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Modeling of Post-Myocardial Infarction
ODE/PDE Analysis with R
- 1st Edition - August 23, 2023
- 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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Request a sales quoteModeling 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
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- References
- Chapter 1: ODE model development
- Abstract
- Introduction
- 1.1. Formulation of ODE post-MI model
- 1.2. Summary and conclusions
- References
- Chapter 2: ODE model implementation
- Abstract
- Introduction
- 2.1. Coding of the post-MI model
- 2.2. Summary and conclusions
- References
- Chapter 3: PDE model formulation and implementation
- Abstract
- Introduction
- 3.1. Formulation of PDE model
- 3.2. Implementation of PDE model
- 3.3. Summary and conclusions
- References
- Chapter 4: PDE model temporal derivative analysis
- Abstract
- Introduction
- 4.1. LHS time derivative analysis of the PDE model
- 4.2. Summary and conclusions
- References
- Chapter 5: Analysis of the PDE model terms
- Abstract
- Introduction
- 5.1. RHS terms of the PDE model
- 5.2. Summary and conclusions
- References
- Appendix A: Functions dss004, dss044
- A.1. dss004 listing
- A.2. dss044 listing
- Index
- No. of pages: 200
- Language: English
- Edition: 1
- Published: August 23, 2023
- Imprint: Academic Press
- Paperback ISBN: 9780443136115
- eBook ISBN: 9780443136122
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