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Modelling the formation of necrotic regions in avascular tumours

Modelling the formation of necrotic regions in avascular tumours
Modelling the formation of necrotic regions in avascular tumours
The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre.

A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration.

However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.
apoptosis, necrosis, multicellular spheroids
0025-5564
34-55
Tindall, M.J.
c9bcfff9-902d-43f9-8d16-4ab49e73b789
Please, C.P.
118dffe7-4b38-4787-a972-9feec535839e
Peddie, M.J.
ec2e9e67-2a5a-4fce-a763-8a4fa277736d
Tindall, M.J.
c9bcfff9-902d-43f9-8d16-4ab49e73b789
Please, C.P.
118dffe7-4b38-4787-a972-9feec535839e
Peddie, M.J.
ec2e9e67-2a5a-4fce-a763-8a4fa277736d

Tindall, M.J., Please, C.P. and Peddie, M.J. (2008) Modelling the formation of necrotic regions in avascular tumours. Mathematical Biosciences, 211 (1), 34-55. (doi:10.1016/j.mbs.2007.09.002). (PMID:18082225)

Record type: Article

Abstract

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre.

A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration.

However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

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More information

e-pub ahead of print date: 5 October 2007
Published date: January 2008
Keywords: apoptosis, necrosis, multicellular spheroids

Identifiers

Local EPrints ID: 146627
URI: http://eprints.soton.ac.uk/id/eprint/146627
ISSN: 0025-5564
PURE UUID: 3cd5133c-d9c2-4da9-beba-20578fa27ac2

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Date deposited: 28 Apr 2010 07:57
Last modified: 08 Jan 2022 02:28

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Contributors

Author: M.J. Tindall
Author: C.P. Please
Author: M.J. Peddie

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