Baltazar D. Aguda (auth.), Avner Friedman (eds.)9783540291626, 3540291628
This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.
Table of contents :
Modeling the Cell Division Cycle….Pages 1-22
Angiogenesis-A Biochemical/Mathematical Perspective….Pages 23-76
Mathematical Modelling of Proteolysis and Cancer Cell Invasion of Tissue….Pages 77-129
Mathematical Modelling of Spatio-temporal Phenomena in Tumour Immunology….Pages 131-183
Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance….Pages 185-221
Cancer Models and Their Mathematical Analysis….Pages 223-246
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