Development of a model of a multi-lymphangion lymphatic vessel incorporating realistic and measured parameter values

Abstract

Our published model of a lymphatic vessel consisting of multiple actively contracting segments between non-return valves has been further developed by the incorporation of properties derived from observations and measurements of rat mesenteric vessels. These included (1) a refractory period between contractions, (2) a highly nonlinear form for the passive part of the pressure-diameter relationship, (3) hysteretic and transmural-pressure-dependent valve opening and closing pressure thresholds, (4) dependence of active tension on muscle length as reflected in local diameter. Experimentally, lymphatic valves are known to be biased to stay open. In consequence, in the improved model, vessel pumping of fluid suffers losses by regurgitation, and valve closure is dependent on backflow first causing an adverse valve pressure drop sufficient to reach the closure threshold. The assumed resistance of an open valve therefore becomes a critical parameter, and experiments to measure this quantity are reported here. However, incorporating this parameter value, along with other parameter values based on existing measurements, led to ineffective pumping. It is argued that the published measurements of valve closing pressure threshold overestimate this quantity owing to neglect of micro-pipette resistance. An estimate is made of the extent of the possible resulting error. Correcting by this amount, the pumping performance is improved, but still very inefficient unless the open-valve resistance is also increased beyond the measured level. Arguments are given as to why this is justified, and other areas where experimental data are lacking are identified. The model is capable of future adaptation as new experimental data appear.

Quantification of the passive and active biaxial mechanical behaviour and microstructural organization of rat thoracic ducts

“…Several important lumped parameter models have been proposed that quantify lymph propulsion through the lymphatic vasculature [14][15][16][17][18][19]. These models have deepened our understanding of lymphatic biomechanics; however, most models to date either neglect the nonlinear, anisotropic behaviour of the tissue or employ empirical pressure-diameter relations.…”

Parameter sensitivity analysis of a lumped-parameter model of a chain of lymphangions in series

“…The model developed by Bertram et al (2) improved on previous models in terms of modeling the valve behavior, the active contraction, and the passive behavior of the vessel, and recent refinements (1,4) have taken these improvements further. However, more accurate estimates of the parameters in the model are crucial if it is to be applied to understanding normal and pathological function.…”

Estimation of the Pressure Drop Required for Lymph Flow through Initial Lymphatic Networks

“…24,26 The mesentery tissue has historically been used to study initial lymphatic vessel structure and function [27][28][29] and is also the most commonly used tissue for investigating contractile mechanisms in collecting lymphatic vessels. 2,3,[5][6][7][8] While future studies will be needed to identify whether tissue-specific geometries might influence the pressure drop requirement, it is logical to speculate that our estimates can be generalized to any branched network.…”

“…The six lymphatic networks ranged in network area (12-129 mm 2 ), maximum branch order (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27), and total number of segments (31-219) (Figs. 2; 3A-C).…”

“…[2][3][4][5][6][7][8] In contrast to collecting lymphatics, initial lymphatic vessels are not wrapped in smooth muscle. With just a single endothelial layer, initial lymphatic function is considered to be passive and remains less understood.…”