Modelling secondary lymphatic valves with a flexible vessel wall: how geometry and material properties combine to provid
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ORIGINAL PAPER
Modelling secondary lymphatic valves with a flexible vessel wall: how geometry and material properties combine to provide function C. D. Bertram1 Received: 31 October 2019 / Accepted: 2 April 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A three-dimensional finite-element fluid/structure interaction model of an intravascular lymphatic valve was constructed, and its properties were investigated under both favourable and adverse pressure differences, simulating valve opening and valve closure, respectively. The shear modulus of the neo-Hookean material of both vascular wall and valve leaflet was varied, as was the degree of valve opening at rest. Also investigated was how the valve characteristics were affected by prior application of pressure inflating the whole valve. The characteristics were parameterised by the volume flow rate through the valve, the hydraulic resistance to flow, and the maximum sinus radius and inter-leaflet-tip gap on the plane of symmetry bisecting the leaflet, all as functions of the applied pressure difference. Maximum sinus radius on the leaflet-bisection plane increased with increasing pressure applied to either end of the valve segment, but also reflected the non-circular deformation of the sinus cross section caused by the leaflet, such that it passed through a minimum at small favourable pressure differences. When the wall was stiff, the inter-leaflet gap increased sigmoidally during valve opening; when it was as flexible as the leaflet, the gap increased more linearly. Less pressure difference was required both to open and to close the valve when either the wall or the leaflet material was more flexible. The degree of bias of the valve characteristics to the open position increased with the inter-leaflet gap in the resting position and with valve inflation pressure. The characteristics of the simulated valve were compared with those specified in an existing lumped-parameter model of one or more collecting lymphangions and used to estimate a revised value for the constant in that model which controls the rate of valve opening/closure with variation in applied pressure difference. The effects of the revised value on the lymph pumping efficacy predicted by the lumpedparameter model were evaluated. Keywords Lymph transport · Fluid–structure interaction · Numerical model · Finite-element model · Valve bias
1 Introduction The lymphatic vascular system contains endothelial primary valves in the wall of initial lymphatics and intravascular secondary valves (Bohlen et al. 2009) which divide collecting lymphatics into lymphangions. The valves are essential for lymph transport, since there is no equivalent of the heart at the upstream end of the system to propel flow. Instead lymphangions, as their name implies, act as pumping chambers in series, utilising either the intermittent passive squeezing of lymphatic vessels resulting from the relative motion of surrounding tissues or the contractions of the unique muscle * C. D. Bertram [email protected]
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