Modified Power Law Dispersion Model for Shear Waves in Soft Tissues

Biological tissues display frequency-dependent non-linear dispersion in shear wave dispersion imaging. The dispersive behavior is due to the viscosity of soft tissues and may be correlated with tissue pathology. This study presents an empirically modified power law dispersion model that incorporates tissue nonlinearity and improves the dispersion modeling in shear wave elastography across an extended frequency bandwidth. The model was validated using numerically simulated phantoms, synthetic phantoms, and ex vivo goat muscle and liver tissues. The results demonstrate a higher goodness of fit compared to conventional models, including the Kelvin–Voigt, linear, and power-law dispersion models. Shear wave phase velocity, dispersion, and concavity maps are reconstructed in phantoms and ex vivo tissue samples. Quantitative values of dispersion are obtained as 1.55 ± 0.67 m/s/100 Hz and 1.68 ± 0.38 m/s/100 Hz in CIRS and PVA phantoms, respectively, and 3.16 ± 0.89 m/s/100 Hz and 1.44 ± 0.58 m/s/100 Hz in ex vivo goat muscle and liver tissues, respectively. The corresponding values of concavity are 4.12±2.11 m/s/kHz and 4.11±0.92 m/s/kHz in CIRS and PVA phantoms, respectively, and 6.52±2.71 m/s/kHz and 3.53±1.72 m/s/kHz in ex vivo goat muscle and liver tissues, respectively.