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Book Review
Anne Beuter, Leon Glass, Michael C. Mackey and Michèle S. Titcombe (Editors):
NONLINEAR DYNAMICS IN PHYSIOLOGY AND MEDICINE, Interdisciplinary Applied Mathematics, vol. 25
Springer-Verlag, New York, 2003, 434 pp., 162 Illustrations, Index, ISBN 0-387-00449-1
The book «Nonlinear Dynamics in Physiology and Medicine» is a multi-author effort. Besides the four authors who also
served as editors, eight more contributors have participated. They, coming from different Canadian universities and one U.S.A.
university, worked under the umbrella of The Centre for Nonlinear Dynamics in Physiology and Medicine, created in 1988 by the
University Senate of McGill University, Canada.
The book contains ten chapters, their subjects being as follows: Theoretical approaches in physiology; Introduction to dynamics
in nonlinear difference and differential equations; Bifurcations involving fixed points and limit cycles in biological systems;
Dynamics of excitable cells; Resetting and entraining biological rhythms; Effects of noise on nonlinear dynamics; Reentry in
excitable media; Cell replication and control; Pupil light reflex: Delays and oscillations; Data analysis and mathematical
modeling of human tremor. The book closes with three appendices: An introduction to XPP; An introduction to Matlab and
Time series analysis.
Taken together, these chapters reveal the focus of this book as an attempt to exercise the subject of nonlinear modelling of
physiological systems as reflected in various specific applications. The work displays a traditional mathematical biology approach,
as has been established during the last half of the 20th century, by systems analysis taking the role of quantitatively describing
physiological processes and systems. Being at the core of biomedical engineering from the field's beginning, systems physiology
(i.e. physiology studied by using vehicles of mathematical systems theory and quantitative modelling) has passed an «explorative»
phase and has evolved into an established approach. Various regulatory, periodic, stable-homeostatic, and transient phenomena in
living systems are amenable to being described and quantitatively understood precisely by employing the mathematical apparatus
of systems analysis. This state of affairs is seen through the virtue of this book in which the co-authors have successfully and
authoritatively employed mathematical apparatus to model, predict or analyse specific physiological/medical problems such as:
cardiac tissue oscillatory behavior, tremor in neuromuscular systems, the pupil light reflex, replication of blood cells,
reentry in excitable media. Either analytical or computational mathematical techniques were used in particular examples, for
which purpose serve the Appendices.
The first four previously mentioned chapters explain mathematical basis, and the remaining six chapters illustrate particular
applications. Each chapter is well grounded in the tradition of a particular theme, so that the reader may follow the traces
of development of a particular area. The book's references list is thorough and valid, not omitting such cybernetics and
electrophysiology classical authors like; Wiener, Rosenblueth, Bernstein, Stark, Nernst, Hodgkin, Huxley, McCulloch, Pitts,
Hill, to name the most prominent.
This book is aimed at all scientists studying physiological systems in general, either at the global, organ or tissue level.
It fits into curricula usually offered by bioengineering departments and – happily more and more - also medical schools. And,
assuming a broader standpoint - and by allowing us to quote the authors themselves - it is directed towards an audience of
physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathematicians, and others interested in
finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical perspective.
The necessary prerequisite for its use are appropriate mathematical skills, primarily in differential and integral calculus
and in ordinary differential equations, and besides a sufficient knowledge of biological systems, the knowledge supposedly
gained through a typical under-graduate biomedical engineering curriculum. Chapters may be studied also one by one, which
gives the possibility to use the book in diverse fields such as for instance biomechanics, cardiac electrophysiology,
neurology, etc.
«Nonlinear Dynamics in Physiology and Medicine» is a book of high standards and is to be recommended. It is a
title worth possessing as a collection of valuable reference material, and also suitable as a textbook in advanced
under-graduate and graduate courses treating systems physiology.
Prof. dr. sc. Vladimir Medved
Email: vmedved@ffk.hr
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