How Good Are the Fits to the Experimental Velocity Profiles in Vivo ?

A new velocity profile equation for the description of microcirculatory blood flow in vivo was proposed in 2009. However various recently published papers still use the assumption of parabolic velocity profile (Poiseuille flow). The purpose of this work was to evaluate the performance of 3 different fitting cases: 1) best parabolic fit, 2) axial fit with the proposed equation and 3) best fit with the proposed equation. Twelve experimental velocity profiles measured by particle image velocimetry in mouse venules were used to compare the fitting efficiency of the 3 cases on the basis of the velocity relative error (RE) expressed as average ± SE (standard error) at ten different radial segments (REj with 1 ≤ j ≤ 10). The parabolic best fit (case 1) leads to serious deviations from the real velocity distribution (RE10 = 65% ± 2%). The proposed equation axial fit (case 2) slightly overestimates blood velocity distribution near the vessel wall but the was below + 12% and it requires only one experimental value near the vessel axis, measurable using the Doppler Effect. The proposed equation best fit (case 3) approximates the experimental data without any serious bias but requires a complete velocity profile data set.