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Keywords:

  • parallel excitation;
  • slice-selective excitation;
  • RF inhomogeneity mitigation;
  • multidimensional RF pulse;
  • RF coil array

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. REFERENCES

Slice-selective RF waveforms that mitigate severe Bmath image inhomogeneity at 7 Tesla using parallel excitation were designed and validated in a water phantom and human studies on six subjects using a 16-element degenerate stripline array coil driven with a butler matrix to utilize the eight most favorable birdcage modes. The parallel RF waveform design applied magnitude least-squares (MLS) criteria with an optimized k-space excitation trajectory to significantly improve profile uniformity compared to conventional least-squares (LS) designs. Parallel excitation RF pulses designed to excite a uniform in-plane flip angle (FA) with slice selection in the z-direction were demonstrated and compared with conventional sinc-pulse excitation and RF shimming. In all cases, the parallel RF excitation significantly mitigated the effects of inhomogeneous Bmath image on the excitation FA. The optimized parallel RF pulses for human Bmath image mitigation were only 67% longer than a conventional sinc-based excitation, but significantly outperformed RF shimming. For example the standard deviations (SDs) of the in-plane FA (averaged over six human studies) were 16.7% for conventional sinc excitation, 13.3% for RF shimming, and 7.6% for parallel excitation. This work demonstrates that excitations with parallel RF systems can provide slice selection with spatially uniform FAs at high field strengths with only a small pulse-duration penalty. Magn Reson Med 60:1422–1432, 2008. © 2008 Wiley-Liss, Inc.

Slice-selective excitation plays a crucial role in MRI. With the push toward higher magnetic field strength, dramatic Bmath image inhomogeneity for human imaging has become a serious issue, causing inhomogeneous flip-angle (FA) distribution in-plane for slice-selective excitations and detrimental nonuniformity for both signal-to-noise ratio (SNR) and image contrast. Several RF design approaches have been suggested to compensate for this inhomogeneity, including adiabatic pulses (1, 2), RF-shimming (3–6), and spatially tailored excitation designs (7–11).

For relatively mild Bmath image inhomogeneity, using the low-FA approximation (12) with appropriate echo-volumnar k-space trajectories (9–11), termed either “fast-kz” or “spokes” excitation trajectories, the within-slice FA inhomogeneity can be corrected. With these pulses, slice selection is achieved with a conventional sinc-like RF pulse during each kz traversal (a spoke), and in-plane FA inhomogeneity is mitigated by the appropriate choice of the complex-valued amplitude that modulates the RF waveform of each spoke. Nonetheless, if the transmit (Tx) Bmath image field is rapidly varying with position, a large number of spokes will be required at correspondingly high kx and ky locations, rendering the RF pulse too lengthy for practical use.

With the introduction of parallel excitation systems (13–16), the k-space trajectory can be undersampled significantly to accelerate the RF pulse and reduce its duration. A number of successful demonstrations of this concept have been reported (e.g., Refs.17–20). For example, it has been demonstrated at 3T (18, 21) and 4.7T (17) that a parallel RF design method using low-FA approximation with spoke-based excitation trajectories can produce highly uniform slice-selective excitation with reasonable excitation durations.

In this work we use spoke-based excitation in combination with magnitude least-square (MLS) optimization (22, 23), k-space excitation trajectory optimization, and B0 field-map incorporation (16, 24) to design parallel RF pulses that demonstrate excellent Bmath image mitigation on both a head-shaped water phantom and brain images of six subjects at 7T.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. REFERENCES

Human Subjects

Six healthy volunteers (20–35 years old, four males and two females) were recruited from the community to serve as subjects for this study. All protocols were approved by the local Institutional Review Board (IRB).

System Hardware

All experiments were run on a Siemens 7T Magnetom scanner (Erlangen, Germany) equipped with an eight-channel Tx RF system, with a body gradient system capable of maximum gradient amplitude of 40 mT/m and slew rate of 200 T/m/s. The two primary RF hardware components related to this study were a 16-channel stripline transmit/receive (Tx/Rx) degenerate birdcage coil array (25) and a 16-channel butler matrix (Fig. 1a). The butler matrix was used to drive the eight optimal birdcage Tx modes from the 16-channel coil, and served to make the best use of the RF excitation system, which has only eight RF power amplifiers. The 16-channel RF array was built around a 28-cm-diameter acrylic tube (Fig. 1a) and was driven through a Tx/Rx switch at each coil. Signal was received in a birdcage mode on the 16 Rx channels of the array.

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Figure 1. a: The 16-channel Tx/Rx stripline coil and the butler matrix used in this work. b: Profiles for combined Tx-Rx, along with estimates of the separate Tx (B1+) and Rx (B1) of the circularly-polarized mode-1 birdcage of the coil for a head-shaped phantom, and (c) axial section in human brain (subject 1). The axes of orientation are denoted by R/L (right/left), and A/P (anterior/posterior) on the right-most image.

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A head-shaped water phantom filled with doped water containing 1.25 g/liter of nickel sulfate and 5 g/liter of sodium chloride (T1 ∼ 500 ms) was used for initial measurements and demonstration of Bmath image mitigation. Figure 1b shows the Tx-Rx circularly polarized (CP) mode-1 birdcage image of this water phantom. The peak-to-trough signal ratio in this image is very large, approximately 15. Also shown are the separate estimates of the Tx and Rx profiles, with the Tx magnitude signal ratio of 6.8 from maximum to minimum within the slice. This variation is more than twice the maximum range we observed for the human studies. Figure 1c shows the relevant profiles for a human brain (subject 1).

Specific Absorption Rate Monitoring

The RF power was monitored in real time for each channel and utilized a 10-s 6-min average. For determining the specific absorption rate (SAR) limit, a very conservative estimate was used. Based on the work by Collins et al. (26) analyzing the worst-case scenario for a similar 16-element stripline array, we utilized a local 10-g SAR to average SAR ratio of 60. To assess this, Collins and colleagues determined the worst-case ratio of local SAR to average SAR using finite difference time domain (FDTD)-generated field maps in a human head model for a 16-element stripline coil. Given that the International Electrotechnical Commission (IEC) allows an average SAR of 3.2 W/kg and local SAR of 10 W/kg (a local-to-average ratio of 3.125, well below the estimated worst-case ratio of 60) these results make it clear that local SAR is the limiting concern. Based on the worst-case local-to-average ratio of 60 and the IEC limit of 10 W/kg for local SAR, we derated the allowable average SAR to 0.167 W/kg. Using a 5-kg head mass, this gives an allowable average total power limit of 0.83 W.

Bmath image and Bmath image mapping

Central to the design of the Bmath image mitigation RF pulses is the estimate of the excitation magnitude and phase profiles of the coil array for both phantom and human studies. Since the Tx/Rx patterns are of opposite circular polarizations, Bmath image and Bmath image, which in general are different at high B0 field (27), the use of a quantitative coil profile mapping technique was required.

Here, an efficient method for quantitative Bmath image mapping of multiple transmission modes/coils is proposed. Instead of directly performing quantitative Bmath image mapping on each of the Tx modes/coils, the first step of this Bmath image mapping procedure is to estimate the density-weighted reception profile. Once this reception profile is estimated, only a single low-voltage measurement will be required from each of the transmission modes/coils for the estimation of the individual Bmath image transmission profiles. This novel method provides an efficient means of obtaining Bmath image maps for parallel transmission systems, especially for systems with large number of transmission modes/coils.

Estimation of the Density-Weighted Reception Profile

The estimation of the density-weighted Rx profile is performed in two steps. First, the mode-1 birdcage transmission profile of the coil array is estimated. This estimate is then used along with the data from an extra acquisition to estimate the Rx profile.

The mode-1 birdcage transmission profile is estimated using a technique similar to the one proposed by Kerr et al. (28). The estimation technique here relies on mode-1 birdcage transmission via slice-selective excitation at a set of n voltages, v,2v,22v, …, 2n−1v, and fitting the sinusoidal signal dependence to the Tx voltages. In this method, BIR-4 magnetization saturation pulse (29) is applied after each readout period to allow for a reduced TR and shorter scan times without a detrimental T1 bias in the FA estimates. Images at a set of transmission voltages are collected and the resulting image intensities are fitted to the following expression, which can be derived from, e.g. Ref.30:

  • equation image(1)

Here, I is the image intensity, ρ is the spin density, RX is the receive coil profile (Bmath image), TSR is the saturation recovery time, T1 is the longitudinal relaxation time constant, θ is the FA, and V is the applied Tx voltage.

With the use of a BIR-4 magnetization saturation pulse, short TR acquisitions can result in high average SAR and reduced SNR (due to reduced T1 recovery time). To avoid this problem, TR = 1.2s was used in this work. A standard nonlinear search algorithm (Simplex) in MATLAB was employed to perform the fitting of the image intensity to obtain the FA map, equation image(x,y,V). We note that the RF pulses for Bmath image mapping are slice-selective in the current implementation, and thus some care must be taken to minimize the effects of imperfect slice selection at large FA during the fitting of Eq. [1]. To this end, data from very large FAs are excluded from the fitting based on a simple criterion. On a pixel-by-pixel basis, the signal intensity, I, was fitted only with measurements corresponding to excitations with v1, v2, …, vmax, where vmax is the voltage corresponding to the first maximum in I(x, y, vi).

From the FA map, estimation of the transmission profile, (TX(x,y)), can be obtained by noting the following relationship between excitation FA and transmission profile:

  • equation image(2)

where γ is the gyromagnetic ratio, and RF(t) is the RF pulse used for the transmission.

With the estimate of the birdcage transmission profile, the density-weighted reception profile, ρ(x,y)RX(x,y), can then be obtained by acquiring an extra slice-selective, low-FA image with mode-1 birdcage transmission at a known voltage (without the magnetization saturation pulse). With the combination of a very low FA (we used a criterion of no more than 8° at maximum, based on the quantitative FA map) and a TR = 1 s, this image is approximately proton-density weighted:

  • equation image(3)

Again, this equation can be derived from Ref.30. By dividing out sin equation image(x,y,V) from the image, the density-weighted birdcage reception profile can be obtained.

Estimation of the Individual Bmath image Transmission Profiles

Once the density-weighted reception profile is estimated, the Bmath image profile of the individual transmission modes can be obtained though a single slice-selective, low-FA image acquisition of each transmission mode. According to Eq. [8], the FA profile of each Tx mode, θMode(j)(x,y,V), can be estimated by dividing the low-FA image, IMode(j)(x,y,V), by the density-weighted reception profile along with taking an inverse sine of the resulting image, pixel-by-pixel:

  • equation image(4)

From this FA profile, the quantitative magnitude Bmath image profile (nT/V) can then be obtained via Eq. [2].

In addition to the magnitude profile, the accompanying phase profile of Bmath image is required as well. In this work, we make use of the spatial distribution of Bmath image phase relative to the Rx profile, ϕTXrelative,Mode(j)TX,Mode(j)RX. This phase is obtained from the phase measured in the low-FA acquisition of each mode. By using this phase in the calculation of parallel excitation pulses, the Rx phase variation is taken into account in the excitation design. As a result, the phase of the reconstructed image, which consists of both the excitation and the reception phase, ϕimageTXRX, should be equal to the design phase, ϕdesign, with the actual excitation phase being ϕTX = ϕ design − ϕRX.

A flowchart in Fig. 2 summarizes the quantitative Bmath image mapping procedure, where first estimation of the Rx profile is performed (steps 1–5), followed by estimation of the Bmath image maps for each individual Tx coil/mode (steps 6 and 7). Figure 3 illustrates the estimation of the individual Bmath image profiles via the use of the density-weighted reception profile for in vivo Bmath image mapping of the first gradient Tx mode in subject 1. As a side note, the use of mode-1 birdcage transmission is not required for the mapping of the Rx profile. Transmission on any coil or mode can be used for this purpose. We note, however, that by using a transmission mode with a relatively low dynamic range of |Bmath image| variation, such as mode-1, only a small number of measurements are required for the Rx profile estimation (four to five voltage steps in this work for human neuroimaging at 7T).

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Figure 2. Flowchart outlining the proposed quantitative B1+ mapping technique, where first a Rx profile of the reception coil is estimated in steps 1–5, after which B1+ maps of the Tx modes/coils can then be obtained via steps 6 and 7.

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Figure 3. In vivo quantitative B1+ mapping of the first gradient Tx mode using a single low-FA acquisition (subject 1). The B1+ map is obtained by dividing the low-FA image with the density-weighted Rx profile estimate along with applying a sine inverse operation.

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We also note that once ρ(x,y)RX(x,y)(1 − emath image) was estimated as a by-product of obtaining mode-1 birdcage transmission profile via Eq. [6], we could have used the reset pulse sequence to estimate the Bmath image profiles of the individual modes without having to estimate ρ(x,y)RX(x,y). Nonetheless, estimating ρ(x,y)RX(x,y) only requires one extra low FA acquisition, and allows us to leave out the use of reset pulse in estimating the Bmath image profiles of the individual modes. This significantly reduces the SAR requirement for the mapping, which is important for in vivo imaging applications. Furthermore, the estimation of the density-weighted Rx profile is needed in dividing the reconstructed image in the parallel excitation experiments to obtain the excitation profiles.

Examples of Tx profiles for the head-shaped phantom and a human subject are shown in Fig. 4. It is noted that the head-shaped phantom experiment was performed prior to the full development of the presented Bmath image mapping technique. The mapping technique used for the head-shape phantom differs slightly to the one presented here in that it does not utilize the BIR-4 reset pulse. Instead, the method relies on long TR acquisition to minimize T1 dependence. On the other hand, for the in vivo Bmath image mapping of all human subjects, the presented method was used. In all acquisitions for Bmath image mapping, a 2D gradient-recalled echo sequence was used with 80 × 80 pixel grid in x,y at 2.5 × 2.5 mm2 resolution over a 20-cm FOV in-plane (TE/BW = 5 ms, 260 Hz/pixel).

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Figure 4. Magnitude (top) and phase (bottom) B1+ maps of the eight optimal modes for (a) the head-shaped phantom, and (b) an axial section in human brain (subject 1).

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B0 Maps

B0 maps were estimated from two gradient-echo acquisitions at TE1/TE2 = 5 ms/6 ms, and were incorporated into the pulse design (16, 24) to improve the robustness of the desired excitation in the presence of unavoidable B0 inhomogeneity. The spoke-based excitation trajectory was shown to be sensitive to off-resonance effects (24) present in vivo at 3T, causing deterioration in performance. With the incorporation of the measured field map, these undesirable effects of B0 inhomogeneity are minimized.

RF Design

We based our parallel RF pulse design on the spatial domain method introduced by Grissom et al. (16). In addition, we applied MLS optimization (22, 23) to improve the excitation magnitude profile and reduce the required RF power at a cost of only a small spatial phase variation in the excitation. Here the method presented in Ref.23 was used. Furthermore, the spoke placement in the k-space excitation trajectory was optimized to provide additional improvement to the excitation performance. For this optimization, the spokes were constrained to be symmetric around the origin in the (kx,ky) plane, and were optimized over a grid defined by 0°, 45°, 90°, and 135° angles, and different separation values (Δk = 1/FOV), with the FOV value ranging from 16 to 36 cm in incremental steps of 2 cm. Examples of the optimized spoke-based k-space excitation trajectory for the phantom and the in vivo studies are shown in Fig. 5.

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Figure 5. The optimized (a) three-spoke and (b) two-spoke k-space excitation trajectories for the pulse design in the head-shaped phantom and human excitation experiment, respectively. The optimized two-spoke placements in (kx,ky) for the in the in vivo experiments varied from subject to subject, but in all cases were two-spoke designs.

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In the RF design, a slice-selective spoke excitation with time-bandwidth-product equal to 4 was used for the sinc subpulses. For our initial phantom work, where Bmath image inhomogeneity was very severe, a three-spoke excitation trajectory was employed. Slice-selective specifications of 1-cm thickness, along with a maximum gradient amplitude constraint of 20 mT/m and slew rate constraint of 150 T/m/s were used. For the in vivo studies, a two-spoke excitation trajectory was used with a slice-selective specification of 0.5-cm thickness, maximum gradient amplitude constraint of 30 mT/m, and slew rate constraint of 150 T/m/s.

The RF shimming design used for comparison in both the phantom and in vivo experiments was cast as a single-spoke RF design at the (kx,ky)-space origin with an MLS optimality criterion. The pulse duration quoted in this work includes the duration of the gradient rephaser applied after the excitation to properly return excitation trajectory to k-space origin. The predicted magnetization patterns were calculated using a Bloch equation simulation of the parallel RF excitation.

Experiments and Comparisons

For experimental verification, the spoke excitations were designed and tested on both a head-shaped phantom with severe Bmath image inhomogeneity and six human subjects with axial slice selection at six different superior/inferior (S/I) axial positions. In addition, for all experiments, excitation via mode-1 birdcage transmission and RF shimming were also acquired for comparison. For the head-shaped-phantom experiment, data were also collected to compare the performance of the conventional least-squares (LS) vs. the MLS design of the spoke-based RF pulses. The RF excitation pulses were adjusted so that for all the experiments the target FA was 5°.

The excitations were imaged with a 2D gradient-recalled echo sequence with matrix = 80 × 80, FOV = 20 × 20 cm2, voxel resolution = 2.5 × 2.5mm2, TR/TE/BW = 1 s/5 ms/260 Hz/pixel, where the combination of relatively long TR and low-FA excitations resulted in proton-density-weighted images. The FA maps of the excitations were inferred from the proton-density images using the same method as in the individual mode Bmath image profile estimation, i.e., by dividing out the estimated density-weighted Rx profile, ρ(x,y)RX(x,y), and taking the inverse sine.

Standard deviation (SD) and uniformity threshold levels were used for quantitative comparison between mode-1 birdcage, RF shimming, and spoke excitation. For a fair comparison of the SD, the excitation FA profiles were all scaled to have a mean value of 1.0 before the SD was calculated (i.e., normalized SD). The uniformity threshold levels used in the comparisons, “<10% dev” and “<20% dev”, are defined as the percentage of the excitation FA profile that deviate less than ±10% and ±20% from the mean FA value. The pixel set used in these comparisons is defined by the mask used in the generation of the Bmath image maps. For the water phantom, this mask is generated by applying intensity thresholding to the birdcage Tx-Rx image to exclude the region beyond the phantom edge as well as partial-volume pixels in the periphery of the phantom. For the in vivo cases, the mask is also generated using the birdcage Tx-Rx image. However, an additional refinement step of manual “skull stripping” was applied before the mask generation via intensity thresholding. Figure 1b and c show the birdcage Tx-Rx image without masking, and the Tx and Rx profiles with masking for both phantom and in vivo cases.

To demonstrate slice-selection fidelity of the spoke excitation, a 3D readout was also acquired in one of the in vivo study (TE/TR/flip = 5 ms/100 ms/5°, 26 slices, FOV = 20 × 20 × 2.6 cm3, resolution = 2.5 × 2.5 × 1 mm3).

RESULTS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. REFERENCES

Head-Shaped Water Phantom

The head-shaped water phantom used for these experiments poses a very challenging Bmath image mitigation task due to the severity of the Tx profile variation with a peak-to-valley magnitude variation of 6.8-to-1 in Bmath image 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 Bmath image inhomogeneity as a highly nonuniform in-plane FA (Fig. 6a), while RF shimming (single-spoke at DC) is able to partly mitigate the Bmath image variation (Fig. 6b). We note that the mode selected by the RF shimming optimization looks like the first gradient mode (top left of Fig. 4a), with some additional improvements by mixing in contributions from other modes. It is interesting to note that the mode-1 (the last mode in Fig. 4a) in this case is more inhomogeneous than the first gradient mode as measured by the SD of the magnitude across the field of excitation (FOX).

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Figure 6. Head-shaped water phantom B1+ mitigation. FA maps and line profiles for (a) the birdcage mode with conventional 1-ms-long sinc slice-selective excitation, demonstrating a 1:6.8 magnitude variation within the FOX; (b) an RF shimming, 1-ms-long pulse, demonstrating a substantial residual FA inhomogeneity as measured by the SD and threshold metrics; and (c) a three-spoke MLS, slice-selective 2.4-ms-long pulse, demonstrating excellent mitigation of the B1+ inhomogeneity.

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The partial mitigation of the RF shimming is dramatically improved by adding another two spokes to the excitation, as is clear from Fig. 6c. Visually, based on the images and line profiles, the Bmath image mitigation of the spokes is excellent. Also quantitatively, based on the SD across the FOX and the 10% and 20% deviation brackets, the three-spoke mitigation significantly outperforms RF shimming. The trade-off in pulse duration is from 1 ms for RF shimming to 2.4 ms for the three-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 Fig. 4a.

The same head-shaped phantom was used to compare the performance of three-spoke Bmath image 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 a slowly varying spatial phase as a tradeoff in order to improve on the magnitude profile uniformity. Clearly, as seen in Fig. 7, this relaxation of the phase constraint by the MLS design yields a very favorable trade-off for the |Bmath image| mitigation. Further, as seen in Fig. 8, the image phase variation, ϕimageTXRX, which resulted from the MLS excitation is negligible compared to the B0 inhomogeneity-induced phase accrual at gradient-recalled echo time of 5 ms for this phantom at 7T. The image spatial phase (left) is very slowly varying, is far from introducing intravoxel 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 Figs. 7 and 8 are calculated from the acquisition phases at TE = 5 ms by unwinding the effect due to B0 inhomogeneity, ϕunwind = −B0(x,y) × TEeff, where TEeff is the time from the center of excitation k-space to the center of readout k-space.

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Figure 7. Comparison of B1+ mitigation by an (a) LS and (b) MLS 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 Tx inhomogeneity. On the left is a Bloch simulation of the magnitude and phase profiles; on the right are experimental results with line profiles through the magnitude image.

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Figure 8. Comparison between the image phase due to the combined excitation and reception phase (left) and the acquisition phase measured at TE = 5 ms (right), which also includes the phase accrual due to B0 inhomogeneity. Also shown on the far right is the estimated B0 field map. Clearly, the combined excitation and reception phase variation resulting from the MLS design is very small compared to the accrued phase due to B0 inhomogeneity at TE = 5 ms. The phase resulting from the MLS design is slowly varying over the FOX, and thus does not introduce any intravoxel dephasing.

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Bmath image Mitigation In Vivo

Based on the successful mitigation of the significant Bmath image inhomogeneity in the water phantom, we ran in vivo experiments on six human subjects to demonstrate FA correction for brain imaging in the presence of inhomogeneous Bmath image and B0. Figures 9 and 10 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 Fig. 9 are for subject 1, who exhibits an average amount of Bmath image variation in the birdcage excitation, as measured by the SD (σ), when compared to the other subjects. The results in Fig. 10 are for subject 5, who exhibits the largest amount of Bmath image 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 Rx profile (which is estimated here as the 10th-order polynomial fit of the density-weighted Rx profile). On the right of each row is the FA map estimate, along with line profile plots. In both Figs. 9 and 10, RF shimming is more homogenous than the birdcage excitation, but still suffers from significant residual FA inhomogeneity, whereas the two-spoke excitation provides excellent mitigation. It is noted that small amount of residual anatomy exists in the FA map estimates, which most likely arises from small subject movement between the time of density-weighted Rx 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 FA mitigation.

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Figure 9. B1+ mitigation comparison for subject 1. The comparison includes slice selection based on the 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 after the removal of the Rx profile. On the right is the FA map estimate, along with the line profile plots.

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Figure 10. B1+ mitigation comparison for subject 5, who has the most severe B1+ variation (in the mode-1 birdcage excitation) of all the six subjects.

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Table 1 tabulates the SD and pixel fractions for 10% and 20% deviation of the Tx profile for birdcage, RF shimming, and two-spoke excitation for all six 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 homogeneous and reliable excitation for slice-selective Bmath image mitigation. The associated trade-off 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 the one used in the birdcage and RF shimming excitation.

Table 1. SD 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
Subjectσ (%)<10%<20%
BirdcageRF ShimmingTwo-SpokeBirdcageRF ShimmingTwo-SpokeBirdcageRF ShimmingTwo-Spoke
Subject 114.812.26.545.254.190.178.790.399
Subject 212.411.46.654.860.991.388.993.198.8
Subject 319.817.59.339.138.677.766.884.596
Subject 415.112.97.352.259.487.180.688.598.2
Subject 52113.87.844.855.181.768.78698.4
Subject 616.911.78.142.363.48376.49196.9
Average ± SD16.7 ± 3.213.3 ± 2.37.6 ± 1.046.4 ± 6.055.3 ± 8.985.2 ± 5.376.7 ± 8.188.9 ± 3.297.9 ± 1.2

For the in vivo parallel RF pulse design, the optimum 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 optimum 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 SD) is 10.5%, and the average reductions in RF pulse energy and peak power are 9% and 3.4% respectively.

Table 2 tabulates the total energy and peak power of RF pulses used for birdcage, RF shimming, and two-spoke excitation for all six 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 calculations 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 two-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.

Table 2. Total RF Energy and RF Peak Power for Birdcage, RF Shimming, and Two-Spoke Excitation Pulses for All Six Subjects*
 Total energy (mJ)Peak power (W)
BirdcageRF ShimmingTwo-SpokeBirdcageRF ShimmingTwo-Spoke
  • *

    The reported energy and power are for excitation pulses of normalized duration.

Subject 17.6813.813.330.225.930.4
Subject 27.351210.428.826.323.9
Subject 310.829.71842.339.638.7
Subject 47.7917.416.230.425.924.5
Subject 510.724.821.842.147.432
Subject 68.6514.715.833.630.846.1
Average ± SD8.83 ± 1.518.7 ± 7.015.9 ± 3.934.6 ± 6.132.7 ± 9.032.6 ± 8.6

Figure 11 shows the slice profile performance of the two-spoke excitation on a human subject (subject 4). In Fig. 11a, 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 Fig. 11b are the in-plane images (after compensating for the effect of the Rx profile) of 1-mm separation along z, over a 1-cm range around the 0.5-cm excited slice. Good slice selection and Bmath image mitigation performance can be observed.

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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 intensity at that particular z-location. b: A total of 10 in-plane images (aj), at 1-mm separation along z, over a 1-cm range around the 0.5-cm excited slice.

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DISCUSSION

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. REFERENCES

In this work we have successfully demonstrated mitigation of severe Bmath image inhomogeneity at 7T on a head-shaped water phantom and six human subjects. The phantom result is interesting in that the Bmath image inhomogeneity is more than twice as severe as we observed in any of the six subjects. Correspondingly, a three-spoke excitation was used for the phantom excitation, while a two-spoke design was adequate in vivo. The phantom finding suggests that at even higher fields, where the Bmath image inhomogeneity in vivo becomes more pronounced than at 7T, the spoke-based RF design is viable with a very high degree of FA uniformity and a short pulse duration.

The novel Bmath image mapping technique used in this work allows for fast Bmath image estimation, requiring only a single low-FA image acquisition from each transmission mode/coil after the initial density-weighted Rx profile estimation. With this method, the use of the reset pulse is limited to the density-weighted reception profile mapping, resulting in a much lower required SAR, which is particularly relevant for in vivo applications. Future work includes combining this Bmath image mapping technique with more efficient readout methods, such as ones based on spiral, echo-planar, or echo-volumnar trajectories.

A comparison of peak power and total energy of the RF pulses used for birdcage, RF shimming, and spoke excitation is provided in Table 1. This comparison points to similarities in peak power and significant increases in pulse energy for RF shimming and spokes excitation compared to conventional birdcage transmission. However, this work does not address a direct SAR comparison among the three methods. SAR calculation is a topic of an ongoing work, which will be keyed to clinical application of parallel transmission.

A limitation of the current Tx coil array, which is built around a cylindrical ring with local coil elements placed horizontally adjacent to each other, is that it is primarily fit for transversal acceleration and hence mitigation in the axial plane. Future work on coil development will address this point and extend the coil design to allow for longitudinal profile variation between the coil elements, and therefore longitudinal acceleration. We expect that the presented methodology for slice-selective excitation with Bmath image mitigation will hold for sagittal, coronal, and generally oblique scan planes beyond the currently presented axial demonstrations.

As part of the RF design method used in this work, a simple and fast k-space excitation trajectory optimization was employed to provide significant improvement in the excitation performance. Based on the performance of a Linux Intel® Xeon 3 GHz server, in MATLAB, this optimization process can be performed in ∼50 s. We note that the optimization procedure can easily be made more sophisticated by evaluating the optimal spoke placement on a finer grid, but we suggest limiting the search to symmetric placement of spokes in (kx, ky) for these simple designs to maintain them within a regime compatible with the linear class of large tip angle pulses proposed by Pauly et al. (31) and used for parallel Tx work by Xu et al. (19). Such an approach would simplify the extension to larger FAs.

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. REFERENCES

Slice-selective RF waveforms that mitigate severe Bmath image inhomogeneity at 7 Tesla were designed and demonstrated for parallel excitation in a phantom and six human subjects. This work demonstrates that slice-selective excitations with parallel RF systems offer the means to implement slice selection with spatially uniform FA at high field strengths with only a small pulse duration penalty.

REFERENCES

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. CONCLUSIONS
  7. REFERENCES