ODE/PDE Alpha-Synuclein Models for Parkinson’s Disease discusses a mechanism for the evolution of Parkinson’s Disease (PD) based on the dynamics of the protein α-synuclein, a monomer that has been implicated in this disease. Specifically, α-synuclein morphs and aggregates into a polymer that can interfere with functioning neurons and lead to neurodegenerative pathology. This book first demonstrates computer-based implementation of a prototype ODE/PDE model for the dynamics of the α-synuclein monomer and polymer, and then details the methodology for the numerical integration of ODE/PDE systems which can be applied to computer-based analyses of alternative models based on the reader's interest.
This book facilitates immediate computer use for research without the necessity to first learn the basic concepts of numerical analysis for ODE/PDEs and programming algorithms
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Preface - p. vii 6. Chapter 1: ODE Model Formulation - p. viii 7. Chapter 2: ODE Model Application - p. 32 8. Chapter 3: ODE/PDE Model Convection–Reaction Formulation - p. 51 9. Chapter 4: ODE/PDE Model Convection–Reaction Application - p. 83 10. Chapter 5: ODE/PDE Model Convection–Diffusion–Reaction Formulation - p. 114 11. Chapter 6: ODE/PDE Model Convection–Diffusion–Reaction Application - p. 144 12. Chapter 7: ODE/PDE Model Extensions - p. 173 13. Appendix A1: Functions dss012 and dss020 - p. 207 14. Appendix A2: Function dss044 - p. 212 15. Index - p. 217
ODE/PDE Alpha-Synuclein Models for Parkinson’s Disease discusses a mechanism for the evolution of Parkinson’s Disease (PD) based on the dynamics of the protein α-synuclein, a monomer that has been implicated in this disease. Specifically, α-synuclein morphs and aggregates into a polymer that can interfere with functioning neurons and lead to neurodegenerative pathology. This book first demonstrates computer-based implementation of a prototype ODE/PDE model for the dynamics of the α-synuclein monomer and polymer, and then details the methodology for the numerical integration of ODE/PDE systems which can be applied to computer-based analyses of alternative models based on the reader's interest.
This book facilitates immediate computer use for research without the necessity to first learn the basic concepts of numerical analysis for ODE/PDEs and programming algorithms
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Preface - p. vii 6. Chapter 1: ODE Model Formulation - p. viii 7. Chapter 2: ODE Model Application - p. 32 8. Chapter 3: ODE/PDE Model Convection–Reaction Formulation - p. 51 9. Chapter 4: ODE/PDE Model Convection–Reaction Application - p. 83 10. Chapter 5: ODE/PDE Model Convection–Diffusion–Reaction Formulation - p. 114 11. Chapter 6: ODE/PDE Model Convection–Diffusion–Reaction Application - p. 144 12. Chapter 7: ODE/PDE Model Extensions - p. 173 13. Appendix A1: Functions dss012 and dss020 - p. 207 14. Appendix A2: Function dss044 - p. 212 15. Index - p. 217
