Differential Equations For Studies In Computational Electrophysiology
Differential Equations For Studies In Computational Electrophysiology Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Differential Equations For Studies In Computational Electrophysiology book. This book definitely worth reading, it is an incredibly well-written.
Differential Equations for Studies in Computational Electrophysiology by Karoline Horgmo Jæger,Aslak Tveito Pdf
This open access text aims at giving you the simplest possible introduction to differential equations that are used in models of electrophysiology. It covers models at several spatial and temporal scales with associated numerical methods. The text demonstrates that a very limited number of fundamental techniques can be used to define numerical methods for equations ranging from ridiculously simple to extremely complex systems of partial differential equations. Every method is implemented in Matlab and the codes are freely available online. By using these codes, the reader becomes familiar with classical models of electrophysiology, like the cable equation, the monodomain model, and the bidomain model. But modern models that have just started to gain attention in the field of computational electrophysiology are also presented. If you just want to read one book, it should probably not be this one, but if you want a simple introduction to a complex field, it is worth considering the present text.
Computational Electrophysiology by Shinji Doi,Junko Inoue,Zhenxing Pan,Kunichika Tsumoto Pdf
Biological systems inherently possess much ambiguity or uncertainty. Computational electrophysiology is the one area, from among the vast and rapidly growing discipline of computational and systems biology, in which computational or mathematical models have succeeded. This textbook provides a practical and quick guide to both computational electrophysiology and numerical bifurcation analysis. Bifurcation analysis is a very powerful tool for the analysis of such highly nonlinear biological systems. Bifurcation theory provides a way to analyze the effect of a parameter change on a system and to detect a critical parameter value when the qualitative nature of the system changes. Included in this work are many examples of numerical computations of bifurcation analysis of various models as well as mathematical models with different abstraction levels from neuroscience and electrophysiology. This volume will benefit graduate and undergraduate students as well as researchers in diverse fields of science.
Author : Institute of Mathematics and Its Applications Publisher : Oxford University Press, USA Page : 488 pages File Size : 45,6 Mb Release : 1992 Category : Differential equations ISBN : UCAL:B4405916
Computational Ordinary Differential Equations by Institute of Mathematics and Its Applications Pdf
This collection of refereed papers from an international conference provides a comprehensive coverage of recent research on the numerical solution of ordinary differential equations. There are sections on initial value problems, boundary value problems, differential algebraic equations,applications to the solution of partial differential equations, parallel solution methods, and methods of conservation and global error calculation. Within each section the papers have been ordered so that the reader will perceive a gradual movement from the theoretical to the practical. Newchallenges such as the solution of differential-algebraic equations and the impact of parallelism are covered alongside currently topical aspects of older problems such as the interpolation of Runge-Kutta methods and the development of formulas which conserve energy whilst preserving accuracy. Fornumerical analysts in academic and industrial research this book provides detailed coverage of this important subject.
This book is devoted to computer-based modeling in cardiology, by taking an educational point of view, and by summarizing knowledge from several, commonly considered delimited areas of cardiac research in a consistent way. First, the foundations and numerical techniques from mathematics are provided, with a particular focus on the finite element and finite differences methods. Then, the theory of electric fields and continuum mechanics is introduced with respect to numerical calculations in anisotropic biological media. In addition to the presentation of digital image processing techniques, the following chapters deal with particular aspects of cardiac modeling: cardiac anatomy, cardiac electro physiology, cardiac mechanics, modeling of cardiac electro mechanics. This book was written for researchers in modeling and cardiology, for clinical cardiologists, and for advanced students.
Computational Biology of the Heart by Alexander V. Panfilov,Arun V. Holden Pdf
Modelling the genesis and propagation of electrical activity in the heart in quantitative terms is one of the most important recent applications of mathematical modelling in biology. The main research direction, and the most important for biological and medical applications, is the development of realistic models of electrical activity in cardiac tissue and the whole mammalian heart. Recent progress in nonlinear dynamics, advances in computer technology and experiments on cardiac tissue have made feasible the construction of such models. Computational Biology of the Heart is the first book to provide a comprehensive survey of recent research together with a systematic overview of the subject. The contributions, all written by experts in the different areas of the subject, cover all main aspects of whole heart modelling: from excitation in single cells, to two and three dimensional models of cardiac tissue and the whole heart. Various computational models and techniques are described and then applied to reconstruct and visualise modelled activity in both normal and pathological heart tissues. The models are nonlinear and use techniques of ordinary differential equations, partial differential equations and eikonal equations. The book also provides a review of modelling cardiac contraction, mapping electrical activity from electrocardiograms, and recent experimental observations of wave propagation in the whole heart. Graduate students and researchers in such areas as applied mathematical biology, clinical physiology and cardiology will find this book to be an invaluable resource for their work.
Differential Equation Analysis in Biomedical Science and Engineering by William E. Schiesser Pdf
Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-world ODE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear ordinary differential equations. The author’s primary focus is on models expressed as systems of ODEs, which generally result by neglecting spatial effects so that the ODE dependent variables are uniform in space. Therefore, time is the independent variable in most applications of ODE systems. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for ODEs Models as systems of ODEs with explanations of the associated chemistry, physics, biology, and physiology as well as the algebraic equations used to calculate intermediate variables Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general ODE computation through various biomolecular science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Computational Science and Its Applications – ICCSA 2023 Workshops by Osvaldo Gervasi,Beniamino Murgante,Ana Maria A. C. Rocha,Chiara Garau,Francesco Scorza,Yeliz Karaca,Carmelo M. Torre Pdf
This nine-volume set LNCS 14104 – 14112 constitutes the refereed workshop proceedings of the 23rd International Conference on Computational Science and Its Applications, ICCSA 2023, held at Athens, Greece, during July 3–6, 2023. The 350 full papers and 29 short papers and 2 PHD showcase papers included in this volume were carefully reviewed and selected from a total of 876 submissions. These nine-volumes includes the proceedings of the following workshops: Advances in Artificial Intelligence Learning Technologies: Blended Learning, STEM, Computational Thinking and Coding (AAILT 2023); Advanced Processes of Mathematics and Computing Models in Complex Computational Systems (ACMC 2023); Artificial Intelligence supported Medical data examination (AIM 2023); Advanced and Innovative web Apps (AIWA 2023); Assessing Urban Sustainability (ASUS 2023); Advanced Data Science Techniques with applications in Industry and Environmental Sustainability (ATELIERS 2023); Advances in Web Based Learning (AWBL 2023); Blockchain and Distributed Ledgers: Technologies and Applications (BDLTA 2023); Bio and Neuro inspired Computing and Applications (BIONCA 2023); Choices and Actions for Human Scale Cities: Decision Support Systems (CAHSC-DSS 2023); and Computational and Applied Mathematics (CAM 2023).
Differential Equation Analysis in Biomedical Science and Engineering by William E. Schiesser Pdf
Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general PDE computation through various biomedical science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
