A Transverse Oscillation Approach for Estimation of Three-Dimensional Velocity Vectors, Part I: Concept and Simulation Study

A method for 3-D velocity vector estimation us - ing transverse oscillations is presented. The method employs a 2-D transducer and decouples the velocity estimation into three orthogonal components, which are estimated simultane - ously and from the same data. The validity of the method is investigated by conducting simulations emulating a 32 × 32 matrix transducer.

The results are evaluated using two per - formance metrics related to precision and accuracy. The study includes several parameters including 49 flow directions, the SNR, steering angle, and apodization types. The 49 flow direc - tions cover the positive octant of the unit sphere. In terms of accuracy, the median bias is −2%.

The precision of v x and v y depends on the flow angle β and ranges from 5% to 31% rela - tive to the peak velocity magnitude of 1 m/s. For comparison, the range is 0.4 to 2% for v z . The parameter study also reveals, that the velocity estimation breaks down with an SNR between −6 and −3 dB. In terms of computational load, the estimation of the three velocity components requires 0.75 billion floating point operations per second (0.75 Gflops) for a realistic setup.

This is well within the capability of modern scanners.