Robust hepatic shear modulus reconstruction using acoustic radiation force and RANSAC

Liver stiffness may be useful for the staging and management of hepatic fibrosis. Liver shear modulus can be quantified by measuring the shear wave speed (SWS) in the liver using time-of-flight (TOF) methods. In in vivo patient data, this approach is susceptible to gross outliers in the measured shear wave arrival times due to inhomogeneities in the liver and physiological motion. Linear regression and averaging are not suitable for dealing with this type of error, which can lead to skewed SWS reconstructions. Therefore, the use of random sample consensus (RANSAC), an iterative fitting approach robust to outliers, was investigated for estimating SWS from patient livers. Shear waves were generated in the livers of 105 patients immediately before biopsy using acoustic radiation force and were tracked by ultrasound. 6-12 shear wave acquisitions were performed on each patient. RANSAC was able to reconstruct the shear modulus in 86 patients (82%). Unsuccessful reconstructions were typically associated with shear wave displacements of low amplitude. The biopsy results for 79 patients with at least one valid stiffness measurement were available. The stiffness for healthy to mildly fibrotic (F0-F2) livers (N = 64) was 3.03 ± 1.1 kPa (mean ± standard deviation), for severely fibrotic (F3) livers (N = 12) was 6.3 ± 2.8 kPa, and for cirrhotic (F4) livers (N = 3) was 17.8 ± 7.8 kPa. This trend of increasing liver stiffness with fibrosis stage has also been observed by other groups using alternative modalities of shear wave imaging. These results show that RANSAC is a suitable method for SWS estimation from in vivo ultrasonically tracked shear wave displacements.