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VARIABILITY ANALYSIS & ITS APPLICATIONS TO PHYSIOLOGICAL TIME SERIES DATA by FARHAD KAFFASHI Submitted in partial fulfillment of the requirements For the degree of For the degree of Doctor of Philosophy Dissertation Advisor: Dr. Kenneth A. Loparo Department of Electrical Engineering & Computer Science CASE WESTERN RESERVE UNIVERSITY August 2007 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of Farhad Kaffashi candidate for the degree of Doctor of Philosophy * Committee Chair: Dr. Kenneth A. Loparo Thesis Advisor Professor, Department of Electrical Engineering & Computer Science Committee: Dr. Mark S. Scher Professor, Department of Pediatric & Neurology Committee: Dr. Mary Ann Werz Associate Professor, Department of Neurology Committee: Dr. Vira Chankong Associate Professor, Department of Electrical Engineering & Computer Science Committee: Dr. M Cenk C¸avu¸so˘glu Assistant Professor, Department of Electrical Engineering & Computer Science August 2007 *We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents Table of Contents . iii List of Tables . v List of Figures . vii Acknowledgement . ix Abstract . x 1 Introduction 1 2 Variability Analysis Techniques 4 2.1 Detrended Fluctuation Analysis . 5 2.2 Characterization of Power-Law Behavior Using Change Point Detection 8 2.2.1 Gradient Detection Algorithm . 9 2.2.2 Results . 11 2.2.3 Conclusions . 18 2.3 Approximate & Sample Entropy . 18 2.3.1 Incorporating a Time Delay In The Calculation . 20 2.3.2 Parameter Selection . 21 2.3.3 Parameter Validation . 22 2.3.4 Conclusion . 28 3 Complexity Analysis of Neonatal EEG 29 3.1 Data Collection & Description . 30 3.2 The Effect of Time Delay on ApEn & SpEn Computation . 33 3.3 Results & Discussion . 35 3.3.1 Histogram Analysis . 37 3.3.2 Histogram Matching Scheme . 45 3.3.3 Closeness Test . 46 3.4 Conclusions . 47 4 Epilepsy 53 4.1 Data description . 57 iii 4.2 DFA Limitation . 58 4.3 Brain Activity Quantification . 59 4.4 Data Analysis & Results . 60 4.4.1 Brain Activity Index . 63 4.5 Discussion & Conclusions . 74 4.6 Future work & Recommendations . 77 5 Analysis of Respiratory Data 78 5.1 Complexity of network . 78 5.1.1 Methods . 79 5.1.2 In vitro extracellular recording . 79 5.1.3 Parameter selection . 80 5.1.4 Results . 80 5.2 Cardioventilatory Coupling . 83 5.2.1 Methods . 83 5.2.2 Protocol . 84 5.2.3 Surrogate Data Analysis . 85 5.2.4 Data Analysis & Discussion . 86 A Variability Analysis Techniques from the Literature 95 A.1 Non-Parametric Change Point Detection . 95 A.1.1 Statistical Methods . 95 A.1.2 Description of Algorithm . 97 A.2 Correlation Dimension . 98 A.3 Information Theory Based Entropy . 100 A.3.1 Shannon Entropy . 100 A.3.2 Interval Entropy & Entropy of Intervals . 100 A.3.3 Spectral Entropy & Variance . 102 A.4 Surrogate Data Analysis . 102 A.5 Hjorth Parameters . 103 A.6 Dynamical Similarity Index . 104 A.7 Phase Synchronization . 105 Bibliography 106 iv List of Tables 2.1 DFA log-log plot gradient for different signals . 6 2.2 D2 results for intracranial EEG . 16 2.3 ApEn & SamEn Results . 27 2.4 ApEn & SamEn Results for filtered white noise . 27 3.1 Neonate EEG Channels . 32 3.2 Pittsburgh Study Group . 32 3.3 Unity vs. 1 Seconds Time Delay Analysis Results for EEG Number 96 (Mean±STD) . 36 3.4 Time Delay Analysis Results for EEG Number 96 (Mean±STD of STD) 36 3.5 Means of Complexity Results . 39 3.6 Means of Active Complexity Results . 40 3.7 Means of Quiet Complexity Results . 41 3.8 Standard Deviation of Complexity Results . 42 3.9 Standard Deviation of Active Complexity Results . 43 3.10 Standard Deviation of Quiet Complexity Results . 44 3.11 Difference Between Histograms of Pittsburgh & Pilot Studies . 46 3.12 Mean Mahalanobis Distance Between Neonates at 40-41 Week . 48 3.13 Means of Complexity Results after Histogram Matching . 51 3.14 T-test result between Pittsburgh full term and premature at the age 40-41week................................. 52 4.1 Short recording specifics for each patient . 57 4.2 Long recording specifics for each patient . 58 4.3 K-means clustering result . 67 5.1 Subject Demographic Data . 84 5.2 Interested parameters from cardioventilatory system . 88 5.3 Entropy results for normal breathing in healthy subjects . 88 5.4 Entropy results for 5 cm H2O of PEEP breathing in healthy subjects 89 v 5.5 Entropy and ranking result for Cardioventilatory intervals during nor- mal breathing in healthy subjects . 91 5.6 Entropy and ranking result for Cardioventilatory intervals during PEEP breathing in healthy subjects . 92 5.7 Median of Cardioventilatory parameters during normal breathing in healthy subjects . 92 5.8 Median of Cardioventilatory parameters during PEEP breathing in healthy subjects . 93 vi List of Figures 2.1 DFA Results for different frequencies . 7 2.2 Intracranial EEG during ictal & non-ictal . 12 2.3 Diagnostics for DFA of the Lorenz attractor . 13 2.4 Diagnostics for DFA of random noise . 13 2.5 Diagnostics for DFA of intracranial ictal EEG . 14 2.6 Diagnostics for DFA of non-ictal EEG . 14 2.7 Diagnostics for correlation dimension of the Lorenz attractor . 15 2.8 Diagnostics for correlation dimension of the for intracranial non-ictal EEG (W =1)............................... 16 2.9 Diagnostics for correlation dimension of the for intracranial non-ictal EEG (W =10) .............................. 16 2.10 Diagnostics for correlation dimension of the for intracranial ictal EEG (W =1).................................. 17 2.11 Diagnostics for correlation dimension of the for intracranial ictal EEG (W =14) ................................. 17 2.12 Sample Burst Data from an in vitro respiratory slice preparation (neona- talrat)................................... 24 2.13 Normalized auto correlation function . 25 2.14 Histogram of Approximate Entropy for Lorenz Attractor . 26 2.15 Histogram of Sample Entropy for Lorenz Attractor . 26 3.1 Electrodes Placement for International 10-20 System . 31 3.2 Neonatal EEG Autocorrelation Function for Pittsburgh Study . 34 3.3 Normalized Histogram of Approximate Entropy Results for Pittsburgh Study . 48 3.4 Normalized Histogram of Approximate Entropy Results for Pilot Study 49 3.5 Normalized Histogram of Approximate Entropy Results for Pittsburgh Fullterm 40-41 Weeks Study Active vs. Quiet . 49 3.6 Normalized Histogram of Approximate Entropy Results for Pilot Pre- mature 40-41 Weeks Study Active vs. Quiet . 50 vii 3.7 Normalized Histogram of Approximate Entropy Results of Pilot vs. Pittsburgh Study . 50 3.8 Normalized Histogram of Approximate Entropy Results of Pilot vs. Pittsburgh Study After Mean Correction . 51 4.1 DFA result for patient S-1 . 61 4.2 Dynamical similarity index result for patient S-1 . 62 4.3 Phase coherence result for patient S-1 . 63 4.4 Hjorth parameters result for patient L-1 . 64 4.5 DFA result for patient L-1 . 65 4.6 Dynamical similarity index result for patient L-1 . 65 4.7 Phase coherence result for patient L-1 . 66 4.8 Brain activity index for patient L-1 . 68 4.9 Smoothed versus normal brain activity index for patient L-1 . 69 4.10 Smoothed versus normal brain activity index for patient L-2 . 70 4.11 Smoothed versus normal brain activity index for patient L-3 . 71 4.12 Smoothed versus normal brain activity index for patient L-3 . 72 4.13 Smoothed versus normal brain activity index for patient L-4 . 73 4.14 Sample EEG before and after seizure as well as seizure onset . 75 4.15 DFA Result for patient L-4 . 76 5.1 Approximate Entropy result for respiratory network bursts at different potassium concentration . 81 5.2 Sample Entropy result for respiratory network bursts at different potas- sium concentration . 82 5.3 Sample ECG & Breathing . 87 5.4 Entropy of intervals during normal breathing . 89 5.5 Entropy of intervals during PEEP breathing . 90 5.6 Entropy of intervals for Cardioventilatory intervals in healthy subjects 93 5.7 Ranking results for cardioventilatory intervals in healthy subjects . 94 viii ACKNOWLEDGEMENTS First, I would like to thank my father for encouraging me to pursue my doctoral degree. My deepest gratitude goes to Prof. Kenneth A. Loparo for his guidance and support during this study as my advisor and friend. I also would like to express the words of appreciation to the members of my dissertation committee and our collaborators for their time and suggestion to improve this work. I have furthermore to thank the entire faculty, staff and students in the department for their assistance and kindness, especially to my friends Reza Jamasabi and Evren Gurkan for the good times we shared together. ix Variability Analysis & Its Applications to Physiological Time Series Data Abstract by Farhad Kaffashi In this thesis, novel variability analysis techniques are developed and refinements are made to some currently available methods to enhance their use and effectiveness. These variability analysis techniques are applied to physiological time series data to study both health and disease. In particular, the addition of a new parameter, the time delay τ, is proposed to enhance the performance of Approximate and Sample Entropy calculations;.
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