Nonlinear Biomedical Signal Processing, Volume 2 Dynamic Analysis and Modeling

by Akay, Metin

• ISBN13: 9780780360129
• ISBN10: 0780360125
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-09-20
• Publisher: Wiley-IEEE Press

Summary

Featuring current contributions by experts in signal processing and biomedical engineering, this book introduces the concepts, recent advances, and implementations of nonlinear dynamic analysis methods. Together with Volume I in this series, this book provides comprehensive coverage of nonlinear signal and image processing techniques. Nonlinear Biomedical Signal Processing: Volume II combines analytical and biological expertise in the original mathematical simulation and modeling of physiological systems. Detailed discussions of the analysis of steady-state and dynamic systems, discrete-time system theory, and discrete modeling of continuous-time systems are provided. Biomedical examples include the analysis of the respiratory control system, the dynamics of cardiac muscle and the cardiorespiratory function, and neural firing patterns in auditory and vision systems. Examples include relevant MATLABreg; and Pascal programs.Topics covered include: Nonlinear dynamics Behavior and estimation Modeling of biomedical signals and systems Heart rate variability measures, models, and signal assessments Origin of chaos in cardiovascular and gastric myoelectrical activity Measurement of spatio-temporal dynamics of human epileptic seizures A valuable reference book for medical researchers, medical faculty, and advanced graduate students, it is also essential reading for practicing biomedical engineers. Nonlinear Biomedical Signal Processing, Volume II is an excellent companion to Dr. Akay's Nonlinear Biomedical Signal Processing, Volume I: Fuzzy Logic, Neural Networks, and New Algorithms.

Author Biography

About the Editor Metin Akay is currently an assistant professor at Dartmouth College. A noted speaker, editor, and author, Dr. Akay has spent several years conducting research in the areas of fuzzy neural networks and signal processing, wavelet transform, and detection and estimation theory. His biomedical research areas include the autonomic nervous system, maturation, respiratory-related evoked response, noninvasive detection of coronary artery disease, and estimation of cardiac output. Dr. Akay is the founding series editor of the IEEE Press Series on Biomedical Engineering. In 1997 he received the prestigious Early Career Achievement Award from the IEEE Engineering in Medicine and Biology Society (EMBS). He is the program chair of both the annual IEEE EMBS Conference and Summer School for 2001. Dr. Akay has published several papers in the field and authored or coauthored eleven books, including Time Frequency and Wavelets in Biomedical Signal Processing (IEEE Press, 1998) and Nonlinear Biomedical Signal Processing, Volume I: Fuzzy Logic, Neural Networks, and New Algorithms (IEEE Press, 2000). He holds two U.S. patents.

Table of Contents

Preface	xv
List of Contributors	xvii
Nonlinear Dynamics Time Series Analysis	1	(39)
Bruce Henry
Nigel Lovell
Fernando Camacho
Introduction	1	(1)
Dynamical Systems Theory	1	(12)
Deterministic Chaos	1	(2)
Phase Space---Attractors	3	(3)
Lyapunov Exponents	6	(2)
Fractal Dimensions	8	(3)
Grassberger-Procaccia Algorithm	11	(2)
Time Series Analysis	13	(11)
Power Spectrum and Autocorrelation	13	(2)
Phase Space Reconstruction	15	(2)
Optimal Embedding Dimensions	17	(1)
Optimal Delay Time	18	(2)
Measuring Lyapunov Exponents from Time Series	20	(1)
Reliability Checks	21	(1)
Forecasting	21	(2)
Surrogate Data	23	(1)
Discussion	24	(16)
References	26	(3)
Appendix	29	(1)
Dynamical Systems Analysis---MATLAB Programs	29	(1)
Numerical Integration of Three Coupled ODEs	29	(1)
Three-Dimensional Surface of Section	29	(1)
Two-Dimensional Surface of Section	30	(1)
Lyapunov Exponents for Three Coupled ODEs	31	(1)
Grassberger-Procaccia Algorithm	32	(5)
Time Series Analysis---MATLAB Programs	37	(1)
Phase Space Reconstruction	37	(1)
Forecasting	37	(2)
Surrogate Data	39	(1)
Searching for the Origin of Chaos	40	(32)
Tomoyuki Yambe
Makoto Yoshizawa
Kou-ichi Tabayashi
Shin-ichi Nitta
Open-Loop Analysis by Use of an Artificial Heart	40	(5)
Artificial Heart for Investigation of the Cardiovascular Control System	40	(1)
Experimental Preparation for Open-Loop Analysis	41	(2)
Time Series Data Obtained from Open-Loop Analysis	43	(1)
Chaos and Artificial Organs	44	(1)
Direct Recording of Sympathetic Nerve Discharges to Search for the Origin of Chaos	45	(3)
Direct Recording of Autonomic Nerve Discharges	45	(1)
Recording Data of the Sympathetic Nerve Discharges	46	(1)
Nonlinear Relationship in Biological Systems	47	(1)
Predictive Control of an Artificial Heart System	48	(8)
Prediction with Information about Sympathetic Nerve Discharges	48	(1)
Future Prediction by an Autonomic Nerve and Hemodynamics	49	(3)
Mayer Wave Control for an Artificial Heart	52	(1)
Information of the Hemodynamic Fluctuation	52	(1)
Time Series Data Analysis	53	(2)
Consideration of Predictive Control Algorithm	55	(1)
Making of Chaos	56	(6)
Feedback Loop Making Chaos	56	(1)
Chaos and Time Delay	56	(2)
Simulation Model	58	(2)
Model and Time Lag	60	(1)
Nonlinearity and Simulation	61	(1)
Making the Feedback Loop in Circulation by an Artificial Heart System	62	(2)
Biological Information for Artificial Heart Control	62	(1)
Automatic Control for an Artificial Heart	62	(1)
Automatic Control Experiments	62	(1)
Producing Chaos in Animal Experiments	63	(1)
Nonlinear Dynamics of an Artificial baroreflex System	64	(4)
Approaches to Nonlinear Dynamics	64	(1)
Baroreflex System for an Artificial Heart	65	(1)
Nonlinear Dynamical Behavior of an Artificial Baroreflex System	66	(2)
Clinical Application of the Origin of Chaos	68	(4)
Approaches for Clinical Application	68	(1)
Nonlinear Dynamics in the Time Series Data of the Left Ventricular Stroke Volume	68	(2)
Acknowledgments	70	(1)
References	70	(2)
Approximate Entropy and its Application to Biosignal Analysis	72	(20)
Yang Fusheng
Hong Bo
Tang Qingyu
Introduction	72	(1)
Definition and Interpretation	73	(3)
Definition	73	(1)
Interpretation	74	(2)
Fast Algorithm	76	(2)
Cross Approximate Entropy	78	(3)
Properties of Approximate Entropy	81	(6)
Basic Properties	81	(3)
Relation with Other Characteristic Parameters	84	(1)
ApEn and Standard Deviation	85	(1)
Relation with Correlation Dimension and K-S Entropy	85	(2)
ApEn and Ziv's Complexity Measure	87	(1)
Examples of Application	87	(2)
Analysis of Heart Rate Variability (HRV) Signals [4]	87	(1)
Dynamic Analysis of HRV Signal	88	(1)
Analysis of Evoked Potential	89	(1)
Conclusions	89	(3)
References	90	(2)
Parsimonious Modeling of Biomedical Signals and Systems: Applications to the Cardiovascular System	92	(41)
P. Celka
J.M. Vesin
R. Vetter
R. Grueter
G. Thonet
E. Pruvot
H. Duplain
U. Scherrer
Introduction	92	(1)
Polynomial Expansion Models	93	(7)
Problem Statement	93	(2)
NARMA Models	95	(4)
Orthogonal Least-Squares Method	99	(1)
Singular Value Decomposition	99	(1)
Model Selection	100	(8)
Minimum Description Length	100	(2)
Other Selection Criteria	102	(1)
Polynomial Search Method	103	(1)
Validation of the Selection Criteria	104	(1)
Numerical Experiments	104	(1)
Sunspot Time Series	105	(1)
RR-Interval Time Series	106	(2)
Subband Decomposition	108	(4)
Subband Signal Processing	108	(1)
The Wavelet Transform	109	(1)
Wavelets as a Filter Bank	109	(1)
Subband Spectral Estimation and Modeling	110	(1)
Frequency Decomposition of Physical Signals	111	(1)
Modeling of the Human Visual System	111	(1)
Other Physiological Signals	111	(1)
Application to Cardiovascular System Modeling	112	(16)
The Cardiovascular System	112	(2)
Subband Decomposition of the Cardiovascular Signals	114	(1)
Dyadic Filter Bank	114	(1)
Subband Identification	115	(1)
Recording Methods and Medical Protocols	116	(1)
Reording Methods	116	(1)
Medical Protocols	117	(1)
Results on Cardiovascular Modeling	117	(1)
General Description	117	(1)
RR-Interval Prediction	118	(4)
RR-Interval Estimation from ILV and MBP	122	(5)
RR-Interval Estimation from ILV and MSNA	127	(1)
Conclusions	128	(5)
References	129	(4)
Nonlinear Behavior of Heart Rate Variability as Registered After Heart Transplantation	133	(26)
C. Maier
H. Dickhaus
L.M. Khadra
T. Maayah
Introduction	133	(2)
Detection of Nonlinear Dynamics in Time Series	135	(1)
The Detection Scheme for Nonlinearities	136	(5)
Surrogate Data Generation	137	(1)
Nonlinear Prediction	138	(2)
Testing the Hypothesis	140	(1)
Realization Aspects	140	(1)
Simulations	141	(3)
The Choice of Modeling Parameter	143	(1)
Algorithm Robustness	143	(1)
Clinical Study	144	(3)
Discussion	147	(12)
Acknowledgments	149	(1)
References	149	(3)
Appendix	152	(7)
Heart Rate Variability: Measures and Models	159	(55)
Malvin C. Teich
Steven B. Lowen
Bradley M. Jost
Karin Vibe-Rheymer
Conor Heneghan
Introduction	159	(1)
Methods and Measures	160	(15)
The Heartbeat Sequence as a Point Process	160	(1)
Conventional Point Processes	161	(2)
Fractal and Fractal-Rate Point Processes	163	(1)
Standard Frequency-Domain Measures	164	(1)
Standard Time Domain Measures	165	(1)
Other Standard Measures	165	(1)
Novel Scale-Dependent Measures	166	(1)
Allan Factor [A(T)]	166	(1)
Wavelet-Transform Standard Deviation [σwav(m)]	167	(2)
Relationship of Wavelet [σwav(m)] and Spectral Measures [Sτ(f)]	169	(2)
Detrended Fluctuation Analysis [DFA(m)]	171	(1)
Scale-Independent Measures	172	(1)
Detrended-Fluctuation-Analysis Power-Law Exponent (αD)	172	(1)
Wavelet-Transform Power-Law Exponent (αW)	172	(1)
Periodogram Power-Law Exponent (αS)	172	(1)
Allan-Factor Power-Law Exponent (αA)	173	(1)
Rescaled-Range-Analysis Power-Law Exponent (αR)	173	(1)
Estimating the Performance of a Measure	174	(1)
Statistical Significance: p, d', h, and d	174	(1)
Positive and Negative Predictive Values	175	(1)
Receiver Operating Characteristic (ROC) Analysis	175	(1)
Discriminating Heart-Failure Patients From Normal Subjects	175	(14)
Database	176	(1)
Selecting a Scale	176	(1)
Individual Value Plots	177	(2)
Predictive Value Plots	179	(1)
ROC Curves	179	(3)
Comparison with Detection-Distance Measures	182	(1)
ROC-Area Curves	183	(1)
Comparing the Measures for Various Data Lengths	184	(1)
Scale-Independent versus Scale-Dependent Measures	185	(1)
Computation Time of the Various Measures	186	(1)
Comparing the Most Effective Measures	186	(2)
Selecting the Best Measures	188	(1)
Markers for Other Cardiac Pathologies	189	(2)
Does Deterministic Chaos Play a Role in Heart Rate Variability?	191	(5)
Methods	191	(1)
Phase-Space Reconstruction	191	(1)
Removing Correlations in the Data	192	(1)
Surrogate Data Analysis	192	(1)
Absence of Chaos	193	(3)
Mathematical Models for Heart Rate Variability	196	(10)
Integrate-and-Fire Model	196	(1)
Kernel of the Integrate-and-Fire Model	197	(1)
Fractal Gaussian Noise	197	(1)
Fractal Lognormal Noise	198	(1)
Fractal Binomial Noise	198	(1)
Jittered Integrate-and-Fire Model	198	(1)
Simulating the Jittered Integrate-and-Fire Point Process	199	(1)
Statistics of the Simulated Point Process for Normal Subjects and CHF Patients	200	(1)
Simulated Individual Value Plots and ROC-Area Curves	200	(4)
Limitations of the Jittered Integrate-and-Fire Model	204	(1)
Toward an Improved Model of Heart Rate Variability	205	(1)
Conclusion	206	(8)
References	207	(6)
Appendix A	213	(1)
Ventriculo-Arterial Interaction After Acute Increase of the Aortic Input Impedance: Description Using Recurrence Plot Analysis	214	(14)
Stephen Schulz
Robert Bauernschmitt
Andreas Schwarzhaupt
C. F. Vahl
Uwe Kiencke
About Cardiovascular Mechanics and Regulation	214	(2)
Basics Before Applying Recurrence Plots on Aortic and Ventricular Hemodynamic Signals	216	(2)
Definition of a Ventriculoarterial State Space Representation	216	(1)
Visualization of the Ventriculoarterial Dynamics Using Recurrence Plot Strategies	216	(1)
Quantitative Description of Recurrence Plots	217	(1)
Experimental Setting	217	(1)
Application of Recurrence Plots on Hemodynamic Pressure and Flow Signals to Describe Pathophysiologic States	218	(2)
Hemodynamic Measurements and Ventriculoarterial Orbits	218	(1)
Application of Recurrence Plots on the Ventriculoarterial Orbit	218	(2)
Quantification of Ventriculoarterial Dynamics in the Recurrence Plot	220	(1)
Why Nonlinear Recurrence Plot Analysis for Describing Ventriculoarterial Interaction	220	(8)
Acknowledgments	223	(1)
References	223	(1)
Appendix: MATLAB Source Codes	224	(1)
Calculate and Visualize Recurrence Plot	224	(2)
Calculate Parameters	226	(2)
Nonlinear Estimation of Respiratory-Induced Heart Movements and its Application in ECG/VCG Signal Processing	228	(18)
Leif Sornmo
Magnus Astrom
Elena Carro
Martin Stridh
Pablo Laguna
Introduction	228	(1)
Maximum Likelihood VCG Loop Alignment	229	(3)
Model for Respiratory-Induced Heart Movements	229	(1)
Maximum Likelihood Estimation	230	(2)
Loop Alignment and Morphologic Variability	232	(1)
Sensitivity of Loop Alignment to Noise	233	(5)
Parameter Estimation	233	(3)
Noise and Loop Morphology	236	(2)
Spatiotemporal Alignment and QRST Cancellation	238	(4)
Signal Model with Lead-Dependent Amplitude Scaling	240	(1)
Example of QRST Cancellation	241	(1)
Conclusions	242	(4)
References	244	(2)
Detecting Nonlinear Dynamics in Sympathetic Activity Directed to the Heart	246	(17)
Alberto Porta
Giuseppe Baselli
Nicola Montano
Alberto Malliani
Sergio Cerutti
Introduction	246	(1)
Methods	247	(4)
Superposition Plot	247	(1)
Recurrence Map	247	(1)
Space---Time Separation Plot	247	(1)
Frequency Tracking Locus	248	(1)
Autoregressive Power Spectral Analysis	248	(1)
Nonparametric Bispectrum and Bicoherence	249	(1)
Corrected Conditional Entropy	250	(1)
Experimental Protocol	251	(1)
Results	251	(8)
Discussion	259	(2)
Conclusions	261	(2)
References	261	(2)
Assessment of Nonlinear Dynamics in Heart Rate Variability Signal	263	(19)
Maria G. Signorini
Roberto Sassi
Sergio Cerutti
Introduction	263	(2)
Assessment of Nonlinear Properties in Biological Systems: The Time Series Analysis	265	(6)
Review of the Principal Methods for the Estimation of Nonlinear System Characteristics	265	(2)
Estimation of Invariant Properties of the System Attractor	267	(1)
Nonlinear Noise Filtering in the Space State	267	(2)
Self-Similarity Parameters	269	(1)
Approximate Entropy	269	(2)
Nonlinear Physiological Models for the Generation of Heartbeat Dynamics	271	(3)
Realization and Study of a Nonlinear Model of the Heart	271	(1)
An Example of the Model Analysis: The Stability of the Equilibrium Point	272	(2)
Experimental Results: Examples in Cardiovascular Pathologies and Physiological Conditions	274	(4)
Myocardial Infarction	274	(1)
Normal Subjects versus Patients with a Transplanted Heart	274	(2)
ICU Patients: Classification of Death Risk through Hurst Coefficient	276	(1)
Newborn State Classification	277	(1)
Conclusion	278	(4)
References	279	(3)
Nonlinear Deterministic Behavior in Blood Pressure Control	282	(12)
Nigel Lovell
Bruce Henry
Branko Celler
Fernando Camacho
Drew Carlson
Martha Connolly
Introduction	282	(1)
Chaos in the Cardiovascular System	282	(1)
Carotid Baroreflex and Chaotic Behavior	283	(7)
Conclusions	290	(4)
References	291	(3)
Measurement and Quantification of Spatiotemporal Dynamics of Human Epileptic Seizures	294	(25)
L. D. Iasemidis
J. C. Principe
J. C. Sackellares
Introduction	294	(2)
Methods for Nonlinear Dynamical Analysis	296	(9)
Application to the EEG	296	(3)
Estimation of Short-Term Largest Lyapunov Exponents (STLmax)	299	(2)
Selection of p and τ	301	(1)
Selection of Δt	301	(1)
Selection of Vmax	302	(1)
Selection of Δmax	302	(1)
Selection of X(tj)	303	(1)
Selection of T	303	(2)
STLmax Time Series of EEG Data	305	(2)
Spatiotemporal STLmax Profiles	307	(8)
Quantification of the Spatiotemporal Dynamics	310	(5)
Conclusions	315	(4)
Acknowledgments	316	(1)
References	317	(2)
Rhythms AMD Chaos in the Stomach	319	(20)
Z. S. Wang
M. Abo
J. D. Z. Chen
Introduction	319	(2)
Rhythm and Chaos in the Stomach	321	(6)
Gastric Migrating Myoelectrical Complex (MMC)	321	(1)
Subjects and Methods	321	(1)
Subjects	321	(1)
Data Acquisition	322	(1)
Data Analysis Methods	322	(5)
Results	327	(1)
Investigation of Chaos in the Stomach via Modeling of GMA	327	(5)
Modeling of GMA via Modified Hodgkin---Huxley Equations	328	(1)
Electrophysiological Background	328	(1)
Mathematical Model	328	(3)
Bifurcation Analysis of GMA Model	331	(1)
Effects of Water Distention on Chaotic Behavior of GMA in Dogs	332	(1)
Measurements of GMA in Dogs before and after Water Distention	333	(1)
Data Analysis	333	(1)
Results	333	(1)
Discussion and Conclusions	333	(6)
References	335	(4)
Index	339	(2)
About the Editor	341