A model for fluid drainage by the lymphatic system
A model for fluid drainage by the lymphatic system
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.
mechanics, fluid flow, lymphatic system, primary lymphatic valves, euler-bernoulli's beam equation, darcy's law, schwarz christoffel mapping
49-81
Heppell, Charles
72d006af-0fed-4f45-915c-049884536062
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Roose, Tiina
3581ab5b-71e1-4897-8d88-59f13f3bccfe
January 2013
Heppell, Charles
72d006af-0fed-4f45-915c-049884536062
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Roose, Tiina
3581ab5b-71e1-4897-8d88-59f13f3bccfe
Heppell, Charles, Richardson, Giles and Roose, Tiina
(2013)
A model for fluid drainage by the lymphatic system.
Bulletin of Mathematical Biology, 75 (1), .
(doi:10.1007/s11538-012-9793-2).
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.
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Accepted/In Press date: 1 November 2012
Published date: January 2013
Keywords:
mechanics, fluid flow, lymphatic system, primary lymphatic valves, euler-bernoulli's beam equation, darcy's law, schwarz christoffel mapping
Organisations:
Applied Mathematics
Identifiers
Local EPrints ID: 339053
URI: http://eprints.soton.ac.uk/id/eprint/339053
ISSN: 0092-8240
PURE UUID: c627c8c7-a3a6-4b11-ac6b-8fcea5e3bfe9
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Date deposited: 25 Mar 2013 09:37
Last modified: 15 Mar 2024 03:33
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Author:
Charles Heppell
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