Overview
- Highlights the most significant recent results in the field of mathematical oncology
- Contains interdisciplinary contributions by bio mathematicians, computational and theoretical biologists, biophysicists and biomedical researchers
- Includes contributions that focus on the experimental, clinical and ethical aspects of mathematical oncology
- Includes supplementary material: sn.pub/extras
Part of the book series: Modeling and Simulation in Science, Engineering and Technology (MSSET)
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Table of contents (10 chapters)
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Front Matter
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Anti-Tumor Therapies
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Front Matter
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Keywords
About this book
With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how different researchers approach the same problem in various ways.
Tumors are complex entities that present numerous challenges to the mathematical modeler. First and foremost, they grow. Thus their spatial mean field description involves a free boundary problem. Second, their interiors should be modeled as nontrivial porous media using constitutive equations. Third, at the end of anti-cancer therapy, a small number of malignant cells remain, making the post-treatment dynamics inherently stochastic. Fourth, the growth parameters of macroscopic tumors are non-constant, as are the parameters of anti-tumor therapies. Changes in these parameters may induce phenomena that are mathematically equivalent to phase transitions. Fifth, tumor vascular growth is random and self-similar. Finally, the drugs used in chemotherapy diffuse and are taken up by the cells in nonlinear ways.
Mathematical Oncology 2013 will appeal to graduate students and researchers in biomathematics, computational and theoretical biology, biophysics, and bioengineering.
Editors and Affiliations
About the editors
Bibliographic Information
Book Title: Mathematical Oncology 2013
Editors: Alberto d'Onofrio, Alberto Gandolfi
Series Title: Modeling and Simulation in Science, Engineering and Technology
DOI: https://doi.org/10.1007/978-1-4939-0458-7
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2014
Hardcover ISBN: 978-1-4939-0457-0Published: 20 October 2014
Softcover ISBN: 978-1-4939-4803-1Published: 10 September 2016
eBook ISBN: 978-1-4939-0458-7Published: 16 October 2014
Series ISSN: 2164-3679
Series E-ISSN: 2164-3725
Edition Number: 1
Number of Pages: X, 334
Number of Illustrations: 18 b/w illustrations, 78 illustrations in colour
Topics: Physiological, Cellular and Medical Topics, Cancer Research, Biological and Medical Physics, Biophysics