The Effect of Spatial Velocity Gradients on Block-Matching Accuracy for Ultrasound Velocimetry

Abstract

Block matching serves as the foundation for ultrasound velocimetry techniques such as blood speckle tracking and echo-particle image velocimetry. Any spatial velocity gradients (SVGs) inside a block-matching pair will result in tracking error, due to both the finite block size and the ultrasound point-spread-function. We assess, using an in silico sinusoidal flow phantom, the effect of SVG magnitude and beam-to-flow angle on block-matching bias and precision. Secondarily we assess the effect that SVGs have on velocimetry bias when using angled plane-wave compounding. The magnitude and angle of SVGs were varied by adjusting the wavelength and direction of a sinusoidal flow profile. Scatterers displaced by this flow profile were used for simulating ultrasound radio frequency data at discrete time points. After beamforming, the 2-D flow field was estimated using block matching. Two imaging sequences were tested, a single plane-wave and a three-angled plane-wave. Smaller sinusoidal flow wavelengths resulted in increased bias and reduced precision, revealing an inverse relationship between sinusoidal flow wavelength and tracking error, with median errors ranging from 69%-90% for the smallest flow wavelengths (highest SVGs) down to 3%-5% for the largest (lowest SVGs). The SVG angle was also important, in which lateral SVGs (with axially oriented flows) resulted in significant speckle decorrelation and high tracking errors in regions with high SVGs. Conversely, axial SVGs (laterally oriented flow) experienced higher bias in the peak velocity regions of the flow profile. Coherent compounding resulted in higher velocity errors than using a single transmission for lateral SVGs but not for axial SVGs. The highest SVGs that could be measured with ≤10% error was when the sinusoidal flow wavelength was less than 20 times the ultrasound pulse wavelength. The clinical significance is that the high SVGs present in high kinetic energy flows, such as severe carotid stenosis and aortic regurgitation, will limit the ability to accurately quantify the velocities in these flow structures.