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National Immigration Law Center > News Releases > Trump's Relentless Attack on ACA Health Law Is Another Attack on Disenfranchised People |
This entry was posted in News Releases, October 2017 on October 13, 2017 by Richard Irwin. |
← Rep. Pramila Jayapal Joins DACA Mom, Experts, and Allies to Discuss the Imminent Risks to Parents with DACA and their U.S. Citizen Children and Call for a Clean Dream Act We Must Pass a Legislative Solution for Dreamers Before the Year's End →<eot>Biomedical Signal Processing: An ECG Application | SpringerLink |
Leveraging Data Science for Global Health pp 285–303Cite as |
Chen Xie7 |
The electrocardiogram (ECG) is a low-cost non-invasive sensor that measures conduction through the heart. By interpreting the morphology of a person's ECG, clinical domain experts are able to infer the functionality of the underlying heartbeat, and diagnose irregularities. Moreover, a variety of signal processing algor... |
Understand the principles of electrocardiography. |
Understand signals in the time and frequency domain. |
Learn the importance of applying linear filters to clean signals. |
Understand wavelet analysis, a traditional signal processing technique, and apply it to the electrocardiogram (ECG). |
This workshop introduces the concepts and workings of the ECG, and signal processing techniques used to glean information from raw recordings. In the hands-on coding exercises, you will be asked to apply the signal processing methods on a clinical prediction problem. |
Understanding of basic concepts of electrical conduction. |
Understanding of supervised classification (see Chap. 2.06). |
17.2 Physiologic Signal Processing |
A signal conveys information about the underlying system being measured. There are many techniques used to measure time-varying biosignals from human bodies. Examples of invasive signals collected include: intra-arterial blood pressure and cell membrane potential measurements. Much more prevalent however, are non-invas... |
Clinical domain experts are able to interpret the signal shapes, or waveforms, to extract insights. For example, the non-compliant vessels of a patient with stiff arteries may produce a reflected pressure wave in response to systolic pressure (Mills et al. 2008). By examining the patient's arterial blood pressure wavef... |
For the past several decades however, automated algorithms have been developed to detect notable events and diagnose conditions. Although domain experts are usually required to create and validate these algorithms, once they are developed and implemented, they are able to automate tasks and free up human labor. A promi... |
Traditional signal processing techniques have proven very effective in extracting information from signal morphology. This chapter will describe the principles of the ECG, and explore interpretable techniques applied on a relevant clinical problem: the classification of heart beats. |
17.2.2 The Electrocardiogram |
This section provides a simple overview of the ECG to support the signal processing in the rest of the chapter. For an in-depth description of action potentials and the ECG, see (Venegas and Mark 2004). |
The electrocardiogram (ECG) is a non-invasive time-varying voltage recording used by physicians to inspect the functionality of hearts. The potential difference between a set of electrodes attached to different parts of the body's surface, shows the electrical activity of the heart throughout the cardiac cycle. |
17.2.2.1 Action Potentials and the Cardiac Cycle |
The cardiac cycle consists of two phases: diastole, during which the heart muscle (myocardium) relaxes and fills with blood, followed by systole, during which the heart muscle contracts and pumps blood. The mechanism that actually triggers individual muscle cells to contract is the action potential, where the membrane ... |
On a larger scale, each action potential can trigger an action potential in adjacent excitable cells, thereby creating a propagating wave of depolarization and repolarization across the myocardium. During a healthy heartbeat, the depolarization originates in pacemaker cells which 'set the pace', located in the heart's ... |
Conduction pathways of the heart and corresponding membrane potentials (Venegas and Mark 2004) |
17.2.2.2 Electrocardiogram Leads |
The electrical activity of the myocardium produces currents that flow within the body, resulting in potential differences across the surface of the skin that can be measured. Electrodes are conductive pads attached to the skin surface. A pair of electrodes that measure the potential difference between their attachment ... |
The magnitude and direction of reflection measured by a lead depends on the axis that it measures. By combining multiple leads, a more complete picture of the heart's 3-dimensional conduction can be viewed across multiple axes. The standard 12-lead ECG system is arranged as follows: |
Limb Leads—I, II, III. Three electrodes are placed on the limbs: left arm (LA), right arm (RA), and left leg (LL). These electrodes then form leads I = LA–RA, II = LL–RA, and III = LL–LA. The virtual electrode Wilson's Central Terminal is the average of the measurements from each limb electrode. |
Augmented limb leads—aVR, aVL, and aVF. These are derived from the same electrodes as used in the limb leads, and can be calculated from the limb leads. The limb leads and augmented limb leads provide a view of the frontal plane of the heart's electrical activity. |
Precordial leads—V1, V2, V3, V4, V5, V6. These leads measure the electrical activity in the transverse plane. Each lead measures the potential difference between an electrode placed on the torso, and Wilson's Central Terminal (Figs. 17.2, 17.3 and 17.4). |
Frontal leads of the ECG (Npatchett 2020) |
Precordial leads of the ECG (File:EKG leads.png 2016) |
Two channel ECG recording of normal sinus rhythm |
Expert clinicians are able to use different leads to more effectively diagnose different conditions. An arrhythmia that disrupts the regular conduction perpendicular to the axis of a lead may not show up at all in the ECG lead, if all appears normal in the direction of axis. |
But although having 12 leads provides a rich view of the heart, even a single lead may provide plenty of information depending on the problem at hand. In addition, requiring the placement of too many electrodes may be cumbersome and impractical in a remote setting. In this chapter and its practical exercises, we will u... |
17.2.2.3 Interpretation of the Electrocardiogram |
Figure 17.5 shows a model lead II recording of a normal beat. Recall that depolarization towards the positive electrode (LA) produces a positive deflection. The segments of the ECG can be broken down as follows (Fig. 17.6): |
Lead II ECG recording (File:SinusRhythmLabels.svg 2019) |
Cardiac cycle (File:2027 Phases of the Cardiac Cycle.jpg 2017) |
The P wave represents atrial depolarization. Atrial systole begins after the P-wave onset, lasts about 100 ms, and completes before ventricular systole begins. |
The QRS complex represents ventricular depolarization. The ventricular walls have more mass and are thicker than the atrial walls. This, along with the angle and conduction flow of the ventricles relative to lead II, makes the QRS complex the most prominent feature shown in this ECG, and the target of most beat detecto... |
The T wave represents ventricular repolarization, and marks the beginning of ventricular diastole. |
An ECG can convey a large amount of information about the structure of the heart and the function of its underlying conduction system, including: the rate and rhythm of heartbeats, the size and position of the chambers, and the presence of damage to the myocytes or conduction system. |
17.2.2.4 Normal Beats and Arrhythmias |
One of the most useful functionalities of the ECG is its use in monitoring healthy heartbeats and diagnosing arrhythmias. This chapter will focus on identifying four types of beats in particular: |
Normal—The conduction originates in the sinoatrial node, and spreads throughout the atrium, passes through the atrioventricular node down into the bundle of His and into the Purkinje fibers, spreading down and to the left throughout the ventricles. The left and right ventricles contract and depolarize almost simultaneo... |
Left bundle branch block (LBBB)—The left bundle is blocked, while the impulses continue to conduct through the right bundle and depolarize the right ventricle. This initial wave spreads towards lead V1, producing a small positive deflection. Soon after, depolarization spreads from the right ventricle to the left, away ... |
Right bundle branch block (RBBB)—The right bundle is blocked. Depolarization spreads from the left bundle through the left ventricle away from lead V1, producing a negative deflection in V1. After a delay, the depolarization spreads from the left ventricle through the right towards V1, producing a positive deflection. |
Ventricular premature beat—An extra heartbeat originates from one of the ventricles, rather than the SA node. The ventricles are activated by an abnormal firing site, disrupting the regular rhythm. In channel II, this results in the lack of a p-wave, since the beat does not begin with atrial depolarization. Furthermore... |
As a physician looks upon a visual ECG diagram and interprets the underlying workings or irregularities of the heart, so too can algorithms be developed to automatically process these signals and reveal arrhythmias (Fig. 17.7). |
Two channel ECG recordings of four beat types |
17.2.2.5 ECG Databases |
The data used in this chapter is from the MIT-BIH Arrhythmia Database https://physionet.org/physiobank/database/mitdb/, which contains 30 min ECG recordings of patients with a range of arrhythmias and normal beats. It is a landmark database, used as an FDA standard for testing automated arrhythmia detectors. Each recor... |
17.2.3 Time and Frequency Information |
The frequency domain allows the analysis of the signal with respect to frequency, as opposed to the commonly used time domain. We can not only observe how a signal changes over time, but also how much of the signal's energy lies within each frequency band. |
17.2.3.1 ECG Frequency Information |
Frequency analysis is very naturally applied to ECGs, which can be modelled as a sum of oscillators, due to their periodic nature. Most of the clinically relevant energy in a QRS complex has been found to lie within 4 and 30 Hz. Regarding the entire heartbeat, a very slow heart rate of 30 beat per minute (bpm), which l... |
In addition to the signal produced by the heart beats themselves which are of interest, there are several prominent sources of noise which should be removed: baseline wander, power line interference, and muscle noise. Baseline wander is generally low frequency offsets or oscillations due to slow movement that moves the... |
When filtering, the goal is to filter away the noise without also removing the relevant information. Therefore, given all the above information, when filtering ECGs to remove unwanted energy components, a commonly chosen bandpass range is 0.5–40 Hz. A narrow bandstop filter centered about the power line frequency may a... |
17.2.3.2 The Fourier Transform |
The Fourier transform is an operation that converts a function of time into a sum of sinusoids, each of which represent a frequency component in the resultant frequency domain (Freeman 2011). The discrete Fourier transform, applied to sampled digital signals, is a linear transform and also the primary function used for... |
It characterizes a periodic signal more accurately when applied to more complete cycles. Therefore, it would be more effective when applied to a long series of similar ECG beats. But for the task of beat classification, each beat must be observed and treated in isolation, as irregular beats can suddenly manifest and di... |
With the Fourier transform, there is a direct tradeoff between more accurately characterizing the frequency information with a longer signal, and isolating beats with a shorter signal. Another very effective technique for the frequency analysis of individual beats, is wavelet analysis. |
17.2.4 Wavelets |
A wavelet is a time localized oscillation, with an amplitude that begins at zero, rises, and decreases back to zero (Mallat 2009). They can be used to extract information from data such as audio signals, images, and physiologic waveforms. Wavelets are defined by a wavelet function ψ(t) shown in Eq. 17.1, which can also... |
A mother wavelet may be scaled by factor a and translated by factor b to produce a series of child wavelets. Increasing the scale factor stretches the wavelet to make it less localized in time, allowing it to correlate with lower frequency signals, and vice versa. |
$$\psi_{a,b} (t) - \frac{1}{\sqrt a } \psi \left( {\frac{t - b}{a}} \right)\,\,(Wavelet\,series\,equation)$$ |
$$X_{w} (a ,b) = \frac{1}{{\left| a \right|^{1/2} }}\int_{ - \infty }^{\infty } {x(t)\overline{\psi } } \left( {\frac{t - b}{a}} \right)dt\,\,(Continuous\,wavelet\,transform)$$ |
Equation 17.2 shows the formula for the continuous wavelet transform (CWT) of a signal x(t), where the signal is convolved with the complex conjugate of a wavelet of a certain scale. The convolution operation between signal 1 and signal 2 can be thought of as sliding signal 1 from one edge of signal 2 to the other, and... |
Child wavelets of different scale values |
A key advantage of the CWT for frequency analysis is its ability to isolate information from a signal in both frequency and time, due to the variable scale and shift factors. For example, applying a compressed wavelet with a low scale factor may detect high frequency components in the QRS complex of the ECG, but not in... |
17.2.5 Classifying Beats with Wavelets |
There are several steps in using wavelets for the beat classification task: |
Apply the CWT to the ECG beats. |
Derive features from the output of the CWT. |
Feed these final features into a supervised classifier. |
17.2.5.1 Applying the Continuous Wavelet Transform |
The CWT requires two parameters that must be chosen: the wavelet function(s), and the scale factor(s). Observing the two channels for the various beat types, it can be seen that there are two general shapes of the QRS complexes: single spike, and sinusoid. Therefore, it will be effective to choose one wavelet shaped li... |
Two wavelet functions from the Gaussian wavelet family. Generated using (Lee et al. 2019) |
Next, the wavelet scales must be appropriately set to capture the correct frequency information. As previously stated, the frequencies of interest in the ECG are between 0.5 and 40 Hz, there. A larger scale wavelet will pick up a wider complex, which will be useful for example, in differentiating channel V1 of LBBB and... |
If the data is available, using two simultaneous ECG channels can be much more effective than using just a single lead. Each channel provides a different viewpoint of the electrical conduction of the heart, and both clinicians and algorithms can make a more accurate diagnosis when combining multiple sources of informat... |
Figure 17.10 shows the CWT applied to each lead of a normal beat, using the two wavelet functions, at various scales. The heatmap of gaus2 applied to signal MLII is the highest (more red) when the single spike QRS complex aligns with the symmetrical wavelet of a similar width. Conversely, the heat-map of gaus2 applied ... |
Two channel ECG of normal beat and output of applied CWT |
17.2.5.2 Deriving Features from the CWT |
For each beat, we will have a CWT matrix for each channel (c) and wavelet function (w). For instance, 2 × 2 = 4. Each CWT matrix has size equal to the number of scales (s) multiplied by the length of the beat (l). For instance, 5 × 240 = 1200. In total this gives around 4800 data points, which is more than the original... |
As a general rule of thumb, the number of features should never be on the same order of magnitude as the number of data points. With the MITDB dataset, there are several thousand of each beat type, so the number of features must be lower than this. |
Although the CWT has produced more data points, it has transformed the input data into a form in which the same type of time and frequency information can be extracted using a consistent technique. This would not be possible with the raw ECGs in their time domain representation. One such technique may be to take the ma... |
Two channel ECG of RBBB beat and output of applied CWT |
Although feature engineering and parameter tuning is required, these fundamental signal processing techniques offer full transparency and interpretability, which is important in the medical setting. In addition, the algorithms are relatively inexpensive to compute, and simple to implement, making them highly applicable... |
17.2.5.3 Using CWT Features to Perform Classification |
See Chap. 12 for the background description of supervised classification in machine learning. |
Once the features have been extracted from the CWT matrices for each labeled beat, the task is reduced to a straightforward supervised classification problem. Most of the algorithmic novelty is already applied in the signal processing section before actually reaching this point, which is the starting point for many mac... |
In this dataset, there are no missing values to impute as the CWT is able to be applied to each complete beat. However, it is very common to have missing or invalid samples when measuring ECGs, due to factors such as detached electrodes or limbs touching. Usually the raw waveforms themselves are cleaned, selectively se... |
Each feature should be normalized between a fixed range such as 0–1, in order to equally weight the variation in each dimension when applying the classifier. The features can be fed through a supervised classifier, such as a logistic regression classifier, k-nearest neighbors classifier, support vector machine, or feed... |
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