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Mathematics for Biomedical Applications by Stanton A. Glantz Pdf
A qualitative understanding of physiological processes comes from the integration of knowledge of several factors which span many orders of magnitude in space, time, and energy. These factors include behavior exhibited by the entire body, performance of organ systems, histologic structure of the organs, and biochemical reactions inside cells. When one integrates these different perspectives on a problem in an attempt to understand a biological process or to reach a practical decision about how to manage a disease, one often slips from one set of assumptions to another, even though taken as a whole these assumptions might not be logically consistent. In contrast, a quantitative understanding of biological processes, based on mathematics, requires logical consistency above all. Although theoretically it may be possible to consider several factors which scan many orders of magnitude, in practice it is often difficult to obtain numerical solutions when the variables which quantify these factors differ by more than a few orders of magnitude. Thus, successful mathematical analysis generally requires a consistent scale of events. This requirement sometimes restricts use of prior knowledge, but it can help avoid unimportant details.
Mathematical Models and Computer Simulations for Biomedical Applications by Gabriella Bretti,Roberto Natalini,Pasquale Palumbo,Luigi Preziosi Pdf
Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework. Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications. Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems. The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries.
This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS
Fluid-Structure Interaction and Biomedical Applications by Tomáš Bodnár,Giovanni P. Galdi,Šárka Nečasová Pdf
This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI). Generally speaking, FSI is among the most popular and intriguing problems in applied sciences and includes industrial as well as biological applications. Various fundamental aspects of FSI are addressed from different perspectives, with a focus on biomedical applications. More specifically, the book presents a mathematical analysis of basic questions like the well-posedness of the relevant initial and boundary value problems, as well as the modeling and the numerical simulation of a number of fundamental phenomena related to human biology. These latter research topics include blood flow in arteries and veins, blood coagulation and speech modeling. We believe that the variety of the topics discussed, along with the different approaches used to address and solve the corresponding problems, will help readers to develop a more holistic view of the latest findings on the subject, and of the relevant open questions. For the same reason we expect the book to become a trusted companion for researchers from diverse disciplines, such as mathematics, physics, mathematical biology, bioengineering and medicine.
This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS
Mathematical Biology is a richly illustrated textbook in an exciting and fast growing field. Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others. It maintains a consistent level throughout so that graduate students can use it to gain a foothold into this dynamic research area.
An Introduction to Mathematics of Emerging Biomedical Imaging by Habib Ammari Pdf
Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.
Moving Boundary PDE Analysis by William Schiesser Pdf
Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.
Author : Peter J. Costa Publisher : John Wiley & Sons Page : 446 pages File Size : 45,5 Mb Release : 2017-03-27 Category : Mathematics ISBN : 9781119269496
Applied Mathematics for the Analysis of Biomedical Data by Peter J. Costa Pdf
Features a practical approach to the analysis of biomedical data via mathematical methods and provides a MATLAB® toolbox for the collection, visualization, and evaluation of experimental and real-life data Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® presents a practical approach to the task that biological scientists face when analyzing data. The primary focus is on the application of mathematical models and scientific computing methods to provide insight into the behavior of biological systems. The author draws upon his experience in academia, industry, and government–sponsored research as well as his expertise in MATLAB to produce a suite of computer programs with applications in epidemiology, machine learning, and biostatistics. These models are derived from real–world data and concerns. Among the topics included are the spread of infectious disease (HIV/AIDS) through a population, statistical pattern recognition methods to determine the presence of disease in a diagnostic sample, and the fundamentals of hypothesis testing. In addition, the author uses his professional experiences to present unique case studies whose analyses provide detailed insights into biological systems and the problems inherent in their examination. The book contains a well-developed and tested set of MATLAB functions that act as a general toolbox for practitioners of quantitative biology and biostatistics. This combination of MATLAB functions and practical tips amplifies the book’s technical merit and value to industry professionals. Through numerous examples and sample code blocks, the book provides readers with illustrations of MATLAB programming. Moreover, the associated toolbox permits readers to engage in the process of data analysis without needing to delve deeply into the mathematical theory. This gives an accessible view of the material for readers with varied backgrounds. As a result, the book provides a streamlined framework for the development of mathematical models, algorithms, and the corresponding computer code. In addition, the book features: Real–world computational procedures that can be readily applied to similar problems without the need for keen mathematical acumen Clear delineation of topics to accelerate access to data analysis Access to a book companion website containing the MATLAB toolbox created for this book, as well as a Solutions Manual with solutions to selected exercises Applied Mathematics for the Analysis of Biomedical Data: Models, Methods, and MATLAB® is an excellent textbook for students in mathematics, biostatistics, the life and social sciences, and quantitative, computational, and mathematical biology. This book is also an ideal reference for industrial scientists, biostatisticians, product development scientists, and practitioners who use mathematical models of biological systems in biomedical research, medical device development, and pharmaceutical submissions.
Dynamical Systems, PDEs and Networks for Biomedical Applications: Mathematical Modeling, Analysis and Simulations by André H. Erhardt,Krasimira Tsaneva-Atanasova,Glenn Terje Lines,Erik Andreas Martens Pdf
Pattern Recognition Techniques Applied to Biomedical Problems by Martha Refugio Ortiz-Posadas Pdf
This book covers pattern recognition techniques applied to various areas of biomedicine, including disease diagnosis and prognosis, and several problems of classification, with a special focus on—but not limited to—pattern recognition modeling of biomedical signals and images. Multidisciplinary by definition, the book’s topic blends computing, mathematics and other technical sciences towards the development of computational tools and methodologies that can be applied to pattern recognition processes. In this work, the efficacy of such methods and techniques for processing medical information is analyzed and compared, and auxiliary criteria for determining the correct diagnosis and treatment strategies are recommended and applied. Researchers in applied mathematics, the computer sciences, engineering and related fields with a focus on medical applications will benefit from this book, as well as professionals with a special interest in state-of-the-art pattern recognition techniques as applied to biomedicine.
Spatio-temporal Patterns: from Mathematical to Biomedical Applications by VARIOS AUTORES Pdf
The aim of the book can be described as follows: morphogenetic processes appearing during the development of biological organisms as well as genetic and epigenetic spatio-temporal patterns observed in control mechanisms of crucial phases of their life (reproduction, ageing, epidemic spread,...) are due to the combination of physico-chemical phenomena like diffusion, convection, chemotaxy, haptotaxy,... The aim of the book is to present basic mathematical tools underlying the mathematical models used to explain the spatio-temporal patterns associated to the observed phenomenology, and parallelly some examples of modelling and simulation of these phenomena (even through non classical ways like multiagent or individual-centered systems).
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally "not" high and the emphasis is on what is required to solve the "real" biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosciences. The book also shows how mathematics can contribute to the science of the next 100 years and how physical scientists must get involved. It presents a broad view of the field of theoretical and mathematical biology and is a good starting place from which to start genuine interdisciplinary research.
