### Abstract

Simulation and experimental results from 3-D vector flow estimations for a 62 + 62 2-D row–column (RC) array with integrated apodization are presented. A method for implementing a 3-D transverse oscillation (TO) velocity estimator on a 3-MHz RC array is developed and validated. First, a parametric simulation study is conducted, where flow direction, ensemble length, number of pulse cycles, steering angles, transmit/receive apodization, and TO apodization profiles and spacing are varied, to find the optimal parameter configuration. The performance of the estimator is evaluated with respect to relative mean bias B˜ and mean standard deviation σ˜ . Second, the optimal parameter configuration is implemented on the prototype RC probe connected to the experimental ultrasound scanner SARUS. Results from measurements conducted in a flow-rig system containing a constant laminar flow and a straight-vessel phantom with a pulsating flow are presented. Both an M-mode and a steered transmit sequence are applied. The 3-D vector flow is estimated in the flow rig for four representative flow directions. In the setup with 90° beam-to-flow angle, the relative mean bias across the entire velocity profile is (−4.7, −0.9, 0.4)% with a relative standard deviation of (8.7, 5.1, 0.8)% for (vx , vy, vz). The estimated peak velocity is 48.5 ± 3 cm/s giving a −3% bias. The out-of-plane velocity component perpendicular to the cross section is used to estimate volumetric flow rates in the flow rig at a 90° beam-to-flow angle. The estimated mean flow rate in this setup is 91.2 ± 3.1 L/h corresponding to a bias of −11.1%. In a pulsating flow setup, flow rate measured during five cycles is 2.3 ± 0.1 mL/stroke giving a negative 9.7% bias. It is concluded that accurate 3-D vector flow estimation can be obtained using a 2-D RC-addressed array

Original language | English |
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Journal | I E E E Transactions on Ultrasonics, Ferroelectrics and Frequency Control |

Volume | 63 |

Issue number | 11 |

Pages (from-to) | 1799-1814 |

ISSN | 0885-3010 |

DOIs | |

Publication status | Published - 2016 |

### Keywords

- 3-D vector flow imaging
- Blood flow
- Medical ultrasound
- Row-column addressed arrays
- Transverse oscillation

## Cite this

Holbek, S., Christiansen, T. L., Stuart, M. B., Beers, C., Thomsen, E. V., & Jensen, J. A. (2016). 3-D Vector Flow Estimation With Row–Column-Addressed Arrays.

*I E E E Transactions on Ultrasonics, Ferroelectrics and Frequency Control*,*63*(11), 1799-1814. https://doi.org/10.1109/TUFFC.2016.2582536