
Modeling of Post-Myocardial Infarction
ODE/PDE Analysis with R
- 1st Edition - August 23, 2023
- Imprint: Academic Press
- Author: William E. Schiesser
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 3 6 1 1 - 5
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 3 6 1 2 - 2
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
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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.
- 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
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
- Edition: 1
- Published: August 23, 2023
- Imprint: Academic Press
- Language: English
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