The Mathematical Institute, University of Oxford, Eprints Archive

Calculus from the past: multiple delay systems arising in cancer cell modelling

Wake, G. C. and Byrne, H. M. (2012) Calculus from the past: multiple delay systems arising in cancer cell modelling. ANZIAM Journal . (Submitted)

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Abstract

Non-local calculus is often overlooked in the mathematics curriculum. In this paper we present an interesting new class of non-local problems that arise from modelling the growth and division of cells, especially cancer cells, as they progress through the cell cycle. The cellular biomass is assumed to be unstructured in size or position, and its evolution governed by a time-dependent system of ordinary differential equations with multiple time delays. The system is linear and taken to be autonomous. As a result, it is possible to reduce its solution to that of a nonlinear matrix eigenvalue problem. This method is illustrated by considering case studies, including the model of the cell cycle developed in Simms K, Bean N, & Koeber A. [10]. The paper concludes by explaining how asymptotic expressions for the distribution of cells across the compartments can be determined and used to assess the impact of different chemotherapeutic agents.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1655
Deposited By: Peter Hudston
Deposited On:02 Feb 2013 11:07
Last Modified:29 May 2015 19:20

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