Items related to A Survey of Models for Tumor-Immune System Dynamics
Synopsis
1. A Brief History of Immunologic Thinking: Is it Time for Yin and Yang?.- 1.1 Koch's Postulates.- 1.2 Aristotle's Laws of Logical Argument.- 1.3 Antigens and T-Cell Responses.- 1.4 Thinking About the Immune System.- 1.5 Fuzzy T-Cell Model.- 1.6 Acknowledgment.- 2. General Aspects of Modeling Tumor Growth and Immune Response.- 2.1 Introduction.- 2.2 What is a Mathematical Model?.- 2.2.1 Why are mathematical models useful?.- 2.2.2 Limitations of mathematical models.- 2.2.3 Other considerations.- 2.3 Introduction to Deterministic Tumor (or Spheroid) Growth Models.- 2.3.1 Basic models: Description.- 2.3.2 Basic diffusion models: Mathematical aspects.- 2.3.3 Diffusion of growth inhibitor.- 2.3.4 Time-evolutionary diffusion models.- 2.4 A Predator-Prey Approach.- 2.5 A Model of Tumor Cell/Immune System Interaction.- 2.6 Models, Metaphors and Similes: Some Alternative Paradigms.- 2.6.1 The tunneling phenomenon.- 2.6.2 Some speculation.- 2.7 References.- 2.8 Appendices.- 2.8.1 Appendix I - Comments on catastrophe theory.- 2.8.2 Appendix II - Solution existence, uniqueness, stability and bifurcation and the inverse problem.- 3. Mathematical Modeling of Tumor Growth Kinetics.- 3.1 Introduction.- 3.2 Tumor Growth as a Dynamical System.- 3.2.1 Construction of growth rate functions.- 3.3 The Gompertz Model.- 3.3.1 Gompertz model as a simple dynamical system.- 3.3.2 Gompertz model as an S-system.- 3.3.3 Gompertz model and quiescence.- 3.3.4 Gompertz model and cell kinetics.- 3.3.5 Gompertz model and entropy.- 3.3.6 Gompertz model and tumor heterogeneity.- 3.3.7 Other explanations and analyses of Gompertz model.- 3.4 The Logistic Model.- 3.5 Models of von Bertalanffy.- 3.6 Tumor Growth Modeled by Specific Mechanisms.- 3.6.1 Competition among cell populations.- 3.6.2 Cell cycle kinetics and regulation by growth factors.- 3.6.3 Positive feedback mechanisms in tumors.- 3.7 Mathematical Models and Measured Growth Curves.- 3.7.1 Growth data and Gompertz model.- 3.7.2 Comparative studies of deterministic tumor growth models.- 3.8 Concluding Outlooks.- 3.9 Acknowledgment.- 3.10 References.- 4. Tumor Immune System Interactions: The Kinetic Cellular Theory.- 4.1 Introduction.- 4.2 A Concise Guide to the Literature.- 4.3 Guidelines: From Observation to Simulation.- 4.4 Cell Population and Activity.- 4.5 Modeling Cell Interactions.- 4.6 Evolution Kinetic Equations.- 4.7 Experimental Activity.- 4.7.1 Transition to neoplastic behavior and tumor proliferation.- 4.7.2 Preimmunization and recognition of antigens.- 4.7.3 Cytokine genes.- 4.8 Simulation and Validation Problems.- 4.8.1 Simulation methods.- 4.8.2 Some identification and validation problems.- 4.8.3 Discrete models.- 4.9 Remarks Addressed to Applied Mathematicians.- 4.10 Perspectives.- 4.11 References.- 5. From Mutation to Metastasis: The Mathematical Modelling of the Stages of Tumour Development.- 5.1 Introduction.- 5.2 Avascular Tumour Growth: The Multicell Spheroid Model.- 5.2.1 Results.- 5.3 Thmour Angiogenesis. Capillary Sprout Formation and Growth.- 5.3.1 Model improvements and extension.- 5.3.2 Numerical simulations.- 5.4 Vascular Tumour Growth.- 5.4.1 Results.- 5.5 Discussion and Conclusions.- 5.6 References.- 6. Basic Models of Tumor-Immune System Interactions Identification, Analysis and Predictions.- 6.1 Introduction.- 6.2 Kinetics Models of Cellular Cytotoxic Reactions at the Effector Stage of Immune Response.- 6.2.1 Solutions of the model at quasi-stationary approximation.- 6.2.2 Comparison of the minimal model with experimental data.- 6.3 Regulatory Cells at the Effector Stage of the Cellular Immune Response.- 6.4 Modeling of the Recognition Mechanisms of Thmor Cells by NK-like Cells.- 6.5 Switch of Cytolytic Mechanisms: Effector Cells, Target Cells and Bispecific Regulating Molecules.- 6.5.1 Kinetics of the multiple cytotoxic reactions.- 6.5.2 General model.- 6.5.3 Kinetics of ADCC/LDCC reactions.- 6.5.4 One effector cell and two molecular mechanisms recognition.- 6.5.5 Conclusi
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