The results of the motion-free study shown in demonstrate that the constant and linear phase terms are reduced in the “motion-free” case. When the phantom was suspended from the table with the “motion-free” system, the linear phase was decreased significantly. For a FOV consisting of 31 lines, the constant terms had a distribution 1.27±0.81 when the phantom was on the table, compared to −0.22±0.27 with the phantom suspended. For the linear terms, the coefficient decreased from (−6.5±6.2)×10−3 to (0.99±0.81)×10−3. The decrease was statistically significant (P<0.0001) as tested by the Student’s t test. The constant and linear terms can be easily corrected, as described in step two of the displacement map reconstruction.
Figure 4 Comparison between the images acquired with “motion free” setup and the conventional “on the table” setup, both using DE(A) gradients shown in . The fitting results of each line are plotted here. With the reduction (more ...)
After correction for the constant and linear phase terms, an additional phase artifact is seen at the edge of the phantom (dashed arrows in ), when the images are acquired with DE(A) gradients shown in . Since it is in the image with the sound off, this artifact was not related to the ultrasound application. Complex motions are unlikely to be the cause, since the form of the background phase is similar with and without table vibration, as shown in that the second order phase term persists with the “motion-free” system. One way to correct for this artifact is via the acquisition and subtraction of a baseline image with the sound off (optional step 3 of the reconstruction), as described in .
The phase of one line of the baseline image along the readout direction is shown in for several amplitudes of the unipolar encoding gradients. The background phase appears to be a spatially quadratic function and increases linearly with the amplitude of the encoding gradient.
Figure 5 The amplitude of the encoding gradient versus the background phase of images acquired with the unipolar gradients. All the pulse timings were fixed while the gradient amplitude changed from 8 mT/m to 40 mT/m, therefore, the slew rate of the encoding gradients (more ...)
The results of the background phase distortion for each of the three encoding gradients are shown in the first row of . Optional Step 3 of the reconstruction was not performed for these images. The unipolar encoding gradient has the largest background phase, with the repeated bipolar having the smallest background phase. The background phase acquired with the repeated bipolars appeared to be flat throughout the 12 cm phantom, such that a baseline subtraction is not necessary.
Figure 6 The displacement map comparison. The images in the first row are the results before background correction, and the ones in the second row are corrected by the optional step three of the reconstruction, the baseline subtraction, for a fair comparison. (more ...)
The results of the SNR analysis are shown in . Increasing the encoding width initially provides more phase sensitivity. However, as shown in the figure, the loss of SNR with increasing b-value overcomes the phase sensitivity, producing a maximum, as shown. The bipolar encoding gradients show an advantage over the unipolar gradients when the pulse width is longer than 5 ms. The simulation demonstrates the optimized pulse width is 19 ms for white matter when the bipolar gradients are used for encoding. The displacement maps acquired with the three different encoding gradients are demonstrated in the second row of . A pulse width of 18 ms was used, and a significant SNR enhancement (SNRd ,bi / SNR d ,uni
= 2.54) with the bipolar encoding set can be appreciated. This measured enhancement ratio is close to the theoretical ratio 2.84, which is calculated by Eq.7
. This SNR improvement was achieved at no cost of scan time or encoding sensitivity. For these images, the displacement maps were corrected for the background phase in the optional step three of the reconstruction.
Figure 7 SNR comparison of the bipolar gradients and the unipolar gradients. The bipolar gradient set improves the SNR compared to the unipolar set when the pulse width is longer than 5 ms. Simulation shows that the SNR of the displacement map is optimized with (more ...)
The simulation was applied to other tissue types, including kidney, liver, and prostate, to look for the optimized encoding pulse width. The optimized δ is a function of tissue type based on their T2 and ADC (37
). The recommended values for different tissue types are listed in .
Optimized Encoding Pulse Width
Acquisitions with the repeated bipolar gradients are more robust against bulk motion, as shown by the reduction in the constant and linear phase terms shown in . For these images, the phantom was imaged on the scanner bed. The linear artifacts on the image acquired with the repeated bipolars were less severe compared to the ones on the image acquired with the unipolar gradients.
Figure 8 Linear fitting result of each line of the phase difference image, acquired with either the unipolar gradients or the repeated bipolar gradients. The phantom was placed on the scanner table, and the vibration during the scanning caused less phase distortion (more ...)
To assess the heat accumulation, an SPGR sequence was implemented immediately upon the completion of a 5-min MR-ARFI experiment with an electrical power of 80 W with a duty cycle of 3.8%. A temperature increase less than 1°C was observed.
The measured displacement changed as the sonication power changed. As illustrated in , the electrical power of the HIFU system stepped from 0 W to 120 W, and a linear dependence between the power and the displacement at the focal spot was observed. The data were measured by the optimized repeated bipolar gradients, and a displacement less than 0.1 µm was detected.
The displacement measurement was linearly dependent on the applied power. Using the repeated bipolars as the encoding gradient, a displacement less than 0.1 µm was observed at the electrical power level of 10 W.