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 [1] 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 poroe-lastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double poroelastic model [1] is then solved at the macroscale in the context of vascular tumours, for different values of vesssels’ 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 tumors to allow for better drug delivery into the lesions.

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

“…Various articles study the inflation of cylindrical structures, in which the material is subjected to residual stresses. This mathematical framework finds some applications in various engineering problems (for instance [4], [82], [83], [129], and [136]). Moreover, such residual stresses may occur, for example, in engineering composites as the chemical shrinkage of one constituent during the product process, or due to the various thermal expansion coefficients of the different constituents [31], [88], [95], and [174].…”