Survey of Models for Tumor-Immune System Dynamics

• 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?.- 2.3 Introduction to Deterministic Tumor (or Spheroid) Growth 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.- 2.7 References.- 2.8 Appendices.- 3. Mathematical Modeling of Tumor Growth Kinetics.- 3.1 Introduction.- 3.2 Tumor Growth as a Dynamical System.- 3.3 The Gompertz Model.- 3.4 The Logistic Model.- 3.5 Models of von Bertalanffy.- 3.6 Tumor Growth Modeled by Specific Mechanisms.- 3.7 Mathematical Models and Measured Growth Curves.- 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.- 4.8 Simulation and Validation Problems.- 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.- 5.3 Thmour Angiogenesis. Capillary Sprout Formation and Growth.- 5.4 Vascular Tumour Growth.- 5.5 Discussion and Conclusions.- 5.6 References.- 6. Basic Models of Tumor-Immune SystemInteractions Identification, Analysis and Predictions.- 6.1 Introduction.- 6.2 Kinetics Models of Cellular Cytotoxic Reactions at the Effector Stage of Immune Response.- 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.- 6.6 Propagation and Interaction of Tumor Specific Macromolecules in Multicellular Tumors.- 6.7 Conclusion.- 6.8 Acknowledgment.- 6.9 References.- 7. Tumor Heterogeneity and Growth Control.- 7.1 Introduction.- 7.2 The Goal.- 7.3 The Plan.- 7.4 The Foundation and Tools.- 7.5 The Structure.- 7.6 Conclusions.- 7.7 References.- 8. Biological Glossary.

"This book is [a] very helpful tool for mathematicians constructing models in biology and hopefully it can also help biologists to understand some philosophy of mathematical descriptions of biological phenomena with all its pluses and minuses." -Mathematica Bohemica