia libre Ahora, ¿por qué tiene que ser esa la ecuación de campo?. Ni idea. O por lo mismo que la ley de Newton podría haber sido correcta. Votar positivo · 9 8 Manny August FitzStephen Bono Ingeniero de Minas - ETS Minas - Madrid · El autor tiene 3,4 K respuestas y 8,2 M visitas a sus respuestas ·Actualizado el 6 años Relacionada ¿Cómo es la fuerza de gravedad del Sol? ¿Cuánta gravedad hay en el Sol? El Sol es una estrella situada en el centro del Sistema Solar. Se formó hará unos 5.000 millones de años y permanecerá activo otros 5.000 millones de años más. Está formado por gases, principalmente hidrógeno y helio, y su temperatura exterior alcanza los 6.000° C. Su distancia media a la Tierra es de 149.597.871 kilómetros. Para darnos una idea de semejante distancia, un rayo de luz solar (que viaja a 299.792,458 kilómetros por segundo) tarda unos 8 minutos en llegar a la Tierra. El Sol está formado por seis capas que, desde el interior hasta el exterior, son: núcl Seguir leyendo ¿Cuánta gravedad hay en el Sol? El Sol es una estrella situada en el centro del Sistema Solar. Se formó hará unos 5.000 millones de años y permanecerá activo otros 5.000 millones de años más. Está formado por gases, principalmente hidrógeno y helio, y su temperatura exterior alcanza los 6.000° C. Su distancia media a la Tierra es de 149.597.871 kilómetros. Para darnos una idea de semejante distancia, un rayo de luz solar (que viaja a 299.792,458 kilómetros por segundo) tarda unos 8 minutos en llegar a la Tierra. El Sol está formado por seis capas que, desde el interior hasta el exterior, son: núcleo, la zona radiactiva o radiante, la zona convectiva, la fotósfera, la cromósfera y la corona solar. Así como la Luna se mueve alrededor de la Tierra y la Tierra alrededor del Sol, el Sol se mueve alrededor del centro de nuestra galaxia (Vía Láctea) a una velocidad media de 220 km/s o, lo que es lo mismo, a 792.000 km/h. A pesar de la enorme velocidad con la que el Sol se mueve, éste tarda unos 25.000 años luz en realizar una vuelta completa alrededor de nuestra galaxia. Y nosotros con el. En el Sol hay una gravedad de 274 m/s², lo que equivale a unas 27,9 la gravedad de la Tierra. Pero sería preciso saber qué es la gravedad La gravedad es una de las cuatro fuerzas o interacciones fundamentales observadas hasta el momento en la naturaleza. La gravedad es la responsable de la caída de los cuerpos en la Tierra y de los movimientos a gran escala que se observan en el Universo: que la Luna orbite alrededor de la Tierra, que los planetas orbiten alrededor del Sol y que las galaxias estén rotando en torno a un centro. Hasta mediados del siglo XVII los astrónomos habían logrado describir con bastante detalle las trayectorias de la Tierra, la Luna y los planetas. Pero nadie había conseguido averiguar la causa de estos desplazamientos tan precisos. Fue Isaac Newton el que descubrió que "todo sucede como si la materia atrajera a la materia". Pero hizo mucho más: descubrió que existe una relación cuantitativa para la fuerza de atracción entre dos objetos con masa. De sus reflexiones y cálculos, dedujo que todo objeto en el universo que posea masa ejerce una atracción gravitatoria sobre cualquier otro objeto con masa, aún si están separados por una gran distancia. Isaac Newton presentó la ley de Gravitación Universal en su libro publicado en 1687, "Philosophiae Naturalis Principia Mathematica". De acuerdo con esta ley de Newton, cuanta más masa posean los objetos, mayor será la fuerza de atracción, y cuanto más cerca se encuentren entre sí, mayor será esa fuerza. Cada cuerpo ejerce una fuerza sobre el otro, las dos fuerzas son iguales en módulo y dirección, pero contrarias en sentido; al estar aplicadas en diferentes cuerpos no se anulan. Considerando dos cuerpos como la Tierra y la Luna, la ley de gravitación se expresa en forma de una ecuación que cuantifica "la fuerza de gravedad que ejerce la Tierra con masa mT sobre la Luna con masa mL, como el producto de ambas masas, dividido por el cuadrado de la distancia desde el centro de la Tierra hasta el centro de la Luna. La fuerza de gravedad de la Tierra causa una aceleración de la Luna hacia la Tierra. La fuerza de gravedad de la Luna causa una aceleración de la Tierra hacia la Luna. Ambas fuerzas tienen la misma intensidad. Lo mismo sucede, guardando las proporciones, con la Tierra y la manzana (la de Newton) que en la figura aparece de color rojo. Todas las partículas materiales y todos los cuerpos se atraen mutuamente por el simple hecho de tener masa, en proporción directa a esas masas. La gravedad tiene un alcance teórico infinito; pero, la fuerza es mayor si los objetos están próximos, y mientras se van alejando, dicha fuerza pierde intensidad en proporción al cuadrado de la distancia que separa a los cuerpos. Por ejemplo, si se aleja un objeto de otro al triple de distancia, entonces la fuerza de gravedad se reduce a la novena parte. En la fórmula de la gravitación es muy importante la introducción de una constante que sirve para obtener el valor exacto de las fuerzas de atracción gravitacional. Es la famosa "constante G", la constante de gravitación universal. Newton no conocía la causa de esta constante y tampoco su valor exacto. Sólo pudo indicar que se trataba de una constante universal y que su valor era un número bastante pequeño. Sólo mucho tiempo después se desarrollaron las técnicas necesarias para mejorar el cálculo de su valor. Aún hoy es una de las constantes universales conocidas con menor precisión. Isaac Newton fue el primero en explicar que la fuerza que hace que los objetos caigan con aceleración constante en la Tierra (gravedad terrestre), es la misma que mantiene en movimiento los planetas y las estrellas. La fuerza de gravedad siempre es atractiva, nunca es repulsiva y tiene alcance infinito. Por muy alejados que estén entre sí dos cuerpos, siguen experimentando esta fuerza, aunque más débil a medida que aumenta la distancia. La fuerza de gravedad siempre produce atracción entre los cuerpos, cualquiera que sea su composición. La fuerza resultante se produce atrayéndose el centro de gravedad de un objeto con el centro de gravedad del otro. La fuerza gravitatoria es universal y todas las partículas materiales están sometidas a ella, sin excepción. Sin embargo, en el interior de los átomos, la fuerza de gravedad no juega un papel importante, debido a la pequeñísima magnitud de las masas de las partículas elementales. Pero está presente. Utilizando la fórmula matemática de la Gravitación Universal, podemos calcular la fuerza de atracción entre la Tierra y el cuerpo de un astronauta que esté en una órbita ecuatorial a 500 km de la superficie y que tenga una masa de 90 kg incluido su traje espacial. La masa de la Tierra es 5,974 × 10^24 kg. La distancia entre el centro de gravedad de la Tierra (centro de la tierra) y la superficie ecuatorial es de 6.378,28 km. Si agregamos los 500 km de altura, se obtiene una distancia de 6.878,280 metros entre ambos centros de gravedad: el de la Tierra y el del astronauta. G es la constante de gravitación universal y su valor aproximado equivale a 6,674 10^-11 N . m^2/kg^2 Haciendo los cálculos, se obtiene que la fuerza gravitacional de cada uno de estos dos cuerpos (la Tierra y el astronauta) es de 750 Newton, equivalentes aproximadamente a 77 Kg de atracción mutua, Newton explicó cómo se comportan los cuerpos ante la gravedad. Einstein propuso un modelo teórico para explicar el origen de la gravedad. La teoría de la relatividad general hace un análisis diferente de la interacción gravitatoria. De acuerdo con esta teoría, la gravedad puede entenderse como un efecto geométrico de la materia sobre el espacio-tiempo. Cuando una cierta cantidad de materia ocupa una región del espacio-tiempo, ésta provoca que el espacio-tiempo se deforme. Visto así, la fuerza gravitatoria no es una misteriosa "fuerza que atrae", sino el efecto producido por la deformación del espacio-tiempo, de geometría no euclídea, sobre el movimiento de los cuerpos. Dado que todos los objetos (según esta teoría) se mueven en el espacio-tiempo, al deformarse este espacio, parte de esa velocidad será desviada produciéndose aceleración en una dirección, que es la fuerza de gravedad. ¿Cuál es la causa de la gravedad? ¿Por qué existe la gravedad? En términos generales lo que sabemos de la gravedad, desde Isaac Newton y Albert Einstein hasta ahora es que “todo sucede como si la materia atrajera a la materia”. Newton ideó una fórmula matemática que funciona con precisión y que, desde entonces, ha permitido calcular las trayectorias de los astros y de las naves espaciales. Einstein propuso la teoría de la deformación del espacio-tiempo. Pero seguimos sin conocer por qué la materia produce esta interacción que llamamos gravedad. En los ambientes matemáticos y científicos de vanguardia se habla mucho de los gravitones, partículas elementales que emanarían de los campos gravitatorios, y de las ondas gravitacionales. Como paso previo a la búsqueda directa de los gravitones, en la Universidad de Wisconsin y en el Observatorio de Ondas Gravitacionales del Interferómetro Láser (LIGO) se están realizando investigaciones con el fin de encontrar pruebas de la existencia de ondas de gravedad, ondas gravitacionales. En la mecánica clásica se puede medir una onda y actualmente se admite que las ondas están compuestas de partículas. De modo que, si se consigue detectar ondas gravitacionales -ya se ha conseguido-, se tendría una base para sugerir que los gravitones existen de verdad. Esto sería una noticia optimista que animaría a continuar buscándolos. Actualmente es posible detectar partículas sin masa, como los fotones. Pero, según los modelos matemáticos, los gravitones deberían interactuar muy débilmente con la materia. Esta tan débil interacción sería la causa de que, hasta ahora, los gravitones sean indetectables. Simplemente no se sabe cómo detectarlos, aunque ahora, esperemos, sí puedan ser detectados. Votar positivo · 99 18 9 2 9 2 Armando José Molina Estudió Electricidad y Física en Tecnología · El autor tiene 3,9 K respuestas y 6,9 M visitas a sus respuestas ·4 años Relacionada Si la gravedad del Sol mantiene los planetas en órbita, ¿qué evita que sean absorbidos por la misma gravedad? Si la gravedad del Sol mantiene los planetas en órbita, ¿qué evita que sean absorbidos por la misma gravedad ? Absolutamente todo se mueve en el Cosmos. Esta es la a clave para que nada colapse y se mantenga el Universo en equilibrio dinámico electromagnético. Se trata de la combinación de 3 formas de Energía inter-actuando: Movimiento: que hace que todas las masas posean una energía inercial base, al atravesar los campos electromagnéticos activos que inundan el espacio. Magnetismo que controla la dirección de los que se mueve, —a través de los campos magnéticos oscilantes— Electricidad, que con Seguir leyendo Si la gravedad del Sol mantiene los planetas en órbita, ¿qué evita que sean absorbidos por la misma gravedad ? Absolutamente todo se mueve en el Cosmos. Esta es la a clave para que nada colapse y se mantenga el Universo en equilibrio dinámico electromagnético. Se trata de la combinación de 3 formas de Energía inter-actuando: Movimiento: que hace que todas las masas posean una energía inercial base, al atravesar los campos electromagnéticos activos que inundan el espacio. Magnetismo que controla la dirección de los que se mueve, —a través de los campos magnéticos oscilantes— Electricidad, que controla la velocidad de todo lo que se mueve en el Universo. Respuesta: Existe en el Universo la tendencia a que todo se encuentre en movimiento y , además, en equilibrio dinámico electromagnético. Átomos — y los anti átomos— son unidades básicas de energía que se encuentran el equilibrio dinámico electro magneto dinámico. son energía en distintas formas, y se mantienen en movimiento continuo al recargarse con energía a cada instante mediante el cruce de los campos electromagnéticos activos oscilantes que inundan el espacio en forma dinámico estacionaria. Los planetas, al moverse en el espacio tienden a salir despedidos de su órbita: Es la fuerza gravitacional de la masa del Sol, la que impide que éstos planetas, salgan despedidos. tienen Se produce lo que es habitual en el Cosmos: Falta poco para que de una vez por todas, la Física incorpore este concepto como imprescindible. Primicia electromagnética Quora: Los ciudadanos del planeta que leen Quora, tienen la primicia de haberse enterado años antes de este importante concepto que se desprende de la lógica electromagnética Maxwell—Hertz del siglo 19: El equilibrio dinámico, electro magnético. Armando Molina Bariloche Votar positivo · 99 31 9 9 9 4 Luis Medrano CGI, astrónomo de casa, futbolero, guitarrista anterior · El autor tiene 8,7 K respuestas y 16,4 M visitas a sus respuestas ·5 años Relacionada ¿Por qué el Sol no puede atraer la Tierra y todos los demás planetas hacia él por su gravedad? Para los efectos de esta explicación vamos a eliminar la atmósfera de la tierra para evitar la resistencia del aire. Díganos que disparas una bala horizontalmente, paralela al suelo. Esa bala lleva una velocidad X y recorre 300 metros antes de caer al suelo. Ahora disparas una segunda bala, esta vez a una velocidad mucho mayor y la bala llega mucho más lejos. Ahora imagina una tercera bala, esta vez la disparas con tanta velocidad que la curva que describe la bala al caer al suelo es exactamente la curvatura de la tierra, O sea, por más que la bala caiga por gravedad, nunca tocará la superficie Seguir leyendo Para los efectos de esta explicación vamos a eliminar la atmósfera de la tierra para evitar la resistencia del aire. Díganos que disparas una bala horizontalmente, paralela al suelo. Esa bala lleva una velocidad X y recorre 300 metros antes de caer al suelo. Ahora disparas una segunda bala, esta vez a una velocidad mucho mayor y la bala llega mucho más lejos. Ahora imagina una tercera bala, esta vez la disparas con tanta velocidad que la curva que describe la bala al caer al suelo es exactamente la curvatura de la tierra, O sea, por más que la bala caiga por gravedad, nunca tocará la superficie de la Tierra, seguirá intentando caer y tocar el suelo pero la curvatura de la tierra evitará el encuentro. La bala quedará en órbita en una eterna caída libre. Lo mismo le sucede a la Luna al orbitar la Tierra, y a los planetas al orbitar el Sol. Votar positivo · 99 13 Rikki J Prince Facilitador, guerrero y mago · El autor tiene 363 respuestas y 683,5 K visitas a sus respuestas ·6 años Relacionada ¿Si el sol explotara, ¿notaríamos la luz primero o el cambio de gravedad o el impulso? La luz y la gravedad llegan a la misma velocidad. Tardan 8 minutos en recorrer los 150 millones de kilómetros que nos separan. El primer impulso es electromagnético que consiste en frecuencias más allá de la luz visibles, pero todas las frecuencias llegan simultáneamente a la luz y la gravedad (rayos ultravioletas, microondas, rayos x, rayos gama). Finalmente, llega la materia de la explosión que viaja al 13% de la velocidad de la luz, y por lo tanto tarda una hora y un minuto en llegar. La distancia que la Tierra se separa de su órbita durante esta hora es despreciable, y en menos de una hora y Seguir leyendo La luz y la gravedad llegan a la misma velocidad. Tardan 8 minutos en recorrer los 150 millones de kilómetros que nos separan. El primer impulso es electromagnético que consiste en frecuencias más allá de la luz visibles, pero todas las frecuencias llegan simultáneamente a la luz y la gravedad (rayos ultravioletas, microondas, rayos x, rayos gama). Finalmente, llega la materia de la explosión que viaja al 13% de la velocidad de la luz, y por lo tanto tarda una hora y un minuto en llegar. La distancia que la Tierra se separa de su órbita durante esta hora es despreciable, y en menos de una hora y dos minutos llega la materia solar a una Tierra ya desolada por el impulso electromágnetico. En resumén, todos muertos en 8 minutos, y en 54 minutos más, deja de existir la Tierra. Votar positivo · 99 40 99 10 Luis Medrano CGI, astrónomo de casa, futbolero, guitarrista anterior · El autor tiene 8,7 K respuestas y 16,4 M visitas a sus respuestas ·1 año Relacionada ¿Se sabe cuál es el objeto en torno al cual gravita el Sol? El Sol está en órbita alrededor del centro galáctico. O sea, no es un solo objeto la causa de la órbita del Sol. Y como el centro galáctico no es un punto o un objeto único sino que tiene largo ancho y espesor millones de veces mayor que las dimensiones del Sol, el movimiento del Sol es bastante complejo. No es solamente una órbita en un plano sino que además sube y baja, produciendo una figura más o menos sinusoidal. El centro galáctico, esa parte brillante, es millones de veces más masiva que el agujero negro supermasivo que se encuentra en su región central. Ese agujero negro afecta a las es Seguir leyendo El Sol está en órbita alrededor del centro galáctico. O sea, no es un solo objeto la causa de la órbita del Sol. Y como el centro galáctico no es un punto o un objeto único sino que tiene largo ancho y espesor millones de veces mayor que las dimensiones del Sol, el movimiento del Sol es bastante complejo. No es solamente una órbita en un plano sino que además sube y baja, produciendo una figura más o menos sinusoidal. El centro galáctico, esa parte brillante, es millones de veces más masiva que el agujero negro supermasivo que se encuentra en su región central. Ese agujero negro afecta a las estrellas cercanas a él pero no tiene la suficiente gravedad como para forzar al Sol a su órbita actual. Votar positivo · 99 58 9 2 Javier Delgado Editor en Verificiencia (2018–presente) · El autor tiene 1,3 K respuestas y 1,9 M visitas a sus respuestas ·1 año Relacionada ¿Cuál es el valor numérico de la gravedad en la tierra? Existen dos conceptos clave relacionados con la gravedad. Uno es la constante gravitacional, que es una constante universal en todo el universo conocido. El otro es la aceleración de la gravedad, que parece ser el sentido de tu pregunta. Sin embargo, me permitiré explicarte ambos conceptos brevemente. Primero, la ley de la gravitación universal de Newton se expresa así: Donde: F F es la fuerza gravitacional entre dos objetos, G G es la constante gravitacional, m 1 m 1 y m 2 m 2 son las masas de los objetos en kilogramos. d es la distancia entre los centros de las dos masas en metros.. La constante gravitacional G G Seguir leyendo Existen dos conceptos clave relacionados con la gravedad. Uno es la constante gravitacional, que es una constante universal en todo el universo conocido. El otro es la aceleración de la gravedad, que parece ser el sentido de tu pregunta. Sin embargo, me permitiré explicarte ambos conceptos brevemente. Primero, la ley de la gravitación universal de Newton se expresa así: Donde: F F es la fuerza gravitacional entre dos objetos, G G es la constante gravitacional, m 1 m 1 y m 2 m 2 son las masas de los objetos en kilogramos. d es la distancia entre los centros de las dos masas en metros.. La constante gravitacional G G es: G = 6.67 x 10-11 N m2/kg2. Esta constante es la misma en todo el universo y describe la intensidad de la atracción gravitatoria entre dos masas. Aplicado a la tierra Ahora, si aplicamos esta ley a la Tierra, "m 1"m 1" sería la masa de la Tierra, y "m 2 m 2" la masa de cualquier objeto cercano a ella. La distancia "d" sería la distancia desde el centro de la Tierra hasta el objeto. A medida que nos alejamos del centro de la Tierra, la fuerza gravitatoria, y por tanto la aceleración que produce, disminuye. La relación exacta es más compleja debido a que la Tierra no es un punto masivo, sino una esfera, pero para esta discusión podemos simplificarlo. A la aceleración que un objeto experimenta debido a la gravedad en la superficie de la Tierra se le llama "g", con minúscula, para distinguirla de la constante universal "G". En resumen: El valor de "g" no es constante en todo lugar de la Tierra; varía dependiendo de la distancia al centro de la Tierra. Es mayor al nivel del mar, disminuye en zonas montañosas, y es aún menor en lugares como la Estación Espacial Internacional. ¿Hay gravedad en el espacio? Un dato curioso: aunque los astronautas en la Estación Espacial flotan, no están en "gravedad cero". De hecho, aún están bajo la influencia significativa de la gravedad terrestre, que a esa altura es aproximadamente el 90% del valor que tiene en la superficie. La razón por la que flotan es porque están en caída libre constante mientras orbitan la Tierra, no porque no exista gravedad. Así que el valor de "g" no es único y varía según la ubicación. A continuación, algunos ejemplos: a) Al nivel del mar: g≈9.80665 m/s 2 g≈9.80665 m/s 2 g≈9.80665 m/s 2 g≈9.80665 m/s 2 Este es el valor estándar utilizado para la aceleración de la gravedad en la Tierra a nivel del mar. b) Ciudad de México (2,200 m sobre el nivel del mar): g≈9.779 m/s 2 g≈9.779 m/s 2 g≈9.779 m/s 2 g≈9.779 m/s 2 La aceleración gravitatoria disminuye con la altitud. En la Ciudad de México, la diferencia es pequeña, pero significativa. c) Monte Everest (8,848 m sobre el nivel del mar): g≈9.764 m/s 2 g≈9.764 m/s 2 g≈9.764 m/s 2 g≈9.764 m/s 2 En la cima del Monte Everest, debido a la mayor altitud, la gravedad es ligeramente menor. d) Altura de crucero de un avión comercial (10,000-12,000 m): A 11,000 m: g≈9.747 m/s 2 g≈9.747 m/s 2 g≈9.747 m/s 2 g≈9.747 m/s 2 Los aviones comerciales suelen volar a altitudes entre 10 y 12 km, donde la gravedad se reduce más, aunque sigue siendo bastante cercana al valor en la superficie. e) Estación Espacial Internacional (aproximadamente 400 km de altitud): g≈8.7 m/s 2 g≈8.7 m/s 2 g≈8.7 m/s 2 g≈8.7 m/s 2 Aunque los astronautas están en "microgravedad", la aceleración gravitatoria sigue siendo significativa. La sensación de ingravidez se debe a la caída libre constante alrededor de la Tierra. f) La Luna: g≈1.62 m/s 2 g≈1.62 m/s 2 g≈1.62 m/s 2 g≈1.62 m/s 2 La gravedad en la Luna es aproximadamente el 16.5% de la gravedad terrestre. Como puedes ver, "g" varía según la altitud y la ubicación, pero generalmente se toma el valor de 9.80665 m/s² como el estándar en la superficie terrestre a nivel del mar. Votar positivo · 9 3 9 1 Preguntas relacionadas ¿Desde qué altura algo puede caer a la Tierra atraído por la gravedad? ¿Cómo es posible tener gravedad cero en el centro de la tierra? ¿Qué pasó con la gravedad del sol? ¿Cuál podría ser el origen de la gravedad? ¿A qué altura se hace cero la gravedad de la Tierra? ¿Cómo es el valor de la gravedad 9,81? ¿Qué sucedería si el valor de la gravedad fuera mayor? ¿Cuál es el efecto de la gravedad en el tiempo? ¿Cuál es el valor numérico de la gravedad en la tierra? ¿Cuál es la diferencia entre la gravedad según Newton y la gravedad según Einstein? ¿Por qué no sube la gravedad? ¿Qué es la gravedad cero? ¿Cómo se midió la gravedad de la Tierra? ¿Es posible controlar la gravedad de la tierra? ¿Cómo nos afecta la gravedad? ¿Cómo se siente la gravedad? Preguntas relacionadas ¿Desde qué altura algo puede caer a la Tierra atraído por la gravedad? ¿Cómo es posible tener gravedad cero en el centro de la tierra? ¿Qué pasó con la gravedad del sol? ¿Cuál podría ser el origen de la gravedad? ¿A qué altura se hace cero la gravedad de la Tierra? ¿Cómo es el valor de la gravedad 9,81? ¿Qué sucedería si el valor de la gravedad fuera mayor? Publicidad Sobre este espacio · Empleo · Privacidad · Condiciones · Contacto · Idiomas · Prensa · © Quora, Inc. 2025 Privacy Preference Center When you visit any website, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized web experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. 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https://www.quora.com/How-is-a-singleton-set-measurable
How is a singleton set measurable? - Quora Something went wrong. Wait a moment and try again. Try again Skip to content Skip to search Sign In Mathematics Singleton An Introduction to Measur... Measurable Sets (mathematics) Theory of Measurement Geometric Measure Theory Measurable Functions Mathematical Sciences 5 How is a singleton set measurable? All related (34) Sort Recommended Billy Smith Studied at University of Oxford · Author has 108 answers and 187K answer views ·6y Well, here’s a very general answer for why singleton sets (and, more generally, all finite sets and countable sets) are measurable, and why, from the perspective of probability theory, it would be exceedingly strange if they weren’t! We call a topological space (X,T X)(X,T X) a Hausdorff space if, for any two points x,y x,y in the space, we can find open sets U∋x,V∋y U∋x,V∋y containing each point, and not the other point, that are disjoint U∩V=∅U∩V=∅. This is generally an extremely defensible assumption - we can imagine spaces that aren’t Hausdorff, but they’re quite hard to even come up wit Continue Reading Well, here’s a very general answer for why singleton sets (and, more generally, all finite sets and countable sets) are measurable, and why, from the perspective of probability theory, it would be exceedingly strange if they weren’t! We call a topological space (X,T X)(X,T X) a Hausdorff space if, for any two points x,y x,y in the space, we can find open sets U∋x,V∋y U∋x,V∋y containing each point, and not the other point, that are disjoint U∩V=∅U∩V=∅. This is generally an extremely defensible assumption - we can imagine spaces that aren’t Hausdorff, but they’re quite hard to even come up with, and not in general very practical. For example, Hausdorff spaces are general enough to include pretty much all the spaces that you’ll study in quantum physics (as all spaces with a metric, and hence all Banach and Hilbert spaces, are Hausdorff), as well as all the spaces that you’ll study in general relativity (as all manifolds are generally defined to be Hausdorff). And if a property is general enough to include the famously-counterintuitive theories of general relativity and quantum mechanics, it’s probably good enough for your purposes, unless your purposes are very arcane! In fact, the Hausdorffness assumption is so ubiquitous that it’s often not even stated. Next, in a Hausdorff space, it’s easy to prove that all finite sets (including, of course, singleton sets) are closed; I’ll show this directly here. If x,y∈X x,y∈X are any points in a Hausdorff space, then by definition, there exist disjoint sets U x∋x,U y∋y U x∋x,U y∋y that separate them. Now, if we look at a particular point x x, this argument applies to every single point y≠x y≠x in the entire space; let U=⋃y U y U=⋃y U y be the union of all these open sets, which must be an open set itself. As this point contains every single point in X X other than x x, it follows that the singleton set x x, the complement of this open set, is a closed set. Because finite unions of closed sets are finite, it follows that finite sets in Hausdorff spaces are always closed. In probability theory, topologies are mostly interesting - at a first pass - because of the σ σ-algebras they induce, what events they allow us to talk about. The closed sets, in general, are some of the most basic and essential elements of those algebras. If we chose a σ σ-algebra on X X that was so coarse that it didn’t include all the closed sets, which means that it would also not include all the open sets, then the topology is not “inducing” the algebra in any real sense; the two seem pretty unrelated. We therefore generally assume, when using a topology to construct σ σ-algebras, that the algebra we define is fine enough to include at least all of the open sets - which naturally means that it also includes all of the closed sets (and, probably, quite a few other kinds of set as well). If the topology is Hausdorff, this means that the singleton sets and finite sets are measurable - which means that countable unions of these, all countable sets, also must be measurable. Intuitively: to use a topology on the space of outcomes to induce a σ σ-algebra of events is to use that topology to tell us how “close” different outcomes are to one another. If that topology is Hausdorff, then it follows that singleton sets (and finite sets more generally) have to be measurable. It would be extremely strange for it to be otherwise - whether the space X is a simple discrete and finite space, or the set X were an uncountably-large space with some non-measurable sets, a practical algebra in which one could not defensibly assign probabilities to individual outcomes seems hard to imagine. Intuitively, it makes sense that if we’re going to allow the paradoxical objects that are non-measurable sets to even exist, we should really have to work to get them - an algebra that comes from a Hausdorff topology in which the singleton sets aren’t measurable, and in which therefore almost every single open and closed set is non-measurable, would make pretty much all the sets we actually care about non-measurable. However, there is one problem with this argument. Even if one accepts that the Hausdorff assumption is a reasonable one in all cases, why must all algebras be generated by a topology? Intuitively - is it possible to speak of the probability of different events in a setting in which an appropriate concept of “nearness” cannot exist, and if so, is it possible to even envision a practical situation in which one might want to do so? If one accepts from first principles that the σ σ-field, closed under countable union, is the natural setting for probability theory (which is not obvious either), then what additional assumption must one make in order to further require that these algebras result from some choice of topology? This isn’t a completely trivial question, because one can prove that there exist sigma-algebras that are provably not the Borel algebras of any topology. And if discussing algebras that don’t come from topologies is reasonable, then it’s not obvious that in every sigma-algebra of interest, the singleton sets must be measurable. I suspect that the answer to this last question lies in a more structuralist view of probability theory, like that sketched out in Is there an introduction to probability theory from a structuralist/categorical perspective?, in which a category is constructed in which measurable spaces are equivalent to their completions, and in which I suspect it might follow that an element of each equivalence class of measurable spaces can be constructed as the Borel algebra of some topology - though I suppose this may be true only for those measure spaces corresponding to localizable measurable spaces. I don’t actually know. An interesting question that I can’t answer, then, is: in this category of measurable spaces, is every measurable space equivalent to a space that is at least as fine as the Borel algebra generated by some topology - and, if so, what about Hausdorff topologies in particular? Upvote · 9 3 Related questions More answers below What is a singleton set with an example? What is singleton set ? Is an empty set an element of a singleton set, or is an empty set contained in a singleton set? What are some examples of a singleton set? Why is singleton considered a set? Liam Roche MMath in Mathematics, University of Cambridge ·1y In commonly used measures (such as the usual one on a finite dimensional vector space), single point sets are measurable. However, this is not always so. For a trivial counterexample, take a two point set and the sigma-algebra comprising just the whole set (measure 1) and the empty set (measure 0). Both single point subsets are not measurable. (I believe you could create more complex counterexamples from quotients of normal measure spaces where a non-measurable set is sent to a single point). Upvote · MyMathYourMath PhD in Pure Mathematics, University of Houston (Graduated 2024) · Author has 1.7K answers and 376.5K answer views ·3y You can put it in an epsilon ball. I.e., x∈(x−ϵ,x+ϵ)x∈(x−ϵ,x+ϵ) then the size or measure of this set is 2 ϵ 2 ϵ which can be made arbitrarily small and the singleton set {x}{x} Has measure 0 and is thus measurable. Your response is private Was this worth your time? This helps us sort answers on the page. Absolutely not Definitely yes Upvote · 9 1 David Joyce Ph.D. in Mathematics, University of Pennsylvania (Graduated 1979) · Upvoted by Allan Steinhardt , PhD EE, published in various math journals, inventor, hyperbolic Householder and Justin Rising , PhD in statistics · Author has 9.9K answers and 68.4M answer views ·6y Related Why is an empty set, ∅, a measurable set and not a non-measurable set? Why would a set be non-measurable? It would be because there is no single number that you could assign to its measure. What could the measure of the empty set be? Let’s take the standard measure on the real line R.R. The measure of an interval, whether open or closed, is its length, which is the difference between its endpoints. So, for example, the measure of the open interval (1,5)(1,5) is 4.4. The empty set is a subset of that interval, so its measure will have to be less than or equal to 4.4. The empty set is a subset of every interval, so it will have to have a measure less than or equal to t Continue Reading Why would a set be non-measurable? It would be because there is no single number that you could assign to its measure. What could the measure of the empty set be? Let’s take the standard measure on the real line R.R. The measure of an interval, whether open or closed, is its length, which is the difference between its endpoints. So, for example, the measure of the open interval (1,5)(1,5) is 4.4. The empty set is a subset of that interval, so its measure will have to be less than or equal to 4.4. The empty set is a subset of every interval, so it will have to have a measure less than or equal to the length of every interval. Every positive number is the length of some interval, so the measure of the empty set has to be less than every positive number. Since measures cannot be negative, therefore the only number that you could assign as a measure for the empty set is 0.0. In fact, one of the statements in the definition for measures is that the measure of the empty set is 0.0. The above paragraph shows why that has to be so for the standard measure on the real line. Upvote · 99 58 9 6 Related questions More answers below How do you show a given set is measurable? What is difference between singleton set or unit set and equal set? What is the definition of a measurable set? Are all subsets measurable sets? What is the subset of a singleton set? Is an empty set a singleton? Assistant Bot · 1y A singleton set is a set that contains exactly one element. In mathematical terms, a singleton set can be expressed as S={x}S={x}, where x x is the single element of the set. Measurability of Singleton Sets Lebesgue Measure: In the context of Lebesgue measure on the real numbers, a singleton set S={x}S={x} is measurable. In fact, the Lebesgue measure of any singleton set is zero: m({x})=0 m({x})=0 This means that while the set contains an element, it occupies no "length" in one-dimensional space. Borel Measure: Singleton sets are also Borel measurable. The Borel σ σ-algebra i Continue Reading A singleton set is a set that contains exactly one element. In mathematical terms, a singleton set can be expressed as S={x}S={x}, where x x is the single element of the set. Measurability of Singleton Sets Lebesgue Measure: In the context of Lebesgue measure on the real numbers, a singleton set S={x}S={x} is measurable. In fact, the Lebesgue measure of any singleton set is zero: m({x})=0 m({x})=0 This means that while the set contains an element, it occupies no "length" in one-dimensional space. Borel Measure: Singleton sets are also Borel measurable. The Borel σ σ-algebra is generated by open intervals, and since singletons can be constructed from open sets, they are included in this σ σ-algebra. General Measure Theory: In the context of general measure theory, a set is measurable if it is part of the σ σ-algebra associated with the measure. Singleton sets are typically included in any reasonable measure space because they can be formed from open sets through countable unions or intersections. Conclusion In summary, singleton sets are measurable in most common measure theories, including Lebesgue and Borel measures, and they have a measure of zero. This property is essential in various fields of mathematics, including analysis and probability theory. Upvote · Terry Moore M.Sc. in Mathematics, University of Southampton (Graduated 1968) · Upvoted by Justin Rising , PhD in statistics · Author has 16.6K answers and 29.4M answer views ·6y Related How do you show a given set is measurable? How do you show a given set is measurable? The formal definition of “measurable” is not useful in practice. It just provides logical consistency. In practice any set you can describe in a finite English expression will be measurable. The examples of non-measurable sets appeal to the axiom of choice or equivalent to say “pick one element of each member of this uncountably infinite family of sets”. You can usually prove a set is measurable if you want to, but if you can describe it without ambiguity, then it will be. Suppose you are interested in subsets of the real line and Lebesgue measure. Then Continue Reading How do you show a given set is measurable? The formal definition of “measurable” is not useful in practice. It just provides logical consistency. In practice any set you can describe in a finite English expression will be measurable. The examples of non-measurable sets appeal to the axiom of choice or equivalent to say “pick one element of each member of this uncountably infinite family of sets”. You can usually prove a set is measurable if you want to, but if you can describe it without ambiguity, then it will be. Suppose you are interested in subsets of the real line and Lebesgue measure. Then ask yourself some questions. Is it an interval? If yes, it is measurable. Is it a finite or countable union of intervals? If yes it is measurable. Is it the complement of a set you know is measurable? If yes it’s measurable. Is it a countable union or intersection of sets you know to be measurable? If yes it’s measurable. Upvote · 99 12 Justin Rising PhD in statistics · Upvoted by David Joyce , Ph.D. Mathematics, University of Pennsylvania (1979) · Author has 12.1K answers and 26.5M answer views ·6y Related Why is an empty set, ∅, a measurable set and not a non-measurable set? We would like for the measure of A∪∅A∪∅ to be equal to the measure of A A for what I think are pretty obvious reasons. If the empty set were non-measurable, we’d have to take that as a special case, but if we just give it measure zero, then that (and everything else) falls out naturally. Upvote · 9 3 Alon Amit PhD in Mathematics; Mathcircler. · Upvoted by Dan Grubb , Ph. D. Mathematics, Kansas State University (1986) and Yair Livne , Master's Mathematics, Hebrew University of Jerusalem (2007) · Author has 8.8K answers and 173.8M answer views ·13y Related How many Borel measurable sets are there? It's the cardinality of the continuum. Sketch proof: You can prove this by constructing the set of Borel sets by transfinite induction, starting from the intervals [a,b][a,b] along with the empty set and the real line itself. At each step in the induction, add the complements of subsets already constructed and also all countable unions of those subsets. At limit ordinals, just take the union of everything you had so far. Once you get to the first uncountable ordinal ω 1 ω 1, you will have generated all Borel sets (proof: show that the constructed family at this stage is a σ σ-algebra). It's now Continue Reading It's the cardinality of the continuum. Sketch proof: You can prove this by constructing the set of Borel sets by transfinite induction, starting from the intervals [a,b][a,b] along with the empty set and the real line itself. At each step in the induction, add the complements of subsets already constructed and also all countable unions of those subsets. At limit ordinals, just take the union of everything you had so far. Once you get to the first uncountable ordinal ω 1 ω 1, you will have generated all Borel sets (proof: show that the constructed family at this stage is a σ σ-algebra). It's now straightforward to prove that at each step in this process, the cardinality of sets already constructed is just c c, and therefore the same is true for the union of all of them. Interestingly, the family of Lebesgue-measurable sets is way bigger: it has cardinality 2 c 2 c, just as large as the set of all subsets of R R. This is even easier to prove: you just need to know that there exists a set of measure 0 and cardinality c c. The Cantor set fits the bill. Now, any subset of this set is Lebesgue-measurable, QED. Upvote · 99 34 9 1 Roger Pickering Spent 6 years at 2 universities doing maths · Author has 14.9K answers and 5.9M answer views ·7y Related Is an empty set an element of a singleton set, or is an empty set contained in a singleton set? I think you are struggling with the terminology here. A singleton set is just a set with one element. So, for example {2} is a set with a single element, namely 2. And 2 is the only element of this set. In particular, the empty set ϕ ϕ is not an element of this set. However, the empty set is a subset of all sets, including this one. That is part of the definition of the relationship “subset of”. It isn't something that had to be true or is self-evidently true but it was helpful to define it that way. Now it is perfectly possible for the empty set to be contained in a set, for instance the set A= Continue Reading I think you are struggling with the terminology here. A singleton set is just a set with one element. So, for example {2} is a set with a single element, namely 2. And 2 is the only element of this set. In particular, the empty set ϕ ϕ is not an element of this set. However, the empty set is a subset of all sets, including this one. That is part of the definition of the relationship “subset of”. It isn't something that had to be true or is self-evidently true but it was helpful to define it that way. Now it is perfectly possible for the empty set to be contained in a set, for instance the set A= { ϕ ϕ, {2} }. That is a rather special set because its members (elements) are themselves sets. It isn't a singleton though, because it has two elements. Now we can get really tricky and define a new set B={ϕ ϕ}. This is a singleton and it's one element is the set ϕ ϕ. So the empty set is an element of B and in fact it is the only element that B has. One last point, there is only one empty set, denoted ϕ ϕ., although you might arrive at the empty set in many ways. For example {all integers i such that i 2=3 i 2=3} or {all people greater than 4 metres tall}. Both of these are empty sets (for different reasons) but the result is still the same - the set with no elements. Upvote · 9 6 9 2 Eric Platt Ph.D in Mathematics, University of Houston (Graduated 2017) · Upvoted by Terry Moore , M.Sc. Mathematics, University of Southampton (1968) and Michael Lamar , PhD in Applied Mathematics · Author has 2.7K answers and 13.3M answer views ·Updated 3y Related Are there finite sets not measurable by the Lebesgue measure? Every set that is a finite collection of points has Lebesgue measure of zero; the same as a single point or a countable number of points like Q Q. Measures have the property that the measure of finite and countable unions of disjoint sets is the sum of the measures. μ(∞⋃j=1 S j)=∞∑j=1 μ(S j)when i≠j⇒S i∩S j=∅μ(⋃j=1∞S j)=∑j=1∞μ(S j)when i≠j⇒S i∩S j=∅ The Lebesgue measure of an interval is its length. Points have zero Lebesgue measure. λ([a,b])=b−a λ([a,b])=b−a The only way a set can have positive Lebesgue measure or be unmeasurable is if it has an Continue Reading Every set that is a finite collection of points has Lebesgue measure of zero; the same as a single point or a countable number of points like Q Q. Measures have the property that the measure of finite and countable unions of disjoint sets is the sum of the measures. μ(∞⋃j=1 S j)=∞∑j=1 μ(S j)when i≠j⇒S i∩S j=∅μ(⋃j=1∞S j)=∑j=1∞μ(S j)when i≠j⇒S i∩S j=∅ The Lebesgue measure of an interval is its length. Points have zero Lebesgue measure. λ([a,b])=b−a λ([a,b])=b−a The only way a set can have positive Lebesgue measure or be unmeasurable is if it has an uncountable number of points. Sets like the Cantor set have an uncountable number of points while still having zero measure. Upvote · 99 36 Jayanta Mukherjee B Tech IEE in Instrumentation Engineering, Jadavpur University (Graduated 1990) · Author has 43.6K answers and 11.1M answer views ·4y Related What is difference between singleton set or unit set and equal set? Simgleton set and Unit set are the same thing; these are such sets which contain exactly one element in them. Two sets are equal to one another when they have the same cardinality (number of elements in a set) and composition (all constituent elements of a set). Continue Reading Simgleton set and Unit set are the same thing; these are such sets which contain exactly one element in them. Two sets are equal to one another when they have the same cardinality (number of elements in a set) and composition (all constituent elements of a set). Upvote · 9 3 9 1 David Joyce Ph.D. in Mathematics, University of Pennsylvania (Graduated 1979) · Upvoted by José Ilhano Silva , M. S. Mathematics & Differential Geometry, Federal University of Ceará (2017) · Author has 9.9K answers and 68.4M answer views ·1y Related Is a set having an empty set a singleton set or not? A set which has one and only one element is called a singleton set. If S={T},S={T}, then T T is the only element of the set S.S. In set theory, elements themselves can be sets, so that element T T can be a set itself. It might be a set with three elements T={a,b,c},T={a,b,c}, or set with two elements T={a,b},T={a,b}, or a set with one element T={a},T={a}, or even a set with no elements T=∅.T=∅. The set S={∅},S={∅}, which has only the empty set as an element, is a singleton set. Upvote · 99 18 Richi Kar 2y Related What is the outer measure of a measurable set? In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical condition. Continue Reading In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical condition. Upvote · 9 2 Related questions What is a singleton set with an example? What is singleton set ? Is an empty set an element of a singleton set, or is an empty set contained in a singleton set? What are some examples of a singleton set? Why is singleton considered a set? How do you show a given set is measurable? What is difference between singleton set or unit set and equal set? What is the definition of a measurable set? Are all subsets measurable sets? What is the subset of a singleton set? Is an empty set a singleton? What are the singleton alternatives? What is the difference between a singleton and a unique set (as in mathematics)? What is the number of elements in a singleton set? What is the definition of a measurable set? Does every measurable set contain all singletons? What is the difference between a set and a singleton? Related questions What is a singleton set with an example? What is singleton set ? Is an empty set an element of a singleton set, or is an empty set contained in a singleton set? What are some examples of a singleton set? Why is singleton considered a set? How do you show a given set is measurable? Advertisement About · Careers · Privacy · Terms · Contact · Languages · Your Ad Choices · Press · © Quora, Inc. 2025
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https://www.britannica.com/science/liquid-state-of-matter/Solutions-and-solubilities
Liquid - Solutions, Solubilities, Mixtures | Britannica Search Britannica Click here to search Search Britannica Click here to search SUBSCRIBE SUBSCRIBE Login SUBSCRIBE Ask the ChatbotGames & QuizzesHistory & SocietyScience & TechBiographiesAnimals & NatureGeography & TravelArts & CultureProConMoneyVideos liquid Introduction Physical properties of liquids Transitions between states of matter Behaviour of pure liquids Phase diagram of a pure substance Representative values of phase-diagram parameters Behaviour of substances near critical and triple points Surface tension Molecular structure of liquids Speed of sound and electric properties Solutions and solubilities Classes of solutions Electrolytes and nonelectrolytes Weak electrolytes Endothermic and exothermic solutions Properties of solutions Composition ratios Molarity Molality Formality Mole fraction and mole percentage Volume fraction Equilibrium properties Fugacity Raoult’s law Partial miscibility Colligative properties Rise in boiling point Decrease in freezing point Osmotic pressure Transport properties in solutions Viscosity Thermal conductivity Diffusivity Thermodynamics and intermolecular forces in solutions Energy considerations Effects of molecular structure Molecular structure and charge distribution Polar molecules Nonpolar molecules Effects of chemical interactions Hydrogen bonding: association Hydrogen bonding: solvation Theories of solutions Activity coefficients and excess functions Regular and athermal solutions Regular solutions Athermal solutions Associated and solvated solutions Solutions of electrolytes Solubilities of solids and gases References & Edit HistoryQuick Facts & Related Topics Images & Videos For Students liquid summary Quick Summary Ask the Chatbot a Question SciencePhysicsMatter & Energy Solutions and solubilities in liquid Quick Summary Ask the Chatbot Print Cite Share Feedback External Websites Also known as: liquid state Written by Written by John M. Prausnitz Professor of Chemical Engineering, University of California, Berkeley. Author of Molecular Thermodynamics of Fluid-Phase Equilibria. John M. Prausnitz , Bruce E. Poling Professor and Chairman, Department of Chemical Engineering, University of Toledo, Ohio. Coauthor of The Properties of Gases and Liquids. Bruce E. Poling•All Fact-checked by Fact-checked by The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree.... The Editors of Encyclopaedia Britannica Last Updated: Aug. 30, 2025•Article History Table of Contents Table of Contents Quick Summary Ask the Chatbot a Question The ability of liquids to dissolve solids, other liquids, or gases has long been recognized as one of the fundamental phenomena of nature encountered in daily life. The practical importance of solutions and the need to understand their properties have challenged numerous writers since the Ionian philosophers and Aristotle. Though many physicists and chemists have devoted themselves to a study of solutions, as of the early 1990s it was still an incompletely understood subject under active investigation. A solution is a mixture of two or more chemically distinct substances that is said to be homogeneous on the molecular scale—the composition at any one point in the mixture is the same as that at any other point. This is in contrast to a suspension (or slurry), in which small discontinuous particles are surrounded by a continuous fluid. Although the word solution is commonly applied to the liquid state of matter, solutions of solids and gases are also possible; brass, for example, is a solution of copper and zinc, and air is a solution primarily of oxygen and nitrogen with a few other gases present in relatively small amounts. The ability of one substance to dissolve another depends always on the chemical nature of the substances, frequently on the temperature, and occasionally on the pressure. Water, for example, readily dissolves methyl alcohol but does not dissolve mercury; it barely dissolves benzene at room temperature but does so increasingly as the temperature rises. While the solubility in water of the gases present in air is extremely small at atmospheric pressure, it becomes appreciable at high pressures where, in many cases, the solubility of a gas is (approximately) proportional to its pressure. Thus, a diver breathes air (four-fifths nitrogen) at a pressure corresponding to the pressure around him, and, as he goes deeper, more air dissolves in his blood. If he ascends rapidly, the solubility of the gases decreases so that they leave his blood suddenly, forming bubbles in the blood vessels. This condition (known as the bends) is extremely painful and may cause death; it can be alleviated by breathing, instead of air, a mixture of helium and oxygen because the solubility of helium in blood is much lower than that of nitrogen. The solubility of one fluid in another may be complete or partial; thus, at room temperature water and methyl alcohol mix in all proportions, but 100 grams of water dissolve only 0.07 gram of benzene. Though it is generally supposed that all gases are completely miscible—i.e., mutually soluble in all proportions—this is true only at normal pressures. At high pressures pairs of chemically unlike gases may exhibit only limited miscibility; for example, at 20° C helium and xenon are completely miscible at pressures below 200 atmospheres but become increasingly immiscible as the pressure rises. The ability of a liquid to dissolve selectively forms the basis of common separation operations in chemical and related industries. A mixture of two gases, carbon dioxide and nitrogen, can be separated by bringing it into contact with ethanolamine, a liquid solvent that readily dissolves carbon dioxide but barely dissolves nitrogen. In this process, called absorption, the dissolved carbon dioxide is later recovered, and the solvent is made usable again by heating the carbon dioxide-rich solvent, since the solubility of a gas in a liquid usually (but not always) decreases with rising temperature. A similar absorption operation can remove a pollutant such as sulfur dioxide from smokestack gases in a plant using sulfur-containing coal or petroleum as fuel. The process wherein a dissolved substance is transferred from one liquid to another is called extraction. As an example, phenolic pollutants (organic compounds of the types known as phenol, cresol, and resorcinol) are frequently found in industrial aqueous waste streams, and, since these phenolics are damaging to marine life, it is important to remove them before sending the waste stream back to a lake or river. One such removal technique is to bring the waste stream into contact with a water-insoluble solvent (e.g., an organic liquid such as a high-boiling hydrocarbon) that has a strong affinity for the phenolic pollutant. The solubility of the phenolic in the solvent divided by that in water is called the distribution coefficient, and it is clear that for an efficient extraction process it is desirable to have as large a distribution coefficient as possible. Classes of solutions Electrolytes and nonelectrolytes How different solutions conduct electricity Conducting electric current in a solution of electrolytes.(more) See all videos for this article Broadly speaking, liquid mixtures can be classified as either solutions of electrolytes or solutions of nonelectrolytes. Electrolytes are substances that can dissociate into electrically charged particles called ions, while nonelectrolytes consist of molecules that bear no net electric charge. Thus, when ordinary salt (sodium chloride, formula NaCl) is dissolved in water, it forms an electrolytic solution, dissociating into positive sodium ions (Na+) and negative chloride ions (Cl-), whereas sugar dissolved in water maintains its molecular integrity and does not dissociate. Because of its omnipresence, water is the most common solvent for electrolytes; the ocean is a solution of electrolytes. Electrolyte solutions, however, are also formed by other solvents (such as ammonia and sulfur dioxide) that have a large dielectric constant (a measure of the ability of a fluid to decrease the forces of attraction and repulsion between charged particles). The energy required to separate an ion pair (i.e., one ion of positive charge and one ion of negative charge) varies inversely with the dielectric constant, and, therefore, appreciable dissociation into separate ions occurs only in solvents with large dielectric constants. Most electrolytes (for example, salts) are nonvolatile, which means that they have essentially no tendency to enter the vapour phase. There are, however, some notable exceptions, such as hydrogen chloride (HCl), which is readily soluble in water, where it forms hydrogen ions (H+) and chloride ions (Cl-). At normal temperature and pressure, pure hydrogen chloride is a gas, and, in the absence of water or some other ionizing solvent, hydrogen chloride exists in molecular, rather than ionic, form. Solutions of electrolytes readily conduct electricity, whereas nonelectrolyte solutions do not. A dilute solution of hydrogen chloride in water is a good electrical conductor, but a dilute solution of hydrogen chloride in a hydrocarbon is a good insulator. Because of the large difference in dielectric constants, hydrogen chloride is ionized in water but not in hydrocarbons. The ability of a solution to conduct electricity is called conductivity, and it decreases as the concentration of the electrolytes decreases. The molar conductivity of a solution is the conductivity divided by the concentration of the solution measured in moles per volume. Thus as the concentration decreases, the molar conductivity increases. Conductivity is measured in units of siemens per meter (or amperes per volt-meter). The conductivity of a solution is not only affected by the molar concenration of the ions but also by temperature and pressure. Devices called conductivity cells that have two electrodes with a current between them. By measuring the current between them and using solutions of potassium chloride (KCl) as a standard, one can determine the conductivity of the solution. Chatbot answers are created from Britannica articles using AI. This is a beta feature. AI answers may contain errors. Please verify important information using Britannica articles. About Britannica AI. Britannica Chatbot Chatbot answers are created from Britannica articles using AI. This is a beta feature. AI answers may contain errors. Please verify important information using Britannica articles. About Britannica AI. Weak electrolytes While classification under the heading electrolyte-solution or nonelectrolyte-solution is often useful, some solutions have properties near the boundary between these two broad classes. Although such substances as ordinary salt and hydrogen chloride are strong electrolytes—i.e., they dissociate completely in an ionizing solvent—there are many substances, called weak electrolytes, that dissociate to only a small extent in ionizing solvents. For example, in aqueous solution, acetic acid can dissociate into a positive hydrogen ion and a negative acetate ion (CH 3 COO-), but it does so to a limited extent; in an aqueous solution containing 50 grams acetic acid and 1,000 grams water, less than 1 percent of the acetic acid molecules are dissociated into ions. Therefore, a solution of acetic acid in water exhibits some properties associated with electrolyte solutions (e.g., it is a fair conductor of electricity), but in general terms it is more properly classified as a nonelectrolyte solution. By similar reasoning, an aqueous solution of carbon dioxide is also considered a nonelectrolyte solution even though carbon dioxide and water have a slight tendency to form carbonic acid, which, in turn, dissociates to a small extent to hydrogen ions and bicarbonate ions (HCO 3-). Endothermic and exothermic solutions When two substances mix to form a solution, heat is either evolved (an exothermic process) or absorbed (an endothermic process); only in the special case of an ideal solution do substances mix without any heat effect. Most simple molecules mix with a small endothermic heat of solution, while exothermic heats of solution are observed when the components interact strongly with one another. An extreme example of an exothermic heat of mixing is provided by adding an aqueous solution of sodium hydroxide, a powerful base, to an aqueous solution of hydrogen chloride, a powerful acid; the hydroxide ions (OH-) of the base combine with the hydrogen ions of the acid to form water, a highly exothermic reaction that yields 75,300 calories per 100 grams of water formed. In nonelectrolyte solutions, heat effects are usually endothermic and much smaller, often about 100 calories, when roughly equal parts are mixed to form 100 grams of mixture. Formation of a solution usually is accompanied by a small change in volume. If equal parts of benzene and stannic chloride are mixed, the temperature drops; if the mixture is then heated slightly to bring its temperature back to that of the unmixed liquids, the volume increases by about 2 percent. On the other hand, mixing roughly equal parts of acetone and chloroform produces a small decrease in volume, about 0.2 percent. It frequently happens that mixtures with endothermic heats of mixing expand—i.e., show small increases in volume—while mixtures with exothermic heats of mixing tend to contract. A large decrease in volume occurs when a gas is dissolved in a liquid. For example, at 0° C and atmospheric pressure, the volume of 28 grams of nitrogen gas is 22,400 cubic centimetres. When these 28 grams of nitrogen are dissolved in an excess of water, the volume of the water increases only 40 cubic centimetres; the decrease in volume accompanying the dissolution of 28 grams of nitrogen in water is therefore 22,360 cubic centimetres. In this case, it is said that the nitrogen gas has been condensed into a liquid, the word condense meaning “to make dense”—i.e., to decrease the volume. Properties of solutions Composition ratios The composition of a liquid solution means the composition of that solution in the bulk—that is, of that part that is not near the surface. The interface between the liquid solution and some other phase (for example, a gas such as air) has a composition that differs, sometimes very much, from that of the bulk. The environment at an interface is significantly different from that throughout the bulk of the liquid, and in a solution the molecules of a particular component may prefer one environment over the other. If the molecules of one component in the solution prefer to be at the interface as opposed to the bulk, it is said that this component is positively adsorbed at the interface. In aqueous solutions of organic liquids, the organic component is usually positively adsorbed at the solution-air interface; as a result, it is often possible to separate a mixture of an organic solute from water by a process called froth separation. Air is bubbled vigorously into the solution, and a froth is formed. The composition of the froth differs from that of the bulk because the organic solute concentrates at the interfacial region. The froth is mechanically removed and collapsed, and, if further separation is desired, a new froth is generated. The tendency of some dissolved molecules to congregate at the surface has been utilized in water conservation. A certain type of alcohol, when added to water, concentrates at the surface to form a barrier to evaporating water molecules. In warm climates, therefore, water loss by evaporation from lakes can be significantly reduced by introducing a solute that adsorbs positively at the lake-air interface. The composition of a solution can be expressed in a variety of ways, the simplest of which is the weight fraction, or weight percent; for example, the salt content of seawater is about 3.5 weight percent—i.e., of 100 grams of seawater, 3.5 grams is salt. For a fundamental understanding of solution properties, however, it is often useful to express composition in terms of molecular units such as molecular concentration, molality, or mole fraction. To understand these terms, it is necessary to define atomic and molecular weights. The atomic weight of elements is a relative figure, with one atom of the carbon-12 isotope being assigned the atomic weight of 12; the atomic weight of hydrogen is then approximately 1, of oxygen approximately 16, and the molecular weight of water (H 2 O) 18. The atomic and molecular theory of matter asserts that the atomic weight of any element in grams must contain the same number of atoms as the atomic weight in grams (the gram-atomic weight) of any other element. Thus, two grams of molecular hydrogen (H 2)—its gram-molecular weight—contain the same number of molecules as 18 grams of water or 32 grams of oxygen molecules (O 2). Further, a specified volume of any gas (at low pressure) contains the same number of molecules as the same volume of any other gas at the same temperature and pressure. At standard temperature and pressure (0° C and one atmosphere) the volume of one gram-molecular weight of any gas has been determined experimentally to be approximately 22.4 litres (23.7 quarts). The number of molecules in this volume of gas, or in the gram-molecular weight of any compound, is called Avogadro’s number. Load Next Page Feedback Corrections? Updates? Omissions? Let us know if you have suggestions to improve this article (requires login). Feedback Type Your Feedback Submit Feedback Thank you for your feedback Our editors will review what you’ve submitted and determine whether to revise the article. print Print Please select which sections you would like to print: [x] Table Of Contents [x] Introduction [x] Physical properties of liquids [x] Transitions between states of matter [x] Behaviour of pure liquids [x] Solutions and solubilities verified Cite While every effort has been made to follow citation style rules, there may be some discrepancies. Please refer to the appropriate style manual or other sources if you have any questions. Select Citation Style Prausnitz, John M., Poling, Bruce E., Rowlinson, John Shipley. "liquid". Encyclopedia Britannica, 30 Aug. 2025, Accessed 29 September 2025. Copy Citation Share Share to social media FacebookX URL External Websites PNAS - Significant structures in the liquid state (PDF) Nature - Scientific Reports - Duality of liquids Florida State University - Department of Chemistry and Biochemistry - Properties of Liquids Openstax - Chemistry 2e - Properties of Liquids Chemistry LibreTexts - Properties of Liquids LiveScience - Properties of Matter: Liquids Indian Academy of Sciences - Publication of Fellows - The Liquid State NSCC Libraries Pressbooks - Introductory Chemistry – 1st Canadian / NSCC Edition - Properties of Liquids Britannica Websites Articles from Britannica Encyclopedias for elementary and high school students. liquid - Student Encyclopedia (Ages 11 and up)
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https://www.sats-papers.co.uk/wrm/year-3/year-3-mathematics-2022-spring-white-rose-reasoning-problem-solving-paper-2.pdf
Mathematics Paper 2: reasoning and problem solving First name Middle name Last name Date of birth Day Month Year Teacher This progress check has been designed by White Rose Maths. For more information, please visit whiterosemaths.com Spring progress check Year 3 9 781804 780213 ISBN 978-1-80478-021-3 Page 2 of 16 © White Rose Maths 2022 BLANK PAGE Please do not write on this page. Page 3 of 16 © White Rose Maths 2022 Show your method Questions and answers You have 50 minutes to complete this paper. Follow the instructions for each question. Work as quickly and as carefully as you can. If you need to do working out, you can use the space around the question. Some questions have a method box like this: For these questions you may get a mark for showing your method. If you cannot do one of the questions, go on to the next one. You can come back to it later, if you have time. If you finish before the end, go back and check your work. Marks The number under each line at the side of the page tells you the maximum number of marks for each question. Instructions You may not use a calculator to answer any questions in this paper. Page 4 of 16 © White Rose Maths 2022 1 What is the length of the lolly stick? 0 cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 cm 1 mark How tall is the phone? 0 cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 cm mm 1 mark Page 5 of 16 © White Rose Maths 2022 2 Tick the shape that has 1 3 shaded. 1 mark 3 Write two multiplications and two divisions shown by the array. × = × = ÷ = ÷ = 2 marks Page 6 of 16 © White Rose Maths 2022 4 Complete the number line. 0 5 4 5 5 5 1 mark 5 28 children are put into groups of 4 How many groups are there? 1 mark Page 7 of 16 © White Rose Maths 2022 6 Complete the part-whole models. 3 7 7 7 1 mark 1 5 6 1 mark Page 8 of 16 © White Rose Maths 2022 7 What is the volume of liquid in each jug? 1 litre ml 1 mark 2 litre 1 litre l ml 1 mark Page 9 of 16 © White Rose Maths 2022 8 Write a number in each box to make the statements correct. 1 mark 1 mark 9 Here are three number cards. 121 98 145 What is the total of the smallest and greatest numbers? 2 marks 8 > 3 8 1 10 < 1 Page 10 of 16 © White Rose Maths 2022 10 Complete the sentences. 10 less than 397 is 1 mark 100 more than 63 is 1 mark is 10 less than 708 1 mark 11 Complete the number sentences. 40 × 3 = × 30 1 mark 40 × 3 = 20 × 1 mark Page 11 of 16 © White Rose Maths 2022 12 Nijah is using place value counters to multiply. Tens Ones Write her multiplication. × = 1 mark 13 Circle the numbers that are multiples of 10 400 65 80 101 270 Explain your reasoning. 1 mark Page 12 of 16 © White Rose Maths 2022 14 Write the lengths in order. Start with the shortest length. 1 m 180 cm 80 mm 78 cm shortest longest 1 mark 15 What is the mass of an apple? Circle the most appropriate estimate. 1 gram 10 grams 100 grams 1 kilogram 1 mark Page 13 of 16 © White Rose Maths 2022 16 Work out the perimeter of the rectangle. 2 cm 6 cm cm 1 mark 17 Write a fraction that is equivalent to 1 2 You may use the fraction wall to help you. 1 mark Page 14 of 16 © White Rose Maths 2022 18 A B C Jug A has half as much water as Jug C. Jug B has 85 ml less water than jug A. The volume of water in jug C is 1 litre. Work out the volumes of water in jug A and jug B. Show your method 2 marks jug A ml ml jug B Page 15 of 16 © White Rose Maths 2022 19 Eva has 3 m 60 cm of string. She cuts the string into 3 equal pieces. What is the length of each piece of string? m cm 1 mark 20 Huan has more than 30 buttons but fewer than 40 buttons. When he shares them equally into 4 bowls, he has no buttons left over. When he shares them equally into 5 bowls, he has one button left over. How many buttons does Huan have? 1 mark Page 16 of 16 © White Rose Maths 2022 END OF PAPER
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https://zhuanlan.zhihu.com/p/359975221
向量点乘与叉乘的概念及几何意义 - 知乎 首页 知乎直答 焕新 知乎知学堂 等你来答 ​ 切换模式 登录/注册 向量点乘与叉乘的概念及几何意义 首发于全栈游戏开发 切换模式 登录/注册 向量点乘与叉乘的概念及几何意义 Plane老师 官网：www.qiqiker.com，Unity游戏实战课程 收录于 · 全栈游戏开发 2050 人赞同了该文章 向量点乘：（内积） 点乘（Dot Product）的结果是点积，又称数量积或标量积（Scalar Product）。 在空间中有两个向量： a→=(x 1,y 1,z 1)\vec a=(x_1,y_1,z_1) ， b→=(x 2,y 2,z 2)\vec b=(x_2,y_2,z_2)， a→\vec a 与 b→\vec b 之间夹角为 θ\theta。 从代数角度看，点积是对两个向量对应位置上的值相乘再相加的操作，其结果即为点积。 a→⋅b→=x 1 x 2+y 1 y 2+z 1 z 2\vec a\cdot \vec b=x_1x_2+y_1y_2+z_1z_2 从几何角度看，点积是两个向量的长度与它们夹角余弦的积。 a→⋅b→=|a→||b→|cos⁡θ\vec a\cdot \vec b=\left |\vec a \right |\left |\vec b \right |\cos\theta 几何意义： 点乘的结果表示 \vec a 在 \vec b 方向上的投影与 \left |\vec b \right | 的乘积，反映了两个向量在方向上的相似度，结果越大越相似。基于结果可以判断这两个向量是否是同一方向，是否正交垂直，具体对应关系为： \vec a\cdot \vec b>0 则方向基本相同，夹角在0°到90°之间 \vec a\cdot \vec b=0 则正交，相互垂直 \vec a\cdot \vec b<0 则方向基本相反，夹角在90°到180°之间 点乘代数定义推导几何定义：（常用来求向量夹角） 设 \vec a 终点为 A(x_1,y_1,z_1) ， \vec b 的终点为 B(x_2,y_2,z_2) ,原点为 O ，则 \vec {AB}=(x_2-x_1,y_2-y_1,z_2-z_1) 在 \triangle OAB 中，由余弦定理得： \left |\vec {AB}\right |^2=\left |\vec a \right |^2+\left |\vec b \right |^2-2\left |\vec a \right |\left |\vec b \right |\cos\theta 使用距离公式进行处理，可得： \left |\vec a \right |\left |\vec b \right |\cos\theta=\frac {x_1^2+y_1^2+z_1^2+x_2^2+y_2^2+z_2^2-[(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2]}{2} 去括号后合并，可得： \left |\vec a \right |\left |\vec b \right |\cos\theta=x_1x_2+y_1y_2+z_1z_2=\vec a\cdot \vec b 根据上面的工式可计算 \vec a 与 \vec b 之间的夹角： \theta=\arccos (\frac {\vec a\cdot\vec b} {\left |\vec a \right |\left |\vec b \right |}) 向量叉乘：（外积） 叉乘（Cross Product）又称向量积（Vector Product）。 在空间中有两个向量： \vec a=(x_1,y_1,z_1) ， \vec b=(x_2,y_2,z_2)， \vec a 与 \vec b 之间夹角为 \theta。 从代数角度计算： \vec a\times \vec b=(y_1z_2-z_1y_2,z_1x_2-x_1z_2,x_1y_2-y_1x_2) 从几何角度计算：( \vec n 为 \vec a 与 \vec b 所构成平面的单位向量) \vec a\times \vec b=\left |\vec a \right |\left |\vec b \right |\sin\theta \vec n 其运算结果是一个向量，并且与这两个向量都垂直，是这两个向量所在平面的法线向量。使用右手定则确定其方向。 几何意义： 如果以向量\vec a 和\vec b 为边构成一个平行四边形，那么这两个向量外积的模长与这个平行四边形的面积相等。 编辑于 2022-07-08 15:23 Unity（游戏引擎） 游戏物理 向量 ​赞同 2050​​104 条评论 ​分享 ​喜欢​收藏​申请转载 ​ 写下你的评论... 104 条评论 默认 最新 guaner 感谢作者，看了好些篇，我终于在这里彻底明白了，顺便补充几句自己的感受，分享后人：内积是把a向量投影到b向量上面，让两者同向或者反向，让a向量箭头指向b向量里面，所以叫内积，（非官方，本人感受，同直线情况广义指向内里），外积是把a向量投影到b向量的法线方向，所以你看，投影完箭头指向了b向量的外面，所以你看透彻理解多重要，字面意思就都理解了有木有，另外，内积两个向量谁投影谁都没关系，因为最后是一个数值，不影响结果，外积就不一样了，一定是1投影2，因为要用右手确定结果3向量的方向，有前后顺序之分，更像是1带2的扭矩方向的感觉 2021-09-15 ​回复​120 月色 看完你的解释我糊了 2021-11-14 ​回复​67 JJJJJJJJJ 内积的理解很到位，而向量a和向量b的外积得到的那个向量（向量c）是垂直于a、b两个向量的哦，而1.向量b的法向量有无数个；2.如果是把a对向量c作投影，那投影结果是一个点，因为a和c是垂直的。 2022-05-26 ​回复​31 查看全部 12 条回复​ Agnoi 叉乘方向的判断用右手螺旋定律好像更容易理解一些。设：A×B。则用四指从A旋转至B，大拇指所指方向为叉乘方向。（四指正常旋转，两个方向都可以转的人慎用） 2021-05-05 ​回复​42 季夏贰叁247 括号里面足够严谨 2024-04-21 ​回复​4 kkkk 哈哈哈哈哈哈哈哈 2022-06-22 ​回复​1 查看全部 8 条回复​ 弔毛 一句话就能讲明白了：向量点乘得到标量，只有幅值没有方向，幅值为|a||b|cos。叉乘得到矢量，既有幅值也有方向，幅值为|a||b|sin，方向是a、b向量构成的平面的法线的方向，即：既垂直于a，也垂直于b，要用右手判断而不是左手，左手会得出相反的方向结论。确定了幅值和方向，一个矢量就确定了，就是叉乘的结果了。 2023-08-05 ​回复​27 颜yh 叉乘是解决角动量的计算产生的， 点乘是为了解决做功产生的。 2022-04-20 ​回复​23 与水水 alone walker 先有数学模型才有实际易用，叉乘的使用范围多了，比如图形学法线计算，点乘封装快速判定向量方向与筛选等.... 集成于算法中就是单纯的数学模型了，不要去解释他的意义。 2022-10-20 ​回复​17 jamse alone walker 先有的物理模型再有的数学概念，在牛顿的原理之前和之后的一段时间内数学都是这么出来的，向量也是从矢量里衍生出来的，最开始就是为了解决受力，运动，和能量的 2023-10-07 ​回复​11 查看全部 6 条回复​ 知春路换乘13号线 外积那里，向量n应该是和向量a，b平面垂直的单位向量吧 2021-12-15 ​回复​18 知乎用户cgt8gq 最后一句话 “那么这两个向量外积的模长与这个平行四边形的面积。” 没了？最后不应该加个相等之类的么 2021-04-10 ​回复​13 知执质志 其实就是说aXb表示的是：由向量a,b以及垂直于向量a,b所张成的平面(即该平面的基向量为a,b)为三维空间的一个基(三维空间由这三个向量张成)。 由于其中一个垂直于向量a,b所张成的平面，所以该向量可直接表示为aXb 2021-10-04 ​回复​2 WeiMax 相等 2021-12-16 ​回复​喜欢 展开其他 2 条回复​ 知乎用户RAGnuA 叉乘那里，“n为 a与 b所构成平面的单位向量”，应该是单位法向量吧 2022-05-01 ​回复​8 王W 我也觉得 2022-11-07 ​回复​2 知乎用户 应该是垂直的平面上的吧？ 2022-11-14 ​回复​2 展开其他 3 条回复​ 哒哒哒 中间求夹角的推导公式有个写错了吧，应该是 (x₂-x₁)²，而不是 (x₂-x₁²)，y和z也一样 2021-10-12 ​回复​6 Plane老师 作者 手滑了。多谢，已更正。 2022-02-09 ​回复​1 凛冬将至 这个“点乘反映了两个向量的相似度，结果越大越相似。”不太理解，只能反映方向上的相似度吧？ 2021-07-16 ​回复​5 底层思想家 哇! 确实,就是反映方向的相似度.取值为 0 向量垂直,取值为|a||b| 向量同一直线上,负数负数相反. 2022-04-04 ​回复​3 知乎用户20gCth 确实，作者写错了 2022-01-21 ​回复​1 查看全部 7 条回复​ Lyapunov 点乘的几何意义那里，根据图示，是a向量在b向量方向上的投影与b模的乘积 2021-03-30 ​回复​5 爱咋咋地 你这么一说点乘就懂了，叉乘还不懂 2021-04-23 ​回复​2 Plane老师 作者 Thanks. 2021-03-30 ​回复​喜欢 点击查看全部评论 写下你的评论... 关于作者 Plane老师 官网：www.qiqiker.com，Unity游戏实战课程 回答 6文章 12关注者 1,379 ​关注他​发私信 推荐阅读 向量的叉乘、点乘，看这一篇就够了！ ================= 苍溪 发表于机器学习 向量与代数（一）：两种角度理解点积和叉积 ==================== 子扬 发表于代数向量运算（叉乘几何意义） ============ 向量的叉乘，即求同时垂直两个向量的向量，即c垂直于a，同时c垂直于b（a与c的夹角为90°，b与c的夹角为90°） c = a×b = （a.yb.z-b.ya.z , b.xa.z-a.xb.z , a.xb.y-b.xa.y） 以上图… mmtest012 向量外积的高中数学运用 =========== 烧风 想来知乎工作？请发送邮件到 jobs@zhihu.com 打开知乎App 在「我的页」右上角打开扫一扫 其他扫码方式：微信 下载知乎App 无障碍模式 验证码登录 密码登录 开通机构号 中国 +86 获取短信验证码 获取语音验证码 登录/注册 其他方式登录 未注册手机验证后自动登录，注册即代表同意《知乎协议》《隐私保护指引》 扫码下载知乎 App 关闭二维码 打开知乎App 在「我的页」右上角打开扫一扫 其他扫码方式：微信 下载知乎App 无障碍模式 验证码登录 密码登录 开通机构号 中国 +86 获取短信验证码 获取语音验证码 登录/注册 其他方式登录 未注册手机验证后自动登录，注册即代表同意《知乎协议》《隐私保护指引》 扫码下载知乎 App 关闭二维码
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https://www.whitman.edu/mathematics/calculus_online/section12.05.html
Home » Three Dimensions » Lines and Planes 12.5 Lines and Planes [Jump to exercises] Expand menu Collapse menu Introduction 1 Analytic Geometry 1. Lines 2. Distance Between Two Points; Circles 3. Functions 4. Shifts and Dilations 2 Instantaneous Rate of Change: The Derivative 1. The slope of a function 2. An example 3. Limits 4. The Derivative Function 5. Properties of Functions 3 Rules for Finding Derivatives 1. The Power Rule 2. Linearity of the Derivative 3. The Product Rule 4. The Quotient Rule 5. The Chain Rule 4 Transcendental Functions 1. Trigonometric Functions 2. The Derivative of $\sin x$ 3. A hard limit 4. The Derivative of $\sin x$, continued 5. Derivatives of the Trigonometric Functions 6. Exponential and Logarithmic functions 7. Derivatives of the exponential and logarithmic functions 8. Implicit Differentiation 9. Inverse Trigonometric Functions 10. Limits revisited 11. Hyperbolic Functions 5 Curve Sketching 1. Maxima and Minima 2. The first derivative test 3. The second derivative test 4. Concavity and inflection points 5. Asymptotes and Other Things to Look For 6 Applications of the Derivative 1. Optimization 2. Related Rates 3. Newton's Method 4. Linear Approximations 5. The Mean Value Theorem 7 Integration 1. Two examples 2. The Fundamental Theorem of Calculus 3. Some Properties of Integrals 8 Techniques of Integration 1. Substitution 2. Powers of sine and cosine 3. Trigonometric Substitutions 4. Integration by Parts 5. Rational Functions 6. Numerical Integration 7. Additional exercises 9 Applications of Integration 1. Area between curves 2. Distance, Velocity, Acceleration 3. Volume 4. Average value of a function 5. Work 6. Center of Mass 7. Kinetic energy; improper integrals 8. Probability 9. Arc Length 10. Surface Area 10 Polar Coordinates, Parametric Equations 1. Polar Coordinates 2. Slopes in polar coordinates 3. Areas in polar coordinates 4. Parametric Equations 5. Calculus with Parametric Equations 11 Sequences and Series 1. Sequences 2. Series 3. The Integral Test 4. Alternating Series 5. Comparison Tests 6. Absolute Convergence 7. The Ratio and Root Tests 8. Power Series 9. Calculus with Power Series 10. Taylor Series 11. Taylor's Theorem 12. Additional exercises 12 Three Dimensions 1. The Coordinate System 2. Vectors 3. The Dot Product 4. The Cross Product 5. Lines and Planes 6. Other Coordinate Systems 13 Vector Functions 1. Space Curves 2. Calculus with vector functions 3. Arc length and curvature 4. Motion along a curve 14 Partial Differentiation 1. Functions of Several Variables 2. Limits and Continuity 3. Partial Differentiation 4. The Chain Rule 5. Directional Derivatives 6. Higher order derivatives 7. Maxima and minima 8. Lagrange Multipliers 15 Multiple Integration 1. Volume and Average Height 2. Double Integrals in Cylindrical Coordinates 3. Moment and Center of Mass 4. Surface Area 5. Triple Integrals 6. Cylindrical and Spherical Coordinates 7. Change of Variables 16 Vector Calculus 1. Vector Fields 2. Line Integrals 3. The Fundamental Theorem of Line Integrals 4. Green's Theorem 5. Divergence and Curl 6. Vector Functions for Surfaces 7. Surface Integrals 8. Stokes's Theorem 9. The Divergence Theorem 17 Differential Equations 1. First Order Differential Equations 2. First Order Homogeneous Linear Equations 3. First Order Linear Equations 4. Approximation 5. Second Order Homogeneous Equations 6. Second Order Linear Equations 7. Second Order Linear Equations, take two 18 Useful formulas 19 Introduction to Sage 1. Basics 2. Differentiation 3. Integration Lines and planes are perhaps the simplest of curves and surfaces in three dimensional space. They also will prove important as we seek to understand more complicated curves and surfaces. The equation of a line in two dimensions is $ax+by=c$; it is reasonable to expect that a line in three dimensions is given by $ax + by +cz = d$; reasonable, but wrong—it turns out that this is the equation of a plane. A plane does not have an obvious "direction'' as does a line. It is possible to associate a plane with a direction in a very useful way, however: there are exactly two directions perpendicular to a plane. Any vector with one of these two directions is called normal to the plane. So while there are many normal vectors to a given plane, they are all parallel or anti-parallel to each other. Suppose two points $\ds (v_1,v_2,v_3)$ and $\ds (w_1,w_2,w_3)$ are in a plane; then the vector $\ds \langle w_1-v_1,w_2-v_2,w_3-v_3\rangle$ is parallel to the plane; in particular, if this vector is placed with its tail at $\ds (v_1,v_2,v_3)$ then its head is at $\ds (w_1,w_2,w_3)$ and it lies in the plane. As a result, any vector perpendicular to the plane is perpendicular to $\ds \langle w_1-v_1,w_2-v_2,w_3-v_3\rangle$. In fact, it is easy to see that the plane consists of precisely those points $\ds (w_1,w_2,w_3)$ for which $\ds \langle w_1-v_1,w_2-v_2,w_3-v_3\rangle$ is perpendicular to a normal to the plane, as indicated in figure 12.5.1. That is, suppose we know that $\langle a,b,c\rangle$ is normal to a plane containing the point $\ds (v_1,v_2,v_3)$. Then $(x,y,z)$ is in the plane if and only if $\langle a,b,c\rangle$ is perpendicular to $\ds \langle x-v_1,y-v_2,z-v_3\rangle$. In turn, we know that this is true precisely when $\ds \langle a,b,c\rangle\cdot\langle x-v_1,y-v_2,z-v_3\rangle=0$. Thus, $(x,y,z)$ is in the plane if and only if $$\eqalign{ \langle a,b,c\rangle\cdot\langle x-v_1,y-v_2,z-v_3\rangle&=0\cr a(x-v_1)+b(y-v_2)+c(z-v_3)&=0\cr ax+by+cz-av_1-bv_2-cv_3&=0\cr ax+by+cz&=av_1+bv_2+cv_3.\cr }$$ Working backwards, note that if $(x,y,z)$ is a point satisfying $ax+by+cz=d$ then $$\eqalign{ ax+by+cz&=d\cr ax+by+cz-d&=0\cr a(x-d/a)+b(y-0)+c(z-0)&=0\cr \langle a,b,c\rangle\cdot\langle x-d/a,y,z\rangle&=0.\cr }$$ Namely, $\langle a,b,c\rangle$ is perpendicular to the vector with tail at $(d/a,0,0)$ and head at $(x,y,z)$. This means that the points $(x,y,z)$ that satisfy the equation $ax+by+cz=d$ form a plane perpendicular to $\langle a,b,c\rangle$. (This doesn't work if $a=0$, but in that case we can use $b$ or $c$ in the role of $a$. That is, either $a(x-0)+b(y-d/b)+c(z-0)=0$ or $a(x-0)+b(y-0)+c(z-d/c)=0$.) Figure 12.5.1. A plane defined via vectors perpendicular to a normal. Thus, given a vector $\langle a,b,c\rangle$ we know that all planes perpendicular to this vector have the form $ax+by+cz=d$, and any surface of this form is a plane perpendicular to $\langle a,b,c\rangle$. Example 12.5.1 Find an equation for the plane perpendicular to $\langle 1,2,3\rangle$ and containing the point $(5,0,7)$. Using the derivation above, the plane is $1x+2y+3z=1\cdot5+2\cdot0+3\cdot7=26$. Alternately, we know that the plane is $x+2y+3z=d$, and to find $d$ we may substitute the known point on the plane to get $5+2\cdot0+3\cdot7=d$, so $d=26$. We could also write this simply as $(x-5)+2(y)+3(z-7)=0$, which is for many purposes a fine representation; it can always be multiplied out to give $x+2y+3z=26$. $\square$ Example 12.5.2 Find a vector normal to the plane $2x-3y+z=15$. One example is $\langle 2, -3,1\rangle$. Any vector parallel or anti-parallel to this works as well, so for example $-2\langle 2, -3,1\rangle=\langle -4,6,-2\rangle$ is also normal to the plane. $\square$ We will frequently need to find an equation for a plane given certain information about the plane. While there may occasionally be slightly shorter ways to get to the desired result, it is always possible, and usually advisable, to use the given information to find a normal to the plane and a point on the plane, and then to find the equation as above. Example 12.5.3 The planes $x-z=1$ and $y+2z=3$ intersect in a line. Find a third plane that contains this line and is perpendicular to the plane $x+y-2z=1$. First, we note that two planes are perpendicular if and only if their normal vectors are perpendicular. Thus, we seek a vector $\langle a,b,c\rangle$ that is perpendicular to $\langle 1,1,-2\rangle$. In addition, since the desired plane is to contain a certain line, $\langle a,b,c\rangle$ must be perpendicular to any vector parallel to this line. Since $\langle a,b,c\rangle$ must be perpendicular to two vectors, we may find it by computing the cross product of the two. So we need a vector parallel to the line of intersection of the given planes. For this, it suffices to know two points on the line. To find two points on this line, we must find two points that are simultaneously on the two planes, $x-z=1$ and $y+2z=3$. Any point on both planes will satisfy $x-z=1$ and $y+2z=3$. It is easy to find values for $x$ and $z$ satisfying the first, such as $x=1, z=0$ and $x=2, z=1$. Then we can find corresponding values for $y$ using the second equation, namely $y=3$ and $y=1$, so $(1,3,0)$ and $(2,1,1)$ are both on the line of intersection because both are on both planes. Now $\langle 2-1,1-3,1-0\rangle=\langle 1,-2,1\rangle$ is parallel to the line. Finally, we may choose $\langle a,b,c\rangle=\langle 1,1,-2\rangle\times \langle 1,-2,1\rangle=\langle -3,-3,-3\rangle$. While this vector will do perfectly well, any vector parallel or anti-parallel to it will work as well, so for example we might choose $\langle 1,1,1\rangle$ which is anti-parallel to it. Now we know that $\langle 1,1,1\rangle$ is normal to the desired plane and $(2,1,1)$ is a point on the plane. Therefore an equation of the plane is $x+y+z=4$. As a quick check, since $(1,3,0)$ is also on the line, it should be on the plane; since $1+3+0=4$, we see that this is indeed the case. Note that had we used $\langle -3,-3,-3\rangle$ as the normal, we would have discovered the equation $-3x-3y-3z=-12$, then we might well have noticed that we could divide both sides by $-3$ to get the equivalent $x+y+z=4$. $\square$ So we now understand equations of planes; let us turn to lines. Unfortunately, it turns out to be quite inconvenient to represent a typical line with a single equation; we need to approach lines in a different way. Unlike a plane, a line in three dimensions does have an obvious direction, namely, the direction of any vector parallel to it. In fact a line can be defined and uniquely identified by providing one point on the line and a vector parallel to the line (in one of two possible directions). That is, the line consists of exactly those points we can reach by starting at the point and going for some distance in the direction of the vector. Let's see how we can translate this into more mathematical language. Suppose a line contains the point $\ds (v_1,v_2,v_3)$ and is parallel to the vector $\langle a,b,c\rangle$; we call $\langle a,b,c\rangle$ a direction vector for the line. If we place the vector $\ds \langle v_1,v_2,v_3\rangle$ with its tail at the origin and its head at $\ds (v_1,v_2,v_3)$, and if we place the vector $\langle a,b,c\rangle$ with its tail at $\ds (v_1,v_2,v_3)$, then the head of $\langle a,b,c\rangle$ is at a point on the line. We can get to any point on the line by doing the same thing, except using $t\langle a,b,c\rangle$ in place of $\langle a,b,c\rangle$, where $t$ is some real number. Because of the way vector addition works, the point at the head of the vector $t\langle a,b,c\rangle$ is the point at the head of the vector $\ds \langle v_1,v_2,v_3\rangle+t\langle a,b,c\rangle$, namely $\ds (v_1+ta,v_2+tb,v_3+tc)$; see figure 12.5.2. Figure 12.5.2. Vector form of a line. In other words, as $t$ runs through all possible real values, the vector $\ds \langle v_1,v_2,v_3\rangle+t\langle a,b,c\rangle$ points to every point on the line when its tail is placed at the origin. Another common way to write this is as a set of parametric equations: $$ x= v_1+ta\qquad y=v_2+tb \qquad z=v_3+tc.$$ It is occasionally useful to use this form of a line even in two dimensions; a vector form for a line in the $x$-$y$ plane is $\ds \langle v_1,v_2\rangle+t\langle a,b\rangle$, which is the same as $\ds \langle v_1,v_2,0\rangle+t\langle a,b,0\rangle$. Example 12.5.4 Find a vector expression for the line through $(6,1,-3)$ and $(2,4,5)$. To get a vector parallel to the line we subtract $\langle 6,1,-3\rangle-\langle2,4,5\rangle=\langle 4,-3,-8\rangle$. The line is then given by $\langle 2,4,5\rangle+t\langle 4,-3,-8\rangle$; there are of course many other possibilities, such as $\langle 6,1,-3\rangle+t\langle 4,-3,-8\rangle$. $\square$ Example 12.5.5 Determine whether the lines $\langle 1,1,1\rangle+t\langle 1,2,-1\rangle$ and $\langle 3,2,1\rangle+t\langle -1,-5,3\rangle$ are parallel, intersect, or neither. In two dimensions, two lines either intersect or are parallel; in three dimensions, lines that do not intersect might not be parallel. In this case, since the direction vectors for the lines are not parallel or anti-parallel we know the lines are not parallel. If they intersect, there must be two values $a$ and $b$ so that $\langle 1,1,1\rangle+a\langle 1,2,-1\rangle= \langle 3,2,1\rangle+b\langle -1,-5,3\rangle$, that is, $$\eqalign{ 1+a&=3-b\cr 1+2a&=2-5b\cr 1-a&=1+3b\cr }$$ This gives three equations in two unknowns, so there may or may not be a solution in general. In this case, it is easy to discover that $a=3$ and $b=-1$ satisfies all three equations, so the lines do intersect at the point $(4,7,-2)$. $\square$ Example 12.5.6 Find the distance from the point $(1,2,3)$ to the plane $2x-y+3z=5$. The distance from a point $P$ to a plane is the shortest distance from $P$ to any point on the plane; this is the distance measured from $P$ perpendicular to the plane; see figure 12.5.3. This distance is the absolute value of the scalar projection of $\ds \overrightarrow{\strut QP}$ onto a normal vector $\bf n$, where $Q$ is any point on the plane. It is easy to find a point on the plane, say $(1,0,1)$. Thus the distance is $$ {\overrightarrow{\strut QP}\cdot {\bf n}\over|{\bf n}|}= {\langle 0,2,2\rangle\cdot\langle 2,-1,3\rangle\over|\langle 2,-1,3\rangle|}= {4\over\sqrt{14}}. $$ $\square$ Figure 12.5.3. Distance from a point to a plane. Example 12.5.7 Find the distance from the point $(-1,2,1)$ to the line $\langle 1,1,1\rangle + t\langle 2,3,-1\rangle$. Again we want the distance measured perpendicular to the line, as indicated in figure 12.5.4. The desired distance is $$ |\overrightarrow{\strut QP}|\sin\theta= {|\overrightarrow{\strut QP}\times{\bf A}|\over|{\bf A}|}, $$ where $\bf A$ is any vector parallel to the line. From the equation of the line, we can use $Q=(1,1,1)$ and ${\bf A}=\langle 2,3,-1\rangle$, so the distance is $$ {|\langle -2,1,0\rangle\times\langle2,3,-1\rangle|\over\sqrt{14}}= {|\langle-1,-2,-8\rangle|\over\sqrt{14}}={\sqrt{69}\over\sqrt{14}}. $$ $\square$ Figure 12.5.4. Distance from a point to a line. Exercises 12.5 You can use Sage to compute distances to lines and planes, since this just involves vector arithmetic that we have already seen. Of course, you can also use Sage to do some of the computations involved in finding equations of planes and lines. Ex 12.5.1 Find an equation of the plane containing $(6,2,1)$ and perpendicular to $\langle 1,1,1\rangle$. (answer) Ex 12.5.2 Find an equation of the plane containing $(-1,2,-3)$ and perpendicular to $\langle 4,5,-1\rangle$. (answer) Ex 12.5.3 Find an equation of the plane containing $(1,2,-3)$, $(0,1,-2)$ and $(1,2,-2)$. (answer) Ex 12.5.4 Find an equation of the plane containing $(1,0,0)$, $(4,2,0)$ and $(3,2,1)$. (answer) Ex 12.5.5 Find an equation of the plane containing $(1,0,0)$ and the line $\langle 1,0,2\rangle + t\langle 3,2,1\rangle$. (answer) Ex 12.5.6 Find an equation of the plane containing the line of intersection of $x+y+z=1$ and $x-y+2z=2$, and perpendicular to the plane $2x+3y-z=4$. (answer) Ex 12.5.7 Find an equation of the plane containing the line of intersection of $x+2y-z=3$ and $3x-y+4z=7$, and perpendicular to the plane $6x-y+3z=16$. (answer) Ex 12.5.8 Find an equation of the plane containing the line of intersection of $x+3y-z=6$ and $2x+2y-3z=8$, and perpendicular to the plane $3x+y-z=11$. (answer) Ex 12.5.9 Find an equation of the line through $(1,0,3)$ and $(1,2,4)$. (answer) Ex 12.5.10 Find an equation of the line through $(1,0,3)$ and perpendicular to the plane $x+2y-z=1$. (answer) Ex 12.5.11 Find an equation of the line through the origin and perpendicular to the plane $x+y-z=2$. (answer) Ex 12.5.12 Find $a$ and $c$ so that $(a,1,c)$ is on the line through $(0,2,3)$ and $(2,7,5)$. (answer) Ex 12.5.13 Explain how to discover the solution in example 12.5.5. Ex 12.5.14 Determine whether the lines $\langle 1,3,-1\rangle+t\langle 1,1,0\rangle$ and $\langle 0,0,0\rangle+t\langle 1,4,5\rangle$ are parallel, intersect, or neither. (answer) Ex 12.5.15 Determine whether the lines $\langle 1,0,2\rangle+t\langle -1,-1,2\rangle$ and $\langle 4,4,2\rangle+t\langle 2,2,-4\rangle$ are parallel, intersect, or neither. (answer) Ex 12.5.16 Determine whether the lines $\langle 1,2,-1\rangle+t\langle 1,2,3\rangle$ and $\langle 1,0,1\rangle+t\langle 2/3,2,4/3\rangle$ are parallel, intersect, or neither. (answer) Ex 12.5.17 Determine whether the lines $\langle 1,1,2\rangle+t\langle 1,2,-3\rangle$ and $\langle 2,3,-1\rangle+t\langle 2,4,-6\rangle$ are parallel, intersect, or neither. (answer) Ex 12.5.18 Find a unit normal vector to each of the coordinate planes. Ex 12.5.19 Show that $\langle 2,1,3 \rangle + t \langle 1,1,2 \rangle$ and $\langle 3, 2, 5 \rangle + s \langle 2, 2, 4 \rangle$ are the same line. Ex 12.5.20 Give a prose description for each of the following processes: a. Given two distinct points, find the line that goes through them. b. Given three points (not all on the same line), find the plane that goes through them. Why do we need the caveat that not all points be on the same line? c. Given a line and a point not on the line, find the plane that contains them both. d. Given a plane and a point not on the plane, find the line that is perpendicular to the plane through the given point. Ex 12.5.21 Find the distance from $(2,2,2)$ to $x+y+z=-1$. (answer) Ex 12.5.22 Find the distance from $(2,-1,-1)$ to $2x-3y+z=2$. (answer) Ex 12.5.23 Find the distance from $(2,-1,1)$ to $\langle 2,2,0\rangle+t\langle 1,2,3\rangle$. (answer) Ex 12.5.24 Find the distance from $(1,0,1)$ to $\langle 3,2,1\rangle+t\langle 2,-1,-2\rangle$. (answer) Ex 12.5.25 Find the distance between the lines $\langle 5,3,1\rangle+t\langle 2,4,3\rangle$ and $\langle 6,1,0\rangle+t\langle 3,5,7\rangle$. (answer) Ex 12.5.26 Find the distance between the lines $\langle 2,1,3\rangle+t\langle -1,2,-3\rangle$ and $\langle 1,-3,4\rangle+t\langle 4,-4,1\rangle$. (answer) Ex 12.5.27 Find the distance between the lines $\langle 1,2,3\rangle+t\langle 2,-1,3\rangle$ and $\langle 4,5,6\rangle+t\langle -4,2,-6\rangle$. (answer) Ex 12.5.28 Find the distance between the lines $\langle 3,2,1\rangle+t\langle 1,4,-1\rangle$ and $\langle 3,1,3\rangle+t\langle 2,8,-2\rangle$. (answer) Ex 12.5.29 Find the cosine of the angle between the planes $x+y+z=2$ and $x+2y+3z=8$. (answer) Ex 12.5.30 Find the cosine of the angle between the planes $x-y+2z=2$ and $3x-2y+z=5$. (answer)
4081
https://khanacademy.fandom.com/wiki/Equation_practice_with_angle_addition
Equation practice with angle addition | Khan Academy Wiki | Fandom Sign In Register Khan Academy Wiki Explore Main Page Discuss All Pages Community Interactive Maps Recent Blog Posts Please Read! 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Register Sign In Menu Explore More History Advertisement Skip to content Khan Academy Wiki 2,165 pages Explore Main Page Discuss All Pages Community Interactive Maps Recent Blog Posts Please Read! General Rules Chat Policies Common Goals Top Info Leaderboards Challenge Patches Leaderboard Energy Point Leaderboard Videos Watched Leaderboard Badge Count Leaderboard Streak Leaderboard Answer Leaderboard Project Evaluations Leaderboard Golden Winston Leaderboard Council Members Scott Schraeder EytukanStudios Light Runner Tariq Jabbar Trekcelt VirusKA Historians Blaze Runner Tariq Jabbar Greeters HMcCoy Badges Meteorite badges Act I Scene I Programming Scholar Awesome Streak Challenge Accepted Apprentice Programmer Bibliographer Brain Builder Moon badges Apprentice Pre-algebraist Apprentice Trigonometrician Artisan I Algebraist 1000 Kelvin Artisan Arithmetician Apprentice Algebraist Apprentice Tutor Earth badges 299,792,458 Meters per Second 10,000 Year Clock Bristlecone 2014 Patron 2013 Patron 2012 Patron Creative Coder Sun badges Class of Summer '11 Class of Summer '12 Class of Summer '13 Class of Summer '14 Class of Winter '13 Class of Winter '14 Class of Fall '11 Black Hole badges Tesla Atlas Is Sal Galileo Artemis Black Hole Badges tips Herculean Math Missions K-8th grade K-2nd 3rd grade 4th grade 5th grade 6th grade 7th grade 8th grade Foundations Early math Arithmetic Pre-algebra High school and beyond Algebra basics Algebra I Geometry Algebra II Trigonometry Probability and statistics Precalculus Differential calculus Integral calculus in:Math exercises, Eureka Math/EngageNY exercises, 8th grade math exercises, and3 more 8th grade (U.S.): Geometry High school geometry exercises High school geometry: Geometry foundations Equation practice with angle addition Sign in to edit History Purge Talk (0) | Equation practice with angle addition | | | | Description | | Exercise Name: | Equation practice with angle addition | | Math Missions: | 8th grade (U.S.) Math Mission, High school geometry Math Mission | | Types of Problems: | 1 | The Equation practice with angle addition exercise appears under the 8th grade (U.S.) Math Missionand High school geometry Math Mission. This exercise practices setting up equations related to the Angle Addition Postulate. Types of Problems[] There is one type of problem in this exercise: Use the diagram to solve for the angle: This problem provides a diagram with an angle subdivided into two adjacent angles. The user is asked to use the diagram and labels to find the value of one of the smaller angles. Use the diagram to solve for the angle Strategies[] Knowledge of the Angle Addition Postulate and solving linear equations would ensure being able to complete this exercise. The Angle Addition Postulate states that the sum of the measures of two adjacent angles is the measure of the overall angle. This problem always asks for one of the smaller angles, but it can ask for either the top one or the bottom one. It never asks for x{\displaystyle x}. Since the problems are all similar, a computer program can be written in BASIC to solve this problem quickly. Real-life Applications[] Engineers and architects use angles for designs, roads, buildings and sporting facilities. Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas. Artists use their knowledge of angles to sketch portraits and paintings. Categories Categories: Math exercises Eureka Math/EngageNY exercises 8th grade math exercises 8th grade (U.S.): Geometry High school geometry exercises High school geometry: Geometry foundations Community content is available under CC-BY-SA unless otherwise noted. Advertisement Explore properties Fandom Fanatical GameSpot Metacritic TV Guide Honest Entertainment Follow Us Overview What is Fandom? About Careers Press Contact Terms of Use Privacy Policy Digital Services Act Global Sitemap Local Sitemap Do Not Sell My Personal Information Community Community Central Support Help Advertise Media Kit Contact Fandom Apps Take your favorite fandoms with you and never miss a beat. 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4082
https://www.calctool.org/quantum-mechanics/rydberg-equation
Rydberg Equation Calculator Calculating the Rydberg equation allows you to predict the position of the emission lines in the spectra of hydrogen and hydrogen-like atoms. Find more about this fundamental discovery of physics: learn how to calculate the Rydberg equation, the wavelength's dependence on the quantum numbers, and the different values of the Rydberg constant with our short article. Introduction to the Rydberg equation: atomic spectra Spectra are the fingerprints of an atom. If we obtain light from an atom, anywhere in the cosmos, we can also discover information on the chemical nature of the atom itself. Atoms of the same type (element) are identical: they undergo the same excitation and de-excitation processes in which energy is either absorbed or released by electrons in the electronic cloud. Each element does this in its way, allowing us to identify it. To these two processes, we associate two different types of spectra, emission and absorption. On these, you will see either colorful lines over a dark background (if the atoms are emitting light thanks to the jumps of electrons from higher to lower energetic levels) or black lines over a colorful rainbow-like band (the atom's electrons are absorbing some of the light at specific frequencies to raise their energy). The existence of these lines was gradually discovered in the early XVIII century, on top of previous knowledge about spectra. It was already clear that there was a correlation between chemistry and light. With increased knowledge in physics and chemistry and better equipment, scientists discovered more about these lines until the accurate observations of the spectra of many gases, which ushered in quantum mechanics at the end of the XIX century. We credit one of these discoveries to Johannes Rydberg, who first discovered the existence of a mathematical relationship between the wavelength of those lines. The Rydberg formula for hydrogen: how to calculate wavelength from energy levels Rydberg discovered that the spectral lines of hydrogen were not placed randomly on the spectrum, but lay at specific intervals. Those intervals are better seen if we reason in terms of wavenumbers. The wavenumber is nothing but the inverse of the wavelength: n=1/λn=1/\lambdan=1/λ. By observing that emission lines appeared in series, he worked out a relationship now known as Rydberg equation for the wavelength. The Rydberg equation for hydrogen is: Where: 🙋 Do you want to know what precisely the principal quantum number is? Head to our quantum number calculator for a quick and straightforward answer! The Rydberg equation for hydrogen allows you to calculate the wavelength of the various lines of many spectral series. In particular: In all cases n2n_2n2​ varies from n1n_1n1​ to infinity, assuming only integer values. The Rydberg equation for hydrogen-like atoms: a change in the Rydberg constant The Rydberg equation also applies to all hydrogen-like atoms, atoms with a single valence electron. We are talking of alkaline metals such as lithium, sodium, and potassium or single ionized alkaline earth metals, such as magnesium and strontium. We are not changing how we calculate the wavelength from the energy levels,; we only modify the Rydberg constant: Where: 🙋 How many Rydberg constants are out there? The answer is two. For hydrogen, the Rydberg constant has to consider the effect of the non-negligible ratio between an electron's and a proton's mass. For heavier atoms, the electrons' mass is ignored. The values of the constants are: The Rydberg equation for a hydrogen-like atom is then: In the advanced mode of our Rydberg equation calculator, you can find the energy and the frequency corresponding to each wavelength. Learn about the respective conversions at our frequency calculator and photon energy calculator. advanced mode Calculate the wavelength with the Rydberg equation: examples for the Lyman series of hydrogen We use the Rydberg equation to calculate the first four terms of the Lyman series. The lines are four possible excited states of the hydrogen atom, with the electron starting from the lowest possible energy. To find the position of the first line, substitute n1=1n_1=1n1​=1 and n2=2n_2=2n2​=2: Use our Rydberg equation calculator to find the rest of the Lyman series: As you can see, the interval between wavelengths is reducing. The series will eventually converge at the value 91.18 nm91.18\ \text{nm}91.18 nm. This number was crucial to confirm Bohr's model for atomic hydrogen correctness. Learn more about it at our Bohr model calculator. De Broglie wavelength Schwarzschild radius Two-photon absorption
4083
https://demonstrations.wolfram.com/PowerOfAPointTheorem/
Wolfram Demonstrations Project Power of a Point Theorem | | | | | | | | B | | | | | | 1.5 | × | 4.5 | = | 6.75 | | | D | | | | | | 2.59808 | × | 2.59808 | = | 6.75 | | | | | | | | Initializing live version Open Notebook in Cloud Contributed by: Lauren Oh (2017) Open content licensed under CC BY-NC-SA Snapshots Details Permanent Citation Cite this as Related Demonstrations The Chordal Theorem Jay Warendorff A Product of Chord Lengths in a Circle Jay Warendorff The Perpendicular Bisector of a Chord Jay Warendorff Circumcircle and Incircle of a Triangle Chris Boucher Two Lines Determine a Circle John Kiehl The Sum of the Trilinear Coordinates of a Point Minh Trinh Xuan The Sum of the Interior Angles of a Triangle Equals 180 Degrees by Paper Folding Sean G. Corcoran The Sum of Opposite Angles of a Quadrilateral in a Circle is 180 Degrees Jay Warendorff The Plemelj Triangle via the Fixed Point of a Transformation Izidor Hafner The Coordinates of a Point Relative to a Triangle Minh Trinh Xuan The Butterfly Theorem Jay Warendorff Reflections of a Point in the Midpoints of a Triangle's Sides Jay Warendorff Reflecting a Point through the Midpoints of a Triangle's Sides Jay Warendorff Radians on the Circle of a Ferris Wheel Sophia LeRose Problems on Circles XIV: Bisecting the Circumference of Three Circles with a Circle Jaime Rangel-Mondragon Problems on Circles VII: Circles of a Given Size Tangent to Other Two Jaime Rangel-Mondragon Perpendiculars from a Point on the Line between the Endpoints of the Angle Bisectors Jay Warendorff n-Sectors of the Angles of a Triangle Jacques Marchandise Mascheroni's Construction of the Center of a Circle Claude Fabre
4084
https://www.gauthmath.com/solution/1801200733564933/Count-the-number-of-cubes-used-to-build-the-solid-figure-The-solid-figure-has-_u
Question Solution Epilogue. The core claim of the question is to identify the literary term that fits the description provided. In literature, the term "epilogue" refers to the section that occurs after the climax of a story, providing closure or additional information to the narrative. contact@gauthmath.com
4085
https://math.stackexchange.com/questions/3032800/use-the-sine-rule-to-prove-trig-identity
Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams Use the sine rule to prove trig identity [duplicate] Ask Question Asked Modified 6 years, 9 months ago Viewed 359 times 1 $\begingroup$ Using the sine rule: $$ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$ prove, for triangle ABC: $$\sin\left(\frac{B-C}{2}\right) = \frac{b-c}{a} \cos\left(\frac A2\right)$$ Using the sine rule it's easy to translate the RHS into: $$\sin\left(\frac{B-C}{2}\right) = \frac{\sin(B)-\sin(C)}{\sin(A)} \cos\left(\frac A2\right)$$ Yes, I can expand out the LHS, and use the difference of 2 sines in the RHS, but neither makes an obvious equality, especially with terms in a and A in the RHS. A nudge in the right direction would really be appreciated. Thanks. trigonometry Share edited Dec 9, 2018 at 19:25 Larry 5,17044 gold badges2222 silver badges4949 bronze badges asked Dec 9, 2018 at 19:01 GurnemanzGurnemanz 2122 bronze badges $\endgroup$ 0 Add a comment | 2 Answers 2 Reset to default 1 $\begingroup$ Just assume that $a/sin(A)=b/sin(B)=c/sin(C)=1/k$. So $sin(A)=ka, sin(B)=kb,sin(C)=kc$. Now substitute this and you will get the desired result. Share answered Dec 9, 2018 at 19:08 Avanish SinghAvanish Singh 54244 silver badges1717 bronze badges $\endgroup$ 3 $\begingroup$ Are you sure this leads anywhere different from what OP's tried? $\endgroup$ TheSimpliFire – TheSimpliFire ♦ 2018-12-09 19:20:26 +00:00 Commented Dec 9, 2018 at 19:20 $\begingroup$ Well he has given here his method and his last step. Now if we do what I have stated we will get the RHS. $\endgroup$ Avanish Singh – Avanish Singh 2018-12-09 19:22:35 +00:00 Commented Dec 9, 2018 at 19:22 $\begingroup$ I might have overlooked this, but how would you handle $\sin(B-C/2)$ and $\cos(A/2)$ using those substitutions? $\endgroup$ TheSimpliFire – TheSimpliFire ♦ 2018-12-09 19:25:43 +00:00 Commented Dec 9, 2018 at 19:25 Add a comment | -2 $\begingroup$ Since $A+B+C=\pi$, the difference formula for $\sin$ gives \begin{align}\frac{\sin B-\sin C}{\sin A} \cos\frac A2&=\frac{2\cos\frac{B+C}2\sin\frac{B-C}2}{\sin(\pi-B-C)}\cos\frac{\pi-B-C}2\&=\frac{2\sqrt{\frac{1+\cos(B+C)}2}\sin\frac{B-C}2}{\sin(B+C)}\sqrt{\frac{1+\cos(\pi-B-C)}2}\&=\frac{2\sqrt{\frac{1+\cos(B+C)}2}\sin\frac{B-C}2}{\sin(B+C)}\sqrt{\frac{1-\cos(B+C)}2}\&=\frac{\sin\frac{B-C}2}{\sin(B+C)}\sqrt{1-\cos^2(B+C)}\&=\frac{\sin\frac{B-C}2}{\sin(B+C)}\sin(B+C)=\sin\frac{B-C}2\end{align} as required. Share answered Dec 9, 2018 at 19:20 TheSimpliFire♦TheSimpliFire 28.3k1010 gold badges6666 silver badges137137 bronze badges $\endgroup$ Add a comment | Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions trigonometry See similar questions with these tags. 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分层采样（stratified sampling）-CSDN博客 博客 下载 学习 社区 GitCode InsCodeAI 会议 搜索 AI 搜索 登录 登录后您可以： 复制代码和一键运行 与博主大V深度互动 解锁海量精选资源 获取前沿技术资讯 立即登录 会员·新人礼包 消息 历史 创作中心 创作 分层采样（stratified sampling） 最新推荐文章于 2025-08-16 14:43:45 发布 Zoey29于 2016-12-07 16:30:04 发布 阅读量2.5w收藏 12 点赞数 11 CC 4.0 BY-SA版权 分类专栏：零散知识文章标签：分层采样采样stratifiedsampling 版权声明：本文为博主原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接和本声明。 本文链接： 2048 AI社区 文章已被社区收录 加入社区 零散知识 专栏收录该内容 8 篇文章 订阅专栏 本文介绍了保留类别比例的分层抽样方法，该方法通过将总体按某种特征分为多个子群体（层），再从每层中进行随机抽样，以提高样本估计值的精确度。文章还提供了一个实例，说明如何保持训练集和测试集中样本类别的比例一致。 保留类别比例的采样方式。 先将总体的单位按某种特征分为若干次级总体（层），然后再从每一层内进行单纯随机抽样，组成一个样本。分层可以提高总体指标估计值的精确度，它可以将一个内部变异很大的总体分成一些内部变异较小的层（次总体）。 每一层内个体变异越小越好，层间变异则越大越好。 AI运行代码 1 分层抽样比单纯随机抽样所得到的结果准确性更高，组织管理更方便，而且它能保证总体中每一层都有个体被抽到。这样除了能估计总体的参数值，还可以分别估计各个层内的情况，因此分层抽样技术常被采用。 实例介绍 例如，通过对包含1000个样本的数据集D进行分层抽样而获得70%样本的训练集S和含30%样本的测试集T，若D包含500个正例、500个反例，则分层采样得到的S应包含350个正例、350个反例，而T则包含150个正例、150个反例； 若S、T中样本类别比例差别很大，则误差估计将由于训练/测试数据分布的差异而产生偏差。 确定要放弃本次机会？ 福利倒计时 : : 立减 ¥ 普通VIP年卡可用 立即使用 Zoey29 关注关注 11点赞 踩 12 收藏 觉得还不错? 一键收藏 0评论 分享复制链接 分享到 QQ 分享到新浪微博 扫一扫 举报 举报 专栏目录 R 分层 抽样（Stratified Sampling） data+scenario+science+insight 07-15 2613 R 分层 抽样（Stratified Sampling） 目录 R 分层 抽样（Stratified Sampling） R 分层 抽样 基于行数的 分层 抽样 基于行数比例的 分层 抽样 研究人员通常从一个总体（population）中提取样本 ( sample )，并利用样本（sample）中的数据得出关于整个总体（population）的结论。 一种常用的抽样方法是 分层 随机抽样（Stratified Sampling），将一个群体分成几组（group），从每组中随机选择一定数量的成员纳入样本集中. 参与评论 您还未登录，请先 登录 后发表或查看评论 机器学习 ( 三 )--关于 分层 采样 的理解 9-15 python的 分层 采样 data = np.array ( range ( 10 ) ) traget = array ([0, 0, 0,0, 0, 0, 0, 1, 1, 1]) from sklearn.model_selection import Stratified SuffldSplit as ss split = ss ( n_split = 5, test_size = 0.4, random_state = 42 ) #采样 的组数, 测试比例大小,随机数值 for train_index, ... 数据 采样 技术:上 采样、下 采样 与 分层 抽样 9-24 上 采样+下 采样+分层 抽样 本文介绍了数据 采样 中的关键方法,包括过 采样 ( 上 采样 )、下 采样 和 分层 抽样。过 采样 用于增加少数类样本数量,但可能导致噪声增加,此时可通过TomekLink或EditedNearestNeighbours进行样本清洗。下 采样 则减少多数类样本,但可能丢失信息。分层 抽样保持各类别比例。SMOTETomek和SMOTEENN是过 采样 与下 采样 结合... R语言数值抽样方法：分层 抽样（Stratified Sampling）、分层 随机抽样（Stratified Sampling） statistics+insight+vista+power 07-07 468 R语言数值抽样方法：分层 抽样（Stratified Sampling）、分层 随机抽样（Stratified Sampling），将一个群体分成几组（group），从每组中随机选择一定数量的成员纳入样本集中，这样获得的训练集和测试集都具有代表性 机器学习（三）--关于 分层 采样 的理解 monk96的博客 05-17 2794 [最近学到关于数据 分层 采样 的内容，总结一下 分层 采样 的定义： 根据不同群体的比例在数据里通过比例进行 采样，减少 采样 的误差，针对数据量过大时会显得没那么有意义，ps： 小数据量有必要，大数据没必要 举例：比如取100个学生里，70%个男生，30%个女生，取有没有收藏笔记本的爱好，如果随机 采样，会 有偏差，但如果按比例来调查，70%的男生，30%的女生，会符合学校的学生特征。 python 的 分层 采样 data = np.array ( range ( 10 ) ) traget = array (0, 0, 0,0 自助法 ( bootstrapping ) 划分数据集_自助法分割数据集 9-22 在将数据集划分为训练集和测试集时,测试样本应从真实分布中独立同分布 采样 获得;同时测试集应该尽可能与训练集互斥,也就是测试样本尽量不要在训练集中出现、未在训练过程中使用过。 多数情况下采用留出法 ( hold-out ),即从数据集中 分层 采样 ( stratified sampling ) 出约30%的数据作为测试集。分层 采样 的目的是要保持数据分... 数据处理笔记3: 分层 采样-k折交叉验证_skfolds.split 9-28 数据处理笔记3: 分层 采样-k折交叉验证 这篇博客介绍了如何在Python中使用 Stratified KFold进行交叉验证,以确保在训练和验证数据集中各类别的样本比例保持一致。作者首先展示了MNIST数据集的加载和预处理,然后演示了在SGDClassifier模型上的应用。在应用过程中遇到了导入问题、分层 采样 错误、随机状态设置问题以及混淆矩阵计算。 【前端开发】从0到1：Bootstrap带你飞 最新发布 大雨的博客 08-16 1099 Bootstrap是一个基于HTML、CSS和JavaScript的开源前端框架，由Twitter开发，主要用于快速构建响应式网页。文章首先介绍了Bootstrap的定义及其响应式设计特性，能够自动适应不同设备屏幕。接着阐述了选择Bootstrap的优势，包括提高开发效率、兼容主流浏览器和丰富的社区资源。详细讲解了如何引入Bootstrap、使用容器布局和12列网格系统。在组件部分，重点介绍了导航栏、按钮样式和表单组件的实现方法。还探讨了响应式设计技巧和自定义扩展方式，并通过电商网站案例演示了实际应用。 数据预处理与特征工程—11.分层 采样 柳杰的博客 04-14 952 分层 采样 的目的是为了防止数据有偏 自定义 分层 采样 函数 def split_train_test ( data, test_size=0.2 ): """ 保证训练集与测试集的类别比例与原数据集中的相等 :param data: 原数据 :param test_size: 测试集比例 :return: 训练集与测试集 """ label = set ( data.iloc[:, -1]) data_tr = pd.DataFrame ( ) dat sklearn 分层 采样 示例 9-23 1、函数 sklearn.model_selection.train_test_split ( 数据集[test_size测试集大小,train_size训练集大小,random_state整数——随机数种子,否则为随机数生成器],stratify数组[分层 采样 的标记数组]或none ) 返回值:一个列表,依次给出一/多个数据集划分的结果:训练集、测试集。 【自动驾驶轨迹规划之 分层 采样】自动驾驶 _采样 9-21 本文详细介绍了自动驾驶中的轨迹规划策略,重点讲解了道路 分层 采样 和基于动态规划的 采样 搜索方法。在Frenet坐标系中,通过 分层 采样 和动态规划,优化路径决策和速度决策,确保安全性、稳定性和驾驶效率。文章还讨论了路径片段的评价函数设计,以确保车辆避免碰撞、保持稳定并提高驾驶舒适度。 机器学习 | 使用Scikit-Learn实现 分层 抽样 python收藏家的博客 04-14 3409 分层 抽样是一种抽样方法，首先将总体的单位按某种特征分为若干次级总体（层），然后再从每一层内进行单纯随机抽样，组成一个样本。可以提高总体指标估计值的精确度。在抽样时，将总体分成互不交叉的层，然后按一定的比例，从各层次独立地抽取一定数量的个体，将各层次取出的个体合在一起作为样本，这种抽样方法是一种 分层 抽样。分层 抽样的特点是将科学分组法与抽样法结合在一起，分组减小了各抽样层变异性的影响，抽样保证了所抽取的样本具有足够的代表性。 分层 抽样（Stratified sampling） weixin_30363817的博客 04-19 883 1. 基本概念 统计学理论中，分层 抽样针对的是对一个总体（population）进行抽样的方法。尤其适用于当总体内部，子总体（subpopulations）间差异较大时。每一个 subpopulation，也称为层（stratum）。 2. 均值与方差 Stratified sampling μs=1N∑h=1LNhμhσ2s=∑h=1L ( NhN ) 2 (... Stratified Sampling（分层 采样） qq_32096491的博客 03-26 5395 一、问题描述在一个正方形内 采样 点，假设正方形的面积为A，如果使用完全随机均匀 采样，期望是？方差是？ 如果将正方形均匀分成NN个网格，在每个网格中进行随机均匀 采样，那么整体的期望和方差与之前的策略相比有什么变化？ Refined Stratified Sampling：细化 分层 采样 ( RSS ) 用于顺序蒙特卡罗 采样-matlab开发 05-30 RSS 代码促进了真正的顺序蒙特卡罗 采样 方法，以实现自适应不确定性分析，同时仍然实现显着的方差减少。 该方法详细描述于： Shields, MD、Teferra, K.、Hapij, A. 和 Daddazio, RP “用于基于蒙特卡罗的高效不确定性... Partially Stratified Sampling：根据Partially Stratified Sampling 生成n维随机向量的随机样本-matlab开发 05-30 “拉丁超立方体 采样 的推广。” 可靠性工程和系统安全。 148：96-108。 提供了一个简单的演示，以图形方式显示了如何根据两个二维子域和一个一维子域的 分层 来构建五维样本。 还提供了适用于 Shields 和 Zhang 提出的... Stratified Sampling 06-10 Stratified Sampling（分层 抽样）是一种优化随机抽样的方法，它将总体分为若干个层次，并在每个层次内进行单独的随机抽样。Stratified Sampling 通常是在样本不足或总体分布不均匀的情况下使用，以确保样本更好地代表... R语言实现 分层 抽样 ( Stratified Sampling ) 以iris数据集为例 chuanglongquan4694的博客 05-08 3022 1.观察数据集 head ( iris ) 选取数据集中前6个数据，我们可以看出iris数据集一共有5个字段。 dim ( iris ) iris数据集一共有150条数据，5个字段 summary ( iris ) 观察各个变量的内容，可以看出前四个变量（Sepal.L... 分层 抽样法 dongyu1703的博客 03-17 5716 转载自： 分层 抽样法也叫类型抽样法。它是从一个可以分成不同子总体（或称为层）的总体中，按规定的比例从不同层中随机抽取样品（个体）的方法。这种方法的优点是，样本的代表性比较好，抽样误差比较小。缺点是抽样手续较简单随... Active-Learning 主动学习（三）—— Hierarchical Sampling 分层 采样 Jingyang.Zhang的博客 02-26 3890 算法综述 首先对数据进行 unsupervised 分类，进行 Hierarchical Clustering 操作，得到 分层 聚类结构。 给定一些标记好样本，可以在上一步得到的 分层 聚类结构的基础上得到 classification map 和 confidence map（评价聚类被赋予给定类别的置信度）。 采用AL算法选择最有信息量的样本，来增加分类的置信度。 算法背景 如何利用 分层 聚类方法进行 分层 抽样 u010970317的博客 09-27 591 分层 抽样 import pandas as pd import numpy as np df=pd.DataFrame ( np.random.randn ( 20 ).reshape ( 10,2 ) ) df['2'] = [5,5,5,5,5,2,2,2,3,3] typicalNDict={ 5:3, 2:2, 3:1 } #函数定义 def typicalsamling ( group,typicalNDict ): name=group 关于我们 招贤纳士 商务合作 寻求报道 400-660-0108 kefu@csdn.net 在线客服 工作时间 8:30-22:00 公安备案号11010502030143 京ICP备19004658号 京网文〔2020〕1039-165号 经营性网站备案信息 北京互联网违法和不良信息举报中心 家长监护 网络110报警服务 中国互联网举报中心 Chrome商店下载 账号管理规范 版权与免责声明 版权申诉 出版物许可证 营业执照 ©1999-2025北京创新乐知网络技术有限公司 Zoey29 博客等级 码龄11年 107 原创174 点赞 397 收藏 51 粉丝 关注 私信 亚马逊云科技 性价比之选 - 基于 ARM 架构 Graviton4 处理器实例🚀性能提升30%！广告 热门文章 闭式解（解析解） 27657 分层采样（stratified sampling） 25902 Moore–Penrose pseudoinverse 20727 信息检索模型 20394 欠定方程与超定方程 20340 分类专栏 NLP Java62篇 C/C++4篇 算法12篇 数学24篇 数据挖掘与信息检索14篇 数据结构1篇 计算机基础7篇 零散知识8篇 Linux/Unix9篇 机器学习20篇 Python8篇 TCP/IP网络协议 读书笔记6篇 工具软件2篇 Java Web 数据库1篇 数据科学3篇 展开全部收起 上一篇： Borda count 下一篇： 闭式解（解析解） 最新评论 原码, 反码, 补码 详解 做而论道_CS:补码，是一个 “代替负数” 的正数。 补码，并不是 “原码取反加一”。 补码，它是来自于【算法】。 你看吧： 25 － 1 = 24 25 + 99 = (一百) 24 你如果舍弃进位： +99 就能代替－1。 减法，也就用加法代替了。 但是，如果保留进位，+99，就还是 +99。 只要舍弃了进位，补码，就诞生了。 补码的理论依据，就是这么简单。 原码, 反码, 补码 详解 做而论道_CS:实际上，任意负数（－X）的补码，都是：0 － X。 你用二进制简单算一下，立刻就能得到结果。 （－128 的 8 位补码，也就是这样求出来的。） 同理，任意正数（＋X）的补码，也都是：0 ＋ X。 这还用算？ 0 ＋ X，不就是 X 吗？ 即，正数的补码，就是 X 本身！ 求补码，就是这么简单。 符号位原码反码取反加一符号位不变模... 这些垃圾，并无任何用处。 计算机专家说这些，不过是 “拿个鞋拔子当如意” 而已。 原码, 反码, 补码 详解 做而论道_CS:学习计算机，首先要记住： 1. 计算机使用二进制。 2. 计算机的字长是固定的。 八位机，每次计算，就是 8 位数。 3. 计算机只有加法器。 负数以及减法，都必须用加法来实现。 －－－－－－－－－－－－－－－－－－－ 那么，14－14 = 0，计算机将怎么计算呢？ 八位机的算法是： 0000 1110 + xxxx xxxx = 0000 0000。 这里的 xx...x，就是【－14 的补码】。 这个 xx...x，究竟是什么？ 你自己，肯定可以推导出来。 先移项：xxxx xxxx = 0000 0000－0000 1110。 可算出：xxxx xxxx = (借位 1) 1111 0010。 取八位：xxxx xxxx = 1111 0010。 此时，就求出了 [－14]补码 = 1111 0010。 简单不简单？ 意外不意外？ －－－－－－－－－－－－－－－－－－－ 你用 “取反加一”，也能求出这个结果。 但是，用 “取反加一”，你就不能理解： 减法，怎么就变成加法了？ 计算机专家和计算机老师，都是小学没毕业就迷上了计算机。 （即使毕业了，也没有达到相应的水平。） 很简单的事，也弄不明白，就胡乱的猜想，编造理由。 显然，他们就是一帮： 【知其然不知其所以然】的货色。 原码, 反码, 补码 详解 做而论道_CS:补码，它就是补码。 补码，与原码反码，都没有任何关系。 如果码长是 8 位，各码的表示范围是： 原码：－127 ~ +127； 反码：－127 ~ +127； 补码：－128 ~ +127。 看到了吗？ －128 只有补码，并没有原码和反码。 没有原码，拿什么取反？ 没有反码，拿什么加一？ 用 “符号位原码反码取反加一” 这一套， 来定义补码，就是一个谎言。 java受检异常与运行时异常 ！巴普洛夫的狗:写的很棒！ 大家在看 云原生联调利器：Telepresence实战指南 97 SpringBoot3+Vue3打造分布式医疗挂号系统 88 SpringBoot+Vue3全栈CRUD实战 528 VSCode配置C/C++保姆级教程 653 最新文章 K均值算法 如何得到一个较好的机器学习系统 统计学习三要素个人理解 2018年 36篇 2017年 91篇 2016年 30篇 2015年 1篇 亚马逊云科技 性价比之选 - 基于 ARM 架构 Graviton4 处理器实例🚀性能提升30%！广告 上一篇： Borda count 下一篇： 闭式解（解析解） 分类专栏 NLP Java62篇 C/C++4篇 算法12篇 数学24篇 数据挖掘与信息检索14篇 数据结构1篇 计算机基础7篇 零散知识8篇 Linux/Unix9篇 机器学习20篇 Python8篇 TCP/IP网络协议 读书笔记6篇 工具软件2篇 Java Web 数据库1篇 数据科学3篇 展开全部收起 登录后您可以享受以下权益： 免费复制代码 和博主大V互动 下载海量资源 发动态/写文章/加入社区 ×立即登录 评论 被折叠的 条评论 为什么被折叠?到【灌水乐园】发言 查看更多评论 添加红包 祝福语 请填写红包祝福语或标题 红包数量 个 红包个数最小为10个 红包总金额 元 红包金额最低5元 余额支付 当前余额 3.43 元 前往充值 > 需支付：10.00 元 取消 确定 成就一亿技术人! 领取后你会自动成为博主和红包主的粉丝 规则 hope_wisdom 发出的红包 实付 元 使用余额支付 点击重新获取 扫码支付 钱包余额 0 抵扣说明： 1.余额是钱包充值的虚拟货币，按照1:1的比例进行支付金额的抵扣。 2.余额无法直接购买下载，可以购买VIP、付费专栏及课程。 余额充值 确定 取消 举报 选择你想要举报的内容（必选） 内容涉黄 政治相关 内容抄袭 涉嫌广告 内容侵权 侮辱谩骂 样式问题 其他 原文链接（必填） 请选择具体原因（必选） 包含不实信息 涉及个人隐私 请选择具体原因（必选） 侮辱谩骂 诽谤 请选择具体原因（必选） 搬家样式 博文样式 补充说明（选填） 取消 确定 AI助手 AI 搜索 智能体 AI 编程 AI 作业助手 下载APP 程序员都在用的中文IT技术交流社区 公众号 专业的中文 IT 技术社区，与千万技术人共成长 视频号 关注【CSDN】视频号，行业资讯、技术分享精彩不断，直播好礼送不停！客服返回顶部
4087
https://www.youtube.com/watch?v=t0ZSTPF8a1s
How to Graph y=(1/2)x-2 Minute Math 85600 subscribers 78 likes Description 16144 views Posted: 7 Jun 2018 In this math video lesson I show how to graph y=(1/2)x-2. The equation in this video is in slope-intercept form, y=mx+b, and is a common way to graph an equation of a line. #graphtheline #slopeinterceptform #algebra Every Month we have a new GIVEAWAY that is FREE to Enter. See link below for details. You can enter Every Month! Visit our website for links to all of our videos: Visit our STEM Store for all your Math and Science Gear: Get Free Trials to Amazon Prime and others here: Nominate a Great Teacher Here: Have Math Lesson you would like to add to our community of videos? Click here: Check out our Finance, Business and Life YouTube Channel: Consider supporting us on Patreon... Follow us for... Tweets: Instagram: Facebook: Instagram Shop: Facebook Shop: Business and Personal Instagram: 4 comments Transcript: hi I'm Sean again and there's a minute math today we're more about graphing lots where I sketch the graph of each line so violin is given in this equation y equals 1/2 X minus 2 okay well minus 2 is our y-intercept so that's where it crosses the y axis so the y axis got negative 2 right there put a point then and toss our slope or end about it is 1/2 so we go up one unit over to I spawn up one year over to that corner point is 2 comma negative 1 then we do it again up one unit over to another point right there and it is 4 comma 0 okay and shoot let's go one more go up one more unit over to that point right there and that is 6 comma 1 so we can connect all these dots here hopefully nice little here we have a line that represents the equation y equals 1/2 X minus G so quick recap we're giving negative 2 as a wiper giving the equation y equals 1/2 X minus 2 negative 2 is our y-intercept the point right there our slope is 1/2 so it went up 1 or 2 months that up 1 over 2 minutes then up 1 over 2 years to the positive to the right we applied those points all right then we connect the dots have a line right it's all should be on the straight line which it is and we have now it's
4088
https://flexbooks.ck12.org/cbook/ck-12-cbse-math-class-10/section/14.2/primary/lesson/mean-of-grouped-data/
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Learn. Interact. eXplore. CCSS Math Concepts and FlexBooks aligned to Common Core NGSS Concepts aligned to Next Generation Science Standards Certified Educator Stand out as an educator. Become CK-12 Certified. Webinars Live and archived sessions to learn about CK-12 Other Resources CK-12 Resources Concept Map Testimonials CK-12 Mission Meet the Team CK-12 Helpdesk FlexLets Know the essentials. Pick a Subject Donate Sign Up 14.2 Mean of Grouped Data Written by:Neha Khandelwal Fact-checked by:The CK-12 Editorial Team Last Modified: Aug 01, 2025 Consider the height of 5 students: 144 cm, 158 cm, 153 cm, 156 cm, 162 cm. Then the arithmetic mean of the height of these five students is given by: Mean height=Sum of heightsNumber of students223=(144+158+153+156+162)5=7735=154.6 cmIn general, if x1, x2, …xn are n variables of a variable X, then the arithmetic mean or simply the mean of these values is denoted by ¯X and is defined as ¯X=x1+x2+x3+⋯+xnnor¯X=n∑i=1xinHere, the symbol n∑i=1xi denotes x1+x2+x3+⋯+xn. When a data set is large, a frequency distribution table is often used to display the data in an organised way. A frequency distribution table lists the data values, as well as the number of times each value appears in the data set. In a discrete frequency distribution the arithmetic mean may be computed by any one of the following methods: Direct method Shortcut method Step-Deviation method Mean of Grouped Data: Direct Method If x1, x2, x3, …xn are observations having respective frequencies f1, f2, …fn. This means that x1 occurs f1 times, x2 occurred f2 times and so on. Then, Sum of the values of observations=x1f1+x2f2+ ⋯+xnfn and sum of frequencies=f1+f2+⋯+fn ¯X=f1x1+f2x2+ ⋯+fnxnf1+f2+ ⋯+fn=n∑i=1xifin∑i=1fi 1) The following data represents which numbers are rolled with a standard six-sided dice: 1, 3, 5, 3, 2, 1, 2, 5, 6, 4, 5, 2, 6, 1, 4, 3, 6, 1, 2, 4, 6, 1, 3, 1, 3, 5, 6 | | | | --- | Number xi | Frequency fi | fixi | | 1 | 6 | 6 | | 2 | 4 | 8 | | 3 | 5 | 15 | | 4 | 3 | 12 | | 5 | 4 | 20 | | 6 | 5 | 30 | | | 6∑i=1fi=27 | 6∑i=1fixi=91 | ∴¯X=6∑i=1xifi6∑i=1fi=9127=3.37 Sometimes, data is so large that it is very difficult to find its mean. In this situation, we make groups of the data with a suitable class interval. Then, we find the classmark which is given: Mid-value, xi=Upper class limit+Lower class limit2 In this method, while allotting frequencies to each class interval, it should be noted that frequency equal to upper-class interval should not be put in the same class interval i.e., it should not be put in the next class interval. For example, in the class interval 25-35, 35 should not be put in the next class interval, i.e., 35-45 class interval. 2) In Tarun's school, there are 25 teachers. Each teacher travels to school every morning in his or her own car. The distribution of the driving times (in minutes) from home to school for the teachers is shown in the table below: | Driving time (in minutes) | Number of Teachers | --- | | 0-10 | 3 | | 10-20 | 10 | | 20-30 | 6 | | 30-40 | 4 | | 40-50 | 2 | Calculate the mean of the driving times. To better represent the problem and its solution, a table can be drawn as follows: | Driving time (in minutes) | Mid-values xi | Number of teachers fi | fixi | --- --- | | 0-10 | 5 | 3 | 15 | | 10-20 | 15 | 10 | 150 | | 20-30 | 25 | 6 | 150 | | 30-40 | 35 | 4 | 140 | | 40-50 | 45 | 2 | 90 | | | | ∑fi=25 | ∑fixi=545 | We have, ¯X=∑fixi∑fi=54525¯X=21.8Each teacher spends a mean time of 21.8 minutes driving from home to school each morning. Steps to Compute Mean of Grouped Data using Direct Method: We can use the following steps to compute the arithmetic mean by the direct method: Step 1: Prepare the frequency table in such a way that its second column consists of the observations (mid-value) and the third column the respective frequency. Step 2: The fourth column consists of the product of the frequency of each row with the respective observations i.e., fixi. Step 3: Add all the frequencies in the third column to obtain n∑i=1fi. Step 4: Add all the products in the fourth column to obtain n∑i=1fixi. Step 5: To calculate mean, use the formula ¯X=n∑i=1fixin∑i=1fiIn some problems, where the number of observations is large or the values of fi or xi are large, then the calculations become tedious. In order to overcome this difficulty, we use another method called the shortcut method. Mean of Grouped Data: Shortcut Method In this method, an approximate mean ( called assumed mean ) is taken ( preferably near the middle ), say A, and we calculate the deviation di=xi−A for each value of xi. Then the mean (¯X) is given by the formula:¯X=A+n∑i=1fidin∑i=1fiNote that the assumed mean (A) may not be one of the observations xi i.e., A may be any non-zero real number. The value of mean does not depend upon the choice of A. Let's consider an example. 3) The following table shows the weight of 15 students: | | | | | | | --- --- --- | | Weight ( in kg ) | 47 | 48 | 49 | 50 | 51 | | Number of students | 6 | 4 | 2 | 2 | 1 | Find the mean weight. Let the assumed mean be A=49. | | | | | --- --- | | Weight ( in kg )xi | Number of students fi | di=xi−A=xi−49 | fidi | | 47 | 6 | -2 | -12 | | 48 | 4 | -1 | -4 | | 49 | 2 | 0 | 0 | | 50 | 2 | 1 | 2 | | 51 | 1 | 2 | 2 | | | ∑fi=15 | | ∑fidi=−12 | We have, ∑fi=15, ∑fidi=−12 and A=49 We know,Mean=A+n∑i=1fidin∑i=1fi=49+(−1215)=49−0.8=48.2 Hence, mean weight = 48.2 kg. 4) The following table gives the distribution of weekly wages in rupees of workers in a certain factory. | | | | | | | | | | --- --- --- --- | Weekly wages ( in ₹ ) | 300-350 | 350-400 | 400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | | Number of workers | 24 | 40 | 33 | 28 | 30 | 22 | 16 | 7 | Find the mean weekly wages. Let the assumed mean be A=475. | | | | | | --- --- | Weekly wages ( in ₹) | Number of workersfi | Mid-value xi | di=xi−475 | fidi | | 300-350 | 24 | 325 | -150 | -3600 | | 350-400 | 40 | 375 | -100 | -4000 | | 400-450 | 33 | 425 | -50 | -1650 | | 450-500 | 28 | 475 | 0 | 0 | | 500-550 | 30 | 525 | 50 | 1500 | | 550-600 | 22 | 575 | 100 | 2200 | | 600-650 | 16 | 625 | 150 | 2400 | | 650-700 | 7 | 675 | 200 | 1400 | | | ∑fi=200 | | | ∑fidi=−1750 | We have, A=475, ∑fi=200 and ∑fidi=−1750 We know, ¯X=A+n∑i=1fidin∑i=1fi=475+−1750200=475−8.75=466.25 Hence, the mean weekly wages of workers = ₹466.25. Steps to Compute Mean of Grouped Data using Short-Cut Method: We can use the following steps to compute the arithmetic mean by the short-cut method: Step 1: Prepare the frequency table in such a way that its first column consists of the observation, the second column the respective frequencies and the third column for the mid-values. Step 2: Choose the assumed mean (A) and take deviations di=xi−A. Write these deviations against the respective frequencies in the fourth column. Step 3: The fifth column consists of the product of the frequency of each row with the respective deviation i.e., fidi. Step 4: Add all the frequencies in the second column to obtain n∑i=1fi. Step 5: Add all the products in the fifth column to obtain n∑i=1fidi. Step 6: To calculate mean, use the formula¯X=A+n∑i=1fidin∑i=1fi Mean of Grouped Data: Step-Deviation Method In most of the problems, the width of all the classes is the same, so in such cases, the deviations di, are divisible by a common number, say h. We can further simplify the calculations of the mean by computing the coded mean i.e., the mean of u1, u2, …un where ui=xi−Ah Then the mean ¯X is given by the formula¯X=A+h[n∑i=1fiuin∑i=1fi]Let's consider an example. 5) The heights of the students of a school ( in cm ) were recorded as under. | | | | | | | --- --- --- | | Height ( in cm ) | 150 | 155 | 160 | 165 | 170 | | Number of students | 10 | 15 | 8 | 14 | 13 | Find the mean height. Let the assumed mean be A=160 and h=5. | | | | | | --- --- | Height ( in cm ) | Number of studentsfi | di=xi−160 | ui=xi−1605 | fiui | | 150 | 10 | -10 | -2 | -20 | | 155 | 15 | -5 | -1 | -15 | | 160 | 8 | 0 | 0 | 0 | | 165 | 14 | 5 | 1 | 14 | | 170 | 13 | 10 | 2 | 26 | | | ∑fi=60 | | | ∑fiui=5 | We have, A=160, h=5, ∑fi=60, ∑fiui=5 We know, ¯X=A+h[n∑i=1fiuin∑i=1fi]=160+5=160+2560=160+0.42=160.42Hence, the mean height of the students is 160.42 cm. 6) Find the mean of the following frequency distribution: | | | | | | | | | | | | --- --- --- --- --- | Class interval | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 | | Frequency | 1 | 2 | 4 | 8 | 11 | 9 | 7 | 4 | 3 | 1 | Let the assumed mean be A=42.5 and h=5. | | | | | | | --- --- --- | | Class interval | Frequency fi | Mid-value xi | di=xi−42.5 | ui=xi−42.55 | fiui | | 20-25 | 1 | 22.5 | -20 | -4 | -4 | | 25-30 | 2 | 27.5 | -15 | -3 | -6 | | 30-35 | 4 | 32.5 | -10 | -2 | -8 | | 35-40 | 8 | 37.5 | -5 | -1 | -8 | | 40-45 | 11 | 42.5 | 0 | 0 | 0 | | 45-50 | 9 | 47.5 | 5 | 1 | 9 | | 50-55 | 7 | 52.5 | 10 | 2 | 14 | | 55-60 | 4 | 57.5 | 15 | 3 | 12 | | 60-65 | 3 | 62.5 | 20 | 4 | 12 | | 65-70 | 1 | 67.5 | 25 | 5 | 5 | | | ∑fi=50 | | | | ∑fiui=26 | We have, A=42.5, h=5, ∑fi=50, ∑fiui=26 We know, ¯X=A+h[n∑i=1fiuin∑i=1fi]=42.5+5=42.5+2.6=45.1 Steps to Compute Mean of Grouped Data using Step-Deviation Method: We can use the following steps to compute the arithmetic mean by the step-deviation method: Step 1: Prepare the frequency table in such a way that its first column consists of the observation, the second column the respective frequencies and the third column for the mid-values. Step 2: Choose the assumed mean (A) and take deviations di=xi−A. Write these deviations against the respective frequencies in the fourth column. Step 3: Choose a number h, the common factor of all the deviations, divide di by h to get ui. Write these ui in the fifth column against the respective di. Step 4: The sixth column consists of the product of the frequency of each row with the respective ui i.e., fiui. Step 5: Add all the frequencies in the second column to obtain n∑i=1fi. Step 6: Add all the products in the sixth column to obtain n∑i=1fiui. Step 7: To calculate mean, use the formula¯X=A+h[n∑i=1fiuin∑i=1fi] Mean of Grouped Data - Examples Example 1 Estimate the average wage of a worker from the following table: | | | | | | --- --- | Wages ( in ₹ ) | Number of workers | | Wages ( in ₹ ) | Number of workers | | Below 100 | 15 | | Below 500 | 96 | | Below 200 | 35 | | Below 600 | 127 | | Below 300 | 60 | | Below 700 | 198 | | Below 400 | 84 | | Below 800 | 250 | The given table gives a cumulative frequency distribution and hence must be changed to an absolute frequency table. Direct Method | | | | | --- --- | | Wages ( in ₹) | Number of workers fi | Mid-value xi | fixi | | 0-99 | 15 | 49.5 | 742.5 | | 100-199 | 20 (35-15) | 149.5 | 2990.0 | | 200-299 | 25 (60-35) | 249.5 | 6237.5 | | 300-399 | 24 (84-60) | 349.5 | 8388.0 | | 400-499 | 12 (96-84) | 449.5 | 5394.0 | | 500-599 | 31 (127-96) | 549.5 | 17034.5 | | 600-699 | 71 (198-127) | 649.5 | 46114.5 | | 700-799 | 52 (250-198) | 749.5 | 38974.0 | | | ∑fi=250 | | ∑fixi=125875 | We have, ∑fi=250, ∑fixi=125875 Then, ¯X=n∑i=1fixin∑i=1fi=125875250=503.5 Hence, average wage of a worker = ₹503.5. Shortcut Method Let the assumed mean be A=449.5. | | | | | | --- --- | Wages ( in ₹) | Number of workers fi | Mid-valuexi | di=xi−449.5 | fidi | | 0-99 | 15 | 49.5 | -400 | -6000 | | 100-199 | 20 (35-15) | 149.5 | -300 | -6000 | | 200-299 | 25 (60-35) | 249.5 | -200 | -5000 | | 300-399 | 24(84-60) | 349.5 | -100 | -2400 | | 400-499 | 12 (96-84) | 449.5 | 0 | 0 | | 500-599 | 31 (127-96) | 549.5 | 100 | 3100 | | 600-699 | 71 (198-127) | 649.5 | 200 | 14200 | | 700-799 | 52(250-198) | 749.5 | 300 | 15600 | | | ∑fi=250 | | | ∑fidi=13500 | We have, A=449.5, ∑fi=250,∑fidi=13500Then, ¯X=A+n∑i=1fidin∑i=1fi=449.5+13500250=449.5+54=503.5 Hence, average wage of a worker = ₹503.5. Step-deviation Method Let the assumed mean be A=449.5 and h=100. | | | | | | | --- --- --- | | Wages ( in ₹) | Number of workers fi | Mid-valuexi | di=xi−449.5 | ui=xi−449.5100 | fiui | | 0-99 | 15 | 49.5 | -400 | -4 | -60 | | 100-199 | 20 (35-15) | 149.5 | -300 | -3 | -60 | | 200-299 | 25 (60-35) | 249.5 | -200 | -2 | -50 | | 300-399 | 24 (84-60) | 349.5 | -100 | -1 | -24 | | 400-499 | 12 (96-84) | 449.5 | 0 | 0 | 0 | | 500-599 | 31 (127-96) | 549.5 | 100 | 1 | 31 | | 600-699 | 71 (198 -127) | 649.5 | 200 | 2 | 142 | | 700-799 | 52 (250-198) | 749.5 | 300 | 3 | 156 | | | ∑fi=250 | | | | ∑fiui=135 | We have, A=449.5, ∑fi=250,∑fiui=135Then, ¯X=A+h[n∑i=1fiuin∑i=1fi]=449.5+100=449.5+54=503.5 Hence, the average wage of a worker = ₹503.5. Example 2 Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 56. | | | | | | | | | --- --- --- --- | | Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | Total | | Frequency | 16 | f1 | 25 | f2 | 12 | 10 | 90 | | | | | | --- --- | | Class | Frequency fi | Mid-value xi | fixi | | 0-20 | 16 | 10 | 160 | | 20-40 | f1 | 30 | 30f1 | | 40-60 | 25 | 50 | 1250 | | 60-80 | f2 | 70 | 70f2 | | 80-100 | 12 | 90 | 1080 | | 100-120 | 10 | 110 | 1100 | | | ∑fi=63+f1+f2 | | ∑fixi=3590+30f1+70f2 | We have, ∑fi=9063+f1+f2=90f1+f2=27f2=27−f1……(1) Also, ¯X=56n∑i=1fixin∑i=1fi=563590+30f1+70f290=563590+30f1+70(27−f1)=50403590+30f1+1890−70f1=50405480−40f1=5040440=40f1f1=11Substituting f1=11 in (1), we get∴f2=27−11=16 Hence, the missing frequencies are 11 and 16. Example 3 Find the value of p, if the mean of the following distribution is 18. | | | | | | | | --- --- --- | x | 13 | 15 | 17 | 19 | 20+p | 23 | | f | 8 | 2 | 3 | 4 | 5p | 6 | | | | | --- | x | f | fx | | 13 | 8 | 104 | | 15 | 2 | 30 | | 17 | 3 | 51 | | 19 | 4 | 76 | | 20+p | 5p | 100p+5p2 | | 23 | 6 | 138 | | | ∑f=23+5p | ∑fx=399+100p+5p2 | We have, ¯X=18∑fx∑f=18399+100p+5p223+5p=18399+100p+5p2=414+90p5p2+10p−15=0p2+2p−3=0p2+3p−p−3=0p(p+3)−1(p+3)=0(p+3)(p−1)=0⇒p+3=0orp−1=0p=−3orp=1 But the frequency cannot be negative, therefore p=1. Example 4 The histogram below represents the scores by 20 students in a test. Calculate the mean score. The frequency distribution obtained from the histogram is as follows: | | | | | --- --- | | Scores | Frequency fi | Mid-value xi | fixi | | 0-10 | 2 | 5 | 10 | | 10-20 | 5 | 15 | 75 | | 20-30 | 6 | 25 | 150 | | 30-40 | 4 | 35 | 140 | | 40-50 | 3 | 45 | 135 | | | ∑fi=20 | | ∑fixi=510 | We have, ¯X=n∑i=1fixin∑i=1fi=51020=25.5 Summary If x1, x2,…,xn are n variables of a variable X, then the arithmetic mean or simply the mean of these values is denoted by ¯X and is defined as : ¯X=x1+x2+x3+⋯+xnnor¯X=n∑i=1xin Mid-value, xi=Upper class limit + Lower class limit2. The Formula for Mean of Grouped Data - Direct Method: If x1, x2, x3,…xn are observations having respective frequencies f1, f2,…,fn. : ¯X=n∑i=1xifin∑i=1fi The Formula for Mean of Grouped Data - Short-cut Method: In this method, an approximate mean ( called assumed mean ) is taken ( preferably near the middle ), say A, and we calculate the deviation di=xi−A for each value of xi. : ¯X=A+n∑i=1fidin∑i=1fi. The Formula for Mean of Grouped Data - Step-Deviation Method: In this method, the mean is given by : ¯X=A+h[n∑i=1fiuin∑i=1fi] where ui=xi−Ah. Mean of Grouped Data - Review Questions What is the algebraic sum of the deviations of a frequency distribution from its mean? What is the mean of -6, -3, 0, 3 and 6? Find the mean of the first five multiples of 5. Find the mean of the first eight prime numbers. The mean of 10 numbers is 36. If 6 is subtracted from each number, what will the new mean be? The mean of 8 numbers is 25. If 10 is added to each number, what will the new mean be? Given that ¯X is the mean of x1, x2,…xn, find the mean of x1a, x2a, …,xna. The mean of 10 numbers is 2. If each number is multiplied by 1.5, find the mean of the new set of numbers. The mean height of six boys is 161 cm. Individual heights of five boys ( in cm ) are 156, 167, 149, 155 and 171 respectively. Find the height of the sixth boy. The mean of 100 items was found to be 50. Later on, it was found that the values of two items were taken as 63 and 7 instead of 163 and 77. Find the correct mean. Consider the prices in ₹, of various computing books at a bookstore: 119, 244.50, 346.50, 265, 440.50, 389.50, 564, 487.50, 293, 356.50. Find the mean price of the books. The number of goals scored per match by a team during football season was recorded. | | | | | | | | | --- --- --- --- | | Number of goals | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | Number of matches | 1 | 9 | 6 | 7 | 3 | 3 | 1 | Find The total number of matches played. Total number of goals scored. The mean number of goals scored per match by the team. Find the mean of the following distribution. | | | | | | | | --- --- --- | x | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | | f | 30 | 60 | 20 | 40 | 10 | 50 | The marks obtained in Mathematics test by 40 students were recorded. | | | | | | | | --- --- --- | Marks | 0-8 | 8-16 | 16-24 | 24-32 | 32-40 | 40-48 | | Number of students | 5 | 3 | 10 | 16 | 4 | 2 | Find the mean marks of the students. The heights, measured to the nearest cm, of the plants in a nursery are recorded. | | | | | | | --- --- --- | | Height ( in cm ) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | | Number of plants | 4 | 6 | 14 | 6 | 10 | Calculate the mean height of the plants. 100 trucks are required to transport raw materials from a quarry to a construction site. The travel time ( in minutes ) of the trucks using a fixed route was recorded. | | | | | | | | | | --- --- --- --- | Time taken ( in min ) | 100-105 | 105-110 | 110-115 | 115-120 | 120-125 | 125-130 | 130-135 | 135-140 | | Number of trucks | 1 | 6 | 23 | 28 | 27 | 9 | 5 | 1 | Calculate the mean travelling time of the trucks. Find the trucks which took less than 125 minutes to travel from the quarry to the construction site. Speed cameras were set up at a location along an expressway to monitor the average speed of vehicles as they travel along the accident - prone area of the expressway during the peak hours. The average speed ( in km/hr ), during a short interval, are recorded in the table. | | | | | | | --- --- --- | | Speed ( in km /hr ) | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | | Number of vehicles | 2 | 6 | 26 | 12 | 4 | Calculate the average speed of the vehicles. Find the mean of the following data. | | | | | | | --- --- --- | | Class | Less than 20 | Less than 40 | Less than 60 | Less than 80 | Less than 100 | | Frequency | 6 | 28 | 65 | 90 | 111 | Find the missing frequency in the following data is the arithmetic mean is 19.92. | | | | | | | | | | | --- --- --- --- --- | | Class | 4-8 | 8-12 | 12-16 | 16-20 | 20-24 | 24-28 | 28-32 | 32-36 | 36-40 | | Frequency | 11 | 13 | 16 | 14 | f | 9 | 17 | 6 | 4 | The mean of the following frequency distribution is 57.2 and the sum of all the frequencies is 400. Compute the missing frequencies. | | | | | | | --- --- --- | | Class | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 | | Frequency | f1 | 110 | 135 | 115 | f2 | | Image | Reference | Attributions | --- | | | Credit: CK-12 Source: CK-12 License: CC BY-NC 3.0 | Student Sign Up Are you a teacher? Having issues? Click here By signing up, I confirm that I have read and agree to the Terms of use and Privacy Policy Already have an account? Save this section to your Library in order to add a Practice or Quiz to it. (Edit Title)20/ 100 This lesson has been added to your library. |Searching in: | | | Looks like this FlexBook 2.0 has changed since you visited it last time. We found the following sections in the book that match the one you are looking for: Go to the Table of Contents No Results Found Your search did not match anything in .
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https://chemistry.stackexchange.com/questions/84351/how-does-a-combustion-process-produce-carbon-monoxide
Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Visit Stack Exchange Teams Q&A for work Connect and share knowledge within a single location that is structured and easy to search. Learn more about Teams How does a combustion process produce carbon monoxide? Ask Question Asked Modified 7 years, 11 months ago Viewed 3k times 6 $\begingroup$ My question is in the context of combustion heater safety- I want to identify the mechanism by which CO is produced, and hopefully have additional understanding, and clues to the warning signs, to identify unsafe stoves or installations. The primary safety measures will always be CO detectors and good ventilation. The worst horror stories usually concern charcoal barbecues in confined spaces- solid carbon burning at about 900 °C. Is it a safe educated guess that the main combustion product here is CO, which fails to burn fully to CO2 in depleted oxygen levels? Or is a more complex process at work? How does the yellow combustion of an oil or gas flame produce CO? Is it a simple matter of poor gas flow in the flue, and depleted oxygen in the feed air? Thanks for any help everyday-chemistry Share edited Oct 17, 2017 at 14:30 mhchem 3,35622 gold badges1919 silver badges3535 bronze badges asked Oct 17, 2017 at 14:07 Brian HughesBrian Hughes 17111 silver badge33 bronze badges $\endgroup$ 4 3 $\begingroup$ That's right, it is ultimately a matter of incomplete combustion due to the lack of oxygen. $\endgroup$ Ivan Neretin – Ivan Neretin 2017-10-17 14:18:15 +00:00 Commented Oct 17, 2017 at 14:18 $\begingroup$ CO2+C->2CO, kind of a comproportionation reaction. $\endgroup$ Ariana – Ariana 2017-10-17 16:25:37 +00:00 Commented Oct 17, 2017 at 16:25 $\begingroup$ Since your question is in "the context of heater safety", you might get a more specific and relevant answer if you briefly described the nature of the heater of interest and the environment in which it operates. $\endgroup$ airhuff – airhuff 2017-10-17 20:37:18 +00:00 Commented Oct 17, 2017 at 20:37 1 $\begingroup$ @airhuff Good point. A bit more context- my primary interest is in outdoor burners, with a slight twist in that I burn wood to charcoal for use as biochar. On the strength of this, I'm being approached for advice from residents of an Off-Grid intentional community on installation and operation of wood-burning stoves to heat cabins- advice which I'm not really experienced to give. I don't want anyone gassed or cremated because of my advice or lack of it, so the best I can do is learn to spot installations that are really dangerous, and why, before they get lit up in the cold weather. $\endgroup$ Brian Hughes – Brian Hughes 2017-10-17 21:20:58 +00:00 Commented Oct 17, 2017 at 21:20 Add a comment | 1 Answer 1 Reset to default 1 $\begingroup$ If combustion occurs in oxygen, (at least) the following reactions are relevant: $$\ce{C + O2 -> CO2} $$ $$\ce{C + 1/2 O2 -> CO} $$ You can favor the first reaction by having more oxygen in the gas phase, since it required twice $\ce{O2}$ as the first. However, one of the most important factors is the temperature: high temperature always favors the $\ce{CO}$ product, since reaction wants to proceed fast and react with any available oxygen. You can clearly see these dependences in the Figure 6 of this article, at low temperatures the CO/CO2 ratio is low, but quickly increases by heating. More detailed information is easily found in some classical papers, a full PhD thesis on it, or even calculations with modern quantum chemistry methods. Share answered Oct 28, 2017 at 10:42 NandoNando 41833 silver badges1212 bronze badges $\endgroup$ Add a comment | Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions everyday-chemistry See similar questions with these tags. Featured on Meta Spevacus has joined us as a Community Manager Introducing a new proactive anti-spam measure Related 3 Can carbon monoxide contaminate water? About how much carbon monoxide is produced in these two different reations? How much yeast is necessary to produce the same amount of carbon dioxide that I exhale? 1 Why does charcoal not produce smoke when heated? 5 Does rubbing alcohol + bleach really produce chloroform? Hot Network Questions How can the problem of a warlock with two spell slots be solved? Quantizing EM field by imposing canonical commutation relations Why do universities push for high impact journal publications? Is it possible that heinous sins result in a hellish life as a person, NOT always animal birth? Is it safe to route top layer traces under header pins, SMD IC? How do trees drop their leaves? Bypassing C64's PETSCII to screen code mapping What is the meaning of 率 in this report? What were "milk bars" in 1920s Japan? What "real mistakes" exist in the Messier catalog? Checking model assumptions at cluster level vs global level? Another way to draw RegionDifference of a cylinder and Cuboid Why is the definite article used in “Mi deporte favorito es el fútbol”? Can peaty/boggy/wet/soggy/marshy ground be solid enough to support several tonnes of foot traffic per minute but NOT support a road? If Israel is explicitly called God’s firstborn, how should Christians understand the place of the Church? How to home-make rubber feet stoppers for table legs? ICC in Hague not prosecuting an individual brought before them in a questionable manner? What is the feature between the Attendant Call and Ground Call push buttons on a B737 overhead panel? how do I remove a item from the applications menu "Unexpected"-type comic story. Aboard a space ark/colony ship. Everyone's a vampire/werewolf Calculating the node voltage Is existence always locational? Lingering odor presumably from bad chicken Suspicious of theorem 36.2 in Munkres “Analysis on Manifolds” more hot questions Question feed
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https://medium.com/@lovelyndavid/mastering-the-sliding-window-technique-max-sum-subarray-in-python-1a843f62e114
Sitemap Open in app Sign in Sign in Mastering the Sliding Window Technique: Max Sum Subarray in Python Lovelyn David 3 min readApr 10, 2025 When solving array problems in programming, efficiency is everything. One technique that stands out for optimizing problems involving subarrays or substrings is the Sliding Window technique. In this blog, we’ll explore this concept with a classic problem: Finding the maximum sum of all subarrays of size k. The Problem Statement We are given an array of integers, and an integer k, representing the subarray (or window) size. Goal: Find the subarray of size k that has the maximum sum. Example Let’s take this array: [2, 1, 5, 1, 3, 2]2, 1, 5, 1, 3, 2 Let k = 3. The possible subarrays of size k are: [2, 1, 5] → Sum = 8 [1, 5, 1] → Sum = 7 [5, 1, 3] → Sum = 9 [1, 3, 2] → Sum = 6 Answer: The maximum sum is 9, from the subarray [5, 1, 3]. Why Use Sliding Window? The sliding window technique is an optimization strategy for problems where you need to examine subsets of a larger dataset (like subarrays or substrings) — especially when these subsets are contiguous and of a fixed size. Visualization of the Sliding Window Consider this example array: [5, 7, 65, 8, 7, 99]5, 7, 65, 8, 7, 99 And let k = 3. Get Lovelyn David’s stories in your inbox Join Medium for free to get updates from this writer. Here’s how the window moves: First window: [5, 7, 65] → Sum = 77 Slide right → [7, 65, 8] Slide again → [65, 8, 7] And again → [8, 7, 99] The sliding window solution works as follows: Start by computing the sum of the first window (i.e., the first k elements of the array). This gives you an initial value to compare with later window sums. Then slide the window one element at a time. Remove the element that’s no longer in the window (i.e., the one at the leftmost end). Add the new element that has entered the window from the right. This lets you compute the new window’s sum in constant time — without recalculating the entire sum from scratch. Keep track of the maximum window sum seen so far. Update it whenever a new window sum is greater than the current maximum. Analogy: Finding the Maximum Element This is conceptually similar to finding the maximum element in an array: You iterate through the array. At each step, you compare the current number with the maximum found so far. If the current number is larger, you update your max. Python Code: Max Sum Subarray Using Sliding Window Here’s a simple and efficient Python function: ``` def max_sum_subarray(arr, k): n = len(arr) if n < k: return -1 # Not enough elements # Compute the sum of the first window window_sum = sum(arr[:k]) # Time Complexity: O(k) max_sum = window_sum # Slide the window for i in range(k, n): # Single loop O(n-k) window_sum += arr[i] - arr[i - k] # add next element, remove first element of previous window max_sum = max(max_sum, window_sum) return max_sum def max_sum_subarrayarr, k len if return 1 Not enough elements Compute the sum of the first window sum Time Complexity: O(k) Slide the window for in range Single loop O(n-k) add next element, remove first element of previous window max return ``` ``` test_cases = [ ([2, 1, 5, 1, 3, 2], 3, 9), #(arr, k, expected) ([1, 9, 2, 5, 1, 3], 2, 11), ([1, 1, 1, 1, 1], 5, 5), ([5, -1, 2, -3, 7, 1], 4, 7), # Edge Case ([1, 2], 3, -1), # Invalid Case]for i, (arr, k, expected) in enumerate(test_cases, 1): result = max_sum_subarray(arr, k) print(f"Test Case {i}: {'PASS' if result == expected else 'FAIL'} (Output: {result}, Expected: {expected})") 2 1 5 1 3 2 3 9 (arr, k, expected) 1 9 2 5 1 3 2 11 1 1 1 1 1 5 5 5 1 2 3 7 1 4 7 Edge Case 1 2 3 1 Invalid Case for in enumerate 1 printf"Test Case {i}: {'PASS' if result == expected else 'FAIL'} (Output: {result}, Expected: {expected})"{i}{'PASS' if result == expected else 'FAIL'} 'PASS' if else 'FAIL'{result}{expected} ``` Time Complexity Analysis Calculating the sum in the first window: O(k) Sliding the window over n - k elements: O(n-k) Each statement inside loop: O(1) Total time complexity: O(k) + O(n - k)= O(k + n - k)= O(n) O O O O Space complexity: O(1) (only using a few variables) This is significantly better than brute force, which is O(nk). Be the first to hear about new stories from Lovelyn David ## Written by Lovelyn David 49 followers ·15 following Responses (1) Write a response What are your thoughts? Jaganadh Gopinadhan Apr 10 ``` Great notes Dr Lovelyn. ``` More from Lovelyn David Lovelyn David ## MCP in Cursor AI In this article we will add tools to enhance the capability of Cursor AI. Apr 16 5 Lovelyn David ## LangGraph Series-2-Creating a Conversational Bot with Memory Using LangGraph In the previous article, we explored how to construct a graph using LangGraph. In this article, we will take it a step further by building… Apr 11 16 1 Lovelyn David ## LangGraph Beginner Guide — Part 1 This is a beginner guide and the first in the series. We will start by looking at what LangGraph is and then explore its key components. Apr 9 2 1 Lovelyn David ## Candidate Elimination Algorithm with the infamous Aldo Example In this blog, we will see in detail how to solve the infamous Aldo example step by step using the Candidate-elimination Algorithm with… Jan 9, 2024 1 See all from Lovelyn David Recommended from Medium Observability Guy ## These 16 DSA Patterns Did What 3000 LeetCode Problems Couldn’t Master essential data structures and algorithms patterns to solve problems faster than thousands of random challenges Aug 10 53 Amit kharche ## RNN, LSTM, GRU in NLP: A Deep Dive into Sequence Modeling Mastering Sequential Neural Networks with Mathematical Precision and Practical Insights May 25 3 1 In Artificial Intelligence in Plain English by Kushagra Pandya ## Understanding the Attention Mechanism in Transformers Unlocking the Power of Focus in AI Models Aug 4 5 Elshad Karimov ## Top 10 Data Structures to Master in Python 🐍 🌟 Special Offer for My Readers 🌟 Aug 12 1 In Data Science Collective by Egor Howell ## I Tried 50 Data Science Courses: Here Are The BEST 5 Great teaching at a low cost 3d ago 56 2 ## A Complete Beginner’s Guide to Python Loops New to Python? 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https://blog.csdn.net/wszdzh/article/details/8547161
利用差分法求解数列问题-CSDN博客 博客 下载 学习 社区 GitCode InsCodeAI 会议 搜索 AI 搜索 登录 登录后您可以： 复制代码和一键运行 与博主大V深度互动 解锁海量精选资源 获取前沿技术资讯 立即登录 会员·新人礼包 消息 历史 创作中心 创作 差分法求数列后几项 最新推荐文章于 2025-01-10 19:29:02 发布 原创 于 2013-01-27 21:59:06 发布·898 阅读 · 0 · 0· CC 4.0 BY-SA版权 版权声明：本文为博主原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接和本声明。 Algorithm 同时被 2 个专栏收录 8 篇文章 订阅专栏 C/C++ 6 篇文章 订阅专栏 这篇博客探讨了如何使用差分法来解决数列的后续项预测问题。作者指出，相比于拉格朗日插值法可能面临的精度挑战，差分法提供了一个避免浮点数操作的有效途径。通过举例说明，如1 2 4 7 11 16 22 29数列，进行一阶和二阶差分，可以发现数列的规律并推导出通项公式。这种方法对于存在多项式通项的数列尤为适用。 差分法。曾经在自己的脑子里模拟过，但是不知道细节，没有系统学习过，就是这么悲剧了。 每次都是说 很久没有写 算法 题了。又水一道。 见转载的一个解法： 题目给出了一个数列的前若干项，要求推测后面的项。我们很容易想到拉格朗日插值法，但是精度就变成了一个大问题。这个问题虽然保证了所有的值都是整数，但是并没有保证其多项式的系数也是整数，因此在计算方面存在很大的困难。 除了插值法，求解这种数列问题我们有更好的差分方法，过程中完全不涉及浮点数操作。比如说，对于1 2 4 7 11 16 22 29这个数列，我们对于每一项做其和前一项的差，也就是2-1=1, 4-2=2, 7-4=3, ....这样，我们得到一个1阶差分：1, 2, 3, 4, 5, 6, 7。我们再求得2阶差分是：1, 1, 1, 1, 1, 1。这时，规律已经有些明显了。 也就是说，对于任意一个存在合理多项式通项的数列，用差分的方法是可以得到它的解的：只要求得这个n项数列的n-1阶差分，然后倒推回去就可以了。 ```cpp include #include using namespace std; const int MAXN = 100+5; int n,m,s[MAXN][MAXN]; int main() { int ncase; scanf("%d",&ncase); while (ncase--) { scanf("%d%d",&n,&m); for (int i = 0; i<n; i++) scanf("%d",&s[i]); for (int i = 1; i<n; i++) for (int j = 0; i+j<n; j++) s[i][j] = s[i-1][j+1]-s[i-1][j]; for (int i = 1; i<=m; i++) s[n-1][i] = s[n-1]; for (int i = n-2; i>=0; i--) for (int j = 0; j<m; j++) s[i][n-i+j] = s[i][n-i+j-1]+s[i+1][n-i+j-1]; for (int i = 0; i<m-1; i++) printf("%d ",s[n+i]); printf("%d\n",s[n+m-1]); } return 0;} ``` AI写代码 cpp 运行 确定要放弃本次机会？ 福利倒计时 : : 立减 ¥ 普通VIP年卡可用 立即使用 wszdzh 关注关注 0点赞 踩 0 收藏 觉得还不错? 一键收藏 0评论 分享复制链接 分享到 QQ 分享到新浪微博 扫一扫 举报 举报 专栏目录 所有排列中的最大和，带你认识差分数组 OnlyloveCuracao的博客 09-22 1999 所有排列中的最大和、差分数组、如何理解差分数组、差分数组的引用 参与评论 您还未登录，请先 登录 后发表或查看评论 差分法~超详细(公式+原理+例题) 9-28 一个 数列 要在很多不 确定 的区间内加上相同的一个数,如果直接在原 数列 上操作是非常复杂且耗时的,差分法 就是先将 数列 拆分,构造一个拆分的新 数列,在这个新 数列 上进行我们想要的操作之后,在将这个 数列 合并起来即可。 听起来好像复杂了很多,其实不然,这样处理反而能减少很多操作,比如不用对给定区间内的原 数列 的每 一项 进... k阶常系数线性非齐次递归方程-dp108ausb声卡资源 9-2 现在还没有一个寻找特解的有效方法,一 般是根据递归方程中g(n)的形式来 确定 特解。 再把特解代入原递归方程,用待定系数法 确定 特解的系数。下面是常见的几种形式: ① g(n)是n 的m 次多项式,即 如果a 不是特征方程的重根,特解f ( n ) 为 : f (n)=(A 1 n m+A 2 n m-1+⋯+A m n... 差分法 qq_43531919的博客 03-27 1427 差分 差分就是将 数列 中的每 一项 分别与前 一项 数做差，例如： 一个序列[1 7 6 5 2 4],差分后得到[1 6 -1 -1 -3 -2 -4] 差分序列第一个数和原序列第一个数相同（相当于第一个数减去0） 差分序列最后比原序列多一个数（相当于0减去最后一个数） 性质 差分序列 求 前缀和可得原序列 将原序列区间[L,R]中全部的元素+1，可以转化操作为差分序列L处+1，R+1处-1 按照性质2得到，每次修改原序列一个区间+1,那么差分序列修改处增加的和减少的相同 例子 题目描述 ------天才程序员菜哭 差分法 求 高阶等差 数列 的通项公式 Happig的博客 09-21 4873 高阶等差 数列 对于一个给定的 数列，将连续两项之间的差bn=an+1−anb_n=a_{n+1}-a_nbn​=an+1​−an​得到一个新的 数列，那么bnb_nbn​称为原 数列 的一阶等差 数列，若cn=bn+1−bnc_n=b_{n+1}-b_ncn​=bn+1​−bn​，那么cnc_ncn​称为原 数列 的二阶等差 数列，以此类推… 高阶等差 数列 都有一个多项式的通项公式。 差分法 给定序列aaa，依次 求 出该序列的kkk阶等差序列，直到某个序列全为000为止，按照下列排列规则排列在纸上 Cn+11&nb 从递推式到通项公式 特征方程学习笔记_递推方程,特征方程,通过通项公式... 9-25 本文介绍了一种 求 解递推式通项公式的有效方法——特征方程法。通过引入一次和二次线性递推式的概念,详细探讨了如何通过构造特征方程来 求 解 数列 的通项公式,特别关注于处理特殊情况下递推式的 求 解。 参考文章ruanxingzhi引入对于一些递推式,我们常常会有关于 求 数列 某 一项 的问题,如果我们能推出其通项公式,那么问题就会... 组合数学之递推关系(二)常系数线性齐次递推关系及其通项 求 解_线性常系... 9-27 我们先来解读一下名字中的名词: 常系数:系数kiki为常数 线性齐次:递推式里的an−ian−i的指数全为一次 递推关系:就递推的意思 还有几个定义: 特征多项式:就是上面的式子左边-右边,然后把aiai变成xixi后形成的式子 即:xm−k1∗xm−1−k2∗xm−2−...−km−1∗x−km∗1=0xm−k1... 浅谈差分数组的原理及简单应用 aua4137的博客 02-27 564 一、差分数组的定义及用途 1.定义： 对于已知有n个元素的离线 数列 d，我们可以建立记录它每项与前 一项 差值的差分数组f：显然，f=d-0=d;对于整数i∈[2,n]，我们让f[i]=d[i]-d[i-1]。 2.简单性质： (1)计算 数列 各项的值：观察d=f+f=d+d-d=d可知，数列 第i项的值是可以用差分数组的前i项的和计算的... 差分法 在二元一次多项式中的应用 weixin_30375247的博客 07-14 513 人- vs - 计算机 ax2+bx+c=0 人：直接用规则。 x=2a分之负b加减根号b的平方减4ac。 计算机：一个数一个数的代入，只要等号成立那么就找到x的解。方法笨但是简单，计算量也大。 差分法： n n2 alpha(一阶差分) bata(二阶差分) 0 0 1 1 1 2 4 3(=4-1) ... 波浪作用下斜坡上护面块体应力分布的数值模拟(2013年)_Hudson震源... 9-6 边坡滑动面的数值模拟分析,王喜刚,金俐伶,边坡稳定性分析主要是 确定 滑动面和安全系数,而 确定 最危险滑动面的理论计算方法(解析法)比较复杂,确定 出来的最危险滑动面也是按� 格式:pdf资源大小:673.5KB页数:7 波浪作用下螺母块体护面的稳定计算 浏览:99 backward（扩散方程的后项 差分法）MATLAB 10-31 应用显格子法解决扩散偏微分方程 MATLAB解法 2.3-等差 数列 前项n和的性质及推导--2.3(第二课时).pdf 04-21 这些性质的推导方法多种多样，如数学归纳法可以用来证明前n项和的公式，而差分序列法和中项法则可以用来探索等差 数列 其他深层的特性。掌握这些证明方法，不仅能够加深对等差 数列 性质的理解，也能够培养逻辑推理和... 数列 通项公式的 求 法(最全).pptx 07-05 - 当 数列 的前n项和Sn满足特定函数关系，如Sn=n^2+2n-1时，可以采用 差分法，将an表示为Sn-Sn-1，然后通过解方程得到an的表达式。 - 对于递推 数列，如an=-SnSn-1，同样可以利用Sn-Sn-1的关系，然后解方程组找到an。 ... 数列 通项公式的 求 法(较全).doc 10-06 数列 通项公式的 求 法是数学中一个重要的部分，主要应用于解决等差 数列、等比 数列 以及更复杂的递推序列问题。以下将详细解释几种常见的 求 解方法： 1. 定义法： - 等差 数列：如果 数列 是等差 数列，那么 数列 的... 求 数列 通项公式方法总结.docx 10-05 1. 归纳法：这种方法通过观察 数列 的前 几项 来推测通项公式。例如，数列 3 14, 5 18, 7 116, 9 132，可以通过分析每 一项 的构成规律发现，每个奇数项是连续奇数，偶数项是连续偶数的平方分之一，因此通项公式可能是an = ... 求 数列 通项公式十种方法.docx 10-05 观察法的核心在于分析 数列 的前 几项，从中找出潜在的规律。一旦规律被发现，就需要通过数学归纳法或其他证明方法来验证。例如，对于 数列{an}，如果a1=1，a2=2，a3=4，我们可能会猜测an=2^(n-1)。接下来，我们必须使用... 差分法 求 函数值 03-02 matlab实现 差分法 求 函数值，函数。 算法（二）——一维差分、等差 数列 差分 xiaokuer_的博客 01-10 1106 一维差分、等差 数列 差分 差分数组 weixin_30736301的博客 07-27 253 今天学习了一下差分数组，觉得好神奇啊。 1.定义： 对于已知有n个元素的离线 数列 d，我们可以建立记录它每项与前 一项 差值的差分数组f：显然，f=d-0=d;对于整数i∈[2,n]，我们让f[i]=d[i]-d[i-1]。 2.简单性质： (1)计算 数列 各项的值：观察d=f+f=d+d-d=d可知，数... 前向差分、后向差分、中心差分精度，matlab仿真 热门推荐 qq_44588244的博客 01-13 2万+ 前向差分、后向差分、中心差分的精度分析，以及matlab仿真观察其精度 ZZUOJ10471: 数列 游戏 I（差分 数列） weixin_34355881的博客 03-14 370 10471: 数列 游戏 I Time Limit:2 SecMemory Limit:128 MB Submit:63Solved:13 [Submit][Status][Web Board] Description 给定一个长度为N的序列，首先进行A次操作，每次操作在Li和Ri这个区间加上一个数Ci。然后有B次询问，每次询问Li到Ri... 差分 数列 Qianyri的博客 08-10 1539 差分 数列（学习笔记） weixin_30297281的博客 03-21 360 转载于: 利用差分 求 非齐次多项式的通项公式 qq_45778406的博客 03-12 657 as 数列 求 通项公式 最新发布 04-19 1. 观察归纳法：通过前 几项 猜测通项，并用数学归纳法证明。例如等差 数列、等比 数列。 2. 累加累乘法：适用于a_{n+1} - a_n = f(n)或a_{n+1}/a_n = f(n)的形式。 3. 特征方程法：针对线性递推 数列，如a_{n+2} = pa_{... 关于我们 招贤纳士 商务合作 寻求报道 400-660-0108 kefu@csdn.net 在线客服 工作时间 8:30-22:00 公安备案号11010502030143 京ICP备19004658号 京网文〔2020〕1039-165号 经营性网站备案信息 北京互联网违法和不良信息举报中心 家长监护 网络110报警服务 中国互联网举报中心 Chrome商店下载 账号管理规范 版权与免责声明 版权申诉 出版物许可证 营业执照 ©1999-2025北京创新乐知网络技术有限公司 wszdzh 博客等级 码龄16年 33 原创31 点赞 44 收藏 19 粉丝 关注 私信 热门文章 聊聊 APK —— AAR 的合并进 APK 1774 关于汉诺塔问题 1743 Webview.apk —— Google 官方的私有插件化方案 1583 离散数学——图论（1） 1570 FileShare —— 基于 Windows IOCP 无状态高并发Socket I/O 模型 1428 分类专栏 realloc()11篇 Season.2篇 Java/Android1篇 C/C++6篇 Algorithm8篇 上一篇： [SPOJ] 大数竖式计算输出 下一篇： 费马小定理（MR素数探测法） v2.0 最新评论 Gradle Builds Everything —— 处理依赖（aar） guodongAndroid:您好，感谢您的文章，对我很有帮助。有个问题想请教下您：我想在AarTransform执行前先处理下aar文件，可以实现么？ 聊聊 APK —— AAR 的合并进 APK 小道安全:感谢分享，学习一波 聊聊 APK —— AAR 的合并进 APK 普通网友:博主写的很详细，作为小白的我，都能看得懂，谢谢分享！ 最近我也在学习写博客,有空来看看我呀，一起互相学习。期待你的关注与支持 聊聊 APK —— AAR 的合并进 APK Java劝退师、:好文，鉴定完毕！ 最近我也在学习写博客,有空来看看我呀，一起互相学习。期待你的关注与支持 聊聊 APK —— AAR 的合并进 APK LaoYuanPython:博主辛苦了！谢谢分享！ 原创不易，必须支持！ 伙计，加油! 不好意思拉个票，本人正参与博客之星评选，今天是投票最后一天，如方便敬请支持！谢谢！ 投票链接：[code=python] [/code] 或到老猿博文首页内的置顶博文跳转！ 大家在看 AI美女时钟广告创意解析 16 IEC 60730-1标准核心解析 基于Springboot+Vue的餐饮财务管理系统的设计与实现毕业设计项目 从零开始获取股票数据：手把手教你调用免费股票API数据接口 1765 算法中的 “并” 之美：从数组、链表到并查集的统一思想 最新文章 无限乐观和自我救赎 AI 悲观论 2025 2025年 3篇 2021年 1篇 2020年 6篇 2019年 2篇 2013年 4篇 2012年 13篇 2010年 8篇 上一篇： [SPOJ] 大数竖式计算输出 下一篇： 费马小定理（MR素数探测法） v2.0 分类专栏 realloc()11篇 Season.2篇 Java/Android1篇 C/C++6篇 Algorithm8篇 展开全部收起 登录后您可以享受以下权益： 免费复制代码 和博主大V互动 下载海量资源 发动态/写文章/加入社区 ×立即登录 评论 被折叠的 条评论 为什么被折叠?到【灌水乐园】发言 查看更多评论 添加红包 祝福语 请填写红包祝福语或标题 红包数量 个 红包个数最小为10个 红包总金额 元 红包金额最低5元 余额支付 当前余额 3.43 元 前往充值 > 需支付：10.00 元 取消 确定 成就一亿技术人! 领取后你会自动成为博主和红包主的粉丝 规则 hope_wisdom 发出的红包 实付 元 使用余额支付 点击重新获取 扫码支付 钱包余额 0 抵扣说明： 1.余额是钱包充值的虚拟货币，按照1:1的比例进行支付金额的抵扣。 2.余额无法直接购买下载，可以购买VIP、付费专栏及课程。 余额充值 确定 取消 举报 选择你想要举报的内容（必选） 内容涉黄 政治相关 内容抄袭 涉嫌广告 内容侵权 侮辱谩骂 样式问题 其他 原文链接（必填） 请选择具体原因（必选） 包含不实信息 涉及个人隐私 请选择具体原因（必选） 侮辱谩骂 诽谤 请选择具体原因（必选） 搬家样式 博文样式 补充说明（选填） 取消 确定 点击体验 DeepSeekR1满血版 下载APP 程序员都在用的中文IT技术交流社区 公众号 专业的中文 IT 技术社区，与千万技术人共成长 视频号 关注【CSDN】视频号，行业资讯、技术分享精彩不断，直播好礼送不停！客服返回顶部
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https://arxiv.org/pdf/1104.4957
arXiv:1104.4957v1 [math.NT] 26 Apr 2011 RANDOMNESS OF CHARACTER SUMS MODULO m YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU Abstract. Using a probabilistic model, based on random walks on the additive group Z/m Z, we prove that the values of certain real character sums are uniformly distributed in residue classes modulo m. Introduction A central question in number theory is to gain an understanding of character sums Sχ(x) = ∑ n≤x χ(n), where χ is a Dirichlet character modulo q. When q = p is a prime number and χp =( · p ) is the Legendre symbol modulo p, the character sums Sp(x) = Sχp (x) encode information on the distribution of quadratic residues and non-residues modulo p (see for example Davenport and Erd¨ os , and Peralta ). In particular, bounds for the order of magnitude of Sp(x) lead to results on the size of the least quadratic non-residue modulo p (see the work of Ankeny ; Banks, Garaev, Heath-Brown and Shparlinski ; Burgess ; Graham and Ringrose ; Lau and Wu ; Linnik ; and Montgomery ). Quadratic residues and non-residues appear to occur in a rather random pattern modulo p, which suggests that the values of χp(n) mimic a random variable that takes the values 1 and −1 with equal probability 1 /2. This fact was recently exploited by Granville and Soundararajan while investigating the distribution of the values of Dirichlet L-functions attached to quadratic characters at s = 1. Furthermore, a result of Davenport and Erd¨ os shows that short real character sums are indeed random in some sense. More specifically, they established that the values Sp(n + H) − Sp(n)are distributed according to a Gaussian distribution of mean zero and variance H as H → ∞ in the range log H/ log p → 0 when p → ∞ .In this paper, we investigate a new aspect of the randomness of these character sums. To describe our results, we first need some notation. Let F (X) be a square-free 2010 Mathematics Subject Classification. Primary 11L40; Secondary 11B50, 60G50. Key words and phrases. Character sums, distribution in residue classes, random walks on finite groups. The First author is supported by a postdoctoral fellowship from the Natural Sciences and Engi-neering Research Council of Canada. Research of the second author is supported by the NSF grant DMS-0901621. 12YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU polynomial of degree dF ≥ 1 over the finite field Fp = Z/p Z, and define Sp(F, k ) := ∑ n≤k χp(F (n)) , for all positive integers k ≤ p. Moreover, let Φ p(F ; m, a ) be the proportion of positive integers k ≤ p for which Sp(F, k ) ≡ a mod m; that is Φp(F ; m, a ) = 1 p|{ k ≤ p : Sp(F, k ) ≡ a mod m}| . Since the values χp(F (n)) are expected to be randomly distributed, one might guess that Φ p(F ; m, a ) ∼ 1/m for all a mod m as p → ∞ . We show that this is indeed the case in Corollary 1 below, uniformly for all m in the range m = o((log p)1/4) as p → ∞ .Our strategy is to introduce a probabilistic model for the values Sp(F, k ) based on random walks. A simple random walk on Z is a stochastic process {Sk}k≥1 where Sk = X1 + · · · + Xk, and {Xj }j≥1 is a sequence of independent random variables taking the values 1 and −1with equal probability 1 /2 (for further reference see Spitzer ). We shall model the values Sp(F, k ) mod m by the stochastic process {Sk mod m} which may be regarded as a simple random walk on the additive group Z/m Z. To this end we consider the random variable Φrand (N; m, a ) := 1 N |{ k ≤ N : Sk ≡ a mod m}| . Here and throughout E(Y ) will denote the expectation of the random variable Y . We first study the probabilistic model and prove Proposition 1. Let m ≥ 2 be a positive integer. Then, for all N ≥ m2 we have m−1 ∑ a=0 E (( Φrand (N; m, a ) − 1 m )2) ≪ m2 N . Appealing to Markov’s inequality, we deduce from this result that Φrand (N; m, a ) = 1 m(1 + o(1)) with probability 1 − o(1) provided that N/m 2 → ∞ . Using Proposition 1, we establish an analogous estimate for the second moment of the difference Φ p(F ; m, a ) − 1/m (which may be regarded as the “variance” of Φp(F ; m, a )). Theorem 1. Let p be a large prime number and F (X) ∈ Fp(X) be a square-free polynomial of degree dF ≥ 1. Then, for any integer 2 ≤ m ≪ (log p)1/4 we have m−1 ∑ a=0 ( Φp(F ; m, a ) − 1 m )2 ≪dF m2 log p.RANDOMNESS OF CHARACTER SUMS MODULO m 3 As a consequence, we obtain Corollary 1. Under the same assumptions of Theorem 1, we have uniformly for all 0 ≤ a ≤ m − 1Φp(F ; m, a ) = 1 m + OdF ( m √log p ) . Let Rp(F, k ) be the number of positive integers n ≤ k such that F (n) is a quadratic residue modulo p, and similarly denote by Np(F, k ) the number of n ≤ k for which F (n)is a quadratic non-residue mod p. Using a slight variation of our method we also prove that the values Rp(F, k ) (and Np(F, k )) are uniformly distributed in residue classes modulo m. In this case, the corresponding probabilistic model involves random walks on the non-negative integers, where each step is 0 or 1 with equal probability. Define ˜Φp(F ; m, a ) = 1 p|{ k ≤ p : Rp(F, k ) ≡ a mod m}| . Then, using a similar result to Proposition 1 in this case (see Proposition 3.3 below) we establish Theorem 2. Let p be a large prime number and F (X) ∈ Fp(X) be a square-free polynomial of degree dF ≥ 1. Then, for any integer 2 ≤ m ≪ (log p)1/4 we have m−1 ∑ a=0 (˜Φp(F ; m, a ) − 1 m )2 ≪dF m2 log p. A similar result holds replacing Rp(F, k ) with Np(F, k ). An important question in the theory of random walks on finite groups is to in-vestigate how close is the distribution of the k-th step of the walk to the uniform distribution on the corresponding group (see for example Hildebrand ). In our case this corresponds to investigating the distribution of Sk mod m. Define Ψrand (k; m, a ) = Prob( Sk ≡ a mod m). Proposition 2. Let m ≥ 3 be an odd integer and 0 ≤ a ≤ m − 1. Then Ψrand (k; m, a ) = 1 m + O ( exp ( − π2k 3m2 )) . This shows that the distribution of Sk is close to the uniform distribution on Z/m Z when m = o(k1/2) as k → ∞ . Although this result is classical (see for example Theorem 2 of Aldous and Diaconis ), we chose to include its proof for the sake of completeness. We now describe an analogous result that we derive for character sums. Let N be large, and for each prime p ≤ N, we consider the walk on Z/m Z whose i-th step corresponds to the value of χp(qi) mod m, where qi is the i-th prime number. One might guess that as p varies over the primes below N, the distribution of the k-th step of this 4 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU walk will be close to the uniform distribution in Z/m Z, as N, k → ∞ if m = o(k1/2). Define Sk(p) = ∑ j≤k χp(qj ), and ΨN (k; m, a ) = 1 π(N)|{ p ≤ N : Sk(p) ≡ a mod m}| . Here and throughout log j will denote the j-th iterated logarithm, so that log 1 n = log n and log j n = log(log j−1 n) for each j ≥ 2. We prove Theorem 3. Fix A ≥ 1. Let N be large, and k ≤ A(log 2 N)/(log 3 N) be a positive integer. Then we have ΨN (k; m, a ) = Ψ rand (k; m, a ) + OA ( 1 log A N ) . Hence, using Proposition 2 we deduce Corollary 2. Let m be an odd integer such that 3 ≤ m ≤ k1/2. Then under the same assumptions of Theorem 3 we have uniformly for all 0 ≤ a ≤ m − 1 that ΨN (k; m, a ) = 1 m + OA ( exp ( − π2k 3m2 ) 1 log A N ) . We remark that under the assumption of the Generalized Riemann Hypothesis for Dirichlet L-functions, we can improve the range of validity of Theorem 3 to k ≪ (log N)/(log 2 N). Preliminary lemmas In this section we collect together some preliminary results which will be useful in our subsequent work. Here and throughout we shall use the notation em(x) = exp (2πix m ) . Recall the orthogonal relation (2.1) 1 m m−1 ∑ t=0 em(tn ) = { 1 if n ≡ 0 mod m, 0 otherwise. Our first lemma gives the classical bound for incomplete exponential sums over Fp of the form SI (P1, P 2) = ∑ n∈I χp(P1(n)) ep(P2(n)) , where I is a subinterval of {0, 1, . . . , p − 1}, and P1(X), P 2(X) ∈ Fp[X], such that P1(X) is a nontrivial square-free polynomial. Lemma 2.1. Let p ≥ 3 be a prime number and I, P 1(X), P 2(X) be as above. Then we have |SI (P1, P 2)| ≤ 2D√p log p, RANDOMNESS OF CHARACTER SUMS MODULO m 5 where D = deg P1(X) + deg P2(X). Proof. First if I = {0, . . . , p − 1}, then SI (P1, P 2) = S(P1, P 2) is a complete sum and the result follows from the classical Weil bound for exponential sums : (2.2) |S(P1, P 2)| ≤ Dp 1/2. Now, if I is proper subinterval of {0, . . . , p − 1}, we shall use a standard procedure to express our incomplete sum in terms of complete sums of the same type. Using equation (2.1) we see that SI (P1, P 2) = ∑ nmod p χp(P1(n)) ep(P2(n)) (∑ m∈I 1 p ∑ tmod p ep(t(m − n)) ) . Changing the order of summation and noting that the inner double sum is a product of two sums, one being a geometric progression and the other a complete exponential sum, we obtain SI (P1, P 2) = 1 p ∑ tmod p ( ∑ m∈I ep(tm ) )( ∑ nmod p χp(P1(n)) ep(P2(n) − tn ) ) =1 p ∑ tmod p FI (t)S(P1, ˜P2 ), (2.3) where ˜P2(X) = P2(X) − tX and FI (t) = ∑ m∈I ep(tm ). If t ≡ 0 mod p then FI (t) = |I|.Otherwise if I = {M + 1 , . . . , M + N}, say, then FI (t) = ep (t(M + 1) ) − ep (t(M + N + 1) ) 1 − ep(t) . Here the numerator has absolute value at most 2, while the absolute value of the denominator is 2 | sin( tπ/p )|. Hence |FI (t)| ≤ ∣∣∣∣sin (tπ p )∣ ∣∣∣ −1 ≤ ( 2 ∣∣∣∣∣∣∣∣ t p ∣∣∣∣∣∣∣∣)−1 , where || · || stands for the distance to the nearest integer. As a set of representatives modulo p we choose {− p−1 2 , · · · , p−1 2 }, so that for t 6 = 0 in this set we have (2.4) |FI (t)| ≤ p 2|t|. Now, we insert (2.2) and (2.4) in (2.3) to obtain |SI (P1, P 2)| ≤ D p1/2 |I| + ∑ 1≤| t|≤ p−1 2 p 2|t|  ≤ 2D√p log p. This completes the proof of the lemma. The following lemma will be later used to prove that the product of distinct shifts of a square-free polynomial cannot be a square in Fp(X). 6 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU Lemma 2.2. Let r ≥ 2, and z1, . . . , z r, be distinct elements of Fp. Moreover, let M be a nonempty finite subset of the algebraic closure Fp of Fp with 4|M| < p 1 r . Then there exists a j ∈ { 1, . . . , r } such that the translate M+zj is not contained in ∪i6 =j (M+zi). Proof. Suppose that ( z1, . . . , z r, M) provides a counterexample to the statement of the lemma. Then clearly for any nonzero t ∈ Fp, (tz 1, · · · , tz r, t M) is also a counterexam-ple. We now use Minkowski’s theorem on lattice points in a symmetric convex body to find a nonzero integer t such that  |t| ≤ p − 1∣∣∣∣∣∣tz 1 p ∣∣∣∣∣∣ ≤ (p − 1) − 1 r ...∣∣∣∣∣∣tz r p ∣∣∣∣∣∣ ≤ (p − 1) − 1 r Another way to express this is that there are integers (2.5) { |yj | ≤ p(p − 1) − 1 r yj ≡ tz j (mod p)for any j ∈ { 1, . . . , r }. Thus ( y1, . . . , y r, t M) provides a counterexample. Now let j0 be such that |yj0 | = max 1≤j≤r |yj |. Choose α ∈ tM and consider the set ˜M = tM ∩ (α + Fp). Then ( y1, . . . , y r, ˜M) will also be a counterexample. Note that α + Fp can be written as a union of |M| intervals whose endpoints are in ˜M. Let {α + a, α + a + 1 , · · · , α + b} be the longest of these intervals. Then |b − a| ≥ p | ˜M| ≥ p |M| . By this, (2.5) and the hypothesis 4 |M| < p 1 r we deduce |b − a| > 4p1− 1 r 2|yj0 |. Now the point is that if yj0 > 0 then α + a + yj0 belongs to ˜M + yj0 but does not belong to ⋃ i6=j0 ( ˜M + yi), while if yj0 < 0 then α + b + yj0 belongs to ˜M + yj0 but does not belong to ⋃ i6=j0 ( ˜M + yi). This completes the proof of the lemma. Using this lemma, we prove the following result Lemma 2.3. Let F (X) ∈ Fp(X) be a square-free polynomial of degree dF ≥ 1. Let b1, . . . , b L be distinct elements in Fp such that L < (log p)/ log(4 dF ). Then, for any RANDOMNESS OF CHARACTER SUMS MODULO m 7 a ∈ Fp the polynomial H(X) = L ∏ j=1 F (aX + bj ), is not a square in Fp(X).Proof. Let α1, . . . , α s be the roots of F (X) in Fp. Since F (X) is square-free then the αj are distinct and s = dF . Let M = {a−1α1, . . . , a −1αs}, and write zj = −a−1bj for all 1 ≤ j ≤ L. Then note that M + zj is the set of the roots of F (ax + bj ) in Fp. By our hypothesis it follows that 4 |M| < p 1/L . Hence, we infer from Lemma 2.2 that there exists a j ∈ { 1, . . . , L } such that at least one of the roots of F (ax + bj ) is distinct from all the roots of ∏ l6=j F (ax + bl). This shows that H(X) is not a square in Fp(X) as desired. Random walks on the integers modulo m In this section we shall study the distribution of the random walk {Sk mod m}k≥1 and prove Propositions 1 and 2. To this end, we establish the following preliminary lemmas. Lemma 3.1. If m ≥ 3 is an odd integer, then (3.1) max 1≤t≤m−1 ∣∣∣∣cos (2πt m )∣ ∣∣∣ ≤ 1 − π2 3m2 , and max 1≤t≤m−1 |1 + em(t)| ≤ 2 − π2 6m2 . Proof. We begin by proving the first assertion. If m ≥ 5 is odd, then max 1≤t≤m−1 ∣∣∣∣cos ( 2πt m )∣ ∣∣∣ = cos ( 2π m ) . Moreover we know that cos( x) ≤ 1 − x2/3 for 0 ≤ x ≤ π/ 2. This yields max 1≤t≤m−1 ∣∣∣∣cos ( 2πt m )∣ ∣∣∣ ≤ 1 − 4π2 3m2 . Now, when m = 3 we have max 1≤t≤2 | cos(2 πt/m )| = cos( π/m ) ≤ 1 − π2/(3 m2). This establishes the first part of the lemma. Moreover, we have |1 + em(t)|2 = 2 + 2 cos(2 πt/m ) ≤ 4 ( 1 − π2 6m2 ) , which follows from (3.1). Therefore, using that √1 − x ≤ 1 − x/ 2 for 0 ≤ x ≤ 1 we obtain the second assertion of the lemma. 8 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU Lemma 3.2. If m ≥ 2 is an integer, then m−1 ∑ t=1 ∑ 1≤j1<j 2≤N cos (2πt m )j2−j1 = O(m3N), and m−1∑ t=1 ∑ 1≤j1<j 2≤N (1 + em(t) 2 )j2−j1 = O(m3N). Proof. We prove only the first statement, since the proof of the second is similar. For d ∈ { 1, . . . , N − 1}, the number of pairs 1 ≤ j1 < j 2 ≤ N such that j2 − j1 = d equals N − d. Therefore, the sum we are seeking to bound equals (3.2) m−1 ∑ t=1 N−1 ∑ d=1 (N − d) cos (2πt m )d . First, when m is odd, Lemma 3.1 implies that the last sum is ≤ mN N−1 ∑ d=1 max 1≤t≤m−1 ∣∣∣∣cos ( 2πt m )∣ ∣∣∣ d ≤ mN 1 − max 1≤t≤m−1 ∣∣cos (2πt m )∣ ∣ ≤ 3m3N π2 . Now, when m = 2 r is even, then either cos( πt/r ) = −1 or | cos( πt/r )| < 1. In the latter case the proof of Lemma 3.1 implies that | cos( πt/r )| ≤ 1 − π2/(3 r2). Hence, in this case we obtain N −1∑ d=1 (N − d) ∣∣∣∣cos (πt r )∣ ∣∣∣ d ≪ m2N. On the other hand if cos( πt/r ) = −1, then our sum become N−1 ∑ d=1 (N − d)( −1) d ≤ 2N. This completes the proof. We begin by proving Proposition 2 first, since its proof is both short and simple. Proof of Proposition 2. Recall that Ψrand (k; m, a ) = Prob( X1 + · · · + Xk ≡ a mod m) = 1 2k ∑ v=( v1,...,v k)∈{− 1,1}k v1+··· +vk≡amod m 1. Hence, using (2.1) we deduce (3.3) Ψrand (k; m, a ) = 1 2km ∑ v=( v1,...,v k)∈{− 1,1}k m−1 ∑ t=0 em ( t (v1 + · · · + vk − a) ) .RANDOMNESS OF CHARACTER SUMS MODULO m 9 The contribution of the term t = 0 to the above sum equals 1 /m . Moreover, since ∑ α∈{− 1,1} em(αt ) = 2 cos(2 πt/m ), then the contribution of the remaining terms equals 1 2km m−1 ∑ t=1 em (−at ) ∑ v=( v1,...,v k)∈{− 1,1}k em ( t(v1 + · · · + vk) ) = 1 m m−1 ∑ t=1 em (−at ) cos (2πt m )k . Thus, the result follows upon using Lemma 3.1. Proof of Proposition 1. First, note that Φrand (N; m, a ) = 1 N N ∑ j=1 Yj where Yj = { 1 if Sj ≡ a mod m 0 otherwise . On the other hand, if v = ( v1, . . . , v N ) ∈ {− 1, 1}N , then (2.1) yields |{ 1 ≤ j ≤ N : v1 + · · · + vj ≡ a mod m}| = 1 m N ∑ j=1 m−1 ∑ t=0 em ( t(v1 + · · · + vj − a) ) . This implies (3.4) E (( Φrand (N; m, a ) − 1 m )2) = 1 2N ∑ v=( v1,...,v N)∈{− 1,1}N  1 N ∑ 1≤j≤Nv1+··· +vj≡amod m 1 − 1 m  2 = 1 2N (mN )2 ∑ v=( v1,...,v N)∈{− 1,1}N ∣∣∣∣∣ N ∑ j=1 m−1 ∑ t=0 em ( t(v1 + · · · + vj − a) ) − N ∣∣∣∣∣ 2 . Now, expanding the summand on the RHS of (3.4) we derive ∣∣∣∣∣ N ∑ j=1 m−1 ∑ t=0 em ( t(v1 + · · · + vj − a) ) − N ∣∣∣∣∣ 2 = ∣∣∣∣∣ N ∑ j=1 m−1 ∑ t=1 em ( t(v1 + · · · + vj − a) )∣∣∣∣∣ 2 = ∑ 1≤t1,t 2≤m−1 em (a(t2 − t1)) ∑ 1≤j1,j 2≤N em ( t1(v1 + · · · + vj1 ) − t2(v1 + · · · + vj2 ) ) . Hence, we infer from (2.1) that (3.5) m−1 ∑ a=0 ∣∣∣∣∣ N ∑ j=1 m−1 ∑ t=0 em ( t(v1 + · · · + vj − a) ) − N ∣∣∣∣∣ 2 = m m−1 ∑ t=1 ∑ 1≤j1,j 2≤N em ( t((v1 + · · · + vj1 ) − (v1 + · · · + vj2 ))) = m2N + m m−1 ∑ t=1 ∑ 1≤j1<j 2≤N ( em ( t(vj1+1 + · · · + vj2 ) ) em ( − t(vj1+1 + · · · + vj2 ) )) .10 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU Inserting this estimate into (3.4), and using that ∑ α∈{− 1,1} em(αt ) = 2 cos(2 πt/m ), we obtain m−1 ∑ a=0 E (( Φrand (N; m, a ) − 1 m )2) = 1 N + 2 mN 2 m−1 ∑ t=1 ∑ 1≤j1<j 2≤N cos (2πt m )j2−j1 . The result follows upon using Lemma 3.2 to bound the RHS of the last identity. In order to prove Theorem 2 we require an analogous result to Proposition 1 in the case of a random walk on the non-negative integers, where each step is 0 or 1 (rather than −1 or 1). To this end, we take { ˜Xj }j≥1 to be a sequence of independent random variables taking the values 0 and 1 with equal probability 1 /2, and define ˜Sk = ˜X1 + · · · + ˜Xk, and ˜Φrand (N; m, a ) = 1 N |{ 1 ≤ j ≤ N : ˜Sj ≡ a mod m}| . Using a similar approach to the proof of Proposition 1 we establish: Proposition 3.3. Let m ≥ 2 be a positive integer. Then, for all N ≥ m2 we have m−1 ∑ a=0 E ((˜Φrand (N; m, a ) − 1 m )2) ≪ m2 N . Proof. We follow closely the proof of Proposition 1. First, a similar analysis used to derive (3.4) allows us to obtain (3.6) E ((˜Φrand (N; m, a ) − 1 m )2) = 1 2N (mN )2 ∑ v=( v1,...,v N)∈{ 0,1}N ∣∣∣∣∣ N ∑ j=1 m−1 ∑ t=0 em ( t(v1 + · · · + vj − a) ) − N ∣∣∣∣∣ 2 . Hence, using the identity (3.5) in equation (3.6) we get (3.7) m−1 ∑ a=0 E ((˜Φrand (N; m, a ) − 1 m )2) = 1 N + 1 mN 2 m−1 ∑ t=1 ∑ 1≤j1<j 2≤N ((1 + em(t) 2 )j2−j1 + (1 + em(−t) 2 )j2−j1 ) = 1 N + 2 mN 2 m−1 ∑ t=1 ∑ 1≤j1<j 2≤N ( 1 + em(t) 2 )j2−j1 , upon noting that m−1∑ t=1 (1 + em(t) 2 )d = m−1 ∑ r=1 (1 + em(−r) 2 )d ,RANDOMNESS OF CHARACTER SUMS MODULO m 11 by making the simple change of variables r = m−t. Appealing to Lemma 3.2 completes the proof. Character sums with polynomials: proof of Theorems 1 and 2 We begin by proving the following key proposition which establishes the required link with random walks. Let p be a large prime number and F (X) ∈ Fp(X) be a square-free polynomial of degree dF ≥ 1 in Fp(X). Moreover, let L ≤ (log p)/ log(4 dF )be a positive integer, and put N = [ p/L ] − 1. Furthermore, for any v = ( v1, . . . , v L) ∈{− 1, 1}L we define (4.1) Dp,F (v, L ) = {0 ≤ s ≤ N : χp(F (sL + j)) = vj for all 1 ≤ j ≤ L}. Proposition 4.1. Let p, L, and F (X) be as above. Then for any v = ( v1, . . . , v L) ∈{− 1, 1}L we have |Dp,F (v, L )| = p 2LL ( 1 + OdF (p−1/10 ) ) . Proof. Let S be the set of non-negative integers 0 ≤ s ≤ N such that F (sL + j) 6 = 0 for all 1 ≤ j ≤ L. Then |S| = N + OdF (1). Moreover, note that for s ∈ S we have (4.2) 1 2LL∏ j=1 (1 + vj χp(F (sL + j))) = { 1 if s ∈ Dp,F (v, L ), 0 otherwise . This yields |Dp,F (v, L )| = 1 2LN∑ s=0 L ∏ j=1 (1 + vj χp(F (sL + j))) + OdF (1) . Expanding the product on the RHS of the previous estimate, we find that |Dp,F (v, L )| equals (4.3) 1 2LN∑ s=0 ( 1 + L ∑ l=1 ∑ 1≤i1<i 2<··· <i l≤L vi1 · · · vil χp (F (sL + i1) · · · F (sL + il))) OdF (1) . = N 2L + 1 2LL∑ l=1 ∑ 1≤i1<··· <i l≤L vi1 · · · vil N ∑ s=0 χp (F (sL + i1) · · · F (sL + il)) + OdF (1) . Since F (X) is a square-free polynomial, then it follows from Lemma 2.3 that the polynomial Hi1,...,i l (X) = F (LX +i1) · · · F (LX +il) is not a square in Fp(X). Therefore, using Lemma 2.1 with P1(X) = Hi1,...,i l (X), P2(X) = 0 and I = {0, . . . , N }, we obtain ∣∣∣∣∣ N ∑ s=0 χp (F (sL + i1) · · · F (sL + il))∣∣∣∣∣ ≤ 2dF L√p log p. 12 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU Inserting this bound in (4.3) we get (4.4) |Dp,F (v, L )| = p 2LL + OdF (L√p log p) , which completes the proof. Proof of Theorem 1. Recall that Φp(F ; m, a ) = 1 p|{ 1 ≤ k ≤ p : Sp(F, k ) ≡ a mod m}| . Let L = [(log p)/(log(4 dF )] , and put N = [ p/L ] − 1. Moreover, for any 0 ≤ s ≤ N, we define ML(s; m, a ) = |{ 1 ≤ l ≤ L : Sp(F, sL + l) ≡ a mod m}| . Then, note that (4.5) ∣∣∣∣Φp(F ; m, a ) − 1 m ∣∣∣∣ ≤ 1 p N ∑ s=0 ∣∣∣∣ML(s; m, a ) − L m ∣∣∣∣ + O (L p ) . To bound the sum on the RHS of (4.5), we use the Cauchy-Schwarz inequality which gives ( N∑ s=0 ∣∣∣∣ML(s; m, a ) − L m ∣∣∣∣)2 ≤ (N + 1) N ∑ s=0 ( ML(s; m, a ) − L m )2 . Hence, combining this estimate with (4.5), we deduce (4.6) ( Φp(F ; m, a ) − 1 m )2 ≪ N p2 N ∑ s=0 ( ML(s; m, a ) − L m )2 L2 p2 . On the other hand, since Sp(sL + l) = Sp(sL ) + ∑lj=1 χp (F (sL + j)), then (4.7) m−1 ∑ a=0 ( ML(s; m, a ) − L m )2 = m−1 ∑ b=0 ( ∆L(s; m, b ) − L m )2 , where ∆L(s; m, b ) = |{ 1 ≤ l ≤ L : l ∑ j=1 χp (F (sL + j)) ≡ b mod m}| . Therefore, upon combining (4.6) and (4.7) we obtain (4.8) m−1 ∑ a=0 ( Φp(F ; m, a ) − 1 m )2 ≪ N p2 m−1 ∑ a=0 N ∑ s=0 ( ∆L(s; m, a ) − L m )2 mL 2 p2 .RANDOMNESS OF CHARACTER SUMS MODULO m 13 Now we evaluate the inner sum on the RHS of the previous inequality. Using (2.1) we get (4.9) N ∑ s=0 ( ∆L(s; m, a ) − L m )2 = 1 m2 N ∑ s=0 ∣∣∣∣∣ L ∑ l=1 m−1 ∑ t=0 em ( t ( ∑ 1≤j≤l χp (F (sL + j)) − a )) − L ∣∣∣∣∣ 2 = 1 m2 N ∑ s=0 ∣∣∣∣∣ L ∑ l=1 m−1 ∑ t=1 em ( t ( ∑ 1≤j≤l χp (F (sL + j)) − a ))∣ ∣∣∣∣ 2 = 1 m2 ∑ v∈{− 1,1}L ∣∣∣∣∣ L ∑ l=1 m−1 ∑ t=1 em ( t(v1 + · · · + vl − a))∣∣∣∣∣ 2 Dp,F (v, L ). Hence, using Proposition 4.1 along with the identity (3.4) obtained in the random walk setting, we derive N ∑ s=0 ( ∆L(s; m, a ) − L m )2 = p 2Lm2L ∑ v∈{− 1,1}L ∣∣∣∣∣ L ∑ l=1 m−1 ∑ t=1 em ( t(v1 + · · · + vl − a))∣∣∣∣∣ 2 (1 + OdF (p−1/10 )) = pL E (( Φrand (L; m, a ) − 1 m )2) (1 + OdF (p−1/10 )) . Finally, combining this estimate with (4.8) we obtain m−1 ∑ a=0 ( Φp(F ; m, a ) − 1 m )2 ≪dF m−1 ∑ a=0 E (( Φrand (L; m, a ) − 1 m )2) m(log p)2 p2 ≪dF m2 log p, which follows from Proposition 1. This completes the proof. Proof of Theorem 2. We only prove the result for Rp(F, k ), since the proof for Np(F, k )is similar. Define δF (j) = { 1 if χp(F (j)) = 1 0 otherwise. Then, note that Rp(F, k ) = k ∑ j=1 δF (j). We follow closely the proof of Theorem 1. Let L = [(log p)/ log(4 dF )], and N = [ p/L ]−1. For any 0 ≤ s ≤ N we define ˜∆L(s; m, b ) = |{ 1 ≤ l ≤ L : l ∑ j=1 δF (sL + j) ≡ b mod m}| .14 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU Then, similarly to the estimate (4.8) we obtain (4.10) m−1 ∑ a=0 (˜Φp(F ; m, a ) − 1 m )2 ≪ N p2 m−1 ∑ a=0 N ∑ s=0 (˜∆L(s; m, a ) − L m )2 m(log p)2 p2 . Moreover, an analogous approach which leads to the identity (4.9) also gives N ∑ s=0 (˜∆F (s; m, a ) − L m )2 = 1 m2 ∑ v∈{ 0,1}L ∣∣∣∣∣ L ∑ l=1 m−1 ∑ t=1 em ( t(v1 + · · · + vl − a))∣∣∣∣∣ 2 ∑ 0≤s≤NδF(sL +j)= vj for all 1 ≤j≤L 1. Remark that if F does not vanish in the interval [ sL + 1 , sL + L] then δF (sL + j) = 1 + χp (F (sL + j)) 2 , for all 1 ≤ j ≤ L. Hence, writing ˜v = ( ˜v1, . . . , ˜vL) with ˜vj = 2 vj − 1, we deduce ∑ 0≤s≤NδF(sL +j)= vj for all 1 ≤j≤L 1 = |Dp(˜v, L, F )| + OdF (1) = p 2LL ( 1 + OdF (p−1/10 ) ) , which follows from Proposition 4.1. Thus, appealing to the identity (3.6) obtained in the random walk setting, we derive N ∑ s=0 (˜∆F (s; m, a ) − L m )2 = pL E ((˜Φrand (L; m, a ) − 1 m )2) (1 + OdF (p−1/10 )) . Therefore, inserting this estimate in (4.10) and using Proposition 3.3 we obtain m−1 ∑ a=0 (˜Φp(F ; m, a ) − 1 m )2 ≪dF m−1 ∑ a=0 E ((˜Φrand (L; m, a ) − 1 m )2) m(log p)2 p2 ≪dF m2 log p, as desired. Character sums of fixed length: Proof of Theorem 3 We shall derive Theorem 3 from the following proposition Proposition 5.1. Fix A ≥ 1. Let N be large, and k ≤ A(log 2 N)/(log 3 N). Then for any v = ( v1, . . . , v k) ∈ {− 1, 1}k we have 1 π(N)|{ p ≤ N : χp(qj ) = vj for all 1 ≤ j ≤ k}| = 1 2k ( 1 + OA ( 1 log A N )) . Proof. If log N ≤ p ≤ N then 1 2kk∏ j=1 (1 + vj χp(qj )) = { 1 if χp(qj ) = vj for all 1 ≤ j ≤ k, 0 otherwise .RANDOMNESS OF CHARACTER SUMS MODULO m 15 Therefore we deduce that the number of primes p ≤ N such that χp(qj ) = vj for all 1 ≤ j ≤ k, equals (5.1) = 1 2k ∑ p≤Nk ∏ j=1 (1 + vj χp(qj )) + O(log N)= 1 2k ∑ p≤N ( 1 + k ∑ l=1 ∑ 1≤i1<··· <i l≤k vi1 · · · vil χp(qi1 · · · qil ) ) O(log N)= π(N) 2k + 1 2kk∑ l=1 ∑ 1≤i1<··· <i l≤k vi1 · · · vil ∑ p≤N (qi1 · · · qil p ) O(log N). For 1 ≤ i1 < · · · < i l ≤ k we let Qi1,...,i l = qi1 . . . q il . Then it follows from the prime number theorem that Qi1,...,i l ≤ ∏ j≤k qj = ek log k(1+ o(1)) ≤ (log N)A+o(1) . On the other hand, quadratic reciprocity implies that ( Qi1,...,i l · ) is a character of modulus Qi1,...,i l or 4 Qi1,...,i l . Therefore, appealing to the Siegel-Walfisz Theorem (see Corollary 5.29 of Iwaniec-Kowalski ), we deduce ∑ p≤N (Qi1,...,i l p ) ≪A (Qi1,...,i l )1/2 N log 2A N . Inserting this estimate in (5.1) completes the proof. Proof of Theorem 3. Using (2.1) we obtain (5.2) ΨN (k; m, a ) = 1 π(N)|{ p ≤ N : Sk(p) ≡ a mod m}| . = 1 mπ (N) ∑ p≤Nm−1 ∑ t=0 em (t(Sk(p) − a)) = 1 mπ (N) m−1 ∑ t=0 ∑ v∈{− 1,1}k em ( t(v1 + · · · + vk − a) ) ∑ p≤Nχp(qj)= vjfor 1 ≤j≤k 1Thus, appealing to Proposition 5.1 along with the identity (3.3) obtained in the random walk setting we derive ΨN (k; m, a ) = 1 2km m−1 ∑ t=0 ∑ v∈{− 1,1}k em ( t(v1 + · · · + vk − a) ) OA ( 1 log A N ) = Ψ rand (k; m, a ) + OA ( 1 log A N ) , which completes the proof. References D. Aldous and P. Diaconis, Shuffling cards and stopping times , Amer. Math. Monthly 93 (1986), no. 5, 333-348. 16 YOUNESS LAMZOURI AND ALEXANDRU ZAHARESCU N. C. Ankeny, The least quadratic non residue , Ann. of Math. (2) 55, (1952). 65-72. W. Banks, M. Z. Garaev, D. R. Heath-Brown and I. E. Shparlinski, Density of non-residues in Burgess-type intervals and applications , Bull. Lond. Math. Soc. 40 (2008), 88-96. D. A. Burgess, The distribution of quadratic residues and non-residues , Mathematika 4 1957 106-112. H. Davenport and P. Erd¨ os, The distribution of quadratic and higher residues , Publ. Math. Debrecen 2, (1952). 252-265. S. W. Graham and C. J. Ringrose, Lower bounds for least quadratic nonresidues , Analytic number theory (Allerton Park, IL, 1989), 269–309. A. Granville and K. Soundararajan, The distribution of values of L(1 , χ d), Geometric and Funct. Anal. 13 (2003), 992–1028. M. Hildebrand, A survey of results on random walks on finite groups , Probab. Surv. 2 (2005), 33-63. H. Iwaniec and E. Kowalski, Analytic number theory , American Mathematical Society Col-loquium Publications, 53. American Mathematical Society, Providence, RI, 2004. Y. K. Lau and J. Wu, On the least quadratic non-residue , Int. J. Number Theory 4 (2008), no. 3, 423-435. U. V. Linnik, A remark on the least quadratic non-residue , C. R. (Doklady) Acad. Sci. URSS (N.S.) 36 (1942) 119-120. H. L. Montgomery, Topics in multiplicative number theory , Lecture Notes in Mathematics, Vol. 227. Springer-Verlag, Berlin-New York, 1971. R. Peralta, On the distribution of quadratic residues and nonresidues modulo a prime number ,Math. Comp. 58 (1992), no. 197, 433-440. F. Spitzer, Principles of random walks , Graduate Texts in Mathematics, Vol. 34. Springer-Verlag, New York-Heidelberg, 1976. A. Weil, On some exponential sums , Proc. Nat. Acad. Sci. U. S. A. 34, (1948). 204-207. Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Alt-geld Hall, MC-382, 1409 W. Green Street, Urbana, Illinois 61801, USA E-mail address : lamzouri@math.uiuc.edu Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Alt-geld Hall, MC-382, 1409 W. Green Street, Urbana, Illinois 61801, USA E-mail address : Zaharesu@math.uiuc.edu
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Verifying Trigonometric Identities Objective: To verify that two expressions are equivalent. That is, we want to verify that what we have is an identity. • To do this, we generally pick the expression on one side of the given identity and manipulate that expression until we get the other side. • In most cases, it is best to start with the more complex looking side and try to simply to match the less complex side. • You must be very familiar with the fundamental trigonometric identities, especially the Pythagorean Identities. In some cases, a direct substitution using these fundamental identities will verify the identity you are trying to prove (Exercise 8 at the end of this document is one example). • Some special approaches are useful for certain types of identities, which are provided below. Identity Type Verification Approach Type 1: Sometimes it is easier if we just rewrite everything in terms of sine and cosine to see if the expression simplifies. Verify: 𝐜𝐨𝐭𝒙+ 𝟏= 𝐜𝐬𝐜𝒙(𝐜𝐨𝐬𝒙+ 𝐬𝐢𝐧𝒙) RHS →𝐜𝐬𝐜𝒙(𝐜𝐨𝐬𝒙+ 𝐬𝐢𝐧𝒙) = 1 sin𝑥(cos 𝑥+ sin 𝑥) = cos𝑥 sin𝑥+ sin 𝑥 sin 𝑥 = 𝐜𝐨𝐭𝒙+ 𝟏 • Start with more complex RHS. • Rewrite csc𝑥 in terms of sine or cosine. • Remember, csc 𝑥= 1/sin 𝑥 • Also note, cos 𝑥/sin 𝑥 = cot 𝑥 • The RHS simplifies to original LHS. Type 2: In some cases, the more complex side involves a fraction that can be split up. Then we rewrite everything in terms of sine and cosine. Verify: 𝐭𝐚𝐧𝒕−𝐜𝐨𝐭𝒕 𝐬𝐢𝐧𝒕𝐜𝐨𝐬𝒕 = 𝐬𝐞𝐜𝟐𝒕−𝐜𝐬𝐜𝟐𝒕 LHS →𝐭𝐚𝐧𝒕−𝐜𝐨𝐭𝒕 𝐬𝐢𝐧𝒕𝐜𝐨𝐬𝒕= tan 𝑡 sin𝑡cos 𝑡− cot𝑡 sin 𝑡cos 𝑡 = tan 𝑡⋅ 1 sin 𝑡cos 𝑡−cot 𝑡⋅ 1 sin 𝑡cos 𝑡 = sin 𝑡 cos 𝑡⋅ 1 sin 𝑡cos 𝑡− cos 𝑡 sin 𝑡⋅ 1 sin 𝑡cos 𝑡 = 1 cos2 𝑡− 1 sin2 𝑡 = 𝐬𝐞𝐜𝟐𝒕−𝐜𝐬𝐜𝟐𝒕 • Start with the more complex LHS. • Rewrite the LHS as difference of two fractions. • Split out tan 𝑡 and cot 𝑡 to make it easier to simplify. • Notice in the first term, the sin𝑡 cancels out; and in the second term, cos 𝑡 cancels out. • The new terms are reciprocal identities • The LHS simplifies to the original RHS. Verifying Trigonometric Identities Identity Type Verification Approach Type 3: Using the property of conjugates is sometimes helpful. For an expression like 𝑎+ 𝑏, the conjugate would be 𝑎−𝑏. When you multiply conjugates, you often get a more useful expression, e.g., (𝑎+ 𝑏)(𝑎−𝑏). Sometimes multiplying by the conjugate will simplify an expression and help in verifying the given identity. Verify: 𝐜𝐨𝐬𝒙 𝟏−𝐬𝐢𝐧𝒙= 𝟏+ 𝐬𝐢𝐧𝒙 𝐜𝐨𝐬𝒙 RHS →𝟏+ 𝐬𝐢𝐧𝒙 𝐜𝐨𝐬𝒙 = 1 + sin𝑥 cos𝑥 ൬1 −sin𝑥 1 −sin𝑥൰ = 1 −sin2 𝑥 cos 𝑥(1 −sin 𝑥) = cos2 𝑥 cos 𝑥(1 −sin 𝑥) = cos 𝑥cos 𝑥 cos 𝑥(1 −sin 𝑥) = 𝐜𝐨𝐬𝒙 𝟏−𝐬𝐢𝐧𝒙 • We could start with either side; but here we will start with the RHS. • The conjugate of the numerator 1 + sin𝑥 is 1 −sin𝑥. • Multiply by 1 −sin 𝑥 1 −sin 𝑥= 1 • Remember, 1 −sin2 𝑥= cos2 𝑥 • Once we reduce the fraction, we get the LHS of the original identity. Type 4: Combining fractions before using identities may be an appropriate strategy. Verify: 𝟏 𝟏−𝐬𝐢𝐧𝜶+ 𝟏 𝟏+ 𝐬𝐢𝐧𝜶= 𝟐𝐬𝐞𝐜𝟐𝜶 LHS → 𝟏 𝟏−𝐬𝐢𝐧𝜶+ 𝟏 𝟏+ 𝐬𝐢𝐧𝜶= 1 1 −sin𝛼൬1 + sin 𝛼 1 + sin 𝛼൰+ 1 1 + sin𝛼൬1 −sin 𝛼 1 −sin 𝛼൰ = (1 + sin 𝛼) + (1 −sin 𝛼) (1 −sin 𝛼)(1 + sin 𝛼) = 2 1 −sin2 𝛼 = 2 cos2 𝛼 = 𝟐𝐬𝐞𝐜𝟐𝜶 • Notice that the denominators of the fractions on the LHS are conjugates. • So we will use the property of conjugates to combine the LHS fractions and simplify. Verifying Trigonometric Identities Verify the following trigonometric identities. 1. x x x x sec tan sin cos = + 2. x x x x x x sin csc csc sin sin csc − = − 3. β β β β tan sec tan tan 2 = + 1 4. θ θ θ θ θ sec sin 1 cos cos sin 1 2 = + + + 5. y y y y sin 1 cos tan sec − = + 6. x x x x 2 2 2 2 cos tan 1 sin cos = − − 7. 0 sin 1 cos 1 cos sin = − + + x x x x 8. θ θ θ θ θ 2 2 2 2 2 cot tan 1 cot cos sin = + + + Verifying Trigonometric Identities Solutions to Exercises x x x tan sin cos + → LHS 1.         + = x x x x cos sin sin cos x x x cos sin cos 2 + = x x x x cos sin cos cos 2 2 + = x x x cos sin cos 2 2 + = x cos 1 = x sec = x x x x csc sin sin csc − → LHS 2. ( ) x x x x sin csc csc sin 1 − = x x x x x x sin csc sin 1 csc csc sin 1 − = x x csc 1 sin 1 − = x x sin csc − = β β tan tan + → 1 LHS 3. β β β tan tan tan 2 + = 1 β β tan tan 1 2 + = β β tan sec2 = θ θ θ θ sin 1 cos cos sin 1 + + + → LHS 4.       + +       + + + = θ θ θ θ θ θ θ θ cos cos sin 1 cos sin 1 sin 1 cos sin 1 ( ) ( ) θ θ θ θ sin 1 cos cos sin 1 2 2 + + + = ( ) θ θ θ θ θ sin 1 cos cos sin sin 2 1 2 2 + + + + = ( ) θ θ θ sin 1 cos 1 sin 2 1 + + + = ( ) θ θ θ sin 1 cos sin 2 2 + + = ( ) ( ) θ θ θ sin 1 cos sin 1 2 + + = θ cos 2 = θ sec 2 = Verifying Trigonometric Identities y y sin 1 cos − → RHS 5.         + + − = y y y y sin 1 sin 1 sin 1 cos ( ) y y y 2 sin 1 sin 1 cos − + = ( ) y y y 2 cos sin 1 cos + = y y cos sin 1+ = y y y cos sin cos 1 + = y y tan sec + = x x x 2 2 2 tan 1 sin cos − − → LHS 6. x x x x 2 2 2 2 cos sin 1 sin cos − − = x x x x x 2 2 2 2 2 cos sin cos sin cos − − = ( )         − − = x x x x x 2 2 2 2 2 sin cos cos sin cos x 2 cos = x x x x sin 1 cos 1 cos sin − + + → LHS 7.       + + − +       + = 1 cos 1 cos sin 1 cos sin sin 1 cos sin x x x x x x x x ( ) ( ) 1 cos sin 1 cos 1 cos sin sin 2 2 + − + + = x x x x x x ( ) 1 cos sin 1 cos sin 2 2 + − + = x x x x ( ) 1 cos sin 1 1 + − = x x ( ) 1 cos sin 0 + = x x 0 = θ θ θ θ 2 2 2 2 tan 1 cot cos sin + + + → LHS 8. θ θ 2 2 tan 1 cot 1 + + = θ θ 2 2 sec csc = θ θ 2 2 cos 1 sin 1 =                 = 1 cos sin 1 2 2 θ θ θ θ 2 2 sin cos = θ 2 cot =
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This page has been archived and is no longer updated Major Molecular Events of DNA Replication By: Leslie A. Pray, Ph.D. © 2008 Nature Education Citation: Pray, L. (2008) Major molecular events of DNA replication. Nature Education 1(1):99 Arthur Kornberg compared DNA to a tape recording of instructions that can be copied over and over. How do cells make these near-perfect copies, and does the process ever vary? Aa) Aa) Aa) Scientists have devoted decades of effort to understanding how deoxyribonucleic acid (DNA) replicates itself. In simple terms, replication involves use of an existing strand of DNA as a template for the synthesis of a new, identical strand. American enzymologist and Nobel Prize winner Arthur Kornberg compared this process to a tape recording of instructions for performing a task: "[E]xact copies can be made from it, as from a tape recording, so that this information can be used again and elsewhere in time and space" (Kornberg, 1960). In reality, the process of replication is far more complex than suggested by Kornberg's analogy. Researchers typically utilize simple bacterial cells in their experiments, but they still do not have all the answers, particularly when it comes to eukaryotic replication. Nonetheless, scientists are familiar with the basic steps in the replication process, and they continue to rely on this information as the basis for continued research and experimentation. The Molecular Machinery of Bacterial DNA Replication A typical bacterial cell has anywhere from about 1 million to 4 million base pairs of DNA, compared to the 3 billion base pairs in the genome of the common house mouse (Mus musculus). Still, even in bacteria, with their smaller genomes, DNA replication involves an incredibly sophisticated, highly coordinated series of molecular events. These events are divided into four major stages: initiation, unwinding, primer synthesis, and elongation. Initiation and Unwinding During initiation, so-called initiator proteins bind to the replication origin, a base-pair sequence of nucleotides known as oriC. This binding triggers events that unwind the DNA double helix into two single-stranded DNA molecules. Several groups of proteins are involved in this unwinding (Figure 1). For example, the DNA helicases are responsible for breaking the hydrogen bonds that join the complementary nucleotide bases to each other; these hydrogen bonds are an essential feature of James Watson and Francis Crick's three-dimensional DNA model. Because the newly unwound single strands have a tendency to rejoin, another group of proteins, the single-strand-binding proteins, keep the single strands stable until elongation begins. A third family of proteins, the topoisomerases, reduce some of the torsional strain caused by the unwinding of the double helix. Figure 1: Facilitation of DNA unwinding. During DNA replication, several proteins facilitate the unwinding of the DNA double helix into two single strands. Topoisomerases (red) reduce torsional strain caused by the unwinding of the DNA double helix; DNA helicase (yellow) breaks hydrogen bonds between complementary base-pairs; single-strand binding proteins (SSBs) stabilize the separated strands and prevent them from rejoining. © 2014 Nature Education Adapted from Pierce, Benjamin. Genetics: A Conceptual Approach, 2nd ed. All rights reserved. As previously mentioned, the location at which a DNA strand begins to unwind into two separate single strands is known as the origin of replication. As shown in Figure 1, when the double helix unwinds, replication proceeds along the two single strands at the same time but in opposite directions (i.e., left to right on one strand, and right to left on the other). This forms two replication forks that move along the DNA, replicating as they go. Primer Synthesis Primer synthesis marks the beginning of the actual synthesis of the new DNA molecule. Primers are short stretches of nucleotides (about 10 to 12 bases in length) synthesized by an RNA polymerase enzyme called primase. Primers are required because DNA polymerases, the enzymes responsible for the actual addition of nucleotides to the new DNA strand, can only add deoxyribonucleotides to the 3'-OH group of an existing chain and cannot begin synthesis de novo. Primase, on the other hand, can add ribonucleotides de novo. Later, after elongation is complete, the primer is removed and replaced with DNA nucleotides. Elongation Finally, elongation--the addition of nucleotides to the new DNA strand--begins after the primer has been added. Synthesis of the growing strand involves adding nucleotides, one by one, in the exact order specified by the original (template) strand. Recall that one of the key features of the Watson-Crick DNA model is that adenine is always paired with thymine and cytosine is always paired with guanine. So, for example, if the original strand reads A-G-C-T, the new strand will read T-C-G-A. DNA is always synthesized in the 5'-to-3' direction, meaning that nucleotides are added only to the 3' end of the growing strand. As shown in Figure 2, the 5'-phosphate group of the new nucleotide binds to the 3'-OH group of the last nucleotide of the growing strand. Scientists have yet to identify a polymerase that can add bases to the 5' ends of DNA strands. Figure 2: New DNA is synthesized from deoxyribonucleoside triphosphates (dNTPs). (A) A deoxyribonucleoside triphosphate (dNTP). (B) During DNA replication, the 3'-OH group of the last nucleotide on the new strand attacks the 5'-phosphate group of the incoming dNTP. Two phosphates are cleaved off. (C) A phosphodiester bond forms between the two nucleotides, and phosphate ions are released. © 2014 Nature Education Adapted from Pierce, Benjamin. Genetics: A Conceptual Approach, 2nd ed. All rights reserved. The Discovery of DNA Polymerase While studying E. coli bacteria, enzymologist Arthur Kornberg discovered that DNA polymerases catalyze DNA synthesis. Kornberg's experiment involved mixing all of the basic "ingredients" necessary for E. coli DNA synthesis in a test tube, including nucleotides, E. coli extract, and ATP, and then purifying and testing the enzymes involved. Using this method, Kornberg not only discovered DNA polymerases, but he also performed some of the initial work demonstrating how enzymes add new nucleotides to growing DNA chains (Kornberg, 1959). Scientists have since identified a total of five different DNA polymerases in E. coli, each with a specialized role. For example, DNA polymerase III does most of the elongation work, adding nucleotides one by one to the 3' end of the new and growing single strand. Other enzymes, including DNA polymerase I and RNase H, are responsible for removing the RNA primer after DNA polymerase III has begun its work, replacing it with DNA nucleotides (Ogawa & Okazaki, 1984). When these enzymes finish, they leave a nick between the section of DNA that was formerly the primer and the elongated section of DNA. Another enzyme called DNA ligase then acts to seal the bond between the two adjacent nucleotides. DNA Polymerase Only Moves in One Direction After a primer is synthesized on a strand of DNA and the DNA strands unwind, synthesis and elongation can proceed in only one direction. As previously mentioned, DNA polymerase can only add to the 3' end, so the 5' end of the primer remains unaltered. Consequently, synthesis proceeds immediately only along the so-called leading strand. This immediate replication is known as continuous replication. The other strand (in the 5' direction from the primer) is called the lagging strand, and replication along it is called discontinuous replication. The double helix has to unwind a bit before the synthesis of another primer can be initiated further up on the lagging strand. Synthesis can then occur from the 3' end of that new primer. Next, the double helix unwinds a bit more, and another spurt of replication proceeds. As a result, replication along the lagging strand can only proceed in short, discontinuous spurts (Figure 3). Figure 3: Replication of the leading DNA strand is continuous, while replication along the lagging strand is discontinuous. After a short length of the DNA has been unwound, synthesis must proceed in the 5' to 3' direction; that is, in the direction opposite that of the unwinding. © 2014 Nature Education Adapted from Pierce, Benjamin. Genetics: A Conceptual Approach, 2nd ed. All rights reserved. Figure Detail The fragments of newly synthesized DNA along the lagging strand are called Okazaki fragments, named in honor of their discoverer, Japanese molecular biologist Reiji Okazaki. Okazaki and his colleagues made their discovery by conducting what is known as a pulse-chase experiment, which involved exposing replicating DNA to a short "pulse" of isotope-labeled nucleotides and then varying the length of time that the cells would be exposed to nonlabeled nucleotides. This later period is called the "chase" (Okazaki et al., 1968). The labeled nucleotides were incorporated into growing DNA molecules only during the initial few seconds of the pulse; thereafter, only nonlabeled nucleotides were incorporated during the chase. The scientists then centrifuged the newly synthesized DNA and observed that the shorter chases resulted in most of the radioactivity appearing in "slow" DNA. The sedimentation rate was determined by size: smaller fragments precipitated more slowly than larger fragments because of their lighter weight. As the investigators increased the length of the chases, radioactivity in the "fast" DNA increased with little or no increase of radioactivity in the slow DNA. The researchers correctly interpreted these observations to mean that, with short chases, only very small fragments of DNA were being synthesized along the lagging strand. As the chases increased in length, giving DNA more time to replicate, the lagging strand fragments started integrating into longer, heavier, more rapidly sedimenting DNA strands. Today, scientists know that the Okazaki fragments of bacterial DNA are typically between 1,000 and 2,000 nucleotides long, whereas in eukaryotic cells, they are only about 100 to 200 nucleotides long. The Challenges of Eukaryotic Replication Bacterial and eukaryotic cells share many of the same basic features of replication; for instance, initiation requires a primer, elongation is always in the 5'-to-3' direction, and replication is always continuous along the leading strand and discontinuous along the lagging strand. But there are also important differences between bacterial and eukaryotic replication, some of which biologists are still actively researching in an effort to better understand the molecular details. One difference is that eukaryotic replication is characterized by many replication origins (often thousands), not just one, and the sequences of the replication origins vary widely among species. On the other hand, while the replication origins for bacteria, oriC, vary in length (from about 200 to 1,000 base pairs) and sequence, except among closely related organisms, all bacteria nonetheless have just a single replication origin (Mackiewicz et al., 2004). Eukaryotic replication also utilizes a different set of DNA polymerase enzymes (e.g., DNA polymerase δ and DNA polymerase ε instead of DNA polymerase III). Scientists are still studying the roles of the 13 eukaryotic polymerases discovered to date. In addition, in eukaryotes, the DNA template is compacted by the way it winds around proteins called histones. This DNA-histone complex, called a nucleosome, poses a unique challenge both for the cell and for scientists investigating the molecular details of eukaryotic replication. What happens to nucleosomes during DNA replication? Scientists know from electron micrograph studies that nucleosome reassembly happens very quickly after replication (the reassembled nucleosomes are visible in the electron micrograph images), but they still do not know how this happens (Annunziato, 2005). Also, whereas bacterial chromosomes are circular, eukaryotic chromosomes are linear. During circular DNA replication, the excised primer is readily replaced by nucleotides, leaving no gap in the newly synthesized DNA. In contrast, in linear DNA replication, there is always a small gap left at the very end of the chromosome because of the lack of a 3'-OH group for replacement nucleotides to bind. (As mentioned, DNA synthesis can proceed only in the 5'-to-3' direction.) If there were no way to fill this gap, the DNA molecule would get shorter and shorter with every generation. However, the ends of linear chromosomes—the telomeres—have several properties that prevent this. DNA replication occurs during the S phase of cell division. In E. coli, this means that the entire genome is replicated in just 40 minutes, at a pace of approximately 1,000 nucleotides per second. In eukaryotes, the pace is much slower: about 40 nucleotides per second. The coordination of the protein complexes required for the steps of replication and the speed at which replication must occur in order for cells to divide are impressive, especially considering that enzymes are also proofreading, which leaves very few errors behind. Summary The study of DNA replication started almost as soon as the structure of DNA was elucidated, and it continues to this day. Currently, the stages of initiation, unwinding, primer synthesis, and elongation are understood in the most basic sense, but many questions remain unanswered, particularly when it comes to replication of the eukaryotic genome. Scientists have devoted decades to the study of replication, and researchers such as Kornberg and Okazaki have made a number of important breakthroughs. Nonetheless, much remains to be learned about replication, including how errors in this process contribute to human disease. References and Recommended Reading Annunziato, A. T. Split decision: What happens to nucleosomes during DNA replication? Journal of Biological Chemistry 280, 12065–12068 (2005) Bessman, M. J., et al. Enzymatic synthesis of deoxyribonucleic acid. II. General properties of the reaction. Journal of Biological Chemistry 233, 171–177 (1958) Kornberg, A. The biological synthesis of deoxyribonucleic acid. Nobel Lecture, December 11, 1959. (link to transcript) ———. Biological synthesis of deoxyribonucleic acid. Science 131, 1503–1508 (1960) Lehman, I. R., et al. Enzymatic synthesis of deoxyribonucleic acid. I. Preparation of substrates and partial purification of an enzyme from Escherichia coli. Journal of Biological Chemistry 233, 163–170 (1958) Losick, R., & Shapiro, L. DNA replication: Bringing the mountain to Mohammed. Science 282, 1430–1431 (1998) Mackiewicz, P., et al. Where does bacterial replication start? Rules for predicting the oriC region. Nucleic Acids Research 32, 3781–3791 (2004) Ogawa, T., & Okazaki, T. Function of RNase H in DNA replication revealed by RNase H defective mutants of Escherichia coli. Molecular and General Genetics 193, 231–237 (1984) Okazaki, R., et al. Mechanism of DNA chain growth. I. Possible discontinuity and unusual secondary structure of newly synthesized chains. Proceedings of the National Academy of Sciences 59, 598–605 (1968) Outline | Keywords | Add Content to Group Article History Close Share | Cancel Revoke | Cancel Keywords Flag Inappropriate Close share Close Digg MySpace Google+ StumbleUpon Email your Friend Close This content is currently under construction. 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New lower bounds for the three-dimensional finite bin packing problem - ScienceDirect Typesetting math: 100% Skip to main contentSkip to article Journals & Books ViewPDF Download full issue Search ScienceDirect Outline Abstract Keywords 1. Introduction 2. Problem description 3. Lower bounds for the 3BP|O|F 4. New lower bounds for the 3BP|O|F 5. Lower bounds for the 3BP|M|F 6. Computational results 7. Conclusions Acknowledgements References Show full outline Cited by (45) Figures (2) Tables (3) Table 1 Table 2 Table Discrete Applied Mathematics Volume 140, Issues 1–3, 15 May 2004, Pages 241-258 New lower bounds for the three-dimensional finite bin packing problem Author links open overlay panel Marco A.Boschetti Show more Outline Add to Mendeley Share Cite rights and content Under an Elsevier user license Open archive Abstract The three-dimensional finite bin packing problem (3BP) consists of determining the minimum number of large identical three-dimensional rectangular boxes, bins, that are required for allocating without overlapping a given set of three-dimensional rectangular items. The items are allocated into a bin with their edges always parallel or orthogonal to the bin edges. The problem is strongly NP-hard and finds many practical applications. We propose new lower bounds for the problem where the items have a fixed orientation and then we extend these bounds to the more general problem where for each item the subset of rotations by 90° allowed is specified. The proposed lower bounds have been evaluated on different test problems derived from the literature. Computational results show the effectiveness of the new lower bounds. Previous article in issue Next article in issue Keywords Bin packing Lower bound Combinatorial optimization 1. Introduction The three-dimensional finite bin packing problem (3BP) consists of determining the minimum number of large identical three-dimensional rectangular boxes, bins, that are required for allocating without overlapping a given set of rectangular items, each with a given size. The items are allocated with their edges always parallel or orthogonal to the bin edges and they can have a fixed orientation or can be rotated by 90°. The 3BP finds many practical applications as it is a simplified version of many real world problems, e.g. container and pallet loading. The 3BP is a generalization of the well-known one-dimensional Bin Packing Problem (1BP), where n items of given weight w i have to be packed into the minimum number of bins of capacity W. Therefore, the 3BP is strongly NP-hard as well as the 1BP (see Garey and Johnson ). In practical applications there exist many versions of the 3BP. In the literature the oriented 3BP is the problem where item rotation is not allowed, while the nonoriented 3BP is the problem where every items can perform all the feasible rotations by 90°. According to the classification of Lodi et al. for the two-dimensional Bin Packing Problem (2BP), we denote the oriented and nonoriented 3BP with 3BP|O|F and 3BP|R|F, respectively. In this paper, we first consider the 3BP|O|F and then we extend our results to a more general version of 3BP where for each item the subset of allowed 90° rotations is specified. Following the aforementioned classification scheme we propose to denote this problem with 3BP|M|F. The 3BP|M|F contains as special cases problems 3BP|O|F and 3BP|R|F. Heuristic methods for the 3BP|O|F are recently proposed by Faroe et al. and Lodi et al. . Only one exact method for the 3BP|O|F is presented in the literature and it is proposed by Martello et al. . A new lower bound that dominates those proposed by Martello et al. is discussed in Fekete and Schepers . At our knowledge, neither exact methods nor lower bounds are proposed in the literature for problems 3BP|R|F and 3BP|M|F. Extensive survey on cutting and packing problems can be found in Coffman et al. , Coffman et al. , Dowsland and Dowsland , Dyckhoff and Finke , Dyckhoff et al. , Lodi et al. and Lodi et al. . In this paper, we propose new lower bounds for problems 3BP|O|F of complexity O(n 5) that dominate the ones proposed by Martello et al. and Fekete and Schepers both having complexity O(n 2). The computational analysis on test problems from the literature shows the effectiveness of the new lower bounds once implemented into the same exact algorithm of Martello et al. . The resulting exact method is able to solve problems unsolved by the original exact algorithm of Martello et al. and it requires on average less computing time. The remaining of this paper is organized as follows. In Section 2, we give the problem definition and the notation used throughout the paper. In Section 3, we summarize the lower bounds for the 3BP|O|F presented in the literature. New lower bounds for the 3BP|O|F are presented in Section 4. In Section 5, we extend these new lower bounds to the more general problem 3BP|M|F. In Section 6, the computational performance of the new lower bounds is given on test problems derived from the literature. 2. Problem description An unlimited stock of three-dimensional rectangular bins of size (W,H,D) are given and n three-dimensional rectangular items of sizes (w j,h j,d j),j∈J={1,…,n}, are required to be placed into the bins. The objective is to allocate without overlapping all items into the minimum number of bins. We consider both cases where items cannot be rotated, i.e., 3BP|O|F, and where items can be rotated by 90°, i.e., 3BP|M|F, described in Section 5. We assume that the sizes of bins and of items are positive integers satisfying w j⩽W, h j⩽H and d j⩽D, for every item j∈J. We denote with V=W×H×D the volume of the bin and with v j=w j×h j×d j the volume of item j∈J. 2.1. Definitions Let I be an instance of a minimization problem P,Z(I) be the value of the optimal solution to I and L(I) be the value provided by a lower bound L. The worst-case performance ratio of L is defined as the largest real number ρ such that ρ⩽L(I)/Z(I) for all instance I of P (see also , ). Given a minimization problem P and two different lower bounds L 1 and L 2,L 1 dominates L 2 if and only if L 1(I)⩾L 2(I) for all instance I of P. Henceforth, when L 1 dominates L 2 we also write L 1⩾L 2. 2.2. The continuous lower bound L 0 A simple lower bound L 0 for problems 3BP|O|F and 3BP|M|F, called continuous lower bound, can be computed in O(n) time as follows:(1)L 0=∑j=1 n v j V.Martello et al. have shown that for problem 3BP|O|F the optimal solution value in the worst case can be up to 8 times the L 0 value, i.e., the worst-case performance ratio of lower bound L 0 is 1 8. 3. Lower bounds for the 3BP|O|F In this section, we survey the lower bounds proposed by Martello et al. and Fekete and Schepers for the 3BP|O|F. These bounds will be used in 4 New lower bounds for the 3BP|O|F, 6 Computational results to evaluate the quality of the new proposed lower bounds. 3.1. The lower bound by Martello et al. In this section, we briefly describe the lower bounds L 1 and L 2 proposed by Martello et al. . 3.1.1. Lower bound L 1 The lower bound L 1 makes use of the lower bound L 1BP for the one-dimensional Bin Packing Problem (1BP) defined in the following. 1BP is the problem of packing a set S of items into the minimum number of bins of capacity C, where each item j∈S has a weight c j. A valid lower bound L 1BP to 1BP can be computed according the following theorem. Theorem 1 Given any integer p, such that 1⩽p⩽1 2 C, let S 1={j∈S:c j>C−p}, S 2={j∈S:1 2 C<c j⩽C−p}and S 3={j∈S:p⩽c j⩽1 2 C}. A valid lower bound on the optimal 1BP solution value is(2)L 1 BP(S,C)=max 1⩽p⩽(1/2)C{max{L α(p),L β(p)}},where(3)L α(p)=|S 1∪S 2|+max 0,∑j∈S 3 c j+∑j∈S 2 c j C−|S 2|,(4)L β(p)=|S 1∪S 2|+max 0,|S 3|−∑j∈S 2 C−c j p C p.If the items are sorted according to decreasing weights, L 1BP(S,C) can be computed in O(|S|2) time. Lower bound L 1 is based on the following theorem. Theorem 2 Let J WH={j∈J:w j>1 2 W and h j>1 2 H}. A valid lower bound L 1 WH for problem 3BP|O|F is obtained by computing the lower bound L 1BP(S,C) for the one-dimensional bin packing problem 1 BP-WH where items of S=J WH of weight c j=d j,j∈S, have to be packed into bins of capacity C=D. Similar lower bound L 1 HD is obtained by replacing in J WH and 1BP-WH the width with the depth, i.e., W with D and w j with d j. While, lower bound L 1 WD is obtained by replacing in J WH and 1BP-WH the height with the depth, i.e., H with D and h j with d j. Thus, the overall lower bound can be computed in O(n 2) time as(5)L 1=max{L 1 WH,L 1 HD,L 1 WD}.Martello et al. have shown that no dominance relation exists between L 0 and L 1 and that the worstcase performance of L 1 can be arbitrarily bad. 3.1.2. Lower bound L 2 The lower bound L 2 explicitly takes into account the three dimensions of the items and dominates L 1. However, L 2 makes use of L 1 WH,L 1 HD and L 1 WD. Theorem 3 Given any pair of integers (p,q), such that 1⩽p⩽1 2 W and 1⩽q⩽1 2 H, let(6)K 1(p,q)={j∈J:w j>W−p and h j>H−q},K 2(p,q)={j∈J⧹K 1(p,q):w j>1 2 W and h j>1 2 H},K 3(p,q)={j∈J⧹(K 1(p,q)∪K 2(p,q)):w j⩾p and h j⩾q}.A valid lower bound on the optimal 3BP|O|F solution value is(7)L 2 WH=L 1 WH+max 1⩽p⩽(1/2)W 1⩽q⩽(1/2)H max 0,∑j∈K 2∪K 3 v j+∑j∈K 1 d j WH V−L 1 WH.The lower bound L 2 WH can be computed in O(n 2) time. It is clear that the above results immediately produce two similar lower bounds L 2 HD and L 2 WD. Lower bound L 2 HD is obtained by replacing in , W with D,w j with d j and L 1 WH with L 1 HD. While, L 2 WD is obtained by replacing in , H with D,h j with d j and L 1 WH with L 1 WD. Thus, the overall lower bound can be computed in O(n 2) time as(8)L 2=max{L 2 WH,L 2 HD,L 2 WD}.Martello et al. have shown that L 2 dominates both L 0 and L 1. Therefore, the overall lower bound is L MPV=L 2. 3.2. The lower bound by Fekete and Schepers Fekete and Schepers have proposed a new lower bound for the 3BP|O|F, called L FS, and have shown that L FS⩾L MPV. In computing the lower bound for the 3BP|O|F, Fekete and Schepers normalize the item sizes as w̃j=w j/W, h̃j=h j/H and d̃j=d j/D,∀j∈J, and set (W,H,D)=(1,1,1). Then lower bound L FS is obtained by computing the continuous lower bound L 0 (see Section 2.2) using the volumes of the items transformed by means of the following three dual feasible functions. Dual feasible function 1: Let k∈N. Then u(k)(x)=x, if (k+1)x∈Z, and u(k)(x)=⌊(k+1)x⌋1 k otherwise. Dual feasible function 2: Let ε∈[0,1 2]. Then U(ε)(x)=1, if x>1−ε,U(ε)(x)=x, if ε⩽x⩽1−ε, and U(ε)(x)=0, if x<ε. Dual feasible function 3: Let ε∈(0,1 2]. Then φ(ε)(x)=1−⌊(1−x)ε−1⌋/⌊ε−1⌋, if x>1 2,φ(ε)(x)=1/⌊ε−1⌋, if ε⩽x⩽1 2, and φ(ε)(x)=0, if x<ε. The lower bound L FS is given by the following theorem. Theorem 4 Let α,β∈(0,1 2]. Let(9)v j(1)(α)=u(1)(w̃j)×u(1)(h̃j)×U(α)(d̃j),v j(2)(α)=u(1)(w̃j)×U(α)(h̃j)×u(1)(d̃j),v j(3)(α)=U(α)(w̃j)×u(1)(h̃j)×u(1)(d̃j),v j(4)(α)=u(1)(w̃j)×u(1)(h̃j)×φ(α)(d̃j),v j(5)(α)=u(1)(w̃j)×φ(α)(h̃j)×u(1)(d̃j),v j(6)(α)=φ(α)(w̃j)×u(1)(h̃j)×u(1)(d̃j),v j(7)(α,β)=U(α)(w̃j)×U(β)(h̃j)×d̃j,v j(8)(α,β)=U(α)(w̃j)×h̃j×U(β)(d̃j),v j(9)(α,β)=w̃j×U(α)(h̃j)×U(β)(d̃j).A valid lower bound on the optimal 3BP|O|F solution value is(10)L FS=max max k∈{1,…,6}0<α⩽1/2∑j∈J v j(k)(α),max k∈{7,…,9}0<α⩽1/2,0<β⩽1/2∑j∈J v j(k)(α,β).Moreover, L FS dominates the lower bound L MPV. 4. New lower bounds for the 3BP|O|F In this section, we introduce the new lower bounds L 1 new and L 2 new for the 3BP|O|F. 4.1. Lower bound L 1 new The new lower bound L 1 new takes into account the three dimensions of the items and it is based on the following observations. Given a triplet of integers (p,q,r), such that 1⩽p⩽1 2 W,1⩽q⩽1 2 H and 1⩽r⩽1 2 D, let(11)I 1 W(p)={j∈J:w j>W−p},I 2 W(p)={j∈J:p⩽w j⩽W−p},I 1 H(q)={j∈J:h j>H−q},I 2 H(q)={j∈J:q⩽h j⩽H−q},I 1 D(r)={j∈J:d j>D−r},I 2 D(r)={j∈J:r⩽d j⩽D−r}.Note that for every triplet of integers (p,q,r), such that 1⩽p⩽1 2 W,1⩽q⩽1 2 H and 1⩽r⩽1 2 D, every item of I 1(p,q,r)=I 1 W(p)∩I 1 H(q)∩I 1 D(r) requires a bin. Therefore, |I 1(p,q,r)| is a valid lower bound on the optimal 3BP|O|F solution. Furthermore, this lower bound can be strengthened by observing that items of I 1(p,q,r) cannot be packed together with items of I 2(p,q,r)=I(p,q,r)⧹I 1(p,q,r), where I(p,q,r)={j∈J:w j⩾p,h j⩾q,d j⩾r}. Hence, we can improve the lower bound by adding to |I 1(p,q,r)| a lower bound to the number of bins for packing items I 2(p,q,r). In the following we describe two different lower bounds, called L 1′(p,q,r) and L 1″(p,q,r), to the minimum number of bins required for packing items I(p,q,r). L 1′(p,q,r) is based on the following observations. Every item j∈I 1 W(p) cannot be packed side by side with any item of I(p,q,r), therefore the bin volume at its left- and right-hand sides cannot be used. Hence, every item j∈I 1 W(p), once placed in a bin, occupies at least a volume equal to Wh j d j. Similar considerations can be done for the items of I 1 H(q) and I 1 D(r). Therefore, for each j∈I(p,q,r), an updated volume v j′(p,q,r) can be computed as follows:(12)v j′(p,q,r)=w j′(p)h j′(q)d j′(r),where w j′(k)=W,j∈I 1 W(p),w j otherwise,h j′(k)=H,j∈I 1 H(p),h j otherwise,d j′(k)=D,j∈I 1 D(p),d j otherwise.Hence, L 1′(p,q,r) can be computed as a valid lower bound of the one-dimensional bin packing problem 1BP(p,q,r) where items of S=I(p,q,r) of weight c j=v j′(p,q,r) have to be packed into bins of capacity C=V. Lower bound L 1″(p,q,r) is based on the following observations. Given the three subsets I WH(p,q,r)=I 1 W(p)∩I 1 H(q)∩I 2(p,q,r), I WD(p,q,r)=I 1 W(p)∩I 1 D(r)∩I 2(p,q,r) and I HD(p,q,r)=I 1 H(q)∩I 1 D(r)∩I 2(p,q,r), two items contained in two of these sets cannot be packed in the same bin. For example for every pair of items j 1∈I WH(p,q,r) and j 2∈I HD(p,q,r) we have w j 1+w j 2>W,h j 1+h j 2>H and d j 1+d j 2>D. Furthermore, items of I WH(p,q,r) can be only packed one behind the other as items of I WD(p,q,r) can be only packed one over the other and items of I HD(p,q,r) can be only packed side by side. Therefore, L 1″(p,q,r) can be computed as follows: L 1″(p,q,r)=|I 1(p,q,r)|+L̄WH 1(p,q,r)+L̄WD 1(p,q,r)+L̄HD 1(p,q,r), where: •L̄WH 1(p,q,r) is a valid lower bound to the 1BP defined by setting C=D,S=I WH(p,q,r) and c j=d j, for each item j∈S. •L̄WD 1(p,q,r) is a valid lower bound to the 1BP defined by setting C=H,S=I WD(p,q,r) and c j=h j, for each item j∈S. •L̄HD 1(p,q,r) is a valid lower bound to the 1BP defined by setting C=W,S=I HD(p,q,r) and c j=w j, for each item j∈S. The lower bound L 1 new is computed as follows:(13)L 1 new=max 1⩽p⩽(1/2)W,1⩽q⩽(1/2)H 1⩽r⩽(1/2)D{max{L 1′(p,q,r),L 1″(p,q,r)}}.Note that in expression (13) it is sufficient to consider only the values of p,q and r corresponding to distinct values of w j⩽W/2,h j⩽H/2 and d j⩽D/2, respectively (see also Martello et al. ). Moreover, the set of values {p}, {q} and {r} to consider in evaluating L 1′(p,q,r) can be further reduced by the following observation. If we have two values p and p′ such that w j′(p)⩽w j′(p′), for every item j∈J, then value p can be discarded. Similarly, we can reduce the value sets {q} and {r}. It is easy to show that each of the resulting set of values cannot contain more than n/2 distinct values. Concerning L 1″(p,q,r), it is sufficient to consider the values p∈{w j⩽W/2:j∈I 1 H(1 2)∩I 1 D(1 2)}, q∈{h j⩽H/2:j∈I 1 W(1 2)∩I 1 D(1 2)} and r∈{d j⩽D/2:j∈I 1 W(1 2)∩I 1 H(1 2)}. The lower bound L 1 new can be computed in O(n 3 b) time, where b is the complexity of the algorithm used for computing a valid lower bound of the one-dimensional bin packing problem. In case the lower bound L 1BP(S,C) is used, then the overall complexity is O(n 5), while if the continuous lower bound is used then the complexity is O(n 4). The following theorem shows that the lower bound L 1 new dominates L MPV. Theorem 5 If lower bound L 1 new is computed using L 1BP(S,C) then L 1 new⩾L MPV. Proof By means of the following properties: (i) a+max{b,c}=max{a+b,a+c}, if a,b and c are real; (ii) a+⌈b⌉=⌈a+b⌉, if a is an integer and b is a real; lower bound L 2 WH given by expression (7) can be rewritten as(14)L 2 WH=max{L 1 WH,L̂2 WH},where(15)L̂2 WH=max 1⩽p⩽(1 2)W 1⩽q⩽(1 2)H∑j∈K 2(p,q)∪K 3(p,q)v j+∑j∈K 1(p,q)d j WH V.In order to show that L 1 new⩾L 2 WH, we prove that L 1 new⩾L 1 WH and L 1 new⩾L̂2 WH. Consider L 1′(p,q,r) for the case where p=1 2 W, q=1 2 H and r=1. L 1′(W/2,H/2,1) is computed using L 1BP(S,C) for solving the one-dimensional bin packing problem 1BP(W/2,H/2,1) where items of S=I(W/2,H/2,1) of weight c j=WHd j, if j∈J WH, and c j=v j′, if j∈S⧹J WH, have to be packed into a bins of capacity C=WHD. If we ignore the item of S⧹J WH, then the remaining problem is equivalent to the one-dimensional bin packing problem where the items of weight c j=d j,j∈J WH, have to be packed into bins of capacity C=D, which corresponds to problem 1BP-WH. Since problem 1BP(W/2,H/2,1) also considers the items belonging to S⧹J WH, then we have L 1 new⩾L 1′(W/2,H/2,1)⩾L 1 WH. It is easy to see that L̂2 WH represents the maximum of the continuous lower bounds for the one-dimensional bin packing problems, defined for every pair (p,q) such that 1⩽p⩽1 2 W and 1⩽q⩽1 2 H, where items of weight c j=WHd j⩽v j′(p,q,1), if j∈K 1(p,q), and c j=v j⩽v j′(p,q,1), if j∈K 2(p,q)∪K 3(p,q), have to be packed into bins of capacity C=V. Since, for every pair (p,q),I(p,q,1)=K 1(p,q)∪K 2(p,q)∪K 3(p,q) and c j⩽v j′(p,q,1), for every j∈I(p,q,1), then L 1 new⩾max{L 1′(p,q,1):1⩽p⩽1 2 W,1⩽q⩽1 2 H}⩾L̂2 WH. Therefore, we have that L 1 new⩾L 2 WH and in a similar way we can show that L 1 new⩾L 2 WD and L 1 new⩾L 2 HD. Hence, we have L 1 new⩾L MPV=max{L 2 WH,L 2 WD,L 2 HD} which completes the proof.□ Note that in the proof of Theorem 5 it was sufficient to consider only the component L 1′(p,q,r) of lower bound L 1 new. 4.2. Lower bound L 2 new The lower bound L 2 new is an extension to the 3BP|O|F of the lower bound proposed by Martello and Vigo for the 2BP|O|F. It explicitly takes into account the three dimensions of the items as well as L 1 new, described in Sections 4.1. Between L 1 new and L 2 new no dominance relations hold. Theorem 6 Given a triplet of integers (p,q,r), such that 1⩽p⩽1 2 W, 1⩽q⩽1 2 H and 1⩽r⩽1 2 D, a valid lower bound on the optimal 3BP|O|F solution is(16)L 2 new=max 1⩽p⩽(1/2)W,1⩽q⩽(1/2)H 1⩽r⩽(1/2)D∑j∈J μ(j,p,q,r)⌊W/p⌋⌊H/q⌋⌊D/r⌋,where(17)μ(j,p,q,r)=η(p,w j,W)×η(q,h j,H)×η(r,d j,D)and(18)η(s,z,Z)=Z s−Z−z s if z>Z 2,z s if z⩽Z 2. Proof Note that ⌊W/p⌋⌊H/q⌋⌊D/r⌋ represents the maximum number of elements of size equal to (p,q,r) that can be packed into a bin. For each item j∈J, μ(j,p,q,r) represents a lower bound on the number of (p,q,r) elements covered by item j (see the four two-dimensional examples reported in Fig. 1). Hence, ∑j∈J μ(j,p,q,r) represents a lower bound on the number of (p,q,r) elements required for placing all items of J.□ 1. Download: Download full-size image Fig. 1. Four two-dimensional examples: (a) w j>W/2 and h j>H/2; (b) p⩽w j⩽W/2 and h j>H/2; (c) w j>W/2 and q⩽h j⩽H/2; (d) p⩽w j⩽W/2 and q⩽h j⩽H/2. The lower bound on the number of (p,q) elements covered by item j is given by η(p,w j,W)×η(q,h j,H). In order to reduce the computational complexity of L 2 new we can reduce the number of triplets (p,q,r) used in expression (16) considering only the values of p,q and r corresponding to distinct values of w j⩽W/2,h j⩽H/2 and d j⩽D/2, respectively. Hence, the lower bound L 2 new can be computed in O(n 4) time. Moreover, the set of values {p},{q} and {r} can be further reduced by observing that if there are two values p and p′ such that η(p,w j,W)⌊W/p⌋−1⩽η(p′,w j,W)⌊W/p′⌋−1, for every item j∈J, then value p can be discarded. Similarly, we can reduce the value sets {q} and {r}. 4.3. New lower bound L B for the 3BP|O|F Since no dominance relations hold between L 1 new and L 2 new, but L 1 new dominates L 2, the overall lower bound L B is computed as L B=max{L 1 new,L 2 new}. Theorem 7 If lower bounds L 1′(p,q,r) and L 1″(p,q,r) used in expression (13) for computing L 1 new is computed using the continuous lower bound for the 1 BP, then L B⩾L FS. Proof Among the three dual feasible functions proposed by Fekete and Schepers the following relationships hold: u(1)=U(1/2) and u(1)=φ(1/2). As U(0)(x)=x, then we can rewrite expressions (9) as follows:(19)v j(1)(α)=U(1/2)(w̃j)×U(1/2)(h̃j)×U(α)(d̃j),v j(2)(α)=U(1/2)(w̃j)×U(α)(h̃j)×U(1/2)(d̃j),v j(3)(α)=U(α)(w̃j)×U(1/2)(h̃j)×U(1/2)(d̃j),v j(4)(α)=φ(1/2)(w̃j)×φ(1/2)(h̃j)×φ(α)(d̃j),v j(5)(α)=φ(1/2)(w̃j)×φ(α)(h̃j)×φ(1/2)(d̃j),v j(6)(α)=φ(α)(w̃j)×φ(1/2)(h̃j)×φ(1/2)(d̃j),v j(7)(α,β)=U(α)(w̃j)×U(β)(h̃j)×U(0)(d̃j),v j(8)(α,β)=U(α)(w̃j)×U(0)(h̃j)×U(β)(d̃j),v j(9)(α,β)=U(0)(w̃j)×U(α)(h̃j)×U(β)(d̃j),where w̃j=w j/W,h̃j=h j/H and d̃j=d j/D,∀j∈J. Part 1: Define v j 1(α,β,γ)=U(α)(w̃j)×U(β)(h̃j)×U(γ)(d̃j), where α,β,γ∈[0,1/2]. As U(ε)(x) is a dual feasible function, then we have the following lower bound L P 1:(20)L P1=max 0⩽α⩽1/2,0⩽β⩽1/2 0⩽γ⩽1/2∑j∈J v j 1(α,β,γ).It is clear that(21)L P1⩾max max k∈{1,2,3}0<α⩽1/2∑j∈J v j(k)(α),max k∈{7,8,9}0<α⩽1/2 0<β⩽1/2∑j∈J v j(k)(α,β).Consider the set I(p,q,r)={j∈J:w j⩾p,h j⩾q,d j⩾r} defined in Section 4.1. Let p=αW,q=βH and r=γD and define v j′(p,q,r) according to expression (12) for every j∈I(p,q,r) and v j′(p,q,r)=0 otherwise. From the definition of U(ε)(x) is easy to see that v j 1(α,β,γ)=v j′(p,q,r)/V, for every j∈I(p,q,r), and v j 1(α,β,γ)=0 otherwise. Therefore, L P 1 can be rewritten as follows:(22)L P1=max 1⩽p⩽(1/2)W,1⩽q⩽(1/2)H 1⩽r⩽(1/2)D∑j∈I(p,q,r)v j′(p,q,r)V.Note that the term in the maximization of expression (22) is the continuous lower bound of problem 1BP(p,q,r) used in Section 4.1 for computing L 1′(p,q,r). Hence L 1 new⩾L 1′(p,q,r)⩾L P 1. Part 2: Define v j 2(α,β,γ)=φ(α)(w̃j)×φ(β)(h̃j)×φ(γ)(d̃j), where α,β,γ∈(0,1 2]. Since φ(ε)(x) is a dual feasible function, then we have the following lower bound L P 2:(23)L P2=max 0<α⩽1 2,0<β⩽1 2 0<γ⩽1 2∑j∈J v j 2(α,β,γ)⩾max k∈{4,5,6}0<α⩽1 2∑j∈J v j(k)(α).Define x=z/Z and ε=s/Z, then we have φ(ε)(x)=⌊Z/s⌋−⌊(Z−z)/s⌋/⌊Z/s⌋, if z>Z/2,φ(ε)(x)=1/⌊Z/s⌋, if s⩽z⩽Z/2 and φ(ε)(x)=0, otherwise. Therefore, L P 2 can be rewritten as follows:(24)L P2=max 1⩽p⩽(1/2)W,1⩽q⩽(1/2)H 1⩽r⩽(1/2)D∑j∈J μ′(j,p,q,r)⌊W/p⌋⌊H/q⌋⌊D/r⌋,where(25)μ′(j,p,q,r)=η′(p,w j,W)×η′(q,h j,H)×η′(r,d j,D)and(26)η′(s,z,Z)=Z s−Z−z s if z>Z 2,1 if s⩽z⩽Z 2,0 otherwise.If we consider the lower bound L 2 new, defined in Section 4.2, it is easy to show that η′(s,z,Z)⩽η(s,z,Z) and, consequently, L 2 new⩾L P 2. Hence, we have L B=max{L 1 new,L 2 new}⩾max{L P 1,L P 2}⩾L FS which completes the proof.□ 5. Lower bounds for the 3BP|M|F For the case where items can be rotated by 90°, we can allocate the item into the bin in six different orientations (see the example reported in Fig. 2). Let R={0,1,2,3,4,5} be the index set of the six rotations. For each rotation k∈R we denote the size of each item j∈J with (ŵj(k),ĥj(k),d̂j(k)) where:ŵj(k)=w j,k∈{0,1},h j,k∈{2,3},d j,k∈{4,5},ĥj(k)=w j,k∈{2,5},h j,k∈{0,4},d j,k∈{1,3},d̂j(k)=w j,k∈{3,4},h j,k∈{1,5},d j,k∈{0,2}.We denote with R j⊆R the subset of feasible rotations allowed of the item j∈J; that is R j={k∈R:ŵj(k)⩽W and ĥj(k)⩽H and d̂j(k)⩽D}. 1. Download: Download full-size image Fig. 2. The six different rotations for item j of size (w j,h j,d j)=(3,2,1). Note that in practical application only a subset of R j can be allowed for item j. In this case, we assume that R j is specified in input as required by the particular application. If for every item j∈J the subset R j contains all the feasible rotations, then problem 3BP|M|F corresponds to problem 3BP|R|F. The continuous lower bound L 0 can be also used for the 3BP|M|F as it involves only item and bin volumes. 5.1. Lower bound L 1 M The lower bounds described in Section 4 can be used for the 3BP|M|F once the item sizes w j,h j and d j are replaced with the following modified sizes: w̄j=min{ŵj(k):k∈R j},h̄j=min{ĥj(k):k∈R j} and d̄j=min{d̂j(k):k∈R j}, while the item volume v j,j∈J, does not need to be modified. However, lower bound L′(p,q,r), described in Section 4.1, can be improved if in defining problem 1 BP(p,q,r) we set c j=max{v j,v j′(p,q,r)}, for every j∈S=I(p,q,r). We denote with L 1 M the lower bound obtained as described above. In the following we describe lower bound L 2 M which explicitly takes into account both dimensions and the specified feasible rotations R j of each item j. 5.2. Lower bound L 2 M Lower bound L 2 M is defined by the following theorem. Theorem 8 A valid lower bound on the optimal solution value of the 3BP|M|F is(27)L 2 M=max 1⩽p⩽(1/2)W,1⩽q⩽(1/2)H 1⩽r⩽(1/2)D∑j∈J μ′(j,p,q,r)⌊W/p⌋⌊H/q⌋⌊D/r⌋,where μ′(j,p,q,r)=min{η(p,ŵj(k),W)×η(q,ĥj(k),H)×η(r,d̂j(k),D):k∈R j}and η(s,z,Z) is defined by expression (18). Lower bound L 2 M can be computed in O(n 4) time. Proof Note that ⌊W/p⌋⌊H/q⌋⌊D/r⌋ represents the maximum number of elements of size equal to (p,q,r) that can be packed into a bin. For each item j∈J,μ(j,p,q,r) represents a lower bound on the number of (p,q,r) elements covered by item j. Hence, ∑j∈J μ(j,p,q,r) represents a lower bound on the number of (p,q,r) elements required for placing all items of J.□ 5.3. Overall lower bound L B M for the 3BP|M|F Lower bound L B M is maximum between L 1 M, computed using the modified item sizes (w̄j,h̄j,d̄j),j∈J, and L 2 M given by expression (27), that is L B M=max{L 1 M,L 2 M}. 6. Computational results The algorithms presented in this paper have been implemented in C and run on a Pentium III Intel 933 MHz. We have considered the eight classes of test problems proposed by Martello et al. . The first five classes of randomly generated problems that are generalizations of the instances considered by Martello and Vigo for the two-dimensional bin packing problem (2BP). The bin size is (W,H,D)=(100,100,100), and five types of items are considered, as described in Table 1. Each class k∈{1,…,5} of instances is obtained by including items of type k with probability 60% and items of the other four types with probability 10% each. Table 1. Item generation for Classes 1–5. For each type of item, the dimensions are uniformly random generated in the given range. | Type | w j | h j | d j | --- --- | | 1 | [1,1 2 W] | [2 3 H,H] | [2 3 D,D] | | 2 | [2 3 W,W] | [1,1 2 H] | [2 3 D,D] | | 3 | [2 3 W,W] | [2 3 H,H] | [1,1 2 D] | | 4 | [1 2 W,W] | [1 2 H,H] | [1 2 D,D] | | 5 | [1,1 2 W] | [1,1 2 H] | [1,1 2 D] | The last three classes of randomly generated problems are generalizations of the instances presented by Berkey and Wang for the 2BP and are defined as follows: •Class 6: bin size (W,H,D)=(10,10,10); items sizes (w j,h j,d j) are uniformly random generated in [1,10]; •Class 7: bin size (W,H,D)=(40,40,40); items sizes (w j,h j,d j) are uniformly random generated in [1,35]; •Class 8: bin size (W,H,D)=(100,100,100); items sizes (w j,h j,d j) are uniformly random generated in [1,100]. The test problem instances have been generated using the code available on website “ and each class contains 10 different problems. Table 2 shows the results when items cannot be rotated. The computational results obtained by the new lower bound L B are compared with the ones obtained by the lower bound L MPV proposed by Martello et al. and our implementation of the lower bound L FS proposed by Fekete and Schepers . Moreover, Table 2 shows the results obtained by the exact method proposed by Martello et al. (the code is available on the website “ using their lower bound L MPV, our implementation of L FS and the new lower bound L B within the time limit of 300 s. Table 2. Lower bounds for the 3BP|O|F. | Problem | MPV 2000 | FS ’97 | New lower bound | --- --- | | Class | n | G MPV | T MPV | N MPV | O MPV | G FS | T FS | N FS | O FS | G B | T B | N B | O B | | I | 20 | 13.62 | 0.05 | 154.9 | 10 | 6.52 | 0.04 | 110.9 | 10 | 3.43 | 0.03 | 37.5 | 10 | | | 40 | 6.50 | 21.17 | 1266415.3 | 9 | 4.67 | 34.69 | 1264027.7 | 9 | 2.22 | 15.35 | 139873.9 | 10 | | | 60 | 8.95 | 20.11 | 205616.0 | 1 | 7.59 | 57.56 | 205616.0 | 1 | 7.01 | 41.08 | 205616.0 | 1 | | | 80 | 7.97 | — | — | 0 | 5.21 | — | — | 0 | 4.68 | 125.48 | 222481.5 | 2 | | | 100 | 8.39 | — | — | 0 | 6.63 | — | — | 0 | 4.74 | 1.79 | 1870.0 | 2 | | | | | | | | | | | | | | | | | II | 20 | 11.90 | 0.03 | 958.9 | 10 | 9.90 | 0.05 | 952.2 | 10 | 4.03 | 0.05 | 531.5 | 10 | | | 40 | 9.27 | 8.08 | 103450.1 | 8 | 5.78 | 14.17 | 71922.9 | 8 | 3.56 | 6.23 | 54171.6 | 8 | | | 60 | 8.99 | 69.32 | 8689786.0 | 1 | 7.10 | 36.25 | 4346047.5 | 2 | 5.14 | 0.44 | 1185.0 | 2 | | | 80 | 8.59 | — | — | 0 | 5.68 | 13.89 | 81.0 | 1 | 5.20 | 7.14 | 81.0 | 2 | | | 100 | 8.74 | — | — | 0 | 6.47 | — | — | 0 | 5.68 | 0.60 | 101.0 | 1 | | | | | | | | | | | | | | | | | III | 20 | 17.29 | 0.02 | 112.1 | 10 | 10.52 | 0.03 | 39.3 | 10 | 7.10 | 0.02 | 31.0 | 10 | | | 40 | 10.10 | 77.12 | 5440608.1 | 8 | 6.11 | 76.21 | 4948050.6 | 7 | 5.11 | 53.11 | 3776889.9 | 8 | | | 60 | 8.54 | — | — | 0 | 4.56 | 97.84 | 104608.0 | 3 | 3.72 | 51.34 | 78471.3 | 4 | | | 80 | 7.85 | 0.99 | 81.0 | 1 | 6.45 | 1.10 | 81.0 | 1 | 5.55 | 1.21 | 81.0 | 1 | | | 100 | 9.19 | — | — | 0 | 7.34 | — | — | 0 | 6.65 | — | — | 0 | | | | | | | | | | | | | | | | | IV | 20 | 0.77 | 0.01 | 1.9 | 10 | 0.77 | 0.01 | 1.9 | 10 | 0.00 | 0.01 | 0.0 | 10 | | | 40 | 2.10 | 0.05 | 572.0 | 10 | 1.28 | 0.05 | 462.6 | 10 | 0.00 | 0.05 | 0.0 | 10 | | | 60 | 2.02 | 5.24 | 333185.7 | 9 | 0.87 | 0.20 | 3619.7 | 9 | 0.00 | 0.13 | 40.6 | 10 | | | 80 | 2.65 | 1.29 | 41969.5 | 4 | 1.02 | 0.35 | 1899.5 | 6 | 0.00 | 0.24 | 0.0 | 10 | | | 100 | 2.39 | 0.38 | 97.0 | 1 | 0.68 | 0.40 | 49.2 | 6 | 0.00 | 0.36 | 29.5 | 10 | | | | | | | | | | | | | | | | | V | 20 | 15.00 | 0.13 | 5.2 | 10 | 13.33 | 0.13 | 5.2 | 10 | 0.00 | 0.12 | 1.4 | 10 | | | 40 | 21.83 | 0.36 | 16.0 | 4 | 18.58 | 0.35 | 16.0 | 4 | 10.42 | 1.58 | 22.2 | 5 | | | 60 | 26.00 | 2.63 | 122.0 | 1 | 23.64 | 2.80 | 122.0 | 1 | 16.37 | 1.97 | 122.0 | 1 | | | 80 | 22.83 | — | — | 0 | 22.11 | — | — | 0 | 15.56 | — | — | 0 | | | 100 | 24.15 | — | — | 0 | 22.56 | — | — | 0 | 18.23 | — | — | 0 | | | | | | | | | | | | | | | | | VI | 20 | 14.10 | 0.09 | 12.9 | 10 | 12.43 | 0.09 | 12.3 | 10 | 5.10 | 0.09 | 7.5 | 10 | | | 40 | 7.33 | 9.04 | 3294.9 | 10 | 3.50 | 8.93 | 3274.1 | 10 | 3.50 | 8.29 | 3274.1 | 10 | | | 60 | 10.23 | 60.69 | 131016.0 | 7 | 5.60 | 48.53 | 127529.7 | 7 | 3.98 | 36.70 | 111546.9 | 8 | | | 80 | 10.27 | 8.68 | 168358.8 | 4 | 5.43 | 9.82 | 168153.3 | 4 | 4.31 | 8.66 | 163672.0 | 4 | | | 100 | 9.35 | 57.62 | 3503294.5 | 2 | 4.73 | 59.24 | 3153301.0 | 2 | 4.73 | 53.06 | 3153301.0 | 2 | | | | | | | | | | | | | | | | | VII | 20 | 14.17 | 0.11 | 8.3 | 10 | 8.33 | 0.11 | 7.2 | 10 | 5.00 | 0.11 | 6.7 | 10 | | | 40 | 30.27 | 0.22 | 54.0 | 2 | 25.91 | 0.28 | 54.0 | 2 | 24.48 | 0.22 | 54.0 | 2 | | | 60 | 28.65 | — | — | 0 | 25.63 | — | — | 0 | 22.81 | — | — | 0 | | | 80 | 26.94 | — | — | 0 | 23.82 | — | — | 0 | 21.39 | — | — | 0 | | | 100 | 26.81 | — | — | 0 | 24.34 | — | — | 0 | 22.53 | — | — | 0 | | | | | | | | | | | | | | | | | VIII | 20 | 13.17 | 0.09 | 6.9 | 10 | 11.50 | 0.09 | 6.9 | 10 | 4.17 | 0.09 | 4.2 | 10 | | | 40 | 12.92 | 18.10 | 229.4 | 8 | 12.92 | 18.25 | 229.4 | 8 | 6.13 | 17.46 | 208.1 | 8 | | | 60 | 13.15 | 72.60 | 27518.0 | 5 | 11.49 | 73.76 | 27518.0 | 5 | 9.94 | 69.56 | 27518.0 | 5 | | | 80 | 18.29 | 38.61 | 7953.0 | 2 | 16.20 | 38.78 | 7953.0 | 2 | 12.58 | 36.44 | 7953.0 | 2 | | | 100 | 14.74 | 118.89 | 238339.0 | 2 | 13.66 | 117.69 | 238339.0 | 2 | 9.78 | 110.68 | 84240.5 | 2 | Let UB be the best upper bound known. In Table 2 for each test problem we report: G MPV,G FS,G B:average percentage ratio between the lower bound value obtained by L MPV,L FS and L B, respectively, and the best upper bound known, i.e., G MPV=UB−L MPV UB×100,G FS=UB−L FS UB×100 and G B=UB−L B UB×100; T MPV,T FS,T B:average computing time in Pentium III Intel 933 MHz CPU s, computed over all the solved instances, required by the original exact method of Martello et al. using lower bounds L MPV,L FS and L B, respectively; N MPV,N FS,N B:average number of tree nodes, computed over all the solved instances, required by the original exact method of Martello et al. using lower bounds L MPV,L FS and L B, respectively; O MPV,O FS,O B:number of instances solved to optimality within the time limit of 300 s by the exact method of Martello et al. using lower bounds L MPV,L FS and L B, respectively. We do not report the computing time of the lower bounds as they are negligible. Table 2 shows that G MPV⩾G FS⩾G B, i.e., L MPV⩽L FS⩽L B, thus confirming the better quality of the new lower bound L B. Not reported in Table 2, lower bound L B for 234 instances out of 400 improves L MPV of Martello et al. and for 118 instances out of 400 improves our implementation of L FS of Fekete and Schepers . Table 2 also shows that the exact method of Martello et al. using the new lower bound L B is able to solve to optimality 31 new instances no solved by the same exact method using L MPV. While, the exact method using L FS is able to solve to optimality only 12 new instances, but it is not able to solve to optimality one instance solved by Martello et al. Moreover, columns T MPV,T FS and T B show that the computational performance of the exact method using the new lower bound L B is on average better than the computational performance of the exact method using L MPV and L FS. Therefore, the larger theoretical computational complexity of L B with respect to L MPV and L FS is repaid by the advantages obtained by having a better lower bound; i.e., a smaller number of tree nodes required to reach the optimal solution (see columns N MPV,N FS and N B). While, even if L MPV and L FS have the same theoretical computational complexity, i.e., O(n 2), and L FS dominates L MPV, the lower bound L FS is more time consuming than L MPV but it is not able to reduce enough the number of tree nodes. In our computational experiments we have also tested the new lower bound L B when the continuous lower bound for the 1BP is used, instead of L 1BP(S,C), so as to achieve the O(n 4) complexity. The results obtained are similar to the ones reported in Table 2 for the version of complexity O(n 5) but they are always inferior. 7. Conclusions In this paper, we propose new lower bounds for the three-dimensional finite bin-packing problem where items have a fixed orientation (3BP|O|F) and for the more general case where for each item the subset of rotations allowed is specified (3BP|M|F). We show that the new lower bound for the 3BP|O|F dominates all other lower bounds presented in the literature so far. The computational results show the effectiveness of the new lower bound L B for the 3BP|O|F and indicate that the exact algorithm proposed by Martello et al. using L B solves to optimality more instances and requires on average less computing time than the exact algorithm using L MPV and L FS. In this paper, no results on the worst-case performance ratio of the new lower bound L B are reported. Therefore, further research is required to give an answer to this important question. In the literature, the worstcase performance ratio is defined only for the well-known continuous lower bound L 0 (see Martello et al. ). Acknowledgements The author would like to thank the referees for their useful comments and suggestions which contributed to the improvement of this paper. Recommended articles References J.O. Berkey, P.Y. Wang Two dimensional finite bin packing algorithms J. Oper. Res. Soc., 38 (1987), pp. 423-429 View in ScopusGoogle Scholar E.G. Coffman, G. Galambos, S. Martello, D. Vigo Bin packing approximation algorithms: combinatorial analysis D.Z. Du, P.M. Pardalos (Eds.), Handbook of Combinatorial Optimization, Kluwer Academic Publishers, Boston (1999) Google Scholar E.G. Coffman, M.R. Garey, D.S. Johnson Approximation algorithms for bin packing: a survey D.S. Hochbaum (Ed.), Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, Boston (1997) Google Scholar K.A. Dowsland, W.B. Dowsland Packing problems European J. Oper. Res., 56 (1992), pp. 2-14 View PDFView articleView in ScopusGoogle Scholar H. Dyckhoff, U. Finke Cutting and packing in production and distribution, Physica-Verlag, Heidelberg (1992) Google Scholar H. Dyckhoff, G. Scheithauer, J. Terno Cutting and packing (C&P) M. Dell'Amico, F. Maffioli, S. Martello (Eds.), Annotated Bibliographies in Combinatorial Optimization, Wiley, Chichester (1997), pp. 393-413 Google Scholar O. Faroe, D. Pisinger, M. Zachariasen, Guided local search for the three-dimensional bin packing problem, Technical Report 99/13, DIKU, University of Copenhagen, Denmark, 1999. Google Scholar S.P. Fekete, J. Schepers, New classes of lower bounds for bin-packing problem, IPCO 98, Springer Lecture Notes in Computer Science, Vol. 1412, 1998, pp. 257–270. Google Scholar S.P. Fekete, J. Schepers, On more-dimensional packing II: bounds, Technical Report 97.289, Universität zu Köln, Germany, 2000. Google Scholar M.R. Garey, D.S. Johnson Computer and intractability, a guide to the theory of np-completeness, Freeman, New York (1979) Google Scholar A. Lodi, S. Martello, M. Monaci The two-dimensional packing problems: a survey European J. Oper. Res., 141 (2002), pp. 3-13 Google Scholar A. Lodi, S. Martello, D. Vigo Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems INFORMS J. Comput., 11 (1999), pp. 345-357 CrossrefView in ScopusGoogle Scholar A. Lodi, S. Martello, D. Vigo, Heuristic algorithms for the three-dimensional bin packing problem, DEIS, University of Bologna, Technical Report OR-00-13, 2000. Google Scholar A. Lodi, S. Martello, D. Vigo Recent advances on two-dimensional bin packing problems Discrete Appl. Math., 123–124 (2002), pp. 373-390 Google Scholar S. Martello, D. Pisinger, D. Vigo The three-dimensional bin packing problem Oper. Res., 48 (2000), pp. 256-267 View in ScopusGoogle Scholar S. Martello, D. Vigo Exact solution of the two dimensional finite bin packing problem Manage. Sci., 44 (1998), pp. 388-399 CrossrefView in ScopusGoogle Scholar Cited by (45) A biased random key genetic algorithm for 2D and 3D bin packing problems 2013, International Journal of Production Economics Show abstract In this paper we present a novel biased random-key genetic algorithm (BRKGA) for 2D and 3D bin packing problems. The approach uses a maximal-space representation to manage the free spaces in the bins. The proposed algorithm hybridizes a novel placement procedure with a genetic algorithm based on random keys. The BRKGA is used to evolve the order in which the boxes are packed into the bins and the parameters used by the placement procedure. Two new placement heuristics are used to determine the bin and the free maximal space where each box is placed. A novel fitness function that improves significantly the solution quality is also developed. The new approach is extensively tested on 858 problem instances and compared with other approaches published in the literature. The computational experiment results demonstrate that the new approach consistently equals or outperforms the other approaches and the statistical analysis confirms that the approach is significantly better than all the other approaches. ### Constraints in container loading-A state-of-the-art review 2013, European Journal of Operational Research Show abstract Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice. In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which – from a practical point of view – need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities. ### TS2PACK: A two-level tabu search for the three-dimensional bin packing problem 2009, European Journal of Operational Research Citation Excerpt : The authors extend the use of dual feasible functions, first introduced by Johnson , to two and three dimensional packing problems, including 3D-SBSBPP. The most recent lower bound, proposed by Boschetti , introduces new dual feasible functions. The derived bound is able to dominate both the bounds by Martello, Pisinger and Vigo and the ones by Fekete and Schepers. Show abstract Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing ones. ### Routing problems with loading constraints 2010, Top ### Extreme point-based heuristics for three-dimensional bin packing 2008, Informs Journal on Computing ### A comparative review of 3D container loading algorithms 2016, International Transactions in Operational Research View all citing articles on Scopus Copyright © 2003 Elsevier B.V. All rights reserved. Recommended articles Bromodomain Histone Readers and Cancer Journal of Molecular Biology, Volume 429, Issue 13, 2017, pp. 2003-2010 Abhinav K Jain, Michelle C Barton ### An iterative dynamic programming approach for the temporal knapsack problem European Journal of Operational Research, Volume 293, Issue 2, 2021, pp. 442-456 F.Clautiaux, …, G.Guillot ### On the discrepancy of circular sequences of reals Journal of Number Theory, Volume 164, 2016, pp. 52-65 Fan Chung, Ron Graham View PDF ### Knapsack problems — An overview of recent advances. Part II: Multiple, multidimensional, and quadratic knapsack problems Computers & Operations Research, Volume 143, 2022, Article 105693 Valentina Cacchiani, …, Silvano Martello ### Multiple bin-size bin packing problem considering incompatible product categories Expert Systems with Applications, Volume 247, 2024, Article 123340 Yu-Chung Tsao, …, Tsung-Hui Chen ### Mathematical models for Multi Container Loading Problems with practical constraints Computers & Industrial Engineering, Volume 127, 2019, pp. 722-733 M.T.Alonso, …, F.Parreño Show 3 more articles Article Metrics Citations Citation Indexes 45 Captures Mendeley Readers 46 View details About ScienceDirect Remote access Contact and support Terms and conditions Privacy policy Cookies are used by this site.Cookie settings All content on this site: Copyright © 2025 Elsevier B.V., its licensors, and contributors. All rights are reserved, including those for text and data mining, AI training, and similar technologies. 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https://physics.stackexchange.com/questions/168142/mass-flow-rate-and-force-on-moving-disk
fluid dynamics - Mass flow rate and force on moving disk - Physics Stack Exchange Join Physics By clicking “Sign up”, you agree to our terms of service and acknowledge you have read our privacy policy. Sign up with Google OR Email Password Sign up Already have an account? Log in Skip to main content Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 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Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Save this post for later Not now Thanks for your vote! You now have 5 free votes weekly. Free votes count toward the total vote score does not give reputation to the author Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges, earn reputation. Got it!Go to help center to learn more Mass flow rate and force on moving disk Ask Question Asked 10 years, 7 months ago Modified6 years, 8 months ago Viewed 2k times This question shows research effort; it is useful and clear 2 Save this question. Show activity on this post. If I understood correctly, the force F F related to a given mass flow rate m˙m˙ through orifice area A A (or, say, on a disk of area A A) is given by Newton's 2nd law of motion - assuming a constant velocity - with F⃗=d d t(m v⃗)=d m d t v⃗=m˙v⃗=ρ A v⃗2 F→=d d t(m v→)=d m d t v→=m˙v→=ρ A v→2 I am wondering what would happen if the area A A itself would be moving with a constant velocity v⃗0 v→0 along the direction of m˙m˙. If we assume v⃗r e l=v⃗−v⃗0 v→r e l=v→−v→0 would it be correct to say F⃗=m˙v⃗r e l=ρ A v⃗v⃗r e l=ρ A(v⃗2−v⃗v⃗0)F→=m˙v→r e l=ρ A v→v→r e l=ρ A(v→2−v→v→0) that is, the mass flow rate is still ρ A v ρ A v but the relative velocity of the disk is v−v 0 v−v 0? Or should it be F⃗=ρ A v⃗2 r e l=ρ A(v⃗2−2 v⃗v⃗0+v⃗2 0)F→=ρ A v→r e l 2=ρ A(v→2−2 v→v→0+v→0 2) that is, the mass flow rate being ρ A v r e l ρ A v r e l? Also, is this mathematically correct? It feels kind of weird to apply the Hadamard/Schur product to the velocity vectors just to obtain another velocity in the same direction. forces fluid-dynamics aerodynamics Share Share a link to this question Copy linkCC BY-SA 3.0 Cite Improve this question Follow Follow this question to receive notifications edited Mar 3, 2015 at 12:17 sunsidesunside asked Mar 3, 2015 at 11:18 sunsidesunside 131 5 5 bronze badges 3 1 Not my area of expertise but I have to believe that in the frame of reference of the disk, only the relative velocity cm can matter. The answer should be independent of frame of reference.Floris –Floris 2015-03-03 12:59:41 +00:00 Commented Mar 3, 2015 at 12:59 That does make sense indeed.sunside –sunside 2015-03-04 04:48:59 +00:00 Commented Mar 4, 2015 at 4:48 1 It is actually the second answer, with relative mass flow that is correct. But your point of departure is questionable: it is an open system and you have to do a careful balance of momentum (Reynolds formula).Vincent Fraticelli –Vincent Fraticelli 2019-01-13 13:32:25 +00:00 Commented Jan 13, 2019 at 13:32 Add a comment| 1 Answer 1 Sorted by: Reset to default This answer is useful 1 Save this answer. Show activity on this post. The second one as the mass flow rate also changes from Relative frame of reference Share Share a link to this answer Copy linkCC BY-SA 4.0 Cite Improve this answer Follow Follow this answer to receive notifications answered Dec 13, 2018 at 1:29 VenkateshVenkatesh 11 1 1 bronze badge 1 2 This could be a potentially good answer, if you fleshed it out a bit.Nephente –Nephente 2018-12-13 08:25:22 +00:00 Commented Dec 13, 2018 at 8:25 Add a comment| Your Answer Thanks for contributing an answer to Physics Stack Exchange! Please be sure to answer the question. Provide details and share your research! 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4097
https://www.aap.org/en/practice-management/bright-futures/bright-futures-family-centered-care/well-child-visits-parent-and-patient-education/bright-futures-information-for-parents-12-month-visit/?srsltid=AfmBOooXdMMEsbYv2sg5QWBo-QXIqzxf9rC6QOwmszQpLrTDjlPJmduN
Internet Explorer Alert It appears you are using Internet Explorer as your web browser. Please note, Internet Explorer is no longer up-to-date and can cause problems in how this website functions This site functions best using the latest versions of any of the following browsers: Edge, Firefox, Chrome, Opera, or Safari. You can find the latest versions of these browsers at Shopping cart Order Subtotal Your cart is empty. Looks like you haven't added anything to your cart. Loading Shopping cart Order Subtotal Your cart is empty. Looks like you haven't added anything to your cart. Loading Bright Futures Information for Parents: 12 Month Visit Here are some suggestions from Bright Futures experts that may be of value to your family.​​ How Your Family Is Doing If you are worried about your living or food situation, reach out for help. Community agencies and programs such as WIC and SNAP can provide information and assistance. Don’t smoke or use e-cigarettes. Keep your home and car smoke-free. Tobacco-free spaces keep children healthy. Don’t use alcohol or drugs. Make sure everyone who cares for your child offers healthy foods, avoids sweets, provides time for active play, and uses the same rules for discipline that you do. Make sure the places your child stays are safe. Think about joining a toddler playgroup or taking a parenting class. Take time for yourself and your partner. Keep in contact with family and friends. Establishing Routines Praise your child when he does what you ask him to do. Use short and simple rules for your child. Try not to hit, spank, or yell at your child. Use short time-outs when your child isn’t following directions. Distract your child with something he likes when he starts to get upset. Play with and read to your child often. Your child should have at least one nap a day. Make the hour before bedtime loving and calm, with reading, singing, and a favorite toy. Avoid letting your child watch TV or play on a tablet or smartphone. Consider making a family media plan. It helps you make rules for media use and balance screen time with other activities, including exercise. Feeding Your Child Offer healthy foods for meals and snacks. Give 3 meals and 2 to 3 snacks spaced evenly over the day. Avoid small, hard foods that can cause choking— popcorn, hot dogs, grapes, nuts, and hard, raw vegetables. Have your child eat with the rest of the family during mealtime. Encourage your child to feed herself. Use a small plate and cup for eating and drinking. Be patient with your child as she learns to eat without help. Let your child decide what and how much to eat. End her meal when she stops eating. Make sure caregivers follow the same ideas and routines for meals that you do. Finding a Dentist Take your child for a first dental visit as soon as her first tooth erupts or by 12 months of age. Brush your child’s teeth twice a day with a soft toothbrush. Use a small smear of fluoride toothpaste (no more than a grain of rice). If you are still using a bottle, offer only water. Safety Make sure your child’s car safety seat is rear facing until he reaches the highest weight or height allowed by the car safety seat’s manufacturer. In most cases, this will be well past the second birthday. Never put your child in the front seat of a vehicle that has a passenger airbag. The back seat is safest. Place gates at the top and bottom of stairs. Install operable window guards on windows at the second story and higher. Operable means that, in an emergency, an adult can open the window. Keep furniture away from windows. Make sure TVs, furniture, and other heavy items are secure so your child can’t pull them over. Keep your child within arm’s reach when he is near or in water. Empty buckets, pools, and tubs when you are finished using them. Never leave young brothers or sisters in charge of your child. When you go out, put a hat on your child, have him wear sun protection clothing, and apply sunscreen with SPF of 15 or higher on his exposed skin. Limit time outside when the sun is strongest (11:00 am–3:00 pm). Keep your child away when your pet is eating. Be close by when he plays with your pet. Keep poisons, medicines, and cleaning supplies in locked cabinets and out of your child’s sight and reach. Keep cords, latex balloons, plastic bags, and small objects, such as marbles and batteries, away from your child. Cover all electrical outlets. Put the Poison Help number into all phones, including cell phones. Call your health care professional if you are worried your child has swallowed something harmful. Do not make your child vomit. What to Expect at Your Child's 15 Month Visit We will talk about: Helpful Resources: Consistent with Bright Futures: Guidelines for Health Supervision of Infants, Children, and Adolescents, 4th Edition The information contained in this webpage should not be used as a substitute for the medical care and advice of your pediatrician. There may be variations in treatment that your pediatrician may recommend based on individual facts and circumstances. Original handout included as part of the Bright Futures Tool and Resource Kit, 2nd Edition. Inclusion in this webpage does not imply an endorsement by the American Academy of Pediatrics (AAP). The AAP is not responsible for the content of the resources mentioned in this webpage. Website addresses are as current as possible but may change at any time. The American Academy of Pediatrics (AAP) does not review or endorse any modifications made to this handout and in no event shall the AAP be liable for any such changes. Last Updated 04/19/2022 Source American Academy of Pediatrics © Copyright 2025 American Academy of Pediatrics. All rights reserved.
4098
https://bestpractice.bmj.com/topics/en-us/217/aetiology
Skip to search Measles infection  Menu Close Overview  Theory  Diagnosis  Management  Follow up  Resources  This topic is available for free Etiology Measles is caused by a spherical RNA virus of the genus Morbillivirus and family Paramyxoviridae. It is relatively large, with an RNA genome. It is related to canine distemper and rinderpest viruses, but measles differs from these 2 viruses because it does not possess specific neuraminidases, and it hemagglutinates while the others do not. Measles virus is heat labile. Humans are the natural host but monkeys can become infected. Laboratory strains can infect mice and hamsters.[Figure caption and citation for the preceding image starts]: Transmission electron micrograph shows the ultrastructural appearance of a single measles virusCenters for Disease Control and Prevention [Citation ends]. Pathophysiology Measles virus is transmitted via person to person contact or via airborne spread of droplets. Virus infects epithelial cells of the nose and conjunctivae, multiplies in these cells, and then extends to the regional lymph nodes. Primary viremia occurs 2 to 3 days after infection, and measles virus continues to replicate in epithelial and reticuloendothelial system tissue over the next few days. Secondary viremia occurs on days 5 to 7, and infection becomes established in the skin and other tissues including the respiratory tract on days 7 to 11. The prodromal phase, which lasts 2 to 4 days, occurs at this time with fever, malaise, cough, coryza, and conjunctivitis. Koplik spots may develop on the buccal mucosa about 1 to 2 days before the rash and may be apparent for 1 to 2 days after rash onset. The rash then develops at about 14 days after infection; at this time virus can be found in blood, skin, respiratory tract, and other organs. Over the next few days, viremia gradually decreases as the rash coalesces and gradually resolves along with the other signs and symptoms. Measles-specific immunoglobulin M antibodies appear at the time of the rash and can be detected up to 2 months after the onset of the rash.Hübschen JM, Gouandjika-Vasilache I, Dina J. Measles. Lancet. 2022 Feb 12;399(10325):678-90. Classification Classification of viruses Genus Morbillivirus, family Paramyxoviridae. Related to canine distemper and rinderpest viruses. Use of this content is subject to our disclaimer Log in or subscribe to access all of BMJ Best Practice Log in or subscribe to access all of BMJ Best Practice Log in to access all of BMJ Best Practice person personal subscriptionor user profileAccess through your institution OR SUBSCRIPTION OPTIONS
4099
https://www.thesaurus.com/browse/affluence
Daily Crossword Word Puzzle Word Finder All games Word of the Day Word of the Year New words Language stories All featured Slang Emoji Memes Acronyms Gender and sexuality All culture Writing tips Writing hub Grammar essentials Commonly confused All writing tips Games Featured Culture Writing tips Advertisement View definitions for affluence affluence noun as in wealth Strongest matches abundance prosperity Strong matches fortune luxury opulence plenty riches wealthiness Discover More Example Sentences Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com. "We see a lot of affluence - a lot of wealth - and that's not something that you see a huge amount on screen in Wales." FromBBC I thought I wanted a piece of all that; not so much the affluence, but the ease with which he moved through the world with money and social strata no deterrence. FromLos Angeles Times The art is revealing more about the affluence of the area where they were found - described by the team as the "Beverly Hills of Roman London". FromBBC Charlotte is always tightly seamed and belted, while Lisa, a filmmaker, wears bright colors and straddles the line between adventurous pop art flair and polished affluence. FromSalon But aesthetically and tonally, whiffs of affluence are in reach for those who want a taste. FromLos Angeles Times Advertisement Discover More Related Words Words related to affluence are not direct synonyms, but are associated with the word affluence. Browse related words to learn more about word associations. abundance nounas in great amount or supply affluence ampleness bounty copiousness fortune myriad opulence plenitude plenty plethora profusion prosperity prosperousness riches thriving wealth copiousness nounas in abundance affluence amplitude bountifulness bounty cornucopia exuberance fullness horn of plenty lavishness luxuriance plentifulness plenty richness superabundance ease nounas in peace, quiet; lack of difficulty affluence ataraxia bed of roses calm calmness comfort content contentment easiness gratification happiness idleness inactivity inertia inertness leisure luxury peace of mind prosperity quietness quietude relaxation repose requiescence rest restfulness satisfaction security serenity supinity tranquility easy street nounas in financial security Elysium Fat City affluence bed of roses clover gracious life hog heaven lap of luxury life of luxury prosperity velvet wealth exuberance nounas in profusion abundance affluence copiousness effusiveness exaggeration excessiveness fulsomeness lavishness lushness luxuriance plenitude plenty prodigality richness superabundance superfluity teemingness Viewing 5/24related words From Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group. Advertisement Advertisement Advertisement