Numerical modeling of fluid exchange between a collecting lymphatic vessel and the surrounding tissue

Lymphatic vessel dysfunction is increasingly recognized in metabolic diseases, contributing to edema, dyslipidemia, and tissue lipid accumulation. Type 2 diabetes has been experimentally linked to lymphatic vascular defects characterized by enhanced permeability resulting from low nitric oxide (NO) bioavailability. To examine the effects of this dysfunction, we developed a mathematical model of fluid exchange between a collecting lymphatic vessel and the surrounding tissue. The lymph flow is modeled using the Stokes equations for an incompressible, viscous fluid, while the collecting vessel is represented by a thin Koiter shell model. The main novelty of our approach is that the interstitium is described as poroelastic, and modeled using the Biot equations, which capture both porous medium flow and the displacement. Lymph movement within the vessel is regulated by biological factors, specifically calcium ion ( ${\text{Ca}}^{2+}$ ) concentration and NO production, which are included to modulate the pumping mechanism. Using this model, we quantify lymph flow and fluid exchange for both wild-type (WT) and diabetic vessels. Our findings illustrate how variations in NO production rate, Young's modulus, and hydraulic conductivity impact leakage and pumping efficiency. The results demonstrate that reduced NO production in diabetic conditions leads to increased fluid leakage and altered pulsation frequency, while increased vessel stiffness further compromises lymphatic function.