Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R

Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R provides mathematical models for the dynamics of a post-myocardial (post-MI),aka,a heart attack. The system of six ODEs is extended to include a spatial effect by the addition of diffusion terms, and is integrated by the numerical method of lines (MOL).

Format: Paperback / softback
Length: 144 pages
Publication date: 25 August 2023
Publisher: Elsevier Science Publishing Co Inc

Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R

Post-myocardial infarction (post-MI), commonly known as a heart attack, is a significant cardiovascular event that requires mathematical modeling to understand its dynamics. In this context, the book Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R presents a comprehensive framework for analyzing the complex processes involved in the aftermath of a myocardial infarction.

The mathematical models discussed in this text consist of six ordinary differential equations (ODEs) with dependent variables such as Mun, M1, M2, IL10, Ta, and IL1. These variables represent different aspects of the post-MI cardiovascular system, including cell density, macrophage populations, interleukin concentrations, and tumor necrosis factor levels. By studying these ODEs, researchers can gain insights into the mechanisms underlying the progression of the disease and develop effective treatment strategies.

However, it is important to note that the system of six ODEs does not capture the spatial aspect of an MI in the cardiac tissue. To address this limitation, the ODE model is extended by incorporating diffusion terms. These terms introduce the concept of space into the analysis, allowing for a more comprehensive understanding of the dynamics of the post-MI cardiovascular system.

The resulting system of six diffusion PDEs, with x (space) and t (time) as independent variables, is solved using the numerical method of lines (MOL), a general numerical algorithm for PDEs. This method enables researchers to obtain accurate solutions to the complex equations governing the post-MI cardiovascular system, providing valuable insights into the disease's progression and potential treatment options.

Overall, Modeling of Post-Myocardial Infarction: ODE/PDE Analysis with R is a valuable resource for researchers, clinicians, and healthcare professionals interested in studying the dynamics of post-MI cardiovascular systems. By presenting mathematical models that capture the essential aspects of the disease, this book enables researchers to develop new insights and contribute to the development of effective treatment strategies for heart attack patients.

Weight: 450g
Dimension: 235 x 191 (mm)
ISBN-13: 9780443136115