Ebook: Mathematical Methods and Models in Biomedicine

Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.

---

Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.

---

Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Spatial Aspects of HIV Infection....Pages 3-31
Basic Principles in Modeling Adaptive Regulation and Immunodominance....Pages 33-57
Evolutionary Principles in Viral Epitopes....Pages 59-83
Front Matter....Pages 85-85
A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: The Role of Randomness....Pages 87-115
Modeling Tumor Blood Vessel Dynamics....Pages 117-147
Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms....Pages 149-175
Front Matter....Pages 177-177
The Steady State of Multicellular Tumour Spheroids: A Modelling Challenge....Pages 179-202
Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification....Pages 203-232
Data Assimilation in Brain Tumor Models....Pages 233-262
Front Matter....Pages 263-263
Optimisation of Cancer Drug Treatments Using Cell Population Dynamics....Pages 265-309
Tumor Development Under Combination Treatments with Anti-angiogenic Therapies....Pages 311-337
Saturable Fractal Pharmacokinetics and Its Applications....Pages 339-366
A Mathematical Model of Gene Therapy for the Treatment of Cancer....Pages 367-385
Front Matter....Pages 387-387
Epidemiological Models with Seasonality....Pages 389-410
Periodic Incidence in a Discrete-Time SIS Epidemic Model....Pages 411-427

---

Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Spatial Aspects of HIV Infection....Pages 3-31
Basic Principles in Modeling Adaptive Regulation and Immunodominance....Pages 33-57
Evolutionary Principles in Viral Epitopes....Pages 59-83
Front Matter....Pages 85-85
A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: The Role of Randomness....Pages 87-115
Modeling Tumor Blood Vessel Dynamics....Pages 117-147
Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms....Pages 149-175
Front Matter....Pages 177-177
The Steady State of Multicellular Tumour Spheroids: A Modelling Challenge....Pages 179-202
Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification....Pages 203-232
Data Assimilation in Brain Tumor Models....Pages 233-262
Front Matter....Pages 263-263
Optimisation of Cancer Drug Treatments Using Cell Population Dynamics....Pages 265-309
Tumor Development Under Combination Treatments with Anti-angiogenic Therapies....Pages 311-337
Saturable Fractal Pharmacokinetics and Its Applications....Pages 339-366
A Mathematical Model of Gene Therapy for the Treatment of Cancer....Pages 367-385
Front Matter....Pages 387-387
Epidemiological Models with Seasonality....Pages 389-410
Periodic Incidence in a Discrete-Time SIS Epidemic Model....Pages 411-427
....