A Two-Dimensional Computational Model of Lymph Transport Across Primary Lymphatic Valves

This study utilizes a finite element model to characterize the transendothelial transport through overlapping endothelial cells in primary lymphatics during the uptake of interstitial fluid. The computational model is built upon the analytical model of these junctions created by Mendoza and Schmid-Schonbein (2003, “A Model for Mechanics of Primary Lymphatic Valves,” J. Biomed. Eng., 125, pp. 407–414). The goal of the present study is to investigate how adding more sophisticated and physiologically representative biomechanics affects the model’s prediction of fluid uptake. These changes include incorporating a porous domain to represent interstitial space, accounting for finite deformation of the deflecting endothelial cell, and utilizing an arbitrary Lagrangian–Eulerian algorithm to account for interacting and nonlinear mechanics of the junctions. First, the present model is compared with the analytical model in order to understand its effects on parameters such as cell deflection, pressure distribution, and velocity profile of the fluid entering the lumen. Without accounting for the porous nature of the interstitium, the computational model predicts greater cell deflection and consequently higher lymph velocities and flow rates than the analytical model. However, incorporating the porous domain attenuates the cell deflection and flow rate to values below that predicted by the analytical model for a given transmural pressure. Second, the present model incorporates recent experimental data for parameters such as lymph viscosity, transmural pressure measurements, and others to evaluate the ability of these junctions to act as unidirectional valves. The volume of flow through the valve is calculated to be $0.114nL/μm$ per cycle for a transmural pressure varying between 8.0 mm Hg and −1.0 mm Hg at 0.4 Hz. Though experimental data for the absorption of lymph through these endothelial junctions are scarce, several measurements of lymph velocity and flow rates are cited to validate the present model.