© 2014

Mathematical Modeling in Renal Physiology

  • Written by experts in academia

  • Provides the mathematical and biological basis needed to understand transport phenomena in the kidney

  • First book of this kind on the market


Table of contents

  1. Front Matter
    Pages i-viii
  2. Anita T. Layton, Aurélie Edwards
    Pages 1-5
  3. Anita T. Layton, Aurélie Edwards
    Pages 7-41
  4. Anita T. Layton, Aurélie Edwards
    Pages 43-61
  5. Anita T. Layton, Aurélie Edwards
    Pages 63-83
  6. Anita T. Layton, Aurélie Edwards
    Pages 85-106
  7. Anita T. Layton, Aurélie Edwards
    Pages 107-140
  8. Anita T. Layton, Aurélie Edwards
    Pages 141-154
  9. Anita T. Layton, Aurélie Edwards
    Pages 155-183
  10. Anita T. Layton, Aurélie Edwards
    Pages 185-218
  11. Back Matter
    Pages 219-221

About this book


This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical modeling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of physiology.

With the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. The models presented in this book describe the main homeostatic functions performed by the kidney, including blood filtration, excretion of water and salt, maintenance of electrolyte balance, and regulation of blood pressure. Each chapter includes an introduction to the basic relevant physiology, a derivation of the essential conservation equations, and then a discussion of a series of mathematical models, with increasing level of complexity.

This volume will be of interest to biological and mathematical scientists, as well as physiologists and nephrologists, who would like an introduction to mathematical techniques that can be applied to renal transport and function. The material is written for students who have had college-level calculus, but can be used in modeling courses in applied mathematics at all levels through early graduate courses.

Anita T. Layton is the Robert R. and Katherine B. Penn Associate Professor of Mathematics at Duke University.

Aurélie Edwards is director of the Laboratory of Renal Physiology at the Cordeliers Research Center in Paris, in affiliation with the French National Center for Scientific Research (CNRS).


92C30, 92B99 biology differential equations kidney mathematical modeling physiology

Authors and affiliations

  1. 1.Duke University Department of MathematicsDurhamUSA
  2. 2.Centre de Recherche des Cordeliers ERL 8228, UMRS 1138 Equipe 3ParisFrance

About the authors

Anita Layton is a faculty member in the Department of Mathematics at Duke University. In her work, she uses mathematical analysis and computational techniques to investigate aspects of kidney physiology, including the means by which the kidney controls blood flow or produces a highly concentrated urine during periods of water deprivation.

Aurélie Edwards is a director of research at the French National Center for Scientific Research, with a background in biological engineering. Her modeling work focuses on elucidating cellular signaling pathways in renal capillaries and tubules and the role of vasoactive agents in regulating oxygen balance and salt transport in the kidney.

Bibliographic information