Mathematical Methods and Models in Biomedicine

1. Front Matter

   Pages i-xi

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2. Immune System Modeling

   1. Front Matter

      Pages 1-1

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   2. Spatial Aspects of HIV Infection

      • Frederik Graw, Alan S. Perelson

      Pages 3-31

   3. Basic Principles in Modeling Adaptive Regulation and Immunodominance

      • Peter S. Kim, Peter P. Lee, Doron Levy

      Pages 33-57

   4. Evolutionary Principles in Viral Epitopes

      • Yaakov Maman, Alexandra Agranovich, Tal Vider Shalit, Yoram Louzoun

      Pages 59-83

3. Blood Vessel Dynamics

   1. Front Matter

      Pages 85-85

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   2. A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: The Role of Randomness

      • Vincenzo Capasso, Daniela Morale

      Pages 87-115

   3. Modeling Tumor Blood Vessel Dynamics

      • Lance L. Munn, Christian Kunert, J. Alex Tyrrell

      Pages 117-147

   4. Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms

      • Susana Ramalho, Alexandra B. Moura, Alberto M. Gambaruto, Adélia Sequeira

      Pages 149-175

4. Cancer Modeling

   1. Front Matter

      Pages 177-177

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   2. The Steady State of Multicellular Tumour Spheroids: A Modelling Challenge

      • Antonio Fasano, Alberto Gandolfi

      Pages 179-202

   3. Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification

      • Gili Hochman, Zvia Agur

      Pages 203-232

   4. Data Assimilation in Brain Tumor Models

      • Joshua McDaniel, Eric Kostelich, Yang Kuang, John Nagy, Mark C. Preul, Nina Z. Moore et al.

      Pages 233-262

5. Cancer Treatment

   1. Front Matter

      Pages 263-263

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   2. Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

      • Frédérique Billy, Jean Clairambault, Olivier Fercoq

      Pages 265-309

   3. Tumor Development Under Combination Treatments with Anti-angiogenic Therapies

      • Urszula Ledzewicz, Alberto d’Onofrio, Heinz Schättler

      Pages 311-337

   4. Saturable Fractal Pharmacokinetics and Its Applications

      • Rebeccah E. Marsh, Jack A. Tuszyński

      Pages 339-366

   5. A Mathematical Model of Gene Therapy for the Treatment of Cancer

      • Alexei Tsygvintsev, Simeone Marino, Denise E. Kirschner

      Pages 367-385

6. Epidemiological Models

   1. Front Matter

      Pages 387-387

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   2. Epidemiological Models with Seasonality

      • Avner Friedman

      Pages 389-410

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 modeling
• biomedical applications
• cancer dynamics
• cancer treatment
• epidemiology
• immune system

• , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, USA

  Urszula Ledzewicz

• , Electrical and Systems Engineering, Washington University, Saint Louis, USA

  Heinz Schättler

• Mathematical Biosciences Institute, Ohio State University, Columbus, USA

  Avner Friedman

• Tel Aviv University, Tel Aviv, Israel

  Eugene Kashdan

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