Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 843765, 9 pages
Research Article

Mathematical Model of the Effect of Interstitial Fluid Pressure on Angiogenic Behavior in Solid Tumors

1Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1
2Center for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada M5T 3J1

Received 6 April 2011; Accepted 29 June 2011

Academic Editor: Michele Migliore

Copyright © 2011 Colin Phipps and Mohammad Kohandel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a mathematical model for the concentrations of proangiogenic and antiangiogenic growth factors, and their resulting balance/imbalance, in host and tumor tissue. In addition to production, diffusion, and degradation of these angiogenic growth factors (AGFs), we include interstitial convection to study the locally destabilizing effects of interstitial fluid pressure (IFP) on the activity of these factors. The molecular sizes of representative AGFs and the outward flow of interstitial fluid in tumors suggest that convection is a significant mode of transport for these molecules. The results of our modeling approach suggest that changes in the physiological parameters that determine interstitial fluid pressure have as profound an impact on tumor angiogenesis as those parameters controlling production, diffusion, and degradation of AGFs. This model has predictive potential for determining the angiogenic behavior of solid tumors and the effects of cytotoxic and antiangiogenic therapies on tumor angiogenesis.