A poroelasticity model for interstitial fluid flow and matrix deformation in a non-homogeneous solid tumor

Abstract

This paper describes a small-strain poroelasticity model to examine the interstitial fluid pressure and matrix deformation in a non-homogeneous solid tumor consisting of an inner core with a reduced specific microvascular area encapsulated in an outer tissue shell with a regular specific microvascular area. A singular perturbation technique is employed to capture the transitional behavior at the interface between the inner core and outer shell under a cyclic microvascular pressure. The perturbation solution reveals the existence of two boundary layers: one at the interface between the inner core and outer shell, and the other at the tumor surface. The amplitude of the tumor interstitial fluid (TIF) pressure is at a lower constant level in the inner core and increases rapidly in the boundary layer at the interface between the inner core and outer shell to the pressure value of the corresponding homogeneous tumor with the outer shell properties. The radial strain undergoes dramatic changes in the boundary layers, and reaches the peak near the interface between the inner core and outer shell. The behavior of the effective stresses remains similar to that of the TIF pressure.