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Super-resolution ultrasound imaging relies on the sub-wavelength localizationof microbubble contrast agents. By tracking individual microbubbles, thevelocity and flow within microvessels can be estimated. However, a 2Dsuper-resolution image can only localize bubbles with sub-wavelength resolutionin the imaging plane whereas the resolution in the elevation plane is limitedby conventional beamwidth physics. Since ultrasound imaging integrates echoesover the elevation dimension, velocity estimates at a single location in theimaging plane include information throughout the imaging slice thickness. Thisslice thickness is typically a few orders or magnitude larger than thesuper-resolution limit. It is shown here that in order to estimate thevelocity, a spatial integration over the elevation direction must beconsidered. This operation yields a multiplicative correction factor thatcompensates for the elevation integration. A correlation-based velocityestimation technique is then presented. Calibrated microtube phantomexperiments are used to validate the proposed velocity estimation method andthe proposed elevation integration correction factor. It is shown that velocitymeasurements are in agreement with theoretical predictions within theconsidered range of flow rates (10 to 90 $\mu$L/min). Then, the proposedtechnique is applied to two in-vivo mouse tail experiments imaged with a lowfrequency human clinical transducer with human clinical concentrations ofmicrobubbles. In the first experiment, a vein was visible with a diameter of140 $\mu$m and a peak flow velocity of 0.8 mm/s. In the second experiment, avein was observed in the super-resolved image with a diameter of 120~$\mu$m andwith maximum local velocity of $\approx$~4.4~mm/s. It is shown that theparabolic flow profiles within these micro-vessels are resolvable.

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