Wall Shear Rate Estimation Research Articles

Time-Resolved Wall Shear Rate Mapping Using High-Frame-Rate Ultrasound Imaging.

In atherosclerosis, low wall shear stress (WSS) is known to favor plaque development, while high WSS increases plaque rupture risk. To improve plaque diagnostics, WSS monitoring is crucial. Here, we propose wall shear imaging (WASHI), a noninvasive contrast-free framework that leverages high-frame-rate ultrasound (HiFRUS) to map the wall shear rate (WSR) that relates to WSS by the blood viscosity coefficient. Our method measures WSR as the tangential flow velocity gradient along the arterial wall from the flow vector field derived using a multi-angle vector Doppler technique. To improve the WSR estimation performance, WASHI semiautomatically tracks the wall position throughout the cardiac cycle. WASHI was first evaluated with an in vitro linear WSR gradient model; the estimated WSR was consistent with theoretical values (an average error of 4.6% ± 12.4 %). The framework was then tested on healthy and diseased carotid bifurcation models. In both scenarios, key spatiotemporal dynamics of WSR were noted: 1) oscillating shear patterns were present in the carotid bulb and downstream to the internal carotid artery (ICA) where retrograde flow occurs; and 2) high WSR was observed particularly in the diseased model where the measured WSR peaked at 810 [Formula: see text] due to flow jetting. We also showed that WASHI could consistently track arterial wall motion to map its WSR. Overall, WASHI enables high temporal resolution mapping of WSR that could facilitate investigations on causal effects between WSS and atherosclerosis.

Continuous Simultaneous Recording of Brachial Artery Distension and Wall Shear Rate: A New Boost for Flow-Mediated Vasodilation.

Vascular ultrasound has been extensively applied in the clinical setting to noninvasively assess the endothelial function by means of the so-called brachial artery flow mediated dilation (FMD). Despite the usefulness in large-scale epidemiological studies, this approach has revealed some pitfalls for assessing vascular physiology and health in individual subjects. Mainly, a reliable FMD examination should be based on the simultaneous and reliable measurement of both the stimulus, i.e., the wall shear rate (WSR), and the response, i.e., the diameter change. However, multiple technical, practical, and methodological challenges must be faced to meet this goal. In this work, we present the technical developments needed to implement a system to enable the extensive and reliable clinical ultrasound FMD examination. It integrates both a hardware part, i.e., an upgraded version of the ultrasound advanced open platform (ULA-OP), and a software part, i.e., a signal processing and data analysis platform. The system was applied for a two-center pilot clinical study on 35 young and healthy volunteers. Therefore, we present here the results of a statistical analysis on magnitude, time-course, and kinetic parameters of WSR and diameter trends that allowed us to accurately explore the vasodilatory response to the dynamic WSR changes. Our observations demonstrate that a direct and accurate estimation of WSR stimulus by multigate spectral Doppler allows understanding brachial artery vasodilatory response to reactive hyperemia. Drawing inferences on WSR stimulus from the diameter response along with an inaccurate estimation of WSR may cause further uncertainties for the accurate interpretation of the FMD response.

Non-invasive Vascular Radial/Circumferential Strain Imaging and Wall Shear Rate Estimation Using Video Images of Diagnostic Ultrasound

The aim of this work was to develop a convenient method for radial/circumferential strain imaging and shear rate estimation that could be used as a supplement to the current routine screening for carotid atherosclerosis using video images of diagnostic ultrasound. A reflection model-based correction for gray-scale non-uniform distribution was applied to B-mode video images before strain estimation to improve the accuracy of radial/circumferential strain imaging when applied to vessel transverse cross sections. The incremental and cumulative radial/circumferential strain images can then be calculated based on the displacement field between consecutive B-mode images. Finally, the transverse Doppler spectra acquired at different depths along the vessel diameter were used to construct the spatially matched instantaneous wall shear values in a cardiac cycle. Vessel phantom simulation results revealed that the signal-to-noise ratio and contrast-to-noise ratio of the radial and circumferential strain images were increased by 2.8 and 5.9 dB and by 2.3 and 4.4 dB, respectively, after non-uniform correction. Preliminary results for 17 patients indicated that the accuracy of radial/circumferential strain images was improved in the lateral direction after non-uniform correction. The peak-to-peak value of incremental strain and the maximum cumulative strain for calcified plaques are evidently lower than those for other plaque types, and the echolucent plaques had higher values, on average, than the mixed plaques. Moreover, low oscillating wall shear rate values, found near the plaque and stenosis regions, are closely related to plaque formation. In conclusion, the method described can provide additional valuable results as a supplement to the current routine ultrasound examination for carotid atherosclerosis and, therefore, has significant potential as a feasible screening method for atherosclerosis diagnosis in the future.

A Fast Method to Estimate the Wall Shear Stress Waveform in Arteries

Introduction Ultrasound has been applied to measure vessel diameter and blood flow velocity to compute the wall shear rate (WSR) in arteries. This paper describes a fast technique to assess the WSR waveform using an image of a pulsed Doppler waveform downloaded from a modern clinical ultrasound scanner. Methods A walled vascular phantom has been developed to mimic the physiological condition of brachial arteries, from where measurements were made. A MATLAB program has been developed and used to compute the WSR waveform in a flow phantom from a pulsed Doppler image. The mean WSR obtained from the WSR waveform was compared with the mean WSR derived from the flow rate obtained from a timed collection method. Measurement errors in Doppler velocity estimates from ultrasound scanners were also investigated and used to determine correction factors in WSR calculations. Results For three different flow phantom depths, 9.5,14.5 and 19.5 mm, the mean percentage errors between the true and measured WSR were found to be 4.5% (SD = 4.0), 7.4% (SD = 5.1) and 14.2% (SD = 4.1) respectively. Conclusions The results demonstrated the feasibility of calculating WSR based solely on an image of the Doppler spectrum and arterial diameter measurement, which opens up the possibility of obtaining WSR estimates from generic scanners.

Distribution of wall shear rate throughout the arterial tree: A case study

The generally accepted assumption that the arterial system remodels itself to maintain constant wall shear stress throughout is based on Murray’s law, utilising the principle of minimum work for steady flow. However, blood flow in the human arterial system is pulsatile. In this work we outline a method allowing for estimation of wall shear rate in arteries using the flow waveforms as the input signal and estimate wall shear rates in the common carotid, brachial, and femoral arteries to determine the uniformity of distribution of wall shear rates throughout the arterial system. Time-dependent wall shear rates occurring in fully developed pulsatile flow were obtained using Womersley’s theory. Flow waveforms and radii of the arteries measured in a young healthy male subject without any known cardiac disease using magnetic resonance taken from the literature were used as the input to the model. Peak/mean wall shear rates were found to be (1640/403.2 s −1) in common carotid, (908.8/84.95 s −1) in brachial, and (1251/134.2 s −1) in femoral arteries. Our findings suggest a non-uniform distribution of wall shear rates throughout the arterial system. The advantage of using this method is that such input data are being routinely recorded during diagnostic ultrasonography.

Modeling and phantom studies of ultrasonic wall shear rate measurements using coded pulse excitation

Wall shear rate (WSR) is the derivative of blood velocity with respect to vessel radius at the endothelial cell (EC) surface. The product of WSR and blood viscosity is the wall shear stress (WSS) that has been identified as an important factor for atherosclerosis development. High echo signal-to-noise ratio (eSNR) and high spatial resolution are crucial for minimizing the errors in WSR estimates. By transmitting coded pulses with time-bandwidth product greater than one, high eSNR from weak blood scatter can be achieved without increasing instantaneous power or sacrificing spatial resolution. This paper summarizes a series of measurements in a straight tube (5-mm diameter), constant velocity flow phantom using a 10 MHz transducer (60% bandwidth, f/1.5) imaged with a 72 degrees Doppler angle, 125 MHz sampling frequency and 1 kHz pulse repetition frequency. Measurements were made using a frequency-modulated (FM) code, phase-modulated (PM) codes, and uncoded broadband and narrow band pulse transmissions. Both simulation and experimental results show that coded-pulse excitation increases accuracy and precision in WSR estimation for laminar flow over a broad range of peak velocity values when compared to standard pulsing techniques in noise-limited conditions (eSNR < 30 dB). The code sequence and its length are selected to balance range lobe suppression with eSNR and echo coherence enhancements to minimize WSR errors. In our study, the combination of an eight bit Optimal coded pulse with a Wiener compression filter yielded the highest WSR estimation performance.

Wall Shear-Rate Estimation Within the 50cc Penn State Artificial Heart Using Particle Image Velocimetry

Particle image velocimetry (PIV) has been gaining acceptance as a routine tool to evaluate the flow fields associated with fluid mechanical devices. We have developed algorithms to investigate the wall shear-rates within the 50cc Penn State artificial heart using low magnification, conventional particle image velocimetry (PIV). Wall shear has been implicated in clot formation, a major post-implant problem with artificial hearts. To address the issues of wall scattering and incomplete measurement volumes, associated with near wall measurements, we have introduced a zero masking and a fluid centroid shifting technique. Simulations using different velocity fields were conducted with the techniques to assess their viability. Subsequently, the techniques were applied to the experimental data collected. The results indicate that the size of the interrogation region should be chosen to be as small as possible to maximize resolution while large enough to ensure an adequate number of particles per region. In the current study, a 16 x 16 interrogation window performed well with good spatial resolution and particle density for the estimation of wall shear rate. The techniques developed with PIV allow wall shear-rate estimates to be obtained from a large number of sites at one time. Because a planar image of a flow field can be determined relatively rapidly, PIV may prove useful in any preliminary design procedure.

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

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.

Accuracy of velocity and shear rate measurements using pulsed doppler ultrasound: A comparison of signal analysis techniques

An experimental investigation was instituted to evaluate the performance of Doppler ultrasound signal processing techniques for measuring fluid velocity under well-defined flow conditions using a 10-MHz multigated pulsed ultrasound instrument. Conditions of fully developed flow in a rigid, circular tube were varied over a Reynolds number range between 500 and 8000. The velocity across the tube was determined using analog and digital zero crossing detectors and three digital spectrum estimators. Determination of the Doppler frequency from analog or digital zero crossing detectors gave accurate velocity values for laminar and moderately turbulent flow away from the wall (0.969 less than or equal to r less than or equal to 0.986). Three digital spectrum estimators, Fast Fourier Transform, Burg autoregressive method, and minimum variance method, were slightly more accurate than the zero crossing detector (0.984 less than or equal to r less than or equal to 0.994), especially at points close to the walls and with higher levels of turbulence. Steep velocity gradients and transit-time-effects from high velocities produced significantly larger errors in velocity measurement. Wall shear rate estimates were most precise when calculated using the position of the wall and two velocity points. The calculated wall shears were within 20%-30% of theoretically predicted values.