A Modal Approach to the Space-Time Dynamics of Cognitive Biomarkers

Description

This book develops and details a rigorous, canonical modeling approach for analyzing spatio-temporal brain wave dynamics. The nonlinear, nonstationary behavior of brain wave measures and general uncertainty associated with the brain makes it difficult to apply modern system identification techniques to such systems. While there is a substantial amount of literature on the use of stationary analyses for brain waves, relatively less work has considered real-time estimation and imaging of brain waves from noninvasive measurements. This book addresses the issue of modeling and imaging brain waves and biomarkers generally, treating the nonlinear and nonstationary dynamics in near real-time. Using a modal state-space formulation leads to intuitive, physically significant models which are used for analysis and diagnosis. A Modal Approach to the Space-Time Dynamics of Cognitive Biomarkers provides a much-needed reference for practicing researchers in biomarker modeling leveraging the lens of engineering dynamics.  Preface Contents 1 Introduction 1.1 Cognition as a Dynamic Process 1.2 Motivation: A Holistic View of Brain Waves 1.2.1 What is a ``model'' of Brain Waves? 1.2.2 Important Modeling Considerations for Brain Wave Dynamics 1.2.3 Brain Wave Dynamics are Relevant to Many Modeling Outcomes 1.3 Literature Review on Dynamic Models of Brain Waves 1.3.1 Historical Developments and Early Approaches 1.3.2 Limitations of Previous Approaches 1.4 Proposed Approach 1.5 Research Hypothesis 1.6 Contributions of This Work 1.7 Document Outline 2 A Dynamic Systems View of Brain Waves 2.1 Electroencephalography as a Cognitive Biomarker 2.1.1 Relevant Characteristics of EEG for Dynamic Brain Wave Modeling 2.1.2 Statistical Properties of EEG Measures 2.1.3 Biological Sources of Corrupting Noise 2.1.4 Inorganic Sources of Corrupting Noise 2.2 A Canonical Approach to the Analysis of Brain Wave Dynamics 2.2.1 Treating the Nonlinear Effects of Brain Waves 2.3 Modal Analysis of State Space Brain Wave Models 2.3.1 Modes Jointly Capture Space Time Dynamics 2.3.2 Analytical Relevance of Eigenmodes 2.4 System Identification Tools for Brain Wave Analysis 3 System Identification of Brain Wave Modes Using EEG 3.1 Introduction and Motivation 3.1.1 Motivation: Dynamical Models of Biomarkers 3.1.2 Linearization of Neural Dynamics 3.1.3 Evaluation of System Identification Techniques for Brain Wave Modeling 3.1.4 Overview of Considered Output-Only Algorithms 3.2 Evaluation of Output-Only System Identification Techniques 3.2.1 Model Variance Among Subjects 3.2.2 Databases for Initial Brain Wave Modeling 3.2.3 Joint Distributions of Modal Parameters 3.2.4 Assumptions and Constraints 3.3 Results 3.3.1 Reducing the Number of EEG Channels 3.4 Conclusions 3.4.1 Recommendations 4 Modal Analysis of Brain Wave Dynamics 4.1 Research and Modeling Goals 4.2 Technical Approach to Cognitive Modeling 4.2.1 Adaptation of System Identification Algorithms for EEG Data 4.2.2 Analysis of EEG Eigenmodes 4.2.3 The Existence of Stimuli Independent Common Modes 4.3 Results of a Subject Classification Task 4.3.1 Experimental Validation and Verification Using a Neural Network Classifier 4.3.2 An Extension to the EEG Motor Movement/Imagery Dataset 4.3.3 Comparing OMA and DMD for Subject Identification 4.3.4 Optimal System Representations and Neural Network Interpretation 4.4 Conclusions 4.4.1 Recommendations 5 Adaptive Unknown Input Estimators [DELETE] 5.1 Introduction 5.2 Unknown Input Dynamics 5.3 Input Generators as a Model of the Unknown Input 5.4 Main Result: Adaptive Control Architecture for Unknown Input Estimation 5.4.1 Composite Error Dynamics 5.4.2 Proof of Composite Error Convergence 5.5 Illustrative Examples 5.6 Conclusions 6 Reconstructing the Brain Wave Unknown Input 6.1 Introduction and Motivation 6.2 Technical Approach 6.2.1 Treating the Nonlinear Effects of Brain Waves 6.2.2 Treating the Unknown Input 6.2.3 Estimator Architecture and Proof of Convergence 6.2.4 Datasets 6.3 Results 6.3.1 Performance Benefits of UIO 6.3.2 Analytical Benefits of UIO 6.3.3 The Predictive Capability of the UIO 6.3.4 Limitations of the Input Estimate 6.4 Conclusions 6.4.1 Recommendations 7 Conclusions and Future Work 7.1 Summary 7.2 Key Contributions of This Work 7.2.1 Modal Identification of Linear Brain Wave Dynamics 7.2.2 Analysis of Spatio-Temporal Brain Wave Modes 7.2.3 Theoretical Considerations for the Estimation of Unknown Inputs 7.2.4 Online Estimation of Nonlinear Brain Wave Dynamics 7.3 Recommendations for Future Work 7.3.1 Considering Multiple Data Types 7.3.2 Improved Diagnostics and Analysis 7.3.3 Spatial Filtering of Biomarkers 7.3.4 Probabilistic Considerations