Underestimation of Flow Velocity in 2-D Super-Resolution Ultrasound Imaging

Velocity estimation in ultrasound imaging is a technique to measure the speed and direction of blood flow. The flow velocity in small blood vessels, i.e., arterioles, venules, and capillaries, can be estimated using super-resolution ultrasound imaging (SRUS). However, the vessel width in SRUS is relatively small compared with the full-width-half-maximum of the ultrasound beam in the elevation direction, which directly impacts the velocity estimation. By taking into consideration the small vessel widths in SRUS, it is hypothesized that the velocity is underestimated in 2-D SRUS when the vessel diameter is smaller than the full width at half maximum elevation resolution of the transducer (FWHMy). A theoretical model is introduced to show that the velocity of a 3-D parabolic velocity profile is underestimated by up to 33% in 2-D SRUS, if the width of the vessel is smaller than FWHMy. This model was tested using Field II simulations and 3-D-printed micro-flow hydrogel phantom measurements. A Verasonics Vantage 256 scanner and a GE L8-18i-D linear array transducer with FWHMy of approximately $770~\mu {m}$ at the elevation focus were used in the simulations and measurements. Simulations of different parabolic velocity profiles showed that the velocity underestimation was 36.8% $\pm ~1.5$ % (mean ± standard deviation). The measurements showed that the velocity was underestimated by 30% $\pm ~6.9$ %. Moreover, the results of vessel diameters, ranging from $0.125\times $ FWHMy to $3\times $ FWHMy, indicate that velocities are estimated according to the theoretical model. The theoretical model can, therefore, be used for the compensation of velocity estimates under these circumstances.