(a) MRI pulse sequence diagram and assumed displacement of the phantom or tissue at the focus for the different experimental groups. For the first group of experiments, a 42 ms ultrasound pulse began concurrently with the first displacement-encoding gradient and ended immediately after the second slice select gradient. In the second group, the second encoding gradient was used to encode the displacement. This scheme avoided error caused by motion during the encoding gradients but required a longer (75 ms) ultrasound pulse. Assuming that the displacement at the focus due to radiation force was static during the encoding gradients, the phase difference of the MR signal between two acquisitions with opposite encoding polarities was simply proportional to the focal displacement induced by radiation force multiplied by the displacement-encoding gradient strength and the duration . (U.S.: ultrasound.)
Line scan acquisition. (a) Two slice select gradients were applied to select a column. Applying a gradient along the column direction during readout resulted in a one-dimensional array of data with each acquisition. To avoid saturation of neighboring regions by the slice-select gradients, their orientation was rotated approximately with respect to the normal to the imaging plane. This particular angle was selected based on the geometry of the columns. As implemented, approximately 75% of the signal arises from a mm region in the center of each column. Two-dimensional images were created by tiling these columns into a plane. (b) The orientation of the imaging plane and the direction of the displacement encoding could be selected by the user. Separate tests were performed with them either parallel or perpendicular to the direction of the ultrasound beam. In all tests, the columns were oriented perpendicular to the ultrasound beam direction. (U.S.: ultrasound.)
MR-ARFI examples showing displacement at and around the focal spot in the silicone phantom during ultrasound pulses at different acoustic power levels from experimental group 2. Images and plots acquired along the direction of the ultrasound beam (solid lines) and perpendicular to it in the focal plane (dotted lines) are shown. The top image in each pair was oriented along the direction of the ultrasound beam. The bottom image in each pair was acquired perpendicular to this direction in the focal plane. The direction of the displacement-encoding gradients was parallel to the direction of the ultrasound beam. The average of three lines is shown in the plots.
Measurements of the focal displacement as a function of the acoustic power during sonication in the silicone phantom from experimental group 2. At the five lowest powers tested, a linear dependence was observed. Inset: At the two highest powers tested, a large increase in displacement was observed, which was correlated with changes in the phantom that were seen after the experiments. Sonicating at 4.1 W after these higher power sonications yielded a larger displacement than previous sonications at this power. Dotted lines show linear regression of the data at the different imaging orientations ( for both).
MR-ARFI during sonications in the phantom using different phased array patterns. With “mode 0,” all the phased array elements were in phase. In mode 2 and mode 4, multiple focal spots were produced in the shape of a ring around the axis of the ultrasound beam. At the higher modes, the distribution was less sharp and produced only slightly less displacement for the same acoustic power (5.7 W). The images are oriented parallel to the direction of the ultrasound beam. The displacement encoding is also in this direction. The average of three lines is shown in the plots.
MR-ARFI in the silicone phantom with the displacement encoding oriented in the direction of the ultrasound beam propagation and in a transverse direction for sonication at 29 W, from experimental group 1. Left: Images of the displacement with encoding in the different directions. The top images in each pair were oriented parallel to the beam direction; those at the bottom were perpendicular to this direction and at three different depths. The dotted lines indicate the depth location of the plane used in the plots on the right and in the images oriented perpendicular to the ultrasound beam direction. The direction of the encoding gradients is shown in the bottom left corner of each image. Right: Vectors showing the combined longitudinal and transverse displacement components at the three different depths. Below the focal plane, the transverse component was directed inward; behind the focal plane it was directed outward. The insets show the two data sets from which the vectors were created, with dotted lines plotted for the transverse component.
MR-ARFI in an ex vivo kidney sample. (a) T2-weighted image showing the sample, and the transducer. An acoustically absorbent phantom was placed on top of the sample to hold it in place. (B) and (C) Maps of the displacement during two sonications applied before (b) and after (c) focused ultrasound thermal ablation. (D) MR temperature image acquired during ablation. (E) Plots showing displacement in the focal plane before and after ablation. The average of three lines is shown in this plot. The normalized spatial distribution of the temperature rise at peak temperature rise during ablation is also shown. The peak temperature rise achieved during this sonication was .
Artifacts in the imaging. To remove the artifacts, in each line of the phase-difference images, regions to the left and right were selected where it was assumed that no displacement occurred. These regions were fit to polynomials of different orders. The order that produced the least error was then selected. Based on this fit, the artifact in the displaced segment was estimated and subtracted away. Left: MR-ARFI before (a) and after (b) artifact correction. (c) plots of the displacement at the focal depth before and after this correction. Dotted line indicates the fit of the data in the shaded regions and the extrapolation into the focal zone where displacement occurred. The image orientation is parallel to the direction of the ultrasound beam. The displacement encoding is also in this direction.
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