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Derivation of shear rates from near-wall LDA measurements under steady and pulsatile flow conditions
1Department of Biomedical Engineering, University of Akron, OH 44325-0302.
Insights
Accurately measuring wall shear rate is crucial for understanding cardiovascular diseases like atherosclerosis. A third-degree polynomial fit using four points offers the most precise estimation of wall shear rate during the cardiac cycle.
Area of Science:
- Biomedical Engineering
- Cardiovascular Science
- Fluid Dynamics
Background:
- Cardiovascular diseases, including atherosclerosis, thrombosis, and intimal hyperplasia, are significant health concerns.
- Hemodynamics, particularly wall shear rate, are strongly correlated with arterial wall pathology.
- A standardized method for measuring wall shear rate is currently lacking.
Purpose of the Study:
- To evaluate different techniques for estimating wall shear rate.
- To determine the most accurate method for calculating wall shear rate from velocity profiles.
- To assess the impact of measurement proximity to the wall on accuracy.
Main Methods:
- Utilized theoretical and in-vitro experimental methods with steady and pulsatile flow waveforms.
- Obtained velocity profiles in the near-wall region using Laser Doppler Anemometry (LDA).
- Compared experimentally derived wall shear rates with theoretical values to assess approximation accuracy.
Main Results:
- Minimizing velocity data error requires the first measurement to be 500 microns from the wall.
- Linear approximation resulted in errors up to 16.4% at peak systole, increasing significantly during diastole.
- A third-degree polynomial curve fit using four points provided the most accurate wall shear rate estimation throughout the cardiac cycle.
Conclusions:
- Linear approximation is not recommended for wall shear rate estimation due to significant errors.
- A third-degree polynomial fit using four points is the most accurate method for approximating wall shear rate in pulsatile flow.
- Higher-degree polynomial fits may yield unpredictable results due to near-wall oscillations.
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 microns 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.