Multislice B 1 Mapping Method Using Magnetic Resonance Composite Spin Echo Sequences and Simultaneous Echo Refocusing

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Te magnitude-based B 1 mapping methods depend on changes in magnitude of MR signal according to the B 1 feld and include ftting progressively increasing FAs [6], stimulated echoes [7], ratios of MR signals [8][9][10][11][12], signal null at certain FAs [13], ratio of the MR signals acquired at a dual steady state [14], and comparison of spin echo (SE) and stimulated echo signals [15].Tese methods have several combinations of the following problems: T 1 dependence; long acquisition times, mainly from acquiring several images; long repetition time (TR) for mitigating the T 1 acquisition; and inaccuracy over a wide range of B 1 especially at low FAs or FAs close to 90 °or 180 °.Several phase-based B 1 mapping methods have been proposed as an alternative to magnitude-based B 1 mapping methods [16][17][18][19][20]. To generate the MR signal phase dependence on FA, Morrell [16] and Chang [17] proposed the use of a pair of successive orthogonal RF pulses, whereas Sacolick et al. [18] proposed the use of the Bloch-Siegert phase shift efect [21].
Although such efective B 1 mapping methods based on phase or magnitude imaging have been proposed [7, 9, 11, 13-16, 18, 22-25], these methods often require the complex modeling, long acquisition time, or specialized MRI sequences.Terefore, these methods have not been integrated into clinical applications, resulting in an ongoing need for a practical, accurate, and fast B 1 mapping method.
Te multislice excitation technique is commonly used in MRI to obtain three-dimensional (3D) spatial coverage.It can be described as a process during which multiple image planes are independently sampled using diferent frequency ofsets in the RF pulses of otherwise identical MR pulse sequences.Experiments to improve efciency in sequences for SE imaging have been demonstrated using interleaved methods.Te interleaved T 2 -weighted SE sequences where selective RF pulses independently excite and then refocus diferent slice signals, essentially interleaving the SE sequences during the delay time between pairs of excitations and refocusing pulses, have been successfully applied in clinical practice [26].Te multislice sequences are faster and more efcient than conventional analogs since the interleaving process eliminates relatively large sequence dead time.Recently, the simultaneous echo refocusing (SER) technique has been proposed to overcome the interleaved approaches [27].Te MR signals in multiple image planes are generated with slice-selective RF excitations and acquired within an SE pulse, utilizing a shared refocusing process.Te MR signals originating from diferent slices are refocused at diferent times on each read period and further refocused with switched read gradients.In the proposed applications, temporal simultaneity of SER is efectively similar to that in 3D Fourier transform (FT) imaging, only without long data acquisition periods needed in 3D FT to obtain sufcient sampling along two-phase encoding axes.Terefore, the SER method can be used in the B 1 mapping method to extend the 3D spatial coverage only without long data acquisition.Particularly, the B 1 mapping method using composite RF pulses and multislice imaging (by applying SER techniques) is more efcient in reducing data collection time compared to the previous B 1 mapping method using composite RF pulses.
In this study, we proposed the multislice B 1 mapping method using a pair of composite RF pulses, 90 y °− 0 x °− 90 y °and 90 y °− 180 x °− 90 y °, and SER technique.Te performance of the proposed B 1 mapping method was evaluated using the computational simulations and phantom and in vivo human experiments using a 3-Tesla MRI scanner.Particularly, the multislice iterative signal intensity (ISI) mapping method was selected as a reference method for comparison with the proposed B 1 mapping method in all MR experiments because it is an accurate method for signal intensity measurements even if the data acquisition time is long [6].

Theory
2.1.Phase-Based B 1 Mapping Methods.As mentioned above, there are some phase-based B 1 mapping methods.One method by Oh is referred to as the SE phase-sensitive method [19].Tis method uses composite SE pulses for encoding the FA in the phase of the resulting image and requires a baseline subtraction image for removing other sources of image phase, such as main magnetic feld (B 0 ) inhomogeneity and receive phase.One method by Morrell is referred to as the phasesensitive method [16].Tis method uses an excitation pulse with a gradient-recalled echo (GRE) sequence for encoding the FA in the phase of the resulting image instead of using an SE sequence.Tis method has the same long TR requirement as the signal magnitude-based sequences, although it is effective and more accurate in a larger range of FAs than a double angle signal magnitude-based B 1 map [28].Tese two phase-based B 1 mapping methods are based on composite RF pulses and typically employ large FAs.One method by Sacolick introduced the Bloch-Siegert shift method as an alternative to the composite RF pulse methods [18].Te Bloch-Siegert shift method provides a detectable phase shift in FA mapping, enabling the use of sufciently long ofresonance RF pulses with amplitudes compatible with various clinical applications.Te efciency of the Bloch-Siegert shift method is insufcient due to the long RF pulse that requires a long echo time.One method by Chang requires a regular 3D GRE sequence with a magnetization preparation RF pulse of the same FA but orthogonal in phase to the excitation RF pulse for mapping the amplitude of the B 1 of a transmit RF coil in 3D [17].

Multislice B 1 Mapping Using a Pair of Composite RF
Pulses and SER Technique.Figure 1 shows the pulse sequence diagram for the proposed B 1 mapping scheme.Te pulse sequences begin with temporally sequential sliceselective RF pulses with selection gradients to produce signals in multiple adjacent slices.After temporally sequential selective RF pulses, a nonselective composite RF pulse of 90 y °− 180 x °− 90 y °for sequence 1 and nonselective composite RF pulse of 90 y °− 0 x °− 90 y °for sequence 2 are applied to generate the SE signals.Encoding gradients are also applied.Let us assume that the resulting magnetization for k-th slice-selective RF pulse is represented by M k re (B 1 ; t) + iM k im (B 1 ; t).Te resulting complex-numbered signal can be expressed as follows [19]: and S k seq1 (B 1 ; t) and S k seq2 (B 1 ; t) are the resulting signals generated by the k-th slice-selective RF pulse with selection gradient of sequences 1 and 2, respectively.
Tese SE signals are acquired within each readout period and provide phase information that is dependent on the B 1 2 Concepts in Magnetic Resonance Part A, Bridging Education and Research feld strength.Te resulting phase of the k-th slice, ϕ k B1 , can be obtained by calculating the phase diference of two pulse sequences: where phase( ∘ ) is the phase of argument and conj( ∘ ) is the complex conjugate of argument.Because the phase diference between sequences 1 and 2 is identical except the RFdependent phase change due to the 180 x °RF pulse, the proposed B 1 mapping method efectively eliminates all possible phase errors caused by other sources (e.g., RF coildependent phase delays).Although the phase change is directly proportional to the B 1 strength in frst-order approximation, an B 0 inhomogeneity afects the application of nonselective composite RF pulse.Terefore, computational simulations are required to properly analyze the detailed spin behavior during the nonselective composite RF pulse.Practically, since B 0 inhomogeneity is dependent on the length of nonselective composite RF pulse, this length should be minimized.In this study, the Bloch equation for detailed spin behavior was solved using the fourth-order Runge-Kutta method [19].After predicting the B 1 felddependent phase changes for a given B 0 inhomogeneity, the resulting phase behavior can be used to correct B 0 inhomogeneity of the proposed B 1 mapping method.An experimental B 0 inhomogeneity can be calculated using the echo-shifting method [19].Terefore, two MR images were acquired with RF pulses of 90 y °− 180 x °− 90 y °and 90 y °− 180 x °− 90 y °with a shift of 1 ms.B 0 inhomogeneity efects in the resulting phase can be corrected based on the computational simulations.

Materials and Methods
Te proposed B 1 mapping method is based on a phasesensitive method and capable of acquiring multislice images.
To evaluate the performance of the proposed B 1 mapping method, computational simulations were conducted, and it was compared with three other B 1 mapping methods: Morrell's method [16], double angle method (DAM) [11], and Yarnykh's method [14] (see Figure 2).For DAM based on the SE sequence, a simulation parameter was selected with two given FA values (90 °and 180 °for α and 2 α, respectively), to obtain two signal intensity maps (see Figure 2(a)), which involves 1% white Gaussian noise.Ten, two signal intensity maps were calculated using equation ( 1), and the actual FA maps were measured at angles from 0 °to 360 °.For Yarnykh's method, the simulation parameters were selected with TR 1 /TR 2 � 100 ms/400 ms and T 1 � 600 ms, and 1% white Gaussian noise was also used (see Figure 2(b)).Morrell's method was generalized to arbitrary FAs (2α x and α x ) (see Figure 2(c)).If two orthogonal pulses of arbitrary, identical FAs are applied in quick succession, the FA would be estimated by α � arccos (tan(θ)), where θ is the resulting phase.Te proposed B 1 mapping method was based on the phase sensitivity map (see Figure 2(d)).Te phase maps were obtained using the Bloch equations [19].Te actual FA maps were calculated in a manner similar to Morrell's methods (i.e., FA(θ) � I 2 (θ)−I 1 (θ)) using two-phase maps.In computational simulation, the signal-to-noise ratio (SNR) efciency, which is indicated as the angle-to-noise ratio (ANR), was defned as the SNR in the FA map.For initial simulation comparison, readout acceleration along the phase encoding was not considered, and the optimal parameters that rely on the T 1 value of the tissue, target FA value, and T 2 efects were also ignored.
Te study protocol was approved by the Institutional Review Board of the Korea University, and all procedures used in the study were conducted in accordance with the International Ethics Standards and the Declaration of Helsinki.Written informed consent was obtained from one participant (sex, male; age, 30 years) after a full explanation of the study procedures.Te RF pulse sequence was designed with sequence secure data transfer software (Phillips Healthcare, Netherlands).To validate the signal intensity of the proposed B 1 mapping method, all MR experiments were performed in a 3-Tesla MRI scanner (Achieva TX, Philips Healthcare, Te Netherlands) using two B 1 mapping methods: proposed B 1 mapping method and multislice ISI mapping method [6].
Tese methods were compared with the following parameters: TR/TEs � 500 ms/20 ms, 40 ms, and 60 ms; feld of view � 240 × 240 mm 2 ; matrix size � 560 × 560; number of slices � 3; slice thickness � 5 mm; FAs of temporally sequential excitations � 90 °(α); and scan time � 4 : 01.5 per RF pulse (total acquisition time � 8 : 03).Te multislice ISI mapping method was conducted by changing the FA of the refocusing pulse from 5 °to 145 °on the multislice SE with the same parameter resulting in scan time � 4 : 01.5 per FA (total acquisition time � 116 : 43.5), and the FA with the maximum signal was obtained via spatial mapping of the image.A water phantom consisting of CuSO 4 and distilled water (1 g/1 L) with a diameter and height of 200 mm was used in the phantom experiment.A commercial quadrature transmit/receive volume coil (Philips Healthcare, Te Netherlands) was used in all MR experiments.

Results
Te resulting phase of the proposed B 1 mapping method from the numerical result for each RF feld strength, B 0 inhomogeneity, and composite RF pulse duration is shown in Figure 3. Without B 0 and B 1 feld inhomogeneities, the applied RF feld strength and resulting phase are identical (180 °).Without B 0 inhomogeneity, the obtained results show the quite linear RF feld and resulting phase relationship within the given RF feld strength range of [120 °, 240 °] without afecting the composite RF pulse duration.For a given B 0 inhomogeneity, the nonlinearity of the relationship between the resulting phase and RF feld strength increased with increasing B 0 inhomogeneity.By considering RF power and B 0 inhomogeneity, a reasonable composite RF pulse duration for the phantom and in vivo human experiments is 300 μs, which makes the linear RF feld and resulting phase relationship within the given RF feld strength range of [120 °, 240 °].
Figure 4 shows the simulation results of ANR profles for four B 1 mapping methods, including DAM, multislice composite RF pulse (proposed B 1 mapping method), Morrell's method, and Yarnykh's method.Te ANR distribution of Yarnykh's method shows a bell-shaped curve, and the noise value changed at an FA of 180 °.Te ANR distributions of the DAM and Morrell's method show that their noise values increase at FAs of 47 °and 3 °, respectively.For the proposed B 1 mapping method, the noise value increases at an FA of 21 °.Although the proposed B 1 mapping method did not create a large diference compared with Morrell's method (see Figure 4), these results clearly show that the ANR distribution of the proposed B 1 mapping method is more uniformly distributed compared to that of other B 1 mapping methods, indicating that the proposed B 1 mapping method could provide a more accurate FA value over a wider FA range.Moreover, in terms of scan efciency, it should be noted that the proposed method performs 93.1% better than the multislice ISI mapping method.
Figure 5 shows MR magnitude images for three echo signals (RF 1 , RF 2 , and RF 3 ) obtained from the composite RF pulses in the phantom.Especially, the frst row represents MR images by the RF sequence using a composite RF pulse (90 y °− 0 x °− 90 y °), the second row shows MR images by the same RF sequence using a composite RF pulse (90 y °− 180 x °− 90 y °) under the phase shift of 180 °RF pulse on the x-axis, and the third row presents MR images by the RF sequence using a composite RF pulse (90 y °− 180 x °− 90 y °) with 1 ms shift.Additionally, slices 1, 2, and 3 were obtained at diferent TEs of 30 ms, 20 ms, and 10 ms, respectively.
Figure 6 shows the FA distributions of the proposed B 1 mapping method and multislice ISI mapping method with the phantom.Figure 6(a) shows B 0 inhomogeneity maps estimated by RF sequence 1 using a composite RF pulse with 1 ms shift and RF sequence 1 using a composite RF pulse.Te B 1 map estimated by the proposed B 1 mapping method with the no-correction method is shown in Figure 6(b).Based on computational simulations, phase maps generated by the proposed B 1 mapping method (see Figure 6(b)) are corrected with B 0 inhomogeneity (see Figure 6(c)).Te diference between the values after and before correcting B 0 inhomogeneity is shown in Figure 6(d).Furthermore, the B 1 map estimated by a reference method, multislice ISI mapping method, is presented in Figure 6(e).Errors between the proposed B 1 mapping method and multislice ISI method are shown in Figure 6(f ).Tere was no remarkable diference between the two methods regarding the FA distribution with the phantom (<10%).Te main diferences between the two To verify the performance of the proposed B 1 mapping method in an in vivo human brain, MR experiments were performed, and all analyses conducted with the phantom, except for B 0 correction, were repeated.Figure 7 shows the FA maps of the proposed B 1 mapping method, multislice ISI mapping method, and FA error maps for three slices.In the region-of-interest analysis, diferences among the two methods and FA errors were −3.2%, 4.8%, and 6.7%, respectively.

Discussion
A novel B 1 mapping method using a pair of composite RF pulses and SER techniques is presented in this study.Tis B 1 mapping method could improve 3D spatial coverage of B 1 mapping with long TR to reduce the efect of T 1 , and its characteristics were confrmed with computational simulations and phantom and in vivo human experiments on the 3-Tesla MRI scanner.
In computational simulations, the results revealed that the ANR distribution of the proposed B 1 mapping method is more uniform compared to that of Morrell's method [16], DAM [11], and Yarnykh's method [14].Tese results suggest that the proposed B 1 mapping method could provide more accurate B 1 feld strength measurements over a wider B 1 feld strength range.Additionally, our proposed B 1 mapping method has more acquisition time efciency compared with Morrell's method [16] by having multiple excitation RF pulses with diferent RF frequency ofsets on the single TR for multislice MR imaging.Such strength of the proposed B 1 mapping method can be applied to Morrell's method [16] because its methodology is similar to that of Morrell's method [16].
In the phantom experiment, the results showed that there was no signifcant diference in the B 1 feld distribution (<10%) between the proposed B 1 mapping method and multislice ISI mapping method.In addition to phantom experiments, the results of the in vivo human brain study revealed that the diferences between the proposed B 1 mapping method and multislice ISI mapping method were noted at the Gaussian noise level in the FA distribution (<10%).Here, the multislice ISI mapping method was used as a reference method for performance evaluation of the proposed B 1 mapping method due to its accuracy by repeated measurements of signal intensity [8].Based on these results, the proposed B 1 mapping method facilitates FA distribution with high accuracy and temporal resolution within a single TR, regardless of the tissue characteristics.
However, the proposed B 1 mapping method has several limitations in terms of its narrow bandwidth and restricted Concepts in Magnetic Resonance Part A, Bridging Education and Research TR in connection with the slice selectivity and number of RF excitation pulses.Tese limitations can be overcome using a high-power RF amplifer and parallel RF excitation, but the proposed B 1 mapping method can increase the SAR in such situations.Moreover, a multichannel transmission RF coil should be used for parallel excitation in the proposed B 1 mapping method; however, this application is limited in commercial 3-Tesla MRI scanners.
In addition to limitation of the proposed B 1 mapping method, this study has some limitations.First, B 0 correction was not performed in data processing procedure for in vivo human brain due to the diferences in signal intensity between the proposed B 1 mapping method and multislice ISI mapping method observed at the Gaussian noise level.Moreover, the proposed B 1 mapping method was evaluated in brain region only in this work at 3-Tesla MRI scanners.However, in a recent report, the proposed B 1 mapping method had been successfully implemented for the wholebody imaging in the 1.5-Tesla MRI scanners, showing the robustness and feasibility of the proposed method [29].Te B 1 mapping method proposed in this study is based on phase-sensitive B 1 mapping methods.Since both double angle and phase-sensitive B 1 mapping methods require moderately long TRs, the imaging speed using one of these methods depends primarily on the acquisition scheme used.Presaturated double angle B 1 mapping with reduced scan time has been achieved using slice-selective excitation and rapid spiral data acquisition [16].Tis rapid readout scheme could be applied to the phase-sensitive technique to have a similar efect as reducing acquisition time.
Furthermore, the phase-sensitive B 1 mapping methods could only be applied to 3D imaging, as the RF pulses are nonselective.Nonselective excitation is used to minimize the duration of excitation to allow B 1 mapping over a wide range of B 0 inhomogeneity.Moreover, nonselective excitation necessitates large imaging volumes, which leads to low resolution or long acquisition time.Slab selective excitation with high bandwidth pulses for spatially localized 3D imaging could be implemented in the phase-sensitive method for greater ease and fexibility of scan volume prescription.Tis would cause some increase in RF pulse length, with some resulting narrowing of the range of B 0 inhomogeneity over which the method is valid [16].Tis may be investigated in future work.
For some B 1 mapping applications, severe imaging time constraints may make slice-selective excitation desirable to allow rapid B 1 mapping over a single slice.Implementation of slice-selective excitation in the phase-sensitive B 1 mapping methods would more severely restrict the range of B 0 inhomogeneity over which the method is valid and may not be feasible.Tus, there may be some applications requiring extremely short imaging times where the double angle techniques implemented with slice-selective excitation may be more useful than the phase-sensitive B 1 mapping methods.When there are no signifcant time constraints, a precise B 1 mapping is performed using a 3D acquisition method, because any slice-selective method of B 1 mapping will include signal from the transition bands of the slice profle, thus causing systematic errors in the estimation of B 1 .
In this study, the B 1 mapping method based on phasesensitive technique using a pair of composite RF pulses and SER techniques can be applied to clinical applications, such as echo-planar imaging and parallel imaging, along with shorter acquisition time.Moreover, this proposed B 1 mapping method does not need to increase T 1 efect by reducing the TR for shorter acquisition time and is suitable for clinical application due to its wide 3D spatial coverage and long TR, so it is possible to obtain an accurate B 1 mapping even if RF spoiling is unstable.Additionally, this proposed B 1 mapping method allows calibration of the receive delivery and enables accurate B 1 mapping.

Conclusions
We demonstrated that the proposed B 1 mapping method using a pair of composite RF pulses and SER techniques can reliably measure RF B 1 propagation in a multislice imaging and SER technique, providing the efect of acquisition time reduction and wider 3D spatial coverage of B 1 mapping with long T 1 , respectively.Particularly, this B 1 mapping method may be suitable for the B 1 mapping required for accurate FA analysis using high-feld MRI scanners.

Figure 2 :
Figure 2: Computational simulation studies to evaluate the proposed B 1 mapping method using a composite RF pulse (d) and other B 1 mapping methods, such as the double angle method (a), Yarnykh's method (b), and Morrell's method (c).

Figure 3 :Figure 4 :
Figure 3: Phase diferences of two MR images obtained from two composite RF pulse sequences according to B 1 feld strength, B 0 inhomogeneity, and composite RF pulse duration.Tis contour graph was obtained by solving the Bloch equation numerically.

Figure 7 :
Figure 7: FA maps of the proposed B 1 mapping method and multislice ISI mapping method for an in vivo human brain and FA error maps for three echo signals (RF 1 , RF 2 , and RF 3 ).
°− 90 y °for sequence 1 and 90 y °− 0 x °− 90 y °for sequence 2. Concepts in Magnetic Resonance Part A, Bridging Education and Research