Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer

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Avner Friedman
Springer Science & Business Media, Dec 19, 2005 - Mathematics - 246 pages

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.

 

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Contents

Modeling the Cell Division Cycle
1
AngiogenesisA BiochemicalMathematical Perspective
23
Mathematical Modelling of Proteolysis and Cancer Cell Invasion of Tissue
77
Mathematical Modelling of Spatiotemporal Phenomena in Tumour Immunology
131
Benefiting from Phase Dependence and Overcoming Drug Resistance
185
Cancer Models and Their Mathematical Analysis
223
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