UK Nonlinear News, VAR>May 2002
2nd Edition, 2002
ISBN: 0-387-95072-9 (Hardcover)
This second edition by the two eminent authors is about 100 pages longer than the original 1992 book. Much of the new material involves MATLAB programs which are listed in the book and are also available electronically. The order of chapters is changed with the strength of the book (chapters 1 to 6 on physiology) now appearing first. There are chapters on the heart and circulation, lung, cell membrane, kidney, muscle, neural systems, population dynamics, genetics and epidemiology. Nonlinear models arise naturally in these topics but the focus of the book is on developing models rather than exploring nonlinear mathematical methods.
The authors state that they have lectured the material to students in premedicine and biology, mathematics and physics, computer science and engineering. This is a broad range made possible by the avoidance of partial differential equations until the final pages. The book aims to be a textbook and is designed for the reader to work through. Generally it shows mathematics being applied rather than explaining the mathematical tools. One notable exception is the MATLAB material where numerical schemes are discussed.
Readers need to be familiar with ordinary differential equations but otherwise the mathematical requirements are not high. The material in the book, however, is not trivial. The approach taken in the physiology chapters is to guide the reader through a model of the operation of a particular organ or system. Chapter 3, for example, studies the movement of ions into and out of a cell. The equations fairly bristle with parameters and the work would appear hard to most students. A model of cell volume regulation is followed by Hodgkin and Huxley's theory of nerve conduction. These are not sections a reader could dip into. Instead the reader has to read from the beginning of the chapter to collect the physical effects, to follow the logic and to watch the models being built up. With the aid of the MATLAB programs the reader is then encouraged to explore predictions from the model.
The way the authors build up their models is both a strength and a weakness of the book. It is a strength because students work with relatively detailed models. Each chapter has its own set of physical effects and physiological mechanisms. The authors do a good job of introducing these quickly and showing the reader `how to think about the material'. However a lot of explanation is given and the authors have to also stay focused on the progress of their model. The result is that the authors never have the chance to stray very far from the model under discussion. The tightly-focused nature of the book is also evident in the lack of photographs and the small number of rudimentary biological sketches.
There are interesting differences between this book (HP) and Brauer and Castillo-Chavez (2001) (BCC) and also Keener and Sneyd (1998) (KS). BCC is just on population and epidemiological modelling and it covers that area in much more detail than HP could. At over 750 pages KS can cover more physiological systems than HP but it has no material on populations, genetics or epidemiology.
BCC is liberally sprinkled with interesting minor points and many references. These allow a reader to follow up different lines of interest. It is a shame that HP give only a few major references for each chapter. KS is somewhere between the two in this regard. The student problems in HP are often long and project-like. BCC provides more and shorter problems, with several after each chapter section and answers available to the odd-numbered problems. The problems in KS are also short but no answers are provided. Illustrations are more common in KS and there is more discussion. However the mathematics in KS can jump like a mountain goat (and be equally as hard to follow). HP are careful to allow the reader to follow each step.
This (HP) is a book designed for the reader to work through. An accompanying lecturer could greatly assist a reader over difficult passages and provide the missing biological illustrations, but an advanced solo reader could also gain a valuable introduction to mathematical physiology from it. The inclusion of MATLAB material for exploration of the models increases its appeal. In summary this reviewer recommends the book as a course textbook and to readers interested in understanding physiological models. BCC provides a better introduction to population and epidemiological modelling but HP does include useful teaching material in those areas. KS covers more physiological systems, is better illustrated than HP and appears to allow the reader to dip into sections. However it may be a more difficult book than HP for a mathematically less-able reader to work through.
Brauer, F. and C. Castillo-Chavez (2001). ``Mathematical Models in Population
Biology and Epidemiology'', Springer-Verlag.
Keener, J. and J. Sneyd (1998). ``Mathematical Physiology'', Springer-Verlag.
UK Nonlinear News thanks Springer-Verlag for providing a review copy of this book.
A listing of books reviewed in UK Nonlinear News is available.