Transcranial ultrasound modeling using the spectral-element method

This work explores techniques for accurately modeling the propagation of ultrasound waves in lossy fluid-solid media, such as within transcranial ultrasound, using the spectral-element method. The objectives of this work are twofold, namely, (1) to present a formulation of the coupled viscoacoustic-viscoelastic wave equation for the spectral-element method in order to incorporate attenuation in both fluid and solid regions and (2) to provide an end-to-end workflow for performing spectral-element simulations in transcranial ultrasound. The matrix-free implementation of this high-order finite-element method is very well-suited for performing waveform-based ultrasound simulations for both transcranial imaging and focused ultrasound treatment thanks to its excellent accuracy, flexibility for dealing with complex geometries, and computational efficiency. The ability to explicitly mesh distinct interfaces between regions with high impedance contrasts eliminates staircasing artifacts, which are otherwise non-trivial to mitigate within discretization approaches based on regular grids. This work demonstrates the efficacy of this modeling technique for transcranial ultrasound through a number of numerical examples. While the examples in this work primarily focus on transcranial applications, this type of modeling is equally relevant within other soft tissue-bone systems such as in limb or spine imaging.