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 λ_x 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 λ_x 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 λ_x directly scales the estimated velocities. Optimizing the focusing yields a λ_x 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. λ_x 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 emissions. 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 × 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.