Multiscale analysis of electrically stimulated vascularised tumours

Electroporation-based therapies such as electrochemotherapy (ECT) hold a great promise for improving cancer treatments. While highly effective for superficial tumours, its application for deep-seated malignancies is challenged by complex microstructural properties, and current models often lack a multiscale theoretical framework to capture those phenomena. Here we develop and solve a novel system of coupled partial differential equations of Darcy-Laplace type obtained by applying the asymptotic homogenisation technique. We study the tumour response stimulated by an electric field. We derive effective macroscale equations for the pressure, velocity, and electric potential, whilst incorporating both hydraulic and electric microscale tissue heterogeneities. Our coupled multiscale approach bridges the gap between the tumour microstructure and macroscale dynamics, offering a more comprehensive understanding of how tumour size, morphology, and hydraulic-electrical interactions influence interstitial flow. We present a parametric analysis of the hydraulic conductivity tensor and macroscale numerical simulation results for pressure and velocity fields, highlighting the role of the electric field in modulating fluid flow. Our findings provide meaningful insights towards advancing ECT protocols.