The impact of vascular volume fraction and compressibility of the interstitial matrix on vascularised poroelastic tissues

Abstract

In this work we address the role of the microstructural properties of a vascularised poroelastic material, characterised by the coupling between a poroelastic matrix and a viscous fluid vessels network, on its overall response in terms of pressures, velocities and stress maps. We embrace the recently developed model (Penta and Merodio in Meccanica 52(14):3321–3343, 2017) as a theoretical starting point and present the results obtained by solving the full interplay between the microscale, represented by the intervessels’ distance, and the macroscale, representing the size of the overall tissue. We encode the influence of the vessels’ density and the poroelastic matrix compressibility in the poroelastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double-poroelastic model (Penta and Merodio 2017) is then solved at the macroscale in the context of vascular tumours, for different values of vessels’ walls permeability. The results clearly indicate that improving the compressibility of the matrix and decreasing the vessels’ density enhances the transvascular pressure difference and hence transport of fluid and drug within a tumour mass after a transient time. Our results suggest to combine vessel and interstitial normalization in tumours to allow for better drug delivery into the lesions.

Multiscale homogenization for dual porosity time-dependent Darcy–Brinkman/Darcy coupling and its application to the lymph node

“…In this work, we have assumed a rigid porous matrix to keep the model as simple as possible and due to the lack of biological data regarding this problem; a possible extension of this model is to take into account a deformable matrix that interacts with the lymph flow inside the node, for example by considering the modelling framework developed in [ 91 , 92 ].…”