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A computational model of a network of initial lymphatics and pre-collectors with permeable interstitium

  • B. O. Ikhimwin
  • C. D. BertramEmail author
  • S. Jamalian
  • C. Macaskill
Original Paper
  • 28 Downloads

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.

Keywords

Lymph flow Fluid–structure interaction Numerical model Extrinsic pumping 

Notes

Acknowledgements

We acknowledge the facilities, and the scientific and technical assistance of the Sydney Informatics Hub at the University of Sydney and, in particular, access to the high-performance computing facility Artemis. BI was supported by NIH Grant U01-HL-123420, which also funded the research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • B. O. Ikhimwin
    • 1
  • C. D. Bertram
    • 1
    Email author
  • S. Jamalian
    • 2
  • C. Macaskill
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  2. 2.Department of Biomedical EngineeringJohns Hopkins University School of MedicineBaltimoreUSA

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