Abstract:The lymphatic system is a body-wide network of lymphatic vessels and lymphoid organs. The complexity of the structural and functional organization of the lymphatic system implies the necessity of using computational modeling approaches to unravel the mechanisms of its regulation in quantitative terms. Although it is a vital part of the circulatory and immune systems, the lymphatic system remains poorly investigated as a mathematical modeling object. Modeling of the lymphatic vessel network needs to be established using a systematic approach in order to advance the model-driven research of this important physiological system. In our study, we elucidate key general features underlying the 3D structural organization of the lymphatic system in order to develop computational geometry and network graph models of the human lymphatic system based on available anatomical data (from the PlasticBoy project), which provides an estimate of the structure of the lymphatic system, and to analyze the topological properties of the resulting models.

In this study, we formulated a core mathematical model for describing the one-dimensional lymph flow in lymphatic vessels and branching network of lymphatic vessels. The 1D model was numerically implemented using the 1D haemodynamic modeling tools developed in T.M. Gamilov et al. and S. Simakov et al. [T.M. Gamilov et al., Transl. Med. 6 (2013) 5–13 and S. Simakov et al., Russian J. Numer. Anal. Math. Model. 28 (2013) 485–504]. The formulated model was calibrated using published data on lymph flow dynamics and other modelling studies of lymph flows. The comparison of 0D and 1D formulations of the lymph flow models is presented.

Heparin in concentrations of 10-50 U/ml produced a decrease in the amplitude and frequency of phasic contractions of smooth muscle cells of bovine mesenteric lymphatic vessels. Vascular wall tension was reduced under these conditions. The endothelium-dependent effect of heparin is realized via an increase in the production of nitric oxide by endothelial cells and, to a lesser degree, via the stimulation of prostacyclin synthesis.

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A model of lymph flow in the human lymphatic system in the quasi-one-dimensional approach has been created and investigated under different conditions. The model includes an implementation of contractions and valve influence on lymph flow. We consider contractions of lymphatic vessels and their influence on resulting flow in the whole network of lymphatic vessels and lymph nodes. We have investigated flow with zero pressure gradient and have found parameters, which influence the efficiency of contractions most significantly.

E. coli endotoxin decreased the amplitude and frequency of spontaneous phasic contractions in isolated bovine mesenteric lymphatic vessels. This substance in a concentration of 5 mg/liter blocked spontaneous contractions and reduced tonic tension of smooth muscle cells. The dilatory effect of endotoxin on lymphatic vessels was primarily realized via stimulation of synthesis of NO and prostacyclin by endotheliocytes.

The model of lymph flow in the human lymphatic system in the quasi-one-dimensional approach is considered in the paper. Calculations with natural gravity force influence are presented. Calculations show that in some sets of parameters of lymphatic vessels the physiological flow can be reached in the model with zero global pressure gradient influence only by the “muscle” pump.

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