The choice of viscous or viscoelastic models affects attenuation and velocity determination in simplified skull-mimicking digital phantoms.

Objective: Simulation-guided transcranial focused ultrasound therapies rely on accurately estimating the skull's acoustic properties with pretreatment imaging. The typical imaging resolution (0.5 mm isotropic) is insufficient to resolve the bone microstructure, and as a result, the acoustic properties are underdetermined. Consequently, the determination of acoustic properties is sensitive to methodology. Here, we investigate how viscous or viscoelastic models predict variations in attenuation and phase velocity due to microstructure. Approach: Using viscous and viscoelastic k-Wave implementations, we simulated the transmission of a broadband 625 kHz tone burst ( -6 dB bandwidth: 250 kHz-1 MHz) through skull-mimicking digital phantoms. The phantoms consisted of spherical marrow pores (0.1 mm-1.0 mm diameter) randomly placed within a solid cortical background (2.5%-90% porosity). Virtual sensors measured the attenuation and phase velocity by the time-distance matrix approach. Results: Both models predict that attenuation increases with increasing pore size for a fixed porosity, but the strength of the relationship and its dependence on porosity depend on the simulation technique applied. The viscoelastic model generally predicts that the attenuation peaks at larger porosity values than those predicted by the viscous model. For example, for 1.0 mm pore phantoms, the viscous attenuation peak (1.98 Np/cm) occurs at 20% porosity, while the viscoelastic peak (2.98 Np/cm) occurs at 70%. In general, the phase velocity decreases for larger pore phantoms for both techniques, but the phase velocity/porosity relationship predicted by the viscoelastic model is less sensitive to pore size compared to the viscous model. Significance: Viscous and viscoelastic models predict different attenuation and phase velocity behavior for these idealized bone models. While both approaches predict that properties of bone microstructure have a large impact on acoustic attenuation within the skull, the viscous model indicates that bone microstructure impacts phase velocity within the skull, whereas the viscoelastic model suggests that phase velocity is less sensitive to microstructure. This study highlights the acoustic model's role in predicting transcranial propagation and the need to identify which approach most accurately reflects the physics of the human skull.