Spatio-temporal directional filtering for improved inversion of MR elastography images

Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data

The crawling wave experiment was developed to capture a shear wave induced moving interference pattern that is created by two harmonic vibration sources oscillating at different but almost the same frequencies. Using the vibration sonoelastography technique, the spectral variance image reveals a moving interference pattern. It has been shown that the speed of the moving interference pattern, i.e., the crawling wave speed, is proportional to the shear wave speed with a nonlinear factor. This factor can generate high-speed artifacts in the crawling wave speed images that do not actually correspond to increased stiffness. In this paper, an inverse algorithm is developed to reconstruct both the crawling wave speed and the shear wave speed using the phases of the crawling wave and the shear wave. The feature for the data is the application to in vitro prostate data, while the features for the algorithm include the following: (1) A directional filter is implemented to obtain a wave moving in only one direction; and (2) an L(1) minimization technique with physics inspired constraints is employed to calculate the phase of the crawling wave and to eliminate jump discontinuities from the phase of the shear wave. The algorithm is tested on in vitro prostate data measured at the Rochester Center for Biomedical Ultrasound and University of Rochester. Each aspect of the algorithm is shown to yield image improvement. The results demonstrate that the shear wave speed images can have less artifacts than the crawling wave images. Examples are presented where the shear wave speed recoveries have excellent agreement with histology results on the size, shape, and location of cancerous tissues in the glands.

Shear wave speed recovery in sonoelastography using crawling wave data

The crawling wave experiment, in which two harmonic sources oscillate at different but nearby frequencies, is a development in sonoelastography that allows real-time imaging of propagating shear wave interference patterns. Previously the crawling wave speed was recovered and used as an indicator of shear stiffness; however, it is shown in this paper that the crawling wave speed image can have artifacts that do not represent a change in stiffness. In this paper, the locations and shapes of some of the artifacts are exhibited. In addition, a differential equation is established that enables imaging of the shear wave speed, which is a quantity strongly correlated with shear stiffness change. The full algorithm is as follows: (1) extract the crawling wave phase from the spectral variance data; (2) calculate the crawling wave phase wave speed; (3) solve a first-order PDE for the phase of the wave emanating from one of the sources; and (4) compute and image the shear wave speed on a grid in the image plane.