Head-shaped water phantom
The head-shaped water phantom used for these experiments poses a very challenging B1+ mitigation task due to the severity of the transmit profile variation with a peak-to-valley magnitude variation of 6.8-to-1 in B1+ at an approximately central S/I axial slice through the phantom. The conventional sinc-based mode-1 birdcage excitation demonstrates the consequences of this severe B1+ inhomogeneity as a highly non-uniform in-plane flip-angle (), while RF shimming (single-spoke at DC) is able to partly mitigate the B1+ variation (). We note that the mode selected by the RF shimming optimization looks like the 1st gradient mode (top left of ), with some additional improvements by mixing in contributions from other modes. It is interesting to note that the mode-1 (the last mode in ) in this case is more inhomogeneous than the 1st gradient mode as measured by the standard deviation of the magnitude across the FOX.
Figure 6 Head-shaped water phantom B1+ mitigation. Flip-angle maps and line profiles for: a) birdcage mode with conventional 1-ms long sinc slice-selective excitation, demonstrating a 1:6.8 magnitude variation within the field-of-excitation (FOX); b) RF shimming, (more ...)
The partial mitigation of the RF shimming is dramatically improved by adding another two spokes to the excitation as is clear from . Visually, based on the images and line profiles, the B1+ mitigation of the spokes is excellent. Also quantitatively, based on the standard deviation across the FOX and the 10% and 20% deviation brackets, the three-spoke mitigation significantly outperforms RF shimming. The tradeoff in pulse duration is from 1ms for RF shimming to 2.4 ms for the 3-spoke design. The optimized placement of the spokes yielded a separation of 1/20 cm-1, at an angle of 90° (i.e. along ky), as shown in .
The same head-shaped phantom was used to compare the performance of three-spoke B1+ mitigation designed with conventional LS and MLS. The LS design strives to create an image with a uniform phase and magnitude, while the MLS allows slowly-varying spatial phase as a tradeoff in order to improve on the magnitude profile uniformity. Clearly, as seen in , this relaxation of the phase constraint by the MLS design yields a very favorable tradeoff for the |B1+| mitigation. Further, as seen in , the image phase variation, Φimage = ΦTX +ΦRX , which resulted from the MLS excitation is negligible compared to the B0 inhomogeneity-induced phase accrual at gradient-recalled echo time of 5ms for this phantom at 7T. The image spatial phase (left) is very slowly varying, is far from introducing intra-voxel dephasing, and is much smaller than the accrued B0 inhomogeneity-induced phase in the acquisition phase image (right). The image phases of the experimental results in both Figure and are calculated from the acquisition phases at TE=5ms by unwinding the effect due to B0 inhomogeneity, Φunwind = -B0(x,y)×TEeff , where TEeff is the time from center of excitation k-space to center of readout k-space.
Figure 7 Comparison of B1+ mitigation by a) a least-squares, and b) a magnitude-least-squares three-spoke RF design with the same k-space trajectory (2.4 ms) and pulse shape (sinc, time-bandwidth product=4) as demonstrated on a head-shaped water phantom with substantial (more ...)
Figure 8 Comparison between the image phase due to the combined excitation and reception phase (left) and the acquisition phase measured at TE=5ms (right), which also includes the phase accrual due to B0 inhomogeneity. Also shown on the far right is the estimated (more ...)
B1+ mitigation in vivo
Based on the successful mitigation of the significant B1+ inhomogeneity in the water phantom, we ran in vivo experiments on six human subjects to demonstrate flip-angle correction for brain imaging in the presence of inhomogeneous B1+ and B0. Figures and compare the excitation performance of mode-1 birdcage (top row), RF shimming (center row), and two-spoke excitation pulses (bottom row) for two of the six subjects. The results in are for subject 1 who exhibits an average amount of B1+ variation in the birdcage excitation, as measured by the standard deviation (σ), when compared to the other subjects. The results in are for subject 5 who exhibits the largest amount of B1+ variation in the birdcage excitation. In each figure, on the left of each row is the in-plane image of the excited slice after the removal of the received profile (which is estimated here as the 10th-order polynomial fit of the density-weighted receive profile). On the right of each row is the flip-angle map estimate, along with line profile plots. In both Figures and , RF shimming is more homogenous than the birdcage excitation, but still suffers from significant residual flip-angle inhomogeneity, whereas the two-spoke excitation provides excellent mitigation. It is noted that small amount of residual anatomy exists in the flip-angle map estimates, which most likely arises from small subject movement between the time of density-weighted receive profile estimation and the imaging of the mitigated excitation. Nonetheless, given the considerable improvement in the mitigation performance by the spoke excitation, this minor estimation artifact does not affect the overall conclusion that the two-spoke, slice-selective parallel RF excitation yields very effective flip-angle mitigation.
Figure 9 B1+ mitigation comparison for subject 1. The comparison includes slice selection based on mode-1 birdcage (top row), RF shimming (center row), and two-spoke (bottom row) excitation pulses. On the left of each row is the in-plane image of the excited slice (more ...)
B1+ mitigation comparison for subject 5, who has the most severe B1+ variation (in the mode-1 birdcage excitation) out of all the six subjects.
tabulates the standard deviation and pixel fractions for 10% and 20% deviation of the transmit profile for birdcage, RF shimming, and two-spoke excitation for all 6 subjects. The trend across the data is very clear. The birdcage excitation is by far the most inhomogeneous, the RF shimming provides some improvement, and the two-spoke excitation is the most homogenous and reliable excitation for slice-selective B1+ mitigation. The associated tradeoff in pulse duration is 2.29 ms for two-spoke excitation vs. 1.37 ms for birdcage and RF shimming excitation. Note that the increase in pulse duration of the two-spoke excitation over the birdcage and RF shimming excitation is 67% rather than 100%, since the two-spoke excitation utilizes a single gradient rephasing lobe identical to one used in the birdcage and RF shimming excitation.
Standard deviation and pixel fractions for 10% and 20% deviation of the flip-angle map of birdcage, RF Shimming, and two-spoke excitation for all six subjects.
For the in vivo parallel RF pulse design, the optimal spoke placement varies dramatically between subjects and does not seem to be intuitive. When compared to the default placement (assumed here to be at Δk = 1/20 cm-1, along the kx-axis), the optimal spoke placement provides significant improvement in excitation performance. Based on simulation results obtained for the six human subjects, the average reduction in excitation error (measured here as the standard deviation) is 10.5%, and the average reduction in RF pulse energy and peak power are 9% and 3.4% respectively.
tabulates the total energy and peak power of RF pulses used for birdcage, RF shimming, and two-spoke excitation for all 6 subjects. To provide a fairer comparison, the longer pulse duration of the two-spoke excitation is accounted for. Namely, the RF energy and peak power calculation for the birdcage and RF shimming excitation are performed for an excitation that concatenate two consecutive, identical sinc RF excitations at half the RF amplitude of the actual single sinc RF pulse used in the experiments. This procedure reduces the RF energy of the birdcage and RF shimming by a factor of 2 and the peak power by a factor of 4, and yields a normalized comparison in terms of pulse duration. Based on this normalization, the RF pulse energy of the 2-spoke excitation is approximately double that of the birdcage excitation and is slightly lower than that of the RF shimming. On the other hand, the peak-power values of all the three excitations are similar.
Total RF energy and RF peak power for birdcage, RF Shimming, and two-spoke excitation pulses for all six subjects. The reported energy and power are for excitation pulses of normalized duration.
shows the slice profile performance of the two-spoke excitation on a human subject (subject 4). In , the experimental slice profile is plotted as circles, along with the predicted profile by simulation which is shown as a solid line. Each data point along the profile represents the average in-plane intensity at that particular z-location. Good agreement between experiment and prediction can be observed, with excellent slice selection behavior. In are the in-plane images (after compensating for the effect of the receive profile) of 1-mm separation along z, over a 1-cm range around the 0.5 cm excited slice. Good slice selection and B1+ mitigation performance can be observed.
Figure 11 Two-spoke excitation for subject 4 with a 3D readout. a) Slice profile plot, where the solid line represents the predicted profile and the circles represent the experimental data. Each data point along the slice profile represents the average in-plane (more ...)