Journal of Theoretical Medicine
Volume 2 (1999), Issue 1, Pages 55-71

The Non-Uniform Spatial Development of a Micrometastasis

Department of Applied Mathematics, The University of Leeds, Leeds LS2 9JT, UK

Received 11 May 1998; Revised 26 October 1998; Accepted 29 January 1999

Copyright © 1999 Hindawi Publishing Corporation. 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.


This paper presents a mathematical model for the growth of a cancer micrometastasis in the form of a vascular cuff. The model postulates the possibility of a local imbalance between the rate of cell proliferation and the rate of cell death through apoptosis which is taken as dependent on the concentration of an angiogenesis-inhibitor such as angiostatin. This imbalance produces non-zero cell velocities within the micrometastasis. The local cell velocity is related to an interstitial pressure gradient through a Darcy's Law type of equation, and the spatio-temporal development of the micrometastasis in an environment with a non-uniform nutrient concentration is followed by treating its outer boundary as an advancing front.