The choice of viscous or viscoelastic models affects attenuation and velocity determination in simplified skull-mimicking digital phantoms
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Simulation-guided transcranial focused ultrasound therapies rely on estimating skull acoustic properties from pretreatment imaging. Typical clinical resolution (0.5 mm isotropic) cannot resolve bone microstructure, making the acoustic properties underdetermined and sensitive to modeling assumptions. Here, we examine how viscous and viscoelastic models predict changes in attenuation and phase velocity due to microstructure. Using viscous and viscoelastic k-Wave implementations, we simulated transmission of a broadband 625 kHz tone burst (250 kHz-1 MHz) through skull-mimicking digital phantoms. The phantoms contained spherical pores (0.1-1.0 mm diameter) randomly embedded within cortical bone (2.5%-90% porosity). Virtual sensors measured attenuation and phase velocity using a time-distance matrix approach. Both models predict increased attenuation with increasing pore size at a fixed porosity, but differ in the strength and porosity dependence of this relationship. The viscoelastic model generally predicts attenuation peaks at higher porosities than the viscous model. For 1.0 mm pores, the viscous peak (1.98 Np/cm) occurs at 20% porosity, while the viscoelastic peak (2.98 Np/cm) occurs at 70%. Phase velocity decreases with pore size for both models, though the viscoelastic predictions are less sensitive to pore size. These results demonstrate that viscous and viscoelastic models exhibit distinct attenuation and phase-velocity behavior for idealized bone microstructures. While both indicate that microstructure has a strong impact on attenuation, it has a lesser effect on phase velocity for the viscoelastic model compared to the viscous model. This work highlights the importance of acoustic model choice when estimating skull acoustic properties from computed tomography images. Future work will identify which acoustic model best represents ultrasound propagation through skull microstructure.
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