Cell-free marginal layer model: Difference between revisions

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{{Short description|Mathematical model used in hemodynamics}}

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==

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:<math> \mu_{e}=\frac{\mu_p}{[1-(1-\frac{\delta}{R})^4(1-\frac{\mu_p}{\mu_c})]} </math>

It can be realized when the radius of the [[blood vessel]] is much larger than the thickness of the cell-free [[Blood plasma|plasma]] layer, the effective [[viscosity]] is equal to bulk [[blood viscosity]] <math> \mu_c </math> at high shear rates ([[Newtonian fluid]]).

'''Relation between hematocrit and apparent/effective viscosity'''

[[Conservation of mass|Conservation of Mass]] Requires:

<math>QH_D=Q_cH_c</math>

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<math>\frac{u_p}{u_e}=1+\sigma^4[\frac{u_a}{u_c}-1]</math>

Blood viscosity as a fraction of [[hematocrit]]:

<math>\frac{u_e}{u}=1-\alpha H</math>