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. The highly vascularized lymph node connects the lymphatic and blood systems, emphasizing its essential role in maintaining the fluid balance in the body. In this work, we describe a mathematical model in a steady setting to describe the lymph transport in a lymph node. We couple the fluid flow in the SCS governed by an incompressible Stokes equation with the fluid flow in LC, described by a model obtained by means of asymptotic homogenisation technique, taking into account the multiscale nature of the node and the fluid exchange with the blood vessels inside it. We solve this model using numerical simulations and we analyze the lymph transport inside the node to elucidate its regulatory mechanisms and significance. Our results highlight the crucial role of the microstructure of the lymph node in regularising its fluid balance. These results can pave the way to a better understanding of the mechanisms underlying the lymph node's multiscale functionalities which can be significantly affected by specific physiological and pathological conditions, such as those characterising malignant tissues.