MRI is based on the spatial variation of the measured signal in the imaged volume, which reflects the distribution and various properties of water protons depending on the measurement sequence used. However, several additional effects can alter the image appearance that are related to imperfections in the scanner hardware, as well as to interactions between the magnetic field and the examined tissue. Among these, the inhomogeneous radiofrequency (RF) magnetic field is an essential source of error for the quantification of MRI and MR spectroscopy (MRS) parameters. Inhomogeneous RF distribution results in variations in the signal strength and a spatially variable image contrast. Apart from the imperfect homogeneity of RF in the unloaded transmitting coil caused by the coil construction, interactions between the tissue and magnetic fields, such as RF eddy and displacement currents, make the RF distribution dependent on the coil loading and sample geometry (1, 2). The manifestation of a dielectric resonance is strongly pronounced at higher field strengths, resulting in a large RF variation in the sample (3). Knowledge of the RF distribution in the sample helps to identify possible artifacts and enables the correction of RF-related signal variations.
Different approaches have been used to calculate the RF distribution in the sample. If the coil geometry and a model of the sample are known, one can calculate the RF distribution by finding the solution to the Maxwell equations (4–6). Although the results of such simulations are highly valuable for assessing the specific absorption rate (SAR) delivered in human tissues, they cannot provide the exact RF distribution in an individual subject. However, the RF distribution in vivo can be imaged directly with the use of dedicated sequences. Several approaches for mapping the RF distribution directly in the subject have been proposed. They can be divided into three types of methods: 1) those that increment transmitter reference amplitudes and fit an assumed signal behavior (7–9); 2) those that acquire several echoes and calculate the RF distribution by their proper combination (10–12), and eventually use a compensating pulse to achieve identical saturation (13); and 3) those that use preparation pulses or additional pulses in various sequences (14–16). Due to time constraints, published sequences have been adopted in 2D mode exclusively. Recently, however, the echo-planar imaging (EPI) readout was used in a magnetization-prepared gradient-echo sequence to acquire 3D RF maps (17), and the acquisition of the 3D RF map took 4 min.
In this paper a 3D modification of the method introduced by Akoka et al. (10) based on the simultaneous acquisition of a spin echo (SE) and a stimulated echo (STE) is proposed. To make the 3D acquisition possible, two EPI readouts (one for the SE and one for the STE) were implemented in the sequence. The proposed method allows 3D RF mapping to be achieved with sufficient resolution in 1.5 min. This is demonstrated by measurements in both a phantom and a healthy volunteer.
MATERIALS AND METHODS
It is well known that a train of RF pulses gives rise to several different echoes (18). In the method proposed here, a primary SE and an STE are measured in a three-pulse sequence: α - TE/2 - 2α - TE/2 - data_acq - α - TE/2 - data_acq. The intensity of the SE (ISE) and STE (ISTE) in the described sequence can be written as (18):
where k includes saturation attenuation of the signal associated with finite TR and a reception scaling factor. The mixing time (TM) is the distance between the second and third pulses. Since in this sequence both SEs and STEs are acquired with the same TE and are subject to the same degree of saturation, the division of ISTE and ISE yields
regardless of the nominal flip angle of the first pulse.
Since Eq.  does not depend on the TR, a short TR can be used. On the other hand, signal ISTE of the STE has to be corrected for the T1 relaxation during a TM period. When the accurate T1 value is not known, the calculated flip angles are biased. The bias Δα in the calculated flip angle (defined as the difference of the flip angle αc calculated using the correct T1 value T and the flip angle αi calculated using the incorrect value T) according to Eq.  equals
From Eq.  it follows that the bias Δα in calculated α values due to inaccurate knowledge of T1 increases with TM and αc.
The adoption of the measurement sequence is depicted in Fig. 1. Following fat suppression (not shown in the figure), SE and STE are acquired using EPI readouts. The first excitation pulse is the spatially-selective Hamming-filtered sinc pulse (2.6-ms duration) with the nominal flip angle value set to 90°. The second and third pulses are nonselective rectangular pulses of 1-ms and 0.5-ms duration, respectively, with adjustable nominal flip angles 2β and β. Identical EPI readouts are used for SE and STE acquisitions with the echo spacing equal to 0.4 ms. 3D encoding is accomplished by a conventional single-shot 2D EPI acquisition and the application of additional partition encoding in the slice direction (19). Three reference echoes for the phase correction, according to Heid (20), are acquired before each EPI readout prior to phase and partition encoding. Although the acquisition of the reference echoes and the application of partition encoding after the first pulse is advantageous, the separate acquisition of the echoes is required by the EPI reconstruction routine implemented in the scanner.
Because the SE is acquired in the TM period, the shortest achievable TM is limited by the data acquisition time (TA) and hence by the matrix size. The shortest achievable TM and TE times for the two matrix sizes (64 × 64 and 64 × 48) used for the measurements are as follows: TM = 34 ms, TE = 37 ms for matrix = 64 × 64, and TM = 28 ms, TE = 31 ms for matrix = 64 × 48.
Equation  does not allow a separation of angles α = 90° + δ° and α = 90° − δ° if only the magnitude values of ISE and ISTE are used. To differentiate between both cases, the phases of the SE and STE signals are required. Although a ghost artifact in magnitude images was almost eliminated after the phase correction, the real and imaginary parts of SE and STE images often remained partially mixed and did not allow the correct phase determination. Therefore, a procedure was established to enable the calculation of the correct α values from magnitude images acquired with different nominal flip angles (2β for the second pulse, and β for the third pulse).
For each β value, two possible α values (α = 90° + δ° and α = 90° − δ°) are calculated in each voxel according to Eq. , and the correct α value is determined based on the known direct proportionality between the actual flip angle value α and the nominal flip angle value β. The proportionality implies that the ratio α/β is a constant for a correct α value, whereas it is a decreasing linear function of β for an incorrect α value, as shown in Fig. 2. In our current implementation, three magnitude SE and STE images with nominal flip angle values (β1 = 80°, β2 = 90° and β3 = 100°) are measured, and for each β value two possible angles (α) are calculated in each voxel according to Eq. . This yields six α/β ratios (three with constant dependence on β, and three with decreasing linear dependence on β). One can automatically identify the ratios with a constant dependence on β by finding the linear function with the lowest deviation from the calculated ratios and the slope closest to zero using linear regression. When the constant ratios are identified, the α/90° ratio is calculated from the corresponding regressed line at the point β = 90°. The resulting α is the true flip angle in the given voxel corresponding to the nominal flip angle 90°.
The sequence was tested in both a phantom and a healthy volunteer. The phantom was a homogeneous spherical phantom (17 cm in diameter) containing water doped with NiSO4.
The sequence parameters for the phantom measurements were as follows: TE/TM/TR = 37 ms/34 ms/500 ms, FOV = 256 × 256 mm, matrix = 64 × 64, 96 partitions, slice thickness = 2 mm, and excited slab thickness = 100 mm. The correction for the relaxation time T1 according to Eq.  was performed using a value of T1 = 285 ± 5 ms, as estimated from inversion-recovery measurements. To test the accuracy of the proposed method, the calculated 3D RF map was compared with the 3D RF map obtained from repeated 3D stimulated-echo acquisition mode (STEAM)-EPI measurements. In the 3D STEAM-EPI measurements the nominal flip angles β of three nonselective rectangular pulses of 0.5-ms duration were varied from 40° to 140° in increments of 5°, and the dependence of the signal (normalized to one at the maximum) on β was fitted in each voxel by the function sin3(k · β), with k as a fitting parameter (21). A 3D flip angle distribution corresponding to the nominal flip angle β equal to 90° was calculated from the product k · 90 and compared with the RF map obtained using the proposed RF mapping sequence. The identical EPI readouts were implemented into the STEAM-EPI sequence and the RF mapping sequence to ensure equivalent image distortions. The TR of the STEAM-EPI sequence was set to 1500 ms to ensure complete recovery of the longitudinal magnetization prior to each repetition. The measurements were performed without repositioning of the phantom and with the same shimming.
A 3D RF map of the brain was acquired from the measurement of a healthy volunteer. An oblique axial slab was measured with the following parameters: TE/TM/TR = 31 ms/28 ms/500 ms, FOV = 256 × 256 mm, matrix = 64 × 48 zero-filled to 64 × 64, 64 partitions, slice thickness = 2.5 mm, and thickness of the excited slab = 80 mm. For the T1 relaxation time correction, a constant value of T1 = 1192 ms was used for all tissues in the brain. The value represents the average T1 value for white (WM) and gray matter (GM) at 3T, as reported by Ethofer et al. (22).
The measurements were approved by the local ethics committee, and the subject provided written consent prior to the examination. All measurements were performed using a whole-body 3T scanner (Trio Tim; Siemens, Erlangen, Germany) and a multichannel head coil.
The RF map of the selected partition of the phantom is shown in Fig. 3. The distribution of the flip angles in the RF map, which range from 62° to 115°, can be seen as a consequence of the dielectric resonance at 3T. The SE and STE images were of good quality and showed only small ghost artifacts. The proposed method to select the correct α value from two possible values calculated from Eq. , based on measurements with three different nominal flip angles β, proved to be robust.
The difference between the flip angles estimated by the proposed RF mapping sequence and by fitting signal behavior in the 3D STEAM-EPI sequence did not exceed 1.5° in the majority of voxels. A difference of up to 2° was observed in only a small percentage of voxels at the border of the phantom. The fitted signal in the 3D STEAM sequence perfectly matched sin3(k · β) dependence. This is apparent in Fig. 4, which shows the signal dependence on the nominal flip angle β in one selected voxel.
The SE and STE images acquired in vivo, as well as the calculated RF maps, showed good quality and no significant artifacts. Only a weak residual fat signal was observed in the low-signal-intensity areas of several STE images in the proximity of the top of the head, as a result of suboptimal fat suppression due to B0 inhomogeneity and eddy currents. The RF maps corresponding to four partitions acquired in a human brain are shown in Fig. 5. In this figure the SE image and the corresponding RF map are shown. The flip angle values increase toward the middle of the head, similarly to the situation with the phantom in Fig. 3. The influence of the bias Δα due to the significantly higher T1 of cerebrospinal fluid (CSF) compared to T1 = 1192 ms used for the flip angle calculation can be identified in Fig. 5 as a decrease of flip angle values in areas with high CSF percentage. In the measured brain volume, α values ranging from 76° to 113° were observed.
To correct for effects of RF inhomogeneities in 3D data sets, it is necessary to have knowledge of the 3D RF distribution in the sample. However, due to time constraints, it is not possible to acquire 3D field maps with sufficient resolution using previously described methods. To allow for 3D acquisitions in a short time, we employed two EPI readouts to acquire the SE and STE in one sequence. The use of EPI readouts makes the sequence more sensitive to inhomogeneities in the static magnetic field. Therefore, the proposed sequence is dedicated mainly to RF mapping in the head and eventually in the limbs.
In principle, two measurements with different nominal flip angles β are sufficient to determine the flip angle value α. However, since the resulting flip angle is determined from the linear regression of results of all measurements, the acquisition of the RF maps with more nominal flip angles reduces the sensitivity of the calculated α values to the noise. Conversely, more measurements increase the total measurement time and sensitivity to the subject's motion. As a compromise, we propose performing three measurements, which typically take 1.5 min. For applications in which knowledge of the flip angle deviations from 90° is sufficient, the deviation map can be calculated directly from one measurement with β = 90° according to Eq. .
Assuming artifact-free images, the accuracy of the calculated flip angles is influenced by the accuracy of the T1 value used in Eq.  to account for signal losses in the STE image during the TM period. In contrast to the original sequence developed by Akoka et al. , the TM period is not negligible as a result of the incorporation of the EPI readout. Because T1 values in the subjects are generally position-dependent, the exact correction using one T1 value is not (in principle) possible, and the calculated flip angles are biased, according to Eq. . In this study, one T1 value (1192 ms) was assumed regardless of tissue type. The value was obtained as an average of T1 values in the occipital GM, occipital WM, motor cortex, frontoparietal WM, and thalamus at 3T, as reported by Ethofer et al. (22). The bias Δα in the calculated flip angles is for frontoparietal WM, occipital GM, and CSF, shown as a function of the flip angle αc in Fig. 6. Frontoparietal WM represents the lowest T1 value (1060 ms) and occipital GM represents the highest T1 value (1470 ms) in the measured brain tissue. All T1 values were adopted from 3T measurements reported by Ethofer et al. (22), except for the T1 value for CSF (3300 ms), which was approximated by T1 of the salt solution measured at 3T. The bias values were calculated for TM = 28 ms corresponding to the 64 × 48 matrix size, which was used for in vivo measurements. From Fig. 6 it follows that in the range of flip angles (60–120°) the maximum bias Δα is about 0.2° in brain tissue and 0.5° in CSF.
A reduction of the matrix size to 64 × 32 would lead to TM = 21 ms and consequently to a bias Δα below 0.15° for brain tissue and below 0.4° for CSF. Generally, the sensitivity of the calculated flip angles to T1 can be reduced with the use of smaller matrix sizes, resulting in a shorter TM. The lowest reasonable resolution of the RF map has to be determined with respect to the particular application. In this study we chose the matrix size of 64 × 48 with the corresponding TM = 28 ms as a compromise between low resolution and sensitivity to the T1 relaxation time. The resulting lower resolution of the RF map of the brain is usually sufficient, due to the slow changes of the flip angles. Alternatively, by knowing the accurate T1 values in the examined tissues, one can perform tissue segmentation and correct for the individual tissues separately.
Akoka et al. (10) demonstrated a good agreement between theoretical and experimental signal dependencies, and concluded that accurate flip angle determination was possible in the range of 60–130°; however, they did not specify the accuracy of the calculated flip angles. Because there is no gold standard for calculating a 3D RF map, we compared calculated flip angles with flip angles estimated by 3D STEAM-EPI measurements. The flip angles estimated by both methods did not differ by more than 1.5°. The use of the nonselective second and third pulses in the proposed sequence eliminates the influence of the slice profile—an effect that was identified as a major source of error in the original sequence by Akoka et al. (10). Apart from the influence of T1 time, as discussed above, additional sources of error can be ascribed to the low SNR of the STE image in areas with a flip angle close to 90° and to the eventual nonlinearities of the transmitter. Also, since a ratio of ISTE and ISE is used for the calculation of flip angles, the result will be prone to error when the denominator is close to zero. Assuming maximal bias in the calculated flip angle values observed in the human brain at 3T due to inaccurate knowledge of T1 equal to 0.2°, we can estimate the resulting error in the calculated flip angle values using a matrix size of 64 × 48 below 2°.
The signal dephasing evoked by the inhomogeneity of the static magnetic field induces additional signal losses, which leads to decreased SNR and image distortions. Therefore, the high static field homogeneity in the imaged volume is an important factor. Because of the nature of the method, the RF maps cannot be accurately assessed in areas with a signal void, such as the sinuses or bones. In the event of the occurrence of artifacts in the SE or STE images, the larger deviations from the constant dependence of α/β on β can be observed. Therefore, the inspection of slopes serves as an indicator of the reliability of the α value calculated in the given voxel.
One possible application of the proposed 3D RF mapping technique is the correction of signal variations related to RF inhomogeneity in 3D spectroscopic imaging at 3T.