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.

The uptake kinetics of a 14C-labelled trypanocidal compound isometamidium chloride (SamorinR, RMB Animal Health Ltd, UK) was measured in drug-resistant and drug-sensitive Trypanosoma congolense. It was established that drug uptake was significantly more rapid and quantitatively greater in drug-sensitive parasites. There was clear evidence that drug uptake in both the resistant and sensitive trypanosomes was by a specific, receptor-mediated process. This specific drug transport was energy-dependent, being sensitive to metabolic inhibition with SHAM/glycerol. Significant differences in drug transport were observed which could be correlated with resistance to isometamidium. The optimal pH for drug accumulation was lowered in the resistant trypanosomes; this finding, along with an observed change in specificity for the related compound homidium bromide, suggested that the specific receptor for isometamidium is altered in the resistant trypanosomes, possibly resulting in a reduction in drug uptake. In addition to these alterations in drug uptake, efflux of isometamidium also appears to occur in the resistant trypanosomes. Both a reduction in incubation temperature and metabolic inhibition increased the level of trypanosome-associated isometamidium in the resistant parasites. This was in contrast to observations using drug-sensitive parasites. Furthermore, the addition of calcium flux-modulating agents to the incubation medium also resulted in an increase in accumulation by the resistant parasites.