ODE/PDE Analysis of Multiple Myeloma: Programming in R

This book presents mathematical models for multiple myeloma using ordinary and partial differential equations (ODE/PDEs), starting with a basic ODE model and concluding with a detailed ODE/PDE model that describes the spatiotemporal distribution of four dependent variable components in the bone marrow and peripheral blood. The models are implemented in R, a scientific computing system, and are designed to be accessible to readers with modest computer resources.

Format: Paperback / softback
Length: 136 pages
Publication date: 01 February 2022
Publisher: Taylor & Francis Ltd

Multiple myeloma, a type of bone cancer, specifically affects the plasma cells found in bone marrow, which is the soft tissue within bones. These plasma cells are crucial components of the immune system. In this book, mathematical models for multiple myeloma are presented, utilizing ordinary and partial differential equations (ODE/PDEs). The journey begins with a basic ODE model in Chapter 1, gradually progressing to a comprehensive ODE/PDE model in Chapter 4. This model captures the spatiotemporal distribution of four key variables: (1) the M protein, a protein produced by multiple myeloma cells; (2) cytotoxic T lymphocytes (CTLs); (3) natural killer (NK) cells; and (4) regulatory T cells (Tregs).

To facilitate the computer-based implementation of these models, routines coded in the R programming language are presented. R is a renowned scientific computing system that is freely accessible through the Internet. The focus is on practical application, with minimal use of formal mathematics. Instead, detailed examples are provided, allowing readers, researchers, and analysts to execute these models on modest computers using the R routines readily available for download. The PDE analysis is based on the method of lines (MOL), a well-established general algorithm for PDEs, implemented with finite differences.

By employing these mathematical models, researchers can gain insights into the dynamics of multiple myeloma, explore treatment options, and predict disease progression. The computer-based implementation enables real-time analysis and simulation, providing valuable tools for personalized medicine and improving patient outcomes.

Weight: 240g
Dimension: 156 x 235 x 14 (mm)
ISBN-13: 9780367495510