Download or read book Dynamical Systems PDEs and Networks for Biomedical Applications Mathematical Modeling Analysis and Simulations written by André H. Erhardt and published by Frontiers Media SA. This book was released on 2023-02-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Modeling of Biological Systems Volume II written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Modeling of Biological Systems Volume I written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-06-15 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Moving Boundary PDE Analysis written by William Schiesser and published by CRC Press. This book was released on 2019-05-29 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Models and Computer Simulations for Biomedical Applications written by Gabriella Bretti and published by Springer Nature. This book was released on 2023-09-17 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Modeling of Biological Systems Volume II written by Andreas Deutsch and published by Birkhäuser. This book was released on 2007-10-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Time Delay ODE PDE Models written by W.E. Schiesser and published by CRC Press. This book was released on 2019-11-25 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Modeling in Systems Biology written by Brian P. Ingalls and published by MIT Press. This book was released on 2022-06-07 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Methods and Models in Biomedicine written by Urszula Ledzewicz and published by Springer Science & Business Media. This book was released on 2012-10-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to Mathematical Biology written by Ching Shan Chou and published by Springer. This book was released on 2016-04-27 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Dynamics in Computational Biology written by Stefanie Winkelmann and published by Springer Nature. This book was released on 2021-01-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Systems Biology written by Jinzhi Lei and published by Springer Nature. This book was released on 2021-05-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Dynamical System Models in the Life Sciences and Their Underlying Scientific Issues written by Frederic Y. M. Wan and published by World Scientific Publishing Company. This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modeling and Simulation in Biomedical Engineering Applications in Cardiorespiratory Physiology written by Willem L. van Meurs and published by McGraw Hill Professional. This book was released on 2011-08-07 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: THEORY AND PRACTICE OF MODELING AND SIMULATING HUMAN PHYSIOLOGY Written by a coinventor of the Human Patient Simulator (HPS) and past president of the Society in Europe for Simulation Applied to Medicine (SESAM), Modeling and Simulation in Biomedical Engineering: Applications in Cardiorespiratory Physiology is a compact and consistent introduction to this expanding field. The book divides the modeling and simulation process into five manageable steps--requirements, conceptual models, mathematical models, software implementation, and simulation results and validation. A framework and a basic set of deterministic, continuous-time models for the cardiorespiratory system are provided. This timely resource also addresses advanced topics, including sensitivity analysis and setting model requirements as part of an encompassing simulation and simulator design. Practical examples provide you with the skills to evaluate and adapt existing physiologic models or create new ones for specific applications. Coverage includes: Signals and systems Model requirements Conceptual models Mathematical models Software implementation Simulation results and model validation Cardiorespiratory system model Circulation Respiration Physiologic control Sensitivity analysis of a cardiovascular model Design of model-driven acute care training simulators “Uniquely qualified to author such a text, van Meurs is one of the original developers of CAE Healthcare’s Human Patient Simulator (HPS). ...His understanding of mathematics, human physiology, pharmacology, control systems, and systems engineering, combined with a conversational writing style, results in a readable text. ...The ample illustrations and tables also break up the text and make reading the book easier on the eyes. ...concise yet in conversational style, with real-life examples. This book is highly recommended for coursework in physiologic modeling and for all who are interested in simulator design and development. The book pulls all these topics together under one cover and is an important contribution to biomedical literature.” --IEEE Pulse, January 2014 “This book is written by a professional engineer who is unique in that he seems to have a natural understanding of 3 key areas as follows: the hardware involved with simulators, human physiology, and mathematical modeling. Willem van Meurs is one of the inventors of the model-driven human patient simulator (HPS), and so, he is very qualified to write this book. The book is written in a clear way, using the first person throughout, in a conversational manner, with a style that involves posing questions and answering them in subsequent text. ...The book starts with a very useful introduction and background chapter, setting out the scene for the rest of the book. ...I have used his book in enhancing my own talks and understanding human patient simulation and can strongly recommend it.” --Simulation in Healthcare December, 2012 Reviewed by Mark A. Tooley, Ph.D., Department of Medical Physics and Bioengineering, Royal United Hospital, Combe Park, Bath, UK.

Download or read book Reduced Order Methods for Modeling and Computational Reduction written by Alfio Quarteroni and published by Springer. This book was released on 2014-06-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Download or read book Biomedical Modeling and Simulation written by Jerome Eisenfeld and published by North Holland. This book was released on 1992-01-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of quantitative biology is in the midst of a creative explosion. The increasing sophistication of data analysis is now combining with technical advances in computer hardware and software to allow for a substantially faster output of work than previously. In parallel, the mathematical modeling techniques have grown rapidly in sophistication and predictive value. These techniques include areas of mathematics which have recently become prominent, such as dynamical systems and fractals, as well as older areas, such as partial differential equations and statistics. The recent advances in all these disciplines (biological/medical and mathematical/computer scientific) are best exploited by frequent communication across discipline boundaries.This book brings together work from an interdisciplinary group of quantitatively-oriented scientists to facilitate the exchange of information and ideas on (1) recent methodological advances in mathematics and computer science that have the potential for contributing to the solution of a variety of biomedical problems, (2) current applications in selected areas of biomedical research, and (3) identification of those areas in which the needs for mathematical/computer scientific treatment will be greatest in the coming years.This collection of articles should convey to the biomedical community a sense of the areas in which mathematics and computer science approaches can be usefully applied, and it is hoped that this series will expose the mathematical community to some of the most important quantitative questions in the fields of biology and medicine.

Download or read book Mathematical Modelling of Dynamic Biological Systems written by Ludwik Finkelstein and published by John Wiley & Sons. This book was released on 1985-05-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces readers to the methodology of dynamic systems analysis, using mathematical modelling techniques as an aid to understanding biological phenomena. It creates an ability to appreciate current medical and biological literature, in which mathematical models are being used with increasing frequency, and provides an introduction to the more advanced techniques of systems science. Mathematical concepts are illustrated by reference to frequent biological examples. By the use of case studies drawn from physiology, the various levels of mathematical modelling which can be adopted are presented.