Quasi-Frobenius ring: Difference between revisions
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:''Should not be confused with "[[Fåhræus–Lindqvist effect]]"'' | |||
The dependence of [[apparent viscosity]] of human [[blood]] on the [[capillary]] size it is flowing through is identified as the [[Fåhræus–Lindqvist effect]]. There is a related but different effect called the Fåhræus effect.<ref>{{cite book|title=Fahraeus, R., (1929) The suspension stability of the blood. Physiol. Rev. 9, 241274.}}</ref> This is the decrease in average concentration of [[red blood cell]]s in [[human blood]] as the diameter of the glass tube in which it is flowing decreases. In other words, in [[blood vessel]]s with diameters less than 500 [[micrometre|micrometers]], both the [[hematocrit]] decreases with decreasing [[capillary]] diameter. The Fåhræus effect definitely influences the [[Fåhræus–Lindqvist effect]] but the former is not the only cause of the latter.<ref>{{cite web|author=Name(required) |url=http://www.nonoscience.info/2010/09/02/blood-flow-and-fahraeus-effect/ |title=Blood Flow and Fahraeus Effect |publisher=Nonoscience.info |date= |accessdate=2011-05-09}}</ref> | |||
==Mathematical Model== | |||
Considering [[steady flow|steady]] [[laminar flow|laminar]] fully developed [[blood flow]] in a small tube with radius of <math>r_0</math>, whole blood separates into a cell-free plasma layer along the tube wall and enriched central core. As a result, the tube hematocrit, <math>H_t</math>, is smaller than the out flow hematocrit, <math>H_0</math>. | |||
A simple mathematical treatment of the Fåhræus effect was shown in Sutera et al. (1970).<ref>{{cite journal|title=Sutera, S. P., Seshadri, V., Croce, P. A. and Hochmuth, R. M. |year=1970|title= Capillary blood flow: II. Deformable model cells in tube flow|journal= Microvascular Research|volume= 2|issue=4|pages= 420–433| DOI= 10.1016/0026-2862(70)90035-X}}</ref> This seems to be the earliest analysis: | |||
:<math> \frac{H_t}{ H_0 }=\frac{1}{2-(1-(\frac {\delta}{r_0}))^2}</math> | |||
where: | |||
:<math>H_t</math> is the tube [[hematocrit]] | |||
:<math>H_0</math> is the outlet [[hematocrit]] | |||
:<math>\delta</math> is the cell-free [[Blood plasma|plasma]] layer thickness | |||
:<math>r_0</math> is the radius of the tube | |||
Also, the following expression was developed by Pries et al. (1990)<ref>{{cite book|title=Pries AR, Secomb TW, Gaehtgens P and Gross JF. Blood flow in microvascular networks: Experiments and simulation. Circulation Research 67:826-834, 1990}}</ref> to represent tube [[hematocrit]],<math>H_t</math>, as a function of discharge [[hematocrit]],<math>H_d</math>, and tube diameter. | |||
:<math> \frac{H_t}{ H_d }= H_d+(1-H_d)(1+1.7 exp (-0.415 D)-0.6exp(-0.011D))</math> | |||
where: | |||
:<math>H_t</math> is the tube [[hematocrit]] | |||
:<math>H_d</math> is the discharge [[hematocrit]] | |||
:<math>D</math> is the diameter of the tube in µm | |||
== Further reading == | |||
* C. Kleinstrauer, (2007) Bio-Fluid Dynamics, Taylor and Francis Pub. | |||
==See also== | |||
*[[Cell-free marginal layer model]] | |||
*[[Fåhræus–Lindqvist effect]] | |||
*[[Blood viscosity]] | |||
*[[hemodynamics]] | |||
==References== | |||
{{Reflist}} | |||
{{DEFAULTSORT:Fahraeus Effect}} | |||
[[Category:Cardiovascular physiology]] | |||
Revision as of 03:27, 7 March 2013
- Should not be confused with "Fåhræus–Lindqvist effect"
The dependence of apparent viscosity of human blood on the capillary size it is flowing through is identified as the Fåhræus–Lindqvist effect. There is a related but different effect called the Fåhræus effect.[1] This is the decrease in average concentration of red blood cells in human blood as the diameter of the glass tube in which it is flowing decreases. In other words, in blood vessels with diameters less than 500 micrometers, both the hematocrit decreases with decreasing capillary diameter. The Fåhræus effect definitely influences the Fåhræus–Lindqvist effect but the former is not the only cause of the latter.[2]
Mathematical Model
Considering steady laminar fully developed blood flow in a small tube with radius of , whole blood separates into a cell-free plasma layer along the tube wall and enriched central core. As a result, the tube hematocrit, , is smaller than the out flow hematocrit, . A simple mathematical treatment of the Fåhræus effect was shown in Sutera et al. (1970).[3] This seems to be the earliest analysis:
where:
- is the tube hematocrit
- is the outlet hematocrit
- is the cell-free plasma layer thickness
- is the radius of the tube
Also, the following expression was developed by Pries et al. (1990)[4] to represent tube hematocrit,, as a function of discharge hematocrit,, and tube diameter.
where:
- is the tube hematocrit
- is the discharge hematocrit
- is the diameter of the tube in µm
Further reading
- C. Kleinstrauer, (2007) Bio-Fluid Dynamics, Taylor and Francis Pub.
See also
References
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