Optimization of Transverse Oscillating Fields for Vector Velocity Estimation with Convex Arrays

A method for making Vector Flow Images using the transverse oscillation (TO) approach on a convex array is presented. The paper presents optimization schemes for TO fields for convex probes and evaluates their performance using Field II simulations and measurements using the SARUS experimental scanner.

A 3 MHz 192 elements convex array probe (pitch 0.33 mm) is used in both simulations and measurements. An F-number of 5 is used in transmit and two 32 element wide peaks are used in receive separated by 96 elements between peaks. Parabolic velocity profiles are simulated at beam-to-flow angles from 90 to 45 degrees in steps of 15 degrees.

The optimization routine changes the lateral oscillation period lx to yield the best possible estimates based on the energy ratio between positive and negative spatial frequencies in the ultrasound field. The basic equation for lx gives 1.14 mm at 40 mm, and 1.51 mm from the simulated point spread function.

This results in a bias of 35% as lx directly scales the estimated velocities. Optimizing the focusing yields a lx of 1.61 mm. The energy ratio is reduced from -12.8 dB to -20.1 dB and the spectral bandwidth from 115.1 m􀀀1 to 96.5 m􀀀1. lx is maintained between 1.47 and 1.70 mm from 25 mm to 70 mm and is increased to 2.8 mm at a depth of 100 mm.

Parabolic profiles are estimated using 16 missions. The optimization gives a reduction in std. from 8.5% to 5.9% with a reduction in bias from 35% to 1.02% at 90 degrees (transverse flow) at a depth of 40 mm. Measurements have been made using the SARUS experimental ultrasound scanner and a BK Medical 8820e convex array transducer.

Sixty-four elements was used in transmit and 2 x 32 elements in receive for creating a color flow map image of a flow rig phantom with a laminar, parabolic flow. At 75 degrees a bias of less than 1% was obtained.