FULL PAPER Magnetic Resonance in Medicine 75:801–809 (2016)
Signal-to-Noise Ratio and MR Tissue Parameters in Human Brain Imaging at 3, 7, and 9.4 Tesla Using Current Receive Coil Arrays Rolf Pohmann,1* Oliver Speck,2,3,4,5 and Klaus Scheffler1,6 Purpose: Relaxation times, transmit homogeneity, signal-tonoise ratio (SNR) and parallel imaging g-factor were determined in the human brain at 3T, 7T, and 9.4T, using standard, tight-fitting coil arrays. Methods: The same human subjects were scanned at all three field strengths, using identical sequence parameters and similar 31- or 32-channel receive coil arrays. The SNR of threedimensional (3D) gradient echo images was determined using a multiple replica approach and corrected with measured flip angle and T2* distributions and the T1 of white matter to obtain the intrinsic SNR. The g-factor maps were derived from 3D gradient echo images with several GRAPPA accelerations. Results: As expected, T1 values increased, T2* decreased and the B1-homogeneity deteriorated with increasing field. The SNR showed a distinctly supralinear increase with field strength by a factor of 3.10 6 0.20 from 3T to 7T, and 1.76 6 0.13 from 7T to 9.4T over the entire cerebrum. The gfactors did not show the expected decrease, indicating a dominating role of coil design. Conclusion: In standard experimental conditions, SNR increased supralinearly with field strength (SNR B01.65). To take full advantage of this gain, the deteriorating B1-homogeneity and the decreasing T2* have to be overcome. Magn C 2015 Wiley Periodicals, Reson Med 75:801–809, 2016. V Inc. Key words: ultra-high field; signal-to-noise ratio; relaxation times
INTRODUCTION In recent years, available field strengths for MRI instruments have increased rapidly, both for human and animal applications (1). While 7 Tesla (T) has developed
1 Max Planck Institute for Biological Cybernetics, Magnetic Resonance €bingen, Germany. Center, Tu 2 Department of Biomedical Magnetic Resonance, Otto-von-Guericke University Magdeburg, Germany. 3 German Centre for Neurodegenerative Diseases (DZNE), Site Magdeburg, Germany. 4 Leibniz Institute for Neurobiology, Magdeburg, Germany. 5 Center for Behavioral Brain Sciences, Magdeburg, Germany. 6 €bingen, Department for Biomedical Magnetic Resonance, University of Tu €bingen, Germany. Tu
*Correspondence to: Rolf Pohmann, Ph.D., Max Planck Institute for Biological Cybernetics, Magnetic Resonance Center, Spemannstr. 41, 72076 €bingen, Germany. E-mail: [email protected] Tu Received 25 July 2014; revised 4 February 2015; accepted 9 February 2015 DOI 10.1002/mrm.25677 Published online 29 March 2015 in Wiley Online Library (wileyonlinelibrary. com). C 2015 Wiley Periodicals, Inc. V
into a standard field strength for ultra-high field MR in humans, the interest in even stronger magnets remains high, causing a slow but steady increase in scanners operating at 9.4T or above. The main driving force for this trend is the gain in intrinsic signal-to-noise ratio (SNR), which is expected to grow at least linearly with field strength (2–4). However, with increasing static field, the homogeneity of the RF-fields declines, the longitudinal relaxation time T1 increases, while T2 and T2* decrease. In addition, the construction of RF coils for high frequencies becomes more and more involved, mainly because of the need to combine the multichannel receive arrays with tight-fitting multielement transmit coils needed to reach the required transmit homogeneity (5). This poses the question of how much of the expected gain in sensitivity can be realized in practical experiments. While in general this question has to be investigated for every application separately, because the changing magnetic field may have different effects on the contrasts to be observed in a specific experiment, the intrinsic SNR and the relaxation times as the underlying MR parameters are certainly of interest for many studies and allow predictions for various applications. In addition, the B1 homogeneity (6) and the g-factor of parallel imaging applications (7) are expected to change with field strength and can play an important role in practical experiments. The aim of this study is to investigate variations in those MR parameters and in the SNR by a direct comparison between 3T, 7T, and 9.4T. While relaxation times and transmit field inhomogeneity can be determined and their influences on the final SNR be taken into account, the effect of different receive coils cannot easily be assessed because this would require determining the absolute receive sensitivity, which, for a multi channel array coil, is hardly feasible. While at lower fields, the principle of reciprocity can be used to connect the easily measurable transmit field with the receive sensitivity of a single channel coil, this is no longer possible at 7T and above (8). In addition, using a birdcage or other single channel transceiver coil would ignore common experimental practice. Instead, by using highly efficient, multi-channel receive-only coil arrays with similar shape and similar number of elements that are used in many current MR studies, we try to address the actual SNR behavior in typical studies investigating the human brain. METHODS In a simple, RF-spoiled gradient-echo acquisition, the SNR is given by:
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1 eTR =T1 sina eTE =T2 ; 1 cosa eTR =T1
[1]
where T1 and T2* are the longitudinal and the apparent transverse relaxation times, respectively, TR and TE are the repetition and the echo time of the measurement, a is the flip angle and Sc is the sensitivity of the receive coil(s), including the noise figure of the receive chain. Even though not explicitly noted, all parameters except for TE and TR depend on the position. By measuring the SNR of a gradient echo image as well as the other relevant parameters from Eq. [1], this equation can be used to obtain SNR0, which is the SNR that would be obtained with a homogeneous flip angle of 90 , an infinite repetition time and an echo time of zero, and thus includes the influence of the spin density. While these corrections can easily be applied for the relaxation times and the flip angle, quantitative values for the receive coil sensitivities cannot be determined experimentally. Thus, it is in practice only possible to calculate the product of SNR0 and Sc. To be able to derive a meaningful estimation of the intrinsic SNR at different field strengths, the difference in the receive coil sensitivities at the different fields should be small. We therefore used receive coil combinations with similar geometric properties in all measurements. Instrumentation Experiments were performed on three similar whole body scanners of the same hardware generation (Siemens Healthcare, Erlangen, Germany) with magnetic field strengths of 3T (Tim Trio, actually operating at a field strength of 2.9T), 7T (Magnetom 7T), and 9.4T (Magnetom 9.4T). All scanners worked with the same software version (VB 17) and equal versions of both vendorsupplied and self-written sequences were used. To obtain measurements that are comparable to each other, but also give insight in the situation encountered in current experiments, multi-channel receive-only coil arrays with similar shape and size and a similar number of array elements were used. At 3T, the 32-channel helmetshaped product coil was combined with the body coil for transmission. At 7T, a similar coil (Nova Medical Inc., Wilmington, MA) was used, again with 32 tightfitting receive elements and combined with a local birdcage transmit coil. At 9.4T, a home-built 31-channel receive helmet was combined with a 16-channel transmit array (9), which was driven in circularly polarized mode in all experiments. Experiments The same three volunteers (two male) were examined at all three field strengths with identical sequences and sequence parameters with approval by the local review boards of the participating institutions. After adjustments and shimming, a three-dimensional flip angle map was acquired using a home-written AFI (actual flip angle imaging) sequence (10), implemented following the phase and gradient spoiling schemes recommended by Yarnykh (11). This sequence has been shown to generate reliable B1-maps even at ultra-high
field without exceeding the SAR limits (12). The images spanned a field-of-view (FOV) of 256 224 160 mm3 with a spatial resolution of (2 4 4) mm3. With repetition times of 20 ms and 100 ms, this scan took approximately 4:29 min and mapped a nominal flip angle of 60 . Then, a three-dimensional gradient echo image was acquired, with equal FOV but with an improved isotropic resolution of 1 mm. The nominal flip angle was 4 or 5 , repetition and echo times were 8 ms and 2 ms, respectively, and the acquisition bandwidth was 490 Hz/ voxel at all three field strengths. This scan was repeated with a flip angle of 0 to obtain accurate noise correlation maps. For determination of the parallel imaging performance, the same gradient echo sequence was repeated with nine different GRAPPA acceleration factors between two and eight. GRAPPA schemes were (given as accelerations in anterior–posterior/left–right directions): 2/1, 3/ 1, 4/1, 1/2, 1/3, 1/4, 2/2, 3/2, 4/2. Twenty-four calibration lines were acquired in each direction. For some GRAPPA scans, the scanner software did not allow selecting the desired acceleration factors (especially all accelerations in left–right direction at 3T) or enforced changes in other parameters (like oversampling in left– right direction for all 1/3 scans). In those cases, GRAPPA data was extracted from the unaccelerated dataset, applying exactly the same GRAPPA parameters as used in the corresponding scans. The GRAPPA experiments were also repeated on a head-and-shoulder phantom filled with a solution with similar electromagnetic properties as the brain at 9.4T (13). For T2*-mapping, a multi-echo gradient echo sequence with 12 echo times between 2 ms and 55 ms, a spatial resolution of 1 2 2 mm3 and a repetition time of 60 ms was used, again over the same FOV. With a GRAPPA factor of two and a partial Fourier acceleration of 6/8, this scan took around 4.3 min. The longitudinal relaxation time T1 was measured in one white matter voxel, using a spectroscopic inversion recovery sequence with STEAM (stimulated echo acquisition mode) localization. Spectra without water suppression were acquired from a (5 mm)3 voxel after a hyperbolic secant inversion pulse. In 18 repetitions, the inversion delay was varied between 50 ms and 12 s, with a relaxation delay of 12 s between successive scans. Reconstruction and Postprocessing All data were reconstructed and postprocessed using home-written routines in Cþþ and Matlab to avoid any unknown processing step such as raw or image data filtering. First, the STEAM-FIDs were reconstructed and integrated over the water line. To obtain T1, the equation M ðTI Þ ¼ M0 1 2beTI =T1 was fitted to the relaxation curve. Including the inversion efficiency b, ranging from zero for none to one for perfect inversion, allows for nonperfect inversion. T2*-maps were generated by an exponential fit to the multi-echo data for every voxel within the brain, using Matlab least squares fitting. Data were excluded if the relative fitting error as returned by the fitting routine was above 25%, the absolute fitting error was above 15
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FIG. 1. Typical images from one volunteer acquired in the SNR scan at 3T, 7T, and 9.4T (left) and compartment structure for analysis. All images in this and the following figures show the same slices from the same subject.
ms or the resulting T2*-value was above 150 ms, in which case it was assumed that either the fitting failed or the data originated from a CSF-voxel. The AFI map was zero-filled to the same size as the gradient echo images and was used to generate maps of transmit efficiency and to correct for flip angle variations in the gradient echo images. The noise covariance matrix was calculated from the noise images (with a ¼ 0 ) and used to calculate the final SNR of the combined images by a pseudo-multiple replica approach (14): Artificial noise was generated for all receive channels, having the same noise covariance as determined with the noise scans. This noise was added to the raw data and the resulting dataset was Fourier transformed. The single coil images were combined with a root-sum-of-squares approach (15), using sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X Ic ðx; y Þ2 I ðx; y Þ ¼ ; s2c c
[2]
where Ic(x,y) and I(x,y) are the single coil and combined image intensities at position (x,y), sc is the coil variance of coil c as measured in the noise scan and the sum adds over all coils c. The entire process was repeated 128 times to determine the SNR as the ratio of mean image intensity over all 128 images and their standard deviation. Finally, the determined SNR maps were corrected for the flip angle and T2*-maps and the white matter T1-values according to Eq. [1] to obtain the intrinsic SNR0, weighted by the coil sensitivities. The parallel imaging performance was assessed by calculating g-factor maps: The SNR of the nonaccelerated image (SNRnoPI) and of the accelerated images (SNRPI) were determined as described above, again generating 128 pseudo-replica with a home-written Cþþ-implementation of a three-dimensional (3D) GRAPPA algorithm. The g-factor was then calculated as g¼
SNRnoPI pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; NnoPI =NPI
SNRPI
[3]
where NnoPI and NPI are the total number of scans acquired for the conventional and the accelerated image (including reference scans), respectively.
GRAPPA weights were calculated from 24 autocalibration lines in the accelerated direction and 64 and 32 points in read and the nonaccelerated phase encoding directions (16,17), respectively, using a 3D-kernel with a size of 5 5 5 points. The pseudoinverse was calculated using a singular value decomposition with Tikhonov regularization (18). For a quantitative evaluation of B1 field homogeneity, transmit efficiency, T2* variation, SNR and g-factor, the 3T images were used to subdivide the brain into four compartments (Fig. 1): Brain stem and cerebellum, inner and outer brain, and ventricles. The outer brain was defined as a region encompassing approximately 2 cm on the surface of the brain, where the main part of cortical gray matter is situated, while the inner brain compartment comprises the rest of the cerebrum. The ventricles were classified as a separate compartment and excluded from T2* and SNR evaluations. To obtain representative values for gray and white matter T2*, 21 circular regions of interest (ROIs) in gray and 15 ROIs in white matter with a diameter of four voxels were defined, based on the T2*-weighted images, distributed evenly over the entire cerebrum. The compartment masks were then coregistered to the 7T and 9.4T images and, where necessary, manually corrected for small deviations in geometry, potentially due to differences in geometric distortions. For visual illustration, transmit efficiency, T2*, SNR, and g-factor maps from 7T and 9.4T were coregistered to the 3T images to allow for direct comparison of identical brain regions. RESULTS All values were calculated by first computing the mean values of the parameter in question over the ROI for each subject. The mean of the values for the three subjects is given together with the standard deviation over the three subjects. Relations for the field dependence of the parameters are determined using the real field strength of 2.9T for the 3T data. Typical images from one volunteer in all three orientations are shown in Figure 1. All parameter images show the same three slices of the same subject. Table 1 contains the measured parameter values for the different brain compartments.
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Table 1 Measured Field Dependent Parameters for Different Anatomical Structuresa B1 3T
7T
9.4T
Whole brain Whole cerebrum Outer brain Inner brain Cerebellum/brain stem Whole brain Whole cerebrum Outer brain Inner brain Cerebellum/brain stem Whole brain Whole cerebrum Outer brain Inner brain Cerebellum/brain stem
SNR
b
Efficiency
Homogeneity
31.966.5 31.566.4 29.465.9 33.766.8 35.166.8 38.964.3 40.063.9 38.963.0 41.164.6 30.368.2 21.6 62.1 22.062.1 23.162. 0 20.862.6 17.763.5
0.1160.01 0.1160.01 0.0860.02 0.0860.01 0.1060.02 0.2560.02 0.2260.003 0.1960.01 0.2460.007 0.3760.09 0.2860.01 0.2560.006 0.2060.02 0.3060.01 0.4160.06
c
d
Absolute
Increasee
1001649 1044653 13306131 753638 646621 31436144 32326150 39196139 25276133 24386231 55146609 57076690 68206827 44826233 48516214
3.1460.23 3.1060.20 2.9660.22 3.3660.24 3.7860.37 1.7860.12 1.7660.13 1.7460.17 1.7860.10 2.0060.13
a
Mean values over compartments defined in Figure 1. Given values are mean and standard deviations over subjects Transmit efficiency over compartment, in nT/V. c Relative standard deviation of the transmit efficiency over compartment. d SNR after correction for flip angle, T1 and T2*. e Relative SNR increase compared to the next lower magnetic field strength. b
Longitudinal Relaxation Time T1 The white matter relaxation times determined with the single voxel inversion-recovery STEAM experiments are (947.4 6 66.1) ms at 3T, (1334.2 6 21.7) ms at 7T, and (1426.7 6 51.8) ms at 9.4T. A comparison of these values with published data from references [1,19–24) (Fig. 2A) shows that this is well within the expected range. A dependence of the form (25) T1 ðB0 Þ ¼ a Bb0 faithfully describes the measured values for a ¼ 659 ms/T and b ¼ 0.35.
values are (33.4 6 2.9) ms (gray) and (24.1 6 0.8) ms (white) at 7T and (23.8 6 1.0) ms (gray) and (19.2 6 0.9) ms (white) at 9.4T (Fig. 2B). An exponential function T2 ¼ a ebB0 =T describes this dependence best for a ¼ 0.090 s and b ¼ -0.142 T1 for gray and with a ¼ 0.064 s and b ¼ 0.132 T1 for white matter. For illustration, these functions are plotted with the experimental data in Figure 2. However, data from a still larger field range (esp. lower field) would be necessary for a reliable determination of the relation between T2* and field strength.
Apparent Transverse Relaxation Time T2*
Efficiency and Transmit Inhomogeneity
T2*-maps
Figure 4 shows transmit efficiency maps for all three field strengths. The absolute transmit efficiency varies strongly between the fields due to differences in size and technology used for the transmit coils: While the 3T body coil used for excitation is relatively inefficient due to its large size, the narrow 7T local birdcage coil shows
from one volunteer for all three field strengths are shown in Figure 3, indicating a drop to approximately half when going from 3T to 7T and another 20% at 9.4T. An analysis of the gray and white matter ROIs show T2*-values of (59.9 6 3.0) ms and (43.5 6 1.8) ms for gray and white matter at 3T, while the corresponding
FIG. 2. A: Measured values for T1 at 3T, 7T, and 9.4T in white matter (large dots) compared with literature values for white (small dots) and gray matter (crosses). The values are well described by a T1 ¼ 659 ms/TB00.35 - dependence (line). B: T2* values for gray (red) and white (blue) matter with the exponential fit results (parameters see text).
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FIG. 3. T2* maps at the three field strengths (top row) and relative T2* differences between the fields.
superior efficiency. The 9.4T coil, though similar in size, is a full multi-channel transmit array, which causes additional loss due to the large number of lossy components. Because the efficiency itself can always be compensated by higher transmitter power, the much more relevant parameter is the transmit field inhomogeneity, visualized by the plot of the relative standard deviation of the field over the different compartments (Fig. 5A). For the entire cerebrum, this value doubles from 0.11 6 0.01 at 3T to 0.22 6 0.004 at 7T and increases further to 0.25 6 0.006 at 9.4T.
dependent increase is slightly larger in the inside of the brain than at the surface: In the outer brain region the increase is with 2.96 6 0.22 from 3T to 7T and 1.74 6 0.17 to 9.4T lower than in the inner brain (3.36 6 0.24 and 1.78 6 0.10), which is well visible in the relative SNR images in Figure 6. The SNR gain in the cerebellum (3.78 6 0.37 and 2.00 6 0.12) is slightly larger, which is probably due to differences in the coverage of the cerebellum by the different RF coils. Assuming an exponential increase of SNR with field strength, a relation of SNR B01.65 provides a good agreement with the measured values for the cerebrum (Fig. 5B).
SNR After correction for T1, T2*, and flip angle differences, Figure 6 shows the distribution of image SNR for the three different field strengths (first row) and the respective relative changes between the field strengths (second row). The numerical analysis demonstrated a distinctly supralinear increase of SNR with magnetic field strength, with an improvement over the entire cerebrum by a factor of 3.10 6 0.20 from 3T to 7T, and a further increase by a factor of 1.76 6 0.13 from 7T to 9.4T. The field-
FIG. 4. Transmit efficiencies of the coils used at 3T, 7T, and 9.4T. Different color scales were used to emphasize the B1 homogeneity changes.
g-factor g-factor maps for the nine different acceleration factors are shown for all three field strengths in Figure 7, while mean values over the entire cerebrum are shown in Figure 5C. Surprisingly, no clear improvement with increasing field strength is visible. In contrast, for most acceleration factors, the g-factor of the 3T measurements is lowest, though the pattern varies strongly with direction and acceleration factor. The phantom measurements
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(dotted lines in Figure 7) show lower g-factors, especially for the high fields, but similar behavior with field and acceleration factor as the subject data. DISCUSSION
FIG. 5. A: transmit inhomogeneity as relative standard deviations of the B1 field over the entire cerebrum. B: SNR0 values in four different brain compartments. The red line represents fitting results on the SNR over the entire cerebrum as SNR0 ¼ B01.65. C: The g-factor for nine different acceleration patterns and all three fields. Acceleration in the two phase encode directions are described as (anterior–posterior)/ (left–right) accelerations.
So far, no studies have investigated the SNR gain from 7T to 9.4T due to the to date still small number of magnets and the lack of mature receive coils for the latter field. It is, however, surprising how few studies have systematically investigated the SNR advantage of 7T compared with lower fields. In a comparison between 4T and 7T, using similar TEM coils (26), a mean increase of a factor of 1.6 was found, in approximate agreement with a linear SNR increase with field strength, although a slightly larger gain was seen in the center of the brain in that study. Similarly, an increase of approximately 80% was observed in echo planar images when going from 3T to 7T (27), indicating an SNR dependence on field strength of slightly less than linear. In contrast to the current study, no corrections for flip angle and relaxation time differences were applied. The discrepancy between those studies and our results is, however, most likely due to the different hardware. While both above studies used single-channel volume coils, we applied an array of surface coils for signal reception. Thus, the supralinear SNR increase at high field strength observed here might only be realized when using surface coils for acquisition. We are, however, not aware of any publication that compared the SNR at different field strengths using state-of-the-art receive arrays. Even though only little experimental confirmation for the observed behavior is found in the literature, our results are not necessarily surprising, as they have been predicted by several theoretical studies. Already in 1991, Keltner et al (28) reported a distinctly supralinear increase of SNR with frequencies above 150 MHz, if surface coils are used. Using electrodynamic simulations, Wiesinger et al (29) calculated the ultimate SNR in different positions inside a brain model, finding a strong supralinear behavior in the center of the brain, which became less distinct when moving closer to the surface. This was explained by the different characteristics of the near field and the far field of the coil: While the SNR increase in the far field regime was predicted to be higher than linear, the near field behavior was supposed to grow less than linearly. Similar results were reported by Lattanzi and Sodickson (30,31). These findings also deliver an explanation for the weaker SNR gain with field strength in the studies mentioned above: because volume coils were used for transmission and reception, which mainly operate in the near field regime, only the slightly below linear behavior of the near field was observed. In addition, the predicted stronger increase of SNR in the center of the brain compared with the surface can be recognized in our results, especially between 3T and 7T (Fig. 6). The aim of this study was to determine the intrinsic SNR, eliminating all other influencing factors such as relaxation times or flip angle distribution. One factor that we were not able to take into account is the different sensitivity of the receive coils, which is not easily determined
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FIG. 6. Top: SNR distributions over three slices of the same volunteer at all three fields. Bottom: relative SNR differences between the fields.
experimentally. By using similar coils, which are also applied in a large number of neuroscientific studies, we approach this issue in two respects: First, the 3T and 7T coils can be considered the gold standard high end coils for brain imaging at their field strength for the chosen manufacturer. The 9.4T coil used here was applied in some of the still very rare applications at this field strength in human proton MRI (32–35). Even if the influence of the coils cannot be fully eliminated, comparing SNRs with these coils can give insight into the advantages of high field strength in practical neuroscientific applications, many of which apply these coils. Furthermore, the similarities in geometry and design of the three coils are high, so that similar sensitivity can be assumed: They all have a comparable tight-fitting helmet shape, with a similar total number of elements distributed in four rows at the back, while the number of rows is reduced down to two in the front to keep the eyes free. Differences in the exact placing of the coil elements as well as their diameter and overlap will
FIG. 7. The g-factor maps over the three fields and nine different acceleration patterns for one subject. Acceleration in the two phase encode directions are described as (anterior–posterior)/ (left–right) accelerations.
certainly have an effect; however, their influence on the SNR in the brain can be assumed to be relatively modest, while the SNR in brainstem and cerebellum may vary due to differences in the coverage of these areas. The exact analysis presented here will, however, change when other coils are used, although the main outcome – the strongly supralinear SNR increase with field strength, can be assumed to be maintained even for different setups of multi-channel coils. For the parallel imaging behavior, the results are less clear: Here, electrodynamic calculations (7,29), supported by experimental data (7) clearly indicate a decrease of the g-factors for higher field strength due to the more localized fields of the single receive array elements. Our data, however, do not show these expected characteristics, with 3T g-factors being lowest for most accelerations for both subject and phantom measurements. The details of the coil design may thus play the dominant role in the parallel imaging performance. In fact, despite the similarities in coil shape and size of the
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FIG. 8. Coil correlation plots for all three coil arrays, measured in one of the subjects, showing clear differences in coupling characteristics.
entire receive arrays as well as in the number of coil elements, a detailed investigation of the coil design shows strong differences, e.g., in the size of the different array elements (3T: 10 cm, overlapping; 7T: 5 cm 4 cm, pairwise overlapping; 9.4T: 6 cm, each element overlapping with two above and two below) or the distribution of the coil elements on the helmet. The noise correlation maps (Fig. 8) illustrate the differences in coil design as strong variations in the coupling characteristics. Thus, the effect of receive array optimization will still be the decisive factor to achieve good parallel imaging performance with low g-factors. The varying relaxation times form another important factor in the determination of intrinsic and actual SNR at different field strengths. We have tried to eliminate their influence by measuring both T1 and T2* and correcting for them. T2* may be a potential confound due to its strong sensitivity toward veins or the orientation of fiber tracts (36), and thus has to be taken into account for accurate SNR measurements. To keep the measuring time short, we measured T2* with a reduced spatial resolution of 1 2 2 mm3, as compared to the isotropic 1 1 1 mm3 voxels used in the SNR scan. Because T2* is voxel-size dependent, the correction will therefore not be completely accurate. To estimate the extent of this effect, we measured T2*-values for the highest field strength with both resolutions, finding an increase of T2* for the smaller voxels from (23.8 6 1.0) ms to (26.8 6 0.3) ms in gray and from (19.2 6 0.9) ms to (19.5 6 0.5) ms in white matter. Due to the short TE used in the measurements, the effect of this T2* difference is negligible, leading to a change in the corrected SNR of less than 2%. For lower field strengths, this effect is probably even smaller, because intra voxel dephasing effects, that cause a large part of the T2*effect, increase with field strength. A larger inaccuracy may be introduced by the method for T1 determination: Due to restrictions in B1 homogeneity and SAR, a high-resolution T1-map could not be acquired at 9.4T within reasonable time. Therefore, a single T1 value for white matter was determined and used for correction of the SNR. For a worst case estimation of the size of the corresponding error, we calculated the SNRs again, corrected with gray matter T1-values of 1711 ms (23), 2132 ms (1), and 2300 ms (extrapolated by fitting a power dependence to the literature data shown in Figure 2A) for 3T, 7T, and 9.4T, respectively. Under these circumstances, the SNR gain for the entire cerebrum from 3T to 7T would increase to 3.22, and from 7T
to 9.4T decrease to 1.62. However, even in this case the strong supralinear behavior remains. CONCLUSIONS The results show experimental evidence of a supralinear increase in SNR with field strength in human brain MR with standard experimental setups, confirming theoretical predictions. However, the changes in the relaxation times and the degraded B1 homogeneity pose new challenges. While the increasing T1 has been shown to affect the SNR gain only slightly as long as optimal imaging parameters are used, even up to much higher fields (37), the reduction in T2 and T2* will require further developments in sequence design. Even more important is to overcome the growing transmit field inhomogeneity by highly efficient multi-element transmit arrays, improved parallel transmit techniques and an optimized control of the specific absorption rate. In addition, novel techniques that are less affected by those ultra-high field specific issues, like phase imaging, where the contrast does not depend on the flip angle, or even can benefit from them, like T2*-weighted imaging, which gets faster with decreasing T2* values, will gain importance and make it possible to fully take advantage of the high SNR increase at yet higher fields (38). REFERENCES 1. Rooney WD, Johnson G, Li X, Cohen ER, Kim SG, Ugurbil K, Springer CS Jr. Magnetic field and tissue dependencies of human brain longitudinal 1H2O relaxation in vivo. Magn Reson Med 2007; 57:308–318. 2. Hoult DI, Lauterbur PC. Sensitivity of the zeugmatographic experiment involving human samples. J Magn Reson 1979;34:425–433. 3. Redpath TW. Signal-to-noise ratio in MRI. Br J Radiol 1998;71:704– 707. 4. Collins CM, Smith MB. Signal-to-noise ratio and absorbed power as functions of main magnetic field strength, and definition of “90 degrees” RF pulse for the head in the birdcage coil. Magn Reson Med 2001;45:684–691. 5. Ibrahim TS. Ultrahigh-field MRI whole-slice and localized RF field excitations using the same RF transmit array. IEEE Trans Med Imaging 2006;25:1341–1347. 6. Van de Moortele PF, Akgun C, Adriany G, Moeller S, Ritter J, Collins CM, Smith MB, Vaughan JT, Ugurbil K. B(1) destructive interferences and spatial phase patterns at 7 T with a head transceiver array coil. Magn Reson Med 2005;54:1503–1518. 7. Wiesinger F, Van de Moortele PF, Adriany G, De Zanche N, Ugurbil K, Pruessmann KP. Parallel imaging performance as a function of field strength–an experimental investigation using electrodynamic scaling. Magn Reson Med 2004;52:953–964. 8. Hoult DI. The principle of reciprocity in signal strength calculations—A mathematical guide. Concepts Magn Reson 2000;12:173– 187.
SNR at 9.4T 9. Shajan G, Kozlov M, Hoffmann J, Turner R, Scheffler K, Pohmann R. A 16-channel dual-row transmit array in combination with a 31element receive array for human brain imaging at 9.4 T. Magn Reson Med 2014;71:870–879. 10. Yarnykh VL. Actual flip-angle imaging in the pulsed steady state: a method for rapid three-dimensional mapping of the transmitted radiofrequency field. Magn Reson Med 2007;57:192–200. 11. Yarnykh VL. Optimal radiofrequency and gradient spoiling for improved accuracy of T1 and B1 measurements using fast steadystate techniques. Magn Reson Med 2010;63:1610–1626. 12. Pohmann R, Scheffler K. A theoretical and experimental comparison of different techniques for B1 mapping at very high fields. NMR Biomed 2013;26:265–275. 13. Hoffmann J, Shajan G, Budde J, Scheffler K, Pohmann R. Human brain imaging at 9.4 T using a tunable patch antenna for transmission. Magn Reson Med 2013;69:1494–1500. 14. Robson PM, Grant AK, Madhuranthakam AJ, Lattanzi R, Sodickson DK, McKenzie CA. Comprehensive quantification of signal-to-noise ratio and g-factor for image-based and k-space-based parallel imaging reconstructions. Magn Reson Med 2008;60:895–907. 15. Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson Med 1990;16:192–225. 16. Wang Z, Wang J, Detre JA. Improved data reconstruction method for GRAPPA. Magn Reson Med 2005;54:738–742. 17. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002;47:1202–1210. 18. Qu P, Wang C, Shen GX. Discrepancy-based adaptive regularization for GRAPPA reconstruction. J Magn Reson Imaging 2006;24:248–255. 19. Stanisz GJ, Odrobina EE, Pun J, Escaravage M, Graham SJ, Bronskill MJ, Henkelman RM. T1, T2 relaxation and magnetization transfer in tissue at 3T. Magn Reson Med 2005;54:507–512. 20. Wansapura JP, Holland SK, Dunn RS, Ball WS Jr. NMR relaxation times in the human brain at 3.0 Tesla. J Magn Reson Imaging 1999;9: 531–538. 21. Gelman N, Ewing JR, Gorell JM, Spickler EM, Solomon EG. Interregional variation of longitudinal relaxation rates in human brain at 3.0 T: relation to estimated iron and water contents. Magn Reson Med 2001;45:71–79. 22. Lu H, Nagae-Poetscher LM, Golay X, Lin D, Pomper M, van Zijl PC. Routine clinical brain MRI sequences for use at 3.0 Tesla. J Magn Reson Imaging 2005;22:13–22. 23. Pohmann R. Accurate, localized quantification of white matter perfusion with single-voxel ASL. Magn Reson Med 2010;64:1109–1113. 24. Wright PJ, Mougin OE, Totman JJ, et al. Water proton T1 measurements in brain tissue at 7, 3, and 1.5 T using IR-EPI, IR-TSE, and MPRAGE: results and optimization. MAGMA 2008;21:121–130.
809 25. Bottomley PA, Foster TH, Argersinger RE, Pfeifer LM. A review of normal tissue hydrogen NMR relaxation times and relaxation mechanisms from 1-100 MHz: dependence on tissue type, NMR frequency, temperature, species, excision, and age. Med Phys 1984;11:425–448. 26. Vaughan JT, Garwood M, Collins CM, et al. 7T vs. 4T: RF power, homogeneity, and signal-to-noise comparison in head images. Magn Reson Med 2001;46:24–30. 27. Triantafyllou C, Hoge RD, Krueger G, Wiggins CJ, Potthast A, Wiggins GC, Wald LL. Comparison of physiological noise at 1.5 T, 3 T and 7 T and optimization of fMRI acquisition parameters. Neuroimage 2005;26:243–250. 28. Keltner JR, Carlson JW, Roos MS, Wong STS, Wong TL, Budinger TF. Electromagnetic fields of surface coil in vivo NMR at high frequencies. Magn Reson Med 1991;22:467–480. 29. Wiesinger F, Boesiger P, Pruessmann KP. Electrodynamics and ultimate SNR in parallel MR imaging. Magn Reson Med 2004;52:376–390. 30. Lattanzi R, Sodickson DK. Ideal current patterns yielding optimal signal-to-noise ratio and specific absorption rate in magnetic resonance imaging: computational methods and physical insights. Magn Reson Med 2012;68:286–304. 31. Schnell W, Renz W, Vester M, Ermert H. Ultimate signal-to-noiseratio of surface and body antennas for magnetic resonance imaging. IEEE Trans Antennas Propag 2000;48:418–428. 32. Budde J, Shajan G, Scheffler K, Pohmann R. Ultra-high resolution imaging of the human brain using acquisition-weighted imaging at 9.4T. Neuroimage 2014;86:592–598. 33. Bause J, Ehses P, Mirkes C, Shajan G, Scheffler K, Pohmann R. Quantitative and Functional Pulsed Arterial Spin Labeling in the Human Brain at 9.4 T. Magn Reson Med 2015: Doi: 10.1002/mrm.25671. [Epub ahead of print] 34. Chadzynski G, Henning A, Ehses P, Hoffmann J, Shajan G, Scheffler K. High-resolution free induction decay proton MRSI in the human brain at 9.4 T. In Proceedings of the 22nd Annual Meeting of ISMRM, Milan, Italy, 2014. Abstract 2904. 35. Ehses P, Bause J, Shajan G, Scheffler K. Efficient Generation of T2*Weighted Contrast by Interslice Echo-Shifting for Human Functional and Anatomical Imaging at 9.4 Tesla. Magn Reson Med 2015;74: 1698–1704. 36. Wharton S, Bowtell R. Fiber orientation-dependent white matter contrast in gradient echo MRI. Proc Natl Acad Sci U S A 2012;109: 18559–18564. 37. Pohmann R, Shajan G, Balla DZ. Contrast at high field: relaxation times, magnetization transfer and phase in the rat brain at 16.4 T. Magn Reson Med 2011;66:1572–1581. 38. Budde J, Shajan G, Hoffmann J, Ugurbil K, Pohmann R. Human imaging at 9.4 T using T(2) *-, phase-, and susceptibility-weighted contrast. Magn Reson Med 2011;65:544–550.
Signal-to-Noise Ratio and MR Tissue Parameters in Human Brain Imaging at 3, 7, and 9.4 Tesla Using Current Receive Coil Arrays Rolf Pohmann,1* Oliver Speck,2,3,4,5 and Klaus Scheffler1,6 Purpose: Relaxation times, transmit homogeneity, signal-tonoise ratio (SNR) and parallel imaging g-factor were determined in the human brain at 3T, 7T, and 9.4T, using standard, tight-fitting coil arrays. Methods: The same human subjects were scanned at all three field strengths, using identical sequence parameters and similar 31- or 32-channel receive coil arrays. The SNR of threedimensional (3D) gradient echo images was determined using a multiple replica approach and corrected with measured flip angle and T2* distributions and the T1 of white matter to obtain the intrinsic SNR. The g-factor maps were derived from 3D gradient echo images with several GRAPPA accelerations. Results: As expected, T1 values increased, T2* decreased and the B1-homogeneity deteriorated with increasing field. The SNR showed a distinctly supralinear increase with field strength by a factor of 3.10 6 0.20 from 3T to 7T, and 1.76 6 0.13 from 7T to 9.4T over the entire cerebrum. The gfactors did not show the expected decrease, indicating a dominating role of coil design. Conclusion: In standard experimental conditions, SNR increased supralinearly with field strength (SNR B01.65). To take full advantage of this gain, the deteriorating B1-homogeneity and the decreasing T2* have to be overcome. Magn C 2015 Wiley Periodicals, Reson Med 75:801–809, 2016. V Inc. Key words: ultra-high field; signal-to-noise ratio; relaxation times
INTRODUCTION In recent years, available field strengths for MRI instruments have increased rapidly, both for human and animal applications (1). While 7 Tesla (T) has developed
1 Max Planck Institute for Biological Cybernetics, Magnetic Resonance €bingen, Germany. Center, Tu 2 Department of Biomedical Magnetic Resonance, Otto-von-Guericke University Magdeburg, Germany. 3 German Centre for Neurodegenerative Diseases (DZNE), Site Magdeburg, Germany. 4 Leibniz Institute for Neurobiology, Magdeburg, Germany. 5 Center for Behavioral Brain Sciences, Magdeburg, Germany. 6 €bingen, Department for Biomedical Magnetic Resonance, University of Tu €bingen, Germany. Tu
*Correspondence to: Rolf Pohmann, Ph.D., Max Planck Institute for Biological Cybernetics, Magnetic Resonance Center, Spemannstr. 41, 72076 €bingen, Germany. E-mail: [email protected] Tu Received 25 July 2014; revised 4 February 2015; accepted 9 February 2015 DOI 10.1002/mrm.25677 Published online 29 March 2015 in Wiley Online Library (wileyonlinelibrary. com). C 2015 Wiley Periodicals, Inc. V
into a standard field strength for ultra-high field MR in humans, the interest in even stronger magnets remains high, causing a slow but steady increase in scanners operating at 9.4T or above. The main driving force for this trend is the gain in intrinsic signal-to-noise ratio (SNR), which is expected to grow at least linearly with field strength (2–4). However, with increasing static field, the homogeneity of the RF-fields declines, the longitudinal relaxation time T1 increases, while T2 and T2* decrease. In addition, the construction of RF coils for high frequencies becomes more and more involved, mainly because of the need to combine the multichannel receive arrays with tight-fitting multielement transmit coils needed to reach the required transmit homogeneity (5). This poses the question of how much of the expected gain in sensitivity can be realized in practical experiments. While in general this question has to be investigated for every application separately, because the changing magnetic field may have different effects on the contrasts to be observed in a specific experiment, the intrinsic SNR and the relaxation times as the underlying MR parameters are certainly of interest for many studies and allow predictions for various applications. In addition, the B1 homogeneity (6) and the g-factor of parallel imaging applications (7) are expected to change with field strength and can play an important role in practical experiments. The aim of this study is to investigate variations in those MR parameters and in the SNR by a direct comparison between 3T, 7T, and 9.4T. While relaxation times and transmit field inhomogeneity can be determined and their influences on the final SNR be taken into account, the effect of different receive coils cannot easily be assessed because this would require determining the absolute receive sensitivity, which, for a multi channel array coil, is hardly feasible. While at lower fields, the principle of reciprocity can be used to connect the easily measurable transmit field with the receive sensitivity of a single channel coil, this is no longer possible at 7T and above (8). In addition, using a birdcage or other single channel transceiver coil would ignore common experimental practice. Instead, by using highly efficient, multi-channel receive-only coil arrays with similar shape and similar number of elements that are used in many current MR studies, we try to address the actual SNR behavior in typical studies investigating the human brain. METHODS In a simple, RF-spoiled gradient-echo acquisition, the SNR is given by:
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1 eTR =T1 sina eTE =T2 ; 1 cosa eTR =T1
[1]
where T1 and T2* are the longitudinal and the apparent transverse relaxation times, respectively, TR and TE are the repetition and the echo time of the measurement, a is the flip angle and Sc is the sensitivity of the receive coil(s), including the noise figure of the receive chain. Even though not explicitly noted, all parameters except for TE and TR depend on the position. By measuring the SNR of a gradient echo image as well as the other relevant parameters from Eq. [1], this equation can be used to obtain SNR0, which is the SNR that would be obtained with a homogeneous flip angle of 90 , an infinite repetition time and an echo time of zero, and thus includes the influence of the spin density. While these corrections can easily be applied for the relaxation times and the flip angle, quantitative values for the receive coil sensitivities cannot be determined experimentally. Thus, it is in practice only possible to calculate the product of SNR0 and Sc. To be able to derive a meaningful estimation of the intrinsic SNR at different field strengths, the difference in the receive coil sensitivities at the different fields should be small. We therefore used receive coil combinations with similar geometric properties in all measurements. Instrumentation Experiments were performed on three similar whole body scanners of the same hardware generation (Siemens Healthcare, Erlangen, Germany) with magnetic field strengths of 3T (Tim Trio, actually operating at a field strength of 2.9T), 7T (Magnetom 7T), and 9.4T (Magnetom 9.4T). All scanners worked with the same software version (VB 17) and equal versions of both vendorsupplied and self-written sequences were used. To obtain measurements that are comparable to each other, but also give insight in the situation encountered in current experiments, multi-channel receive-only coil arrays with similar shape and size and a similar number of array elements were used. At 3T, the 32-channel helmetshaped product coil was combined with the body coil for transmission. At 7T, a similar coil (Nova Medical Inc., Wilmington, MA) was used, again with 32 tightfitting receive elements and combined with a local birdcage transmit coil. At 9.4T, a home-built 31-channel receive helmet was combined with a 16-channel transmit array (9), which was driven in circularly polarized mode in all experiments. Experiments The same three volunteers (two male) were examined at all three field strengths with identical sequences and sequence parameters with approval by the local review boards of the participating institutions. After adjustments and shimming, a three-dimensional flip angle map was acquired using a home-written AFI (actual flip angle imaging) sequence (10), implemented following the phase and gradient spoiling schemes recommended by Yarnykh (11). This sequence has been shown to generate reliable B1-maps even at ultra-high
field without exceeding the SAR limits (12). The images spanned a field-of-view (FOV) of 256 224 160 mm3 with a spatial resolution of (2 4 4) mm3. With repetition times of 20 ms and 100 ms, this scan took approximately 4:29 min and mapped a nominal flip angle of 60 . Then, a three-dimensional gradient echo image was acquired, with equal FOV but with an improved isotropic resolution of 1 mm. The nominal flip angle was 4 or 5 , repetition and echo times were 8 ms and 2 ms, respectively, and the acquisition bandwidth was 490 Hz/ voxel at all three field strengths. This scan was repeated with a flip angle of 0 to obtain accurate noise correlation maps. For determination of the parallel imaging performance, the same gradient echo sequence was repeated with nine different GRAPPA acceleration factors between two and eight. GRAPPA schemes were (given as accelerations in anterior–posterior/left–right directions): 2/1, 3/ 1, 4/1, 1/2, 1/3, 1/4, 2/2, 3/2, 4/2. Twenty-four calibration lines were acquired in each direction. For some GRAPPA scans, the scanner software did not allow selecting the desired acceleration factors (especially all accelerations in left–right direction at 3T) or enforced changes in other parameters (like oversampling in left– right direction for all 1/3 scans). In those cases, GRAPPA data was extracted from the unaccelerated dataset, applying exactly the same GRAPPA parameters as used in the corresponding scans. The GRAPPA experiments were also repeated on a head-and-shoulder phantom filled with a solution with similar electromagnetic properties as the brain at 9.4T (13). For T2*-mapping, a multi-echo gradient echo sequence with 12 echo times between 2 ms and 55 ms, a spatial resolution of 1 2 2 mm3 and a repetition time of 60 ms was used, again over the same FOV. With a GRAPPA factor of two and a partial Fourier acceleration of 6/8, this scan took around 4.3 min. The longitudinal relaxation time T1 was measured in one white matter voxel, using a spectroscopic inversion recovery sequence with STEAM (stimulated echo acquisition mode) localization. Spectra without water suppression were acquired from a (5 mm)3 voxel after a hyperbolic secant inversion pulse. In 18 repetitions, the inversion delay was varied between 50 ms and 12 s, with a relaxation delay of 12 s between successive scans. Reconstruction and Postprocessing All data were reconstructed and postprocessed using home-written routines in Cþþ and Matlab to avoid any unknown processing step such as raw or image data filtering. First, the STEAM-FIDs were reconstructed and integrated over the water line. To obtain T1, the equation M ðTI Þ ¼ M0 1 2beTI =T1 was fitted to the relaxation curve. Including the inversion efficiency b, ranging from zero for none to one for perfect inversion, allows for nonperfect inversion. T2*-maps were generated by an exponential fit to the multi-echo data for every voxel within the brain, using Matlab least squares fitting. Data were excluded if the relative fitting error as returned by the fitting routine was above 25%, the absolute fitting error was above 15
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FIG. 1. Typical images from one volunteer acquired in the SNR scan at 3T, 7T, and 9.4T (left) and compartment structure for analysis. All images in this and the following figures show the same slices from the same subject.
ms or the resulting T2*-value was above 150 ms, in which case it was assumed that either the fitting failed or the data originated from a CSF-voxel. The AFI map was zero-filled to the same size as the gradient echo images and was used to generate maps of transmit efficiency and to correct for flip angle variations in the gradient echo images. The noise covariance matrix was calculated from the noise images (with a ¼ 0 ) and used to calculate the final SNR of the combined images by a pseudo-multiple replica approach (14): Artificial noise was generated for all receive channels, having the same noise covariance as determined with the noise scans. This noise was added to the raw data and the resulting dataset was Fourier transformed. The single coil images were combined with a root-sum-of-squares approach (15), using sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X Ic ðx; y Þ2 I ðx; y Þ ¼ ; s2c c
[2]
where Ic(x,y) and I(x,y) are the single coil and combined image intensities at position (x,y), sc is the coil variance of coil c as measured in the noise scan and the sum adds over all coils c. The entire process was repeated 128 times to determine the SNR as the ratio of mean image intensity over all 128 images and their standard deviation. Finally, the determined SNR maps were corrected for the flip angle and T2*-maps and the white matter T1-values according to Eq. [1] to obtain the intrinsic SNR0, weighted by the coil sensitivities. The parallel imaging performance was assessed by calculating g-factor maps: The SNR of the nonaccelerated image (SNRnoPI) and of the accelerated images (SNRPI) were determined as described above, again generating 128 pseudo-replica with a home-written Cþþ-implementation of a three-dimensional (3D) GRAPPA algorithm. The g-factor was then calculated as g¼
SNRnoPI pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; NnoPI =NPI
SNRPI
[3]
where NnoPI and NPI are the total number of scans acquired for the conventional and the accelerated image (including reference scans), respectively.
GRAPPA weights were calculated from 24 autocalibration lines in the accelerated direction and 64 and 32 points in read and the nonaccelerated phase encoding directions (16,17), respectively, using a 3D-kernel with a size of 5 5 5 points. The pseudoinverse was calculated using a singular value decomposition with Tikhonov regularization (18). For a quantitative evaluation of B1 field homogeneity, transmit efficiency, T2* variation, SNR and g-factor, the 3T images were used to subdivide the brain into four compartments (Fig. 1): Brain stem and cerebellum, inner and outer brain, and ventricles. The outer brain was defined as a region encompassing approximately 2 cm on the surface of the brain, where the main part of cortical gray matter is situated, while the inner brain compartment comprises the rest of the cerebrum. The ventricles were classified as a separate compartment and excluded from T2* and SNR evaluations. To obtain representative values for gray and white matter T2*, 21 circular regions of interest (ROIs) in gray and 15 ROIs in white matter with a diameter of four voxels were defined, based on the T2*-weighted images, distributed evenly over the entire cerebrum. The compartment masks were then coregistered to the 7T and 9.4T images and, where necessary, manually corrected for small deviations in geometry, potentially due to differences in geometric distortions. For visual illustration, transmit efficiency, T2*, SNR, and g-factor maps from 7T and 9.4T were coregistered to the 3T images to allow for direct comparison of identical brain regions. RESULTS All values were calculated by first computing the mean values of the parameter in question over the ROI for each subject. The mean of the values for the three subjects is given together with the standard deviation over the three subjects. Relations for the field dependence of the parameters are determined using the real field strength of 2.9T for the 3T data. Typical images from one volunteer in all three orientations are shown in Figure 1. All parameter images show the same three slices of the same subject. Table 1 contains the measured parameter values for the different brain compartments.
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Table 1 Measured Field Dependent Parameters for Different Anatomical Structuresa B1 3T
7T
9.4T
Whole brain Whole cerebrum Outer brain Inner brain Cerebellum/brain stem Whole brain Whole cerebrum Outer brain Inner brain Cerebellum/brain stem Whole brain Whole cerebrum Outer brain Inner brain Cerebellum/brain stem
SNR
b
Efficiency
Homogeneity
31.966.5 31.566.4 29.465.9 33.766.8 35.166.8 38.964.3 40.063.9 38.963.0 41.164.6 30.368.2 21.6 62.1 22.062.1 23.162. 0 20.862.6 17.763.5
0.1160.01 0.1160.01 0.0860.02 0.0860.01 0.1060.02 0.2560.02 0.2260.003 0.1960.01 0.2460.007 0.3760.09 0.2860.01 0.2560.006 0.2060.02 0.3060.01 0.4160.06
c
d
Absolute
Increasee
1001649 1044653 13306131 753638 646621 31436144 32326150 39196139 25276133 24386231 55146609 57076690 68206827 44826233 48516214
3.1460.23 3.1060.20 2.9660.22 3.3660.24 3.7860.37 1.7860.12 1.7660.13 1.7460.17 1.7860.10 2.0060.13
a
Mean values over compartments defined in Figure 1. Given values are mean and standard deviations over subjects Transmit efficiency over compartment, in nT/V. c Relative standard deviation of the transmit efficiency over compartment. d SNR after correction for flip angle, T1 and T2*. e Relative SNR increase compared to the next lower magnetic field strength. b
Longitudinal Relaxation Time T1 The white matter relaxation times determined with the single voxel inversion-recovery STEAM experiments are (947.4 6 66.1) ms at 3T, (1334.2 6 21.7) ms at 7T, and (1426.7 6 51.8) ms at 9.4T. A comparison of these values with published data from references [1,19–24) (Fig. 2A) shows that this is well within the expected range. A dependence of the form (25) T1 ðB0 Þ ¼ a Bb0 faithfully describes the measured values for a ¼ 659 ms/T and b ¼ 0.35.
values are (33.4 6 2.9) ms (gray) and (24.1 6 0.8) ms (white) at 7T and (23.8 6 1.0) ms (gray) and (19.2 6 0.9) ms (white) at 9.4T (Fig. 2B). An exponential function T2 ¼ a ebB0 =T describes this dependence best for a ¼ 0.090 s and b ¼ -0.142 T1 for gray and with a ¼ 0.064 s and b ¼ 0.132 T1 for white matter. For illustration, these functions are plotted with the experimental data in Figure 2. However, data from a still larger field range (esp. lower field) would be necessary for a reliable determination of the relation between T2* and field strength.
Apparent Transverse Relaxation Time T2*
Efficiency and Transmit Inhomogeneity
T2*-maps
Figure 4 shows transmit efficiency maps for all three field strengths. The absolute transmit efficiency varies strongly between the fields due to differences in size and technology used for the transmit coils: While the 3T body coil used for excitation is relatively inefficient due to its large size, the narrow 7T local birdcage coil shows
from one volunteer for all three field strengths are shown in Figure 3, indicating a drop to approximately half when going from 3T to 7T and another 20% at 9.4T. An analysis of the gray and white matter ROIs show T2*-values of (59.9 6 3.0) ms and (43.5 6 1.8) ms for gray and white matter at 3T, while the corresponding
FIG. 2. A: Measured values for T1 at 3T, 7T, and 9.4T in white matter (large dots) compared with literature values for white (small dots) and gray matter (crosses). The values are well described by a T1 ¼ 659 ms/TB00.35 - dependence (line). B: T2* values for gray (red) and white (blue) matter with the exponential fit results (parameters see text).
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FIG. 3. T2* maps at the three field strengths (top row) and relative T2* differences between the fields.
superior efficiency. The 9.4T coil, though similar in size, is a full multi-channel transmit array, which causes additional loss due to the large number of lossy components. Because the efficiency itself can always be compensated by higher transmitter power, the much more relevant parameter is the transmit field inhomogeneity, visualized by the plot of the relative standard deviation of the field over the different compartments (Fig. 5A). For the entire cerebrum, this value doubles from 0.11 6 0.01 at 3T to 0.22 6 0.004 at 7T and increases further to 0.25 6 0.006 at 9.4T.
dependent increase is slightly larger in the inside of the brain than at the surface: In the outer brain region the increase is with 2.96 6 0.22 from 3T to 7T and 1.74 6 0.17 to 9.4T lower than in the inner brain (3.36 6 0.24 and 1.78 6 0.10), which is well visible in the relative SNR images in Figure 6. The SNR gain in the cerebellum (3.78 6 0.37 and 2.00 6 0.12) is slightly larger, which is probably due to differences in the coverage of the cerebellum by the different RF coils. Assuming an exponential increase of SNR with field strength, a relation of SNR B01.65 provides a good agreement with the measured values for the cerebrum (Fig. 5B).
SNR After correction for T1, T2*, and flip angle differences, Figure 6 shows the distribution of image SNR for the three different field strengths (first row) and the respective relative changes between the field strengths (second row). The numerical analysis demonstrated a distinctly supralinear increase of SNR with magnetic field strength, with an improvement over the entire cerebrum by a factor of 3.10 6 0.20 from 3T to 7T, and a further increase by a factor of 1.76 6 0.13 from 7T to 9.4T. The field-
FIG. 4. Transmit efficiencies of the coils used at 3T, 7T, and 9.4T. Different color scales were used to emphasize the B1 homogeneity changes.
g-factor g-factor maps for the nine different acceleration factors are shown for all three field strengths in Figure 7, while mean values over the entire cerebrum are shown in Figure 5C. Surprisingly, no clear improvement with increasing field strength is visible. In contrast, for most acceleration factors, the g-factor of the 3T measurements is lowest, though the pattern varies strongly with direction and acceleration factor. The phantom measurements
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(dotted lines in Figure 7) show lower g-factors, especially for the high fields, but similar behavior with field and acceleration factor as the subject data. DISCUSSION
FIG. 5. A: transmit inhomogeneity as relative standard deviations of the B1 field over the entire cerebrum. B: SNR0 values in four different brain compartments. The red line represents fitting results on the SNR over the entire cerebrum as SNR0 ¼ B01.65. C: The g-factor for nine different acceleration patterns and all three fields. Acceleration in the two phase encode directions are described as (anterior–posterior)/ (left–right) accelerations.
So far, no studies have investigated the SNR gain from 7T to 9.4T due to the to date still small number of magnets and the lack of mature receive coils for the latter field. It is, however, surprising how few studies have systematically investigated the SNR advantage of 7T compared with lower fields. In a comparison between 4T and 7T, using similar TEM coils (26), a mean increase of a factor of 1.6 was found, in approximate agreement with a linear SNR increase with field strength, although a slightly larger gain was seen in the center of the brain in that study. Similarly, an increase of approximately 80% was observed in echo planar images when going from 3T to 7T (27), indicating an SNR dependence on field strength of slightly less than linear. In contrast to the current study, no corrections for flip angle and relaxation time differences were applied. The discrepancy between those studies and our results is, however, most likely due to the different hardware. While both above studies used single-channel volume coils, we applied an array of surface coils for signal reception. Thus, the supralinear SNR increase at high field strength observed here might only be realized when using surface coils for acquisition. We are, however, not aware of any publication that compared the SNR at different field strengths using state-of-the-art receive arrays. Even though only little experimental confirmation for the observed behavior is found in the literature, our results are not necessarily surprising, as they have been predicted by several theoretical studies. Already in 1991, Keltner et al (28) reported a distinctly supralinear increase of SNR with frequencies above 150 MHz, if surface coils are used. Using electrodynamic simulations, Wiesinger et al (29) calculated the ultimate SNR in different positions inside a brain model, finding a strong supralinear behavior in the center of the brain, which became less distinct when moving closer to the surface. This was explained by the different characteristics of the near field and the far field of the coil: While the SNR increase in the far field regime was predicted to be higher than linear, the near field behavior was supposed to grow less than linearly. Similar results were reported by Lattanzi and Sodickson (30,31). These findings also deliver an explanation for the weaker SNR gain with field strength in the studies mentioned above: because volume coils were used for transmission and reception, which mainly operate in the near field regime, only the slightly below linear behavior of the near field was observed. In addition, the predicted stronger increase of SNR in the center of the brain compared with the surface can be recognized in our results, especially between 3T and 7T (Fig. 6). The aim of this study was to determine the intrinsic SNR, eliminating all other influencing factors such as relaxation times or flip angle distribution. One factor that we were not able to take into account is the different sensitivity of the receive coils, which is not easily determined
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FIG. 6. Top: SNR distributions over three slices of the same volunteer at all three fields. Bottom: relative SNR differences between the fields.
experimentally. By using similar coils, which are also applied in a large number of neuroscientific studies, we approach this issue in two respects: First, the 3T and 7T coils can be considered the gold standard high end coils for brain imaging at their field strength for the chosen manufacturer. The 9.4T coil used here was applied in some of the still very rare applications at this field strength in human proton MRI (32–35). Even if the influence of the coils cannot be fully eliminated, comparing SNRs with these coils can give insight into the advantages of high field strength in practical neuroscientific applications, many of which apply these coils. Furthermore, the similarities in geometry and design of the three coils are high, so that similar sensitivity can be assumed: They all have a comparable tight-fitting helmet shape, with a similar total number of elements distributed in four rows at the back, while the number of rows is reduced down to two in the front to keep the eyes free. Differences in the exact placing of the coil elements as well as their diameter and overlap will
FIG. 7. The g-factor maps over the three fields and nine different acceleration patterns for one subject. Acceleration in the two phase encode directions are described as (anterior–posterior)/ (left–right) accelerations.
certainly have an effect; however, their influence on the SNR in the brain can be assumed to be relatively modest, while the SNR in brainstem and cerebellum may vary due to differences in the coverage of these areas. The exact analysis presented here will, however, change when other coils are used, although the main outcome – the strongly supralinear SNR increase with field strength, can be assumed to be maintained even for different setups of multi-channel coils. For the parallel imaging behavior, the results are less clear: Here, electrodynamic calculations (7,29), supported by experimental data (7) clearly indicate a decrease of the g-factors for higher field strength due to the more localized fields of the single receive array elements. Our data, however, do not show these expected characteristics, with 3T g-factors being lowest for most accelerations for both subject and phantom measurements. The details of the coil design may thus play the dominant role in the parallel imaging performance. In fact, despite the similarities in coil shape and size of the
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FIG. 8. Coil correlation plots for all three coil arrays, measured in one of the subjects, showing clear differences in coupling characteristics.
entire receive arrays as well as in the number of coil elements, a detailed investigation of the coil design shows strong differences, e.g., in the size of the different array elements (3T: 10 cm, overlapping; 7T: 5 cm 4 cm, pairwise overlapping; 9.4T: 6 cm, each element overlapping with two above and two below) or the distribution of the coil elements on the helmet. The noise correlation maps (Fig. 8) illustrate the differences in coil design as strong variations in the coupling characteristics. Thus, the effect of receive array optimization will still be the decisive factor to achieve good parallel imaging performance with low g-factors. The varying relaxation times form another important factor in the determination of intrinsic and actual SNR at different field strengths. We have tried to eliminate their influence by measuring both T1 and T2* and correcting for them. T2* may be a potential confound due to its strong sensitivity toward veins or the orientation of fiber tracts (36), and thus has to be taken into account for accurate SNR measurements. To keep the measuring time short, we measured T2* with a reduced spatial resolution of 1 2 2 mm3, as compared to the isotropic 1 1 1 mm3 voxels used in the SNR scan. Because T2* is voxel-size dependent, the correction will therefore not be completely accurate. To estimate the extent of this effect, we measured T2*-values for the highest field strength with both resolutions, finding an increase of T2* for the smaller voxels from (23.8 6 1.0) ms to (26.8 6 0.3) ms in gray and from (19.2 6 0.9) ms to (19.5 6 0.5) ms in white matter. Due to the short TE used in the measurements, the effect of this T2* difference is negligible, leading to a change in the corrected SNR of less than 2%. For lower field strengths, this effect is probably even smaller, because intra voxel dephasing effects, that cause a large part of the T2*effect, increase with field strength. A larger inaccuracy may be introduced by the method for T1 determination: Due to restrictions in B1 homogeneity and SAR, a high-resolution T1-map could not be acquired at 9.4T within reasonable time. Therefore, a single T1 value for white matter was determined and used for correction of the SNR. For a worst case estimation of the size of the corresponding error, we calculated the SNRs again, corrected with gray matter T1-values of 1711 ms (23), 2132 ms (1), and 2300 ms (extrapolated by fitting a power dependence to the literature data shown in Figure 2A) for 3T, 7T, and 9.4T, respectively. Under these circumstances, the SNR gain for the entire cerebrum from 3T to 7T would increase to 3.22, and from 7T
to 9.4T decrease to 1.62. However, even in this case the strong supralinear behavior remains. CONCLUSIONS The results show experimental evidence of a supralinear increase in SNR with field strength in human brain MR with standard experimental setups, confirming theoretical predictions. However, the changes in the relaxation times and the degraded B1 homogeneity pose new challenges. While the increasing T1 has been shown to affect the SNR gain only slightly as long as optimal imaging parameters are used, even up to much higher fields (37), the reduction in T2 and T2* will require further developments in sequence design. Even more important is to overcome the growing transmit field inhomogeneity by highly efficient multi-element transmit arrays, improved parallel transmit techniques and an optimized control of the specific absorption rate. In addition, novel techniques that are less affected by those ultra-high field specific issues, like phase imaging, where the contrast does not depend on the flip angle, or even can benefit from them, like T2*-weighted imaging, which gets faster with decreasing T2* values, will gain importance and make it possible to fully take advantage of the high SNR increase at yet higher fields (38). REFERENCES 1. Rooney WD, Johnson G, Li X, Cohen ER, Kim SG, Ugurbil K, Springer CS Jr. Magnetic field and tissue dependencies of human brain longitudinal 1H2O relaxation in vivo. Magn Reson Med 2007; 57:308–318. 2. Hoult DI, Lauterbur PC. Sensitivity of the zeugmatographic experiment involving human samples. J Magn Reson 1979;34:425–433. 3. Redpath TW. Signal-to-noise ratio in MRI. Br J Radiol 1998;71:704– 707. 4. Collins CM, Smith MB. Signal-to-noise ratio and absorbed power as functions of main magnetic field strength, and definition of “90 degrees” RF pulse for the head in the birdcage coil. Magn Reson Med 2001;45:684–691. 5. Ibrahim TS. Ultrahigh-field MRI whole-slice and localized RF field excitations using the same RF transmit array. IEEE Trans Med Imaging 2006;25:1341–1347. 6. Van de Moortele PF, Akgun C, Adriany G, Moeller S, Ritter J, Collins CM, Smith MB, Vaughan JT, Ugurbil K. B(1) destructive interferences and spatial phase patterns at 7 T with a head transceiver array coil. Magn Reson Med 2005;54:1503–1518. 7. Wiesinger F, Van de Moortele PF, Adriany G, De Zanche N, Ugurbil K, Pruessmann KP. Parallel imaging performance as a function of field strength–an experimental investigation using electrodynamic scaling. Magn Reson Med 2004;52:953–964. 8. Hoult DI. The principle of reciprocity in signal strength calculations—A mathematical guide. Concepts Magn Reson 2000;12:173– 187.
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