A multiscale analysis of drug transport and response for a multiphase tumor model
Collis, Joe and Hubbard, Matthew E. and O'Dea, Reuben D. (2016) A multiscale analysis of drug transport and response for a multiphase tumor model. European Journal of Applied Mathematics . ISSN 1469-4425
Official URL: http://dx.doi.org/10.1017/S0956792516000413
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.
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