Comparison of five viscoelastic models for estimating viscoelastic parameters using ultrasound shear wave elastography

The purpose of this study is to compare five viscoelastic models (Voigt, Maxwell, standard linear solid, spring-pot, and fractional Voigt models) for estimating viscoelastic properties based on ultrasound shear wave elastography measurements. We performed the forward problem analysis, the inverse problem analysis, and experiments. In the forward problem analysis, the shear wave speeds at different frequencies were calculated using the Voigt model for given shear elasticity and varying shear viscosity. In the inverse problem analysis, the viscoelastic parameters were estimated from the given wave speeds for the five viscoelastic models using the least-square regression. The experiment was performed in a tissue-mimicking phantom. A local harmonic vibration was generated via a mechanical shaker on the phantom at five frequencies (100, 150, 200, 250, and 300 Hz) and an ultrasound transducer was used to capture the tissue motion. Shear wave speed of the phantom was measured using the ultrasound shear wave elastography technique. The parameters for different viscoelastic models for the phantom were identified. For both analytical and experimental studies, ratios of storage to loss modulus as a function of excitation frequency for different viscoelastic models were calculated. We found that the Voigt and fractional Voigt models fit well with the shear wave speed - frequency and ratio of storage to loss modulus - frequency relationships both in analytical and experimental studies.