## 4 Discussion  
Plane-by-plane interleaved technique for TVI in a full 3D volume using TO in combination with a cross-correlation estimator was investigated. Implementation and validation was performed by simulations. In this paper TO was combined with a sliding aperture sequence. Figure 8: RSD and RB for 90 degrees beam-to-flow angle and 0 degrees rotation angle, all cross planes along the vessel. The dashed lines show the relative standard deviation, the solid lines show the relative bias. The red color is \(v_{x}\), the black is \(v_{y}\) and the blue is \(v_{z}\) components of the flow. Figure 9: RSD and RB for 60 degrees beam-to-flow angle and 45 degrees rotation angle, all cross planes along the vessel.The dashed lines show the relative standard deviation, the solid lines show the relative bias. The red color is \(v_{x}\), the black is \(v_{y}\) and the blue is \(v_{z}\) components of the flow. The highest RSD is 6.29% and is calculated for the case in which the beam-to-flow angle is 60 degrees and 45 degrees of rotation angle. The lowest RSD is 1.288% for non-zero component and is calculated for 90 degrees beam-to-flow angle and 0 degrees rotation angle. For comparison, a non-interleaved sequence was also simulated with the same setup in all other aspects. Such method was first presented by [PERSON] et al. (2020) who achieved 8.7% of RSD for 90 degree beam-to-flow angle. They used \(f_{prf}\) = 10 kHz and 9 + 11 steered planes. Here, the non-interleaved sequence was simulated for \(f_{prf}\) = 5 kHz and for \(f_{prf}\) = 10 kHz. Figure 10 presents results for 90 degrees beam-to-flow angle and 0 degrees rotation angle for interleaved, non-interleaved with \(f_{prf}\) = 5 kHz and non-interleaved with \(f_{prf}\) = 10 kHz. Cross planes for each velocity component are shown for all three sequences, which were mentioned above. The top line shows cross planes for the interleaved sequence with \(f_{prf}\) = 5 kHz, and the second line shows the non-interleaved sequence with \(f_{prf}\) = 5 kHz. On the bottom line the non-interleaved sequence with \(f_{prf}\) = 10 kHz is shown. As seen, the non-interleaved sequence with \(f_{prf}\) = 5 kHz (middle line) fails to estimate the flow. In comparison, the interleaved sequence and non-interleaved with \(f_{prf}\) = 10 kHz show good results. The time between lines being correlated is \(T_{prf}\) for the interleaved sequence and 22 \(T_{prf}\) for the non-interleaved sequence. At \(v_{peak}\) = 0.3 m/s, the scatterers move 0.06 mm or \(\lambda/8\) between the emissions correlated for interleaved sequence, 1.32 mm or \(2.75*\lambda\) for non-interleaved sequence with\(f_{prf}\) = 5 kHz and 0.66 mm or \(1.38*\lambda\) for non-interleaved sequence with \(f_{prf}\) = 10 kHz. [PERSON] et al designed their sequence in this way to have continuous data throughout the volume ([PERSON] et al., 2020). The interleaved sequence attains this goal with only 1 T  
Figure 10: Cross planes for three representative methods. On the left side is \(v_{x}\), on the middle is \(v_{y}\), on the right is \(v_{z}\) components of the flow. For all situations the beam-to-flow angle was 90 degrees and azimuth rotation angle is 0 degrees. The top row shows a cross planes from the interleaved sequence. The middle row shows cross planes from the non-interleaved sequence with \(f_{prf}\) = 5 kHz, the bottom row shows cross planes from the non-interleaved sequence with \(f_{prf}\) = 10 kHz. Full 3D velocity vector field in a volume by row-column addressed array was presented by [PERSON] el al. [24]. They also used an interleaved sequence and SA imaging, which requires beamforming of the entire volume for all emissions. Our method only needs beamforming of small sub-planes for \(v_{x}\) and \(v_{y}\) components of the flow and only one line for the \(v_{z}\) component. Thus, in the method presented here, the \(v_{z}\) velocity component requires 188 samples to beamform, and the \(v_{x}\) or \(v_{y}\) components requires 1474 samples each. The SA method requires 11 times as many beamforming operations per emission.