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A multi-scale analysis of drug transport and response for a multi-phase tumour model†

Published online by Cambridge University Press:  05 October 2016

J. COLLIS ,
M. E. HUBBARD  and
R. D. O'DEA
J. COLLIS
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK email: Joe.Collis@nottingham.ac.uk, Matthew.Hubbard@nottingham.ac.uk, Reuben.O'Dea@nottingham.ac.uk
M. E. HUBBARD
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK email: Joe.Collis@nottingham.ac.uk, Matthew.Hubbard@nottingham.ac.uk, Reuben.O'Dea@nottingham.ac.uk
R. D. O'DEA
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK email: Joe.Collis@nottingham.ac.uk, Matthew.Hubbard@nottingham.ac.uk, Reuben.O'Dea@nottingham.ac.uk
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Abstract

In this article, we consider the spatial homogenisation of a multi-phase model for avascular tumour growth and response to chemotherapeutic treatment. The key contribution of this work is the derivation of a system of homogenised partial differential equations describing macroscopic tumour growth, coupled to transport of drug and nutrient, that explicitly incorporates details of the structure and dynamics of the tumour at the microscale. In order to derive these equations, we employ an asymptotic homogenisation of a microscopic description under the assumption of strong interphase drag, periodic microstructure, and strong separation of scales. The resulting macroscale model comprises a Darcy flow coupled to a system of reaction–advection partial differential equations. The coupled growth, response, and transport dynamics on the tissue scale are investigated via numerical experiments for simple academic test cases of microstructural information and tissue geometry, in which we observe drug- and nutrient-regulated growth and response consistent with the anticipated dynamics of the macroscale system.

Keywords

Cancer modellingmulti-scale homogenisationdrug transportporous media

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 3 , June 2017 , pp. 499 - 534
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

†

The first and second authors wish to acknowledge the support of EPSRC grant number EP/K039342/1.

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