Influence of bone microstructure on ultrasound loss through skull-mimicking digital phantoms

Transcranial focused ultrasound treatments rely on precisely delivering ultrasound through the inhomogeneous human skull. Full-wave ultrasound simulations are a means to predict and correct the resulting ultrasound aberrations and attenuation. To do this, the acoustic properties of the skull, including phase velocity and attenuation, must be determined. A common approach relates computed tomography (CT) Hounsfield Units (HU) to these acoustic properties. In the trabecular regions of skulls, the CT HU values will depend on the fraction of bone and marrow within an image volume element, but they are typically insensitive to the microstructure of the bone and marrow.

This study explores the influence of bone/marrow microstructures on determining the relationship of acoustic properties, particularly loss, to CT HUs. The typical clinical CT resolution (0.5 mm) cannot resolve fine trabecular bone microstructure, suggesting the relationship of attenuation to HU may be ill-determined.

The ultrasound insertion loss was found through various skull-mimicking digital phantoms consisting of two constituent materials (red marrow and cortical bone) from 0 to 75% porosity. The phantoms were assigned one of six pore diameters ranging from 0.2 mm to 1.0 mm. Ultrasound simulations were computed using k-Wave with a continuous 230 kHz or 650 kHz uniform pressure source. The insertion loss with and without absorption was defined as the mean pressure through the phantom with respect to the mean pressure in a water-only reference.

The simulations at 230 kHz showed that the loss changed with porosity, but specific microstructure had little effect. However, in both non-absorbing and absorbing 650 kHz source simulations, the insertion loss depended on porosity and pore diameter. Larger pore diameter phantoms generally had higher losses than smaller pore diameter phantoms at the same porosity. In the non-absorbing phantoms, the maximum range in insertion loss was 2% to 52% over the range of pore diameters, which occurred at 20% porosity. Absorbing phantoms increased the loss by an average of 8.2%, with the greatest increase of 13% occurring for the smallest pore diameter at 2.5% porosity. Coherent multiple reflections from the phantom's planar interfaces influenced the loss within smaller pore diameter phantoms. The phase coherence of these reflections was disrupted by increased scattering within the larger pore diameter phantoms.

The results suggest that the relationship between attenuation and clinical HUs is ill-determined at 650 kHz, since the insertion loss depends on both porosity and pore diameter. The demonstrated uncertainty has important implications for developing CT-derived acoustic models of skull bone, as no single attenuation value can be related to HUs comprised of variable microstructures. Generally, our results show larger pore diameters (coarse microstructures) have higher loss than smaller pore diameters (fine microstructures) at the same porosity, which is consistent with scattering theory.