## 4 Discussion
In Table 2 the results of [PERSON] et al and the method in this work are compared. The top part shows the RSD and RB for 90 degrees beam-to-flow angle and 45 degrees rotation angle. The bottom part shows the RSD and RB for 60 degrees beam-to-flow angle and 45 degrees rotation angle. Our method attains a smaller RSD, but a higher RB. However, the small RSD enables compensating for the RB. [PERSON] et al. [25] expanded [PERSON]'s work [24] to add motion correction to improve the velocity estimation. However, due the motion correction the SA beamforming needs to be done multiple times for each estimate. It improved on the method without motion compensation, but at the expense of at least twice higher computational complexity than SA flow without motion compensation. TVI has been investigated in other works as well. [PERSON] et al. [34] did TVI using a fully addressed, 1024 element matrix array and synthetic aperture imaging. A RSD of 1.46% was attained for the same range of vessel orientations, but at a more shallow depth. This study also used SA imaging with beamforming of the full volume for all emissions. It used a 1024-element fully addressed array, which require 8 times more channels for 1/4 surface area of the array at the same center frequency compared to RC addressed array. Scaling the fully addressed array to the same size as the 62 + 62 RC array used in this work, the computational complexity is increased 62 times in addition to the increase in complexity from SA imaging. Such a method would furthermore require a system with 4 k channels, which is 16 times more than modern commercial systems have. [PERSON] et al. [16] presented 4D vector flow imaging using a commercial 2D matrix array transducer with ECG-gating. The ECG-gating is utilized to separate a full volume \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{90 degrees beam-to-flow, 45 degrees rotation angle} \\ \hline Parameters & Schou’s results & our results \\ \hline RSD \(v_{x}\) & 3.3 & 1.32 \\ \hline RSD \(v_{y}\) & 3.4 & 1.19 \\ \hline RSD \(v_{z}\) & 0.4 & 0.44 \\ \hline RB \(v_{x}\) & \(-\)3.3 & 10.3 \\ \hline RB \(v_{y}\) & \(-\)3.9 & 9.75 \\ \hline RB \(v_{z}\) & \(-\)0.1 & 0.45 \\ \hline \multicolumn{1}{c}{60 degrees beam-to-flow, 45 degrees rotation angle} \\ \hline Parameters & [PERSON]’s results & our results \\ \hline RSD \(v_{x}\) & 8.9 & 4.95 \\ \hline RSD \(v_{y}\) & 9.1 & 6.29 \\ \hline RSD \(v_{z}\) & 0.8 & 1.06 \\ \hline RB \(v_{x}\) & \(-\)7.6 & \(-\)13.5 \\ \hline RB \(v_{y}\) & \(-\)9.5 & \(-\)9.09 \\ \hline RB \(v_{z}\) & \(-\)7.2 & 14.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of [PERSON]’s method [24] and our method. into multiple sub-volume acquisitions. They also used a subaperture beamforming (SAP) to perform a partial in-probe beamforming to reduce the number of channels coming from the transducer with a subsequent beamforming stage in the system. After that to make second beamforming stage is necessary. The computational complexity of this method is comparable with SA imaging. RSD and RB were presented in absolute units (m/s) and from a different evaluation setup with a spinning disk. By normalizing with the peak velocity of this disk as done in (7), gives a RSD of 1 to 3%, which is comparable to the results of the method presented here. Commercial ultrasound systems handle 128-256 transducer channels, and they can beamform around 16-32 lines in parallel. These values are comparable to the method, presented here. The computational complexity thus is similar to what is performed in modern ultrasound systems, and this method should be implementable on such systems. In comparison, SA imaging or other methods with similar computational complexity can currently not be implemented in real-time on such systems. In the review paper by [PERSON] et al. [35] results for different techniques were presented. For 2D vector flow imaging (VFI) RSD is typically between 5.5% and 14.7%. As was shown in this work, TVI with low computational complexity can provide similar precision.