Modelling acidosis and the cell cycle in multicellular tumour spheroids

Tindall, Marcus J. and Dyson, Louise and Smallbone, Kieran and Maini, Philip K. (2009) Modelling acidosis and the cell cycle in multicellular tumour spheroids. [MIMS Preprint]

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Abstract

A partial differential equation model is developed to understand the effect that nutrient and acidosis have on the distribution of proliferating and quiescent cells within a multicellular tumour spheroid. The rates of cell quiescence and necrosis are assumed to depend upon the local nutrient and acid concentrations. Quiescent cells are assumed to consume less nutrient and produce less acid than proliferating cells and a description of anaerobic metabolism by the cells is included. Parameterised with data from the literature, our model predicts that the tumour size is reduced in the presence of acid. Analysis of the differences in nutrient consumption and acid production by quiescent and proliferating cells shows low nutrient levels do not necessarily lead to increased acid concentration via anaerobic metabolism. Instead it is the balance between proliferating and quiescent cells within the tumour which is important; decreased nutrient levels lead to more quiescent cells, which produce less acid than proliferating cells. We examine this effect via a sensitivity analysis which also includes a quantification of the effect that nutrient and acid concentrations have on the rates of cell quiescence and necrosis.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 92 Biology and other natural sciences
Depositing User: Dr Kieran Smallbone
Date Deposited: 14 Dec 2009
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1367

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