The objectives of the study were multiple: (i) the evaluation of the speed with which the adopted diet leads to the improvement of anthropometric parameters; (ii) the evaluation of the effects induced by different dietary therapies on metabolic and hormonal parameters affecting PCOS patient fitness and reproductive outcomes; and (iii) the evaluation of the incidence of the risk of developing ovarian hyperstimulation syndrome (OHSS) during hormone stimulation aimed at intracytoplasmic sperm injection (ICSI) in obese/overweight patients undergoing diet therapy.


The VLCKD group initially followed the "intensive phase" protocol for 60 days; during this period, patients used substitute foods, such as protein and carbohydrate sources already balanced specifically for this regimen, to which fresh non-starchy vegetables and some accompanying foods (roast chicken and turkey, bresaola, ham, salmon, tuna or swordfish) were added at each main meal.

The substitute foods used for the VLCKD contained plant-based and animal proteins.

Whey protein appears to substantially contribute to the preservation of muscle performance [35].

The sources of plant protein were peas and soybeans.

Regarding the possible harmful effects of soy, all patients accessing the IVF center are screened (breast ultrasound, mammogram, and Papanicolaou test) to diagnose pre-cancerous or cancerous lesions in estrogen-sensitive tissues.

This is because patients who access our center to undergo IVF will undergo hormone therapy (gonadotropins) with significantly increased levels of 17-beta estradiol.

Our study patients, therefore, had no contraindications to soy intake.

Vegetables were divided into unlimited and limited consumption, as described in Table S1.

During the first 3 days, we added medium-chain triglyceride (MCT) oil, which promotes and accelerates entry into ketosis under conditions of glucose restriction and consequently limits the effects of keto-adaptation [36].

The use of MCT oil has been discontinued because ketosis must be generated entirely by the oxidation of the endogenous lipids (excess adipose tissue).

MCT oil was optional according to the clinician's opinion and had the function of speeding up the patients' entry into ketosis.

Evaluation of the entry into ketosis was assessed by test strips for the measurement of ketone bodies in urine.

The consumption of fruit juices, sugary drinks, and alcohol was forbidden.

A maximum of 2 tablespoons of EVO per day was allowed.

The use of vinegar, pepper, lemon, and spices was possible.

The consumption of at least 2 L of water per day was strongly recommended.


Other supplements, explained in Table S2, were optional according to the clinician's opinion and doses were administered via 2 daily sachets.

Supplements were prescribed to all patients, under the recommendation of the nutritional biologist and the gynecological surgeon, because the VLCKD's limited intake of fruits and vegetables does not cover the daily requirement of vitamins and minerals.

In addition, the intake of magnesium and potassium helped to avoid muscle cramps, which are one of the possible side effects of the VLCKD.

The daily low-calorie intake was 800 kcal; nutrient intakes were 20% carbohydrates (25 g), 50% protein (67 g), and 30% lipids (50 g).

The nutrition plan was divided into 4 meals, schematized in Table S3: breakfast (20% kcal daily), lunch (35% kcal daily), snack (10% kcal daily), and dinner (35% kcal daily).

Tables S4-S7 show the nutritional information panels of the substitute foods.


To preserve the results obtained, the VLCKD's intensive phase was followed by a 30-day transition period in which there was an increase in daily kcal in the VLCKD group.

The daily calorie intake was 800 kcal from Monday to Friday, 1300 kcal on Saturday, and 1400 on Sunday.

The type of diet in this phase was a hypocaloric Mediterranean regimen with 4 meals per day: breakfast, lunch, snack, and dinner (schematized in Table S3).


The Mediterranean group consisted of patients who preferred to adhere to traditional nutritional education.

The diet therapy was a low-calorie Mediterranean regimen, in which the daily calorie intake was 1400 kcal for 90 days.

The composition was 55% carbohydrates (10% simple ones), 15% proteins, and 30% lipids.

The nutrition plan was divided into 5 meals (schematized in Table S3): breakfast (20% kcal daily), snack (10% kcal daily), lunch (30% kcal daily), snack (10% kcal daily), and dinner (30% kcal daily).

Rice and pasta were allowed twice a week.

The higher calorie intake in this diet is due to the lack of the appetite suppressant effect that can be achieved with the VLCKD regimen.


Parameters were collected by the staff of the UOC of Reproductive Pathophysiology and Andrology.

The UOC deals with infertile couples from the diagnostic stage to the therapeutic indication and to the performance of the IVF technique.

Diagnosis of this syndrome occurs during preliminary meetings, which then lead to the decision to possibly perform an IVF technique.

In the case of overweight/obese PCOS patients, during the first medical examination, a routine assessment of anthropometric indices and metabolic parameters is performed, because eventual alterations in them could be associated with the syndrome.

During counseling, the patient is made aware of the worsening effects of overweight/obesity on PCOS itself, on the success of IVF, and on the complications that can occur during hormonal stimulation aimed at IVF and on pregnancy (adverse effects on the pregnant woman, the fetus, and later on the newborn) [1,21,22].

Therefore, the patient may decide to embark on a nutritional course aimed at BMI normalization.

Data related to the IVF cycle (hormonal stimulation, follicle development, hormone dosages of estradiol and progesterone during stimulation, the development of an OHSS risk condition, the number and quality of retrieved oocytes) are recorded in the couple's medical record.


From this database, the patients were recruited to the study.

Recruitment took place after the positive response of the Ethical Committee of the Asl Roma 2 hospital company on 5 July 2022.

At this point, the use of the data was authorized and the diet therapies were proposed to patients.


Statistical analyses of the obtained parameters were performed with the Statistics Kingdom (2017) software and GraphPad Prism 9.2.0.

Ordinal variables are presented as mean ± standard deviation (SD), while categorical variables are described as absolute frequencies.

The normal distribution of data was checked with the Shapiro-Wilk test.

For comparison between two groups, we performed the t test for normal data and the Mann-Whitney test for non-normal data.

The χ 2 test with a p-value of 0.05 was used for parameters with categorical variables.

The statistical significance threshold was set to 0.05.


Anthropometric measurements, as shown in Figure 1, revealed a greater BMI loss (13.16 ± 7.37 kg/m 2 in 90 days, 17.03 ± 8.79 kg/m 2 in 120 days) in PCOS patients undergo- ing VLCKD than in PCOS patients undergoing the Mediterranean diet (7.29 ± 5.41 kg/m 2 in 90 days, 8.94 ± 6.28 kg/m 2 in 120 days) (p value < 0.0001 in 90 and 120 days, re- spectively, t test and Mann-Whitney test).

The difference in BMI loss, according to the two treatments, can also be found in particular anthropometric indices, such as waist (9.20 ± 6.31 cm in 90 days and 12.27 ± 8.13 cm in 120 days for VLCKD; 4.14 ± 3.82 cm in 90 days and 5.10 ± 4.71 cm in 120 days for Mediterranean; p value < 0.0001 for both, Mann-Whitney test), hip (8.85 ± 6.81 cm in 90 days and 10.90 ± 8.20 cm in 120 days for VLCKD; 4.65 ± 3.63 cm in 90 days and 5.87 ± 4.79 cm in 120 days for Mediterranean; p value < 0.0001 in 90 days and p value < 0.001 in 120 days, Mann-Whitney test), and abdomen circumferences (8.23 ± 6.64 cm in 90 days and 11.05 ± 8.80 cm in 120 days for VLCKD; 4.31 ± 3.38 cm in 90 days and 5.48 ± 4.02 cm in 120 days for Mediterranean; p value < 0.001 in 90 days and p value < 0.05 in 120 days, Mann-Whitney test), and WHR (0.02 ± 0.06 in 90 days and -0.03 ± 0.07 in 120 days


The metabolic profile seemed to vary according to the diet therapy: after VLCKD therapy, as shown in Figure 2, cholesterol and triglyceride levels and the HOMA index decreased, while HDL levels increased.

Cholesterol levels decreased more in VLCKD patients (−16.10 ± 21.02 mg/dL in 90 days; −25.81 ± 30.07 mg/dL in 120 days) than in Mediterranean diet patients (−9.43 ± 18.19 mg/dL in 90 days; −15.29 ± 21.62 mg/dL in 120 days; p value < 0.05 for both, Mann-Whitney test).


In contrast, triglyceride levels appeared to decrease more in the VLCKD group only at 90 days (−17.05 ± 24.23 mg/dL in VLCKD, −13.57 ± 36.30 mg/dL in Mediterranean; p value < 0.05, Mann-Whitney test), whereas, at 120 days, there appeared to be no statisti- cally significant difference.


A greater increase in HDL levels was observed at 120 days in VLCKD patients (4.87 ± 8.59 mg/dL) than in Mediterranean diet patients (7.08 ± 8.79 mg/dL) (p value < 0.05, t test).


Moreover, the HOMA index decreased more in VLCKD patients (−1.45 ± 1.31 in 90 days; −1.47 ± 2.41 in 120 days) than in Mediterranean diet patients (−0.33 ± 1.60 in 90 days; 0.26 ± 3.08 in 120 days; p value < 0.001 at 90 days and p value < 0.05 at 120 days, t test for both).


Regarding the hormone profile, no statistically significant differences were observed, after 90 and 120 days of treatment, in serum variations in the concentration of FSH (1.04 ± 2.03 mUI/mL in 90 days and 1.60 ± 2.70 mUI/mL in 120 days for VLCKD; 0.37 ± 1.81 in 90 days and 0.65 ± 2.00 mUI/mL in 120 days for Mediterranean; p value > 0.05, t test) and LH (−0.84 ± 3.72 mUI/mL in 90 days and −1.40 ± 5.12 mUI/mL in 90 days for VLCKD; −0.94 ± 2.87 mUI/mL in 90 days and −0.81 ± 3.24 mUI/mL in 120 days for Mediterranean; p value > 0.05, Mann-Whitney test).

However, the FSH/LH ratio showed a statistically significant difference as a function of treatment at 120 days (0.47 ± 0.96 in VLCKD patients, 0.15 ± 0.48 in Mediterranean patients; p value < 0.05, Mann-Whitney test), but not at 90 (0.20 ± 0.56 in VLCKD pa- tients, 0.11 ± 0.46 in Mediterranean patients; p value > 0.05, t test).

The same trend was exhibited by the levels of 17-alpha-hydroxy-progesterone (−0.20 ± 0.64 ng/mL in 90 days and −0.36 ± 0.75 ng/mL in 120 days for VLCKD; −0.01 ± 0.34 ng/mL in 90 days and −0.07 ± 0.35 ng/mL in 120 days for Mediterranean; p value < 0.05 in 120 days, Mann- Whitney test).


In contrast, AMH levels appeared to change as a function of the diet therapy at 90 days (−1.79 ± 2.05 ng/mL for VLCKD and −0.92 ± 1.61 ng/mL for Mediterranean; p value < 0.05, t test) but not at 120 (−2.23 ± 2.28 ng/mL for VLCKD and −1.38 ± 2.05 ng/mL for Mediter- ranean; p value < 0.05, t test).


Estradiol levels, on the other hand, did not appear to alter according to the diet therapy followed by the patients at either 90 (1.08 ± 21.78 pg/mL in VLCKD, −0.45 ± 25.25 pg/mL in Mediterranean; p value > 0.05, t test) or 120 days (8.06 ± 28.08 pg/mL in VLCKD, 5.22 ± 32.89 pg/mL in Mediterranean; p value > 0.05, t test).

Interesting results, shown in Figure 3, were obtained at both 90 and 120 days of diet ther- apy in terms of androstenedione (−0.54 ± 0.47 ng/mL in 90 days and −0.73 ± 0.60 ng/mL in 120 days for VLCKD; −0.27 ± 0.50 ng/mL in 90 days and −0.19 ± 0.87 ng/mL in 120 days for Mediterranean; p value < 0.5, t test for both) and testosterone levels (−0.40 ± 0.49 nmol/mL in 90 days and −0.62 ± 0.78 nmol/mL in 120 days for VLCKD; −0.03 ± 0.36 nmol/mL in 90 days and −0.12 ± 0.48 nmol/mL in 120 days for Mediterranean; p value < 0.001, t test at 90 days, p value < 0.05, Mann-Whitney test) and antral follicle count (AFC) (−4.31 ± 3.23 in 90 days and −5.98 ± 4.16 in 120 days for VLCKD, −1.95 ± 2.45 in 90 days and −2.95 ± 3.10 in 120 days for Mediterranean; p value < 0.001, t test for both times).


Considering the change in menstrual regularity condition in PCOS patients after 90 and 120 days of the VLCKD and Mediterranean diet, a statistically significant difference was observed regarding the percentages of improvement from the initial condition in 90 (p value < 0.05, χ 2 test) and 120 days (p value < 0.001, χ 2 test).


As shown in Figure 4A, VLCKD treatment resulted in an improvement from the initial condition in 50% and 71% of cases, respectively, in 90 and 120 days; there was no change from the initial condition in 50% and 29% of cases, and a worsening condition was not observed in any of the patients under study.

In contrast, Mediterranean diet therapy resulted in an improvement from the initial situation in 17% and 26% of cases, respectively, in 90 and 120 days; in no change in 81% and 71%; and in a worsening condition in 2% of cases.


In addition, both the success and failure of the treatment concerning the menstrual parameter were evaluated.

As success was considered for any patient who, after 90 and 120 days from the start of treatment, presented a condition of regularity or irregularity (but starting with the amenorrhea condition); as failure, we considered a condition of amenorrhea or irregularity (starting from a pre-existing condition of irregularity).

Again, a statistically significant difference was observed in the effect on the success and failure rates obtained following the two diet therapy treatments at both times (p value < 0.05 in 90 days, p value < 0.0001 in 120 days, χ 2 test).

As shown in Figure 4B, the ketogenic diet treatment resulted in a success rate of 74% in 90 days and 95% in 120 days, while the Mediterranean diet treatment resulted in a success rate of 48% in 90 days and 59% in 120 days.


An analysis of the risk of developing OHSS in PCOS patients according to treatment revealed a statistically significant difference: as shown in Figure 5, patients who followed the VLCKD had a 27% risk rate of OHSS, while patients who followed the Mediterranean diet had a 68% risk rate of OHSS (p value < 0.05, χ 2 test).

None of the patients developed thromboembolic complications during stimulation.


Overweight/obesity and PCOS influence each other, probably also due to an increase in obesity-related inflammatory factors [16].

We evaluated the changes in anthropometric parameters as a function of different diet therapies, to determine the implications for the patient's reproductive health.

In the context of IVF, the time factor is essential, because female fertility progressively decreases as age increases.

Therefore, the time range in which the results are obtained is a key element.

Our data indicate that both the Mediterranean diet and VLCKD showed interesting results regarding an improvement in anthropomet- ric parameters.


Specifically, the VLCKD in PCOS patients appeared to lead to better anthropometric outcomes in a reduced time, particularly in those areas where central adiposity was con- cerned.

As we hoped, these improvements were mainly concentrated in the BMI, WHR, and abdomen, waist, and hip circumferences.

The BMI, while not a direct measure of adiposity, does provide a practical means to estimate body fat mass.

Anthropometric indices, such as WC and WHR, estimate the body composition and, in particular, the visceral fat [37].

Thus, BMI, WC, and WHR represent a sufficiently reliable estimate of the body fat distribution that is non-invasive, low-cost, repeatable, and easy to measure.

The gold standards for the quantification of visceral fat are magnetic resonance, computed tomography, dual-energy X-ray absorptiometry (DXA), and bioimpedance, but the equipment is not available in every hospital facility [38-42].


The results of the VLCKD can be attributed to the reduced calorie intake, which is possible because of the satiating effect of protein and the appetite suppression induced by ketosis [41,43].

Several pieces of evidence show that the VLCKD is characterized by a protective effect toward muscle mass, and different mechanisms have been proposed to support this theory: increased adrenergic stimulation, the braking effect of ketone bodies on muscle protein breakdown, and the stimulation of muscle protein synthesis due to increased growth hormone (GH) and protein intake from the diet.

De- spite this, the study, focusing only on the assessment of anthropometric parameters, does not allow us to exclude that the increased loss of mass is caused by the loss of muscle mass and/or fat mass [44-46].

However, it must be emphasized that all anthropometric parameters had a non-negligible standard deviation.

This could be due to the differences in the adherence of patients to the dietary regimens, but it represents a major limitation of this study.

The future implementation of a sample unit could resolve this issue.


The results obtained with the VLCKD, and, to a lesser extent, the Mediterranean diet, suggest that these nutritional approaches lead to weight reduction and to an improvement in the condition of central adiposity within a very narrow time range.

Obesity represents a state of chronic inflammation, which can lead to the development of insulin resistance [47].

The VLCKD allows patients to tolerate a very low amount of kcal.

However, the difference in this dietary pattern, which makes it more suitable for women suffering from PCOS, is in the distribution of nutrients, with a greater intake of proteins compared to carbohydrates.


A loss of central metabolically active fat could therefore lead to a break in the typical vicious cycle of PCOS.

Our results show that greater weight loss, and thus greater visceral fat loss, is accompanied by a significant improvement in the metabolic profile in VLCKD PCOS patients.

The improvement in the metabolic profile (increase in HDL and decrease in triglycerides, cholesterol, and HOMA index) achieved following the VLCKD could lead to an interruption in the vicious cycle of pathological events associated with PCOS, or at least to its reduction.

The latter seems to be effectively reflected in the marked improvement in the reproductive health of PCOS patients during IVF preparation.


In fact, the VLCKD seems to be related to an improvement in reproductive health (menstrual regularity, lower AFC, and reduced risk of developing OHSS) in PCOS patients, due to the modification of key metabolic pathways, as reported in a recent study [48].

Restoring menstrual regularity is very important for the less complicated management of the patient's ovulation and, at the same time, allows the possibility of intervention through targeted intercourse.

Meanwhile, decreasing AFC and the risk of developing OHSS allows the easier and safer management of the patient during hormonal stimulation, aimed at IVF.

The VLCKD-induced reduction in the risk of OHSS is likely due to the lowered antral follicle count, which, together with PCOS, is a risk factor for the development of the syndrome.

Furthermore, we draw attention to the fact that none of the patients developed thromboembolic complications during stimulation.

This was linked, in addition to the reduction in body weight, to the careful screening to which we subject all our patients before starting therapy aimed at IVF.


The increased safety profile could be related to the improved hormonal sexual profile following the VLCKD.

Abdominal obesity in PCOS patients seems to be co-responsible for the development of hyperandrogenism due to the insulin-mediated overstimulation of ovarian steroidogenesis [7].

In our study, the increased weight loss in VLCKD PCOS patients was indeed accompanied by an increased FSH/LH ratio and decreased androstene- dione and testosterone levels.

Regarding the AMH value, our data showed a reduction in the value with the VLKCD diet, but these data are in contrast with a previous work [49].

This difference might be caused by the distinct populations examined; in particular, our group was only composed of PCOS patients, who usually present higher values of AMH, with respect to the obese patient group in the other work, which was not investigated regarding the PCOS condition.


Moreover, our results are in accordance with a recent study by Magagnini et al., in which VLKCD patients showed a significant reduction in BMI, WC, the HOMA index, and serum AMH levels, as was the case in our cohort of VLKCD patients [50].

These results might be explained also by the positive impact of the polyunsaturated fatty acid compo- sition presented in both diets.

Such fatty acids can stimulate carbohydrate metabolism and insulin sensitivity, improving the BMI, HOMA index, and metabolic-hormonal profile, leading to lower lipogenesis and a reduced inflammation status [51].

Despite this fact, we did not analyze specifically the contribution of fatty acids during weight reduction; the amount of fatty acids included are presented in additional Tables S4-S7.


Our data confirm the VLCKD diet as an optimal choice for preparation for entry into IVF, especially because of the time range in which these results are achieved and in relation to the patient's safety and health.

The results could be due to the loss of lean and/or fat mass, changes in some endocrinological and metabolic parameters, and/or a decrease in inflammatory status [8,24].

Indeed, the VLCKD group showed greater weight and BMI loss, particularly in those body areas where central adiposity is concentrated.

Due to the low glycemic load, the VLCKD may improve hyperglycemia, insulin sensitivity, dyslipidemia, and blood pressure, resulting in a reduction in inflammatory status [52].

In fact, lower carbohydrate intake, which is possible in the VLCKD diet but not in the Mediterranean diet, results in reduced inflammation and oxidative stress.

Simple carbohydrates result in the de novo synthesis of simple fatty acids, leading to both lipotoxicity and hyperinsulinemia.

This results in the nuclear translocation of NF-kB, the extracellular release of proinflammatory mediators from macrophages, and, finally, systemic insulin resistance, resulting in systemic inflammation.

Indeed, in a high-fat diet, as demonstrated in a mouse model, obesity triggers inflammation in the adipose tissue, leading to organ damage, such as hepatic inflammation [53].


Thus, the relationship between the inflammatory state and IR is caused by the action of proinflammatory cytokines released by macrophages in the adipose tissue, which block the action of insulin in various tissues, including the adipose tissue, liver, and skeletal muscle.

The enhancement in hyperinsulinemia could have several favorable effects on re- productive function because (i) it has both direct and indirect effects on the folliculogenesis and steroidogenesis of granulosa and theca cells driven by intraovarian gonadotropins and (ii) it results in a more favorable biochemical environment in the ovaries [24,25].

Thus, weight/BMI loss induces both a decrease in the inflammatory state and an improvement in IR.

This could regulate both hormonal imbalance and ovarian function.

Thus, addressing the obesity/overweight condition could lead to a decrease in the risk of abortion, gesta- tional diabetes mellitus, pregnancy-induced hypertension, preeclampsia, and poor infant outcomes [1,6,7].

Therefore, VLCKD diet therapy in obese/overweight PCOS patients could decrease both infertility problems and gestational and/or neonatal complications.


In addition, the drastic body change has a noticeable effect on the patient's degree of satisfaction.

Indeed, all patients in both groups adhered to the diet regimens for the whole study period of 120 days and none of them reported side effects or complaints, and this may favor the maintenance of an appropriate lifestyle.


The importance of pre-pregnancy nutritional strategies must be evaluated considering the worldwide trend of increasing obesity, which today can be considered a global epi- demic [8,10,17].

This trend could lead to an increase in both the incidence and severity of PCOS.

Considering that the onset of the syndrome occurs in adolescence and the increased incidence of obesity is mainly found in childhood, these issues need to be evaluated to avoid the exacerbation of the symptomatology typical of PCOS.

Fortunately, lifestyle changes improve metabolic abnormalities and symptomatology [2,3].


Hence, the Mediterranean diet could be an optimal nutritional education strategy, as well as the VLKCD, which, in a previous study, was shown to be more effective than a standard low-calorie diet [54].

Despite this, a "fertility diet" has not been yet identified.

This is because each person has a unique genome, proteome, metabolome, microbiome, and exposome, and the aim of future studies and nutritional strategies will be toward personalized medicine and nutritional support, tailored to individual features.


However, we chose these two dietary regimens because they represent key strategies in obese/overweight patients, especially those suffer- ing from PCOS, who have higher reproductive risks, as well cardiovascular and metabolic conditions, such as diabetes.

The focus of the present study was not to emphasize one diet with respect to another, but to underline how different nutritional approaches can increase the likelihood of restoring fertility and lead to the success of IVF in obese/overweight PCOS patients.

Indeed, weight reduction leads to better reproductive performance and is functional for a healthy pregnancy in such patients [8].


The results obtained with the different nutritional therapeutic approaches, particularly the improvements after only 120 days of treatment, are very interesting.

The purpose of this study was to achieve weight loss in the shortest possible period, prior to IVF in patients affected by PCOS.

Patients who attend an IVF center aim to achieve pregnancy, in most cases after years of unsuccessful attempts.

Indeed, the proposal of long-term diet therapy could result in a high drop-out rate.

In addition, for reproductive purposes, the patient's age is crucial, and a greater patient age is counterproductive to the IVF program.

Therefore, a dietary regimen that achieves a BMI compatible with access to IVF therapy in the short term (at our center, BMI < 30 kg/m 2 ) results in greater patient compliance and is more suitable for the needs of an IVF center.

As a result, the advantage of the VLCKD has been demonstrated from the perspective of the short time range in which the results are obtained; as reported by the American Society for Reproductive Medicine recently, the health benefits of postponing pregnancy (and IVF) to achieve weight loss must be balanced against the risk of declining fertility with advancing age.

In addition, the VLCKD's side effects (headache, muscle cramps, asthenia, and halitosis) were transient, moderate, and well tolerated [55].


An important outcome, concerning women's health during IVF treatment, is the significant reduction in the risk of developing OHSS in VLCKD patients, compared with Mediterranean diet patients.

This result could be related to the reduction in AFC and to the greater weight loss in such patients.

However, the link between obesity/overweight and an increased risk of developing OHSS is still controversial [56,57].

Future works will be needed to clarify the molecular mechanisms modified by diet interventions that lead to improved symptomatology and reproductive success.

In addition, weight loss positively impacts thrombotic risk up to the entire first trimester of pregnancy, as well as the risk of obstetric, neonatal, and postnatal complications and metabolic diseases [58-62].


Our data confirm that weight and BMI reduction results in improved fertility.

Al- though the decision to postpone IVF treatment to allow weight loss often results in increased maternal age in patients who are no longer very young, a dietary approach, such as the VLCKD, allows them to achieve a better outcome in the shortest possible time.


The following abbreviations are used in this manuscript:


We read with great interest the recent article by Meneghini et al. on the assessment of the effects of different alimentary regimens, included Mediterranean diet (MD), on polycystic ovary syndrome (PCOS) patients prior to in vitro fertilization cycles [1].

Lifestyle changes, focused on healthy diet, have been reported as the first-line approach in the management of PCOS, with the primary aim to normalize metabolic features and to restore the reproductive profile [2].

Data from the literature suggest that MD may be useful in the prevention and in the management of gonadal disorders [3].

These beneficial effects could be related to antioxidant properties of MD and its high rate of fruits, vegetables, whole grains, and heart-healthy fats [4].

Additionally, MD eliminates processed meats, saturated fats, and refined sugar, which worsen systemic inflammatory status [4].

Recently, scientific interest in antioxidant-rich foods has increased, as epidemiology has shown an inverse relationship between the adoption of a diet rich in nutraceuticals and the onset of metabolic disorders [5].

MD is a complete alimentary model characterized by the richness of natural compounds, with different biological activities such as phenols, flavonoids, and sterols.


In healthy subjects, several trials have shown the efficacy of healthy diet in gene expression and metabolic pathways, suggesting that the inflammatory status reflects the antioxidant properties of foods [5].

In this context, metabolic diseases, including PCOS, show altered pathways of oxidative stress [6].

For this reason, it is necessary to identify therapeutic strategies that contemplate the use of personalized diet rich in antioxidants as MD.

Polyphenols are heterogeneous plant-derived molecules that include several hydrosoluble antioxidants commonly used in the maintenance of good health and the prevention of different metabolic conditions [7].

Currently, there is an increasing volume of evidence on the effects of food rich in polyphenols on PCOS and its accompanying metabolic features such as insulin resistance, lipid profile impairment, inflammation, and oxidative stress [8].

In recent years, our group have confirmed the role of MD in body fat mass reduction and the improvement of lipid profile and insulin resistance parameters [9].

Furthermore, the synergic effect of MD and a healthy lifestyle has been evaluated in patients with liver steatosis, with a significant reduction in or regression of hepatic fat accumulation and improvement of liver enzyme levels and anthropometric parameters [10].


Supported by our data and according to Meneghini et al., we can conclude that MD associated with healthy lifestyle changes is a useful approach to normalize metabolic features in patients with metabolic syndrome or PCOS.

We support the use of MD as a treatment and as a preventive measure to improve the clinical management of these subjects.

However, more large randomized clinical trials are needed to confirm these data.


Thanks for your comment [1].

In our work, we have stated that the Mediterranean diet is an indisputable cornerstone of nutrition which certainly leads to an improvement in the patient’s overall state of health [2].

However, our objective was to demonstrate that a VLCKD represents a valid alternative that allows patients to achieve their goals in a shorter period (120 days) and then proceed to medically assisted procreation (PMA).


Furthermore, after the intensive phase, our patients reintegrate a low-calorie Mediterranean diet during pregnancy.

This further demonstrates that we hold the Mediterranean diet in high regard.

We are continuing to recruit patients, and therefore our sample is destined to become larger.

We thank you for the attention that has been paid to our work and for your valuable suggestions.


This article provides an overview of the conceptual structure of the 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) and references to additional articles that descriie the computational implementation of this structure.

In~the 1996 WIPP PA provides the primary numerical results used in the 1996 compliance certification application (CCA) by the U.S. Department of Energ' (DOE) to the U.S. Environmental Protection Agency (EPA) for the certification of the WIPP for the disposal of transuranic (TRU) waste.l


Perfo~ce assessmen t for the WIPP began shortly after the EPA promulgated its standard for the geologic (i.e., deep underground) disposal of radioactive waste, Environmental Radiation Prelection Standards for the Management and Disposal of Spent Nuclear Fuel, High-Level and Transuranic Radioactive Wastes (40 CFR 191)-Z 3 In particular, PAs were carried out for the WIPP in 1989 (Refs.

4- 6), 1990 (Ref. 7), 1991 (Ref. 8), and 1992 (Ref. 9), with summaries of the 1991 and 1992 PAs available in the journal literature. ]' 12 In gene@ each PA was more sophisticated than its predecessors as more insights were gained about the WIPP and the appropriate organization of a PA for the WIPP (see Ref.

13 for a history of the development of the WIPP).


A system prioritization methodology (SPM) was applied to the WIPP in 1994 (Refs.

14- 16) and 1995 (Refs. 17- 19).

The SPM was a specialized PA intended to provide guidance to the WIPP project on experimental programs and design modifications to support as part of the DOE's development of the WIPP.


The conceptual stmcture of the 1996 WIPP PA emerged horn insights gained in the earlier analys~s and also from the req u&meiNs imposed by the EPA's standard for the geologic disposal of radioactive waste.20* 21 Preliminary descriptions of this structure appear in a sequence of conference papers prepared at various points in the development of the 1996 WIPP PA (Refk 22- 24).

The conceptual structure of the 1996 WIPP PA is also covered in varying levels of detail in several recent journal articles2$27 &d is repeated here as a convenience for the readers of the special issue of Reliability Engineering and System Safety describing the 1996 WIPP PA of which this article is a part.

Inclusion of this material in the special issue facilitates describing the 1996 WIPP PA and identi&ing the articles in the issue that provide detailed information on the individual parts of the analysis.


This article derives fi-om Chapt.

2 of Ref. 28 and is organized as follows.

Firs+ a brief overview of the EPA regulations that influence the conceptual structure of the 1996 WIPP PA is given (Sect. 2).


Them the three basic conceptual entities that underlie the PA are discussed: a probabilistic characterization of what could occur at the WIPP over the next 10,000 yT (Sect. 3); a procedure for estimating radionuclide releases to the accessible environment associated with each of the possible futures that could occur at the WIPP over the next 10,000 yr (Sect.

4); and a probabilistic characterization of the uncertainty present in the characterizations of the two preceding entities (Sect. 5)-


A discussion of the 1996 WIPP P.4 in the context of other analyses for complex systems is provided (Sect. 6). and finally, the article ends with a concluding discussion (Sect. 7).


The conceptual structure of the 1996 PA for the WIPP derives from the regulatory requirements imposed on this facility.zo~21J 29 The primary regulation dete rmining this structure is the U.S. EPA's standard for the geologic disposal of radioactive waste (40 CFR 191).

The following is the central requirement in 40 CFR 191 and the t of the conceptual structure of the 1996 WIPP PA (p. 38086, Ref. 2): primary determinant $191.13 Containment requirements:


(a) Disposal systems for spent nuclear fuel or high-level or trammmic radioactive wastes shall be designed to provide a reasonable expectation, based upon performance assessments, that cumulative releases of radionuclides to the accessl%le environment for 10,000 years after disposal horn all significant processes and events that may affect the disposal system shalk -;


(1) Have a likelihood of less than one chance in 10 of exceeding the quantities calculated according to Table 1 (Appendix-4); and . ..


(2) Have a likelihood of less than one chance in 1,000 of exceeding ten times the quantities calculated according to Table 1 (Appendix A).


(b) Performance assessments need not provide complete assurance that the requirements of 191. 13(a) wdl be met.

Because of the long time period involved and the nature of the events and processes of interest there will inevitably be substantial uncertainties in projecting disposal system performance.


Proof of the future performance of a disposal system is not to be had in the ordinary sense of the word in situations that deal with much shorter time ties.

Instea& what is required is a reasonable expectatio~on the basis of the record before the implementing agency, that compliance with 191. 13(a) will be achieved.

M Containment Requirement 191 .13(a) refers to "quantities calculated according to Table 1 (Appendix A)," which means a normalized radionuclide release to the accessible environment based on the type of waste being disposed OK the initial waste inventory, and the release that takes place (App.

A, Ref. 2).


Table 1 (Appendix A) specifies allowable releases (i.e., release limits) for individual radionuclides and is reproduced as Table 1 of this presentation.

The WIPP is intended for transuranic waste, which is defined to be "waste containing more than 100 nanocuries of alpha-emitting transuranic isotopes, with half-Iives greater than twenty years, per gram of waste" (p. 38084, Ref. 2).

Specifically, R=~i where Qi is the normalized release R for transuranic waste is defined by ()( o ) lx106Ci/C, (1) 1 the cumulative release of radionuclide i to the accessible environment during the 10,000-yr period following closure of the repository (Ci), Li is the release limit for radionuclide i given in Table 1 (Ci) and C is the amount of transuranic waste emplaced in the repository (Ci).

In the 1996 WIPP PA, C = 3.44 x 106 Ci (Refs. 30, 31).

Further, accessible environment means ( 1) the atmosphere, (2) land surfaces, (3) surface waters, (4) oceans, and (5) all of the lithosphere that is beyond the controlled are% and controlled area means ( 1) a surface location, to be identified by passive institutional controls, that encompasses no more than 100 square kilometers and extends horizontally no more than five kilometers in any direction from the outer boundary of the original location of the radioactive wastes in a disposal system and (3) the subsurface underlying such a surface location.


To help clarify tbe intent of 40 CFR 191, the EPA ako published 40 CFR 194, Criteria for tize Certi~cation and Recerh~cation of the Waste Isolation Pilot Plant's Compliance with 40 CFR Part 191 Disposal Regulations; Final Rule (Ref 32).

There, the following elaboration on the intent of 40 CFR 191.13 is given (pp. 5242-5243, Ref 32): $194.34 Results of performance assessments.

When viewed at a high level,, three basic entities (ENl, EN2, EN3) underlie the results required in 191.13 and 194.34 and ultimately determine the conceptual and computational structure of the 1996 WIPP PA ENI, EN2, EN3, Together, a probabilistic characterization of the likelihood of different futures occurring at the WIPP site over the next 10,000 yr, a procedure for estimating the radionuclide releases to the accessible environment associated with each of the possible fkures that could occur at the WIPP site over the next 10,000 yr, a probabilistic characterization of the uncertainty in the parameters used in the deftition of EN 1 and EN2.


EN1 and EN2 give rise to the CCDF specified in 191.13(a) (Fig. 1), and EN3 corresponds to the distributions indicated in 194.34(b).


The preceding entities arise from an attempt to answer three questions about the WIPP, Q1:


What occurrences could take place at the WIPP site over the next 10,000 yr?


In the 1996 WIPP PA EN1 provides answers to Q1 and Q2, EN2 provides an answer to Q3, and EN3 provides an answer to Q4.

The mtnre of EN 1, EN2 and EN3 and the role that they play in the 1996 WIPP PA are elaborated on in"ibe next three sections.


The entity EN 1 is the outcome of the scemrio development process for the WIPP34 and provides a probabilistic characterization of the likelihood of different futures that could occur at the WIPP site over the next 10,000 yr, with the period of 10,000 yr specified in 40 CFR 191.

When viewed formally, EN1 is defined by a probability space (S~l, .l,p~z), with the sample space S,l given W u S~, = {X$,: X,l is a possible 10,000 yr sequence of occurrences at the WKPP}. ( 2) The subscript st refers to stochastic (i.e., aleatory) uncertainty and is used because (S~t,~~,, p,l) is providing a probabilistic characterization of occurrences that may take place in the fiture.

As a reminder, a probability space (S,~, p) consists of three components: a set S that contains everything that could occur in the particular %niverse" under consideratio~a suitably restricted set J of subsets of S, and a fimction p defined for elements of~that actually defines probability (Sect.

IV.4, Ref. 36).

In the terminology of probability theory, S is the sample space, the elements of S are elementary events, the subsets of S contained inã re events, and p is a probability measure.

In most applied problems, the fimction p defined on~is replaced by a probability density fimction (PDF) d.


The scenario development process for the WIPP identified exploratory drilling for natural resources as the only disruption with sufilcient likelihood and consequence for inclusion in the deftition of EN I (App. SC~Ref.

1; Ref. 34).

In addition, 40 CFR 194 specifies that the occurrence of mining within the land withdrawal "boundary must be included in the analysis.

As a resul~the elements x~, of S~f are vectors of the form x~, =[tl, 11,el,~, PI, al, t2, 129e2y h7 P2Y a27 -"-ytn, In, en, /ln, pn, an, t~i~] (3)~I St inhusion 2nd intrusion Jh inm~ion in the 1996 WIPP PA where n is the number of drilling intrusions, ti is the time (yr) of the $h intrusior& Ii designates the location of the Z* intrusion, ei designates the penetration of an excavated or nonexcavated area by the $h intnzsio% bi designates where or not the Zth intrusion penetrates pressurized brine in the Castile FormatiorL pi designates the plugging procedure used with the # intrusion (i.e., cozztirnzous plug, two discrete plugs, three discrete plugs), ai designates the type of waste penetrated by the Z* intrusion (i.e., no waste, contact-handled (CH) waste, remotely-handled (RI-I) waste), and tmin is the time at which potash mining occurs within the land withdrawal boundary.

In the development of (S~t,~.{, p.l), the probabilistic characterization of n, ti, Ii and ei derives from the assumption that drilling intrusions occur zandomly in time and space (i.e., follow a Poisson process), the probabilistic characterization of bi derives from assessed properties of brine pockets, the probabilistic characterization of ai derives from the properties of the waste to be emplaced at the WIPP, and the probabilistic characterization of pi derives from current drilling practices in the sedimentary basin (i.e., the Delaware Basin) in which the WIPP is located A vector notation is used for ai because it is possible for a given drilling intrusion to penetrate several different types of waste.

Further, the probabilistic characterization for tminfollows from the guidance in 40 CFR 194 that the occurrence of potash mining within the land withdrawal boundary should be assumed to occur randomly in time (i.e., follow a Poisson process with a rate constant of km = 10+ yr-l), with all commercially viable potash reserves within the land withdrawal boundary being extracted at time tmin.

With respect to the previously indicated questions, S~l provides an answer to Q 1, while~~{and p~[ provide an answer to Q2.

In practice, Q2 will be answered by specifying distributions for n, ti, Ii, ei, 1,p,, al, an b . .

d tmin, WhiCh in turn lead to definitions for~~1and p~,.

The CCDF in 40 CFR 191 will be obtained by evaluating an integral iZZVOiViZIg (S.l, if~,p~l) (Fig.


The deftition of (S.,,~.,, pJ is discussed in more detail in Ref.


The entity EN2 is the outcome of the model development process for the WIPP and provides a procedure for estimating radionuclide releases to the accessible environment for the different fiztures (i.e., elements x~, of S~t) that could occur at the WIPP.

hzsights on the processes to be modeled were provided as part of the scenario development process.34 This procedure can be represented by a fimction fixJ In practice, f is models implemented in the computer programs indicated in Fig. 3 and Table 2.


modified version of BIL4GFL0 designated BRAGFLO_DB~this calculation requires spalhngs results obtained from CUllTNGS_S (i.e., fsp[x~l, fB (xJ]) and BR4GFL0 resdts (i.e., fB(x~~)) as @U$ release through anbydrite marker beds to accessible environment for Xst calculated with NUTS; this calculation requires BRAGFLO results (i.e., f~x,t)) as input release through Dewey Lake Red Beds to accessible environment for x~l calculated with hWTTS; this calculation requires BRAGFLO results (i.e., fB(x,/)) as i.npu$ release to land surface due to brine flow up a plugged borehole for x~~calculated with h~s or pANEL; this caIctdation requkes B~GFLO results (i.e.,~&ij(X~~)) inpuf low field calculated for Xsl,o with SECOFL2D, release to Culebra for X$t calculated with NUTS or PANEL as appropriate; this calculation requires BFL4GFL0 results (i.e., f~x~,)) as input, , Ji-+sr,o? fs-+s,,o)> h+., > h(h)]} - groundwater transport release through Culebra to accessible environment calculated with SECOTP2D; this calculation requires SECOFL2D results (i.e., -&~x~l,O)) and NUTS or PANEL results (i.e., jN_p[X.l, fjB(xJ]) as inpu~X,l,o is used as & argument to fs_T because drilling intrusions are assumed to cause no perturbations to the flow field in the Culebra.


The probability space (S~{,~~,, p~t) and the fhnction~give rise to the CCDF specified in 40 Cl% 191.13(a), which can be represented as integral off over $~(Fig.

The models that underlie f (Fig. 3, Table 2) are too complex to permit a closed form evaluation of the integral in Fig. 2 that defies the CCDF specified in 40 CFR 191.

Rather, a Monte Carlo procedure is used in the 1996 WIPP PA.

Specifically, elements X~,j, i= 1,2, . .

.. nS. (5) are randomly sampled from S~l in consistency with the definition of (S~,, J~z,pJ. Theq the inte.gal in Fig. 2, and hence the associated CCDF, is approximated by (6) where 6Rfj(xJ] = 1 iffixJ > R and O if flx~t) < R and d~t is the density fimction associated with th:probability space (Ss,, J ,j, p~l) for stochastic uncertainty.~The manner in which the random sampling from S~t and associated CCDF construction is carried out is described in Ref.


The models that underlie fare too computationally intensive to permit their evaluation for every element x~r,i of S~r in Eq. ( 5).

Due to this constrain~these models are evaluated for representative elements of S.,, and then the results of these evaluations are used to construct values ofjfor the large number of x~f~(i.e., nS = 10,000 in the 1996 WIPP PA) in Eq. ( 5).

The specific elements of S,l for which calculations are performed are descnied in Sect.

12 of Ref.

37, and the associated construction procedures for other elements of S.( are described in Ref 44 for fc and fsp, Ref41 for fDBF, Ref 48 for fMB, fDL, fs and fN+ and Ref 53 for fS_T.


With respect to the previously indicated questions, the models that underlie the function f in Eq.. (4) are providing an answer to Q3.

These models, and hence the fimctionj are discussed in more detailinRefs.


The entity EN3 is the outcome of the data development effort for the WIPP and provides a probabilistic characterization of the uncertainty in the parameters that underlie the WIPP PA.

When viewed formally, EN3 is defined by a probability space (S$u,~~U,p~U),with the sample space Sm given by Sm = {xm: Xm is possl%ly the correct vector of parameter values to use in the WIPP PA models).

( 7) The subscript SU refers to subjective (i.e., epistemic) uncertainty and is used because (S,u, J ,., p..) is protidmg a probabilistic characterization of where the appropriate inputs to use in the WIPP PA are believed to be locatecL35 In practice, some elements of Xw could affect the definition of (S~~,~~t, p.l) (e.g., the rate constant~used to define the Poisson process for drilling intrusions or the probability that a randomly placed drilling intrusion will penetrate pressurized brine in the Castile Fm) and other elements could relate to the models in Fig. 3 and Table 2 that determine the function-fin Eq. ( 4) and Fig. 3 (e.g., radionuclide solubilities in Castile brine or ficture spacing in the Culebra Dolomite).

However, in the 1996 WIPP PA, all elements of xm relate to tie models in Fig. 3 and Table 2.


If the value for Xm was precisely lmo~then the CCDF in Fig. 2 could be determined with certainty and compared with the boundary line specified in 40 CFR 191.

However, given the complexity of the WIPP site and the 10,000 yr time period under consideratio~x~u can never be knovm with certainty.

Rather, uncertain~in Xsu as characterized by (Sm,~~, p,.) will lead to a distribution of CCDFS (Fig. 4), with a different CCDF n%whing for each Possl%le value that Xw can take on.

The proximity of this distribution to the boundary line in Fig. 2 provides an indication of the confidence with which 40 CFR 191 will be met-


The distribution of CCDFS in Fig. 4 can be summariz ed by distributions of exceedance probabilities conditional on individual release vaIues (Fig. 5).

For a given release value R, this dish-iiution is defined by a double integral over S~Uand SS1(Refs.

33, 35).

In practice, this integral is too complex to permit a closed-form evaluation Instea& the WIPP PA uses Latin hypercube samplings to evaluate the integral over S~Uan~as indicated in Eq. ( 6), simple random sampling to evaluate the integral over S.,.

Specifically, a Latin hypercube sample (LHS) XXUA, k = 1, 2, .--, nLHS, (8) is generated from Sm in consistency with the definition of (S~u,~SU,pm) and a random sample x~r,i, i = 1, 2, .-., nS, as indicated~Eq. ( 5) is generated from S~r in consistency with the deftition of (SS,,~S1, pJ.


The probability prob(p < P~) in Fig. 5 is then approximated by - (9) ,. . where prob(p < PIR) designates the probability that the exceedance probability (i.e., p) for a release of size R will be Iess than or equal to P, and~~, and also 6P, are defined the same as 6R in Eq. ( 6).


The result of the preceding calculation is typically displayed by plotting percentile values (e.g., Po.l, P0.5, and Po.g from Fig. 5), which are obtained by solving Eq. ( 9) for P with prob(ps P~) = 0.1, 0.5 and 0.9, respectively, and also mean values (i.e.,f rom Fig. 5) for exceedance probabilities above the corresponding release values (i.e., R) and then connecting these points to form continuous curves (Fig. 6).

The proximity of these curves to the indicated boundary line provides an indication of the confidence with which 40 CFR 191 will be met.


With respect to the previously indicated questions, (Sw,~SU,pm) and results derived from (Sw,~~, pm) (e.g., the distributions in Figs. 4- 6) are providing an answer to Q4.

The definition of (Sw,~~, pm) and the generation of the Latin hypercube sample in Eq. ( 7) are discussed in Ref.


Generation of the LHS in Eq. ( 8) and evaluation of the fimctionfin Eq. ( 4 for selected elements x~t of S~r(see Sect.

12, Ref. 37) generates a mapping (lo) [xsuJ>f(xs,>xmJ)l> k= 1,2,..., ? LLm, horn uncertain analysis inputs to analysis results.

More generally, the mapping can be expressed as (11) [x.~~,Y(%,~)], k= 1,2,..., nLHS, 4 where y(xw J denotes the results obtained witA the model or models under consideration.

A vector rotation is used for y because, in genera~a large number of predicted results is produced by each of the models used in the 1996 WIPP P.4; in additio~y(x~u J could also correspond to a CCDF constructed from model results associated with x*u,k


Once generate~the mappings in Eqs. ( 10) and (11) provide a summary of the (subjective) uncertainty in~and y, and can be explored with sensitivity analysis techniques based on the examination of scatterplots, regression analysis and correlation analysis (Sect. 9, Ref. 56; Sect.

3.5, Ref. 57).


Uncertainty and sensitivity analysis results for individ~l components of~(i.e., YB,&, &, -f&M,~~B, j&., Js, JAI+ -1'&) are given in Refs.

41, % 48, 53, 59, 60.


Further, uncertainty and sensitivity analysis results for CCDFS are giveninRefs.41, 44,48,53,60.


The importance of identifying, characterizing and displaying the uncertainty in the outcomes of analyses for complex systems is now widely recognized.


The EPA's requirements for such results are explicitly stated in the quotes from 40 CFR 191 and 40 CFR 194 in Sect.

2. As other examples, the following statements are made in the indicated documents: The Commission is aware that uncertainties are not caused by use of quantitative methodology in decisionmaking but are merely highlighted through use of the quantification process.

Confidence in the use of probabilistic and risk assessment techniques has steadily improved since the time these were used in the Reactor Safety Study.

In fac~through use of quantitative techniques, importmt uncertainties have been and continue to be brought into better focus and may even be reduced compared to those that would remain with sole reliance on deterministic decisionrnaking.

To the extent practicable, the Commission intends to ensure that the quantitative techniques used for regulatory decisionrimking take into account the potential uncertainties that exist so than an estimate can be made on the confidence level to be ascribed to the quantitative results.

Uncertainties could be discussed in the methods section of a repofi and the consequences of uncertainties described in the discussion section.


End-point selection is an important component of ecological risk assessment.

Uncertainties about the selection of end points need to be addressed.

The Committee believes strongly that the explicit disclosure of uncertainty in quantitative risk assessment is necessary any time the assessment is taken beyond a screening calculation. ... The need for regulatory action must be based on more realistic estimates of risk.

Realistic risk esrirnating, however, requires a fill disclosure of uncertainty.

The disclosure of uncertainty enables the scientific reviewer, as w'ell as the decision-maker, to evaluate the degree of cotildence that one should have in the risk assessment.


The cotildence in the risk assessment should be a major factor in determining g strategies for regulato~action.

Large uncertainty in the risk estimate, although undesirable, may not be critical if the cotildence internals about the risk estimate indicate that risks are clearly below reegdatory levels of concern.

On the other hand, when these confidence intervals overlap the regulatory levels of concec onsideration should be given to acquiring additional information to reduce the uncertainty in the . risk estimate by focusing research on the factors that dominate the uncertainty.

The dominant factors controlling the overall uncertainty are readily identified through a sensitivity analysis conducted as art integral part of quantitative uncertainty analysis.

Acquiring additional data to reduce the uncertainty in the risk estimates is especially important when the cost of regulation is high.

Ultimately, the explicit disclosure (of the uncertainty) in the risk estimate should be factored into analyses of the cost-effectiveness of risk reduction as welI as in setting priorities for the allocation of regulatory resources for reducing risk.


A distinction between uncertainty (i.e., degree of potential error) and inter-individual variability (i.e., population heterogeneity) is generally required if the resulting quantitative risk characterization is to be optimally useful for regulatory purposes, particularly insofm as risk characterizations are treated quantitatively.

The distinction between uncertainty and individual variability ought to be maintained rigorously at the leveI of separate risk-assessment components (e.g., ambient concentration uptake and potency) as well as at the level of an integrated risk characterization.

( p. 242) When reporting estimates of risk to decision-makers and the public, EPA should report not only point estimates of risk but also the sources and magnitudes of uncertainty associated with these estimates.

( p. 263)


Because EPA often fails to characteri& fidly the uncertainty in risk assessments, inappropriate decisions and insufficiently or excessively conservative analyses can result. ( p. 267) u Guiding Principles for A40nte Carlo AnaIysis (p. 3, Ref. 67) . .

the basic goal of a Monte Carlo analysis is to characterize, quantitatively, the uncertainty and variability in estimates of exposure or risk.

A secondary goal is to identi~key sources to the overall variance and range of model results.


"Consistent with EPA principles and policies, an analysis of variability and uncertainty should provide its audience with clear and concise infoiirtation on the variability in individual exposures and risks; it should provide information on population risk (extent of harm in the exposed population); it should provide information on the distribution of exposures and risks to highly exposed or highly susceptkde populations; it should describe qualitatively and quantitatively the scientific uncertainty in the models applie& the data utilized and the specific risk estimates that are used.


When viewed at a high level, the uncertainty refened to in 40 CFR 191, 194 (Sect. 2) and also in the preceding quotes can usually be divided into two types: stochastic (i.e., aleatory) uncertainty, which arises because the system under study can behave in many different ways and is thus a property of the system and subjective (i.e., epistemic) uncertainty, which arises from a lack of knowledge about the system and is thus a property of the analysts performing the study.

When a distinction between stochastic and subjective uncertainty is not maintained, the deleterious events associated with a system the likelihood of such events, and the cofiidence with which both likelihood and i . , consequences can be estimated become commingled in a way that makes it difficult to draw useful insights.

Due to the pervasiveness and importance of these two types of uncertainty, they have attracted many investigators (e.g., Refs. 20, 35, 68- 87) and also many names (e.g., aleatory, type A, irreducible, and variability as alternatives to the desi.gmtion stochastic, and epistemic, type B, reducible, and state of knowledge as alternatives to the designation subjective).

IndeeL this distinction can be traced back to the beginnings of the formal development of probability theory in the seventeenthcentury.sg'89


As an example, probabilistic risk assessments (PIL4s) for nuclear power plants and other complex engineered facilities involve stochastic uncertainty due to the many different types of accidents that can occur and subjective uncertainty due to the inability of the analysts involved to precisely determine the frequency and consequences of these accidents.


The recent reassessment of the risk tiom nuclear power plants conducted by the U.S. Nuclear Regulatory Commission (NUREG-1 150) provides an example of a very large analysis in which an extensive effort -. was made to separate stochastic and subjective uncertainty (Refk. 80, 90).

This analysis was instituted in response to criticisms that the Reactor Safety Study91 had inadequately characterized the uncertainty in its results.92 Similarly, the EPA's standard for the geologic disposal of radioactive waste (Sect. 2) can be interpreted as requiring (1) the estimation of a CCDF, which arises from the different disruptions that could occur at a waste disposal site and is thus a summary of the effects of stochastic uncertainty (Sect. 3), and (2) the assessment of the uncertainty associated with the estimation of this CCDF, with this uncertainty deriving from a lack of knowledge on the part of the analysts involved and thus providing a representation for the effects of subjective uncertainty (Sect. 5).


Conceptually, similar problems also arise in the assessment of health effects within a population exposed to a carcinogenic~hemical or some other stress, where variability within the population can be viewed as stochastic uncertainty and the inability to exactly characterize this variability and eitimate associated exposures and health effects can be viewed as subjective uncertainty (e.g., Refs.

93- 99).

Other examples also exist of analyses that maintain a separation of stochastic and aleatory uncertainty (e.g., Refs. 100 - 104).

Thus, by maintaining a separation between stochastic and subjective uncertainty as indicated in Sects.

3-5 and described in more detail in other articles (Refs.

37,41, 44,48, 53, 56, 60), the 1996 WIPP Pa is in the main stream of current analyses for complex systems.


Many individuals believe that the boundary line associated with 40 CFR 191.13 and illustrated in Fig. 1 is a novel concept.


Actually, this construction is an example of the Fanner limit line approach to the definition of acceptable risk.

i05-] 07 A similar construction was used in the NUREG-1 150 analyses80' 90 to implement the proposed" large release safety goal for reactor accidents.63' 108 Thus, agafi the 1996 WIPP PA involves widely used ideas, although the actual scale of the amlysis is much larger than that of a typical PA.


This article presents a formal description of the conceptual structure of the 1996 WIPP PA.

In particular, the structure of the PA is descnied in terms of a probability space (S$,,~~t, p~r) for stochastic (i.e., aleatov) uncertainty, a probability space (S~U,~SU, pm) for subjective (i.e., epistemic) uncertainty, and a fimction~(x~l, x~u) defined for elements x~l and x~U of the sample spaces S.* and S~u. The probability space (S~t,~~p pJ characterizes the likelihood of different 10,000 yr fimres (i.e., x~l) that could occur at the WIPP and underlies the CCDF specified by the EPA in 40 CFR 191; the probability space (Sm,~S U,P,U) cticteties a degree of belief with respect to where the appropriate parameter values for use in the 1996 WIPP PA (i.e., Xm) are located, and the fi.mction f {X.l, XJ estimates normalized radionuclide releases (an& in generaL many other quantities) that derive from x~, and Xw.


Introduction of this formal description of the stmcture of the 1996 WIPP PA provides a way to give names and symbols to the important parts of the analysis.


Once names and symbols are assigned it is then possible to unambi.mously describe the individual parts of the PA and how these parts fit together to make the complete PA.

Without these names and symbols, it is difficult to give a precise description of the individual parts of the PA and how these parts come together in the computational implementation of the PA.


As an example, large PAs make extensive and sometimes complex use of probability.

In such applications, it is I essential to understand how probability is being use+ and in particular, to what type of "entity" probability is being assigned.

As a s% it is essential to know what the sample space is.

It is always disconcerting to re%ze that a probabilistic calculation is being can-ied out without a clear concept of what the sample space is.

In the 1996 WIPP PA, there are two distinct sample spaces (i.e., S@ and Sin), each with its elements (i.e., x~f and Xw) clearly defined.


A suggestion: When considering a probabilistic calculation always ask yourselt or the individuals carrying out the calculation% what constitutes the sample space.

Without a satisfactory answer to this questio~a clear understanding of the calculation cannot be developed.


The use of a formal structure to describe the 1996 WIPP PA provides a way to distinguish between concept and approximation.


For example, the 1996 WIPP PA presents uncertainty distributions arising from stochastic uncertainty alone, subjective uncertainty alone, and stochastic and subjective uncertainty combined.

Such distributions can be unambiguously defined in terms of integrals over S$, and/or S~U. Such integrals provide a way to express exactly what is being calculated but do not constitute a suitable computatioml procedure; rather, they must be approximated with some type of numerical procedure.


The 1996 WIPP PA used simple random sampling for intebgations involving the probability space (S~l,~~,,p~z) and Latin hypercube sampling for integrations involving the probability space (S~U, K!~u, p~u).

The use of such sampling-based numerical approximations is often referred to as Monte Carlo amlysis.


As an aside, some individuals express concern, or worse, over the use of Monte Carlo analyses.

Given that Monte Carlo analysis is just a way to approximate an integral, this does not really make sense (would the same concern be expressed if the analysts stated that a Gaussian quadrature procedure was being used to evaluate the inte-g-al in question?)


Rather, if there is reason for concern, it should be respect to the appropriateness of the fimction being integrated or the probability space being integrated over.

The particular integration procedure being used should not be an object of concern beyond considerations of convergence and accuracy.


A benefit of representing a PA with probability spaces, fictions and integrals is that it provides a description of the PA in the same notation that is used in formal developments of probability.

This representation of the PA in a widely used format facilitates understanding of the conceptual and computational details of the PA within the PA project itself and the cornmuni cation of these detaiIs to reviewers and other individuals outside the project.

For example, such a representation helps clar@ the concept of a scenario, with a scenario being either a subset ES, of the sample space S~l for stochastic uncertainty (i.e., an element of X$~1), a subset E~U of the sample space Sm for subjective uncertainty (i.e., and element of~~) or a subset E of S = S~~x Sw (i.e., an element of~~r x~~).

Thus, a scenario is what is typically called an event in a formal development of probability and the corresponding scenario probabilities are given by p~l(E~r), p~U(E~U) and P(E) = p~t(E~l) p~u(E~u), respectively, where the representation for the probability of E (i.e., p(E)) holds provided E = E~f x Em and the elements of E~l and Em are independent in a probabilistic sense (i.e., the occurrence of E~~has no effect on tie occurrence of E~U and vice versa).

The preceding indicates three distinct but legitimate, uses of the concept of a scenario.

Because these three uses involve diffkrent types of occurrences, it is important to clearly indicate which usage is intended wh~n the idea of a scenario is employed.


A formal use of probability also helps clarify what types of events (i.e., scenarios) can have nonzero probabilities.


For example, it is important to recognize that individual elements of S~~(i.e., 10,000 yr Mures at the WIPP) or S~U (e.g-, elements of tie LHS used to propagate subjective uncertainty) have a probability of zero.

The single exception is the element x~l of SS1 corresponding to undisturbed conditions.

Thus, with this one exceptioñ onzero probabilities only apply to subsets of S~,, S~Uand S~t x S*Ucontaining infiitely many elements.

This is an important conceptual point that affects how results are interpreted.


In random and LHS procedures, individual sample elements are assiegned a weight equal to the reciprocal of the sample size (i.e., l/nS, UnL.HS) for use in estirnating'expected values and dism%utions; however, such weights are not the same as probabilities.


The formal representation also helps show how different analysis approaches are simply different ways of approximating the same quantities.

For example, the Kaplan/Garrick ordered triple representation for riskbs might initially appear to be quite different from the sampling-based approach used in the 1996 WIPP PA.

However. the KaplaniGarnck approach and the sampling-based approach used in the 1996 WIPP PA are simply different ways of approximating integrals involving the probability spaces (S~r,~~r p~l) and (S~U,'~~U,p~U).

.4 proper level of abstraction makes this easily apparent (Sect. 13, Ref. 37).


Further, modem probabilistic risk assessments (PRAs) for nuclear power stations have exactly the same conceptual structure as the 1996 WIPP PA, although the processes under consideration and the models in use are very different.

Agafi a description of these analyses at an appropriate level of abstraction makes this similarity readilyapparent.35'82


Now that the overall structure of the 1996 WKPP PA has been summariz ed in terms of a probability space (SS,, s,, pJ for stochastic uncertainty, a probability space (Sm,~~, p~u) for subjective uncertainty and a fimctiond efined on S~l x S- de)ailed information on (S~l,~~1,pfl), (S~b Z$~1,p~t) and f and their use in the 1996 WIPP PA can be obtained fforn other articles.

In particular, (S$t,~,,, pJ is descriied in Ref 37; (S=u,~~, pm) is descriied in Ref 56; Jand its component functions are described in Refs.

39, 41, 44, 48, 53; the construction of CCDFS for comparison with the release knits specified in 40 CFR 191 is discussed in Refs.

41,44,48,53, 6@ and uncertainty and sensitivity analysis for both individual model results (i.e., evaluations off and its component fitnctions) and CCDFS is discussed in Refs.


In 1979, six years after selecting the Delaware Basin as a potential disposal area, Congress authorized the U.S. Department of Energy to build the Waste Isolation Pilot Plant (WIPP) near Carlsbad, New Mexico, as a research and development facility for the safe management, storage, and disposal of waste contaminated with transuranic radioisotopes.

In 1998, 19 years after authorization and 25 years after site selection, the U.S. Environmental Protection Agency (EPA) certified that the WIPP disposal system complied with its regulations.

The EPA’s decision was primarily based on the results from a performance assessment conducted in 1996, which is summarized in this special issue of Reliability Engineering and System Safety.

This performance assessment was the culmination of four preliminary performance assessments conducted between 1989 and 1992.

This paper provides a historical setting and context for how the performance of the deep geologic repository at the WIPP was analyzed.

Also included is background on political forces acting on the project.

In 1998, 25 years after selection of the Delaware Basin in southeastern New Mexico as a potential disposal site for radioactive waste, the U.S. Environmental Protection Agency (EPA) certified that the Waste Isolation Pilot Plant (WIPP), an underground geologic disposal system, complied with its regulations.

This paper presents a historical summary of the system characterization, engineering analyses, and scientific investigations undertaken by the WIPP Project over the past 25 years and provides a context for the results presented in this special issue of Reliability Engineering and System Safety. Although it is not essential to know the WIPP’s history to comprehend the engineering analysis, an understanding of the issues that the project faced can be helpful.


Many paths were followed during these 25 years to discern which phenomena were important at the WIPP, and often these paths were initiated in response to evolving notions of what kind of scientific information was significant, what level of understanding was required, and how society could use this scientific information to decide whether deep geologic disposal of nuclear waste was acceptable.


The choice of New Mexico as a potential disposal site for nuclear waste in 1973 was one in a series of episodes in which New Mexico had figured prominently with regard to nuclear phenomena.

In 1942, the Manhattan Engineering District selected New Mexico as the location for assembling the scientists, engineers, and technicians who would develop the first atomic bomb.

As a direct consequence of that development, the first atomic explosion took place in 1945 in the desert near Alamogordo, New Mexico.

Sixteen years later, in 1961, scientists with the Gnome Project detonated a device in the Delaware Basin in bedded salt near Carlsbad, New Mexico, as part of the Plowshare Program, which was exploring nonmilitary uses of nuclear explosives.

After a potential disposal site in bedded salt in Kansas had been rejected in the early 1970s, citizens invited the Atomic Energy Commission to New Mexico to consider the bedded salt deposits in the Delaware Basin.

The search for a specific site in the basin occurred between 1973 and 1976.

The site was then characterized by Sandia National Laboratories for the U.S. Department of Energy in support of its Draft Environmental Impact Statement, which was completed in 1979.


The wastes intended for the WIPP included waste contaminated with transuranic (TRU) nuclear elements and hazardous chemicals generated during the production of nuclear weapons.

The Atomic Energy Commission had been segregating and storing these wastes above ground for eventual disposal since 1970, three years before site selection.

Nearly ten years later, in December 1979, Congress authorized the DOE to construct the WIPP for eventual disposal of this TRU waste.

The first shaft was drilled in 1981, and full construction began in 1983.

Construction of the WIPP facility was substantially complete by the end of 1988.

Along with construction, a suite of characterization studies were initiated in the 1980s in response to agreements with the State of New Mexico.

The final site characterization studies were completed in the 1990s.


The characterization of the WIPP provided input for the 1996 performance assessment (PA), an engineering analysis documented in the Compliance Certification Application (CCA), which was submitted to the EPA in October 1996 and which is described in this special issue of Reliability Engineering and System Safety.


The Waste Isolation Pilot Plant (WIPP) is developed by the U.S. Department of Energy for geologic disposal of transuranic waste.

The 1996 performance assessment (PA) constructed complementary cumulative distribution functions (CCDFs) for radionuclide release, showing compliance with EPA standards (40 CFR 191) for radioactive waste disposal 【6】.

The PA emphasized an iterative approach, uncertainty and sensitivity analysis, and stakeholder involvement 【15】【19】.

The CCDFs combined releases from cuttings, cavings, spallings, and brine release, indicating compliance with EPA standards 【10】【12】【13】.

The PA process evolved through several iterations, improving model sophistication and regulatory alignment 【32】【36】.

The final PA was crucial for the DOE's successful Compliance Certification Application to the EPA 【23】.


The study was approved by the University of California, San Diego, Human Subjects Committee.

Written informed consent was obtained from all subjects before study participation began.

Seventy�one patients with known or suspected OSA who had not received previous OSA treatment were recruited via adver� tisements, word�of�mouth referral, and referral from local med� ical practices in the San Diego area.

Participants' ages ranged from 29 to 50 years.

Body mass index (BMI) ranged from 20


Effect of CPAP on Fatigue in OSA Patients-Tomfohr et al to 50 kg/m 2 .

Potential participants were excluded if they had a history of heart, liver, or renal disease; diabetes; psychosis; nar� colepsy; current alcohol or drug abuse; severe asthma; or cere� brovascular disease or were taking prescription medications.

Women were excluded if pregnant.

Patients who were taking hypertensive medications were withdrawn from their medica� tions with permission of their physician and followed during a 3�week washout period while being monitored by a study phy� �week washout period while being monitored by a study phy� sician.

If blood pressure remained consistently below 170/105 mm Hg, subjects were entered into the study.

The 2 subjects who were withdrawn from antihypertensive medications com� pleted the washout period without incident.


Potential participants contacted the lab and underwent an initial phone screening to determine eligibility.

If it appeared that the subject met the inclusion criteria of the study, a prelimi� nary OSA screening was conducted with an unattended home sleep study (Stardust home monitoring system, Respironics, Inc., Murrysville, PA).

Subjects with an apnea�hypopnea index (AHI) of at least 10 were given a provisional diagnosis of OSA and were invited back to be assessed with a 1�night standard regimen of polysomnographic sleep monitoring conducted at the UCSD General Clinical Research Center Gillin Laboratory of Sleep and Chronobiology.

Those participants who had an AHI of at least 10 on the in�laboratory study were diagnosed with OSA and randomly assigned to receive either therapeutic CPAP or the placebo CPAP in a double�blind fashion.


All participants then spent a second night in the sleep labora� tory.

Patients randomly assigned to receive therapeutic CPAP underwent standard CPAP titration.

CPAP was started at a pres� sure of 4 cm H 2 O and was increased by 1� to 2�cm H 2 O incre� ments based on the presence of apneas, hypopneas, snoring, or respiratory effort�related arousals.

Titration was considered successful when all significant respiratory events stopped and the patient had spent at least 15 minutes of sleep in the final CPAP level.


Patients randomly assigned to the placebo�CPAP group un� derwent a mock�titration night.

The placebo�CPAP system was a modified version of the sham CPAP.

11 This placebo�CPAP con� sisted of a modified nasal or full face (nasal oral) CPAP mask with 10 one�quarter�inch drill holes to allow free exchange of air during inhalation and exhalation, plus a pressure reducer placed in the CPAP tubing.

With this system, the CPAP gen� erator could be placed at any pressure to control for machine noise, but the pressure at the nose and mouth was 0.5 cm H 2 O during exhalation and 0 cm H 2 O during inhalation.

Of impor� tance to the placebo�CPAP blinding, the subject was able to feel a gentle breeze at the nose.

To control for CPAP�blower noise, the pressure was set at 8 cm H 2 O. In both treatment conditions, the CPAP systems were the same (ResMed S7 Elite CPAP with HumidAire 2i™ integrated heated humidifier; ResMed Corp. San Diego, CA).

On the first night, the appropriate CPAP mask (therapeutic or placebo) was fitted, and the patient was trained on the use of the equipment.


After the titration night, patients in both groups were sent home with their assigned treatment equipment.

Proper equip� ment use and setup was ensured by telephone calls and home visits by a sleep technician who was not involved in outcome assessments.

The CPAP units each contained a hidden compli� ance clock that measured the amount of time the equipment was used at the designated pressure.

Compliance data were down� loaded by the sleep technician at the end of the treatment period and were used to determine the average number of hours CPAP was used over the study period.


Upon completion of the 3�week treatment period, patients returned to the sleep laboratory for a final polysomnogram, per� formed while the patients were using their assigned therapy.

All questionnaires were also repeated at this time.


For all overnight polysomnography studies, electroenceph� alography, electrocardiography, electrooculography, chin and tibialis anterior electromyography, pulse oximetry, nasal�oral airflow by nasal cannula pressure transducer and thermistor, and thoracic and abdominal respiratory effort were recorded on a Grass Heritage digital polysomnograph (Model PSG36�2, Astro�Med, Inc., West Warwick, RI).

Recordings were scored by a trained sleep technician according to criteria from Re� chtschaffen and Kales.

12 Apneas were defined as decrements in airflow of at least 90% from baseline for a minimum of 10 seconds.

Hypopneas were defined as decrements in airflow of at least 50% but less than 90% from baseline for a minimum of 10 seconds.

Significant oxyhemoglobin desaturations were defined as transient drops in oxyhemoglobin saturation by at least 3% from baseline.

The total number of apneas and hy� popneas per hour of sleep were calculated to yield the AHI.

Participants with an AHI of 10 or more during the attended polysomnogram were considered to have OSA and were in� cluded in the study.


Questionnaire data were obtained prior to study random� ization and after the 3�week intervention period, prior to the final polysomnogram.

Questionnaires were administered by a research coordinator who was blinded to treatment condition.


The Multidimensional Fatigue Symptom Inventory- Short Form (MFSI�sf) is a 30�item self�report measure de� signed to assess multidimensional aspects of fatigue.

Items are rated on a 5�point scale, and respondents report how true each statement was for them during the previous week (0 = not all; 4 = extremely).

Scores are summed to obtain sub� scale scores that include general fatigue, emotional fatigue, physical fatigue, mental fatigue, and vigor.

The vigor sub� scale score is subtracted from the sum of the 4 fatigue sub� 4 fatigue sub� fatigue sub� scales to yield a total fatigue score.

Subscale scores range from 0 to 24, and MFSI�sf total scores range from �24 to 96, with higher scores indicating more fatigue.

13 MFSI�sf total scores above 0.85 represent significant fatigue.

14 The MFSI� sf has been used extensively in multiple patient populations, including those with OSA.

5,15 .


In this sample, it showed good internal consistency (α = 0.84).


The Profile of Mood States (POMS) is an established mea� sure of psychological distress, which has shown high levels of Effect of CPAP on Fatigue in OSA Patients-Tomfohr et al reliability and validity.

16 The scale consists of 65 adjec� tives that are self�rated on a 5�point scale (0 = not at all to 4 = extremely).

Patients respond to the question, "How often have you been feeling… during the past week in� cluding today?" The adjectives can be combined into 6 subscales, 2 of which were the focus of this study: (1) fatigue�inertia scale (range 0�28, with higher scores indi� cating more weariness, low energy, and fatigue) and (2) vigor�activity scale (range 0�32, with higher scores indi� cating more energy and vigor).

16 The subscales showed good internal consistency (POMS fatigue α = 0.91; POMS vigor α = 0.94)


The Epworth Sleepiness Scale (ESS) is a well�validated questionnaire that assesses the likelihood of falling asleep in a variety of common situations.

The scale consists of 8 items that are self�rated on a 4�point scale (0 = would never doze to 3 = high chance of dozing).

Scores range from 0 to 24, with higher scores indicating more sleepi� ness.

17 In this sample, the scale showed good internal con� sistency (α = 0.88).


A P value 0.05 or less was considered significant, and all testing was 2 tailed.

Statistical analyses were per� formed using the SPSS statistical software package (SPSS for Windows 17.0; SPSS Inc.; Chicago, IL).

Student t tests were used to compare groups on baseline characteristics with continuous outcome measures, χ² tests were used to compare multicategorical outcome measures.

Differenc� es between the 2 groups over time were assessed using repeated�measures analysis of variance (ANOVA).

This analysis allowed testing for a main effect of treatment (thera� peutic CPAP vs placebo CPAP), a time effect (prior to treatment and after 21 days of treatment), and the interaction of time by treatment.

A time effect alone implies that the treatment effects were nonspecific (i.e., placebo effects).

A treatment�by�time in� teraction implies that subjects responded to a specific treatment over time with a significant response.


The recruitment profile is shown in Figure 1.

Patient char� acteristics are presented in Table 1.

A total of 59 patients (29 therapeutic CPAP and 30 placebo CPAP) completed treatment.

The groups did not significantly differ on baseline character� istics, including age, body mass index, sex, race or ethnicity, daytime sleepiness, fatigue, vigor, or AHI.

The groups also did not differ in the number of nights they used the CPAP treat� ment during the course of the study (therapeutic CPAP = 18.82 ± 1.98 vs placebo CPAP 18.73 ± 2.68; P = 0.89).

However, there was a significant difference in how many hours the groups used the CPAP each night.

The therapeuticCPAP group used the treatment for an average of 5.46 ± 1.09 hours per day over the 3�week treatment period.

In contrast, the placebo�CPAP group used treatment for longer periods each night, an average of 6.59 ± 1.40 hours per day (P = 0.01).


Significant time�by�treatment interactions were observed for the MFSI�sf total score (P = 0.02) and the POMS fatigue subscale (P = 0.03).

When compared with the placebo�CPAP group, individuals in the therapeutic�CPAP group evidenced a significant reduction in MFSI�sf total scores (see Figure 2) and POMS fatigue scores (see Figure 3).

A significant time�by� treatment interaction was also observed for vigor (P = 0.02), with the therapeutic�CPAP group reporting increased energy when compared with the placebo�CPAP group (see Figure 4).


We also investigated whether there were fatigue and energy changes in the placebo�CPAP group (i.e., a placebo effect).

Sig� nificant reductions in fatigue were not observed in the place� bo�CPAP group (P values > 0.36), nor did the placebo group demonstrate changes in energy/vigor (P = 0.20).


Significant time�by�treatment differences were not observed for the ESS scores (P > 0.05).

Because the literature suggests that, the sleepier the patients feel before CPAP intervention, the greater their response to treatment, 6 we split our sample us� ing the ESS cutoff for excessive sleepiness (ESS ≥ 9).

17 The therapeutic�CPAP and placebo�CPAP groups did not differ significantly in terms of the proportion of excessively sleepy (55.9%) versus not sleepy (44.1%) participants (χ 2 = 0.06,


As expected, after the 3�week intervention there was a signif� icant time�by�treatment interaction for AHI with the therapeu� tic�CPAP group showing significant AHI decreases (baseline 38.64 ± 24.28 vs posttreatment 6.25 ± 6.47), compared to AHI in the placebo�CPAP group (baseline 31.67 ± 18.72 vs post� Effect of CPAP on Fatigue in OSA Patients-Tomfohr et al creases in two independent measures of fatigue and an associ� ated increase in vigor, lend support to the finding that CPAP treatment significantly decreases fatigue and increases energy in patients with OSA.

We also observed that individuals who were excessively fatigued at the study onset received greater therapeutic benefit from treatment with CPAP, as compared with those who were not experiencing clinically significant lev� els of fatigue at study onset.


Several studies have shown large changes in sleepiness in patients with OSA treated with therapeutic CPAP.

There are two main differences between those studies and our own.


First, in� vestigations that have observed significant reductions in sleepi� ness recruited participants who were excessively sleepy.

7 Our patients' ESS scores (mean = 10.2) were 35% to 40% lower than the scores of patients with OSA who have been recently studied.


Second, studies that have observed reductions in sleepiness have generally employed a longer treatment protocol than did our study, raising the possibility that longer treatment may be necessary to reduce sleepiness.

18�20 Although we could not lengthen our treatment protocol, we did investigate whether initial sleepiness level was predictive of treatment response.


We found that excessively sleepy subjects treated with therapeutic CPAP showed a significant reduction in ESS scores, compared with those subjects treated with placebo CPAP.

No significant changes in sleepiness were observed in participants who were not excessively sleepy at the start of treatment.


These results lend support to previous work suggesting that, the sleepier pa� tients are at the onset of treatment, the greater their sleepiness scores decline over time.


The groups were comparable in terms of days that they used CPAP during the study period, but the placebo group used the CPAP for more hours per night.

This may have been a chance observation.

On the other hand, one could also speculate that the CPAP group experienced such benefit from treatment that they did not feel it necessary to be as conscientious about com� pliance.

Nonetheless, the compliance level in both groups was good, exceeding 4 hours per night.


We acknowledge several limitations of the current investiga� tion.

First, the population under study was free from other ill� nesses.

Although all participants suffered from OSA, they may not represent the typical patients at a sleep medicine center, who are more likely to have comorbidities, such as diabetes or symptomatic coronary disease.

Our patients, nonetheless, had unquestionable and moderately severe OSA (AHI > 30).

Sec� ond, our treatment period of only 3 weeks was relatively short.

P = 0.81).


To test for a specific effect of treatment in both groups, we conducted a repeated�measure ANOVA with ESS scores as the outcome mea� sure.

Results of the ANOVA showed a significant time�by�treatment effect in the excessively sleepy group (F 1,31 = 7.54, P = 0.01, η 2 = 0.19), whereby the therapeutic CPAP group had significantly re� duced ESS scores in comparison with the placebo group (see Table 2).

In contrast, the time�by�treat� ment interaction in the nonsleepy group was not significant (F 1,24 = 1.35, P = 0.26, η 2 = 0.05).


As noted above, CPAP was effective in reduc� ing sleepiness in those subjects with high levels of sleepiness before commencing treatment.

We next investigated whether this finding was also true with regard to fatigue.

First, we in� vestigated changes in the MFSI�sf, stratifying individuals as either fatigued or nonfatigued based on the MFSI�sf clinical cutoff score for fatigue (0.85).

The proportion of excessively fatigued (59.3%) versus not fatigued (40.7%) participants did not differ significantly between therapeutic� and placebo�CPAP groups (χ 2 = 0.18, P = 0.67).

To test for a specific effect of treat� ment in the high� and low�fatigued groups, we conducted a repeated�measure ANOVA with MFSI�sf scores as the outcome measure.

There was a significant time�by�treatment effect in the fatigued group (F 1,33 = 4.42, P = 0.04, η 2 = 0.12; those who were treated with therapeutic CPAP had significantly reduced MFSI�sf scores, in comparison with those treated with placebo CPAP (see Table 2).

The time�by�treatment interaction in the nonfatigued group was not significant (F 1,22 = 0.88, P = 0.36, η 2 = 0.04).


A similar story emerged when the POMS fatigue scale was used as the outcome measure.

We performed a median split, breaking the groups into high (POMS ≥ 6) and low (POMS < 6) fatigue groups and conducting a repeated�measure ANOVA with POMS fatigue scores as the outcome measure.

Again, therapeu� tic�CPAP and placebo�CPAP groups did not differ significant� ly in terms of the proportion of excessively fatigued (47.5%) versus not fatigued (52.5%) participants (χ 2 = 0.85, P = 0.36).

Results of the ANOVA showed a significant time�by�treatment effect in the fatigued group (F 1,26 = 8.34, P < 0.01, η 2 = 0.24), whereby the therapeutic�CPAP group had significantly reduced POMS fatigue scores in comparison with the placebo group (see Table 2).

In contrast, the time�by�treatment interaction in the nonfatigued group was not significant (F 1,29 = 0.60, P = 0.44, η 2 = 0.02).


Individuals with OSA experience significant sleepiness and fatigue.

The aim of this study was to identify whether treat� ment with therapeutic CPAP was associated with improvement in sleepiness, fatigue, and vigor above and beyond nonspecific placebo effects.

Findings revealed that, over a 3�week interven� 3�week interven� �week interven� tion period, treatment with therapeutic CPAP reduced fatigue and increased energy.

In fact, at the end of treatment, mean scores from the therapeutic�CPAP group indicated that partici� pants were no longer suffering from clinically significant levels of fatigue.

14 The convergence of results, demonstrated by de� Previous work from our group failed to discern a specific ben� eficial effect of CPAP treatment on fatigue levels after 1 and 2 weeks of treatment.

9,10 On the other hand, this study found clear and compelling evidence that a 3�week CPAP intervention led to significant improvements of fatigue and sleepiness.

The con� vergent validity of these observations is striking, given that they were supported by multiple measures (MFSI�sf fatigue, POMS fatigue, POMS vigor, and ESS).

Current planned National Insti� tutes of Health initiatives to examine long�term effects of CPAP in a double�blind fashion will be able to determine if these ben� eficial effects of CPAP persist in longer�term trials and in pa� tients with OSA who have additional comorbidities.


Finally, we are left with questions about what mechanisms underlie the observed changes in fatigue.

A possible theory is that CPAP reduces inflammation in patients with OSA, which thereby impacts fatigue.

Patients with OSA have increased levels of local (upper airway) and systemic inflammation.

21 In� creases in inflammatory markers in individuals with OSA have been related to elevated fatigue.

5,22 In turn, CPAP used continu� ously for more than 4 hours per night has been shown to reduce markers of inflammation.

23 A logical next step in this research would involve extended studies focused on the long�term use of CPAP and associated measures of inflammation and fatigue.


In summary, patients with OSA who received therapeutic CPAP (vs placebo) had significant reductions in fatigue and re� ported improved vigor over a 3�week treatment period.

CPAP appeared to be especially beneficial in reducing fatigue in those who were excessively fatigued or sleepy before treatment.


We have read with interest the studies of Dr. Tomfohr [1] and Dr Antic [2] published in Sleep (2011; Vol 34, issue 1).

Dr. Tomfohr et al., in a very short-term randomized study (CPAP placebo vs therapeutic CPAP), found that optimal CPAP in patients with somnolence at the onset of treatment significantly reduces somnolence and increases energy.

Dr. Antic et al., in an observational study, analyzed the neurobehavioral outcomes in OSA patients.

The main findings were that there are a number of patients that do not normalize their neurobehavioral responses despite good compliance with CPAP.

However, many patients had normal results at baseline, and some tests were only performed at the end of the trial, making comparisons impossible.


We think these studies merit a comment.

These findings are not new.

They have been long reported by our group and others [3], and we think that it has now been well established that CPAP treatment is mandatory in symptomatic OSA patients.

Furthermore, other authors have raised the importance of using longer night-time durations of CPAP to achieve normal functioning levels [4] and neurobehavioral improvement with CPAP, as has been also studied [5].

However, we think that is important to consider at present that we are entering in a new phase that requires all our combined efforts; the most important unresolved issues perhaps lie elsewhere and so research could focus on different areas, such as cardiovascular outcomes.


Our Spanish Group of Sleep Breathing Disorder has started to perform several multicenter studies with large numbers of patients in which we have demonstrated the importance of OSA in cardiovascular mortality and morbidity, as well as the efficacy of CPAP [6, 7].

These effects are independent of the severity of symptoms per se and suggest that CPAP should be applied not only with the aim of improving symptoms, but also in order to improve survival.

Similarly, OSA appears to increase the rate of motor vehicle accidents irrespective of the subjective somnolence, and CPAP reverses this excess risk in all patients.


However, more studies are urgently needed on large numbers of patients from different groups (women, elderly, etc.) in the relatively non-symptomatic or non-clinical population.

These issues are important on account of both the possible high number of patients involved and the possibility of opening new windows on the treatment of diseases in which optimal treatment does not always lead to improvements.

In addition to these factors, this line of investigation could also have important social and financial consequences.


In response to the letter by Montserrat et al. ( 2011) [1], we agree with the authors on a number of points.

Larger studies, investigating groups not normally included in CPAP trials are critically important and successful treatment of OSA may be an avenue leading to better management of comorbid diseases.

However, we disagree that the issues of fatigue and neuropsychological outcomes are resolved and do not warrant further attention.


Montserrat et al. state that our study found that CPAP treatment reduced somnolence and increased energy, but fail to mention the main finding, that CPAP treatment significantly reduced fatigue above and beyond the effect of placebo [2].

It is true that variables associated with fatigue such as sleepiness and attention have been studied in the context of successful OSA treatment, yet fatigue as a distinct construct has been an understudied outcome, not just within OSA, but in the field of sleep medicine.


Results from our investigation suggest that fatigue is a psychological variable that is extremely sensitive to change.

The finding coupled with information about how patients talk about apnea symptoms could help to open up new research avenues and modify how clinicians discuss treatment responses with their patients [3].

We think it is important to examine these issues from a clinical standpoint.


As clinicians, we would agree that CPAP treatment is important in all patients diagnosed with OSA.

As clinicians we also know that adherence with treatment recommendations can be abysmal.

Learning more about positive changes associated with treatment (i.e., reductions in fatigue, decreases in neuropsychological impairments) give clinicians struggling to motivate patient use of CPAP one more motivating factor with which to encourage compliance.


Regarding neuropsychological outcomes and sleep apnea, we assume that Antic and colleagues [4] will be responding, but it bears mention that we were favorably impressed by the findings from their study and agree that the neuropsychological aspects of obstructive sleep apnea and CPAP treatment are yet to be fully resolved.