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E-raamat: Dynamics Of Cancer: Mathematical Foundations Of Oncology

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(Univ Of California, Irvine, Usa), (Univ Of California, Irvine, Usa)
  • Formaat: 532 pages
  • Ilmumisaeg: 24-Apr-2014
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814566384
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Dynamics Of Cancer: Mathematical Foundations Of OncologySuurem pilt
  • Formaat: 532 pages
  • Ilmumisaeg: 24-Apr-2014
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814566384
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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.
Preface vii
1 Teaching guide
1(4)
1.1 How to use this book
1(1)
1.2 A sample syllabus for a Mathematics course
2(1)
1.3 A sample syllabus for a Biology course
3(2)
2 Cancer and somatic evolution
5(14)
2.1 What is cancer?
5(1)
2.2 Basic cancer genetics
6(2)
2.3 Multi-stage carcinogenesis and colon cancer
8(2)
2.4 Genetic instability
10(2)
2.5 Barriers to cancer progression: importance of the micro-environment
12(3)
2.6 Cellular hierarchies in cancer
15(1)
2.7 Genetic and epigenetic changes
15(2)
2.8 Evolutionary theory and Darwinian selection
17(2)
3 Mathematical modeling of tumorigenesis
19(14)
3.1 Ordinary differential equations
20(2)
3.2 Extensions of ODE modeling
22(1)
3.2.1 Optimal control
22(1)
3.2.2 ODEs and cancer epidemiology
23(1)
3.3 Partial differential equations
23(2)
3.4 Stochastic modeling
25(3)
3.5 Cellular automaton models
28(2)
3.6 Hybrid and multiscale modeling
30(3)
Basic growth dynamics and deterministic models
33(98)
4 Single species growth
35(12)
4.1 Exponential growth
35(2)
4.2 Surface growth
37(2)
4.3 Sigmoidal growth
39(4)
4.3.1 Logistic growth
39(2)
4.3.2 Other sigmoidal laws
41(2)
4.4 Atypical growth
43(1)
4.5 Multistep growth
44(1)
4.6 Conclusions
44(3)
5 Two-species competition dynamics
47(10)
5.1 Logistic growth of two species and the basic dynamics of competition
47(3)
5.2 Two-species dynamics: the axiomatic approach
50(5)
5.3 Summary
55(2)
6 Competition between genetically stable and unstable cells
57(24)
6.1 Competition dynamics
58(5)
6.2 Competition dynamics and cancer evolution
63(13)
6.2.1 A quasispecies model
63(8)
6.2.2 Strong apoptosis
71(3)
6.2.3 Weak apoptosis
74(2)
6.3 Overview of the insights obtained so far
76(1)
6.4 Can competition be reversed by chemotherapy?
77(2)
6.5 Summary
79(2)
7 Chromosomal instability and tumor growth
81(24)
7.1 The effect of chromosome loss on the generation of cancer
82(2)
7.2 Calculating the optimal rate of chromosome loss
84(5)
7.3 The optimal rate of LOH: a time-dependent problem
89(11)
7.3.1 Formulation of the time-dependent problem
91(3)
7.3.2 Mathematical apparatus
94(4)
7.3.3 The optimal strategy for cancer
98(2)
7.4 The bigger picture
100(5)
7.4.1 Does cancer solve an optimization problem?
102(1)
7.4.2 Summary
102(3)
8 Angiogenesis, inhibitors, promoters, and spatial growth
105(26)
8.1 Model 1: Angiogenesis inhibition induces cell death
107(5)
8.2 Model 2: Angiogenesis inhibition prevents tumor cell division
112(3)
8.2.1 Linear stability analysis of the ODEs
113(2)
8.2.2 Conclusions from the linear analysis
115(1)
8.3 Spread of tumors across space
115(6)
8.3.1 Turing stability analysis
116(3)
8.3.2 Stationary periodic solutions
119(1)
8.3.3 Biological implications and numerical simulations
120(1)
8.4 Somatic cancer evolution and progression
121(6)
8.5 Summary and clinical implications
127(4)
Evolutionary dynamics and stochastic models
131(200)
9 Evolutionary dynamics of tumor initiation through oncogenes: the gain-of-function model
133(14)
9.1 Introduction
133(2)
9.2 Mutation-selection diagrams and the stochastic Moran process
135(2)
9.3 Analysis
137(3)
9.3.1 The method of differential equations
138(1)
9.3.2 The probability of absorption
139(1)
9.4 Probability and timing of mutant fixation
140(5)
9.4.1 The approximation of “r;almost absorbing”r; states and the growth of mutants
143(1)
9.4.2 Nearly-deterministic regime
144(1)
9.5 Summary
145(2)
10 Evolutionary dynamics of tumor initiation through tumor-suppressor genes: the loss-of-function model and stochastic tunneling
147(24)
10.1 Introduction
147(1)
10.2 Process description and the mutation-selection diagram
148(2)
10.3 Three regimes: a two-step process, stochastic tunneling, and a nearly-deterministic regime
150(1)
10.4 The transition matrix
151(1)
10.5 Mathematical theory
152(10)
10.5.1 The Kolmogorov forward equation in the absence of intermediate mutant fixation
152(1)
10.5.2 The probability generating function
153(1)
10.5.3 The method of characteristics and the Riccati equation
154(2)
10.5.4 Tunneling for disadvantageous, neutral, and advantageous intermediate mutants
156(1)
10.5.5 Genuine two-step process vs tunneling
157(1)
10.5.6 Time-scales of the process
157(1)
10.5.7 Neutral intermediate mutants
158(2)
10.5.8 Disadvantageous intermediate mutants
160(1)
10.5.9 Advantageous intermediate mutants
161(1)
10.6 Dynamics of loss-of-function mutations
162(6)
10.6.1 The genuine two-step processes
162(1)
10.6.2 Tunneling
163(2)
10.6.3 Nearly deterministic regime
165(1)
10.6.4 Disadvantageous, neutral and advantageous intermediate mutants
165(1)
10.6.5 The role of the population size
166(2)
10.7 Summary
168(3)
11 Microsatellite and chromosomal instability in sporadic and familial colorectal cancers
171(26)
11.1 Some biological facts about genetic instability in colon cancer
173(1)
11.2 A model for the initiation of sporadic colorectal cancers
173(11)
11.2.1 The first model of the APC gene inactivation: no instabilities
173(6)
11.2.2 Colorectal cancer and chromosomal instability
179(5)
11.3 Sporadic colorectal cancers, CIN and MSI
184(5)
11.4 FAP
189(2)
11.5 HNPCC
191(1)
11.6 Summary
192(5)
12 Evolutionary dynamics in hierarchical populations
197(28)
12.1 Introduction
197(1)
12.2 Types of stem cells divisions
198(2)
12.3 The set-up
200(2)
12.4 Methodology
202(8)
12.4.1 Analysis of the Moran process
202(6)
12.4.2 Numerical simulations
208(2)
12.5 Generation of mutations in a hierarchical population
210(8)
12.5.1 Tunneling rates
210(1)
12.5.2 Double-hit mutants are produced slower under symmetric compared to asymmetric divisions
211(2)
12.5.3 Comparison with the homogeneous model
213(1)
12.5.4 The optimal fraction of stem cells
214(2)
12.5.5 Do mutations in TA cells produce double-mutants?
216(2)
12.6 Biological discussion
218(5)
12.6.1 Symmetric divisions can have a cancer-delaying effect
219(2)
12.6.2 Can TA cells create double-hit mutants?
221(1)
12.6.3 Cancer stem cell hypothesis
222(1)
12.7 Summary
223(2)
13 Spatial evolutionary dynamics of tumor initiation
225(22)
13.1 Introduction
225(1)
13.2 1D spatial Moran process
226(2)
13.3 Two-species dynamics
228(3)
13.3.1 Preliminaries
228(1)
13.3.2 Probability of mutant fixation
229(2)
13.4 Three-species dynamics
231(7)
13.4.1 Calculating the tunneling rate by the doubly-stochastic approximation
231(3)
13.4.2 Limiting cases and the tunneling rate approximations
234(2)
13.4.3 When is tunneling important?
236(2)
13.5 Dynamics of mutant generation
238(6)
13.5.1 Gain-of-function mutations: a two-species problem
238(1)
13.5.2 Loss-of-function mutations: a three-species problem
239(2)
13.5.3 Definition of neutrality
241(1)
13.5.4 Three-species dynamic: a comparison with the space-free model
241(3)
13.6 Outlook
244(3)
14 Complex tumor dynamics in space
247(28)
14.1 Introduction
247(1)
14.2 Complex traits and fitness valleys
248(1)
14.3 The Moran process
249(9)
14.3.1 Spatial restriction accelerates evolution
250(2)
14.3.2 Dependence on parameters
252(6)
14.4 The contact process
258(7)
14.4.1 The steady-state density of cells
259(4)
14.4.2 Complex effects of spatial restriction
263(1)
14.4.3 Parameter dependencies
264(1)
14.5 Advantageous intermediate mutants
265(3)
14.6 Summary and discussion
268(7)
15 Stochastic modeling of cancer growth, treatment, and resistance generation
275(26)
15.1 Introduction
275(1)
15.2 The basic model of cancer growth and generation of mutations
276(6)
15.2.1 The concept: a birth-death process with mutations
276(1)
15.2.2 Summary of all the probabilities
277(1)
15.2.3 Stochastic description: the example of one mutation
278(2)
15.2.4 The probability generating function description
280(1)
15.2.5 The method of characteristics
281(1)
15.3 Application to cancer treatment and generation of resistance
282(6)
15.3.1 The framework
283(2)
15.3.2 Treatment regimes
285(1)
15.3.3 Probability of extinction and treatment success
286(1)
15.3.4 Symmetric coefficients
287(1)
15.4 Example: the case of two drugs
288(3)
15.4.1 Equations for the moments
289(1)
15.4.2 Equations for the characteristics
290(1)
15.5 Mutant production before and during treatment
291(8)
15.5.1 General theory
291(3)
15.5.2 The case of one drug
294(3)
15.5.3 The case of two drugs
297(2)
15.6 Outlook
299(2)
16 Evolutionary dynamics of drug resistance in chronic myeloid leukemia
301(30)
16.1 Biology of CML
302(1)
16.2 Therapy and targeted small molecule inhibitors
302(3)
16.3 The computational framework
305(2)
16.4 When do resistant cells emerge?
307(1)
16.5 Cancer turnover and the evolution of resistance
308(1)
16.6 Combination therapy and the prevention of resistance
309(3)
16.7 Parameters and CML
312(2)
16.8 Tumor architecture and tumor stem cells
314(3)
16.9 Short-term versus long-term treatment strategies
317(2)
16.10 Cross-resistance and combination therapy
319(5)
16.11 Combination versus cyclic sequential treatment
324(4)
16.12 Summary
328(3)
Advanced topics
331(132)
17 Evolutionary dynamics of stem-cell driven tumor growth
333(14)
17.1 The model
334(2)
17.2 Evolutionary dynamics in ODE models
336(3)
17.3 Evolutionary dynamics in a stochastic, spatial model
339(1)
17.4 Predicted versus observed tumor growth patterns
340(2)
17.5 The order of phenotypic transitions
342(3)
17.6 Summary
345(2)
18 Tumor growth kinetics and disease progression
347(12)
18.1 Cell death and mutant generation
349(4)
18.2 Does PCD protect against cancer?
353(3)
18.3 Cell turnover and pathology
356(1)
18.4 Conclusions
357(2)
19 Epigenetic changes and the rate of DNA methylation
359(16)
19.1 De novo methylation kinetics in CIMP and non-CIMP cells following demethylation
361(2)
19.2 Quantifying the de novo methylation kinetics
363(3)
19.3 Interpreting the results with the help of a mathematical model
366(5)
19.4 De novo methylation kinetics in highly methylated cells
371(1)
19.5 Importance of experimental verification
372(1)
19.6 Summary
372(3)
20 Telomeres and cancer protection
375(28)
20.1 Lineages and replication limits
377(3)
20.2 Model analysis
380(9)
20.2.1 Population turnover and replication capacity: analytical results
380(7)
20.2.2 Agent-based model
387(1)
20.2.3 Decrease in the replication capacity of stem cells
388(1)
20.3 Tissue architecture and the development of cancer
389(9)
20.4 Theory and observed tissue architecture
398(3)
20.5 Summary
401(2)
21 Gene therapy and oncolytic virus therapy
403(28)
21.1 A basic ordinary differential equation model
404(7)
21.1.1 Non-replicating viruses
407(1)
21.1.2 Replicating viruses
408(3)
21.2 Different mathematical formulations and the robustness of results
411(1)
21.3 A spatially explicit model of oncolytic virus dynamics
412(12)
21.3.1 Initial virus growth patterns
413(2)
21.3.2 Growth patterns and the extinction of cells
415(9)
21.4 Experimentally observed patterns of virus spread
424(4)
21.5 Conclusions
428(3)
22 Immune responses, tumor growth, and therapy
431(28)
22.1 Some facts about immune responses
433(2)
22.2 The model
435(4)
22.3 Properties of equilibria and parameter dependencies
439(3)
22.4 Immunity versus tolerance
442(1)
22.5 Cancer initiation
443(1)
22.6 Tumor dormancy, evolution, and progression
443(3)
22.7 Immunotherapy against cancers
446(3)
22.8 Case study: immune responses and the treatment for chronic myeloid leukemia
449(3)
22.9 Role of immunity and resistance in driving treatment dynamics
452(4)
22.10 Possible role of immune stimulation for long-term remission
456(1)
22.11 Summary
457(2)
23 Towards higher complexities: social interactions
459(4)
23.1 Microenvironment
459(1)
23.2 Cooperation and division of labor
460(2)
23.3 Conclusion
462(1)
Bibliography 463(48)
Index 511
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