On-axis radiation-force-based quantitative stiffness estimation with a Bayesian displacement estimator

In traditional shear wave elasticity imaging (SWEI), shear wave velocity is measured away from the acoustic radiation force (ARF) axis. Instead, we measure the time-to-peak displacement of tissue directly along the ARF axis. Measuring displacements along this axis rather than off-axis simplifies hardware required for quantifying tissue stiffness. Previously this method has been demonstrated, but the measurement variance was too high for practical feasibility. To reduce stiffness estimation error, we apply our Bayesian displacement estimator. To evaluate the Bayesian estimator, we used 3D finite element analysis to model soft tissue response to the acoustic radiation force and Field II to simulate the radio-frequency (RF) data of the tissue response. The Bayesian displacement estimator is applied to RF data to improve tissue displacement estimates, which then improves time-to-peak displacement estimates and the final stiffness estimate. Time-to-peak displacement is proportional to shear wave speed if we assume the medium is linear, elastic, and isotropic. Here, shear wave speed is directly related to shear stiffness, and we create look-up tables to estimate stiffness using time-to-peak displacement as a function of depth. We modeled an L12-5 50 mm linear transducer with a transmit frequency of 7.8 MHz, 2 cm focus, and push F/2.5. The average displacement data from 20 speckle realizations of each tissue stiffness were used to generate the stiffness look-up tables. Our Bayesian displacement estimator had lower mean square error (MSE) in stiffness estimates compared to using a traditional Normalized Cross-Correlation (NCC) estimator.