Journal of Theoretical Medicine
Volume 1 (1998), Issue 3, Pages 223-235

Necrosis and Apoptosis: Distinct Cell Loss Mechanisms in a Mathematical Model of Avascular Tumour Growth

1Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, UK
2Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, UK

Received 11 March 1997; Accepted 9 June 1997

Copyright © 1998 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.


During the initial avascular phase of solid tumour growth, it is the balance between cell proliferation and cell loss that determines whether the tumour colony expands or regresses. Experimentalists have identified two distinct mechanisms that contribute to cell loss. These are apoptosis and nicrosis. Cell loss due to apoptosis may be riferred to as programmed-cell-death, occurring,for example, when a cell exceeds its natural lifespan. In contrast, cell loss due to necrosis is induced by changes in the cells microenvironment,occurring, for example, in nutrient-depleted regions of the tumour.

In this paper we present a mathematical model that describes the growth of an avascular tumour which compuises a centual core of necrotic cells, surrounded by an outer annulus of puoliferating cells. The model distinguishes between apoptisis and necrosis. Using a combination of numerical and analytical techniques we present results which suggest how the relative importance of apoptisis and necrosis changes as the tumour develops. The implications of these results are discussed buiefly.