A One-dimensional Model of the Lymph Flow in a Contractile Lymphangion

Abstract

The lymphatic system relies on the rhythmic contractions of lymphangions to move lymph against the pressure gradient caused by the heart's pulsation. Lymphangions are the segments of the collecting lymphatic vessels between two valves, and they function as both pumps and conduits, contracting to push lymph forward against adverse pressure gradients and serving as conduits when there is a favorable pressure gradient, inhibiting contractions with the help of nitric oxide. In this paper, we propose a one-dimensional model using the theory of quasilinear hyperbolic systems to describe the fluid flow in a lymphangion. To this aim, we use a phenomenological pressure-cross sectional area relationship taking into account most of the information available in the literature. We solve the obtained differential equations numerically and the solution obtained is in accordance with the literature results. Furthermore, through the solution derived from these numerical simulations, we gain the capability to elucidate and enhance our comprehension of lymphatic flow dynamics within the lymphangion.