CALCULUS FROM THE PAST: MULTIPLE DELAY SYSTEMS ARISING IN CANCER CELL MODELLING

Handle URI:
http://hdl.handle.net/10754/597715
Title:
CALCULUS FROM THE PAST: MULTIPLE DELAY SYSTEMS ARISING IN CANCER CELL MODELLING
Authors:
WAKE, G. C.; BYRNE, H. M.
Abstract:
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.
Citation:
WAKE GC, BYRNE HM (2013) CALCULUS FROM THE PAST: MULTIPLE DELAY SYSTEMS ARISING IN CANCER CELL MODELLING. The ANZIAM Journal 54: 117–126. Available: http://dx.doi.org/10.1017/S1446181113000102.
Publisher:
Cambridge University Press (CUP)
Journal:
The ANZIAM Journal
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2013
DOI:
10.1017/S1446181113000102
Type:
Article
ISSN:
1446-1811; 1446-8735
Sponsors:
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.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorWAKE, G. C.en
dc.contributor.authorBYRNE, H. M.en
dc.date.accessioned2016-02-25T12:55:21Zen
dc.date.available2016-02-25T12:55:21Zen
dc.date.issued2013-01en
dc.identifier.citationWAKE GC, BYRNE HM (2013) CALCULUS FROM THE PAST: MULTIPLE DELAY SYSTEMS ARISING IN CANCER CELL MODELLING. The ANZIAM Journal 54: 117–126. Available: http://dx.doi.org/10.1017/S1446181113000102.en
dc.identifier.issn1446-1811en
dc.identifier.issn1446-8735en
dc.identifier.doi10.1017/S1446181113000102en
dc.identifier.urihttp://hdl.handle.net/10754/597715en
dc.description.abstractNonlocal 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.en
dc.description.sponsorshipThis 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.en
dc.publisherCambridge University Press (CUP)en
dc.subjectasymptoticsen
dc.subjectcell phasesen
dc.subjectnonlocal calculusen
dc.titleCALCULUS FROM THE PAST: MULTIPLE DELAY SYSTEMS ARISING IN CANCER CELL MODELLINGen
dc.typeArticleen
dc.identifier.journalThe ANZIAM Journalen
dc.contributor.institutionMassey University, Palmerston North, New Zealanden
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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