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Tutorials in Mathematical Biosciences III

Cell Cycle, Proliferation, and Cancer

  • Book
  • © 2006

Overview

Editors:
  1. Avner Friedman
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1872)

Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VII
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  2. Modeling the Cell Division Cycle

    • Baltazar D. Aguda
    Pages 1-22

  3. Angiogenesis-A Biochemical/Mathematical Perspective

    • Howard A. Levine, Marit Nilsen-Hamilton
    Pages 23-76

  4. Mathematical Modelling of Proteolysis and Cancer Cell Invasion of Tissue

    • Georgios Lolas
    Pages 77-129

  5. Mathematical Modelling of Spatio-temporal Phenomena in Tumour Immunology

    • Mark Chaplain, Anastasios Matzavinos
    Pages 131-183

  6. Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance

    • Marek Kimmel, Andrzej Swierniak
    Pages 185-221

  7. Cancer Models and Their Mathematical Analysis

    • Avner Friedman
    Pages 223-246

  8. Back Matter

    Pages 247-250
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About this book

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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