Introduction to Mathematical Oncology

ISBN-13: 9781584889908 / Angielski / Twarda / 2016 / 490 str.

Yang Kuang;John Nagy

Opis

Introduction to Mathematical Oncology presents biologically well-motivated and mathematically tractable models that facilitate both a deep understanding of cancer biology and better cancer treatment designs. It covers the medical and biological background of the diseases, modeling issues, and existing methods and their limitations. The authors introduce mathematical and programming tools, along with analytical and numerical studies of the models. They also develop new mathematical tools and look to future improvements on dynamical models. After introducing the general theory of medicine and exploring how mathematics can be essential in its understanding, the text describes well-known, practical, and insightful mathematical models of avascular tumor growth and mathematically tractable treatment models based on ordinary differential equations. It continues the topic of avascular tumor growth in the context of partial differential equation models by incorporating the spatial structure and physiological structure, such as cell size. The book then focuses on the recent active multi-scale modeling efforts on prostate cancer growth and treatment dynamics. It also examines more mechanistically formulated models, including cell quota-based population growth models, with applications to real tumors and validation using clinical data. The remainder of the text presents abundant additional historical, biological, and medical background materials for advanced and specific treatment modeling efforts. Extensively classroom-tested in undergraduate and graduate courses, this self-contained book allows instructors to emphasize specific topics relevant to clinical cancer biology and treatment. It can be used in a variety of ways, including a single-semester undergraduate course, a more ambitious graduate course, or a full-year sequence on mathematical oncology.

This self-contained book focuses on three categories of disease: cancer, viral diseases, and dynamical diseases. It presents the medical and biological background of the diseases, specific issues to be modeled, and existing methods and their limitations. The book introduces mathematical and programming tools, along with analytical and numerical studies of the models. The authors also develop new mathematical tools and look to future improvements on dynamical models. The text provides exercises and projects at the end of most chapters, hints and answers to selected problems at the back of the book, and a supplementary website with lecture notes, homework problems, useful computer programs, and other reference material.

Spis treści

Introduction to Theory in Medicine. Introduction to Cancer Modeling. Spatially Structured Tumor Growth. Physiologically Structured Tumor Growth. Prostate Cancer: PSA, AR, and ADT Dynamics. Resource Competition and Cell Quota in Cancer Models. Natural History of Clinical Cancer. Evolutionary Ecology of Cancer. Models of Chemotherapy. Major Anti-Cancer Chemotherapies. Radiation Therapy. Chemical Kinetics. Epilogue: Toward a Quantitative Theory of Oncology.