Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer / Edition 1

by Avner Friedman, B. Aguda, M. Chaplain, A. Friedman, M. Kimmel

Overview

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.

Product Details

ISBN-13:	9783540291626
Publisher:	Springer Berlin Heidelberg
Publication date:	02/10/2006
Series:	Lecture Notes in Mathematics , #1872
Edition description:	2006
Pages:	246
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Modeling the Cell Division Cycle (B. Aguda).- Angiogenesis - A Biochemical/Mathematical Prospective (H. A. Levine and M. Nilsen-Hamilton).- Spatio-Temporal Models of the uPA System and Tissue Invasion (G. Lolas).- Mathematical Modeling of Spatio-Temporal Phenomena in Tumor Immunology (M. Chaplain and A. Matzavinos).- Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance (M. Kimmel and A. Swierniak).- Cancer Models and their Mathematical Analysis (A. Friedman).