Overview
- Provides appropriate models for each biological phenomenon against not necessarily complete measurements, by a systematic study of mathematical modeling
- Presents a rigorous study of stochastic simulation, a modern, promising method because it is not intended to reproduce models faithfully
- Develops new mathematical analysis in the study of these models, particularly the method of the weak scaling limit
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes on Mathematical Modelling in the Life Sciences (LMML)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.
Reviews
“The author, in this short book, develops a variety of multi-scale mathematical models for cancer cell phenomena that occur at several different stages in the development and progression of cancer. … this book is a useful addition to the growing literature on the mathematical biology of the evolution and behavior of cancer and tumor cells. This book should appeal to a wide audience of applied mathematicians working in mathematical biology or the applied mathematics of ordinary and partial differential equations.” (Jason M. Graham, Mathematical Reviews, November, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Mathematical Methods for Cancer Evolution
Authors: Takashi Suzuki
Series Title: Lecture Notes on Mathematical Modelling in the Life Sciences
DOI: https://doi.org/10.1007/978-981-10-3671-2
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2017
Softcover ISBN: 978-981-10-3670-5Published: 20 June 2017
eBook ISBN: 978-981-10-3671-2Published: 13 June 2017
Series ISSN: 2193-4789
Series E-ISSN: 2193-4797
Edition Number: 1
Number of Pages: VII, 144
Number of Illustrations: 23 b/w illustrations
Topics: Mathematical and Computational Biology, Partial Differential Equations