Cell-free marginal layer model: Difference between revisions

Revision as of 22:23, 26 October 2022

Revision as of 10:03, 22 March 2023

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In small [[capillary]] [[hemodynamics]], the cell-free layer is a near-wall layer of [[Blood plasma|plasma]] absent of [[red blood cell]]s since they are subject to migration to the [[capillary]] [[Centre (geometry)|center]] in [[Poiseuille flow]].<ref>{{cite journal|author=W. Pan, B. Caswell and G. E. Karniadakis |year=2010|title=A low-dimensional model for the red blood cell|journal= Soft Matter|doi=10.1039/C0SM00183J|pmc=3838865|pmid=24282440|volume=6|issue=18 |page=4366|bibcode=2010SMat....6.4366P }}</ref> '''Cell-free marginal layer model''' is a [[mathematical model]] which tries to explain [[Fåhræus–Lindqvist effect]] mathematically.

==Mathematical modeling==

===Governing equations===

Consider [[steady flow]] of [[blood]] through a [[capillary]] of [[radius]] <math>R</math>. The [[capillary]] cross section can be divided into a [[wikt:core|core]] region and cell-free [[Blood plasma|plasma]] region near the wall. The governing equations for both regions can be given by the following equations:<ref>{{cite book|last=Krishnan B. Chandran|first=Alit P. Yoganathan , Ajit P. Yoganathan , Stanley E. Rittgers|title=Biofluid mechanics : the human circulation|year=2007|publisher=CRC/Taylor & Francis|___location=Boca Raton|isbn=978-0-8493-7328-2|url=https://www.amazon.com/Biofluid-Mechanics-Circulation-Krishnan-Chandran/dp/084937328X}}</ref>

:<math> \frac{ -\Delta P}{ L }=\frac{1}{r}\frac{d}{dr}(\mu_c r \frac{du_c}{dr});</math> <math> 0 \le r\ \le R-\delta\,</math>

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==References==

{{Reflist}}

* {{cite journal | last1 = Chebbi | first1 = R | year = 2015 | title = Dynamics of blood flow: modeling of the Fahraeus-Lindqvist effect | journal = Journal of Biological Physics | volume = 41| issue = 3 | pages = 313–26| doi = 10.1007/s10867-015-9376-1 | pmid = 25702195 | pmc = 4456490 }}

[[Category:Fluid dynamics]]