Ikhimwin BO, Bertram CD, Jamalian S, Macaskill C. A computational model of a network of initial lymphatics and pre-collectors with permeable interstitium.
Biomech Model Mechanobiol 2019;
19:661-676. [PMID:
31696326 DOI:
10.1007/s10237-019-01238-x]
[Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2019] [Accepted: 10/09/2019] [Indexed: 10/25/2022]
Abstract
Initial lymphatic vessels are made up of overlapped endothelial cells that act as unidirectional valves enabling one-way drainage of tissue fluid into the lumen of the initial lymphatics when there is a favourable pressure gradient. Initial lymphatics subsequently drain this fluid into the collecting lymphatics. This paper describes a computational model for a network of passive rat mesenteric lymphatic vessels with sparse secondary valves. The network was simulated with the secondary valves both operational and non-operational. The effects on the cycle-mean outflow-rate from the network of both inflammation and the resistance of the surrounding interstitium were considered. The cycle-mean outflow-rate is sensitive to vessel stiffness. If the influence of primary-valve resistance is reduced relative to that of interstitial resistance and intravascular resistance, there is no absolute advantage of extrinsic pumping, since maximum outflow-rate occurs when vessels are rigid. However, there is relative advantage, in that the outflow-rate at intermediate stiffness is higher with the secondary valves functioning than when they are deactivated. If primary-valve resistance dominates, then extrinsic pumping of non-rigid vessels provides absolute advantage. The nonlinear relation between pressure drop and flow-rate of the endothelial primary valves, combined with downstream compliance and pulsatile external pressure, constitutes a separate mechanism of pumping. By enabling the consideration of interactions between multiple phenomena (primary valves, secondary valves, a real network geometry with multiple branches, deformable vessel walls, interstitial resistance and external pressures), the model offers a perspective for delineating physiological phenomena that have not yet been fully linked to the biomechanics of fluid flow through initial lymphatic networks.
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