Analysis of a Model for Epilepsy: Application of a Max-Type Difference Equation to Mesial Temporal Lobe Epilepsy

ISBN-13: 9781032255385 / Angielski / Twarda / 2022 / 174 str.

Candace M. Kent; David M. Chan

Opis

The authors of this book and their colleagues investigated the first known application of a "max-type" difference equation. Their equation is a phenomenological model of epileptic seizures. In this book, the authors expand on that research and present a more comprehensive development of mathematical, numerical, and biological results.

Spis treści

1. Introduction: Epilepsy. 1.1. Brief Overview. 1.2. Mesial Temporal Lobe Epilepsy and Other Examples. 2. The Model. 2.1. Model Description. 2.2. Connection to a Simpler Model. 2.3. Connection Between the Model and Epileptic Seizures. 2.4. Open Problem: Seizure Threshold as a Function of Time. 3. Eventual Periodicity of the Model. 3.1. Bounded and Persistent Solutions. 3.2. Eventually Periodic Solutions with Periods Multiples of Six. 3.3. Eventually Periodic Solutions with Period 4. 3.4. Partially and Completely Seizure-Free States. 4. Rippled Almost Periodic Solutions. 4.1. Rippled Behaviour. 4.2. Rippled Almost Periodic Solutions. 4.3. Lyapunov Exponent. 4.4. The State of Status Epilepticus. 4.5. On Termination of Repetition. 5. Numerical Results and Biological Conclusions. 5.1. Bifurcation Diagrams. 5.2. Variability in Seizure Characteristics. 5.3. A Case of Variability in Region 1. 5.4. The Hyperexcitable State. 5.5. Impact of Individual Historical Differences. 6. Epilogue