A multiscale analysis of drug transport and response for a multiphase tumor model

Collis, Joe; Hubbard, Matthew E.; O'Dea, Reuben D.

Abstract

In this article we consider the spatial homogenization of a multi- phase model for avascular tumour growth and response to chemother- apeutic treatment. The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscopic tumour growth, coupled to transport of drug and nutri- ent, 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 homogenization of a microscopic description under the assumption of strong interphase drag, periodic microstructure, and strong separation of scales. The resulting macroscale model com- prises 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 experi- ments 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.

Citation

Collis, J., Hubbard, M. E., & O'Dea, R. D. (in press). A multiscale analysis of drug transport and response for a multiphase tumor model. European Journal of Applied Mathematics, https://doi.org/10.1017/S0956792516000413

• Journal Article Type: Article
• Acceptance Date: Sep 5, 2016
• Online Publication Date: Oct 5, 2016
• Deposit Date: Oct 6, 2016
• Publicly Available Date: Oct 6, 2016
• Journal: European Journal of Applied Mathematics
• Print ISSN: 0956-7925
• Electronic ISSN: 1469-4425
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1017/S0956792516000413
• Keywords: Cancer modelling, Multiscale homogenization, Drug transport, Porous media
• Public URL: https://nottingham-repository.worktribe.com/output/824578
• Publisher URL: http://dx.doi.org/10.1017/S0956792516000413
• Additional Information: © Cambridge University Press 2016