ODE/PDE α-synuclein Models for Parkinson’s Disease

ODE/PDE α-synuclein Models for Parkinson’s Disease

1st Edition - February 13, 2018

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  • Author: William Schiesser
  • Paperback ISBN: 9780128146149
  • eBook ISBN: 9780128148020

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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 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

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 relating 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

Product details

  • No. of pages: 228
  • Language: English
  • Copyright: © Academic Press 2018
  • Published: February 13, 2018
  • Imprint: Academic Press
  • Paperback ISBN: 9780128146149
  • eBook ISBN: 9780128148020

About the Author

William Schiesser

The R routines are available from http://www.lehigh.edu/~wes1/pd_download Queries about the routines can be directed to wes1@lehigh.edu 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

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