Derivation of Shear Rates From Near-Wall LDA Measurements Under Steady and Pulsatile Flow Conditions

Abstract

Atherosclerosis, thrombosis, and intimal hyperplasia are major forms of cardiovascular diseases in the United States. Previous studies indicate a significant correlation between hemodynamics, in particular, wall shear rate, and pathology of the arterial walls. While results of these studies implicate morphologic and functional changes related to wall shear rate magnitude, a standard technique for wall shear rate measurement has not been established. In this study, theoretical and in-vitro experimental fully developed steady and physiologic pulsatile flow waveforms have been used to obtain velocity profiles in the near-wall region. The estimated wall shear rates from these results are compared to the theoretical value to assess the accuracy of the approximating technique. Experimentally obtained results from LDA suggest that in order to minimize the error in velocity data, and subsequently, the wall shear rate, the first measured velocity has to be 500 μm away from the wall. While a linear approximation did not produce errors larger than 16.4 percent at peak systole, these errors substantially increased as the velocity magnitudes decreased during late systole and diastole. Overall, a third degree polynomial curve fit using four points produced the most accurate estimation of wall shear rate through out the cardiac cycle. Results of higher degree curve-fitting functions can be unpredictable due to potential oscillations of the function near the wall. Hence, based on the results of this study, use of a linear approximation is not recommended; a third degree curve-fitting polynomial, using four points provided the most accurate approximation for these flow waveforms.