B 10 M ED I CAL SIGNAL ANALYSIS A Case-Study Approach Rangaraj M. Rangayyan Univeristy of Calgary Calgary, Alberta, Canada IEEE Engineering in Medicine @B and Biology Society, Sponsor IEEE Press Series on Biomedical Engineering Metin Akay, Series Editor *IEEE IEEE Press @ R L E N C E JOHN WILEY & SONS, INC. This text is printed on acid-free paper. @ Copyright 8 2002 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any fonn or by any means. electronic, mechanical, photocopying. recording, scanning or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act. without either the prior written permission of the Publisher. or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. 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ISBN 0-471-2081 1-6 10 9 8 7 6 5 4 3 2 Dedication Preface About the Author Acknowledgments Symbols and Abbreviations 1 Introduction to Biomedical Signals 1.1 The Nature of Biomedical Signals 1.2 Examples of Biomedical Signals 1.2.1 The action potential 1.2.2 The electroneurogram (ENG) 1.2.3 The electromyogram (EMG) 1.2.4 The electrocardiogram (ECG) 1.2.5 The electroencephalogram (EEG) 1.2.6 Event-related potentials (ERPs) 1.2.7 The electrogastrogram (EGG) 1.2.8 The phonocardiograrn (PCG) 1.2.9 The carotid pulse (CP) Contents vii ix xiv xvii xxix 1 1 5 5 9 11 14 28 30 31 34 38 xxi XXil CONTENTS 1.2.10 Signals from catheter-tip sensors 1.2.1 1 The speech signal 1.2.12 The vibromyogram (VMG) 1.2.13 The vibroarthrogram (VAG) 1.2.14 Oto-acoustic emission signals Objectives of Biomedical Signal Analysis Difficulties in Biomedical Signal Analysis 1.3 1.4 1.5 Computer-aided Diagnosis 1.6 Remarks 1.7 Study Questions and Problems 1.8 Laboratory Exercises and Projects 2 Concurrent, Coupled, and Correlated Processes 2.1 Problem Statement 2.2 Illustration of the Problem with Case-studies 2.2.1 2.2.2 2.2.3 2.2.4 Cardio-respiratory interaction 2.2.5 2.2.6 2.3 Application: Segmentation of the PCG 2.4 Remarks 2.5 Study Questions and Problems 2.6 Laboratory Exercises and Projects The electrocardiogram and the phonocardiogram The phonocardiogram and the carotid pulse The ECG and the atrial electrogram The electromyogram and the vibromyogram The knee-joint and muscle vibration signals 3 Filtering for Removal of Artifacts 3.1 Problem Statement Random noise, structured noise, and physiological interference 3.1.1 3.1.2 Stationary versus nonstationary processes Illustration of the Problem with Case-studies 3.2.1 Noise in event-related potentials 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2 High-frequency noise in the ECG Motion artifact in the ECG Power-line interference in ECG signals Maternal interference in fetal ECG Muscle-contraction interference in VAG signals Potential solutions to the problem 40 40 46 46 48 48 52 55 57 58 59 61 62 62 62 63 64 66 67 67 69 71 71 71 73 73 74 81 85 85 85 87 87 90 91 93 CONTENTS xxiii 3.3 Time-domain Filters 93 3.3.1 Synchronized averaging 94 3.3.2 Moving-average filters 99 3.3.3 Derivative-based operators to remove low-frequency artifacts 109 3.4 Frequency-domain Filters 115 3.4.1 Removal of high-frequency noise: Butterworth lowpass filters 118 3.4.2 Removal of low-frequency noise: Butterworth highpass filters 127 3.4.3 Removal of periodic artifacts: Notch and comb filters 130 3.5 3.6 Optimal Filtering: The Wiener Filter Adaptive Filters for Removal of Interference 3.6.1 The adaptive noise canceler 3.6.2 The least-mean-squares adaptive filter 3.6.3 3.7 Selecting an Appropriate Filter 3.8 Application: Removal of Artifacts in the ECG 3.9 Application: Maternal - Fetal ECG 3.10 Application: Muscle-contraction Interference 3.11 Remarks 3.12 Study Questions and Problems 3.13 Laboratory Exercises and Projects The recursive least-squares adaptive filter 4 Event Detection 4.1 Problem Statement 4.2 Illustration of the Problem with Case-studies 4.2.1 The P, QRS, and T waves in the ECG 4.2.2 The first and second heart sounds 4.2.3 The dicrotic notch in the carotid pulse 4.2.4 EEG rhythms, waves, and transients Detection of Events and Waves 4.3.1 Derivative-based methods for QRS detection 4.3.2 The Pan-Tompkins algorithm for QRS detection 4.3.3 Detection of the dicrotic notch Correlation Analysis of EEG channels 4.4.1 Detection of EEG rhythms 4.4.2 4.3 4.4 Template matching for EEG spike-and-wave detection 137 146 147 150 15 1 158 162 165 166 171 171 175 177 177 178 178 179 180 180 182 183 187 191 191 193 200 xxiv CONTENTS 4.5 Cross-spectral Techniques 4.5.1 4.6 The Matched Filter 4.6.1 4.7 Detection of the P Wave 4.8 Homomorphic Filtering 4.8.1 Generalized linear filtering 4.8.2 Homomorphic deconvolution 4.8.3 4.9 Application: ECG Rhythm Analysis 4.10 Application: Identification of Heart Sounds 4.1 1 Application: Detection of the Aortic Component of S2 4.12 Remarks 4.13 Study Questions and Problems 4.14 Laboratory Exercises and Projects Coherence analysis of EEG channels Detection of EEG spike-and-wave complexes Extraction of the vocal-tract response 5 Waveshape and Waveform Complexity 5.1 Problem Statement 5.2 Illustration of the Problem with Case-studies 200 200 204 204 205 212 212 213 216 222 225 227 23 1 233 234 237 237 238 5.2.1 The QRS complex in the case of bundle-branch block 238 5.2.2 5.2.3 Ectopic beats 5.2.4 EMG interference pattern complexity 5.2.5 PCG intensity patterns 5.3 Analysis of Event-related Potentials 5.4 Morphological Analysis of ECG Waves 5.4.1 Correlation coefficient 5.4.2 5.4.3 ECG waveform analysis 5.5.1 Amplitude demodulation 5.5.2 5.5.3 The envelogram 5.6.1 The root mean-squared value 5.6.2 Zero-crossing rate 5.6.3 Turns count 5.6.4 Form factor The effect of myocardial ischemia and infarction on QRS waveshape The minimum-phase correspondent and signal length 5.5 Envelope Extraction and Analysis Synchronized averaging of PCG envelopes 5.6 Analysis of Activity 238 238 239 239 240 240 240 24 1 248 249 25 1 252 255 256 259 259 260 262 CONTENTS 5.7 Application: Normal and Ectopic ECG Beats 5.8 Application: Analysis of Exercise ECG 5.9 Application: Analysis of Respiration 5.10 Application: Correlates of Muscular Contraction 5.11 Remarks 5.12 Study Questions and Problems 5.13 Laboratory Exercises and Projects 6 Frequency-domain Characterization 6.1 Problem Statement 6.2 Illustration of the Problem with Case-studies 6.2.1 6.2.2 The effect of myocardial elasticity on heart sound spectra Frequency analysis of murmurs to diagnose valvular defects 6.3 The Fourier Spectrum 6.4 Estimation of the Power Spectral Density Function 6.4.1 The periodogram 6.4.2 The need for averaging 6.4.3 6.4.4 6.4.5 6.5.1 Moments of PSD functions 6.5.2 Spectral power ratios Application: Evaluation of Prosthetic Valves The use of windows: Spectral resolution and leakage Estimation of the autocorrelation function Synchronized averaging of PCG spectra 6.5 Measures Derived from PSDs 6.6 6.7 Remarks 6.8 Study Questions and Problems 6.9 Laboratory Exercises and Projects 7 Modeling Biomedical Systems 7.1 Problem Statement 7.2 Illustration of the Problem 7.2.1 Motor-unit firing patterns 7.2.2 Cardiac rhythm 7.2.3 7.2.4 Patello-femoral crepitus Formants and pitch in speech 7.3 Point Processes 7.4 Parametric Svstem Modeling xxv 263 265 266 269 269 272 274 277 278 279 279 280 282 287 288 289 29 1 297 298 302 305 307 308 3 10 311 312 315 315 316 3 16 317 317 319 3 20 327 XXVi CONTENTS 7.5 Autoregressive or All-pole Modeling 7.5.1 Spectral matching and parameterization 7.5.2 Optimal model order 7.5.3 Relationship between AR and cepstral coefficients 7.6.1 Sequential estimation of poles and zeros 7.6.2 Iterative system identification 7.6.3 Homomorphic prediction and modeling Electromechanical Models of Signal Generation 7.7.1 Sound generation in coronary arteries 7.7.2 Sound generation in knee joints Application: Spectral Modeling and Analysis of PCG Signals 7.6 Pole-zero Modeling 7.7 7.8 Application: Heart-rate Variability 7.9 7.10 Application: Coronary Artery Disease 7.11 Remarks 7.12 Study Questions and Problems 7.13 Laboratory Exercises and Projects 8 Analysis of Nonstationary Signals 8.1 Problem Statement 8.2 Illustration of the Problem with Case-studies 8.2.1 Heart sounds and murmurs 8.2.2 EEG rhythms and waves 8.2.3 8.3.1 Articular cartilage damage and knee-joint vibrations Characterization of nonstationary signals and dynamic systems 8.3 Time-variant Systems 8.4 Fixed Segmentation 8.4.1 The short-time Fourier transform 8.4.2 Considerations in short-time analysis 8.5.1 Spectral error measure 8.5.2 ACF distance 8.5.3 The generalized likelihood ratio 8.5.4 Use of Adaptive Filters for Segmentation 8.6.1 Monitoring the RLS filter 8.5 Adaptive Segmentation Comparative analysis of the ACF, SEM, and GLR methods 8.6 333 339 342 346 355 358 360 366 37 1 37 1 374 377 380 386 386 389 390 39 1 392 392 392 393 393 396 397 399 400 402 405 408 413 414 416 419 420 8.6.2 The RLS lattice filter 42 1 8.7 Application: Adaptive Segmentation of EEG Signals 43 1 8.8 Application: Adaptive Segmentation of PCG Signals 438 8.9 Application: Time-varying Analysis of Heart-rate Variability 438 8.10 Remarks 8.1 1 Study Questions and Problems 8.12 Laboratory Exercises and Projects 9 Pattern Classification and Diagnostic Decision 9.1 Problem Statement 9.2 Illustration of the Problem with Case-studies 9.2.1 Diagnosis of bundle-branch block 9.2.2 Normal or ectopic ECG beat? 9.2.3 Is there an alpha rhythm? 9.2.4 Is a murmur present? 9.3 Pattern Classification 9.4 Supervised Pattern Classification 9.4.1 Discriminant and decision functions 9.4.2 Distance functions 9.4.3 The nearest-neighbor rule 9.5.1 ’ Cluster-seeking methods Probabilistic Models and Statistical Decision 9.6.1 9.6.2 9.7 Logistic Regression Analysis 9.8 The Training and Test Steps 9.8.1 The leave-one-out method 9.9 Neural Networks 9.10 Measures of Diagnostic Accuracy and Cost 9.10.1 Receiver operating characteristics 9.10.2 McNemar’s test of symmetry 9.1 1 Reliability of Classifiers and Decisions 9.12 Application: Normal versus Ectopic ECG Beats 9.13 Application: Detection of Knee-joint Cartilage Pathology 9.14 Remarks 9.15 Study Questions and Problems 9.16 Laboratory Exercises and Projects 9.5 Unsupervised Pattern Classification 9.6 Likelihood functions and statistical decision Bayes classifier for normal patterns 444 44.4 444 445 446 446 446 447 448 448 449 450 450 45 1 452 453 453 457 457 460 462 463 463 464 466 469 472 473 474 480 483 485 487 xxviil CONTENTS References Index 489 509