# Mathematical Models in Cell Biology and Cancer Chemotherapy

• MartinĀ Eisen
Book

Part of the Lecture Notes in Biomathematics book series (LNBM, volume 30)

1. Front Matter
Pages N2-IX
2. Martin Eisen
Pages 1-4
3. Martin Eisen
Pages 5-43
4. Martin Eisen
Pages 44-72
5. Martin Eisen
Pages 73-121
6. Martin Eisen
Pages 122-151
7. Martin Eisen
Pages 152-166
8. Martin Eisen
Pages 167-218
9. Martin Eisen
Pages 219-274
10. Martin Eisen
Pages 275-332
11. Martin Eisen
Pages 333-385
12. Back Matter
Pages 386-439

### Introduction

The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on cell biology and a chapter on control theory have been included. Those readers who have had some exposure to biology may prefer to omit Chapter I (Cell Biology) and only use it as a reference when required. However, few biologists have been exposed to control theory. Chapter 7 provides a short, coherent and comprehensible presentation of this subject. The concepts of control theory are necessary for a full understanding of Chapters 8 and 9.

### Keywords

Biomathematik Control theory Eisen Zelle calculus cancer Chemotherapy cell biology equation function mathematical modelling

#### Authors and affiliations

• MartinĀ Eisen
• 1

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-93126-0
• Copyright Information Springer-Verlag Berlin Heidelberg 1979
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-09709-9
• Online ISBN 978-3-642-93126-0
• Series Print ISSN 0341-633X
• Buy this book on publisher's site