SNR Versus Resolution in 3D 1 H MRS of the Human Brain at High Magnetic Fields

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1 COMMUNICATIONS Magnetic Resonance in Medicine 46: (200) SNR Versus Resolution in 3D H MRS of the Human Brain at High Magnetic Fields Belinda S.Y. Li, Juleiga Regal, and Oded Gonen* It is commonly accepted that the signal-to-noise ratio (SNR peak-signal/rms-noise) per-unit-time of proton MR spectroscopy ( H-MRS) is linearly proportional to the voxel volume. Consequently, with a headcoil and 30-min acquisition, cm 3 is considered the SNR-limited spatial resolution barrier in the human brain. However, since local linewidths, * ( T* 2 ) -, at high magnetic fields (B 0 ), are dominated by regional inhomogeneities ( B 0 ), i.e., T* 2 T 2, reducing the voxel dimensions may increase T* 2. This could compensate, in part, for signal loss with volume decrease. It is shown that for two cubic voxels of sides l and l 2, l > l 2,asthe volume decreases by (l /l 2 ) 3, their SNR ratio is reduced by only (l /l 2 ) 2 due to a commensurate T* 2 increase of l /l 2. This is demonstrated in a phantom and the brains of volunteers, with 3D H-MRS in a headcoil at 4 T. It is shown that while the cubic voxels dimensions were all halved, reducing their volume eightfold, their metabolites SNR decreased only fourfold, due to their *s twofold decrease. In other words, both spatial and spectral resolutions were doubled at a significantly, 2, smaller-than-expected SNR loss. This advantage was exploited to produce quality high spatial resolution, cm 3, metabolic maps in a 27-min acquisition. Magn Reson Med 46: , Wiley-Liss, Inc. Key words: 3D-MRS; brain; high magnetic field; proton MRS; spatial resolution It is widely accepted that the smallest voxel size, i.e., highest spatial resolution, of in vivo H-MRS is dictated by the measurement time and the sensitivity of the nucleus ( 3). This notion is based on the premise that the limiting factor the SNR [peak-signal/rms-noise (4)] per-unit-time is determined only by the number of spins in the voxel, while all other properties, including the linewidth, * ( T* 2 ) -, are unchanged. Consequently, with headcoils, voxel sizes of cm 3 are commonly used in singlevoxel H-MRS in 7-min acquisition. Smaller, 3.5 cm 3, voxels are typically acquired with 2D and 3D MRS in 30 min (2). The constant linewidth assumption is shown here to be incorrect if/when T* 2 is determined by local magnetic field inhomogeneities, B 0 (5). These are caused primarily by susceptibility differences,, at tissue interfaces and by incomplete shimming of the magnet s intrinsic B 0 imperfections (6 8). Although this is worst (.0 ppm/cm) near the air/tissue interfaces, e.g., air-filled sinuses and auditory canals, and bone/tissue regions, B 0 s are present at any tissue transition zone (7,8). They cannot be completely removed with the first- and second-order shims found in clinical MR imagers, as pointed out by Gruetter (9), and worsen linearly with field increase. Under these conditions, decreasing the voxel size will sample less B 0, thus increasing T* 2. This in turn mitigates the anticipated linear loss of the peak s amplitude, and hence its SNR, with volume. In this article we demonstrate that ) even in well-shimmed samples, T* 2 is dominated by B 0 ; and 2) at a high, 4 T, magnetic field, voxels well below cm 3 can still be obtained with good SNR using 3D H- MRS and a headcoil in under 30 min. THEORY The linewidth from an ensemble of identical spins in a homogeneous macroscopic sample with a local inhomogeneity, B 0, across it is commonly given by (6,7,0): T* 2 B T 0, [] Sample 2 where T 2 is the spin spin transverse relaxation time and is the gyromagnetic ratio. Equation [] implicitly models the inhomogeneity as a linear field gradient, g mt.m -, across the sample: B 0 g L; g ig X jg Y kg Z, L il X jl Y kl Z, [2] where L X, L Y, and L Z are the sample s dimensions, g X, g Y, and g Z the gradient s strengths and i, j and k are the unit vectors in the X, Y, and Z directions, respectively. By analogy, in a localizing experiment, in a voxel of dimensions l X L X,l Y L Y, and l Z L Z contained entirely within the object, T* 2 will be: T* 2 g l g l if g ; T voxel 2 T 2 l il X jl Y kl Z. [3] Department of Radiology, University of Pennsylvania Medical Center, Philadelphia, Pennsylvania. Grant sponsor: NIH; Grant numbers: NS33385; NS *Correspondence to: Oded Gonen, Department of Radiology, New York University School of Medicine, 550 First Avenue, New York, NY oded.gonen@med.nyu.edu Received 29 May 200; revised 7 August 200; accepted 9 September Wiley-Liss, Inc. 049 The approximation that g is linear is obviously better across a voxel in Eq. [3] than across the entire sample in Eq. [], since l L (5). Furthermore, although the T 2 s of the major H-MRS metabolites: N-acetylaspartate (NAA), choline (Cho), and creatine (Cr), reported at 4 T, range from ms, i.e.,.4.8 Hz for Lorentzian

2 050 Li et al. Table Average and Standard-Deviation of *s and SNRs (cf. Eq. [5]) of the NAA Peak Obtained in the Phantom and in the Volunteers as a Function of the Cubic Voxel Dimensions * NAA [Hz] SNR (NAA) Voxel dimensions (cm 3 ) Phantom (N) a In vivo (N) Phantom a In vivo (8.0) 7.2 () (2) b b (3.4) (4) (8) c c (.0) (6) (60) b b (0.42) (36) (6) c c (0.2) (00) 9 2 a Average of N voxels measured in back-to-back acquisitions on the phantom with all instrumental parameters unchanged. b,c Average of N voxels in b Volunteer # and c Volunteer #2. The consistently worse linewidths of volunteer #2 are probably due to the many fillings in her teeth, versus none in subject #. lineshapes (,2), the observed * s are 7 Hz, as shown in Table. Therefore, in an actual experiment the g l term dominates the linewidth. For a Lorentzian line of total area A, the peak-height, h, equals T* 2 A (3). Since A is proportional to the voxel volume, i.e., the product of its dimensions, l 3, whereas T* 2, according to Eq. [3], is inversely proportional to their sum, then, assuming g X g Y g Z g l l X l Y l Z h A T* 2 g l X l Y l Z O X l Y l Z l l 2. [4] Thus, when a voxel volume is reduced from (l ) 3 to (l 2 ) 3, where l l 2, the peak-area ratio, A 2 /A, will be (l 2 /l ) 3, whereas h 2 /h will only be (l 2 /l ) 2 due to a T* 2 increase of l /l 2. Note that Eq. [4] would also be valid for the general case of l X l Y l Z. Expressing l Y a l X and l Z b l X, where a b, the proportionality in Eq. [4] would consist of an extra factor of (a b)/( a b). Since this factor will remain a constant as long as all three voxel sides are changed by the same proportion, the relationship h l 2 of Eq. [4] will hold. Equations [3] and [4] predict two interesting outcomes. First, as long as the spectra are inhomogeneously broadened, i.e., ( T 2 ) - g lort 2 T* 2, halving l will approximately halve the voxel linewidth. Second, while this halving will yield a voxel with /8th the volume, doubling the spatial resolution, the peak heights will decrease by only 4, not 8. Since noise is not a function of voxel size, the SNR will also incur only 4 loss, contrary to the prevailing SNR volume concept (3). MRS All experiments were performed in a General Electric Signa 4 Tesla full-body imager with a circularly polarized Vaughan TEM headcoil (4) and actively shielded gradients (GE Medical Systems, Milwaukee, WI). Our 3D chemical shift imaging (CSI)-based autoshim procedure optimized the 7 first, second, third, and higher-order channels in 5 min. to yield consistent 25 5 Hz fullwidth-at-half-maximum whole-head water linewidth and 2 5 Hz on a 2L phantom. Three CHESS and a BASING pulses, shown in Fig., were used to suppress the VOI s water signal by more than 0 3 -fold (5,6). T -weighted MRI in the sagittal, coronal, and axial planes followed. Then a 6 LR 6 AP L IS cm 3 (L 0.5, 0.75,,.5, 2, 3, or 4) left-right (LR) anterior posterior (AP) inferior superior (IS) parallelepiped VOI ( 8 44 cm 3 ) was excited using PRESS with TE 35 ms (7). These VOIs were subdivided, with Hadamard spectroscopic imaging (HSI), into, 2, or 4 axial slices. Each slice was further partitioned into 6 LR 6 AP voxel arrays with 2D CSI within a field-of-view (FOV) appropriate for the spatial resolution (cf. Fig. ) (8,9). The acquisition bandwidth was 2 KHz, with 2048 complex points, giving ahzspectral resolution. Phantom The GE standard brain spectroscopy phantom comprising several metabolites found in the brain, in water, at near physiological concentrations: NAA, mm; Cr, 8 mm; Cho, 2.5 mm was used. Its overall solution ionic strength EXPERIMENTAL Human Subjects Two healthy female volunteers, 3 and 32 years old, were recruited for this study. They were briefed on the procedure and gave Institutional Review Board-approved written consent. FIG.. Hybrid HSI/CSI localization sequence used. A 50-Hz CHESS water-suppression was followed by PRESS (TE 35 ms) VOI excitation. Its 5.2 ms 90 also performed HSI along Z IS under a 4.5 mt.m - gradient, followed and ms later by 5.36 ms SLR 80 s under mt m -. Localization along X LR and Y AP was 6 6 CSI. A 2.5 ms Gaussian 80 (BASING) was pulsed between the 80 s for added water suppression.

3 SNR vs. Resolution of Brain 3D HMRS 05 required the same RF power, for a nonlocalized ms 80 pulse, as a typical human head. Five back-to-back experiments were performed on this phantom, each consisting of a different cubic voxel size, l , ,.0 3,.5 3, and cm 3 (the latter two are common in single-voxel in vivo H-MRS). These l s were achieved by changing the slice thickness and in-plane FOVs, while keeping all other instrumental settings fixed. At TR of.6 sec, the acquisition at each spatial resolution took 7 min. Volunteers These experiments were similar to those on the phantom. However, to limit time in the magnet only one back-toback 3D H-MRS cubic spatial resolution-pair was done on each volunteer. One FOV pair was: cm 3 (8 cm 3 voxels) and 6 6 4cm 3 ( cm 3 )witha6 6 4cm 3 VOI. The other FOV pair was cm 3 (3.4 cm 3 ) and 2 2 3cm 3 (0.42 cm 3 )witha6 6 3cm 3 VOI. With the exception of in-plane FOVs and HSI-order, all instrumental parameters were unchanged within each spatial resolution-pair, including positioning and shim. A TR of.6 sec and an MRS acquisition time of 27 min/set were used, resulting in a -hr protocol per subject. This design ensured that: ) voxels of both spatial resolutions 4 were acquired over the same anatomy, and 2) all measurements took the same amount of time. Postprocessing The MRI and MRS data were processed offline using our custom software. Residual water was removed from each FID in the time domain (20). A mild,.3 Hz, Lorentzian filter was applied to the in vivo data only. The FIDs were voxel-shifted to align the CSI grid with the PRESS box, Fourier-transformed in the temporal and two spatial dimensions and Hadamard-transformed along the third. No spatial filters were applied. Finally, the spectra were automatically corrected for frequency and 0th (and first)- order phase shifts, referenced to NAA and Cho peaks in voxels where either (or both) were available. Metabolite Quantification Voxels at the edges of the VOI in the CSI-planes, which suffered loss of metabolite signals due to unidirectional voxel-signal bleed to outside the VOI and imperfect profiles of the 80 pulses in Fig., were excluded from the analyses. The apparent linewidth, *, and relative concentration of NAA were calculated from the peak in each remaining voxel using the parametric spectral modeling and least-squares optimization of Soher et al. (2). This process made use of a priori spectral information and included automatic phasing, nonparametric characterization of baseline signal components, and a Lorentz-Gauss lineshape assumption. Metabolite SNRs were obtained as follows: ) The amplitude, S j, was obtained for the NAA peak in each voxel, j, in the VOI (excluding edge voxels, see above); 2) the RMS noise, noise, was estimated from the signal-free, to 2 ppm, region; 3) voxels in which S j 6 noise were rejected; 4) SNR, S j, was computed in each of noise the remaining voxels. FIG. 2. Plots of average SD for the five back-to-back phantom data sets: a: Linewidth of the NAA peak vs. voxel length (l l X l Y l Z ). b: SNR of the NAA peak versus square of voxel length, l 2. c: Real part of the spectra from overlapping voxels of the five spatial resolutions (l), scaled to equal NAA peak height to emphasize linewidth and SNR changes. Note the line narrowing, especially of the lactate doublet, J 6.7 Hz, at.3 ppm. RESULTS Average standard deviation ( ) of * and SNR for the NAA peak at each spatial resolution in the phantom and in vivo, compiled in Table, were calculated as: X i N N X i j ;and i j N N X i j X i 2 /2, [5] where X i is the average of X (X SNR or *) and i its standard deviation at spatial resolution i (i 2 3,.5 3, 3, ,or0.5 3 cm 3 ), with the index j indicating the voxel number and N the total number of voxels used in the calculation at each spatial resolution. As predicted by Eqs. [3] and [4], they reveal a strong correlation between * and voxel length, l,(p 0.00, r 0.998), shown in Fig. 2a, and between the SNR and l 2 (P 0.00, r 0.999) in Fig. 2b. Representative spectra from overlapping regions in the phantom at each of the five spatial resolutions, in Fig. 2c, demonstrate graphically the * and SNR dependence on l. Table also compiles average of * and SNR for the NAA peak at each spatial resolution in vivo. Their distributions are described more comprehensively by box plots in Fig. 3, together with the predicted values for the smaller voxels (l or.0 cm). These predictions were scaled from the lower-spatial-resolution data (l.5 or 2.0 cm) according to Eqs. [3] and [4] by dividing each voxel s * by l /l 2 2 and SNR by (l /l 2 ) 2 4. Note their agreement with the measured values. In vivo spectra from overlapping voxels (cf. Fig. 4a) at l 0.75 and.5 cm, in the same volunteer, are shown in Fig. 4b,c. The NAA metabolic maps derived from the spectra matrices of this slice at each j

4 052 Li et al. spatial resolution are shown in Fig. 4d,e. Note the superior correspondence of the higher-resolution map, Fig. 4e, with the anatomy in 4a, compared with 4d. FIG. 3. Box plots of the distributions of * (top) and SNRs (bottom) for the NAA peak in vivo: a: Volunteer. Voxel lengths: l 2 cmand l 2cm(and8cm 3, respectively). b: Volunteer 2, with l cm and l.5 cm (0.42 and 3.4 cm 3, respectively). Clear boxes show measured m * and SNR m values. Hatched boxes depict predicted values ( * p and SNR p ) for the higher spatial resolution voxels scaled from the lower-resolution data: * p * m / (l /l 2 ) * m /2; and SNR p SNR m /(l /l 2 ) 2 SNR m /4. DISCUSSION Verification in a Phantom Figure 2a,b shows strong positive correlations between * and l, and between the SNR and l 2, verifying Eqs. [3] and [4]. It is also evident from the correlations p 0 and r values that all the variability in the data is fully explained by our model. Therefore, the possibility of another process being involved is statistically vanishing. The significance of this outcome is demonstrated by the spectra in Fig. 2c: As the voxel size, l, decreases, all linewidths narrow, leading to a progressive improvement of spectral resolution. This is most apparent for the lactate peak at.3 ppm, where the 6.7 Hz J-splitting, obscured by broadening at l 2 or even.5 cm, becomes increasingly wellresolved as l decreases, reaching baseline resolution at l 0.75 cm. At the same time, contrary to the common lore ( 3), the SNR decrease due to a reduction of voxel volume from 2 3 down to cm 3 is not the feared (2/0.5) 3 64, but instead just 20-fold. Verification in the Human Brain Equations [3] and [4] determine the behavior of in vivo linewidths and SNRs as well. This is demonstrated by the box plots of Fig. 3, in which the values for both are predicted for each volunteer for the higher-spatial-resolution voxels from the lower-resolution s measured values. Figure 4b,c again shows that much better spectral resolution, FIG. 4. a: Axial MRI from a slice in Volunteer 2. b,c: Real part of the spectra taken from overlapping regions indicated in a at two resolutions: l.5 and 0.75 cm. They are scaled vertically as described in Fig. 2c. d,e: NAA metabolic maps from the spectra matrices corresponding to a, with l.5 cm and 0.75 cm, respectively. Note the superior spatial resolution for the smaller l.

5 SNR vs. Resolution of Brain 3D HMRS 053 reflected by the Cr Cho peaks separation, is achieved by halving l. Such fine spectral resolution facilitates more accurate quantifications of these peaks, which otherwise, at l.5 cm, partially overlap (cf. Fig. 4b). Here, as in the phantom, the SNR decrease with voxel size is not the (l /l 2 ) 3 8, commensurate with voxel volume (,2), but the moderate (l /l 2 ) 2 4, predicted by Eq. [4]. Hence, as shown in Fig. 4c, excellent SNR, 5, is achieved at a cm 3 spatial resolution in 27-min 3D H-MRS (cf. Table ). The combination of higher spatial and spectral resolutions yield better representation of the anatomy by metabolic maps, evident by comparing Fig. 4e (l 0.75 cm) vs. 4d (l.5 cm) with the MRI of that slice in Fig. 4a. It is noteworthy that there are several brain locations, e.g., mesial temporal lobes and mesial inferior frontal lobes, where susceptibility gradients as strong as ppm/cm, 70 Hz/cm at 4 T, can be expected (7,8). Although the fundamentals of the theory expressed here hold in these regions as well, reducing the voxels l even a full order of magnitude, from.0 to 0. cm, will still yield an unusable 7 Hz line in these 0. 3 cm 3 voxels. Furthermore, the commensurate 00 SNR loss sustained by such 0 3 volume decrease would render the result unacceptable, leaving these regions, for the time being, inaccessible to H-MRS. Highest Cost-Effective Spatial Resolution The advantage of an SNR decrease slower than the change in voxel volume is not unlimited. Equation [3] is operative only as long as the underlying T* 2 T 2 assumption holds. Once l is small enough that T* 2 T 2, the signal becomes proportional to l -3 and rapid SNR decline commences. Just how fine can the spatial resolution be made to still benefit from the favorably slow SNR l 2 decrease can be readily estimated from the average observed * in a given experiment and the published T 2 s at that magnetic field (22 24). For example, the T 2 reported for NAA at 4 T indicates the natural linewidth in brain tissue with inhomogeneity broadening is.5 Hz. Consequently, the average * 7.7 Hz lines (SNR 5) obtained from our (0.75) 3 cm 3 voxels (cf. Table ) suggest that in our experiment l can be halved just once more, to cm (and SNR 4). Further cuts will bring * into the homogeneous broadening regime, T* 2 T 2, with diminishing returns. Such a regime is experimentally achievable in some situations, as recently demonstrated by Gruetter and Tkác (25), where a l 3 cm VOI was locally shimmed to ahz linewidth. Subsequent volume reductions did not improve that *, indicating that shimming has successfully removed all macroscopic inhomogeneity effects. The spatial resolution also depends, of course, on the minimum acceptable SNR. For example, for Cho at that highest spatial resolution the SNR would be a marginal 2, even though SNR l 2 might still be operative. 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