Quantitative sub-resolution blood velocity estimation using ultrasound localization microscopy ex-vivo and in-vivo

Super-resolution ultrasound imaging relies on the sub-wavelength localization of microbubble contrast agents. By tracking individual microbubbles, the velocity and flow within microvessels can be estimated. However, a 2D super-resolution image can only localize bubbles with sub-wavelength resolution in the imaging plane whereas the resolution in the elevation plane is limited by conventional beamwidth physics. Since ultrasound imaging integrates echoes over the elevation dimension, velocity estimates at a single location in the imaging plane include information throughout the imaging slice thickness. This slice thickness is typically a few orders or magnitude larger than the super-resolution limit. It is shown here that in order to estimate the velocity, a spatial integration over the elevation direction must be considered. This operation yields a multiplicative correction factor that compensates for the elevation integration. A correlation-based velocity estimation technique is then presented. Calibrated microtube phantom experiments are used to validate the proposed velocity estimation method and the proposed elevation integration correction factor. It is shown that velocity measurements are in agreement with theoretical predictions within the considered range of flow rates (10 to 90 $\mu$L/min). Then, the proposed technique is applied to two in-vivo mouse tail experiments imaged with a low frequency human clinical transducer with human clinical concentrations of microbubbles. In the first experiment, a vein was visible with a diameter of 140 $\mu$m and a peak flow velocity of 0.8 mm/s. In the second experiment, a vein was observed in the super-resolved image with a diameter of 120~$\mu$m and with maximum local velocity of $\approx$~4.4~mm/s. It is shown that the parabolic flow profiles within these micro-vessels are resolvable.