Constructing a physics-augmented digital twin of the skull is imperative for a wide range of transcranial ultrasound applications including ultrasound computed tomography and focused ultrasound therapy. The high impedance contrast as well as the acoustic-elastic coupling observed between soft tissue and bone increase the complexity of the ultrasound wavefield considerably, thus emphasizing the need for waveform-based inversion approaches. This work applies reverse time migration in conjunction with the spectral-element method to an in vitro human skull to obtain a starting model, which can be used for full-waveform inversion and adjoint-based shape optimization. Two distinct brain phantoms are considered where the cranial cavity of the in vitro human skull was filled with (1) homogeneous water and (2) gelatin with two cylindrical inclusions. A 2D slice through the posterior of the skull was collected using a ring-like aperture consisting of 1024 ultrasound transducers with a bandwidth of approximately 1MHz to 3MHz. Waveform-based reverse time migration was then used to resolve the inner and outer contours of the skull from which a conforming hexahedral finite-element mesh was constructed. The synthetically generated measurements which are obtained by solving the coupled acoustic-viscoelastic wave equation are in good agreement with the observed laboratory measurements. It is demonstrated that using this revised wave speed model for recomputing the reverse time migration reconstructions allows for improved localization of the gelatin inclusions within the cranial cavity.
We present a full-waveform inversion (FWI) of an in-vivo data set acquired with a transmission-reflection optoacoustic ultrasound imaging platform containing a cross-sectional slice through a mouse. FWI is a high-resolution reconstruction method that provides quantitative images of tissue properties such as the speed of sound. As an iterative data-fitting procedure, FWI relies on the ability to accurately predict the physics of wave propagation in heterogeneous media to account for the non-linear relationship between the ultrasonic wavefield and the tissue properties. A key component to accurately predict the ultrasonic field numerically is a precise knowledge of the source characteristics. For realistic problems, however, the source-time function is generally unknown, which necessitates an auxiliary inversion that recovers the time series for each transducer. This study presents an updated sound speed reconstruction of a cross-section through a mouse using source wavelets that are inverted individually per transducer. These source wavelets have been estimated from a set of observed data by application of a source-wavelet correction filter, which is equivalent to a water-level deconvolution. Compared to previous results, the spatial resolution of anatomical features such as the vertebral column is increased whilst artefacts are suppressed.
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.
Full-waveform modelling serves as the basis for many emerging inversion techniques within ultrasound computed tomography. Being able to accurately depict strong material interfaces, such between soft tissue and bone, is particularly important for ensuring that these numerical methods produce physically correct results. We present a procedure for constructing digital twins of various parts of the human body through the use of conforming hexahedral meshes, which are used together with the spectral-element method to accurately model the interactions of the ultrasound wavefield at these sharp material boundaries. In silico cranial and knee phantoms are used as examples.
Full-waveform inversion (FWI) for ultrasound computed tomography is an advanced method to provide quantitative and high-resolution images of tissue properties. Two main reasons hindering the widespread adoption of FWI in clinical practice are (1) its high computational cost and (2) the requirement of a good initial model to mitigate the non-convexity of the inverse problem. The latter is commonly referred to as “cycle-skipping", which occurs for phase differences between synthetic and observed signals and usually traps the inversion in a local minimum. Source-encoding strategies, which simultaneously activate several emitters and have been proposed to reduce the simulation cost, further contribute to this issue due to the multiple arrivals of the wavefronts. We present a time-domain acoustic full-waveform inversion strategy utilizing a recently proposed misfit functional based on optimal transport. Using a graph-space formulation, the discrepancy between simulated and observed signals can be computed efficiently by solving an auxiliary linear program. This approach alleviates the common need for either a good initial model and / or low-frequency data. Furthermore, combining this misfit functional with random source-encoding and a stochastic trust-region method significantly reduces the computational cost per FWI iteration. In-silico examples using a numerical phantom for breast screening ultrasound tomography demonstrate the ability of the proposed inversion strategy to converge to the ground truth even when starting from a weak prior and cycle-skipped data.
We aim to construct the signal between two points inside a model of the human skull as if there were virtual transducers located inside the skull. We show how this can be achieved through the use of time-reversed Green's functions that are measured on opposite sides of the skull. We then demonstrate how to achieve similar results using special wavefields named focusing functions, which are designed to work specifically when injected from a single-side of the medium of interest. We show two ways to obtain these focusing functions, through the use of the iterative Marchenko method and by inversion of a measured Green's function. The inversion of the Green's function shows potential benefits over the use of the Marchenko method, however, this approach requires further studies. We demonstrate how these wavefields function on 2D acoustic in silico data by injecting the time-reversed Green's functions and focusing functions into the model. We also demonstrate how the response between virtual transducers can be obtained directly through use of the homogeneous Green's function representation.
Full-waveform inversion applied to ultrasound computed tomography is a promising technique to provide highresolution quantitative images of soft human tissues, which are otherwise difficult to illuminate by conventional ultrasound imaging. A particular challenge which arises within transcranial ultrasound is the imprint of the solid skull on the measured wavefield. We present an acoustoelastic approach to full-waveform inversion for transcranial ultrasound computed tomography that accurately accounts for the solid-fluid interactions along the skull-tissue interfaces. Using the spectral-element method on cubical meshes, we obtain a scalable and performant method to resolve such a coupled physical system. Moreover, since the volume of the skull is small compared to the entire simulation domain, solving a coupled system of the acoustoelastic wave equation increases the computational cost only by a small margin compared to the acoustic approximation. We perform an in silico forward and inverse modeling study that reveals significant coupling effects at the skull-tissue interfaces when considering the skull as an elastic medium as opposed to an acoustic medium. Applying full-waveform inversion to a set of synthetically generated acoustoelastic forward data allows for favorable reconstructions to be achieved when considering an acoustoelastic prior model of the skull.
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