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Bulletin of Mathematical Biology

, Volume 75, Issue 1, pp 49–81 | Cite as

A Model for Fluid Drainage by the Lymphatic System

  • Charles Heppell
  • Giles Richardson
  • Tiina Roose
Original Article

Abstract

This study investigates the fluid flow through tissues where lymphatic drainage occurs. Lymphatic drainage requires the use of two valve systems, primary and secondary. Primary valves are located in the initial lymphatics. Overlapping endothelial cells around the circumferential lining of lymphatic capillaries are presumed to act as a unidirectional valve system. Secondary valves are located in the lumen of the collecting lymphatics and act as another unidirectional valve system; these are well studied in contrast to primary valves. We propose a model for the drainage of fluid by the lymphatic system that includes the primary valve system. The analysis in this work incorporates the mechanics of the primary lymphatic valves as well as the fluid flow through the interstitium and that through the walls of the blood capillaries. The model predicts a piecewise linear relation between the drainage flux and the pressure difference between the blood and lymphatic capillaries. The model describes a permeable membrane around a blood capillary, an elastic primary lymphatic valve and the interstitium lying between the two.

Keywords

Mechanics Fluid flow Lymphatic system Primary lymphatic valves Euler–Bernoulli’s beam equation Darcy’s law Schwarz Christoffel mapping 

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Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Charles Heppell
    • 1
  • Giles Richardson
    • 1
  • Tiina Roose
    • 2
  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK
  2. 2.Bioengineering Sciences Research Group, Faculty of Engineering and EnvironmentUniversity of SouthamptonSouthamptonUK

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