Dynamics Of Cancer: Mathematical Foundations Of Oncology

Mathematical Foundations of Oncology

Dominik Wodarz, Natalia L Komarova

• Publisher: WSPC
• Year: 2014
• eBook ISBN: 9789814566384
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The book aims to provide an introduction to mathematical models that describe the dynamics of tumor growth and the evolution of tumor cells. It can be used as a textbook for advanced undergraduate or graduate courses, and also serves as a reference book for researchers. The book has a strong evolutionary component and reflects the viewpoint that cancer can be understood rationally through a combination of mathematical and biological tools. It can be used both by mathematicians and biologists. Mathematically, the book starts with relatively simple ordinary differential equation models, and subsequently explores more complex stochastic and spatial models. Biologically, the book starts with explorations of the basic dynamics of tumor growth, including competitive interactions among cells, and subsequently moves on to the evolutionary dynamics of cancer cells, including scenarios of cancer initiation, progression, and treatment. The book finishes with a discussion of advanced topics, which describe how some of the mathematical concepts can be used to gain insights into a variety of questions, such as epigenetics, telomeres, gene therapy, and social interactions of cancer cells.

Contents:

• • Teaching Guide
  • Cancer and Somatic Evolution
  • Mathematical Modeling of Tumorigenesis
• Basic Growth Dynamics and Deterministic Models:
  • Single Species Growth
  • Two-Species Competition Dynamics
  • Competition Between Genetically Stable and Unstable Cells
  • Chromosomal Instability and Tumor Growth
  • Angiogenesis Inhibitors, Promoters, and Spatial Growth
• Evolutionary Dynamics and Stochastic Models:
  • Evolutionary Dynamics of Tumor Initiation Through Oncogenes: The Gain-of-Function Model
  • Evolutionary Dynamics of Tumor Initiation Through Tumor-Suppressor Genes: The Loss-of-Function Model and Stochastic Tunneling
  • Microsatellite and Chromosomal Instability in Sporadic and Familial Colorectal Cancers
  • Evolutionary Dynamics in Hierarchical Populations
  • Spatial Evolutionary Dynamics of Tumor Initiation
  • Complex Tumor Dynamics in Space
  • Stochastic Modeling of Cellular Growth, Treatment, and Resistance Generation
  • Evolutionary Dynamics of Drug Resistance in Chronic Myeloid Leukemia
• Advanced Topics:
  • Evolutionary Dynamics of Stem-Cell Driven Tumor Growth
  • Tumor Growth Kinetics and Disease Progression
  • Epigenetic Changes and the Rate of DNA Methylation
  • Telomeres and Cancer Protection
  • Gene Therapy and Oncolytic Virus Therapy
  • Immune Responses, Tumor Growth, and Therapies
  • Towards Higher Complexities: Social Interactions

Readership: Researchers in mathematical biology, mathematical modeling, biology, mathematical oncology.

Chapter 1

Teaching guide

This book can be used for teaching upper-division undergraduate of graduate classes in Cancer modeling. In this chapter we provide some hints on how to organize a course based on this book’s materials.

1.1How to use this book

The book is written with two audiences in mind. Those who have a solid mathematics background will find very detailed mathematical derivations of all the results. These are printed on a gray background.

In order to follow the “gray” parts of the book, we require some basic knowledge of applied mathematical techniques, such as solutions of linear systems of ODEs, linear stability analysis of ODEs, the method of characteristics for solving first order PDEs, and basic probability.

These parts of the book can be skipped by readers that have less of a mathematical background, without interrupting the logical flow of the exposition.

Each chapter contains a set of problems. There are three kinds of problems. (1) Basic problems are mathematical exercises aimed at a more detailed understanding of the mathematical derivations given in the text, or reviewing some concepts needed to understand the “gray” parts of the book. (2) “Numerical projects” are more advanced problems which require some computer coding. They require some knowledge of a programming language, such as Mathematica, Maple, Matlab, C++, Fortran, etc. These two types of problems should be offered in a course taught to an audience with some applied mathematics background. (3) Finally, the third type of problems termed “Research projects” do not require any knowledge of mathematics, and suggest topics of independent in-depth study of a biological topic or the history of a certain concept or discovery. These can be offered in a course taught to students with a biology background.

The book contains three parts. Part 1, “Basic growth dynamics and deterministic models”, introduces concepts of growth (including single-species growth and two-species competition), and also shows how these concepts can be relevant for studying cancer. It further introduces the important issue of genetic instability and talks about angiogenesis, inhibitors, and promoters. Almost all the mathematical developments in this part of the book are deterministic. Important concepts that come up are exponential and logistic growth, two-species competition and stability analysis, axiomatic modeling, quasispecies equations, and optimization.

Part 2, “Evolutionary dynamics and stochastic models”, introduces stochasticity in the description of cancer. With this powerful tool, it is possible to model cell population dynamics at low numbers, which is important when talking about cancer initiation (Chapters 9-14). In this context, we discuss oncogenes and tumor suppressor genes, sporadic and familial cancers, and stem cells. Stochasticity is also essential when talking about cancer treatment, in particular, the generation of resistance against drugs (Chapters 15-16).

Finally, Part 3, “Advanced topics”, u...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Contents
• Preface
• 1. Teaching guide
• 2. Cancer and somatic evolution
• 3. Mathematical modeling of tumorigenesis
• Basic growth dynamics and deterministic models
• Evolutionary dynamics and stochastic models
• Advanced topics
• Bibliography
• Index