Improving the Robustness of Time-of-Flight Based Shear Wave Speed Reconstruction Methods Using RANSAC in Human Liver in vivo

Abstract The stiffness of tissue can be quantified by measuring the shear wave speed (SWS) within the medium. Ultrasound is a real-time imaging modality capable of tracking the propagation of shear waves in soft tissue. Time-of-flight (TOF) methods have previously been shown to be effective for quantifying SWS from ultrasonically tracked displacements. However, the application of these methods to in vivo data is challenging due to the presence of additional sources of error, such as physiologic motion or spatial inhomogeneities in tissue. This article introduces the use of random sample consensus (RANSAC), a model fitting paradigm robust to the presence of gross outlier data, for estimating the SWS from ultrasonically tracked tissue displacements in vivo . SWS reconstruction is posed as a parameter estimation problem and the RANSAC solution to this problem is described. Simulations using synthetic TOF data show that RANSAC is capable of good stiffness reconstruction accuracy (mean error 0.5 kPa) and precision (standard deviation 0.6 kPa) over a range of shear stiffness (0.6–10 kPa) and proportion of inlier data (50%–95%). As with all TOF SWS estimation methods, the accuracy and precision of the RANSAC reconstructed shear modulus decreases with increasing tissue stiffness. The RANSAC SWS estimator was applied to radiation force induced shear wave data from 123 human patient livers acquired with a modified SONOLINE Antares ultrasound system (Siemens Healthcare, Ultrasound Business Unit, Mountain View, CA, USA) in a clinical setting before liver biopsy was performed. Stiffness measurements were not possible in 19 patients due to the absence of shear wave propagation inside the liver. The mean liver stiffness for the remaining 104 patients ranged from 1.3 to 24.2 kPa and the proportion of inliers for the successful reconstructions ranged between 42% to 99%. Using RANSAC for SWS estimation improved the diagnostic accuracy of liver stiffness for delineating fibrosis stage compared with ordinary least squares (OLS) without outlier removal (AUROC = 0.94 for F ≥ 3 and AUROC = 0.98 for F = 4). These results show that RANSAC is a suitable method for estimating the SWS from noisy in vivo shear wave displacements tracked by ultrasound. (E-mail: michael.h.wang@duke.edu )