An interdisciplinary applied mathematics text for engineers, and perhaps physicists
For those readers who have perused my review of the previous volume on cellular physiology, it is apparent that these interdisciplinary texts are meant to offer a little biology to the engineers and mathematicians and a lot of math to any life scientist bold enough to turn the pages. The stated purpose of these texts in interdisciplinary applied mathematics is to “…meet the current and future needs for the interaction between various science and technology areas on one hand and mathematics on the other.” The editors further state that they point to innovative new uses of mathematics in new areas of applications and “encouraging other scientific disciplines to engage in a dialog with mathematicians…”.
Note that the mathematicians can work on the problems but the other scientific disciplines (read life scientists) can talk to the mathematicians. Here is where my approach to the first volume fell short. In attempting to recommend the book to life scientists, I was aiming at the wrong target! It is far more apparent in this volume that engineers, and perhaps physicists, would be a more appropriate audience.
Whereas introductory mathematical biology texts for biologists tend to use calculus sparingly, preferring to utilize simple algebra whenever possible, these texts think nothing of starting with second year calculus. It was rather amusing (or shocking, depending upon your point of view) to see Ohms law presented as, not the familiar E=IR, but rather in terms of the del operator.
This volume, a continuation of the previous explorations in physiology, concentrates on the following areas:
• circulatory system
• endocrine system
• renal function
• gastrointestinal system
• retina and vision
• inner ear
The above selections may indicate the author’s areas of expertise or merely the ‘ignorance and exhaustion’ that they mention in the preface. It is a shame that highly important areas such as the immune and nervous systems are excluded. Also, in the light of the very important contributions that statistics makes to modern biology, its total omission leaves a gaping hole in the possible analysis of many phenomena. The contributions of this field of mathematics to measurement error alone would be cause enough for inclusion.
As in the first volume, the authors do an excellent job of backfilling biological topics for the mathematicians and physical scientists. The explanations are far more than a bland recitation of facts, containing valuable insights into the functioning of these systems while injecting interesting sidebars that stimulate further thought. Diagrams, graphics and tables supplement these explorations where appropriate. The graphics are very well constructed to convey maximal information. For example, arterial pressure is displayed against urine output, renal blood flow and glomerular filtration rate in such a way as to immediately convey the relationships and asymptotic effects.
As in the previous volume, there are appendices, with some chapters explaining how the biology may be driving the mathematics, but never in sufficient detail so as to allow the reader to quickly verify the results. There is very little in the way of math backgrounders, but an extensive bibliography and a tolerably detailed index at the end. Again, there are exercises at the end of each chapter, but neither solutions nor even answers are given.
It is surprising, however, that in this day and age of huge databases and computational software, there is no use and little mention of either. It appears that the authors would rather ground the physical scientists in the subject matter, and encourage theoretic calculation as well as predictive modeling on a small scale than actually solve any of the more complex convolutions that greet the life scientists on a daily basis. As a text for these aforementioned physical scientists and mathematicians, the book has enough to recommend a second look.
Mathematical Physiology II: Systems Physiology (2nd Ed.) by James Keener and James Sneyd. Springer Science + Business Media LLC. New York (2009). xxv + 503 pp. $79.95
John Wass is a statistician based in Chicago, IL. He may be reached at editor@ScientificComputing.com.