A major challenge in the modeling and simulation of tumor growth is the mathematical description of living matter, which is far more complex than a mathematical description of inert matter. One critical piece of this challenge is creating multiscale models that take into account subcellular, cellular, and macroscopic levels of cancer. The complexity of these different levels requires the development of new mathematical methods and ideas, which are examined in this work.

Written by first-rate researchers in the field of mathematical biology, 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:

• Genetic and epigenetic pathways to colon cancer

• A game theoretical perspective on the somatic evolution of cancer

• Nonlinear modeling and simulation of tumor growth

• Tumor cords and their response to anticancer agents

• Modeling diffusely invading brain tumors

• Multiphase models of tumor growth

• Mathematical modeling of breast carcinogenesis

• Predictive models in tumor immunology

• Multiscale modeling of solid tumor growth

  Selected Topics in Cancer Modeling is an excellent reference for researchers, practitioners, and graduate students in applied mathematics, mathematical biology, and related fields. The book has an overall aim of quantitative, predictive mathematical modeling of solid tumor growth at all scales, from genetics all the way through to treatment therapy for patients.

  Zusammenfassung

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.

Inhalt
Genetic and Epigenetic Pathways to Colon Cancer Relating Experimental Evidence with Modeling.- From Kinetic Theory for Active Particles to Modelling Immune Competition.- Towards Microscopic and Nonlocal Models of Tumour Invasion of Tissue.- Nonlinear Renewal Equations.- A Game Theoretical Perspective on the Somatic Evolution of cancer.- Nonlinear Modeling and Simulation of Tumor Growth.- Tumour Cords and Their Response to Anticancer Agents.- Modeling Diffusely Invading Brain Tumors An Individualized Approach to Quantifying Glioma Evolution and Response to Therapy.- Multiphase Models of Tumour Growth.- The Lymphatic Vascular System in Lymphangiogenesis Invasion and Metastasis A Mathematical Approach.- M for Invasion Morphology Mutation and the Microenvironment.- Methods of Stochastic Geometry and Related Statistical Problems in the Analysis and Therapy of Tumour Growth and Tumour Driven Angiogenesis.- Mathematical Modelling of Breast Carcinogenesis, Treatment with Surgery and Radiotherapy and Local Recurrence.- Predictive Models in Tumor Immunology.- Dynamically Adaptive Tumour Induced Angiogenesis The Impact of Flow on the Developing Capillary Plexus.- Dynamic Irregular Patterns and Invasive Wavefronts The Control of Tumour Growth by Cytotoxic T Lymphocytes.- Multiscale Modelling of Solid Tumour Growth.