A velocity profile equation for blood flow in small arterioles and venules of small mammals in vivo and an evaluation based on literature data

Abstract

An empirical parametric equation with 2 bluntness parameters was introduced for describing the velocity profile of blood in the small arterioles and venules of small mammals, in vivo, with the basic approximations of the axisymmetric flow in cylindrical geometry, zero velocity at the wall and a blunter than parabolic flow profile. The purpose was to evaluate the usefulness of this equation in describing the velocity profile and in estimating the volume flow when only one velocity measurement is available near the vessel axis. The equation was tested on 17 velocity profiles (9 arteriolar and 8 venular) previously measured by particle image velocimetry (PIV) techniques, at diameters ranging from 17 to 38.6 mu m. The correlation coefficients of each experimental profile were higher than 0.96. The average relative error-bias measured at 10 radial segments ranged between -5% to 1%, leading to an average relative volume flow estimation error for all the 17 velocity profiles of -1.8% with a standard deviation of 4.3%.