Journal of Theoretical Medicine
Volume 1 (1997), Issue 2, Pages 153-168

A Mathematical Model of a Micrometastasis

Department of Applied Mathematical Studies, The University of Leeds, Leeds LS2 9JT, UK

Received 10 December 1996

Copyright © 1997 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.


Experimental evidence indicates that tumour metastases can exist for long periods in a dormant state, with cell proliferation balancing cell death. However, this balance can be upset, by removing the primary tumour for instance, which causes the metastasis to grow, or by adminstering a substances inhabiting angiogenesis which causes the metastasis toi regress. A mathematical model is presented for the growth of a tumour metastasis, which by postulating the possibility of a local imbalance between cell proliferation and cell death though apoptosis, is able to explain some of these observations. A prediction of the model is that at any position within the metastasis there will be a radial movement of cells, even in the document state.