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THE DEVELOPMENT AND ANALYSIS OF A VENTRICULAR FIBRILLATION DETECTOR

by

Scott David Greenwald B.S.E., Duke University

(1982)

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF

MASTER OF SCIENCE

IN ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

May 1986

Scott David Greenwald

The author hereby grants to M.I.T. permission to reproduce and to distribute copies of this thesis document in whole or in part.

Signature redacted

Signature of Author__

Department of Electrical Engineering and Computer Science

Signature

redacted

May 22, 1986

Certified b Accepted by( y. I~' ~

S.

novzr ,. ark Thesis Supervisor

Signature redacted,

A- -Z Arthur C. Smith

Archives

Chairman, Departmental Committee on Graduate Students

MASSACHUSETTS INSTITU1E

OF TECHNOLOGY

JUL 2 31986

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2

-DEVELOPMENT AND ANALYSIS OF A

VENTRICULAR FIBRILLATION DETECTOR

by

SCOTT DAVID GREENWALD

Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements

for the Degree of Master of Science May 22, 1986

ABSTRACT

Three detection schemes were developed in order to discriminate

ventricular tachycardia, flutter, and fibrillation from electrode motion noise. The first detection scheme (Detector 0) had been described in the literature and was implemented in this study as a reference for two novel detectors under development (Detectors 1 and 2.) Detectors 1 and 2 estimated the power spectrum of 4-second segments of digitized ECG with a second-order autoregressive (AR(2)) process. The two coefficients of the AR(2) model were used as the features to distinguish between the rhythm classes.

For each of the four classes, the features were assumed to be Gaussian distributed. Thus the conditional distributions of the features for each class were dependent only on two parameters, the mean vector and the covariance matrix. Detectors 1 and 2 differed in their estimation of these two parameters. Detector 1 estimated the mean vector and covari-ance matrix over all the features. Detector 2 estimated these parame-ters by first calculating the parameters for each patient in the data-base and then averaging these patient-specific parameters.

Two cost functions (B1 and B2) were used to evaluate the detectors. The detectors were optimized with respect to gross sensitivity (Bi) and the sum of gross sensitivity and positive predictivity (B2).

The results show that all three detection schemes were equivalent with respect to B1. Detector 2 performed slightly better than Detector 1 and much better than Detector 0 with respect to B2.

Thesis Supervisor : Dr. Roger G. Mark, M.D., Ph.D. Title: Matsushita Associate Professor of

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-Acknowledgements

I know where to begin, it's just tough finding where to end. I want to thank so many people who have helped me over the past years. Not so much for this thesis. This just happens to be what I was working on at the time. I want to thank them for their guidance through my struggle to figure out what MIT was all about, to understand relation-ships, and to understand self.

I now happen to be where I wanted to be when I started out; how-ever, I didn't get here the way I planned. I don't think that I would have started had I known a priori what mountains where ahead of me. But because of the special people mentioned in this all too brief "thank you", I transended the terrain. That is , WE transended the terrain.

I first want to thank Prof. Roger Mark (Roger) for his guidance as a thesis supervisor and as the achetype of dedication, persistance, and forgiveness. Always constructive and giving. The only person I know

that puts self last. Always.

Clearly, without a doubt, I am in greatest debt to Paul Albrecht. Imagine someone with all the answers and no egotisim. He always had the time for one more question. (And there were quite a few.) I owe him thanks for his guidance with this work, for my budding professional career with Computers in Cardiology, for teaching me C and Venix and statistics and .... I am honored to be his friend.

Dr. David Israel, M.D. Soon to be a Ph.D. Remarkably calm amid the BMEC computer confusion. True patience with his work and others. I

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-thank him for his help in making the computer a less formidible machine.

I appreciate the constant encouragement from Jeff Madwed. I came to MIT as an academic sprinter. Unfortunately, a thesis is a marathon

(or two.) Thanks, Jeff, for helping me keep the pace.

I want to thank those people who got me started. George Moody and Wolfram Jarisch played vital roles in launching my thesis. Wolfram is a fine statistician. George knows ECG analysis like Bach knew music... .structured and exact. Phil Devlin, Joe Meitus, Diane Perry, and the Arrhythmia Lab Staff deserve my gratitude for their help in establishing the Malignant-Arrhythmia Database.

I want to thank those people who got me finished. I will remember Paul Ferguson and Imre Gaal for their help with using NROFF, that delightfully simple word processing language with a mind of its own. My

sincere appreciation to Gloria McAvenia, Terry Parekh, Patty Cunningham, and Keiko Oh for their administrative support (and friendship.) I am

(financially) indebted to the Kleberg Foundation who has kindly sup-ported my MEMP fellowship and saw this work to completion.

I want to thank those people who helped me in between. I am indebted to every Medical Engineering/Medical Physics student. What a group of INDIVIDUALS. You can survive anything given you don't do it alone. A special thanks to Debbie Burstein who revitalized the spirit

of MEMP. A'lady. A scholar. She balances them well. I am indebted also to the staff and students of the Biomedical Engineering Center. Thanks.

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-I had to choose my family again, it would be them. I love you. Four hundred miles away but always here.

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6 -Table Of Contents TITLE PAGE... 1 ABSTRACT... 2 ACKNOWLEDGEMENTS... 3 TABLE OF CONTENTS... 6 1.0 INTRODUCTION... 8

1.1 Relevant Cardiac Physiology and Electrocardiography... 8

1.2 The VF Detection/Artifact Rejection Problem for Arrhythmia Detectors... 15

1.3 Formulation of the Detection Problem... 18

2.0 BACKGROUND... 28

2.1 Historical Ventricular Fibrillation Detection... 29

2.1.1 Power Spectral Detection Methods... 30

2.1.1.1 Relative Power About the Spectral Peak Detector (Fixed Bandwidth)... 30

2.1.1.2 Relative Power About the Spectral Peak Detector (Varied Bandwidth)... 35

2.1.1.3 Relative Power in Spectral Bands Detector... 39

2.1.2 Time Domain Detection Methods... 45

2.1.2.1 Shifted Waveform and Addition Detector... 45

2.1.2.2 Peak/Trough Series Detector... 49

2.1.2.3 Amplitude Histogram Detector... 56

2.2 Discriminating Malignant Arrhythmias and Noise Using Autoregressive Modeling... 59

2.2.1 Introduction... 60

2.2.2 Spectral Resonance and Q... 63

2.2.3 Continuous-Time and Discrete-Time Relationships... 67

2.2.4 Autoregressive Modeling... 70

3.0 METHODS... ... 79

3.1 Database Development... o.79 3.1.1 Creation of the Database... 83

3.1.2 Malignant-Arrhythmia Section... 83

3.1.3 Noise Section... 85

3.2 Implementation of a Reference Detector... 86

3.2.1 Digest of the Detection Scheme... 86

3.2.2 Analysis of the Detector... 86

3.3 Implementation of an Autoregressive Model Detector... 92

3.3.1 Digest of the Detection Scheme... 92

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-3.4 Detector Evaluation Methodology... 107

3.4.1 Detector Performance Curves... 107

3.4.2 Estimating Confidence Limits for Arrhythmia Performance Measures... 115

4.0 RESULTS OF THE DETECTION SCHEMES... 126

4.1 Results for the Reference Detector... 126

4.2 Results for the Autoregressive Model Detectors... 126

5.0 DISCUSSION... 212

5.1 Discussion of the Reference Detector Results... 214

5.2 Discussion of the Results of the Autoregressive Model Detectors... 221

6.0 CONCLUSIONS... 231

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8

-Chapter 1

1. INTRODUCTION

1.1. RELEVANT CARDIAC PHYSIOLOGY AND ELECTROCARDIOGRAPHY

Figure 1.1.1 shows a picture of the heart and diagrams its conduc-tion system. The heart is functionally two pumps separated left from right. Each pump is composed of two chambers, an atrium (the top "fil-ling tank"), and a ventricle (the main ejecting unit at the bottom.) These two pumps act in series to oxygenate the blood by pumping blood to

the lungs (right heart) and to pump the oxygen-rich blood to the body (left heart.)

The origin of the heart beat is in a concentrated group of cells located in the left atrium (sino-atrial node (SAN).) These cells, gen-erate action potentials periodically which initiate electrial wavefronta which spread across the atria. Because the SA node initiates the heart beat, the SA node is called the primary pacemaker of the heart. The SAN pacemaker rate is modulated by the nervous system through both parasym-pathetic and symparasym-pathetic innervation.

Tracts of muscle cells preferentially conduct this action potential throughout the heart. These tracts are outlined in figure 1.1.1. The conduction pathways in the atria link the primary pacemaker site (sino-atrial node) with a secondary pacemaker located between the atria and the ventricles (the atrio-ventricular node (AVN).) The AV node is also autogenic but fires at a slower rate than the SA node and is "reset" by the impinging action potiential from the SA node.

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-The heart muscle (myocardium) contracts in response to changes in the electrial potential across the cellular membranes (electro-mechanical coupling.) Thus the resultant spread of electrical activity across the atria causes them to contract.

The atria are electrically isolated from the ventricles except through the AV node. Thus ventricular contraction is initiated by the SAN after the action potential has passed through the AV node. The AVN acts as a delay allowing the atria to contract and "top off" the ventri-cles before they eject the blood from the heart.

The ventricular conduction system begins at the AVN, continues through the Bundles of His, and ends with the Purkinje network that branches into the myocardium. The entire conduction system ensures a synchronized order of atrial-then-ventricular contraction. Because of the electro-mechanical coupling, contraction is coupled to cellular depolarization. Following contraction, cells return to their polarized resting potentials during muscular relaxation.

The electrical activity of the heart is clinically observed with an electrocardiogram (ECG) monitoring system. The composite electrical activity of the heart cells produce potentials at the surface of the body. Monitoring potentials between different electrodes taped to the chest or limbs produce the electrocardiogram.

Figure 1.1.2 shows a segment of an electrocardiogram (ECG) of a normal individual. The figure shows a series of discrete beats which form a nearly periodic signal. Different portions of each beat correspond to physiologically significant events. (Refer to figure

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-1.1.3.) In broad terms, the P wave corresponds to atrial depolarization,

the QRS complex corresponds to ventricular depolarization, and the T wave corresponds to ventricular repolarization. Atrial repolarization occurs during the QRS complex but is masked by the large potential

changes of ventricular depolarization.

If there is insufficient blood flow to the heart muscle, the ven-tricular tissue may become irritable. The result is that the ventricles may initiate a beat independent of the normal pacemaker-conduction mechanism. The resultant beat, which originated in an "ectopic focus", is called a "premature ventricular complex" (PVC) and is shown in figure 1.1.4. This figure shows wide, premature ventricular beats interspersed with narrow, normal sinus beats.

Ectopic ventricular pacemakers may generate series of PVCs rather than isolated beats. A series of three or more in duration at an equivalent rate of 100 per minute is called ventricular tachycardia and is shown in figure 1.1.5. If the ventricular rate increases signifi-cantly (250-300 bpm), then the ventricular complexes begin to superim-pose and mask out the smaller amplitude portions of beat complex. The resultant ECG looks sinusoidal (as shown in figure 1.1.6) and is called ventricular flutter (VFL). (Ventricular flutter is defined here as high grade VT with sinusoidal morpholgy.) Although ventricular flutter may subside back to a lower grade of VT, it frequently rapidly progresses to ventricular fibrillation (VF).

Ventricular fibrillation, as shown in figure 1.1.7, is devoid of isolated ventricular complexes. At this stage, a number of ventricular foci have developed, each competing for the mechanical control of the

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-heart. During VF, because there are a number of isolated foci, the ven-tricles contract chaotically in an unsynchronized fashion. Since the heart pump is uncoordinated, little blood is ejected to the body. Death ensues as the brain deteriorates from lack of oxygen and nutrients.

Thus it is clinically imperative to detect when a patient is in VFL and VF in order to intervene and save the patient's life. Because rapid VT, VFL, and VF are potentially lethal cardiac arrhythmias, they are collectively calles "malignant arrhythmias."

Superior veno cova --- CONDUCTING STRUCTURES

- --- ---SA NODE Right atrium

---Coronary sinus ---.

Tricuspid valve --- -

--- ---- COMMON BUNDLE

Right ventricle --- -- - --- LEFT BUNDLE BRANCH

--- - - RiGHT BUNDLE BRANCH Interventricular --- --- ANTERIOR DIVISION OF

septum LEFT BUNDLE BRANCH

- -POSTERIOR DIVISION OF

L c LEFT BUNDLE BRANCH

Left ventricle --- --- -- -

-.onducting system of the human heart, showing anatomical features of the heart (labels at left) and the conducting structures (labels at right). (Modified from Bennrnghoff: Lehrbuch der Anatomie des Menschen, 1944. J. F. Lehmanns Verlag, Munich.)

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P-R INTERVAL INTERVAl RATE O-T INTERVAL S-T SEGMENT ADULTS 0.18 TO 0.20 SECOND 0.07 TO 0,10 60 0.33 TO 0.43 SECOND 0.14 TO 0.16 SECOND

NORMAl ChILDREN 0.15 TO 0.18 SECOND SECOND 70 0.31 TO 0.41 SECOND 0.13 TO 0.15 SECOND

RANGES 80 0.29 TO 0.38 SECOND 0.12 TO 0.14 SECOND

I ADLTS0. S T 0.0 SCON 0.7

T 0,1 0 0.5 TO 0.32 SECOND 90 0.6 TO 0.01 SECOND0.28 TO 0.36 SECOND 0 11 TO 0.13 SECOND 100 0.27 TO 0.35 SECOND 0.10 TO 0.11 SECOND 120 0.25 70 0.32 SECOND 0.06 TO 0.07 SECOND 0-7 .. ... .- I .... .

S2:! 3 5: _ - _

-NT

VA-CALCULATION COUNT NUMBER OF R-R INTERVALS Q3 N 3 SECONOS (15 TImi SPACES OF 0.2 SECOND EAOE OF RATE

MULTIPLY 3.5 BY 20 TO GIVE RATE PER MINUTE (70 IN THIS CASO

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-Figure 1.1.4 Premature Ventricular Complexes (PVCs) Interspersed with Normal Beats.

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-Figure 1.1.6 Ventricular Flutter.

Figure 1.1.7 Ventricular Fibrillation.

1.2. THE VF DETECTION/ARTIFACT REJECTION PROBLEM FOR ARRHYTHMIA DETECTORS

Because of the clinical relevance of malignant arrhythmias, immedi-ate detection of high grade VT,VFL, and VF is imperative. Since it is so important to detect these episodes, monitoring machines frequently

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-have a high rate of false alarms (alarms due to false positive detec-tions.) It is the purpose of this section to describe the different types of false alarms.

Most arrhythmia monitors classify beats in the electrocardiogram by detecting separate beats as isolated events, extracting features, and classifying the beats based on the particular beat features. Monitoring systems which isolate beats to classify the electrocardiogram perform poorly on rhythm disturbances such as high grade VT, VFL, and VF.

Because VFL or VF is not a periodic signal of discrete events, the beat detection algorithm may cause the monitoring machine to produce three types of mistakes. Two of the mistakes are false alarms which alert the staff. The third mistake is a missed VF episode (false nega-tive), a mistake that endangers a patient's life. life.

The first type of false alarm is not clinically serious. If the amplitude of VF is small ("fine VF"), the beat detector will fail to isolate a beat complex and thus ring an asystole alarm (i.e., an alarm that the heart has stopped beating.) This false alarm caused the system to default so that the patient would receive immediate attention as he/she would require anyway.

The second type of false alarm is due to noise confusing the detec-tion algorithm. Because isolated event detection systems have diffi-culty with undulating waveforms and rhythm disturbances, certain types of noise elicit false positive alarms.

Electrode motion artifact is produced when a patient moves or dis-turbs the electrodes attached to his/her skin. Electrode motion

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-artifact (EM noise) may cause two misclassifications of the observed electrocardiogram. First, if the noise glitches are significanty large, the beat detector may classify the glitches as some form of wide ven-tricular complex. Second, if the artifact masks out the electrocar-diogram without producing distinct glitches, the beat detector would fail to detect a beat and therefore sound an asystole alarm. This mis-take, although benign to a healthly patient who simply moved his/her electrodes, is significant because it diminishes the clinical staff's

confidence in the utility of the machine. An excessive rate of false positives may cause the staff to respond less efficiently to alarms than desired. If a VF episode occured and caused an alarm, the staff may respond too late to successfully resuscitate the patient. Here we have a missed event, not due to the detecton system, but rather due to the effect of excessive false postives on the staff/machine system.

(Optim-izing the staff/machine response is discussed in section 3.4.1.) This research focused on correcting this type of false alarm due to noise.

The third type of error is false negative rejection of a VFL/VF episode. If the peaks of VFL are significant, the beat detector may trigger off every fourth or fifth peak and report that a sequence of wide, bizarre complexes had occurred, but not that anything immediately significant had passed. Like the false negative due to the staff/machine system, this missed event may endanger a patient's life.

The objective of this research was to develop a rhythm detection algorithm that would work in parallel to a primary beat classifier. This parallel processor would discriminate between the collective set of high grade VT, VFL,and VF from noise artifacts.

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-1.3. FORMULATION OF THE DETECTION PROBLEM

This section formulates the general detection problem and intro-duces terminology used in the design and analysis of detection schemes. Figure 1.3.1 shows a block diagram description of the general detection problem.

OBSERVATION DETECTOR 00- DECISION

Figure 1.3.1 Block diagram of the general detector.

A detector may observe one of many different classes of input signals. In this study, for example, the detector may observe an episode from either of the following four classes : 1) Ventricular Tachycardia (VT), 2) Ventricular Flutter (VFL), 3) Ventricular Fibrillation (VF), or 4) electode motion artifact (NOISE). The episodes (observations) from any one class are not identical, but the detector assumes that they are similar enough within each class that it can distinguish between classes. (This is not always the case since the detector will make mis-takes.) The types of detection errors are discussed below. The reasons why particular detection schemes make certain mistakes are presented in the discussion sections (chapter 5).) The output of the detector for an input observation is the decision of the class type from which the

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-observation came.

The following illustrative example describes the binary case of discriminating between two classes. Let the null hypothesis be that the observation was electrode motion arifact (i.e, class NOISE.) Denote this hypothesis by H0 = N. Then the alternative hypothesis must be that the observation was not artifact (i.e., the observation was from either of the classes VT,VFL, or VF.) Let the three malignant arrhythmia classes be combined into the one class, V. Denote this alternative hypothesis

by Hi = V.

The detector's task is to decide if an observation belonged to class N or V. Since observations may be from one of two classes, and the detector may assign an observation to either of those two classes,

the detector may make four different types of decisions over the course of observing all its input episodes. That is, the detector may

1) correctly decide that an observation was from class V (true

positive detection (tp)),

2) incorrectly decide that an observation was from class V (false positive detection (fp)),

3) correctly decide that an observation was from class N (true negative rejection (tn) or correct rejection), or

4) incorrectly decide that an observation was from N (fase nega-tive rejection (fn)).

(This terminolgy is clear if one assumes that the detector is interested in detecting the serious arrhythmia events and rejecting the noisy

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-artifact.)

One can begin to evaluate the performance of a detector by record-ing the number of each of the four types of decisions that the detector makes for a set of observations (i.e., a test database.) To interpret the detector performance, these numbers are ordered in a decision matrix which is frequently called a "confusion matrix." Figure 1.3.2 shows a confusion matrix for the binary decision problem under consideration. The number of events of a particular type of decision are denoted by the captital letters of the decision type.

Once the results of a detctor have been compiled, one can examine its efficacy by defining and evaluating detector performance measures. This section presents three measures for evaluating a detector

sensi-tivity, specificity, and positive predictivity.

The data in a confusion matrix describes how well a detector per-formed over a particular database. It is often important to estimate the probabilities of false postive and true postive decisions that a detector will make. (These measures allow one to compare the perfor-mance of different detectors.) These probabilities are estimated by the false postive rate (FPR) and true positve rate (TPR) calculated from the confusion matrix data. Specifically,

TPR = TP + FN

FPR =

FP + TN

The true positive rate is also called the "sensitivity"(SE) of the detector to detecting observations of class V.

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- 21 -TRUTH ALGORITHM V TP N FN N

Figure 1.3.2 Binary Confusion Matrix. The horizontal axis labels the true class types of the observations. The vertical axis labels the as-signed class types (decisions) for the observations. Each element in the matrix contains the number of observations from class j assigned to class i (where (i,j) is the location of an element in the matrix.) The sum of the elements in any column(j) is the total number of observations in the database of that particular class(j). The sum of the elements in any row(i) is the total number of observations that were assigned to that particular class(i). TP number of true positive decisions. FP number of false positive decisions. TN number of true negative rejec-tions (correct rejecrejec-tions). FN number of false negative rejections.

The "specificity"(SP) of a detector is a measure which describes how well the detector ignores observations from class N (i.e., how well it correctly rejects noise.) It is defined by

SP = ---FP + TN

The FPR is related to the specificity by

FPR = 1 - SP

To understand which performance measures are important, one must FP

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-consider that hospital staff respond to alarms generated by monitoring machines. The machine will sound an alarm for only the true and false positive cases. That is, there is no reason to notify the nurse if the patient is moving and creating motion artifact, nor can the detector create an alarm if it misses a V event. However, the monitor will sound an alarm if noise confuses the detector into deciding the observation was a V event. These false positives create a problem with the hospital

staff. If the FPR is excessive, the staff looses confidence is the mon-itoring machine and may therefore respond to its alarms less effi-ciently. A useful measure of the influence of the false positives on the staff/machine system is the positive predictive accuracy (PPA) defined

by

PPA = TP

TP + FP

The PPA is also called the positive predictivity (+P). A detector which

maxamized these three measures (SE=100%, SP=100%, PPA=100%) would always make the correct decision.

In the design of a detector, one can frequently tweak the detection algorithm so that one can trade off percentage points between the dif-ferent performance measures. For example, one can always make a detec-tor 100% sensitive to V events simply forcing the detecdetec-tor to call every observation a V event. This detector setting would have no TN and therefore have a 0% specificity. Conversely, one could make a detector with a 0% sensitivity and 100% specificity by reversing the roles

between N and V classes. Obviously there are detector settings in between which would yield non-zero performance measures.

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-TP,FP,TN, and FN decisions, detector settings are often set based on assigning costs of making each of the four decisions. Specifically, the four costs would be assigned to the decision types, and the setting that minimized the expected cost of the detector would be selected. The fol-lowing discussion shows the derivation of the detector setting used to minimize the expected cost of a detector for the binary case.

Recall that there are two hypotheses (classes)

H0 =

N

H1 = V

There is an a priori probability that the detector will see each of these events, namely, P(H ) = a priori probability that the observation was N, P(H1) = a priori probability that the observation was V.

A detector makes its decision based on extracting features from the observation. It compares these features with some information it learned from a learning database of episode samples of each class type. (Different detectors extract different features (and even different numbers of features) so the discussion can not be made more specific until specific detection schemes are discussed in sections 2.2, 3.2, and

3.3.)

As an example, consider the case where the detector extracts one feature (x) from the observation (say average amplitude of the episode.) This detector then will decide what class the observation came from based on the value of this single feature (x) with respect to some threshold (,q). For convenience, let the feature be Gaussian distribu-tued under both hypotheses. Let p(xIN) denote the conditional

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probabil-- 24

-ity dens-ity function of feature x given that the feature came from class

N. Likewise let p(x|V) denote the conditional probability density func-tion of feature x given that the feature came from class V. A picture

of this example is diagrammed in figure 1.3.3.

p(xIN) D0 DECIDE N p(xIV) x .- M D

1

DECIDE V 1

Figure 1.3.3 Binary Decision Problem. The conditional distributions of the feature (x) are shown with respect to both hypotheses H0 = N and H1 = V. The decision region where the detector decides class i is denoted by Di on either side of the threshold 1. Changing the threshold alters the (non-overlapping) decision regions and thus alters the

detec-tor results.

The problem is to determine where to set the threshold to achieve the desired results. In this case, we are interested in minimizing the expected cost of the detector given that we have assigned costs to each of the four decision types.

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-Let C denote the cost of deciding that the observation was from class i given that it really was from class j. Then the expected cost the detector is given by,

E(C) = 2C P(xH. IH )P(H.) (1.3.1)

i=Oj=O

where P(xeH IH) is the probability of deciding that the observation with the feature x came from H. when in reality it came from H . P(xeH IH) depends upon the decision region D. and is given by,

P(xeH H

I

) = J, p(xIH )dx

Substituting the definitions for P(xH IH ) into equation 1.3.1 and realizing that the decision regions D and D are non-overlapping and together make up the x-axis gives

E(C) = C00P(H ) + C01P(H1 ) + (1.3.2)

fD 1(CO-C00)P(HO)p(xlHO) (C01-C 1 1)P(HI)p(xIH1 )] dx

This equation reduces to

E(C) = C0 0P(H0) + C0 1P(H1) + (Clo-C00)P(H0 )PF - (C01 C 1)P(Hl)PD

where PF and PD are the probabilities of false and true postive detec-tions respectively.

Equation 1.3.2 shows that the expected cost is minimized by minim-izing the integrand and therefore by assigning each observation to the decision region D when

(C1 0-C0 0)P(HO)p(xIH0) - (C0 1-Cj1)P(H1)p(xIH1) (0. (1.3.3)

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-decision threshold for the detector as

"t

p(x|Hl) > (C1 0-C0 0)P(H0)

p(xIH0) 0 (C01-C11)P(H) =

The expression on the left in equation 1.3.4 is called the "likelihood ratio" because it is a ratio of two probability (likelihood) density

functions and is denoted by L(x).

The likelihood ratio criterion degenerates into two other criteria for specific cost and a priori probabilities : 1) the Minimum

Probabil-ity of Error (also called the Maximum A Posterior: (MAP)) criterion, and 2) the Maximum Likelihood (ML) criterion.

If the costs of making a correct decision are zero, and the costs of incorrect decisions are equal (i.e., C = C.., Cii =0), then L(x) becomes

p(xIH1 ) P(HO) p(xIH0) - P(H 1)

Dividing Eqn. 1.3.5 on both sides by p(x) , using Baye's rule, and rear-ranging gives

P(H Ix) = P(H Ix) (1.3.6)

which says to assign the observation to the class with the higher a pos-terior probability. This is the Maximum A Posteriori Probability detec-tion criterion.

If 1) the costs of making a corect decision are zero, 2) the costs of making an error are equal (as with the MAP detector), and 3) we

assume that the a priori probabilities are equal (i.e., P(H0)

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-p(xIH1) = p(xIHO). (1.3.7) This is the Maximum Likelihood detection criterion.

The ML detector criterion is readily applied to multiple class detection problems since the detector decides to assign the observation to that class with the highest conditional probability density. The ML detection criterion was used in this study as a landmark from which to compare other detectors which were optimized with respect to some cost (benefit) functions. (Refer to section 3.4.1 for a discussion of the benefit functions used in this study.)

As discussed earlier, there is a trade off between the FPR and TPR.

A graph which shows this trade off by plotting the TPR against the FPR

as a function of -q is called a Receiver Operating Characteristic (ROC). Figure 1.3.4 shows a ROC. Each point along the curve specifies a thres-hold for a detector. The selected threshold is a function of the costs assigned the decisions as described above or by maximizing a benefit function with respect to threshold setting (as described in section 3.4.1.)

(29)

28 -ROC 100 D Z SE 0 P F ~ 1-sP 100

Figure 1.3.4 Receiver Operating Characteristic (ROC). The ROC describes the trade off between the TPR and FPR as a function of thres-hold q along the curve. Any one point along the curve specifies a detec-tor.

Chapter 2

2. BACKGROUND

This chapter describes the previous work done in VF detection, and presents the theory for two novel autoregressive detection schemes.

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- 29

-2.1. HISTORICAL VENTRICULAR FIBRILLATION DETECTION

In an initial critical literature search, the state of research in VT, VFL, and VF detection was established. In particular, papers in the field were examined for database sources, detection schemes, and detec-tor response to artifact. A digest of the pertinent research is presented and followed by a comparison of the detection schemes.

The reviewed articles discussed detection schemes as well as data analysis of VT, VFL, and VF characteristics. These papers were divided into the sections indicated below.

Data Analysis schemes

1. Multitransformation[1,2]

2. Autocorrelation[3]

Detection schemes

1. Relative Power About the Spectral Peak Bandwidth )[4]

2. Relative Power About the Spectral Peak Bandwidth )[5]

3. Relative Power in Spectral Bands Detector[6] 4. Shifted Waveform and Addition Detector[7] 5. Peak-Trough Series Detector[8]

6. Amplitude Histogram Detector[9]

Detector ( Fixed

Detector ( Varied

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- 30

-analysis of the characteristics of VF refer to [1-31.

2.1.1. POWER SPECTEAL DETECTION METHODS

The first three detection schemes to be discussed were motivated by the spectral characteristics of VT,VFL, and VF. The power spectra of the malignant arrhythmias frequently contain a principal peak. One standard measure of the breadth of this spectral peak is its Q as defined by

Q =o

Af

where f0 is the frequency of the spectral peak and Af is the half power bandwidth. Nygards, Nolle, and Forster tried to estimate the shape (Q) and properties of the power spectra with a few parameters. These parame-ters were to be used to discriminate among ECG classes. These spectral characterization methods are described below.

2.1.1.1. RELATIVE POWER ABOUT THE SPECTRAL PEAK DETECTOR

(FIXED BANDWIDTH)

Detection Principles

A frequency domain approach to detecting VT and VF was attempted first by Nygards[4] because the power spectra of VT/VF is dissimilar to spectra for most other ECG rhythms. Because the power spectra of VT/VF is narrowly bandlimited about a single high-Q peak, while other ECG waveforms are more broadband, a measure of the Q was estimated in order to descriminate these malignant arrhythmias from other electrocardio-graphic events.

(32)

- 31

-VT and VF were descriminated from other ECG rhythms and artifact through the following steps : 1) selecting input ECG segments as VT/VF

candidates, 2) estimating the power spectrum for each VT/VF candidate waveform, 3) calculating the ratio of power in a fixed bandwidth cen-tered about the spectral peak relative to the total power in the segment (i.e., estimating the Q ) , and 4) classifying the candidate waveform via a rule table based on this ratio, the heart rate, and whether or not

a QRS complex was observed.

Candidate VT/VF waveforms for step (1) were selected from the pre-vious five seconds of input if : 1) less than three normal or supraven-tricular beats were detected, 2) no neighboring QRS complexes with nor-mal morphology or timing were detected, 3) the average signal power exceeded a threshold, and 4) no major artifacts were observed ( e.g., baseline drift, or high derivatives ) . Steps (2) through (4) - the signal processing, feature extraction, and classification methods - are discussed below.

Digest Of The Detection Method

Digital Signal Processing

The total power of the candidate signal was computed in the time domain. Stable power spectral estimates of the input were calculated by averaging power spectral estimates of overlapping sections of the input segment. Specifically, the power spectrum of 3.84 second candidate waveforms were estimated from five 1.28 second overlapping segments of this input. Each 1.28 second segment was zero-padded to 5.12 seconds in order to enhance the appearance of the spectral estimate. Because VT and

(33)

- 32

-VF were principally bandlimited under 10 Hz, power spectral estimates were calculated for input segments effectively sampled at 25Hz.

Feature Extraction

The features of interest are the estimate of the Q of the power spectrum, the heart rate, and the observation of a QRS complex. Unspecified portions of the ECG monitoring algorithm provide an estimate of the heart rate and set a flag for the existance of a QRS peak. The Q was estimated via the following method.

First, the frequency (F) corresponding to the peak of the power spectrum within 1.7 and 9.0 Hz was established. Second, the power in a bandwith of 2/3F to 4/3F was then calculated. Last, the algorithm deter-mined the ratio (R) of this power to the total power of the input sig-nal. With these features established, the detection scheme advanced to

the classification phase.

Classification

The candidate waveform was classified by mapping the estimated feature values to the decision table below. (See 2.1.1.)

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- 33

-Table 2.1.1. VT and VF Descrimination Rules

Relative Heart Rate QRS complexes Diagnosis

Power of (beats per identified ?

spectraj minute) Peak (R.) >= 85%

<

240/min -VT >= 240/minIVF < 85% no

>=

65% yes -

<

65%

--

Undefined L 65 _ - _______L

1 R denotes the ratio of power in a bandwidth 2/3 F to 4/3 F

relative to the total signal power.

Summary of Detector Performance Results

The performance measures used were not based on the standard sensitivity-specificity evaluation of arrhythmia detection schemes. Nygards[4] presented results in two other manners : 1) the number of false positives per 1000 patient hours, and 2) the ratio of true posi-tives to false posiposi-tives.

The descrimination results for Nygards Test Set are presented in table 2.1.2.

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- 34

-Table 2.1.2 Computer classification of VT and VF using Nygards' descrim-ination algorithm

True condition

Computer classification VI IF| SR+high j other

VF VT artifact AF* Po * _______-[-__,V _ _

__ _

IL...i

VF

F

16

119

21 1 17 1 5 114 1

I

VT

6

I

I

I

I

I

VF Sensitivity 72.7%I VF Positive Predictivity 17.4%

lumber False VF Alarms /

000 patient monitoring 3.6

hours

Ratio of True VF Alarms

to False VF Alarms 1:4.75

* AF is atrial fibrillation or flutter ** SR is sinus rhythm

Discussion Of The Detector Results

The sources of false VF alarms were

1) motion artifact,

2) loose electrodes,

3) atrial flutter or fibrillation

(frequently occurring with bundle branch block), 4) sinus rhythm with large P or T waves and small QRS

complexes, and

5) wide ventricular waveforms.

Nygards explained his results by the fact that he worked with lim-ited Test Set, and therefore needed to use wide criteria to detect VF. He suggested that a better descrimination between VT and VF could be

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- 35

-made through an analysis of the time variation of the power spectrum. (This suggestion is followed by Herbschleb. [2] ) In addition, he stated that the electrode impedance could be monitored to reduce false alarms due to motion artifact. Last, he suggested that a scheme which considers the power in the harmonics may help delineate VF from normal rhythms.

(Forster[6] pursued this approach.)

2.1.1.2. RELATIVE POWER ABOUT THE SPECTRAL PEAK DETECTOR (VARIED BANDWIDTH)

Detection Principles

Nolle [5] discriminated VT/VF from artifact and other waveforms by utilizing Nygard's estimate of the Q of the power spectrum of candidate records. This estimator calculates the ratio of power (R) in a bandwidth (Wi) about the frequency corresponding to the spectral peak (F) to the power in a larger bandwidth (W2). Nygards calculated R using a fixed (2/3F to 4/3F) bandwidth and the total signal power; however,

Nolle calculated R as a ratio of the powers in two different bandwidths where the larger, outer bandwidth contained the smaller, inner one. He investigated the changes in percent true and false positive VT/VF

detec-tion as funcdetec-tions of :

1) different inner bandwidths centered about F, 2) different fixed inner bandwidths

(i.e, not centered about F), and

3) different outer bandwidths.

For each selected pair of inner and outer bandwidths, Nolle established receiver operating curves to evaluate the detector's performance.

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- 36

-Digital Signal Processing

The database used for this study was collected from input ECG sig-nals which had caused the monitoring computer to produce multiple alarms. The database was therefore a biased sample, rich in VF-like artifacts. Sixty-one VT/VF records from 49 patients (11VT and 50VF) and 148 artifact records from 69 patients comprised the original database pool. The first 4.096 seconds following the onset of each VT/VF episode (or the onset of artifact) comprised the final database. The alarm coded signals were stored in data-compressed form via the Aztec [10] data compression scheme. The reconstructed records had been effectively sampled at 250 Hz and zero padded when necessary to produce 4.096-second segments. The FFT was applied off-line to estimate the power spectrum

of each of these segments.

Feature Extraction

The frequency of the peak power component (F) was identified and the power in different bandwidths was calculated. The feature used to discriminated between artifact and VT/VF was the ratio R of the power in the inner bandwidth divided by power in the outer bandwidth. Nolle tested different combinations of inner and outer bandwidths to calculate R as shown in table 2.1.3.

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- 37

-Table 2.1.3 : Inner And Outer Bandwidth Pairs Used For The Calculation Of The Power Ratio R

INNER BANDWIDTH W1

Centered About F*

Not Centered About F

| BANDWIDTH USED (Hz) 0.90 F -1.1 F 0.85 F -1.15 F 0.80 F -1.2 F 0.75 F - 1.25 F 0.70 F - 1.3 F 0.65 F - 1.35 F 0.60 F 1.4 F 0.55 F - 1.45 F 0.50 F 1.5 F 0.45 F -1.55 F 0.40 F -1.6 F 0.35 F -1.65 F L_ 0.30 F - 1.7 F 0.25 F - 1.75 F ----I 0.25 - 3.91 OUTER BANDWIDTH W2 1.5 -24

Not Centered About F 0.25 -24

1

I1.5

- 9.75

* F is the frequency of the peak power component.

Nolle presented only the results for different detectors made with the same outer bandwidth (1.5Hz to 24 Hz) and with different inner bandwidths. The inner bandwidths were centered about the peak fre-quency, F, and incremented in steps from (.9 F - 1.1 F) to (.25 F - 1.75

F). Each change in inner bandwidth corresponded to the design of a dif-ferent detector.

Classification

Artifact was discriminated from VT/VF based on the value of R cal-culated for the record. If R was greater than a threshold T, then the input was classified as VT/VF. Otherwise it was labeled artifact. The threshold was varied from 0 (corresponding to all power outside W1) to 1

(39)

- 38

-(corresponding to a WI band limited signal) in order to produce receiver operating curves. The receiver operating curve for Nolle's best selected detector is shown in figure 2.1.4.

100 z 0 U S50-U LLI 0 U 05 0 10 FALSE POSITIVES [%)

Figure 2.1.4. A receiver operating curve shows the proportions of VT/VF records correctly classified versus the false positive proportions of artifact records as the detector threshold (T) is varied from zero to one. The detector bandwidth is 70% in this example.

Results Of The Detection Method

The descrimination results for the selected detector with an inner bandwidth of 70% F on this database are shown in table 2.1.5. The per-formance measures used were the number of true positive detections of

(40)

- 39

-VT/VF and the number of false positive classifications of artifact.

Table 2.1.5 : Detector Performance 1

Threshold (T) % TP2 % FP3

.36 100% 86%

.73 93% 19%

.93 8% 0

---

___

0%

1

Detector architecture Inner bandwidth ( .65 F - 1.35 F

) Hz

2 Outer bandwidth 1.5 -24 Hz

3 TP = True Positive (i.e., VT/VF Detection )

FP = False Positive (i.e., Artifact Misclassification )

Discussion of the Detector Results

This single-feature classification scheme had difficulty in

detect-ing 5% of the VT/VF records because of their low R values due to power

in higher harmonics. Although the first four-second segment of a VT/VF or artifact episode comprised the database, Nolle stated that subsequent segments of most of these "difficult" VT/VF episodes did have suffi-ciently high R values so that the detector could properly classify them. He concluded that had he used longer segments in his classification scheme, he may have been able to discriminnate better. In contrast to presenting the detector's sources of false negatives, Nolle did not dis-cuss which artifact types were particularly difficult to correctly reject.

(41)

- 40

-Detection Principles

Forster[6] applied two different frequency domain feature extrac-tion schemes to discriminate VF from other cardiac rhythms. The two detection schemes described below differ in that the first detection scheme ( Detector 1 ) was a simplified version of the second scheme (

Detector 2 ). Forster did not combine VT and VF as a single class like Nygards and Nolle, but later tested the VF detector with VT to determine its response. Both detection schemes discriminated VF from other rhythms beginning with the following steps : 1) estimating the power

spectrum for each of the candidate waveforms, 2) establishing boundaries between lower, middle, and upper frequency bands, ( See figure 2.1.6. ) and 3) calculating the ratio (R) of power in the middle band ("VF-Band") to the power in the lower band. Detector 1 classified its input by com-paring the calculated ratio to a threshold.

Detector 2 used the ratio R in addition to : 1) examining the lower

frequency band for significant spectral structure, and 2) examining the upper frequency band for significant spectral structure and harmonics. Detector 2 classified the candidate waveform via a rule table based on

(42)

- 41

-the ratio R and -the information in -the upper and lower frequency bands.

fuOO e4CftI Vt I

Is I I H i 'Ceoa .an MCy Band

C

U

j

D

C

Frequency(HZ)

Figure 2.1.6. The lower, middle ('VF-Band'), and upper bands of the power spectrum are indicated for a VF sample spectrum.

Digest of the Detection Method

Digital Signal Processing

The database was composed of records from patients under treatment for cardiac arrest or other life-threatening events. Each record was recorded through stainless steel defibrillation paddles or via silver-silver chloride electrodes. The continuous-time records were digitized at 40 Hz following anti-alias filtering up through 16 Hz. A 128-point

FFT was used to estimate the power spectrum of 3.2 second input

seg-ments. This regimen resulted in spectral resolution of .31 Hz over the

I ~ I I I I I ~\ I I I I I Uj I

I

~/

20

(43)

- 42

-20 Hz bandlimited spectrum.

Feature Extraction

The power spectrum was divided into three sections a low fre-quency band from 0 to 3.5 Hz, a middle frequency ("VF-Band") band from

3.5 Hz to 8.0 Hz, and a high frequency band from 8.0 Hz to 20 Hz. The low and high band boundaries were adjusted so that the major frequency components were in one of the bands. The features used for discrimina-tion were the power ratio R and the two (unspecified) estimates of the significance of the spectral structure in the low and high bands.

Classification

Detector 1 classified the input by comparing the ratio R of the candidate waveform to a threshold. If R exceeded 1.1, the input was classified as VF. Otherwise the input was declared undefined. Detector 2 examined the upper and lower bands because other cardiac rhythms had power in these regions and thus could better discriminate between inputs with this added information. For example, normal sinus rhythm had power in the low frequency band, while both supraventricular tachycardia and abnormalities in depolarization and repolarization had power in the "VF-Band." Detector 2 classified the candidate waveform by mapping the estimated feature values to the decision table below. (See table 2.1.7.)

(44)

- 43

-Table 2.1.7. VF Discrimination Rules | PowerRatio (R) Power Spctral Content

--- ---

I

< 1. -F Undefined

_ Noise OnlyVF

S>.i

Significant Structure Undefined

or Harmonics

1 R denotes the ratio of power in the middle frequency band divided the power in the lower frequency band.

Summary of Detector Performance Results

by

Forster selected 141 VF records and 135 other records to constitute his database. Data segments comprising the VF portion of the database were collected at various times following cardiac arrest and resuscita-tion. Records with various rhythm types completed the database as shown in table 2.1.8.

(45)

- 44

-Table 2.1.8 .

Rhythm Type

Ventricular Fibrillation Normal Sinus Rhythm Normal Sinus Rhythm with Atrial Premature Beats or Ventricular Premature Beats or Abnormal Depo-larization and Repolari-zation

Atrial Arrhythmias with Atrial Flutter or Atrial Tachycardia or Abnormal Depolarization and Repo-larization

Wide QRS or Narrow QRS rhythms or Electrode Motion Artifact

Records were 3.2 seconds long.

Composition Number of Records1 141 32 32 Database

|1

26

The performance measures used were sensitivity, specificity, and predictive accuracy. Forster presented only his final results for the decision criteria displayed in table 2.1.7. Table 2.1.9 summarizes the results for both detectors on this database. Forster also reported the results of testing Detector 1 with 18 episodes of VT. The detector correctly rejected 13 episodes but misclassified 5 as VF. Thus Detector l's specificity to VT was 72%.

Table 2.1.9 Detectors 1 and 2 Performance Results

Detector L% Sensitivity % Specificity__ % Predicitve Accuracy]

1 91 73 78

2__ T 73 9999

(46)

- 45

-Discussion of the Detector Results

Because Forster presented only his final detector results rather than receiver operating curves for the detector, the results do not show the compromise between sensitivity and specificity as a function of the threshold value for either detector. Forster used the threshold of 1.1 to compare the two different detection strategies. He showed that by using more information (i.e., the structure of the outer bands ) he could greatly enhance specificity and predictive accuracy. Because detection of VF is critical to a patient's survival, the sensitivity measure is paramount to specificity and predictive accuracy. Hence, Detector 1 is superior to Detector 2 based on the sensitivity perfor-mance metric.

The results of Detector l's VT discrimination indicate that the detector had difficulty in rejecting VT. Forster states that the heart rate of the 5 misclassified VT episodes was greater than 200 beats per minute, and thus the spectra were similar to those of VF.

2.1.2. TIME DOMAIN DETECTION METHODS

The three previous detectors used spectral properties to detect VF. The last three methods describe detection rules based on time-domain features.

2.1.2.1. SHIFTED WAVEFORM AND ADDITION DETECTOR

Detection Principles

A time-domain feature extraction method was investigated by Kuo[7] because it was computationally less intensive than the presented

(47)

- 46

-frequency domain methods. The algorithm was implemeted on an HP EKG monitoring system. The design philosophy was based on the fact that VT/VF is often sinusoidal in morphology. Because the sum of a sinusoid and itself shifted by half a period is zero, VF could be detected if the sum of itself and a shifted copy were small. VF was classified by an algorithm which 1) selects candidate VF waveforms, 2) estimates the ECG's mean period, 3) shifts a copy of the input record half the mean period, 4) adds the shifted copy to the original input to obtain the sum E, and 5) calculates the ratio A of the waveform amplitude to the normal QRS height. The features E and A were used to classify VF.

Candidate waveforms for step (1) were selected from the input if within the last second there were neither a normal QRS, paced beat, or baseline shifts. The estimation of the mean period, E, and A is presented below.

Digest of the Detection Method

Digital Signal Processing

Preprocessing, sample rate, and digital signal processing of the recorded waveforms was not presented.

Feature Extraction

The feature employed in this detection scheme was the sum of the residual amplitudes given by E. The sum E was calculated following an estimate of the mean period (T) given by equation 2.1

2n

v(j)

T = , =

-.v(j)-v(j-l) (2.1)

(48)

- 47

-where T is the number of sample points in one period, N is the number of points in 3 seconds of data, and v(j) is the amplitude of the jth sam-ple. If the mean frequency ( 1/T ) was between 2 and 9 Hz, the candi-date waveform was still considered a possible VF epsiode. The sum E was calculated by equation 2.2.

SIv (j) +v (j-T/ 2) E =(2.2)

V) 1+1 v(j-T/2)

j=0

where M is the number of samples in two seconds.

The second feature was the ratio of the candidate waveform ampli-tude to the earlier normal QRS complex amplitude. This feature was selected because it was noted that low amplitude VF did not exhibit sinusoidal morphology. The E and A estimates were passed to the clas-sification portion of the detector.

Classification

The input was classified by mapping the estimated feature values to the classification table 2.1.10.

(49)

- 48

-Table 2.1.10. Classification Rules For VF

A 1E2 Diagnosis S(.63 VF < 1/3 ->= .63 Undefined < .41 VF

>=

1/3 ->= .41 Undefined

1 A : The ratio of waveform amplitude to the normal QRS height.

2 E : Sum of the input waveform with a 180 degree phase-shifted copy.

Summary of Detector Performance Results

The algorithm was implemented on a system used to monitor hospital patients. While observing 70 patients over 148 patient days, the detec-tor generated 11 VF alarms. Eight were true VF epsisodes while three were other rhythms. Each of the true VF episodes was detected within four seconds following the onset of the episode. No false negatives were reported. The performance measures used were 1) sensitivity, 2) predictive accuracy ,3) the number of false positives per 1000 patient hours, and 4) the ratio of true to false positive VF detection. The descrimiantion results for this detector are shown in table 2.1.11.

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- 49

-Table 2.1.11 . Computer Classification Of VF

Using Kuo's Descrimination Algorithm | True Condition

Computer Classification AF1 Other2

VF 8

1

L

2

VF Sensitivity 100 %

VF Positive Predictivity 61.5 %

Number True VF Alarms

1000 patient monitoring 2.25 hours

Number False VF Alarms /

1000 patient monitoring 0.85

hours

Ratio of True VF Alarms

to False VF Alarms 1:0.3751

- - - - -

--_-_ I

1 AF is atrial fibrillation or flutter

2 Other false positives were due to rapid changes in ECG morphology of thin to wide QRS complexes.

Discussion of the Detector Results

The sources of false alarms were : 1) atrial flutter, and 2) sudden

ECG changes to small or wide QRS complexes. The perfect sensitvity result is encouraging that such a detection scheme works well. However,

the small database size weakens the significance of the report.

2.1.2.2. PEAK/TROUGH SERIES DETECTOR

Detection Principles

Brekelmans developed a time domain scheme to discriminate among VT, VFL, VF, asystole, and other rhythms. A two-tier detection scheme

(51)

- 50

-encompassing a primary detector with a parallel detector was designed and implemented on a patient monitoring system. (See figure 2.1.12.)

pemor v OCer tor i P Orre due? .ner vats

Grid ok '>c105s,11.0- on

trepshoi COmDuled OurIn noem "' suOf'On

DVOrtIM opere ?t otrms res.uitr on ?rom Successive

Dost"Ine f1tuati ns

Figure 2.1.12. The primary and parallel detector arrangement.

The primary and parallel detector played different roles in the discrimination of the electrocardiogram. The primary detector estimated the RR intervals and classified the QRS complexes via template matching

( correlation ) techniques. It's role was to classify VT and asystole. A Feature Extractor and a Peak-Trough Integrator (PTI) comprised the parallel detector shown in 2.1.13.

Figure

Figure  1.3.3  Binary  Decision  Problem.  The  conditional  distributions  of the  feature  (x)  are  shown with respect  to  both  hypotheses  H 0  =  N  and H 1  =  V
Table  2.1.2  Computer  classification of  VT  and VF using Nygards'  descrim- descrim-ination algorithm
Table  2.1.3  :  Inner  And  Outer  Bandwidth  Pairs Used  For  The  Calculation  Of  The  Power  Ratio  R
Figure  2.1.13.  Feature  Extractor  and Model  of  the  Peak-Trough  Integra- Integra-tor  (PTI).
+7

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