Simultaneous multi-slice multi-band parallel RF excitation with independent slice-specific transmit B1 homogenization

Abstract

Purpose

To develop a new parallel transmit (pTx) pulse design for simultaneous multi-band (MB) excitation in order to tackle simultaneously the problems of transmit B1 (B1+) inhomogeneity and total RF power, so as to allow for optimal RF excitation when using MB pulses for slice acceleration for high and ultrahigh field MRI.

Methods

With the proposed approach, each of the bands that are simultaneously excited is subject to a band-specific set of B1 complex shim weights. The method was validated in the human brain at 7T using a 16-channel pTx system and was compared to conventional MB pulses operating in the circularly polarized (CP) mode. Further numerical simulations based on measured B1 maps were conducted.

Results

The new method improved B1+ homogeneity by 60% when keeping the total RF power constant and reduced total RF power by 72% when keeping the excitation fidelity constant, as compared to the conventional CP mode.

Conclusion

A new pTx pulse design formalism is introduced targeting slice-specific B1+homogenization in MB excitation while constraining total RF power. These pulses lead to significantly improved slice-wise B1+ uniformity and/or largely reduced total RF power, as compared to the conventionally employed MB pulses applied in the CP mode.

Introduction

Recent availability of 7 Tesla (7T) magnets has enabled functional brain imaging (fMRI) studies of the human brain with increasingly higher spatial resolution and fidelity (1-6). Obtaining such fMRI data over the entire human brain, however, encounters the undesirably long volume repetition times (TR) even when single-shot methods, such as slice selective Echo-Planar Imaging (EPI), are employed. A solution to this impediment is simultaneous multiband (MB) RF excitation and acquisition of multiple slices with subsequent unaliasing using parallel imaging (7), thus reducing the volume TR by the number of simultaneously excited slices (MB factor). Especially in conjunction with partial shifting of simultaneously acquired slices along the phase encode dimension using gradient blips (blipped-CAIPI) in EPI (12), the approach has been employed with significant success in task (8,9) and in resting state fMRI (10,11), leading to improved detection of resting state networks (RSNs) (10) and new analysis strategies that reveal RSN temporal dynamics (11). The approach has also allowed significant reductions (10,12) in the otherwise long acquisition times associated with high angular diffusion weighted imaging (HARDI) (13) and DSI (14,15) thereby making the use of these techniques practical and indispensable for efforts like the Human Connectome Project (HCP) (16). .

Despite these gains, however, the optimal use of the multiband approach at high (3 and 4T) and ultrahigh (≥7T) fields is precluded by transmit B1 (B1+) inhomogeneities and power deposition. Signal-to-noise ratio (SNR) and image contrast becomes spatially non-uniform and suboptimal because of B1+ heterogeneity resulting from destructive interferences (17) caused by the traveling wave RF behavior (18). These B1+ inhomogeneities are sufficiently strong even at 3T to induce spatial variations in SNR, especially with spin-echo (SE) sequences. Similarly, maximal MB factors can be limited by power deposition especially at ultrahigh fields and/or with SE sequences. When the number of slices and the volume TR are kept the same, the multiband approach deposits the same power as the conventional single slice excitation. However, accelerating by the MB factor leads to MB-fold increase in power deposition, imposing a limit on performance.

In this study, we introduce a novel parallel transmit (pTx) MB pulse design that tackles the afore-described problem of B1+ inhomogeneity with total RF power regularization, and demonstrate it experimentally in the human brain at 7T using a 16-channel pTx system driving a 16-channel RF transceiver array; the performance of these new pulses was compared to conventional MB pulses for the same RF coil operating in the circularly polarized (CP) mode using both experiments and numerical simulations. The results demonstrate that the new pTx MB pulses provide significantly improved B1+ homogenization in multiple slices simultaneously and/or significantly reduced RF power relative to a single channel CP mode application.

Theory

Two strategies are employed in multi-channel MB excitation to find RF magnitude and phase modulations (i.e., RF shim values) of the base RF pulses so as to mitigate B1+ inhomogeneity. The primary strategy, defined here as Full pTx MB, relies on fully independent multiple transmit channels and calculates, for each transmit channel, a different set of shim values for each of the M bands. This approach, introduced in the form of a conference abstract (19), is fully described here.

In the absence of a full pTx hardware, it is possible to utilize a simpler and less costly hardware that splits the single RF channel of the scanner into multiple channels at the low power stage and impose on the resulting separate channels a channel-specific phase and amplitude change (e.g. (20-23)). With this limited but more readily implementable hardware, a solution that is possible, defined here as MB B1 shim, is a set of channel-specific RF shim values that are applied to all M bands simultaneously, rather than channel and band specific shim values that is possible with full pTx.

In Full pTx MB targeting uniform excitation (i.e. uniform |B1+|), the RF shim values for M-band Q-channel excitation can be obtained by solving the following magnitude least square problem:

$${\min }_{{\mathit{w}}_{\text{full}}}\{\mid \mid \mid {\mathit{A}}_{\text{full}}{\mathit{w}}_{\text{full}}\mid -d\mid {\mid }_2^2+\lambda \mid \mid {\mathit{w}}_{\text{full}}\mid {\mid }_2^2\}$$ [1]

$$\text{with}{\mathit{A}}_{\text{full}}=\left[\begin{array}{ccc}\hfill {\mathit{A}}_1\hfill & \hfill \cdots \hfill & \hfill 0\hfill \\ \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \hfill 0\hfill & \hfill \cdots \hfill & \hfill {\mathit{A}}_M\hfill \end{array}\right]\text{and}{\mathit{w}}_{\text{full}}=\left[\begin{array}{c}\hfill {\mathit{w}}_1\hfill \\ \hfill {\mathit{w}}_2\hfill \\ \hfill ⋮\hfill \\ \hfill {\mathit{w}}_M\hfill \end{array}\right].$$

Here A_full is a block diagonal matrix with the diagonal element matrices A_m(m=1,2,…, M) being the system matrix involving B1+ spatial sensitivity profiles of individual channels and the ΔB₀ map the m-th band, w_full is a concatenated vector with w_m (m=1,2,…, m) being vector for a RF shim values of individual channels for the m-th band, d is a scalar representing the desired transverse magnetization, and λ is the regularization parameter.

Each of the M base RF pulses that constitute the final summed MB pulse is played at a different slice specific frequency. Consequently, by Parseval’s theorem, total RF power is simply determined by the number of slices acquired irrespective of whether the slices are acquired using MB approach or the conventional single slice excitation procedure. As a result, the use of $\mid \mid {\mathit{w}}_{\text{full}}\mid {\mid }_2^2$ is an optimum constraint for total RF power in Full pTx MB

In the MB B1 shim, one can solve:

$${\min }_{\mathit{w}}\{\mid \mid \mid \mathit{Aw}\mid -d\mid {\mid }_2^2+\lambda \mid \mid \mathit{w}\mid {\mid }_2^2\}$$ [2]

$$\text{with}\mathit{A}=\left[\begin{array}{c}\hfill {\mathit{A}}_1\hfill \\ \hfill {\mathit{A}}_2\hfill \\ \hfill ⋮\hfill \\ \hfill {\mathit{A}}_M\hfill \end{array}\right]\text{and}\mathit{w}=\left[\begin{array}{c}\hfill w_1\hfill \\ \hfill w_2\hfill \\ \hfill ⋮\hfill \\ \hfill w_Q\hfill \end{array}\right].$$

Here A is a combined matrix composed of, A_m, and w is a complex valued vector with w_q (q = 1,2, …, Q) being the RF shim value for the q-th channel.

It should also be emphasized that the minimal hardware configuration relying on a single RF channel described above for the MB B1shim pulse would be incapable of generating the Full pTx MB pulses, since a different B1-shim solution is applied for each individual band (see Figure 1).

FIG. 1.

Schematic illustration of Full pTx MB vs MB B1 shim in the context of single-spoke pulse design for two-band excitation. Note that due to different phase evolutions required to target band 1 (red) and band 2 (blue), the two base RF pulses, represented by triangles, are of different pulse shapes. Importantly, although a RF shimming is performed for each band in Full pTx MB, the application of final RF pulses requires full pTx hardware and cannot be realized simply with a magnitude and phase controller. This is because the final RF pulse per channel is the sum of two different base pulses each multiplied by a different weight and thus cannot be represented simply by a channel-specific weight, $w_q^{\prime }$, multiplied by a common pulse.

Methods

All experiments were carried out at 7T driven by a 16-channel prototype pTx system (Siemens, Erlangen, Germany) equipped with 1kW RF amplifier per channel. A transceiver array with 16 azimuthally distributed elements (24) with two short elements to leave an opening for the eyes was used for both RF transmission and MR signal reception. Human brain images were collected in healthy volunteers who signed a consent form approved by local Institutional Review Board. All calculations were conducted in Matlab (The Mathworks Inc., Natick, MA, USA).

Sixteen-channel complex B1+ maps within nine axial slices encompassing the brain region were obtained with a fast hybrid multi-channel B1+ mapping technique (25,26) by combining a high flip angle (FA) 3D AFI (27) with a series of small FA multi-slice gradient echo (GRE) images. The series of multi-slice GRE images were obtained, with one channel transmitting at a time while receiving signals on all channels, with nominal FA = 6°, FOV = 256(RO)×176(PE) mm², matrix size = 128×88, slice thickness = 6 mm, TR/TE = 73/3.4 ms, BW = 260 Hz/pixel, and acquisition time = 3 min 53 s for two averages. Based on these complex images, a B1+ phase shim solution aiming at a CP-mode B1+ distribution over the entire brain was calculated to avoid in subsequent field mapping acquisitions areas of very weak signal (17,28). The 3D AFI dataset was then acquired with a non-selective excitation, nominal FA =60°, orientation = Transversal, FOV = 256(RO)×176(PE)×168(SS) mm³, matrix size = 128×88×48, slice oversampling = 50%, GRAPPA Factor = 2, partial Fourier = 6/8 (PE and SS), TR1/TR2/TE = 30/150/2.1 390 Hz/pixel, acquisition time = 6 min 49 s. Additionally, ΔB₀ maps were derived for the same nine slices from two multi-slice GRE images with different TEs (TE1/TE2 = 4.32/5.34 ms) and were incorporated into RF pulse design to minimize off-resonance effects.

All MB B1 shim and Full pTx MB RF pulses were designed with a single spoke (i.e. without gradient encoding in the transverse plane) to simultaneously excite the desired bands in the brain with |B1+| homogenization. The unity target was defined as homogeneous |B1+| in the desired slices by manually creating a spatial mask only covering the brain tissues in the bands. RF magnitude and phase modulations were calculated with the variable exchange algorithm (29); voxels outside the region of interest (ROI) were not considered. The sub RF pulse used was a Hanning filtered SINC pulse with a bandwidth time product (BWTP) of 10. The final RF pulses were 1 ms in length, defined with a dwell time of 2 μs.

RF pulses were designed for two-band (MB2) and eight-band (MB8) excitation using the two strategies. The inter-slice distance was 56 mm for MB2 and 14 mm for MB8 design. For both MB2 and MB8 cases, L curves quantifying the tradeoff between total RF power and excitation errors were generated by varying the regularization parameter,λ, in the pulse design (see Eqs. 1 and 2). Here the total RF power was calculated via $P\propto {\Sigma }_{q=1}^Q{\Sigma }_{n=1}^N{b}_q^2\left(t_n\right)$ with b_q(t) being the final summed RF pulse shape of the q-th channel and N being the number of time points in the pulse definition. The excitation error, measured by the root mean squared error (RMSE), was given by $\mid \mid \mid \mathit{Aw}\mid -d\mid {\mid }_2∕\sqrt{N_{ROI}}$ for MB B1 shim and $\mid \mid \mid {\mathit{A}}_{\text{full}}{\mathit{w}}_{\text{full}}\mid -d\mid {\mid }_2∕\sqrt{N_{ROI}}$ for Full pTx MB with N_ROI being the number of voxels in the ROI. For comparison, MB2 and MB8 RF pulses were also assembled for the CP mode (referred to as MB CP mode hereafter), mimicking a single channel transmit condition, where the RF magnitudes were adjusted such that the resulting mean FA averaged over the whole brain would be the same as the nominal FA used in MB B1 shim and Full pTx MB pulse design.

3D FA maps of MB2 excitation were estimated to compare the performance of MB CP mode, MB B1 shim and Full pTx MB RF pulses. There was, however, no sequence on the system capable of running fast, large FA B1+ maps with Full pTx MB pulses at the time of this study. Thus, MB RF pulse FA maps were derived by relative comparison with standard RF pulse reference, as will be described in the following, exploiting the inherent proportionality between local |B1+| and signal intensity in small FA GRE images. First, a “reference” 3D GRE image, I_ref, was acquired in the small FA regime (nominal FA = 2°) using a non-selective hard RF pulse in CP-mode, and a 3D AFI was acquired also in CP-mode with a non-selective hard RF pulse (nominal FA = 60°) with similar geometrical parameters. The FA map of the reference image, FA_ref, was directly derived from the 3D AFI map knowing the two corresponding nominal FAs. Second, a 3D GRE image, I_MB, was acquired in the small FA regime (nominal FA = 6°) using the same TR as for I_ref, with a modified 3D GRE sequence where the RF excitation module was replaced by the MB pulse. Finally, the FA map of the MB RF pulse, FA_MB, was estimated by FA_MB = (I_MB/I_ref) · FA_ref. Relevant imaging parameters of the 3D GRE acquisition included: orientation = Sagittal, FOV = 256(RO)×232(PE)×176(SS) mm³, matrix size = 128×58×44, GRAPPA Factor (PE) = 2, partial Fourier = 6/8(PE and SS), TR/TE = 30/3 ms, BW = 390 Hz/pixel, and total acquisition time = 32 s. The 3D CP mode AFI were obtained with the same imaging parameters except for TR1/TR2/TE = 30/150/2.1 ms and total acquisition time = 3 min 11 s.

To demonstrate the feasibility of Full pTx MB when simultaneously exciting a larger number of slices, full pTx RF pulses were designed for four- (MB4), six- (MB6) and eight- (MB8) slice excitation in the brain, and the respective FA maps were estimated using the same imaging protocols as described above for the MB2 excitation. The inter-slice distance was 28 mm in MB4, and 14 mm in MB6 and MB8 pulse design, and the nominal FA was set to 4° for all three cases.

FA map homogeneity was also compared between Full pTx MB and MB CP mode RF pulses when simultaneously exciting four equidistant coronal slices, using similar B1+ and ΔB₀ mapping parameters. The same four slices were also simultaneously imaged with a multi-band GRE sequence using the two types of pulses, followed by un-aliasing of each slice (7). Relevant imaging parameters included: FOV = 256(RO)×176(PE) mm², matrix = 192×132, TR/TE = 100/20 ms, BW = 390 Hz/pixel, acquisition time = 13 s. Reference images for the GRAPPA kernel were collected using the same imaging parameters, while exciting a single band at a time.

Results

For both single spoke MB2 and MB8 pulse design, Full pTx MB yielded better RF performance than MB B1 shim, and both strategies significantly outperformed the MB CP mode (Figure 2). More quantitative analyses based on Bloch simulations (Figure 3) revealed that when using the same total RF power as in the CP mode, the B1+ inhomogeneity, measured by std/mean of B1+ maps, improved from ~25% for MB CP mode, to ~17% for MB B1 shim and to ~10% for Full pTx MB design. When achieving the same excitation fidelity (i.e., same RMSE), the total RF power requirement, which in this case is proportional to total power deposited into the head (i.e. global SAR), decreased by ~58% for MB B1 shim and ~72% for Full pTx MB design, as compared to the MB CP mode. Part of this decrease was due to a decreased mean FA induced by the relatively large regularization imposed on total RF power (Figure 3c). However, even accounting for this resulted in ~56% less RF power in the Full pTx MB design compared to the MB CP mode. Experimental RF power values reported by the SAR monitoring system of the instrument were consistent with the calculated differences.

FIG. 2.

L curves quantifying tradeoffs between total RF power and excitation errors (i.e., root mean square error (RMSE)) in the human brain at 7T for Full pTx MB (○) and MB B1 shim (×), along with MB CP mode (□). For both MB2 and MB8 pulse design with a single spoke, Full pTx MB gave rise to the best excitation fidelity (lowest RMSE) with the same resulting total RF power (as indicated by the horizontal dashed line), or led to the least RF power requirement when achieving the same excitation fidelity (as indicated by the vertical solid line). Note that the single value for MB CP mode (□) is at the crossing between the horizontal and vertical lines.

FIG. 3.

Simulated flip angle (FA) maps for MB8 and MB2 RF excitation in the human brain at 7T for MB CP mode (a), MB B1 shim and Full pTx MB with the same resulting total RF power (b) and with the same excitation fidelity (c), as indicated in Figure 2. Sixteen-channel RF pulses were designed with a single spoke for a nominal FA of 10°. Note that when using Full pTx MB, excitation fidelity significantly improved at a constant total RF power whereas RF power requirement was drastically reduced at a constant fidelity, as compared to MB B1 shim and MB CP mode. Total RF power is in arbitrary units, normalized to the total power required by MB CP mode.

Figure 4 illustrates experimental results of MB2 RF excitation in the human brain using MB CP mode, MB B1 shim and Full pTx MB pulses designed for the same total power. Consistent with Bloch Equation simulations (Figure 3), Full pTx MB strategy yielded the best B1+ homogenization (i.e., the least std/mean value) in the two bands versus the MB B1 shim and MB CP mode, especially for the lower band in the cerebellum. Furthermore, good agreement was seen between experimental results and the numerical predictions.

FIG. 4.

MB2 RF excitation in the human brain at 7T for MB CP mode, MB B1 shim and Full pTx MB with the same resulting total RF power. Sixteen-channel RF pulses were designed with a single spoke with the base pulse being a filtered SINC pulse of BWTP = 10. Pulse duration = 1 ms, nominal flip angle = 6°, slice thickness = 6 mm and inter-slice distance = 56 mm. Note that FA inhomogeneity, measured by std/mean of the FA map, that already improved from 22% for MB CP mode to 18% for MB B1 shim, was significantly reduced to 7% for Full pTx MB. In all cases, experimental results were in good agreement with numerical predictions.

Figure 5 displays the in vivo FA estimations for Full pTx MB4, MB6 and MB8 RF excitation. For all these three MB factors, improved FA uniformity was achieved and the experimental results were in good agreement with the numerical predictions.

FIG. 5.

Full pTx MB RF excitation in the human brain at 7T using higher MB factors. Sixteen-channel RF pulses were designed with a single spoke with the base pulse being a SINC pulse of BWTP = 10. The pulse duration = 1 ms, nominal flip angle (FA) = 4° and slice thickness = 6 mm. The inter-slice distance was 28 mm for MB4, and 14 mm for MB6 and MB8. Note that in all cases satisfactory FA homogenization was achieved, and experimental results were in good agreement with numerical predictions.

Figure 6 illustrates the comparison of MB CP mode to Full pTx MB RF pulse design when simultaneously exciting four coronal slices for the same total RF power. Similar to axial excitations (Figure 4), Full pTx MB yielded significantly improved B1+ homogenization in the four slices with image uniformity effectively restored in the challenging areas (such as the frontal and lower temporal lobes) and right-left asymmetries, as compared to MB CP mode.

FIG. 6.

MB CP mode vs Full pTx MB when simultaneously exciting four coronal slices in the brain at 7T with same resulting total RF power. Second and third rows display the unaliased four slices for MB CP mode and Full pTx MB, respectively, with the leftmost image being the corresponding MB acquisition. Corresponding flip angle (FA) maps are also shown in first and fourth rows with the ROI’s embraced by white curves. RF pulses were designed with a single spoke with the base pulse being a filtered SINC pulse of BWTP = 6. Pulse duration = 1 ms, nominal FA = 24°, slice thickness = 4 mm and inter-slice distance = 44 mm. Note that the signal loss and right-left asymmetries observed in the unaliased images for MB CP mode were effectively restored by Full pTx MB and that the largely overestimated and erroneous values observed within the ROI in the most anterior slice of Full pTx MB FA map arose from the signal dropout in the CP mode 3D GRE reference image which was used as a denominator in the FA calculation.

Figure 7 shows MB image reconstruction of four coronal slices for Full pTx MB4 RF excitation in human brain using either the individual components of the Full pTx MB4 pulse one at a time exciting single slices, or as a Full pTx MB pulse exciting and acquiring simultaneously. In this case, differences are not expected between the two applications. Satisfactory unaliasing of the four slices was obtained with high similarity between the unaliased and separately acquired images. L-factor maps (30) analyzing signal leakage between simultaneously excited and acquired slices were calculated and exhibited small residual aliasing.

FIG. 7.

Image reconstruction for four simultaneously excited coronal slices in human brain at 7T using the same Full pTx MB RF pulses as in Figure 6. All 2D GRE images were obtained with orientation = Coronal, in-plane resolution = 1.3 mm isotropic, FOV = 256(RO)×176(PE) mm², and TR/TE = 100/20 ms. Note that satisfactory separation of the four slices was obtained with high similarity between unaliased and separately acquired images. Also shown in the bottom row are the normalized L-factor maps for the most anterior slice where small residual signal leakage from this slice to the other slices was seen. The mean L-factor quantifying the signal leakage averaged over all the four slices was 0.06.

Discussion

In standard slice selective or 3D applications, pTx methods have been effective in ameliorating B1+ inhomogeneities with a variety of techniques, such as B1-shimming (i.e. single spoke) (20-23,31,32), transmit SENSE (33-36), multi-spoke pulses (3,37,38), k_T-point pulses (39), etc. Here, we demonstrate that the pTx technology permits significant improvements in B1+ homogeneity and/or RF power in multiband pulses, which are increasingly used in fMRI and dMRI.

The Full pTx MB method simultaneously applies multiple independent B1 shimming solutions, each acting on a specific band. Furthermore, the Full pTx MB method relies on standard slice selective RF and gradient waveforms (no additional excitation k-space trajectory). Achieving this, however, requires the capability to transmit an independent and arbitrary RF waveform on each Tx channel; by comparison, with MB B1 Shim, the same MB RF pulse shape is sent to all channels, only requiring channel-specific static phase and magnitude change, which can be achieved with simpler hardware.

The advantages of the new pulses are evaluated in this study by comparing excitation fidelity while keeping total RF power the same and vice versa. The section of the L-curve between the two limits marked by the horizontal and vertical lines that intersect at the CP-mode point (Figure 2), most notably the points near the L-curve inflection region, however, represent compromises that would provide significant improvements in both B1+ homogeneity and RF power compared to the CP mode.

Although this study deals with MB RF pulses specifically and not with the issue of improved unaliasing, four-fold slice accelerated performance with small residual signal leakage is demonstrated using these pulses taking advantage of the coronal plane and azimuthal distribution of the transceivers, with comparable unaliasing performance relative to conventional MB CP pulses. Controlled aliasing methods (CAIPIRINHA (40) or blipped CAIPI (12) for EPI) and the use of separate arrays with a larger number of receivers (e.g. 32) will certainly improve the results, allowing, for example, Full pTx MB8 design as well as unaliasing of the resultant eight slices in the axial orientation.

When regularized only with the total RF power and without a specific constraint on local SAR, the latter may not necessarily be reduced (41,42). Although future work will explore such constraints, at the present we examined the current implementation for local SAR safety guidelines (43) by calculating local 10g average SAR values in a way similar to those in (44,45) for the in vivo experiments when using axial MB8 and coronal MB4 full pTx pulses, based on electromagnetic modeling of the transceiver loaded with a medium-sized head tissue model (Virtual family, Duke, 2×2×2.5 mm³ resolution). The peak 10g local SAR calculated for the utilized flip angle, pulse duration and duty cycle was 0.26 and 1.2 W/kg for the axial MB8 and coronal MB4 pTx experiments, respectively, and was a factor of >8 below the IEC local SAR limit (43). Furthermore, when matched for the total RF power in the axial MB8 case, the peak 10g local SAR was even slightly lower in full pTx MB pulses versus the conventional CP mode implementation (0.26 vs. 0.28 W/kg, respectively). Nevertheless, pTx pulse design also provides additional degrees of freedom to control peak local SAR through regularization (46) or explicit constraints (47,48) and can incorporate simultaneous controls on local SAR, global SAR, peak RF power, etc. This remains to be explored in future studies.

The individual RF pulses corresponding to the different bands in the final summed MB pulse have different frequencies; as previously stated (Theory section), this enables the use of $\mid \mid {\mathit{w}}_{\text{full}}\mid {\mid }_2^2$ as an optimum constraint on total RF power in Full pTx MB in accordance with Parseval’s theorem. Similarly, the use of $\mid \mid {\mathit{S}}_0{\mathit{w}}_{\text{full}}\mid {\mid }_2^2$ (where is the global SAR matrix) would be valid for global SAR constraint. However simply using $\mid \mid {\mathit{w}}_{\text{full}}\mid {\mid }_{\infty }^2$ for peak RF power control as proposed for interleaved slices (47) would no longer be optimal (49).

In this study, the performance of the Full pTx MB RF pulses is demonstrated using small tip angle excitation; however, RF pulses designed with a single spoke, as employed in this study, can actually be also employed for refocusing just by scaling up the RF magnitudes to reach a 180° FA, while still maintaining the same level of FA homogenization. However, when multiple spokes are desired for further improvement of the FA homogeneity, large FA pulse design methods have to be considered (50).

Although the results presented were obtained at 7T, significant gains can also be expected at 3T with respect to both B1+ uniformity and RF power. For example, in the WU-Minn (i.e. Washington University in Saint Louis - University of Minnesota) consortium of the HCP (http://humanconnectome.org), the 3T SE HARDI data are obtained at a high spatial resolution (1.25 mm isotropic) (16,51), with TR ~5.5 s with an MB3 pulses. This is inefficient for temporal SNR; higher MB factors were not possible because of power deposition constraints. Similarly, even at 3T, transmitting with a body coil, the B1+ distribution in the human head displayed up to 30° variation in FA for a 90° target FA (unpublished data). Especially in a SE sequence, this translates into a spatially non-uniform SNR. Finally, it is well recognized that B1+ inhomogeneities exist in the human torso at 3T. Future applications of MB pulses in the human torso would require optimizations as described in this work.

Conclusions

We have introduced Full pTx MB RF pulse design for simultaneous multi-slice RF excitation with B1+ homogenization and total RF power constraint. Experiments obtained in human brain at 7T show that the use of such Full pTx MB pulses can lead to significantly improved B1+ uniformity and/or largely reduced total RF power, as compared to MB B1 shim and the conventionally employed MB CP mode. These gains are expected to alleviate major limitations encountered with the use of slice acceleration not only at 7T but also at the clinically available field strength of 3T.