Improved frequency-shift method for shear wave attenuation computation

Ultrasound shear wave elastography and assessment of attenuation can increase the diagnostic accuracy of numerous diseases. The main objective of this work was to propose two improvements to the frequency shift (FS) method for shear wave attenuation assessment. First, the shape parameter of the gamma distribution employed to fit the spectrum amplitude of shear waves now varies spatially. Second, a random sample consensus (RANSAC) line fitting method is utilized for calculating the attenuation due to its superiority in the presence of noise and outliers. The shear wave propagation in a tissue-mimicking numerical phantom was modeled as a Kelvin-Voigt (KV) viscoelastic material with finite element (FE) simulations in COMSOL. The shear wave amplitude spectrum was fit using a gamma distribution function, and the slope of the rate parameter of this function obtained by the RANSAC method provided the attenuation coefficient. This method was applied to two numerical phantoms (viscosity of 0.5 and 2 Pa.s), two experimental tissue-mimicking viscoelastic phantoms, and two ex vivo blood clot samples embedded in phantoms. Numerical phantoms were also investigated in the presence of Gaussian random noise at SNR levels of 20 dB to 0 dB. Results were compared with FS, two-point frequency shift (2P-FS) method, and attenuation measuring ultrasound shear wave elastography (AMUSE) method. Mean values of the attenuation coefficient, averaged over a region of interest, were compared between implemented methods. For simulations at different SNRs, the proposed, 2P-FS and AMUSE methods gave mean values close to the KV model. At a SNR of 0 dB, biases of the proposed method were 0.0025 and 0.0258 Np/m/Hz, and variances were 0.0024 and 0.0158 (Np/m/Hz)
²
, for viscosities of 0.5 and 2 Pa.s, respectively. For homogeneous gel phantoms, mean values of the proposed method were: #1) 0.4351; #2) 0.4621. For blood clot phantoms, mean values were: #1) 0.2573; #2) 0.9875. Biases of the proposed method compared to KV or AMUSE were smaller for numerical phantoms, whereas its variance was less than 2P-FS for all datasets.