ODE/PDE Analysis of Multiple Myeloma

Programming in R

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

$221

Hardback

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English

CRC Press
15 June 2020

Biology, life sciences

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,
Weight: 349g
ISBN: 9780367471354
ISBN 10: 0367471353
Pages: 136
Publication Date: 15 June 2020
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

1. Introductory ODE Model. 2. Basic PDE Model. 3. PDE Model with External Transfer. 4. ODE/PDE Model Parameter Analysis. 5. Detailed Analysis of PEDs in ODE/PDE Model. Appendix A1: Functions dss004, dss044

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.

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ODE/PDE Analysis of Multiple Myeloma

Programming in R

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

$221

Hardback

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