Computational Modeling of Lymph Filtration and Absorption in the Lymph Node by Boundary Integral Equations

Abstract

We develop a numerical method for solving three-dimensional problems of fluid filtration and absorption in a piecewise homogeneous medium by means of boundary integral equations. This method is applied to a simulation of the lymph flow in a lymph node. The lymph node is considered as a piecewise homogeneous domain containing porous media. The lymph flow is described by Darcy’s law. Taking into account the lymph absorption, we propose an integral representation for the velocity and pressure fields, where the lymph absorption imitates the lymph outflow from a lymph node through a system of capillaries. The original problem is reduced to a system of boundary integral equations, and a numerical algorithm for solving this system is provided. We simulate the lymph velocity and pressure as well as the total lymph flux. The method is verified by comparison with experimental data.

Keywords

• boundary integral equations
• potential theory
• filtration flow
• collocation method