On the depth-dependent accuracy of plane-wave based vector velocity measurements with linear arrays

High-frame-rate vector Doppler methods are used to measure blood velocities over large 2-D regions, but their accuracy is often estimated over a short range of depths. This paper thoroughly examines the dependence of velocity measurement accuracy on the target position. Simulations were carried out on flat and parabolic flow profiles, for different Doppler angles, and considering a 2-D vector flow imaging (2-D VFI) method based on plane wave transmission and speckle tracking. The results were also compared with those obtained by the reference spectral Doppler (SD) method. Although, as expected, the bias and standard deviation generally tend to worsen at increasing depths, the measurements also show that: (1) the errors are much lower for the flat profile (from ≈-4±3% at 20 mm to ≈-17±4% at 100mm), than for the parabolic profile (from ≈-4±3% to ≈-38±%). (2) Only part of the relative estimation error is related to the inherent low resolution of the 2-D VFI method. For example, even for SD, the error bias increases (on average) from -0.7% (20 mm) to -17% (60 mm) up to -26% (100 mm). (3) Conversely, the beam divergence associated to the linear array acoustic lens was found to have great impact on the velocity measurements. By simply removing such lens, the average bias for 2-D VFI at 60 and 100 mm dropped down to -9.4% and -19.4%, respectively. In conclusion, the results indicate that the transmission beam broadening on the elevation plane, which is not limited by reception dynamic focusing, is the main cause of velocity underestimation in the presence of high spatial gradients.