Computational and Mathematical Methods in Medicine

Computational and Mathematical Methods in Medicine / 1999 / Article

Open Access

Volume 2 |Article ID 280176 | 17 pages | https://doi.org/10.1080/17486709909490788

The Non-Uniform Spatial Development of a Micrometastasis

Received11 May 1998
Revised26 Oct 1998
Accepted29 Jan 1999

Abstract

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.

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.


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