The presented method calculates distributions of B₁⁺ fields (expressed as the local flip angle α_local) from the ratio of stimulated echo (STE, nominal flip angle α/2) and spin echo (SE, nominal flip angle α) images acquired successively following spin excitation [15]:(1)where S_SE and S_STE are the intensities of the SE and STE images and TM is the time interval between the spin and stimulated echo RF pulses (mixing time). EPI phase images are affected by susceptibility effects and only magnitude images are used to calculate the local B₁⁺ field. As a result, two possible values of α_local (90+δ and 90−δ) exist at each voxel that obey equation 1. In order to overcome this ambiguity, N pairs of SE and STE images are acquired with different nominal flip angle values α and the correct α_local values are identified as those yielding a constant α_local/α ratio across the repetitions [15]. Here, the local B₁⁺ values are calculated as a percentage of the nominal flip angle (in percent units = p.u.) using the hard pulse approximation [18]:(2)As a result of the acquisition of N pairs of SE and STE images, N estimates of B₁⁺ are calculated at each voxel. In the following, the average of these N values is used as a measure of the local B₁⁺ value. The standard deviation SD_B1+ of B₁⁺ across the N repetitions is used as a measure of the uncertainty in the B₁⁺ calculation. Note that in the experiments described below, a large number of SE/STE pairs were acquired while the number of SE/STE pairs used for calculation of the B₁⁺ field was kept smaller.

Three volunteer subjects were scanned after giving written consent according to the declaration of Helsinki. The study was approved by the ethics committee of the University of Magdeburg. 3D EPI data were acquired on a 7T whole-body system (Siemens Healthcare, Erlangen, Germany), operated with head-only CP transmit and 24-channel receive coils (Nova Medical, Inc., Wilmington MA). One B₁⁺ map was also acquired on each subject using the Actual Flip Imaging (AFI) B₁⁺ mapping method [12], [16]. Additional phantom experiments were conducted on another 7T whole-body system (Siemens Healthcare, Erlangen, Germany) operated with a 32-channel receive coil (Siemens Healthcare, Erlangen, Germany). Image processing was performed offline using Matlab (The MathWorks Inc., Natick, MA) version 7 and SPM8 (www.fil.ion.ucl.ac.uk).

The following parameters were used for data acquisition with the AFI method: matrix size 64×60×48, image resolution 4×4×4 mm³, image orientation: (phase, read, partition) = (A-P, H-F, R-L), FOV 256×240×192 mm³, TE = 2.93 ms. The RF excitation pulse was a non-selective Hamming-filtered sinc pulse with a nominal time-bandwidth product of 1. The RF duration was 820 µs and the nominal flip angle value was 60°. The MR parameters for spoiling of transverse coherences were set following the recommendations given in [25]. The spoiler duration was set to 11 and 55 ms for TR₁ and TR₂ respectively. The spoiler amplitude was set to 26 mT/m, leading to gradient moment values A_G1/A_G2 = 286/1430 mT.ms/m [25]. The repetition times were set to the minimum achievable value given the spoiler duration i.e. 20 ms and 100 ms for TR₁ and TR₂ respectively. RF spoiling was used with a linear phase increment °. Partial Fourier (factor 6/8) was used along the partition direction. The total acquisition time was 4 min 32 s. Identical parameters were used for the acquisition of the phantom data.

A reference B₁⁺ map was acquired on an oil phantom using the 2D DAM method described in [16]. The acquisition parameters were as follows: matrix size: 64×48, image resolution: 4 mm³, TE = 25 ms, image orientation (read, phase, slice) = (R-L, A-P, H-F). 48 slices were acquired and the repetition time was set to 25 s in order to avoid bias due to longitudinal relaxation. The presaturation pulse was a rectangular pulse of duration 500 us and its nominal flip angle value was set to 22° and 66°. The excitation RF pulse was a slice-selective sinc pulse of duration 2560 us. The total acquisition time was 40 min. Due to this long acquisition time this method was only used on the phantom.

The 3D EPI and 3D AFI methods were compared with a reference 2D DAM method on an oil phantom. A deviation of −4.3±0.9 p.u was observed between the 3D EPI and the 2D DAM method and a deviation of −5.5±3 p.u. was found between the 3D AFI and the 2D DAM method. Note that parallel imaging was not implemented for the 3D EPI acquisition on the oil phantom, degrading the quality of the results obtained for this method. In-vivo quantitative measures of the accuracy, reproducibility and linearity of the optimized 3D EPI method were extracted from a group of 3 subjects.

Since no fast reference technique has been validated in-vivo at 7T, accuracy estimates were obtained by calculating the deviations between the 3D EPI and 3D AFI methods. The acquisition parameters of the 3D AFI method were carefully set in order to achieve maximal spoiling of the transverse coherences and highly accurate B₁⁺ maps [25]. Only small (2.6±4.1 p.u.) differences in B₁⁺ values were observed between the two methods in the superior part of the brain. B₁⁺ values larger by 5 to 10 p.u. were measured with the 3D EPI method in the temporal lobes, where the local B₁⁺ values were particularly low. This is in agreement with systematic underestimation of the B₁⁺ field by the 3D AFI method due to suboptimal spoiling conditions where the actual flip angle is low [25] and supports the claim that our method maps the B₁⁺ field accurately over the entire brain. The discrepancies between the two methods in the OFC most likely stem from the off-resonance sensitivity of both methods (see Results section for estimates of the sensitivity of the 3D EPI method to off-resonance effects obtained from numerical Bloch Equation simulations).

The linearity of the 3D EPI B₁⁺ mapping method against varying RF transmit reference voltage is a necessary though not sufficient condition to demonstrate the robustness of the method and is therefore complementary to the reproducibility and accuracy measures supplied here. An average non-linearity of 1.6 p.u. was found across the 3 scanned subjects, demonstrating a highly linear relationship between the measured B₁⁺ maps and RF transmit voltage. The 10% increase in reference voltage used for the linearity test proved to be sufficient in order to demonstrate the improvements from our optimization procedure and was significantly higher than the level of inaccuracy (compared with the 3D AFI method), reproducibility and non-linearity demonstrated here. If a stronger variation of the reference voltage is desired to enhance the sensitivity of the test, special attention should be given to the maximum RF voltage in order to avoid clipping of RF pulses.

A measure of the reproducibility of the 3D EPI method was obtained by calculating the voxel-wise standard deviation of the B₁⁺ maps over three successive acquisitions. An average level of instability of 0.7 p.u. was observed, illustrating the robustness of the method against physiological effects.

A large number of α values was used to allow dense sampling of the large B₁⁺ inhomogeneities present at 7T and increase the dynamic range of the technique. A sub-sample of SE/STE images was selected for each voxel to avoid low signal to noise in the calculation of the B₁⁺ values. This implied a reduction in data sampling efficiency but enabled accurate and precise B₁⁺ mapping over the whole brain. An improved modelling and weighted fitting procedure may allow for use of the whole dataset and increase precision further. Highly accelerated image acquisitions helped keep the total acquisition time sufficiently short (4 min34 s+2 min B₀ map) so that B₁⁺ mapping can remain only a small fraction of a larger scanning protocol. The increased dynamic range of the optimized method led to a 53 p.u. reduction in the non-linearities of the 3D EPI method against RF transmit voltage in the temporal lobes and cerebellum and is essential for whole-brain B₁⁺ mapping at 7T.

Minimization of off-resonance effects consisted of the use of RF pulses with maximal amplitude and minimal duration for all nominal values. This led to a reduction of the non-linearities by 5.2 p.u. in the OFC, in good agreement with the results from the Bloch Equation simulations. Further improvements to the method might involve correcting for the effect of off-resonance precession on the local B₁⁺ values using the results of the Bloch simulations presented here and the acquired B₀ maps.

The average non-linearity and reproducibility of the B₁⁺ maps after optimization was 1.6 p.u. and 0.7 p.u. averaged over the whole brain and across subjects. However, local regions with non-linearities greater than 5 p.u. remained in the temporal lobes and cerebellum. A larger maximum α value (leaving the spacing between consecutive values unchanged) would improve the robustness of the method in these regions without compromising the quality of the B₁⁺ maps in other brain regions. Alternatively, other methods may be suitable for fast and robust whole brain B₁⁺ mapping at 7T (e.g. [12], [14], [16], [26]), although a systematic analysis of the performance of these methods at UHF has not been reported. The 2D STEAM method described in [16], [26] is particularly fast but sensitive to physiological artefacts and requires independent calibration. The 3D STEAM method presented in [15] might alleviate these difficulties and benefit from the shorter acquisition time. However, the problems related to off-resonance and large B₁⁺ deviations present at 7T might also prove problematic for this technique. Long TR gradient-echo techniques such as in [17] yield robust B₁⁺ estimates due to their simplicity. However, their long acquisition time (∼20 mins per slice, see e.g. [17]) renders these methods impractical for in-vivo applications.

The optimized B₁⁺ mapping protocol described here could be implemented on all subjects without clipping of the RF pulses and/or exceeding the SAR safety limits. The reference RF voltage was typically ∼315 V for the subjects scanned, leading to a maximum RF voltage of ∼450 V. This was sufficiently low to accommodate a 10% increase in reference voltage to test the linearity of the method without clipping the RF pulses or exceeding the SAR limit. A maximum nominal flip angle of 340° should therefore be achievable. However, if higher nominal flip angle values are desirable, longer RF pulses should be used with longer TR values in order to comply with safety limitations. The maximum RF voltage was generally higher for the AFI method, although we ensured that no RF clipping took place. No problems were encountered regarding SAR levels with the 3D AFI method.

Note that the 3D EPI method can easily be tuned to produce high quality B₁⁺ maps in one specific region of interest only by setting the range of nominal flip angles appropriately. The number of required nominal flip angles might be significantly reduced as a result, leading to a significant reduction in acquisition time. Although this method has not been tested outside the brain, the possibility of tuning the nominal flip angle values according to a specific region of interest might prove advantageous when other body parts are targeted. However, specific features of the body part of interest (size, tissue density, B₀ homogeneity, …) should be considered with care.

Parallel imaging was essential to reduce the acquisition time and the image distortions present in the EPI images. Despite parallel imaging, image distortions remained visible in the SE and STE images which required correction. For this purpose, B₀ mapping data were acquired using a standard dual-echo gradient-echo sequence. The two corresponding echo times were carefully chosen to provide a high SNR, result in a fat signal in-phase across both echo images and avoid phase wrapping problems in the B₀ map calculated as part of the unwarping procedure. Due to the lack of a distortion correction software on the scanner console, image distortion was implemented offline [16], [23].

We have presented an optimized SE/STE 3D EPI method for mapping of the RF transmit field B₁⁺ at 7T. A robust offline unwarping procedure was used in order to correct for image distortions. The dynamic range of the method was increased to match the higher level of B₁⁺ inhomogeneities at 7T and off-resonance effects were minimized using RF pulses with large amplitudes and short durations. The improvements induced by our optimization were most significant in the temporal lobes, cerebellum and orbitofrontal regions, which are notoriously problematic brain regions at ultra high fields. Whole brain B₁⁺ maps were obtained in a total acquisition time of 4 min34 s (+2 min B₀ map) with non-linearity and reproducibility of 1.6 p.u. and 0.7 p.u. respectively and deviations of 2.6 p.u. from the 3D AFI method in brain regions where the latter method performed satisfactorily.