Multiscale computational analysis of the steady fluid flow through a lymph node.

Lymph Nodes (LNs) are crucial to the immune and lymphatic systems, filtering harmful substances and regulating lymph transport. LNs consist of a lymphoid compartment (LC) that forms a porous bulk region, and a subcapsular sinus (SCS), which is a free-fluid region. Mathematical and mechanical challenges arise in understanding lymph flow dynamics.

A quasilinear hyperbolic one-dimensional model of the lymph flow through a lymphangion with valve dynamics and a contractile wall.

This paper presents a one-dimensional model that describes fluid flow in lymphangions, the segments of lymphatic vessels between valves, using quasilinear hyperbolic systems. The model incorporates a phenomenological pressure-cross-sectional area relationship based on existing literature. Numerical solutions of the differential equations align with known results, offering insights into lymphatic flow dynamics.

A Mathematical Description of the Flow in a Spherical Lymph Node.

The motion of the lymph has a very important role in the immune system, and it is influenced by the porosity of the lymph nodes: more than 90% takes the peripheral path without entering the lymphoid compartment. In this paper, we construct a mathematical model of a lymph node assumed to have a spherical geometry, where the subcapsular sinus is a thin spherical shell near the external wall of the lymph node and the core is a porous material describing the lymphoid compartment. For the mathematical formulation, we assume incompressibility and we use Stokes together with Darcy-Brinkman equation for the flow of the lymph.