Uncertainty quantification for ultrasound image velocimetry

Ultrasound image velocimetry (UIV) is a non-invasive method with high temporal-spatial resolution for measuring flow velocity in opaque media, particularly in biomedical fields. Velocity measurement uncertainty propagates into pressure and shear estimates, which are critical diagnostic parameters. Despite its importance, no method currently quantifies UIV uncertainty due to complex error sources. This study proposes the generalized moment of correlation (GMC), which builds on the moment of correlation technique, widely used for uncertainty prediction in particle image velocimetry. It quantifies uncertainty by calculating the standard deviation of the displacement probability density function (PDF) from image cross-correlation. GMC improves accuracy by convolving the PDF with an elliptical Gaussian kernel to mitigate non-circular peaks caused by speckle stretching in UIV. GMC demonstrated 90% accuracy in predicting velocity errors in artificial images across various particle aspect ratio, noise, density, displacement and shear. In Rankine vortex simulations, GMC-based pressure estimates improved accuracy by 20% over ordinary least squares, which disregards velocity uncertainty. Clinical echocardiograms from six patients demonstrated that GMC-enhanced pressure fields captured more detailed flow features. The GMC method effectively quantifies uncertainty in UIV, enhancing the accuracy of velocity and pressure measurements.