Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system

Abstract

Fluid homeostasis is required for life. Processes involved in fluid balance are strongly related to exchanges at the microvascular level. Computational models have been presented in the literature to analyze the microvascular-interstitial interactions. As far as we know, none of those models consider a physiological description for the lymphatic drainage-interstitial pressure relation. We develop a computational model that consists of a network of straight cylindrical vessels and an isotropic porous media with a uniformly distributed sink term acting as the lymphatic system. In order to describe the lymphatic flow rate, a nonlinear function of the interstitial pressure is defined, based on literature data on the lymphatic system. The proposed model of lymphatic drainage is compared to a linear one, as is typically used in computational models. To evaluate the response of the model, the two are compared with reference to both physiological and pathological conditions. Di↵erences in the local fluid dynamic description have been observed using the non-linear model. In particular, the distribution of interstitial pressure is heterogeneous in all the cases analyzed. The resulting averaged values of the interstitial pressure are also di↵erent, and they agree with literature data when using the non-linear model.

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