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Modeling of Post-Myocardial Infarction

ODE/PDE Analysis with R

  • 1st Edition - August 23, 2023
  • Latest edition
  • Author: William E. Schiesser
  • Language: English

Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R presents mathematical models for the dynamics of a post-myocardial (post-MI), aka, a heart attack. The mathemati… Read more

Description

Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R presents mathematical models for the dynamics of a post-myocardial (post-MI), aka, a heart attack. The mathematical models discussed consist of six ordinary differential equations (ODEs) with dependent variables Mun; M1; M2; IL10; Tα; IL1. The system variables are explained as follows: dependent variable Mun = cell density of unactivated macrophage; dependent variable M1 = cell density of M1 macrophage; dependent variable M2 = cell density of M2 macrophage; dependent variable IL10 = concentration of IL10, (interleuken-10); dependent variable Tα = concentration of TNF-α (tumor necrosis factor-α); dependent variable IL1 = concentration of IL1 (interleuken-1).

The system of six ODEs does not include a spatial aspect of an MI in the cardiac tissue. Therefore, the ODE model is extended to include a spatial effect by the addition of diffusion terms. The resulting system of six diffusion PDEs, with x (space) and t (time) as independent variables, is integrated (solved) by the numerical method of lines (MOL), a general numerical algorithm for PDEs.

Key features

  • Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models
  • Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms
  • Authored by a leading researcher and educator in PDE models

Readership

Researchers in computational modelling and computational biology, biomedical engineers, applied mathematicians, and computer scientists. Other interested audiences will be comprised of researchers, clinicians, and developers in the field of cardiology

Table of contents

Chapter 1: ODE Model Development
(1) Introduction
(1.1) Formulation of ODE post-MI model
(1.2) Summary and conclusions

Chapter 2: ODE Model Implementation
(2) Introduction
(2.1) Coding of the post-MI model
(2.1.1) Main program
(2.1.2) ODE routine
(2.1.3) Numerical, graphical output
(2.1.4) Main program with IL-1 control
(2.1.5) ODE routine with IL-1 control
(2.1.6) Numerical, graphical output
(2.2) Summary and conclusions

Chapter 3: PDE Model Formulation and Implementation
(3) Introduction
(3.1) Formulation of PDE model
(3.2) Implementation of PDE model
(3.2.1) Main program, test cases
(3.2.2) ODE/MOL routine
(3.2.3) Numerical, graphical output
(3.3) Summary and conclusions

Chapter 4: PDE Model Temporal Derivative Analysis
(4) Introduction
(4.1) LHS time derivative analysis of the PDE model
(4.1.1) Addition to the main program
(4.1.2) ODE/MOL routine
(4.1.3) Numerical, graphical output
(4.2) Summary and conclusions

Chapter 5: Analysis of the PDE Model Terms
(5) Introduction
(5.1) RHS terms of the PDE model
(5.1.1) Main program extension
(5.1.2) ODE/MOL routine
(5.1.3) Graphical output
(5.2) Summary and conclusions

Appendix A: Functions dss004, dss044

Product details

  • Edition: 1
  • Latest edition
  • Published: August 25, 2023
  • Language: English

About the author

WS

William E. Schiesser

Dr. William 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 16 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
Emeritus McCann Professor of Chemical and Biomolecular Engineering, and Professor of Mathematics, Lehigh University, USA

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