ODE / PDE alpha-Synuclein Models for Parkinson's Disease - 1st Edition - ISBN: 9780128146149

ODE / PDE alpha-Synuclein Models for Parkinson's Disease

1st Edition

Authors: William Schiesser
Paperback ISBN: 9780128146149
Imprint: Academic Press
Page Count: 170
Tax/VAT will be calculated at check-out

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Description

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, which can interfere with functioning neurons and lead to neurodegenerative pathology. This book is divided into two principal parts: first, demonstrating computer-based implementation of a prototype ODE/PDE model for the dynamics of the Alpha-synuclein monomer and polymer, presented with numerical and graphical output. Secondly, the book 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. ODE/PDE Alpha-Synuclein Models for Parkinson’s Disease facilitates immediate computer use for this research, without having to first learn the basic concepts of numerical analysis for ODE/PDEs and programming algorithms

Key Features

  • 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 as it related to the mathematical model and algorithms
  • Authored by a leading researcher and educator in ODE/PDE models

Readership

Biomedical engineers, researchers, and clinicians in biology, neuroscience, biophysics, biochemistry, and applied mathematics

Table of Contents

Chapter 1 Introduction, ODE Model Formulation

(1.1) ODE Model

(1.2) Main Program

(1.3) ODE Routine

(1.4) Subordinate Routine

(1.5) Model Output

(1.6) Routines for t Derivative

(1.7) Routines for ODE Terms

(1.8) Summary and Conclusions

Chapter 2 Introduction, ODE Model Application

(2.1) ODE Model

(2.1) Main Program (2.2) ODE Routine

(2.3) Model Output

(2.4) Summary and Conclusions

Chapter 3 Introduction, ODE/PDE Model Formulation

(3.1) ODE/PDE Model

(3.2) Main Program

(3.3) ODE/PDE Routine

(3.4) Model Output

(3.5) MOL Variants

(3.6) Summary and Conclusions

Chapter 4 Introduction, ODE/PDE Model Application

(4.1) ODE/PDE Model

(4.2) Main Program

(4.3) ODE/PDE Routine

(4.4) Model Output

(4.5) Model Variants

(4.6) Summary and Conclusions

Chapter 5 Introduction, Convection-Diffusion-Reaction Model Formulation

(5.1) ODE/PDE Model

(5.2) Main Program

(5.3) ODE/PDE Routine

(5.4) Model Output

(5.5) Summary and Conclusions

Chapter 6 Introduction, Convection-Diffusion-Reaction Model Application

(6.1) ODE/PDE Model

(6.2) Main Program

(6.3) ODE/PDE Routine

(6.4) Model Output

(6.5) Summary and Conclusions

Chapter 7 Introduction, Forward and Reverse Axonal Transport

(7.1) ODE/PDE Model

(7.2) Main Program

(7.3) ODE/PDE Routine

(7.4) Model Output

(7.5) Summary and Conclusions

Appendix A1: Function dss012

Appendix A2: Function dss044

Details

No. of pages:
170
Copyright:
© Academic Press 2018
Imprint:
Academic Press
Paperback ISBN:
9780128146149

About the Author

William Schiesser

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.

Affiliations and Expertise

Lehigh University