Real-time Regularized Tracking of Shear-Wave in Ultrasound Elastography

Elastography is a convenient and affordable method for imaging mechanical properties of tissue, which are often correlated with pathologies. An emerging novel elastography technique applies an external acoustic radiation force (ARF) to generate shear-wave in the tissue which are then tracked using ultrasound imaging. Accurate tracking of the small tissue motion (referred to as tissue displacement) is a critical step in shear-wave elastography, but is challenging due to various sources of noise in the ultrasound data. I formulate tissue displacement estimation as an optimization problem and propose two computationally efficient approaches to estimate the displacement field. The first algorithm is referred to as dynamic programming analytic minimization (DPAM), which utilizes first order Taylor series expansion of the highly nonlinear cost function to allow for its efficient optimization. DPAM was previously proposed for quasi-static elastography and I extend the approach to shear-wave elastography. The second algorithm is a novel technique that exploits second-order Taylor expansion of the non-linear cost function. I call the new algorithm as second-order analytic minimization elastography (SESAME). I compare DMAP and SESAME to the standard normalized Cross Correlation (NCC) approach in the context of estimating displacement and elasticity of the medium for shear-wave elastography (SWE). The results of micrometer-order displacement estimation in a uniform simulation phantom illustrate that SESAME outperforms DPAM, which in turn outperforms NCC in terms of signal to noise ratio (SNR) and jitter. In addition, the relative difference between true and reconstructed shear modulus (averaged over several excitations focusing at different focal depths with different scatterers realizations at each depth) is approximately 3.41%, 1.12% and 1.01%, respectively, for NCC, DPAM and SESAME. The performance of the proposed methods is also assessed with real data acquired using a tissue-mimicking phantom, wherein, in comparison to NCC, DPAM and SESAME improve the SNR of displacement by 7.6 dB and 9.5 dB, respectively. Experimental results on a tissue-mimicking phantom also show that shear modulus reconstruction is more accurate with DPAM and SESAME in comparison with NCC