Main description:

This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention. The complexity of modeling living matter requires the development of new mathematical methods and ideas. This volume, written by first-rate researchers in the field of mathematical biology, is one of the first steps in that direction.

Contents:

Preface List of Contributors Genetic and Epigenetic Pathways to Colon Cancer: Relating Experimental Evidence with Modeling / N. L. Komarova, D. Wodarz, C. R. Boland, and A. Goel From Kinetic Theory for Active Particles to Modelling Immune Competition / A. Bellouquid and M. Delitala Towards Microscopic and Nonlocal Models of Tumour Invasion of Tissue / M. Lachowicz Nonlinear Renewal Equations / B. Perthame and S. K. Tumuluri A Game Theoretical Perspective on the Somatic Evolution of Cancer / D. Basanta and A. Deutsch Nonlinear Modeling and Simulation of Tumor Growth / V. Cristini, H. B. Frieboes, X. Li, J. S. Lowengrub, P. Macklin, S. Sanga, S. M. Wise, and X. Zheng Tumour Cords and Their Response to Anticancer Agents / A. Bertuzzi, A. Fasano, A. Gandolfi, and C. Sinisgalli Modeling Diffusely Invading Brain Tumors: An Individualized Approach to Quantifying Glioma Evolution and Response to Therapy / R. Rockne, E. C. Alvord Jr., M. Szeto, S. Gu, G. Chakraborty, and K. R. Swanson Multiphase Models of Tumour Growth / S. Astanin and L. Preziosi The Lymphatic Vascular System in Lymphangiogenesis, Invasion and Metastasis: A Mathematical Approach / M. S. Pepper and G. Lolas M for Invasion: Morphology, Mutation and the Microenvironment / A. R. A. Anderson Methods of Stochastic Geometry, and Related Statistical Problems in the Analysis and Therapy of Tumour Growth and Tumour-Driven Angiogenesis / V. Capasso, E. Dejana, and A. Micheletti Mathematical Modelling of Breast Carcinogenesis, Treatment with Surgery and Radiotherapy, and Local Recurrence / H. Enderling and J. S. Vaidya Predictive Models in Tumour Immunology / P.-L. Lollini, A. Palladini, F. Pappalardo, and S. Motta Dynamically Adaptive Tumour-Induced Angiogenesis: The Impact of Flow on the Developing Capillary Plexus / S. R. McDougall Dynamic Irregular Patterns and Invasive Wavefronts: The Control of Tumour Growth by Cytotoxic T-Lymphocytes / A. Matzavinos Multiscale Modelling of Solid Tumour Growth / H. M. Byrne, I. M. M. van Leeuwen, M. R. Owen, T. Alarcon, and P. K. Maini