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Author : André H. Erhardt,Krasimira Tsaneva-Atanasova,Glenn Terje Lines,Erik Andreas Martens
Publisher : Frontiers Media SA
Page : 209 pages
File Size : 52,6 Mb
Release : 2023-02-15
Category : Science
ISBN : 9782832514580
Author : William Schiesser
Publisher : CRC Press
Page : 195 pages
File Size : 50,5 Mb
Release : 2019-05-29
Category : Mathematics
ISBN : 9781000007886
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 : Andreas Deutsch,Lutz Brusch,Helen Byrne,Gerda de Vries,Hanspeter Herzel
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 50,5 Mb
Release : 2007-06-15
Category : Mathematics
ISBN : 9780817645588
Volume I of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Author : Gabriella Bretti,Roberto Natalini,Pasquale Palumbo,Luigi Preziosi
Publisher : Springer Nature
Page : 261 pages
File Size : 54,6 Mb
Release : 2023-09-17
Category : Mathematics
ISBN : 9783031357152
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.
Author : Andreas Deutsch,Rafael Bravo de la Parra,Rob J. de Boer,Odo Diekmann,Peter Jagers,Eva Kisdi,Mirjam Kretzschmar,Petr Lansky,Hans Metz
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 44,5 Mb
Release : 2007-10-12
Category : Mathematics
ISBN : 9780817645564
Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Author : Andreas Deutsch,Rafael Bravo de la Parra,Rob J. de Boer,Odo Diekmann,Peter Jagers,Eva Kisdi,Mirjam Kretzschmar,Petr Lansky,Hans Metz
Publisher : Birkhäuser
Page : 0 pages
File Size : 43,9 Mb
Release : 2007-10-12
Category : Mathematics
ISBN : 081764556X
Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Author : Jinzhi Lei
Publisher : Springer Nature
Page : 308 pages
File Size : 45,5 Mb
Release : 2021-05-13
Category : Mathematics
ISBN : 9783030730338
This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration. The diffusion of morphogens is addressed by introducing various reaction-diffusion equations based on different hypotheses concerning the process of morphogen gradient formation. The robustness of steady-state gradients is also covered through boundary value problems. The introduction gives an overview of the relevant biological concepts (cells, DNA, organism development) and provides the requisite mathematical preliminaries on continuous dynamics and stochastic modeling. A basic understanding of calculus is assumed. The techniques described in this book encompass a wide range of mechanisms, from molecular behavior to population dynamics, and the inclusion of recent developments in the literature together with first-hand results make it an ideal reference for both new students and experienced researchers in the field of systems biology and applied mathematics.
Author : Albert C.J. Luo,Hüseyin Merdan
Publisher : Springer
Page : 0 pages
File Size : 44,7 Mb
Release : 2016-02-08
Category : Technology & Engineering
ISBN : 3319266284
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.
Author : W.E. Schiesser
Publisher : CRC Press
Page : 235 pages
File Size : 49,5 Mb
Release : 2019-11-25
Category : Medical
ISBN : 9781000763737
Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin. Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, for example, no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the formulation and use of alternative DODE/DPDE models.
Author : Frederic Y. M. Wan
Publisher : World Scientific Publishing Company
Page : 0 pages
File Size : 42,9 Mb
Release : 2018
Category : Biology
ISBN : 9813143703
Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) The case study approach focusing on different specific modeling problems familiar to the particular author, and 2) The methods approach teaching some useful mathematical techniques accessible to the targeted student cohort with different models introduced to illustrate the application of the methods taught. The goal and approach of this new text differ from these two conventional approaches in that its emphasis is on the scientific issues that prompt the mathematical modeling and analysis of a particular phenomenon. For example, in the study of a fish population, we may be interested in the growth and evolution of the population, whether the natural growth or harvested population reaches a steady state (equilibrium or periodically changing) population in a particular environment, is a steady state stable or unstable with respect to a small perturbation from the equilibrium state, whether a small change in the environment would lead to a catastrophic change, etc. Each of these scientific issues requires the introduction of a different kind of model and a different set of mathematical tools to extract information about the same biological organisms or phenomena.Volume I of this three volume set limits its scope to phenomena and scientific issues that can be modeled by ordinary differential equations (ODE) that govern the evolution of the phenomena with time. The scientific issues involved include evolution, equilibrium, stability, bifurcation, feedback, optimization and control. Scientific issues such as signal and wave propagation, diffusion, and shock formation pertaining to phenomena involving spatial dynamics are to be modeled by partial differential equations (PDE) and will be treated in Volume II. Scientific issues involving randomness and uncertainty are deferred to Volume III.
Author : Brian P. Ingalls
Publisher : MIT Press
Page : 423 pages
File Size : 47,5 Mb
Release : 2022-06-07
Category : Science
ISBN : 9780262545822
An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.
Author : Stefanie Winkelmann,Christof Schütte
Publisher : Springer Nature
Page : 284 pages
File Size : 41,6 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9783030623876
The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.
Author : Ching Shan Chou,Avner Friedman
Publisher : Springer
Page : 172 pages
File Size : 53,7 Mb
Release : 2016-04-27
Category : Mathematics
ISBN : 9783319296388
This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience. The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A. Friedman, C.-Y. Kao, Springer – 2014), this book is geared towards undergraduate students with little background in mathematics and no biological background.
Author : William E. Schiesser
Publisher : John Wiley & Sons
Page : 370 pages
File Size : 42,8 Mb
Release : 2016-03-31
Category : Mathematics
ISBN : 9781119130505
Presents the methodology and applications of ODE and PDE models within biomedical science and engineering With an emphasis on the method of lines (MOL) for partial differential equation (PDE) numerical integration, Method of Lines PDE Analysis in Biomedical Science and Engineering demonstrates the use of numerical methods for the computer solution of PDEs as applied to biomedical science and engineering (BMSE). Written by a well-known researcher in the field, the book provides an introduction to basic numerical methods for initial/boundary value PDEs before moving on to specific BMSE applications of PDEs. Featuring a straightforward approach, the book’s chapters follow a consistent and comprehensive format. First, each chapter begins by presenting the model as an ordinary differential equation (ODE)/PDE system, including the initial and boundary conditions. Next, the programming of the model equations is introduced through a series of R routines that primarily implement MOL for PDEs. Subsequently, the resulting numerical and graphical solution is discussed and interpreted with respect to the model equations. Finally, each chapter concludes with a review of the numerical algorithm performance, general observations and results, and possible extensions of the model. Method of Lines PDE Analysis in Biomedical Science and Engineering also includes: Examples of MOL analysis of PDEs, including BMSE applications in wave front resolution in chromatography, VEGF angiogenesis, thermographic tumor location, blood-tissue transport, two fluid and membrane mass transfer, artificial liver support system, cross diffusion epidemiology, oncolytic virotherapy, tumor cell density in glioblastomas, and variable grids Discussions on the use of R software, which facilitates immediate solutions to differential equation problems without having to first learn the basic concepts of numerical analysis for PDEs and the programming of PDE algorithms A companion website that provides source code for the R routines Method of Lines PDE Analysis in Biomedical Science and Engineering is an introductory reference for researchers, scientists, clinicians, medical researchers, mathematicians, statisticians, chemical engineers, epidemiologists, and pharmacokineticists as well as anyone interested in clinical applications and the interpretation of experimental data with differential equation models. The book is also an ideal textbook for graduate-level courses in applied mathematics, BMSE, biology, biophysics, biochemistry, medicine, and engineering.
Author : Urszula Ledzewicz,Heinz Schättler,Avner Friedman,Eugene Kashdan
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 47,9 Mb
Release : 2012-10-20
Category : Mathematics
ISBN : 9781461441786
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.