Mathematical Methods and Models in Biomedicine
By: edited by Urszula Ledzewicz, Heinz Schättler, Avner Friedman, Eugene Kashdan
Contributors: Schättler, Heinz; Friedman, Avner; Kashdan, Eugene; SpringerLink (Online service)
Series: Lecture Notes on Mathematical Modelling in the Life Sciences
Publisher: Springer New York; Imprint: Springer
Published: 2013
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 427
ISBN-13: 9781461441786
Subjects: Life sciences; Life Sciences, general; Mathematical and Computational Biology; Optimization; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematical optimization; Biomedical engineering
Description: 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.
Table of contents: title: <p><b>Spatial aspects of HIV infection; title: Basic Principles in Modeling Adaptive Regulation and </b><b>Immunodominance; title: Evolutionary Principles In Viral Epitopes; title: A Multiscale Approach Leading to Hybrid Mathematical Models for </b><b>Angiogenesis: the Role of Randomness; title: </b><b>Modeling Tumor Blood Vessel Dynamics; title: </b><b>Influence of Blood Rheology and Outflow Boundary Conditions in Numerical Simulations of Cerebral Aneurysms; title: The Steady State of Multicellular Tumour Spheroids: a Modelling </b><b>Challenge; title: Deciphering Fate Decision in Normal and Cancer Stem Cells – Mathematical Models and Their Experimental Verification.</b><i>; title: </i><b>Data Assimilation in Brain Tumor Models; title: Optimisation of Cancer Drug Treatments Using Cell Population Dynamics; title: Tumor Development under Combination Treatments with Antiangiogenic Therapies; title: Saturable Fractal Pharmacokinetics and Its Applications; title: A MathematicalModel of Gene Therapy for the Treatment of Cancer; title: Epidemiological Models with Seasonality; title: Periodic Incidence in a Discrete-Time <i>SIS </i>Epidemic Model.</b></p>.