The role of the lymphatic micro-vasculature in malignant tissue fluid and drug transport.

Abstract

The contribution of lymphatic capillaries in the fluid and drug transport throughout vascularised malignant tissue is qualitatively and quantitatively discussed. Our starting point is the derivation of differential equations for coupled fluid and drug transport across three physical domains present in vascularised tissue: the interstitium, capillary vessels and lymphatic vessels. We begin from mass and momentum balance equations in each physical domain, which are geometrically characterised by the inter-capillary distance (microscale). The Kedem-Katchalsky equations are used to account for blood and drug exchange across the vessel walls. Employing asymptotic homogenisation, we can formulate a multiscale model which allows for a complex microstructure, under the regular assumptions such as local periodicity, accounting for spatial heterogeneity of the angiogenic nature of the capillary and lymphatic networks. At the macroscale, the fluid dynamics are governed by a triple-compartmental porous medium problem characterised by Darcy's law; whereas drug dynamics are characterised by a triple-compartmental advection-diffusion-reaction model. The microscopic properties of the malignant tissue are effectively encoded into a series of macroscopic coefficients, which enable the analysis of geometric changes at the microscale from a macroscopic perspective. Analysis of the models' isotropic case reveals the existence of a favourable permeability for lymphatic vessels, allowing for optimised fluid and drug transport. The purpose of this work is to create a robust theoretical platform that can account for the role of the networks of vessels that are to be considered to improve anti-cancer strategies.