© 1998

Mathematical Physiology


Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 8)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Cellular Physiology

    1. Front Matter
      Pages 1-1
    2. Pages 33-73
    3. Pages 74-115
    4. Pages 116-159
    5. Pages 160-187
    6. Pages 312-332
    7. Pages 333-354
  3. Systems Physiology

    1. Front Matter
      Pages 377-377
    2. Pages 379-433
    3. Pages 434-479
    4. Pages 480-515
    5. Pages 516-541

About this book



Mathematical Physiology provides an introduction into physiology using the tools and perspectives of mathematical modeling and analysis. It describes ways in which mathematical theory may be used to give insights into physiological questions and how physiological questions can in turn lead to new mathematical problems.

The book is divided into two parts, the first dealing with the fundamental principles of cell physiology, and the second with the physiology of systems. In the first part, after an introduction to basic biochemistry and enzyme reactions, the authors discuss volume control, the membrane potential, ionic flow through channels, excitability, calcium dynamics, and electrical bursting. This first part concludes with spatial aspects such as a synaptic transmission, gap junctions, the linear cable equation, nonlinear wave propagation in neurons, and calcium waves.

In the second part, the human body is studied piece by piece, beginning with an introduction to electrocardiology, followed by the physiology of the circulatory system, blood, muscle, hormones, and kidneys. Finally, the authors examine the digestive system and the visual system, ending with the inner ear.

This book will be of interest to researchers, to graduate students and advanced undergraduate students in applied mathematics who wish to learn how to build and analyze mathematical models and to become familiar with new areas of application, as well as to physiologists interested in learning about theoretical approaches to their work.

The inclusion of numerous exercises and models could be used to add further interest and challenge to traditional courses taught by applied mathematicians, bioengineers, and physiologists.


Mathematical Physiology biochemistry cell dynamics enzyme mathematical modeling mathematics physiology respiration retina

Authors and affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Institute of Information and Mathematic SciencesMassey University, Albany CampusAucklandNew Zealand

Bibliographic information

  • Book Title Mathematical Physiology
  • Authors James Keener
    James Sneyd
  • Series Title Interdisciplinary Applied Mathematics
  • DOI
  • Copyright Information Springer-Verlag, New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98381-3
  • Softcover ISBN 978-1-4757-7176-3
  • eBook ISBN 978-0-387-22706-1
  • Series ISSN 0939-6047
  • Edition Number 1
  • Number of Pages XX, 767
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical and Computational Biology
    Human Physiology
  • Buy this book on publisher's site


From the reviews:

"Probably the best book ever written on the subject of mathematical physiology … It contains numerous exercises, enough to keep even the most diligent student busy, and a comprehensive list of approximately 600 references … highly recommended to anybody interested in mathematical or theoretical physiology." Mathematical Reviews

"In addition to being good reading, excellent pedagogy, and appealing science, the exposition is lucid and clear, and there are many good problem sets to choose from … Highly recommended." Journal of the Society of Mathematical Biology