Multiscale modelling of fluid transport in vascular tumours subjected to electrophoresis anti-cancer therapies

Abstract

Electrophoresis facilitated cancer treatment has demonstrated experimental efficacy in enhancing drug delivery within vascularised tumours. However, the lack of realistic mathematical models with direct measurements in the context of eletrochemotheraphy poses a challenge. We investigate the impact of an applied electric potential on the flow of Darcian-type fluid occurring in two distinct phases: the tumour and healthy regions. We employ the asymptotic homogenisation technique, assuming that the macroscale of the tumour domain is larger than the microscale characterised by vessel heterogenities. We retain information about the microstructure by encoding information in the homogenised coefficients. We take into account both vascularisation and the microscale variations of the leading order and fine scale electric potential. The resulting effective differential problem reads as a Darcy-type system of PDEs, where the flow is driven by an effective source. The novel model can be used to predict the effect of an applied electric field on cancerous biological tissues, paving a new way of improving current electrochemotherapy protocols.