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.

The effects of gravity and compression on interstitial fluid transport in the lower limb

“…The vascular absorption time scale corresponding to L v is and the interstitial percolation time scale is where L is the distance over which fluid must transport. These parameters were first applied to solid tumors 27 – 33 and injection sites 34 – 39 where L was on the order of 1 cm. Whereas, here the distance that would be needed to force fluid from beneath a compression wrap would be considerably larger, perhaps approaching the height of the wrap on the limb—i.e., tens of centimeters.…”

“…Typically, the tissue is modeled as a saturated poroelastic material that is divided into solid and fluid subvolumes. At the local scale (about 1 cm) poroelastic methods have been employed in the contexts of solid tumors 27 – 33 , injection sites 34 – 39 , under indentation probes 40 – 42 , near the edge of a compression wraps and in normal tissues 43 – 47 . The local models often include capillary permeability and lymphatic clearance, but over such relatively short distances, gravity has little opportunity to build significant hydrostatic pressures.…”