This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.

This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.

Introduction to Computational Cardiology provides a comprehensive, in-depth treatment of the fundamental concepts and research challenges involved in the mathematical modeling and computer simulation of dynamical processes in the heart, under normal and pathological conditions. About this textbook: - Presents descriptions of models used in both biology and medicine for discovering the mechanisms of heart function and dysfunction on several physiological scales across different species. - Provides several examples throughout the textbook and exercises at the end which facilitate understanding of basic concepts and introduces, for implementation, treated problems to parallel supercomputers. Introduction to Computational Cardiology serves as a secondary textbook or reference book for advanced-level students in computer science, electrical engineering, biomedical engineering, and cardiac electrophysiology. It is also suitable for researchers employing mathematical modeling and computer simulations of biomedical problems.

This book provides a thorough introduction to the topic of mathematical modeling of electrical activity in the heart, from molecular details of ionic channel dynamics to clinically derived patient-specific models. It discusses how cellular ionic models are formulated, introduces commonly used models and explains why there are so many different models available. The chapters cover modeling of the intracellular calcium handling that underlies cellular contraction as well as modeling molecular-level details of cardiac ion channels, and also focus on specialized topics such as cardiomyocyte energetics and signalling pathways. It is an excellent resource for experienced and specialised researchers in the field, but also biological scientists with a limited background in mathematical modelling and computational methods. Part of Biophysical Society-IOP series.

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.

This book on modelling the electrical activity of the heart is an attempt to describe continuum based modelling of cardiac electrical activity from the cell level to the body surface (the forward problem), and back again (the inverse problem). Background anatomy and physiology is covered briefly to provide a suitable context for understanding the detailed modelling that is presented herein. The questions of what is mathematical modelling and why one would want to use mathematical modelling are addressed to give some perspective to the philosophy behind our approach. Our view of mathematical modelling is broad — it is not simply about obtaining a solution to a set of mathematical equations, but includes some material on aspects such as experimental and clinical validation.

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.

Addresses the mathematical and numerical modelling of the human cardiovascular system, from patient data to clinical applications.

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.