ODE/PDE Analysis of Multiple Myeloma

Programming in R

William Schiesser (Lehigh University, Bethlehem, Pennsylvania, USA)

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English

CRC Press
01 February 2022

Biomedical engineering; Applied mathematics; Biotechnology

Multiple myeloma is a form of bone cancer. Specifically, it is a cancer of the plasma cells found in bone marrow (bone soft tissue). Normal plasma cells are an important part of the immune system.

Mathematical models for multiple myeloma based on ordinary and partial differential equations (ODE/PDEs) are presented in this book, starting with a basic ODE model in Chapter 1, and concluding with a detailed ODE/PDE model in Chapter 4 that gives the spatiotemporal distribution of four dependent variable components in the bone marrow and peripheral blood: (1) protein produced by multiple myeloma cells, termed the M protein, (2) cytotoxic T lymphocytes (CTLs), (3) natural killer (NK) cells, and (4) regulatory T cells (Tregs).

The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers using the R routines that are available through a download. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences.

By: William Schiesser (Lehigh University Bethlehem Pennsylvania USA)
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm, Spine: 8mm
Weight: 453g
ISBN: 9780367495510
ISBN 10: 0367495511
Pages: 136
Publication Date: 01 February 2022
Audience: College/higher education , Further / Higher Education
Format: Paperback
Publisher's Status: Active

William E. Schiesser is the Emeritus McCann Professor in the chemical and biomolecular engineering department at Lehigh University as well as a former professor in the mathematics department. He recently authored several books on computer-based solutions to models of living systems, such as the development of Parkinson’s disease. He holds a Ph.D. from Princeton University and an honorary Sc.D. from the University of Mons, Belgium. He is the author or co-author of a series of books in his field of research on 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.