Shape Optimization for Transcranial Ultrasound Computed Tomography

Using waveform-based inversion methods within transcranial ultrasound computed tomography is an attractive emerging reconstruction technique for imaging the human brain. However, such imaging approaches generally rely on possessing an accurate model of the skull in order to account for the complex interactions which occur when the ultrasound waves propagate between soft tissue and bone. In order to recover the shape of the skull within the context of full-waveform inversion, adjoint-based shape optimization is performed within this study. The gradients with respect to the acoustic properties of the tissues which are used in conventional full-waveform inversion act as a proxy for estimating the sensitivities to the shape of the skull. These shape derivatives can be utilized to update the interface between the interior brain tissue and the skull. This technique employs the spectral-element method for solving the wave equation and, thus, allows for the use of a convenient framework for representing the skull interfaces throughout the inversion. Adaptations of the Shepp-Logan phantom are used as a proof of concept to demonstrate this inversion strategy where both the shape of the skull as well as the interior brain tissue are imaged sequentially.