Abstract
This study designed a novel shear wave Time of Flight (TOF) device to measure frequency-dependent shear wave velocity in tissue-mimicking materials, from which viscoelastic parameters were estimated through Kelvin-Voigt fractional derivative modeling to establish a reliable calibration standard. Tissue-mimicking phantoms were fabricated using 10 wt% polyvinyl alcohol (PVA) and 2 wt% α-alumina powder, with mechanical properties modulated through freeze-thaw cycling. Bimorph transducers operating in the 40-180 Hz range induced and captured shear waves. A single-cycle sine wave excitation ensures narrowband propagation, and a custom algorithm based on the cumulative energy technique robustly detects the shear wave arrival time to estimate TOF. Frequency-dependent shear velocity data were fitted to the Kelvin Voigt fractional derivative (KVFD) model to derive the relaxed elastic modulus (Eo), viscosity (η), and fractional order (α), with Poisson's ratio and damping effects accounted for in the model assumptions. The fitting demonstrated high accuracy, with an R² value of 98.8% (RMSE = 0.013 m/s) for the hard phantom and 99.1% (RMSE = 0.002 m/s) for the soft phantom. Validation with standard rheometer data showed reasonable agreement in elasticity, with percent differences of 2.1% for the hard and 13.3% for the soft phantoms. The latter reflects greater sensitivity to damping effects and assumptions on Poisson's ratio, as reported in previous studies. However, η and α showed larger deviations because they are strongly dependent on the measurement band; therefore, a direct comparison of these parameters across techniques with nonoverlapping frequency ranges is inappropriate. To enable a fair cross-method assessment, we performed band-matched velocity domain projections in both directions using the KVFD forward model and a constrained TOF refit with Eo fixed to the rheometer value. This analysis revealed that the discrepancies in η and α primarily stem from frequency band sensitivity rather than methodological bias. These findings support the shear wave TOF device as a robust, frequency-tunable alternative to rheometry for ex vivo tissue characterization and for calibrating clinical elastography. Its immediate clinical relevance is to provide a rapid and low-cost approach for phantom standardization and to inform elastography parameter settings. Key limitations of the present study are the restriction to ex vivo validation, operation within 40-180 Hz, and use of a dispersion-only inversion model; consequently, the viscous parameters (η, α) are frequency sensitive and not directly comparable to low-frequency rheometry. Future evaluation of in vivo performance and spatial heterogeneity is therefore essential.