A three-phase poroelastic-scattering model for skull ultrasound transmission and effective porosity inversion

Transcranial ultrasound is increasingly used in brain imaging, neuromodulation, and therapy guidance, but its performance is severely degraded by the skull, whose porous and heterogeneous microstructure induces strong attenuation, scattering, and phase distortion in the MHz range. However, skull-induced transmission loss is still commonly handled empirically, and its quantitative relationship to interpretable microstructural descriptors remains poorly established. In this work, we develop a three-phase poroelastic-scattering model for porous cranial bone , comprising a mineralized matrix, a trabecular/cellular solid component within the pore space, and pore fluid. The model combines a Bruggeman-type effective-medium formulation for elastic properties, Biot-Johnson-Koplik-Dashen (Biot-JKD) dynamic viscous coupling, and a Rayleigh-type scattering term to describe frequency-dependent transmission loss. Numerical analysis shows that the fast compressional mode exhibits a characteristic dependence on frequency and porosity, with attenuation governed jointly by viscous/tortuosity losses and microstructural scattering, while phase velocity is dominated by effective stiffness. The model was calibrated using through-transmission measurements on 3D-printed porous epoxy-alumina phantoms with porosities from 10% to 40%, and was then applied to ex vivo rat and monkey skulls to estimate a local effective porosity from attenuation spectra.For the monkey skull, the ultrasound-derived estimates were consistent with a CT-derived apparent porosity from the same specimen. These results support a microstructure-informed parameterization of skull transmission loss and provide a quantitative basis for skull-aware propagation modeling and compensation in transcranial ultrasound.