Simulation of lymph flow with consideration of natural gravity force influence

Abstract

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.

Mathematical Modelling of the Structure and Function of the Lymphatic System

“…The consideration of passive contractions, which are not included in the model now, may allow for a reduction in the frequency. The results show that active contractions can produce enough force to make lymphs flow though the whole LS against the pressure gradient [61].…”

“…It is not known whether the contractions can produce sufficient force to provide lymph flow against the gravity force in low or inverse pressure gradients between the interstitial space and upper vena cava. The models of lymph flow in the series of contracting lymphangions and in the whole LS are developed to answer this question [17,22,37,38,61]. In [61], and this question is answered positively with the developed mathematical model (Section 4).…”

“…The models of lymph flow in the series of contracting lymphangions and in the whole LS are developed to answer this question [17,22,37,38,61]. In [61], and this question is answered positively with the developed mathematical model (Section 4). However, the evaluated parameters exceed the physiological values reported in [31,62].…”

“…Flow in the vessels is described by the quasi-one-dimensional equations including valve and active contraction influence, and the conditions of pressure equilibrium and mass conservation are imposed in the bifurcation points. The model of active pumping in this graph and its influence on the total flow are investigated without the influence of gravity force [63] and with influence of gravity force [61]. The increase in amplitude and frequency of phase contractions is shown to increase the output flux.…”

“…(c) The graph from[40]. The graph is spatially oriented, and thus calculations with respect to gravity force are possible[61]. The vessel network includes lymph nodes.…”