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Mathematically modeling the electrical activity of the heart. From cell to body surface and back again. (English) Zbl 1120.92015
Hackensack, NJ: World Scientific (ISBN 981-256-373-3/hbk). xvi, 425 p. (2005).
This book describes continuum based modelling of cardiac electrical activity from the cellular level to the body surface (the forward problem) and back again (the inverse problem). It does not exhaustively review these problems, but, rather, focuses on the “Auckland Heart Model” created by researchers in New Zealand. For the first time, the entire scope of continuum-based modelling in electrocardiology has been brought together in one book. Incorporating the inverse problem within this context appears to be unique. The level of presentation is appropriate for graduate students in applied mathematics, computer science, or bioengineering.
An introductory chapter reviews basic information on the anatomy and physiology of the heart and presents the authors’ rationale for mathematical modelling. The second chapter discusses the concept of geometric modelling using piecewise parametric polynomials to fit experimentally obtained data. The bulk of the book presents models of electrical processes within the heart, starting with an overview of cellular models and then moving on to continuum level models of tissue, the whole heart, and the heart within the body. The authors go on to examine the electrical activity of the heart as viewed from the body surface and seek to answer, through the use of models, the question of what body surface information can tell about the electrical activity of the heart. Finally, they look outward from cardiac electrical modelling to provide models of other cardiac processes.

92C30 Physiology (general)
92C05 Biophysics
92C50 Medical applications (general)
92-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology
93B05 Controllability
93A30 Mathematical modelling of systems (MSC2010)