Mathematical Methods and Models in Biomedicine
Mathematical Methods and Models in Biomedicine

Author: Urszula Ledzewicz

Publisher: Springer Science & Business Media

Published: 2012-10-21

Total Pages: 426

ISBN-13: 1461441773

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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 Methods and Models in Biomedicine
Mathematical Methods and Models in Biomedicine

Author: Urszula Ledzewicz

Publisher: Springer Science & Business Media

Published: 2012-10-20

Total Pages: 426

ISBN-13: 1461441781

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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 Modelling in Biomedicine
Mathematical Modelling in Biomedicine

Author: Vitaly Volpert

Publisher: MDPI

Published: 2021-01-26

Total Pages: 224

ISBN-13: 3039434934

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Mathematical modelling in biomedicine is a rapidly developing scientific discipline at the intersection of medicine, biology, mathematics, physics, and computer science. Its progress is stimulated by fundamental scientific questions and by the applications to public health. This book represents a collection of papers devoted to mathematical modelling of various physiological problems in normal and pathological conditions. It covers a broad range of topics including cardiovascular system and diseases, heart and brain modelling, tumor growth, viral infections, and immune response. Computational models of blood circulation are used to study the influence of heart arrhythmias on coronary blood flow and on operating modes for left-ventricle-assisted devices. Wave propagation in the cardiac tissue is investigated in order to show the influence of tissue heterogeneity and fibrosis. The models of tumor growth are used to determine optimal protocols of antiangiogenic and radiotherapy. The models of viral hepatitis kinetics are considered for the parameter identification, and the evolution of viral quasi-species is investigated. The book presents the state-of-the-art in mathematical modelling in biomedicine and opens new perspectives in this passionate field of research.

Mathematical Models in Biology
Mathematical Models in Biology

Author: Leah Edelstein-Keshet

Publisher: SIAM

Published: 1988-01-01

Total Pages: 629

ISBN-13: 9780898719147

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Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

Optimal Control for Mathematical Models of Cancer Therapies
Optimal Control for Mathematical Models of Cancer Therapies

Author: Heinz Schättler

Publisher: Springer

Published: 2015-09-15

Total Pages: 511

ISBN-13: 1493929720

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This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

Modelling Methodology for Physiology and Medicine
Modelling Methodology for Physiology and Medicine

Author: Ewart Carson

Publisher: Elsevier

Published: 2000-12-31

Total Pages: 437

ISBN-13: 0080511902

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Modelling Methodology for Physiology and Medicine offers a unique approach and an unprecedented range of coverage of the state-of-the-art, advanced modelling methodology that is widely applicable to physiology and medicine. The book opens with a clear and integrated treatment of advanced methodology for developing mathematical models of physiology and medical systems. Readers are then shown how to apply this methodology beneficially to real-world problems in physiology and medicine, such as circulation and respiration. - Builds upon and enhances the readers existing knowledge of modelling methodology and practice - Editors are internationally renowned leaders in their respective fields

Quantitative Medical Data Analysis Using Mathematical Tools And Statistical Techniques
Quantitative Medical Data Analysis Using Mathematical Tools And Statistical Techniques

Author: Don Hong

Publisher: World Scientific

Published: 2007-07-10

Total Pages: 364

ISBN-13: 9814476234

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Quantitative biomedical data analysis is a fast-growing interdisciplinary area of applied and computational mathematics, statistics, computer science, and biomedical science, leading to new fields such as bioinformatics, biomathematics, and biostatistics. In addition to traditional statistical techniques and mathematical models using differential equations, new developments with a very broad spectrum of applications, such as wavelets, spline functions, curve and surface subdivisions, sampling, and learning theory, have found their mathematical home in biomedical data analysis.This book gives a new and integrated introduction to quantitative medical data analysis from the viewpoint of biomathematicians, biostatisticians, and bioinformaticians. It offers a definitive resource to bridge the disciplines of mathematics, statistics, and biomedical sciences. Topics include mathematical models for cancer invasion and clinical sciences, data mining techniques and subset selection in data analysis, survival data analysis and survival models for cancer patients, statistical analysis and neural network techniques for genomic and proteomic data analysis, wavelet and spline applications for mass spectrometry data preprocessing and statistical computing.

Sourcebook of Models for Biomedical Research
Sourcebook of Models for Biomedical Research

Author: P. Michael Conn

Publisher: Springer Science & Business Media

Published: 2008

Total Pages: 756

ISBN-13: 1588299333

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The collection of systems represented in Sourcebook of genomic programs, although this work is certainly well Models for Biomedical Research is an effort to re?ect the represented and indexed. diversity and utility of models that are used in biomedicine. Some models have been omitted due to page limitations That utility is based on the consideration that observations and we have encouraged the authors to use tables and made in particular organisms will provide insight into the ? gures to make comparisons of models so that observations workings of other, more complex, systems. Even the cell not available in primary publications can become useful to cycle in the simple yeast cell has similarities to that in the reader. humans and regulation with similar proteins occurs. We thank Richard Lansing and the staff at Humana for Some models have the advantage that the reproductive, guidance through the publication process. mitotic, development or aging cycles are rapid compared As this book was entering production, we learned of the with those in humans; others are utilized because individual loss of Tom Lanigan, Sr. Tom was a leader and innovator proteins may be studied in an advantageous way and that in scienti?c publishing and a good friend and colleague to have human homologs. Other organisms are facile to grow all in the exploratory enterprise. We dedicate this book to in laboratory settings or lend themselves to convenient analy- his memory. We will miss him greatly.

Causal Analysis in Biomedicine and Epidemiology
Causal Analysis in Biomedicine and Epidemiology

Author: Mikel Aickin

Publisher: CRC Press

Published: 2001-11-09

Total Pages: 240

ISBN-13: 9780824707484

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"Provides current models, tools, and examples for the formulation and evaluation of scientific hypotheses in causal terms. Introduces a new method of model parametritization. Illustrates structural equations and graphical elements for complex causal systems."

Mathematical Methods for Knowledge Discovery and Data Mining
Mathematical Methods for Knowledge Discovery and Data Mining

Author: Felici, Giovanni

Publisher: IGI Global

Published: 2007-10-31

Total Pages: 394

ISBN-13: 1599045303

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"This book focuses on the mathematical models and methods that support most data mining applications and solution techniques, covering such topics as association rules; Bayesian methods; data visualization; kernel methods; neural networks; text, speech, and image recognition; an invaluable resource for scholars and practitioners in the fields of biomedicine, engineering, finance, manufacturing, marketing, performance measurement, and telecommunications"--Provided by publisher.