A mathematical approach to mitigate the impact of compression waves in shear wave elastography

Shear wave elastography (SWE) has emerged as a valuable imaging technique across several modalities such as ultrasound, magnetic resonance imaging, and optical coherence tomography. Its capacity to assess tissue stiffness and identify lesions positions it as a promising clinical tool for diagnosing a wide range of diseases. The primary aim of SWE is to measure shear wave speed (SWS); however, unwanted compression waves and bulk tissue motion can complicate this process. Conventional methods, in many cases, face challenges in separating shear and compression waves, resulting in inaccurate SWS measurements. This study introduces a novel estimator, called integrated difference autocorrelation (IDA), designed to specifically estimate reverberant shear wave speed in the presence of compression waves and noise. Unlike conventional methods, the IDA estimator computes the velocity differences between adjacent particles, effectively mitigating the impact of long-wavelength compression waves and other wide-area movements like those induced by respiration. The effectiveness of the IDA estimator was assessed through several approaches: elastography simulation of a y-shaped cylinder in a soft background, magnetic resonance elastography (MRE) on a brain phantom with two lesions, ultrasound elastography on a breast phantom with a lesion, and ultrasound elastography in the human liver-kidney region. Our findings indicate that the IDA estimator provides accurate SWS estimates (within 19% of reference) even in the presence of strong compression waves that can cause earlier estimators to completely fail. Moreover, the IDA estimator demonstrates consistent performance across different modalities and excitation scenarios, underscoring its robustness and potential clinical applicability.