Phased-array vector velocity estimation using transverse oscillations

A method for estimating the 2-D vector velocity of blood using a phased-array transducer is presented. The approach is based on the transverse oscillation (TO) method. The purposes of this work are to expand the TO method to a phased-array geometry and to broaden the potential clinical applicability of the method.

A phased-array transducer has a smaller footprint and a larger field of view than a linear array, and is therefore more suited for, e.g., cardiac imaging. The method relies on suitable TO fields, and a beamforming strategy employing diverging TO beams is proposed. The implementation of the TO method using a phased-array transducer for vector velocity estimation is evaluated through simulation and flow-rig measurements are acquired using an experimental scanner.

The vast number of calculations needed to perform flow simulations makes the optimization of the TO fields a cumbersome process. Therefore, three performance metrics are proposed. They are calculated based on the complex TO spectrum of the combined TO fields. It is hypothesized that the performance metrics are related to the performance of the velocity estimates.

The simulations show that the squared correlation values range from 0.79 to 0.92, indicating a correlation between the performance metrics of the TO spectrum and the velocity estimates. Because these performance metrics are much more readily computed, the TO fields can be optimized faster for improved velocity estimation of both simulations and measurements.

For simulations of a parabolic flow at a depth of 10 cm, a relative (to the peak velocity) bias and standard deviation of 4% and 8%, respectively, are obtained. Overall, the simulations show that the TO method implemented on a phased-array transducer is robust with relative standard deviations around 10% in most cases.

The flow-rig measurements show similar results. At a depth of 9.5 cm using 32 emissions per estimate, the relative standard deviation is 9% and the relative bias is ????- ????9%. At the center of the vessel, the velocity magnitude is estimated to be 0.25 ± 0.023 m/s, compared with an expected peak velocity magnitude of 0.25 m/s, and the beam-to-flow angle is calculated to be 89.3° ± 0.77°, compared with an expected angle value between 89° and 90°.

For steering angles up to ±20° degrees, the relative standard deviation is less than 20%. The results also show that a 64-element transducer implementation is feasible, but with a poorer performance compared with a 128-element transducer. The simulation and experimental results demonstrate that the TO method is suitable for use in conjunction with a phased-array transducer, and that 2-D vector velocity estimation is possible down to a depth of 15 cm.