Womersley Number-Based Estimates of Blood Flow Rate in Doppler Analysis: In Vivo Validation by Means of Phase-Contrast MRI

The aim of this paper, was to present an in vivo validation of the Womersley number-based formula, by means of 2-D cine phase-contrast MRI (PCMRI)

Method for estimating pulsatile wall shear stress from one-dimensional velocity waveforms

Wall shear stress (WSS)—a key regulator of endothelial function—is commonly estimated in vivo using simplified mathematical models based on Poiseuille\u27s flow, assuming a quasi-steady parabolic velocity distribution, despite evidence that more rapidly time-varying, pulsatile blood flow during each cardiac cycle modulates flow-mediated dilation (FMD) in large arteries of healthy subjects. More exact and accurate models based on the well-established Womersley solution for rapidly changing blood flow have not been adopted clinically, potentially because the Womersley solution relies on the local pressure gradient, which is difficult to measure non-invasively. We have developed an open-source method for automatic reconstruction of unsteady, Womersley-derived velocity profiles, and WSS in conduit arteries. The proposed method (available online at https://doi.org/10.5281/zenodo.7576408) requires only the time-averaged diameter of the vessel and time-varying velocity data available from non-invasive imaging such as Doppler ultrasound. Validation of the method with subject-specific computational fluid dynamics and application to synthetic velocity waveforms in the common carotid, brachial, and femoral arteries reveals that the Poiseuille solution underestimates peak WSS 38.5%–55.1% during the acceleration and deceleration phases of systole and underestimates or neglects retrograde WSS. Following evidence that oscillatory shear significantly augments vasodilator production, it is plausible that mischaracterization of the shear stimulus by assuming parabolic flow leads to systematic underestimates of important biological effects of time-varying blood velocity in conduit arteries

Methods for Improved Estimation of Low Blood Velocities Using Vector Doppler Ultrasound

Accurate estimation of low 3D blood velocities, such as near the wall in recirculation or disturbed flow regions, is important for accurate mapping of velocities to improve estimations of wall shear stress and turbulence, which are associated risk factors for vascular disease and stroke. Doppler ultrasound non-invasively measures blood-velocities but suffers from two major limitations addressed in this thesis. These are angle dependence of the measurements, which requires the knowledge of beam-to-flow angle, and the wall-filter. The high-pass wall filter that is applied to attenuate the high-intensity low-frequency signal from tissue and slowly moving vessel wall also attenuates any low velocity signals from blood thus causing inaccurate estimation of these velocities. This thesis presents two methods to alleviate the angle-dependence limitation and to minimize the effect of the wall filter on low blood-velocity estimates: a multi-receiver technique – vector Doppler ultrasound (VDUS), and a novel method called aperture-translation technique. For the first method – VDUS, theoretical and experimental studies were performed to assess the comparative benefit of three to eight receivers (3R–8R) in Doppler ultrasound configurations in terms of the number of receiver beams, inter-beam angle, and beam- selection method (criterion for discriminating between tissue and blood Doppler signals) for a range of velocity orientations. Accuracy and precision for ≥5 receivers were consistently better over all flow velocity orientations and for all beam-selection methods. Asymmetry in the 5R configuration led to improved accuracy and precision compared to symmetrical 6R and 8R configurations. Second, a novel 2D-VDUS aperture-translation technique using mechanical or electronic translation of the transmit-receive apertures was introduced and assessed experimentally. Both versions of the technique outperformed the conventional 2D-VDUS method for detection of low flow velocities in terms of accuracy and precision. The electronic version, which is more relevant and feasible clinically, showed comparable reliability and better accuracy compared with the idealized mechanical version, therefore suggesting its potential for future development. This work demonstrated that a minimum of five receivers, preferably with an inherent asymmetry with respect to the flow direction, should be considered when designing a 2D-array configuration for improved estimation of low velocities. For estimation of low velocities not measurable with conventional VDUS methods, the aperture-translation technique could be a potential candidate

Model-based assessment of dynamic arterial blood volume flow from ultrasound measurements

To assess in clinical practice arterial blood volume flow (BVF) from ultrasound measurements, the assumption is commonly made that the velocity profile can be approximated by a quasi-static Poiseuille model. However, pulsatile flow behaviour is more accurately described by a Womersley model. No clinical studies have addressed the consequences on the estimated dynamics of the BVF when Poiseuille rather than Womersley models are used. The aim of this study is to determine the influence of assumed Poiseuille profile instead of Womersley profile on the estimation and intrasubject variability of dynamical parameters of the BVF. For this purpose, a low number of volunteers sufficed. Brachial artery centerline velocity waveform and vessel diameter were measured with ultrasound within a small group of six volunteers. Within subjects, the intra- and inter-registration variability of BVF parameters estimates did not significantly differ. Poiseuille profiles compared to Womersley underestimates the maximum BVF by 19%, the maximum retrograde volume flow by 32% and the rise time by 18%. It can be concluded that when estimating in a straight vessel the dynamic properties of the BVF, Womersley profiles should preferably be chosen. © 2009 The Author(s)