Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion.

Ultrasound computed tomography (USCT) is a non-invasive imaging technique that provides information about the acoustic properties of soft tissues in the body, such as the speed of sound (SS) and acoustic attenuation (AA). Knowledge of these properties can improve the discrimination between benign and malignant masses, especially in breast cancer studies. Full wave inversion (FWI) methods for image reconstruction in USCT provide the best image quality compared to more approximate methods. Using FWI, the SS is usually recovered in the time domain, and the AA is usually recovered in the frequency domain. Nevertheless, as both properties can be obtained from the same data, it is desirable to have a common framework to reconstruct both distributions. In this work, an algorithm is proposed to reconstruct both the SS and AA distributions using a time domain FWI methodology based on the fractional Laplacian wave equation, an adjoint field formulation, and a gradient-descent method. The optimization code employs a Compute Unified Device Architecture version of the software k-Wave, which provides high computational efficiency. The performance of the method was evaluated using simulated noisy data from numerical breast phantoms. Errors were less than 0.5% in the recovered SS and 10% in the AA.

Beam distortion due to gold fiducial markers during salvage high-intensity focused ultrasound in the prostate.

PURPOSE: High intensity focused ultrasound (HIFU) provides a non-invasive salvage treatment option for patients with recurrence after external beam radiation therapy (EBRT). As part of EBRT the prostate is frequently implanted with permanent fiducial markers. To date, the impact of these markers on subsequent HIFU treatment is unknown. The objective of this work was to systematically investigate, using computational simulations, how these fiducial markers affect the delivery of HIFU treatment. METHODS: A series of simulations was performed modelling the propagation of ultrasound pressure waves in the prostate with a single spherical or cylindrical gold marker at different positions and orientations. For each marker configuration, a set of metrics (spatial-peak temporal-average intensity, focus shift, focal volume) was evaluated to quantify the distortion introduced at the focus. An analytical model was also developed describing the marker effect on the intensity at the focus. The model was used to examine the marker's impact in a clinical setting through case studies. RESULTS: The simulations show that the presence of the marker in the pre-focal region causes reflections which induce a decrease in the focal intensity and focal volume, and a shift of the maximum pressure point away from the transducer's focus. These effects depend on the shape and orientation of the marker and become more pronounced as its distance from the transducer's focus decreases, with the distortion introduced by the marker greatly increasing when placed within 5 mm of the focus. The analytical model approximates the marker's effect and can be used as an alternative method to the computationally intensive and time consuming simulations for quickly estimating the intensity at the focus. A retrospective review of a small patient cohort selected for focal HIFU after failed EBRT indicates that the presence of the marker may affect HIFU treatment delivery. CONCLUSIONS: The distortion introduced by the marker to the HIFU beam when positioned close to the focus may result in an undertreated region beyond the marker due to less energy arriving at the focus, and an overtreated region due to reflections. Further work is necessary to investigate whether the results presented here justify the revision of the patient selection criteria or the markers' placement protocol.

A first-order k-space model for elastic wave propagation in heterogeneous media.

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.