Errors in the estimation of arterial wall shear rates that result from curve fitting of velocity profiles

An analysis was performed to determine the error that results from the estimation of the wall shear rates based on linear and quadratic curve-fittings of the measured velocity profiles. For steady, fully developed flow in a straight vessel, the error for the linear method is linearly related to the distance between the probe and the wall, dr1, and the error for the quadratic method is zero. With pulsatile flow, especially a physiological pulsatile flow in a large artery, the thickness of the velocity boundary layer, delta is small, and the error in the estimation of wall shear based on curve fitting is much higher than that with steady flow. In addition, there is a phase lag between the actual shear rate and the measured one. In oscillatory flow, the error increases with the distance ratio dr1/delta and, for a quadratic method, also with the distance ratio dr2/dr1, where dr2 is the distance of the second probe from the wall. The quadratic method has a distinct advantage in accuracy over the linear method when dr1/delta << 1, i.e. when the first velocity point is well within the boundary layer. The use of this analysis in arterial flow involves many simplifications, including Newtonian fluid, rigid walls, and the linear summation of the harmonic components, and can provide more qualitative than quantitative guidance.