Quantifying attenuation and scattering in skull-like phantoms using the spectral element method

In both geophysics and medical physics, the propagation of seismic waves through highly complex, heterogeneous viscoacoustic-viscoelastic media follows the same physical principles. The attenuation of seismic waves in the Earth's heterogeneous interior is identical to the way ultrasound waves behave when passing through the human skull or bones (transcranial ultrasound).
In this work, we utilize the core concepts of wave physics and spectral element method (SEM), a well-known numerical simulation technique within geophysics that is used to study the scattering and attenuation caused by the skull during transcranial ultrasound. In the Earth, P-waves can convert to S-waves at interfaces; similarly, at the interface of the skull, ultrasound undergo mode conversions, and also generates Lamb waves, which further complicates the energy transmission. Despite the massive difference in physical scale, both medical ultrasound and geophysics involve a similar number of wavelengths between the source and receiver.

The interface between the skull and soft brain tissue creates a high impedance contrast causing most of the energy to reflect and only a small amount of energy is transmitted through skull.
3D numerical phantoms replicating skull-like properties with varying thicknesses were constructed. SEM, a high-order numerical modeling technique, is used for full waveform modeling of both elastic-acoustic and viscoacoustic-viscoelastic waves through heterogeneous media. A conformal hexahedral mesh is implemented to precisely resolve the irregular geometry of the bone. This ensures that the simulated reflections and refractions are physically accurate and thereby avoid numerical staircasing artifacts. 

The difference in the amplitude and waveform propagation is studied between the acoustic-elastic and viscoacoustic-viscoelastic mediums. Elastic modeling assumes energy is conserved, while viscoelastic modeling incorporates the quality factor (Q) to simulate intrinsic attenuation. 
Amplitude decay measures the difference between the peak pressure value of the transmitted waves. Amplitude decay and difference between wavefields are analyzed to quantify how the heterogeneous internal structure affects the wavefront, and also demonstrating that SEM, a proven geophysical method, effectively simulates and quantifies medical ultrasound wave propagation.