Developmental Disorders of the Lymphatics

An information blog for disorders of the lymphatics. For all articles, please click on "Archives" - Due to spammers, I will no longer allow comments, sorry.

Friday, February 08, 2013

Incorporating measured valve properties into a numerical model of a lymphatic vessel.

Incorporating measured valve properties into a numerical model of a lymphatic vessel.

Feb 2013


a School of Mathematics and Statistics, University of Sydney, New South , Wales , 2006 , Australia.


An existing lumped-parameter model of multiple lymphangions (lymphatic vascular segments) in series is adapted for the incorporation of recent physiological measurements of lymphatic vascular properties. The new data show very marked nonlinearity of the passive pressure-diameter relation during distension, relative to comparable blood vessels, and complex valve behaviour. Since lymph is transported as a result of either the active contraction or the passive squeezing of vascular segments situated between two one-way valves, the performance of these valves is of primary importance. The valves display hysteresis (the opening and closing pressure drop thresholds differ), a bias to staying open (both state changes occur when the trans-valve pressure drop is adverse) and pressure-drop threshold dependence on transmural pressure. These properties, in combination with the strong nonlinearity that valve operation represents, have in turn caused intriguing numerical problems in the model, and we describe numerical stratagems by which we have overcome the problems. The principal problem is also generalised into a relatively simple mathematical example, for which solution detail is provided using two different solvers.

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