Attenuation, scattering, and absorption of ultrasound in the skull bone

Measured values of ultrasound attenuation in bone represent a combination of different loss mechanisms. As a wave is transmitted from a fluid into bone, reflections occur at the interface. In the bone, mode conversion occurs between longitudinal and shear modes and the mechanical wave is scattered by its complex internal microstructure. Finally, part of the wave energy is absorbed by the bone and converted into heat. Due to the complexity of the wave propagation and the difficulty in performing measurements that are capable of separating the various loss mechanisms, there are currently no estimates of the absorption in bone. The aim of this paper is, thus, to quantify the attenuation, scattering, and thermal absorption in bone.

An attenuating model of wave propagation in bone is established and used to develop a three-dimensional finite difference time domain numerical algorithm. Hydrophone and optical heterodyne interferometer measurements of the acoustic field as well as a x-ray microtomography of the bone sample are used to drive the simulations and to measure the attenuation. The acoustic measurements are performed concurrently with an infrared camera that can measure the temperature elevation during insonication. A link between the temperature and the absorption via a three-dimensional thermal simulation is then used to quantify the absorption coefficients for longitudinal and shear waves in cortical bone.

We demonstrate that only a small part of the attenuation is due to absorption in bone and that the majority of the attenuation is due to reflection, scattering, and mode conversion. In the nine samples of a human used for the study, the absorption time constant for cortical bone was determined to be 1.04 μs ± 28%. This corresponds to a longitudinal absorption of 2.7 dB/cm and a shear absorption of 5.4 dB/cm. The experimentally measured attenuation across the approximately 8 mm thick samples was 13.3 ± 0.97 dB/cm.

This first measurement of ultrasound absorption in bone can be used to estimate the amount of heat deposition based on knowledge of the acoustic field.