The speed of sound in skull-mimicking digital phantoms depends on the microstructure

Objective.Transcranial focused ultrasound therapies depend on accurately focusing the ultrasound beam through the skull. Simulated phase aberration correction with properties derived from computed tomography (CT) can partially restore the focus. However, the typical clinical CT resolution (0.5 mm isotropic) cannot resolve the bone microstructure, introducing uncertainty in the velocity relationship to CT Hounsfield units (HUs), which reduces focusing precision.Approach.To demonstrate this, we simulated through-transmission measurements through skull-mimicking digital phantoms consisting of cortical bone and marrow with porosities ranging from 0% to 80%. The phantoms comprised spherical marrow pores (0.1-0.6 mm diameter) randomly placed into a cortical background, forming fine-to-coarse microstructures. Using k-Wave, we simulated pulsed and continuous planar sources at four center frequencies (250 kHz, 500 kHz, 750 kHz, 1 MHz). Group and phase velocities are reported for each pore diameter and porosity. The steady-state phase is reported through representative phantoms.Main results.The velocity varies with pore diameter and porosity, with smaller pores yielding faster velocities than larger pores at the same porosity. At 25% porosity and 500 kHz, group velocity ranges from 3147 to 2211 m s^-1and phase velocity from 3168 to 2345 m s^-1across 0.1-0.6 mm pore diameters. The steady state phase depends on the pore diameter and frequency, with the variation across the measurement plane broadening as both increase, indicating dependence on the microstructure's pore distribution.Significance.The results indicate that the velocity relationship to CT HUs is ill-determined due to the unresolved microstructure. The variation in group velocity impacts pulsed sources, such as those used for histotripsy, while variation in phase velocity affects quasi-continuous sources, including those used for neuromodulation and thermal ablation. Our results emphasize the need to account for the skull microstructure for safer and more effective transcranial focusing.