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Engineering in Brain Research, from the Development of Instrumentation, to the Analysis of Recorded Signals, to the Modelling of Brain Function

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E GINEERI GIN RAIN RES ARCH Processing Electroencephalograms and Chaos in Neural Networks A thesis presented for the degree of Doctor of Philosophy in Electrical and Electronic Engineering at the University of Canterbury, Christchurch, New Zealand. November 1992. Alison A. Dingle B. E. (Hans 1) ABSTRACT The structure and function of the brain, as it is presently understood, is outlined. The importance of technology in acquiring this knowledge is illustrated by tracing the history of brain research, and the contributions that engineering is currently making to brain research are discussed. The manifestation of epilepsy in recordings of the electrical activity of the brain - elec­ troencephalograms (EEGs) is outlined. A new PC-based system for the automated de­ tection of this epileptiform activity is presented. The system consists of three stages: data collection, feature extraction and event detection. The feature extraction stage detects candi­ date epileptiform transients on individual channels, while an expert system is used to detect focal and non-focal epileptiform events. Considerable use of spatial and temporal contextual information present in the EEG aids both in the detection of epileptiform events and in the rejection of artifacts and background activity as events. Classification of events as definite or probable overcomes, to some extent, the problem of maintaining satisfactory detection rates while eliminating false detections. Test results are presented whlch indicate that this system should be capable of performing reliably in routine clinical EEG screening. Neural networks are introduced and their application to real-world problems examined. In particular, the application of back-propagation neural networks to the detection of epilep­ tiform transients is discussed. A number of modifications to the back-propagation learning algorithm are proposed which should enable the desired network performance to be achieved. The phenomenon of deterministic chaos is reviewed and evidence for chaos in the brain presented. A new model of a neuron, termed the versatile neural unit and based on a chaotic system is proposed. This neural unit is relatively simple, yet produces a wide range of activity reminiscent of that observed in neurons. The versatile neural unit provides a means for introducing chaos into neural networks to enhance their performance and, at the same time, provide insights into the roles of chaos in the brain. Networks of versatile neural units are shown to produce activity similar to that observed in EEGs and the introduction of chaos into the self-organizing map is shown to improve its ability to cluster input patterns and model their probability density function. iii ACKNOWLEDGEMENTS I am indebted to many people for the assistance, advice, support and encouragement I have received during the course of my research and thesis preparation. In particular, I would like to thank my supervisors, the late Professor Richard Bates, Dr Richard Jones and Dr John Andreae for their guidance and encouragement. I also wish to thank Grant Carroll and Dr Richard Fright from Christchurch Hospital for the many valuable discussions I had with them. I gratefully acknowledge receipt of New Zealand University Grants Committee Postgrad­ uate Scholarship. Finally, I wish to thank my family, friends and flatmates for their support, understanding and encouragement. j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j v CONTENTS PREFACE ix I INTRODUCTION 1 CHAPTER 1 THE BRAIN 3 1.1 Introduction 3 1.2 Cells of the brain 3 1.2.1 Neurons 4 1.2.2 Glial Cells 5 1.3 Organization of the Brain 5 1.3.1 The Cerebral Cortex 5 1.3.2 Subcortical Structur'es 7 1.4 Protection of the Brain 7 CHAPTER 2 HISTORY OF BRAIN RESEARCH 11 2.1 Introduction 11 2.2 From Antiquity to the Middle Ages 11 2.2.1 Source of Mental Processes 11 2.2.2 Anatomy of the Nervous System 12 2.2.3 Operation of the Nervous System 14 2.3 The Middle Ages to the Nineteenth Century 15 2.3.1 Localization of Brain Function 15 2.3.2 Nerve Function 17 2.3.3 The Neuron 20 2.4 The Twentieth Century and Beyond 22 2.4.1 The Action Potential 23 2.4.2 Neural Communication 23 2.4.3 Neuroanatomy 25 2.4.4 Disorders of the Brain 25 2.4.5 Higher Functions of the Brain 26 CHAPTER 3 ENGINEERS IN BRAIN RESEARCH 29 3.1 Introduction 29 3.2 Recording Techniques 29 3.3 Stimulation Techniques 30 3.4 Signal Processing Techniques 31 3.5 Imaging the Brain 32 3.6 Quantification of Neurologic Function 33 3.7 Modelling Brain Function 33 vi II PROCESSING ELECTROENCEPHALOGRAMS 37 CHAPTER 4 THE ELECTROENCEPHALOGRAM 39 4.1 Introduction 39 4.2 Discovery of the EEG 39 4.3 EEG Recording 40 4.4 EEG Activity 41 4.5 EEG Interpretation 45 4.6 EEG and Epilepsy 46 4.7 Epileptiform Transients 47 4.8 Summary 50 CHAPTER 5 ANALYSIS OF THE ELECTROENCEPHALOGRAM 53 5.1 Introduction 53 5.2 Analysis of Background Activity 53 5.3 Detection of Epileptiform Activity 55 5.3.1 Seizure Patterns 55 5.3.2 Epileptiform Transients 56 5.4 Summary 59 CHAPTER 6 A SYSTEM TO DETECT EPILEPTIFORM ACTIVITY 61 6.1 Introduction 61 6.2 System Objectives and Philosophy 61 6.2.1 Expert Systems 62 6.2.2 The Human Expert 62 6.2.3 System Overview 63 6.3 Data Collection 64 6.4 Feature Extraction 65 6.4.1 Scaling EEG Amplitude 65 6.4.2 Peak Detection 66 6.4.3 Parameters 66 6.4.4 Thresholds 68 6.4.5 Contextual Information 68 6.5 Event Detection 69 6.5.1 Knowledge and Data 70 6.5.2 Use of Spatial Context 70 6.5.3 Use of Temporal Context 74 6.6 System Performance 75 6.6.1 False Detections 77 6.6.2 Missed Detections 78 6.6.3 Comparison with other systems 78 6.7 Summary 79 III NEURAL NETWORKS 81 CHAPTER 7 NEURAL NETWORKS 83 7.1 Introduction 83 7.2 The Development of Neural Networks 83 7.3 Properties of Neural Networks 84 7.4 Components of Neural Networks 85 7.4.1 Network Architecture 85 7.4.2 Neural Units 87 vii 7.4.3 Learning Algorithms 88 7.5 The Hopfield Network 89 7.6 The Self-Organizing Map 91 7.7 Back-Propagation Networks 95 7.8 Hard ware Implementations 98 7.9 Comparison with the Brain 99 7.10 Summary 100 CHAPTER 8 APPLICATIONS OF NEURAL NETWORKS 101 8.1 Introduction 101 8.2 General Considerations 101 8.3 Application Examples 104 8.3.1 Memory 104 8.3.2 Optimization Problems 104 8.3.3 Categorization 105 8.3.4 Control Problems 105 8.3.5 Data Processing 107 8.3.6 Predictive Models 107 8.3.7 Pattern Recognition 108 8.4 Modifying Back-propagation 108 8.4.1 Learning Steepness Parameters 108 8.4.2 Tuning Network Performance 110 8.5 Detection of Epileptiform Transients 111 8.5.1 Neural Network Approaches 111 8.5.2 Preliminary Investigation 112 8.6 Limitations of Neural Networks 113 IV CHAOS IN NEURAL NETWORKS 115 CHAPTER 9 DETERMINISTIC CHAOS 117 9.1 Introduction 117 9.2 Theoretical Background 117 9.2.1 Dynamical Systems 118 9.2.2 Phase Space 120 9.2.3 Attractors 121 9.3 The Discovery of Chaos 122 9.4 Chaotic Systems 123 9.4.1 Lorenz Model 123 9.4.2 Rossler System 127 9.4.3 Henon Map 127 9.4.4 Logistic Map 127 9.5 Strange Attractors 131 9.5.1 Attractor Dimension 131 9.5.2 Entropy 133 9.5.3 Lyapunov Exponents 134 9.6 Distinguishing Chaotic from Random Signals 135 9.6.1 Reconstruction of Attractors 136 9.6.2 Calculation of Lyapunov Exponents 137 9.6.3 Calculation of Attractor Dimension 138 9.6.4 Calculation of Entropy 139 9.6.5 Accuracy of Algorithms 140 viii 9.7 Summary 141 CHAPTER 10 CHAOS AND THE BRAIN 143 10.1 Introduction 143 10.2 Chaotic Activity of Neurons 143 10.3 Chaos in the EEG 144 10.4 Purpose of Chaos in the Brain 145 CHAPTER 11 CHAOTIC NEURAL UNITS 147 11.1 Introduction 147 11.2 Models of Neuron Operation 147 11.2.1 Conventional Neural Units 148 11.2.2 Temporal Summation 148 11.2.3 Refractory Period 149 11.3 Models of Neuron Behaviour 154 11.4 Summary 157 CHAPTER 12 CHAOTIC NEURAL NETWORKS 159 12.1 Introduction 159 12.2 Chaos in Neural Networks 159 12.3 The Chaotic Self-Organizing Map 162 12.3.1 Clustering Input Patterns 165 12.3.2 Modelling the Probability Density Function of Input Patterns 171 12.3.3 Generating a Spatial Order 178 12.4 Summary 180 V IMPLICATIONS FOR BRAIN RESEARCH 185 CHAPTER 13 CONCLUSIONS AND FUTURE RESEARCH 187 13.1 Introduction 187 13.2 Processing Electroencephalograms 187 13.3 Chaos in Neural Networks 188 APPENDIX A THE 10-20 INTERNATIONAL SYSTEM 191 APPENDIX B OPTIMAL PARAMETER DEFINITIONS 193 B.1 Parameters 193 B.2 Discriminant Analysis 194 REFERENCES 199 ix PREFACE "If the human brain were so simple that we could understand it, we would be so simple that we couldn't." Emerson Pugh From time immemorial humans have been interested in understanding the brain.
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