Theoretical and experimental studies have shown at least a linear increase in sensitivity with magnetic field strength (1, 2). On the other hand, the transverse relaxation rate is known to increase with magnetic field strength (3, 4), which can result in reduced sensitivity in spin-echo (SE) experiments. The apparent transverse relaxation time (T) is related to the intrinsic transverse relaxation time (T2) through the following equation:
The first term on the right side of Eq.  is the inverse of the intrinsic T2 and is governed by a number of possible mechanisms, including 1) homonuclear dipole–dipole interaction between protons, which is strongly dependent on rotational correlation time τc; 2) hyperfine (contact) interaction, namely, the change of transverse relaxation time due to interaction with a paramagnetic center; and 3) cross-relaxation, which can be significant in dipole-coupled systems. The second and third terms, T2,Diffusion and T2,Exchange, are the transverse relaxation times related to diffusion and exchange of spins between regions with different magnetic field strengths, respectively. These contributions describe the dynamic dephasing regime, whereby the net magnetization is reduced by diffusion and exchange between regions with different magnetic field strengths, which causes the phases of the different spin packets to average out. The opposite situation is defined as the static dephasing regime. NMR signal loss due to static dephasing can be refocused by SE sequences and is therefore not considered here.
It is important to investigate: 1) how the increase of field strength causes T shortening, and 2) how the signal loss from T decay can be compensated for. Key experiments for answering these questions involve measuring T at different field strengths and attempting to estimate T2. The theory of NMR signal formation in the presence of local magnetic field inhomogeneity was first derived by Carr and Purcell (5), and later generalized by Torrey (6), who incorporated the diffusion effects into the Bloch equations to take into account the actual field distribution. The Carr-Purcell (CP) method is the most valuable technique for determining transverse relaxation times. CP experiments are performed by applying a π/2 pulse followed by a series of π pulses spaced with time interval τcp. The value of T determined with a CP technique can vary with τcp because dynamic dephasing and homonuclear spin-spin coupling can cause significant dephasing of magnetization during the interpulse interval. The ability of a CP technique to suppress these contributions allows T2 values to be determined experimentally.
It has previously been shown (7, 8) that changes induced by neuronal activity can result in changes in the concentration of deoxyhemoglobin, which plays the major role as the intravascular contrast agent for fMRI. Contrast in fMRI originates from the difference between the magnetic properties of oxygenated and deoxygenated hemoglobin (diamagnetic and paramagnetic, respectively), which leads to a difference in T values.
In addition, local magnetic susceptibility alterations can occur in different regions of brain, such as gray and white matter, due to the differences in the concentrations and compartmentalization of iron and deoxyhemoglobin. One of the factors that alters the T value of water is the presence of ferritin, a protein that stores the largest fractions of iron in the brain. Both loading of iron in the ferritin protein and the concentration of ferritin in solution alter the localized field gradients and create intertissue contrast in MRI (9, 10).
It has also been shown that changes in physiology and brain activity can lead to changes in the rotational correlation time τc and the apparent diffusion coefficient D (11, 12). The rotational correlation time of a cerebral metabolite strongly depends on its environment when the metabolite is interacting with slowly tumbling macromolecules. Thus, it is important to investigate the following questions: 1) what is the ratio between the intrinsic and apparent transverse relaxation times of different compounds (water and metabolites) in the human brain; 2) how does this ratio change with the external static magnetic field; and 3) how can this information be utilized to investigate local magnetic susceptibility variations?
The goals of this work were to compare the T values of water, N-acetylaspartate (NAA), and creatine (Cr) in the human visual cortex as measured with a CP-type sequence (localization by adiabatic selective refocusing (LASER)) (13, 14) vs. a Hahn SE sequence (point-resolved spectroscopy (PRESS)) (15, 16), and to investigate their dependence on magnetic field strength (7T vs. 4T).
MATERIALS AND METHODS
Human experiments were performed according to procedures approved by the Institutional Review Board of the University of Minnesota Medical School. MRI/MRS studies were performed with Varian Unity INOVA consoles (Varian Associates, CA) that were interfaced to a 90-cm bore 4T magnet (OMT, Inc., Oxon, UK) and to a 90-cm bore 7T magnet (Magnex Scientific, Abingdon, UK). A 10-cm 1H surface-coil probe was used for measurements at 4T. A quadrature surface coil consisting of two geometrically decoupled turns (each 7 cm in diameter) was used for measurements at 7T. Gradient-echo turbo fast low-angle shot (TurboFLASH) (17) images were acquired for all subjects to define the voxel position in the human visual cortex for localized 1H MRS. Global shimming was performed using the linear x, y, and z shim currents. Fine adjustments of all first- and second-order shim terms were accomplished with a fully adiabatic version of fast automatic shimming technique by mapping along projections, FASTMAP (18).
Transverse relaxation times were measured by 1) a Hahn-type SE sequence using the PRESS single-voxel technique, and 2) a CP-type SE sequence modified from the LASER single-voxel technique (Fig. 1). With LASER, single-shot localization was performed with six adiabatic full-passage (AFP) pulses applied in the presence of slice-selection gradients, after exciting nonselectively with an adiabatic half-passage (AHP) pulse (13). In CP-LASER (Fig. 1), the length of the CP train was increased by inserting additional AFP pulses between the excitation pulse and the six AFPs in the LASER portion of the sequence, with RF phases set according to the MLEV scheme (19). The MLEV scheme provided further compensation for imperfections of the AFP pulses. No additional gradient pulses were used when increasing the CP train length with additional AFP pulses. By keeping τcp constant throughout the sequence, the length of the CP train was varied to achieve different TE values. The length of each AFP pulse (Tp) was 0.0036 s. The AFP pulses were hyperbolic secant (HS) pulses using ATp/π = 20, where A is the amplitude of the frequency sweep in rad/s (20, 21). The RF energy deposited by CP-LASER varied with the number of AFP pulses in the CP train, and was kept below the FDA limit.
In the PRESS sequence, a five-lobe π/2 sinc pulse and an optimized π pulse (22) were used for excitation and refocusing, respectively, with Tp = 2 ms. To improve localization, PRESS was preceded by outer-volume suppression based on a B1-insensitive train to obliterate signal (BISTRO) in three dimensions (23).
Before the excitation pulse in all spectroscopy sequences, water signal was suppressed by eight variable-power RF pulses with optimized relaxation delays (VAPOR) (24). The spectral width was 6 kHz, while NEX = 8 for metabolites and NEX = 2 for water. The voxel size for localized spectroscopy was 12 cm3 (2 × 3 × 2 cm3). Transverse relaxation times were determined by obtaining spectra at different echo times (TEs). Five TEs were used, ranging from 50 to 170 ms at 4T, and from 30 to 130 ms at 7T with the PRESS sequence, and varying from 37.8 to 138.6 ms at both 4T and 7T with the CP-LASER sequence. Dummy scans were used in all experiments to achieve a steady state prior to data collection. Potential contributions from T1 weighting were investigated by performing experiments with different TR values (3 and 4.5 s) with both the PRESS and CP-LASER sequences.
The T values measured with CP-LASER and PRESS sequences were calculated from the linear fit of the natural logarithm of signal intensities measured at different TE values using a linear regression algorithm. Due to the short TE interval, a mono-exponential decay was assumed for all investigated compounds.
With a CP sequence, the multiple refocusing pulses reduce the dynamic dephasing effect as the interpulse interval τcp decreases. Carr and Purcell (5) first examined the effect of varying the number (n) of refocusing pulses on the MR signal intensity (SI) considering a dynamic dephasing regime induced by diffusion in local susceptibility gradients. Subsequently, other authors have contributed to the development of the theory (6, 25, 26). If the diffusion dominates in the dynamic dephasing regime, T can be simplified from Eq.  to:
where D is the apparent diffusion coefficient, γ is the gyromagnetic ratio of the nucleus, and G is the magnetic field gradient imposed either externally by the pulsed field gradients or internally by the heterogeneous susceptibility variations in the sample. In the presence of diffusive motion, the spin dephasing caused by local susceptibility gradients results in signal loss which cannot be fully refocused by a conventional (Hahn) SE sequence using long TE. Equation  predicts 1/T to be a square function of the π pulse spacing (i.e., increasing quadratically with τcp).
Changing τcp, but holding nτcp constant, one can compare the variations of the exponential decay of NMR signal at the same TE as described by (27):
These signal variations are sensitive to the diffusion-related term in Eq.  and other parameters, such as number of refocusing pulses n. The diffusion influence can become significant as the external static magnetic field increases due to increased local susceptibility gradients, G. Thus, it is important to investigate the field dependence of the described NMR signal loss at 7T compared to 4T in the human brain, using interleaved CP and Hahn SE sequences at the same TE.
A comparison of measurements made with CP-LASER using short τcp and LASER using long τcp, at different fields and at the same TE, can be used to calculate the relative dependence of the local susceptibility gradient G on magnetic field strength according to:
where SI(CP-LASER) and SI(LASER) are the NMR SIs detected by the CP-LASER and LASER sequences, respectively. Equation  assumes no effect from diffusion/exchange when using the short τcp in CP-LASER, and full effect when using long τcp in LASER.
Allerhand et al. (25, 26) applied the formalism of Luz and Meiboom (28) for the treatment of the chemical exchange effects on T. The relaxation rate for a multi-site system with the Pi fractional population of nuclei in state i is given by:
where δω is the change in the resonance frequency due to exchange between i and (i + 1) sites, and τex is the correlation time for exchange. Obviously, 1/T increases with increasing τcp and reaches a plateau at long τcp (29). The mechanisms that affect T are similar for both diffusion (Eq. ) and exchange (Eq. ) contributions, although the equations appear to be different. In the first case, the spins dephase because translational diffusive motion changes the Larmor frequency in the presence of local susceptibility gradients. In the second case, the spins dephase because an exchange process causes the Larmor frequency to jump from one value to another; this contribution exists only when a jump places the spin in an environment producing a substantially different Larmor frequency. The functional dependence on TE, τcp, and B0 is distinctive for the two mechanisms. Equation  predicts that when diffusion is operative in the system, the apparent relaxation rate is quadratic in TE. The T values of non-exchanging protons, such as the methyl protons in NAA (2.01 ppm) and Cr (3.03 ppm), are expected to be described by Eq. , whereas water will have contribution from both diffusion and exchange.
RESULTS AND DISCUSSION
Figure 2 shows examples of 1H spectra of cerebral water (Fig. 2a) and metabolites (Fig. 2b) acquired in an interleaved manner using CP-LASER (τcp = 6.3 ms, n = 22) and LASER (τcp = 23.1 ms, n = 6) sequences at 7T. In these experiments, the same TE (138.6 ms) was used for the CP-LASER and LASER sequences. The CP-LASER sequence (n = 22) achieved a significant signal gain as compared to the LASER sequence (n = 6) at the same TE. This is an independent experimental demonstration of the ability of the CP train to increase SI due to the lengthening of T values. Equation  was used to calculate the relative strength of the local susceptibility gradient (G) between 4T and 7T. An approximate linear dependence between G and B0 was observed for NAA and Cr, as described by:
This result is consistent with the expectation that the local susceptibility gradient increases linearly with magnetic field strength. For water, however, (G2)7T/(G2)4T was 1.6, which is significantly less than2 ≈ 3. This low ratio may be caused by the large value of D and fast exchange of water, leading to a reduction in the efficiency of CP-LASER to suppress diffusion and exchange contributions. Contributions from bulk motion of water in blood and CSF could also reduce the refocusing capability and thus lower the (G2)7T/(G2)4T ratio for water compared to NAA and Cr. In addition, possible underestimation of T values due to imperfect π pulses cannot be ruled out.
The average T values (mean ± SD) from measurements on eight different individuals at 7T and on seven individuals at 4T are presented in Table 1. Because TR was not varied with TE, the longitudinal recovery period varied with TE and was slightly different in the CP-LASER and PRESS measurements. However, with the relatively short TE and long TR values used, T1 weighting should have had only a minor effect on the estimates of T2 values. T values of NAA, Cr, and water measured in four studies using TR = 3 and 4.5 s were compared by applying a two-tailed t-test. The difference between measurements made with the different TR values was insignificant (P ≥ 0.24), suggesting that the influence of partial T1 saturation on T measurements was negligible. Thus, the T values presented in Table 1 were found by averaging relaxation times detected with TR = 3 s and 4.5 s.
Table 1. T Time Constants (in ms) of Water and Metabolites Measured With CP-LASER and PRESS Pulse Sequences at 7T and 4T
For all T fits, R2 > 0.96 was obtained. Errors represent standard deviations.
Significant difference (P < 0.0005, two-tailed) in T between CP-LASER and PRESS.
Significant difference (P < 0.015, two-tailed) in T between CP-LASER and PRESS.
Inspection of Table 1 indicates: 1) a large reduction in T values measured by PRESS at 7T in comparison with 4T for all investigated compounds; 2) a significant increase in T values determined by CP-LASER in comparison with that determined by PRESS at both field strengths; and 3) a relatively small decrease of T values measured by CP-LASER at 7T in comparison with 4T.
The strategy of the present study was to approach a Hahn SE using the PRESS technique, which allowed the largest possible interpulse separation for a given TE value. In a separate study (14), we investigated the field dependence of water T in gray matter, white matter, and CSF in the human occipital lobe using an MRI version of the sequence in Fig. 1. In that study, the comparison between T values measured with CP-LASER (τcp ≈ 6 or 7 ms) and LASER (τcp ≥ 10 ms) was presented. The water T values in gray and white matter decreased with field strength, in agreement with the present single-voxel MRS results. In addition, a significant increase in the T values measured with CP-LASER (τcp = 6 or 7 ms) compared to LASER (τcp ≥ 10 ms) was found. At 4T, these ratios were: T(CP-LASER)/T(LASER) ≈ 1.6 for gray matter, and T(CP-LASER)/T(LASER)≈1.4 for white matter. At 7T, these ratios were: T(CP-LASER)/T(LASER) ≈1.4 for both the gray and white matter. The minor differences between the water T(CP-LASER)/T(LASER) ratios of the previous study and the water T(CP-LASER)/T(PRESS) ratios of the present study can be attributed to differences in pulse sequences and to partial volume effects in the present single-voxel MRS experiments. Specifically, the present single-voxel measurements did not permit differentiation between water in brain tissue and CSF (i.e., CSF T value has no dependence on τcp) (14). On the other hand, in the case of intracellular cerebral metabolites, the presence of CSF in the voxel was not a confounding factor. As shown in Table 2, the T(CP-LASER)/T(PRESS) ratios for metabolites were much larger than that of water at both 4T and 7T. The large value of this ratio may also reflect the approximately threefold lower D of NAA and Cr as compared to water (30), which allowed better suppression of diffusion contributions to the T values of cerebral metabolites by CP-LASER.
Table 2. T (CP-LASER)/T (PRESS) Ratios for NAA, Cr and H2O at 4T and 7T
In a comparison of T values measured with CP-LASER vs. PRESS, a larger difference was consistently observed at the higher field (Table 2). The lower T values measured at 7T as compared to 4T can be attributed to the two independent processes described by Eq. . Specifically, decreased T could reflect a reduced intrinsic relaxation time, T2, at the higher field. However, a substantial contribution arises from the G2 term in Eq. , which increases with field strength due to increasing microscopic magnetic susceptibility variations.
From Table 1, it can be seen that the field dependence of T values was less when measured with CP-LASER vs. PRESS. This observation represents additional evidence for a substantial contribution from dynamic dephasing. With the choice of parameters used, the effect of dynamic dephasing on the T values of NAA and Cr in the human brain was partially or completely suppressed when using CP-LASER.
It should be noted that the longer T values measured with CP-LASER could have reflected the fact that the magnetization transiently spends more time along the longitudinal axis as the number of pulses in the CP train increases. In a separate study (14), the maximum contribution of this effect was calculated by simulation of the Bloch equations and was found to produce a maximum T increase of <7% only.
The spectra detected with CP-LASER and LASER sequences at TE = 138.6 ms (Fig. 2b) display other features worth noting. In the spectral region between NAA (2.01 ppm) and Cr (3.03 ppm), other resonances arise, such as glutamate at 2.35 ppm and glutamine at 2.45 ppm. Additional signal contributions from GABA (2.28 ppm) and aspartate (2.8 ppm) also occur in this region. These resonances are homonuclear J-coupled, and therefore their spectral phases depended on the choice of TE and τcp (26). As can be seen in Fig. 2b, at TE = 138.6 ms these resonances were most intense in the LASER spectra (τcp = 23.1 ms, n = 6) and had different spectral phases as compared with those in the CP-LASER spectra (τcp = 6.3 ms, n = 22). Although different contributions from overlapping J-modulated resonances could have influenced the calculated T values in this study, these effects are not expected to be large enough to explain the T differences observed.
The apparent transverse relaxation times T of protons in NAA, Cr, and H2O in human visual cortex were measured and compared at 4T and 7T using different SE pulse sequences. With a Hahn-type SE (PRESS) the results indicated a significant reduction of the T values with increasing field strength. In the case of metabolites (NAA and Cr), the T values measured with CP-type SE (CP-LASER) were significantly longer than those measured with PRESS, and were approaching the intrinsic T2 values of these compounds. These experiments showed that the CP-type sequence can at least partially compensate for the shortening of T values of NAA, Cr, and H2O, and thus minimize signal losses at high fields. These results suggest that the field-dependent reduction in T values measured with the Hahn-type SE sequences is substantially caused by dynamic dephasing effects.