Mathematical Methods and Models in Biomedicine

  • Urszula Ledzewicz
  • Heinz Schättler
  • Avner Friedman
  • Eugene Kashdan

Table of contents

  1. Front Matter
    Pages i-xi
  2. Immune System Modeling

    1. Front Matter
      Pages 1-1
    2. Frederik Graw, Alan S. Perelson
      Pages 3-31
    3. Peter S. Kim, Peter P. Lee, Doron Levy
      Pages 33-57
    4. Yaakov Maman, Alexandra Agranovich, Tal Vider Shalit, Yoram Louzoun
      Pages 59-83
  3. Blood Vessel Dynamics

    1. Front Matter
      Pages 85-85
    2. Lance L. Munn, Christian Kunert, J. Alex Tyrrell
      Pages 117-147
    3. Susana Ramalho, Alexandra B. Moura, Alberto M. Gambaruto, Adélia Sequeira
      Pages 149-175
  4. Cancer Modeling

    1. Front Matter
      Pages 177-177
    2. Antonio Fasano, Alberto Gandolfi
      Pages 179-202
    3. 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
    2. Frédérique Billy, Jean Clairambault, Olivier Fercoq
      Pages 265-309
    3. Urszula Ledzewicz, Alberto d’Onofrio, Heinz Schättler
      Pages 311-337
    4. Rebeccah E. Marsh, Jack A. Tuszyński
      Pages 339-366
    5. Alexei Tsygvintsev, Simeone Marino, Denise E. Kirschner
      Pages 367-385
  6. Epidemiological Models

    1. Front Matter
      Pages 387-387
    2. Avner Friedman
      Pages 389-410

About this book

Introduction

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.

Keywords

Mathematical modeling biomedical applications cancer dynamics cancer treatment epidemiology immune system

Editors and affiliations

  • Urszula Ledzewicz
    • 1
  • Heinz Schättler
    • 2
  • Avner Friedman
    • 3
  • Eugene Kashdan
    • 4
  1. 1., Mathematics and StatisticsSouthern Illinois University EdwardsvillEdwardsvilleUSA
  2. 2., Electrical and Systems EngineeringWashington UniversitySaint LouisUSA
  3. 3.Mathematical Biosciences InstituteOhio State UniversityColumbusUSA
  4. 4.Tel Aviv UniversityTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4178-6
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4177-9
  • Online ISBN 978-1-4614-4178-6
  • Series Print ISSN 2193-4789
  • Series Online ISSN 2193-4797
  • About this book