|
|
1 | (8) |
|
|
7 | (2) |
|
2 Cell Cycle as an Object of Control |
|
|
9 | (46) |
|
2.1 Cell Cycle and Chemotherapy |
|
|
9 | (7) |
|
2.2 Optimization of Cell Cycle Dependent Chemotherapy |
|
|
16 | (14) |
|
2.2.1 Compartmental Models of Cell Cycle with Control Action |
|
|
17 | (3) |
|
2.2.2 Models with a Single Phase-Specific Killing Agent |
|
|
20 | (1) |
|
2.2.3 Multiple Drug Therapy and Control |
|
|
21 | (1) |
|
2.2.4 Optimization of Treatment Protocols |
|
|
22 | (8) |
|
2.3 Pharmacokinetics and Pharmacodynamics |
|
|
30 | (3) |
|
2.4 Resonances, Synchronization, Aftereffects |
|
|
33 | (2) |
|
2.5 Drug Resistance in Chemotherapy |
|
|
35 | (20) |
|
2.5.1 Simple Models of Drug Resistance |
|
|
35 | (1) |
|
2.5.2 Infinite-Dimensional Models of Drug Resistance |
|
|
36 | (9) |
|
2.5.3 Model Transformation and Optimization of Therapy |
|
|
45 | (4) |
|
|
49 | (6) |
|
3 Therapy Optimization in Population Dynamics Models |
|
|
55 | (30) |
|
3.1 Standard Models of Population Dynamics |
|
|
55 | (6) |
|
3.2 Tumor Angiogenesis and Antiangiogenic Therapy |
|
|
61 | (1) |
|
3.3 Models of Cancer Growth Including Vascularization |
|
|
62 | (5) |
|
3.4 Planning Antiangiogenic and Combined Therapies |
|
|
67 | (8) |
|
3.5 Models of Gene and Immunotherapy in Cancer Treatment |
|
|
75 | (10) |
|
|
80 | (5) |
|
4 Structured Models and Their Use in Modeling Anticancer Therapies |
|
|
85 | (54) |
|
4.1 Tumor Growth and Treatment in Two and Three Dimensions |
|
|
85 | (13) |
|
|
86 | (1) |
|
4.1.2 Spheroids and Tumor Cords |
|
|
87 | (2) |
|
|
89 | (3) |
|
4.1.4 Modeling Desmoplastic Tumor |
|
|
92 | (1) |
|
4.1.5 Neovascularization Model |
|
|
92 | (2) |
|
4.1.6 Modeling the Tumor Microenvironment Impact |
|
|
94 | (1) |
|
|
95 | (3) |
|
4.2 Models of Angiogenesis |
|
|
98 | (4) |
|
4.3 Modeling the Effects of Therapeutic Actions |
|
|
102 | (2) |
|
4.4 Structure in Hematopoiesis and Carcinogenesis and Its Role in Cancer Detection, Prevention, and Treatment |
|
|
104 | (14) |
|
4.4.1 Stochasticity or Determinism in Stem Cell Systems? |
|
|
105 | (10) |
|
4.4.2 Models of Mutations and Evolution of Disease |
|
|
115 | (3) |
|
4.4.3 Prevention, Detection, and Treatment of Cancer Given Hierarchical Structure of Cancer and Its Stepwise Progression |
|
|
118 | (1) |
|
4.5 Physiologically Structured Models |
|
|
118 | (5) |
|
4.6 Cellular Automata and Agent Based Approach to Treatment Planning |
|
|
123 | (16) |
|
4.6.1 Biologically Motivated Cellular Automata |
|
|
123 | (3) |
|
4.6.2 Single-Cell-Based Models |
|
|
126 | (2) |
|
4.6.3 Models Containing Therapeutic Actions |
|
|
128 | (2) |
|
|
130 | (9) |
|
5 Signaling Pathways Dynamics and Cancer Treatment |
|
|
139 | (32) |
|
5.1 Deterministic and Stochastic Models of Regulatory Modules in Signaling Pathways |
|
|
139 | (17) |
|
|
139 | (2) |
|
|
141 | (2) |
|
5.1.3 Mathematical Modeling |
|
|
143 | (4) |
|
5.1.4 Basic Principles Used in Development of the Mathematical Model |
|
|
147 | (6) |
|
5.1.5 Stochastic or Deterministic Model? |
|
|
153 | (2) |
|
5.1.6 Deterministic Approximation of the Stochastic System |
|
|
155 | (1) |
|
5.2 Intracellular Processes as Objects of Control |
|
|
156 | (5) |
|
5.3 Example of the Control Signals in the Signaling Pathways |
|
|
161 | (10) |
|
5.3.1 p53 Signaling Pathway |
|
|
161 | (2) |
|
|
163 | (1) |
|
5.3.3 Nutlin-3 as an Example of the Chemical Particle-Based Control |
|
|
164 | (2) |
|
|
166 | (5) |
|
6 Model Identification and Parameter Estimation |
|
|
171 | (28) |
|
|
171 | (2) |
|
6.2 Compartmental Population Models |
|
|
173 | (3) |
|
6.2.1 Length of Cell Cycle Phases |
|
|
174 | (1) |
|
6.2.2 Rates of Missense Mutational Events |
|
|
174 | (1) |
|
6.2.3 Gene Copy Number Variation |
|
|
175 | (1) |
|
6.3 Structured Models, Models Including Angiogenesis and Spatial Models |
|
|
176 | (1) |
|
6.4 Models of Signaling Pathways and Intracellular Processes |
|
|
176 | (6) |
|
6.4.1 Degradation and Transcription Rates |
|
|
178 | (1) |
|
6.4.2 Population vs Single Cell Experiments |
|
|
178 | (2) |
|
6.4.3 Relative vs Absolute Measurements |
|
|
180 | (1) |
|
6.4.4 Algorithms Used to Estimate Kinetic Parameters |
|
|
181 | (1) |
|
6.5 Pharmacokinetics Parameters |
|
|
182 | (1) |
|
6.6 Sensitivity of Regulatory Network Models |
|
|
183 | (16) |
|
6.6.1 Local Sensitivity Analysis |
|
|
184 | (2) |
|
6.6.2 Global Sensitivity Analysis |
|
|
186 | (2) |
|
|
188 | (2) |
|
|
190 | (4) |
|
|
194 | (5) |
|
|
199 | (34) |
|
A Stability and Controllability of Dynamical Systems |
|
|
199 | (8) |
|
|
205 | (2) |
|
B Pontryagin Maximum Principle and Optimal Control |
|
|
207 | (6) |
|
|
211 | (2) |
|
|
213 | (10) |
|
|
214 | (1) |
|
|
215 | (1) |
|
C.3 Pitchfork Bifurcation |
|
|
216 | (3) |
|
C.4 Transcritical Bifurcation |
|
|
219 | (1) |
|
|
220 | (2) |
|
|
222 | (1) |
|
D Numerical Implementation of the Runge--Kutta and Gillespie Methods |
|
|
223 | (10) |
|
D.1 Deterministic Algorithms |
|
|
223 | (2) |
|
D.2 Stochastic Algorithms |
|
|
225 | (1) |
|
D.2.1 Gillespie Algorithm |
|
|
225 | (2) |
|
|
227 | (3) |
|
D.2.3 Haseltine--Rawlings Modification |
|
|
230 | (2) |
|
|
232 | (1) |
Index |
|
233 | |