A Model for Interstitial Drainage Through a Sliding Lymphatic Valve.

Abstract

This study investigates fluid flow and elastic deformation in tissues that are drained by the primary lymphatic system. A model is formulated based on the Rossi hypothesis that states that the primary lymphatic valves, which are formed by overlapping endothelial cells around the circumferential lining of lymphatic capillaries, open in response to swelling of the surrounding tissue. Tissue deformation and interstitial fluid flow through the tissue are treated using the Biot equations of poroelasticity and, the fluid flux (into the interstitium) across the walls of the blood capillaries, is assumed to be linearly related to the pressure difference across the walls via a constant of proportionality (the vascular permeability). The resulting model is solved in a periodic domain containing one blood capillary and one lymphatic capillary starting from a configuration in which the tissue is undeformed. On imposition of a constant pressure difference between blood and lymphatic capillaries, the solutions are found to settle to a steady state. Given that the magnitude of pressure fluctuations in the lymphatic system is much smaller than this pressure difference between blood and lymph, it is postulated that the resulting steady-state solution gives a good representation of the state of the tissue under physiological conditions. The effects of changes to the Young's modulus of the tissue, the blood-lymphatic pressure difference, vascular permeability and valve dimensions on the steady state are investigated and discussed in terms of their effects on oedema in the context of age- and pregnancy-related changes to the body.