Related Experiment Video
Updated: Aug 23, 2025

Blocking Lymph Flow by Suturing Afferent Lymphatic Vessels in Mice
Published on: May 14, 2020
A Mathematical Description of the Flow in a Spherical Lymph Node
Giulia Giantesio1, Alberto Girelli2, Alessandro Musesti3
1Dipartimento di Matematica e Fisica "N. Tartaglia", Università Cattolica del Sacro Cuore, Brescia, Italy.
Abstract:
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. Thanks to the hypothesis of axisymmetric flow with respect to the azimuthal angle and the use of the stream function approach, we find an explicit solution for the fully developed pulsatile flow in terms of Gegenbauer polynomials. A selected set of plots is provided to show the trend of motion in the case of physiological parameters. Then, a finite element simulation is performed and it is compared with the explicit solution.
Related Concept Videos
Detailed Structure and Function of Lymph Nodes
From a histological perspective, lymph nodes can be split into two main areas: the superficial cortex and the deep medulla. The outer cortex is populated by dendritic cells, macrophages, and B lymphocytes, which are densely packed into follicles. When these B-lymphocytes are presented...
Steady, Laminar Flow in Circular Tubes
Velocity Potential
Eulerian and Lagrangian Flow Descriptions
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
Plane Potential Flows
Uniform...
Laminar and Turbulent Flow

