Dynamics of Cancer : Mathematical Foundations of Oncology


Dominik. Wodarz
Bok Engelsk 2014 · Electronic books.
Annen tittel
Medvirkende
Utgitt
Singapore : : World Scientific Publishing Company, , 2014.
Omfang
1 online resource (533 p.)
Opplysninger
Description based upon print version of record.. - Preface; Contents; 1. Teaching guide; 1.1 How to use this book; 1.2 A sample syllabus for a Mathematics course; 1.3 A sample syllabus for a Biology course; 2. Cancer and somatic evolution; 2.1 What is cancer?; 2.2 Basic cancer genetics; 2.3 Multi-stage carcinogenesis and colon cancer; 2.4 Genetic instability; 2.5 Barriers to cancer progression: importance of the micro-environment; 2.6 Cellular hierarchies in cancer; 2.7 Genetic and epigenetic changes; 2.8 Evolutionary theory and Darwinian selection; 3. Mathematical modeling of tumorigenesis; 3.1 Ordinary differential equations. - 3.2 Extensions of ODE modeling3.2.1 Optimal control; 3.2.2 ODEs and cancer epidemiology; 3.3 Partial differential equations; 3.4 Stochastic modeling; 3.5 Cellular automaton models; 3.6 Hybrid and multiscale modeling; Basic growth dynamics and deterministic models; 4. Single species growth; 4.1 Exponential growth; 4.2 Surface growth; 4.3 Sigmoidal growth; 4.3.1 Logistic growth; 4.3.2 Other sigmoidal laws; 4.4 Atypical growth; 4.5 Multistep growth; 4.6 Conclusions; Problems; 5. Two-species competition dynamics; 5.1 Logistic growth of two species and the basic dynamics of competition. - 5.2 Two-species dynamics: the axiomatic approach5.3 Summary; Problems; 6. Competition between genetically stable and unstable cells; 6.1 Competition dynamics; 6.2 Competition dynamics and cancer evolution; 6.2.1 A quasispecies model; 6.2.2 Strong apoptosis; 6.2.3 Weak apoptosis; 6.3 Overview of the insights obtained so far; 6.4 Can competition be reversed by chemotherapy?; 6.5 Summary; Problems; 7. Chromosomal instability and tumor growth; 7.1 The effect of chromosome loss on the generation of cancer; 7.2 Calculating the optimal rate of chromosome loss. - 7.3 The optimal rate of LOH: a time-dependent problem7.3.1 Formulation of the time-dependent problem; 7.3.2 Mathematical apparatus; 7.3.2.1 Statement of the one-step problem; 7.3.2.2 The Maximum Principle; 7.3.3 The optimal strategy for cancer; 7.4 The bigger picture; 7.4.1 Does cancer solve an optimization problem?; 7.4.2 Summary; Problems; 8. Angiogenesis, inhibitors, promoters, and spatial growth; 8.1 Model 1: Angiogenesis inhibition induces cell death; 8.2 Model 2: Angiogenesis inhibition prevents tumor cell division; 8.2.1 Linear stability analysis of the ODEs. - 8.2.2 Conclusions from the linear analysis8.3 Spread of tumors across space; 8.3.1 Turing stability analysis; 8.3.2 Stationary periodic solutions; 8.3.3 Biological implications and numerical simulations; 8.4 Somatic cancer evolution and progression; 8.5 Summary and clinical implications; Problems; Evolutionary dynamics and stochastic models; 9. Evolutionary dynamics of tumor initiation through oncogenes: the gain-of-function model; 9.1 Introduction; 9.2 Mutation-selection diagrams and the stochastic Moran process; 9.3 Analysis; 9.3.1 The method of differential equations. - 9.3.2 The probability of absorption. - 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 subs
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Dewey
ISBN
9789814566360

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