Simulation of a Chain of Collapsible Contracting Lymphangions With Progressive Valve Closure

Abstract

The aim of this investigation was to achieve the first step towards a comprehensive model of the lymphatic system. A numerical model has been constructed of a lymphatic vessel, consisting of a short series chain of contractile segments (lymphangions) and inter-segmental valves. The changing diameter of a segment governs the difference between the flows through inlet and outlet valves, and is itself governed by a balance between transmural pressure, and passive and active wall properties. The compliance of segments is maximal at intermediate diameters, and decreases when the segments are subject to greatly positive or negative transmural pressure. Fluid flow is the result of time-varying active contraction causing diameter to reduce, and is limited by segmental viscous and valvular resistance. The valves effect a smooth transition from low forward-flow resistance to high backflow resistance. Contraction occurs sequentially in successive lymphangions in the forward-flow direction. The behaviour of chains of one to five lymphangions was investigated by means of pump function curves, with variation of valve opening parameters, maximum contractility, lymphangion size gradation, number of lymphangions, and phase delay between adjacent lymphangion contractions. The model was reasonably robust numerically, with mean flow-rate generally reducing as adverse pressure was increased. Sequential contraction was found to be much more efficient than synchronised contraction. At the highest adverse pressures, pumping failed by one of two mechanisms, depending on parameter settings: either mean leakback flow exceeded forward pumping, or contraction failed to open the lymphangion outlet valve. Maximum pressure and maximum flow-rate were both sensitive to the contractile state; maximum pressure was also determined by the number of lymphangions in series. Maximum flow-rate was highly sensitive to the transmural pressure experienced by the most upstream lymphangions, suggesting that many feeding lymphatics would be needed to supply one downstream lymphangion chain pumping at optimal transmural pressure.

Confocal Image-Based Computational Modeling of Nitric Oxide Transport in a Rat Mesenteric Lymphatic Vessel

“…Despite the 2D nature of these models, they provided valuable insight with regard to theoretical framework (e.g., constant parameter and nondimensionalization) that aided in the development of the model presented herein. Other models developed for the lymphatic system are simply lumped-parameter [7,8], onedimensional [7,8], or do not properly take into account the geometry of the valve region [9].…”

Effect of Axial Stretch on Lumen Collapse of Arteries

“…The current model and results help us to better understand the buckling behavior of arteries under these pathological conditions. The model equation can also be used to analyze the buckling behavior of other tubular structures such as veins, lymphatic tubes, ureter, esophagus, or umbilical cord [2,34,35].…”

Multiscale Modelling of Lymphatic Drainage

“…Recently, Bertram et al [5] have attempted to refine the valve modelling within a lumped-parameter chain model. This modelled the valve behaviour more smoothly than a simple on-off diode, with a resistance which ramped smoothly: …”