Fåhræus effect

Mathematical model

Considering steady laminar fully developed blood flow in a small tube with radius of r 0 , whole blood separates into a cell-free plasma layer along the tube wall and enriched central core. As a result, the tube hematocrit H t is smaller than the out flow hematocrit H 0 . A simple mathematical treatment of the Fåhræus effect was shown in Sutera et al. (1970). This seems to be the earliest analysis:

H t H 0 = 1 2 − ( 1 − ( δ r 0 ) ) 2

where:

H t is the tube hematocrit H 0 is the outlet hematocrit δ is the cell-free plasma layer thickness r 0 is the radius of the tube

Also, the following expression was developed by Pries et al. (1990) to represent tube hematocrit, H t , as a function of discharge hematocrit, H d , and tube diameter.

H t H d = H d + ( 1 − H d ) ( 1 + 1.7 e x p ( − 0.415 D ) − 0.6 e x p ( − 0.011 D ) )

where:

H t is the tube hematocrit H d is the discharge hematocrit D is the diameter of the tube in µm