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 ?-synuclein, a monomer that has been implicated in this disease. Specifically, ?-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 ?-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
- Includes PDE routines based on the method of lines (MOL) for computer-based implementation of ODE/PDE models
- Offers transportable computer source codes for readers, with line-by-line code descriptions relating to the mathematical model and algorithms
- Authored by a leading researcher and educator in ODE/PDE models
1. Introduction, ODE Model Formulation 2. Introduction, ODE Model Application 3. Introduction, ODE/PDE Model Formulation 4. Introduction, ODE/PDE Model Application 5. Introduction, Convection-Diffusion-Reaction Model Formulation 6. Introduction, Convection-Diffusion-Reaction Model Application 7. Introduction, Forward and Reverse Axonal Transport
Appendix A1: Function dss012 Appendix A2: Function dss044
W.E. Schiesser is Emeritus McCann Professor of Chemical and Biomolecular Engineering
and Professor of Mathematics at Lehigh University. He holds a PhD from Princeton
University and a ScD (hon) from the University of Mons, Belgium. His research is directed
toward numerical methods and associated software for ordinary, differential-algebraic and
partial differential equations (ODE/DAE/PDEs), and the development of mathematical
models based on ODE/DAE/PDEs. He is the author or coauthor of more than 14 books, and
his ODE/DAE/PDE computer routines have been accessed by some 5,000 colleges and
universities, corporations and government agencies.