Nonlocal calculus is often overlooked in the mathematics curriculum. In this paper we present an interesting new class of nonlocal 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 a model of the cell cycle developed recently by Simms, Bean and Koeber. 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. Copyright © 2013 Australian Mathematical Society.
|Original language||English (US)|
|Number of pages||10|
|Journal||The ANZIAM Journal|
|State||Published - Apr 30 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This paper is based on work supported in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). Thanks are due to Mr. Ali Ashher Zaidi, Ph.D. candidate at Massey University, for the software for the diagrams in Figures 2 and 4, and research assistant Miss Andrea Babylon for technical assistance. We also thank Dr. Kate Simms and her co-workers as well as Springer-Verlag for permission to reproduce Figure 3.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.