Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast

Ultrasound Tomography has seen a revival of interest in the past decade, especially for breast imaging, due to improvements in both ultrasound and computing hardware. In particular, three-dimensional ultrasound tomography, a fully tomographic method in which the medium to be imaged is surrounded by ultrasound transducers, has become feasible. In this paper, a comprehensive derivation and study of a robust framework for large-scale bent-ray ultrasound tomography in 3D for a hemispherical detector array is presented. Two ray-tracing approaches are derived and compared. More significantly, the problem of linking the rays between emitters and receivers, which is challenging in 3D due to the high number of degrees of freedom for the trajectory of rays, is analysed both as a minimisation and as a root-finding problem. The ray-linking problem is parameterised for a convex detection surface and three robust, accurate, and efficient ray-linking algorithms are formulated and demonstrated. To stabilise these methods, novel adaptive-smoothing approaches are proposed that control the conditioning of the update matrices to ensure accurate linking. The nonlinear UST problem of estimating the sound speed was recast as a series of linearised subproblems, each solved using the above algorithms and within a steepest descent scheme. The whole imaging algorithm was demonstrated to be robust and accurate on realistic data simulated using a full-wave acoustic model and an anatomical breast phantom, and incorporating the errors due to time-of-flight picking that would be present with measured data. This method can used to provide a low-artefact, quantitatively accurate, 3D sound speed maps. In addition to being useful in their own right, such 3D sound speed maps can be used to initialise full-wave inversion methods, or as an input to photoacoustic tomography reconstructions

Forward model for quantitative pulse-echo speed-of-sound imaging

Computed ultrasound tomography in echo mode (CUTE) allows determining the spatial distribution of speed-of-sound (SoS) inside tissue using handheld pulse-echo ultrasound (US). This technique is based on measuring the changing phase of beamformed echoes obtained under varying transmit (Tx) and/or receive (Rx) steering angles. The SoS is reconstructed by inverting a forward model describing how the spatial distribution of SoS is related to the spatial distribution of the echo phase shift. CUTE holds promise as a novel diagnostic modality that complements conventional US in a single, real-time handheld system. Here we demonstrate that, in order to obtain robust quantitative results, the forward model must contain two features that were not taken into account so far: a) the phase shift must be detected between pairs of Tx and Rx angles that are centred around a set of common mid-angles, and b) it must account for an additional phase shift induced by the error of the reconstructed position of echoes. In a phantom study mimicking liver imaging, this new model leads to a substantially improved quantitative SoS reconstruction compared to the model that has been used so far. The importance of the new model as a prerequisite for an accurate diagnosis is corroborated in preliminary volunteer results

Refraction corrected transmission imaging based on Bézier curves: first results with KIT 3D USCT

AbstractThe computational complexity of wave-based image ultrasound transmission reconstructionsis very high especially in 3D. Hence, ray-based approximations are often used. Bent rayapproaches like the fast marching method are time-consuming in comparison to the straightray approximation. The B ́ezier curve technique for refraction approximation, introduced byPerez-Liva et al., could be a compromise between computational effort and image quality. Inthis work, the method was extended to 3D and an evaluation on two 3D datasets was carriedout. The first dataset was simulated with the k-wave toolbox, with hemispherically arrangedemitters and receivers and a sound speed inhomogeneity. With a mean squared error of 9.98m/s the method produces similar results as the fast marching method (11.85 m/s). The objectsize is represented better in comparison to the straight ray method. Applied to real data ofthe KIT 3D USCT both methods performed similarly. The object size was better preservedusing bent ray methods. The B ́ezier bent ray method shows first promising results in 3D asit leads to similar results than the fast marching method