Adaptive motion estimation of shear shock waves in soft solids and tissue with ultrasound

Shear shock waves in soft solids, such as in tissue, have different regions of complex motion that can change rapidly across a single wave profile, especially at the shock front. Conventional tracking algorithms are not well adapted to the task of simultaneously tracking the discontinuous shock front and smooth regions away from the shock. An adaptive algorithm based on the normalized cross-correlation and a correlation-weighted median filter is presented. The proposed adaptive algorithm combines two features: first, it adapts the window size to optimize the correlation value based on the deformation, and second, it rejects inaccurate estimates with a median-weighted filter. For simulated ultrasound data, where the displacements are known, it is shown that the estimated velocity error for the adaptive algorithm is less than 1/3 of the error for non-adaptive normalized cross-correlation. The addition of the weighted median filter to the adaptive algorithm significantly improves the shock tracking performance. The shock position and rise-time error is almost an order of magnitude better with the median-weighted filter. This algorithm is then used to track shock wave propagation with data acquired by a high-frame-rate ultrasound scanner in a tissue-mimicking agar and gelatin phantom. The shock front is not resolved with conventional algorithms but it is clearly visible with the proposed adaptive median-weighted algorithm.