On the precision of time-of-flight shear wave speed estimation in homogeneous soft solids: initial results using a matrix array transducer

A system capable of tracking radiation-force-induced shear wave propagation in a 3-D volume using ultrasound is presented. In contrast to existing systems, which use 1-D array transducers, a 2-D matrix array is used for tracking shear wave displacements. A separate single-element transducer is used for radiation force excitation. This system allows shear wave propagation in all directions away from the push to be observed. It is shown that for a limit of 64 tracking beams, by placing the beams at the edges of the measurement region of interest (ROI) at multiple directions from the push, time-of- flight (TOF) shear wave speed (SWS) measurement uncertainty can theoretically be reduced by 40% compared with equally spacing the tracking beams within the ROI along a single plane, as is typical when using a 1-D array for tracking. This was verified by simulation, and a reduction of 30% was experimentally observed on a homogeneous phantom. Analytical expressions are presented for the relationship between TOF SWS measurement uncertainty and various shear wave imaging parameters. It is shown that TOF SWS uncertainty is inversely proportional to ROI size, and inversely proportional to the square root of the number of tracking locations for a given distribution of beam locations relative to the push. TOF SWS uncertainty is shown to increase with the square of the SWS, indicating that TOF SWS measurements are intrinsically less precise for stiffer materials.