Sodium magnetic resonance imaging (23Na MRI) of the human brain and in particular its application to patients with multiple sclerosis (MS) is interesting as it offers the possibility of noninvasively examining sodium in the cellular metabolism. Recently, many 23Na MRI studies were conducted to gain new insights into disease mechanisms and to better understand the role of sodium in the pathological processes in MS.1

Except of only a small number of studies also exploring different contrasts,2–5 the aim of nearly all of the studies was to determine the tissue sodium concentration (TSC) by applying pulse sequences expected to provide a density-weighted image contrast.2,6–14 As intracellular and extracellular sodium cannot be differentiated in human studies, the TSC represents a volume fraction-weighted average of the sodium concentrations of both spaces.15 An increased TSC, as found in MS lesions as well as in normal-appearing white matter (NAWM) and in normal-appearing gray matter (NAGM) for all subtypes of MS (relapsing-remitting MS [RRMS],6,7 secondary progressive MS [SPMS],8,9,14 primary progressive MS [PPMS]8,9), can therefore be related to intra-axonal sodium accumulation as well as extension of the extra-axonal space. Recent studies suggest that, in addition to the commonly assumed intracellular and extracellular space, sodium within the tight sequential wraps of myelin water should be regarded as a distinct third compartment for 23Na MRI.2,16 As a result, altered relaxation characteristics resulting from demyelination could also contribute to changes in measured 23Na signal intensity, which could not be differentiated from alterations of sodium concentration.

In contrast to protons (1H), 23Na nuclei possess a spin of 3/2, and their relaxation dynamic is dominated by the interactions between the nuclear quadrupole moment and surrounding electric field gradients (EFGs).17,18 In biological tissues, these quadrupolar interactions ωQ(t) are time-dependent due to the motion of the 23Na nuclei as well as the motion of their molecular environment. In isotropic environments, the motion is equally distributed in space and sufficiently fast, leading to a time-averaged, also called residual, quadrupolar interaction of ωQ¯=0.19 In general, this results in a biexponential transverse relaxation behavior, and so far, mostly ωQ¯=0 has been assumed for TSC quantification in the human brain (considering intracellular and extracellular space). In anisotropic environments, however, longer correlation times of the environmental EFGs may result in a nonzero residual quadrupolar interaction ωQ¯≠0, which leads to residual quadrupole splitting depending on the orientation in the main magnetic field19:

ωQ¯=eQeq4ℏ3cos2θ−1,

where eQ is the electrical quadrupole moment of the nucleus, and θ describes the polar angle between the orientation of the principal EFG value eq and the main magnetic field. Different studies have shown that at least some 23Na nuclei in the human brain exhibit nonzero residual quadrupolar interactions ωQ¯≠0,16,20 especially in highly ordered white matter (WM) regions with fiber tracts running parallel to the main magnetic field.16 As these nuclei show a much faster relaxation behavior, a third compartment with 23Na nuclei in an ordered, anisotropic environment, that is, thin sequential wraps of myelin water,21 should be considered when determining TSC in the human brain. Residual quadrupolar interaction offers the possibility of exploring tissue structure and order and therefore may be an important target to examine pathological conditions in WM.16

To accurately quantify TSC in brain tissue, which means separating ωQ¯ effects from alterations in sodium concentration, the influence of the very rapid signal loss due to residual quadrupole interaction should be minimized. This, however, is actually not the case for the standard 23Na pulse sequences with 90-degree excitation flip angle (FA) and corresponding relatively long radiofrequency (RF) pulse lengths (TPs) of approximately 0.4 milliseconds and echo times (TE) of approximately 0.25 milliseconds (defined as time between the middle of RF pulse and the acquisition of k-space center) used in most of the 23Na MRI studies, which rather provide a ωQ¯-weighted than a spin density-weighted contrast. As a result, in addition to the already mentioned intra-axonal sodium accumulation and extension of the extra-axonal space, reduced residual quadrupolar interaction due to demyelination is another potential source for the increases in measured TSC in MS patients.2,14,16 A recent study using an optimized pulse sequence that minimizes signal loss from residual quadrupole splitting for the first time did not find any significant elevation of TSC in NAWM of MS patients.2 However, no direct comparison to the commonly used 90-degrees excitation pulse sequence was performed.

The aim of this work is to investigate the influence of residual quadrupolar interaction on quantitative 23Na MRI of the human brain and to further analyze the measured increase of TSC in brain tissue of MS patients in various 23Na MRI studies. Healthy controls (HCs) as well as MS patients of all 3 subtypes (RRMS, SPMS, and PPMS) were examined using 2 different pulse sequences: a commonly used standard 23Na pulse sequence with 90-degree excitation FA as well as a 23Na pulse sequence with lower excitation FA and shorter TP for minimizing signal loss resulting from residual quadrupolar interactions and very short transverse relaxation. As suggested by Stobbe and Beaulieu,16 the term apparent tissue sodium concentration (aTSC) was used for the determined concentration values to account for the not exactly known signal loss resultant from relaxation and pulse sequence characteristics. In both cases, aTSC values were determined using a dedicated measurement setup and postprocessing workflow to accurately analyze the acquired 23Na images,14 including RF coil sensitivity correction, partial volume correction (PVC), and relaxation correction. Simulations of the dynamics of spin-3/2 nuclei were performed to aid in the understanding of the differences between the 2 measurements.

MATERIALS AND METHODS

All MRI measurements were performed on a 7 T whole-body MR system (MAGNETOM Terra; Siemens Healthcare, Erlangen, Germany).

All examined subjects provided informed consent before the MRI examination, and the in vivo MRI measurements were approved by the local ethical review board.

23Na MRI Measurements and aTSC Determination

23Na MRI was done using a dual-tuned 23Na/1H head coil (RAPID Biomedical, Rimpar, Germany), which consists of a 23Na/1H quadrature transceiver birdcage coil and an additionally integrated 32-channel receive phased-array head coil for 23Na MRI. Before every 23Na MRI measurement, a B0-shim based on 1H MRI using the standard brain B0-shim provided by the vendor and a global 23Na FA calibration were performed. All 23Na MRI raw data sets were acquired using a density-adapted 3-dimensional radial (DA-3D-RAD) readout scheme22 and reconstructed offline using a custom-written MATLAB R2019b script (MATLAB; The MathWorks, Natick, MA). A Hamming filter was used to increase SNR and to reduce Gibbs' ringing artifacts.23,24 A density compensation was applied before performing a nonuniform fast Fourier transform25 with a 2-fold grid oversampling. The k-space data were zero-filled to the 0.65-mm isotropic voxel size of the anatomical 1H MRI data sets to improve the PVC by increasing the co-registration and segmentation accuracy.26

Two different 23Na pulse sequences were used for determination of NAWM, NAGM, and MS lesion aTSC values: a commonly used standard 23Na pulse sequence (DA-3D-RADStd), as well as a 23Na pulse sequence with lower excitation FA and shorter TP (DA-3D-RADSP) for minimizing signal loss resulting from residual quadrupolar interactions and very short transverse relaxation. An overview of the specific sequence parameters can be found in Table 1. In addition, for both sequences, noise-only scans (TR = 30 milliseconds, nominal FA = 0 degrees, TAQ = 1 minute, all other parameters identical to the corresponding image acquisition) were used to calculate the noise correlation matrix for adaptive combined reconstruction27 (blocksize = 10, interpolation factor = 2) of the multichannel data.

TABLE 1 - Overview of the Sequence Parameters of the 2 23Na Pulse Sequences Used for Determination of aTSC Values Sequence DA-3D-RADStd DA-3D-RADSP Repetition time 120 ms 85 ms RF pulse length 0.6 ms 0.15 ms Nominal flip angle 87–90 degrees (restricted by patient-specific SAR limitations) 33–35 degrees (restricted by maximal allowed RF power) Echo time 0.35 ms 0.13 ms Readout time 10 ms 10 ms Acquisition time 14 min 0 s 14 min 10 s Nominal spatial resolution 2.5 × 2.5 × 2.5 mm3 2.5 × 2.5 × 2.5 mm3

aTSC, apparent tissue sodium concentrations; DA-3D-RAD, density-adapted 3-dimensional radial readout scheme; RF, radiofrequency; SAR, specific absorption rate.

After image reconstruction, the images of both sequences were analyzed using the postprocessing pipeline adopted from Wilferth et al,14 which will be shortly described in the following: a universal sensitivity map calculated by averaging 8 individually calculated receive profiles was used to correct the coil sensitivity profile of the 23Na 32-channel receive phased-array head coil.28 Furthermore, relaxation-caused differences between the different brain compartments were corrected. Generally, a homogeneous FA over the whole examined brain region was assumed and validated by the acquisition of FA maps of 1 healthy volunteer (see Supplemental Content 1, https://links.lww.com/RLI/A805). In NAWM and NAGM, the relaxation behavior was modeled by a biexponential transverse relaxation with the relaxation times T2f* = 4.2 milliseconds and T2s* = 34.4 milliseconds29 and a monoexponential longitudinal relaxation with T1 = 37.1 milliseconds.30 In cerebrospinal fluid (CSF), for both transverse and longitudinal relaxation, a monoexponential behavior was assumed (T2f* = T2s* = T2* = 54.4 milliseconds,29 T1 = 64 milliseconds30). The exact relaxation parameters of MS lesions are not known and depend at least partially on the specific lesion. However, as the pathology of MS lesions is characterized by WM degeneration processes with expected loss of structure and enlargement of the extra-axonal space, the MS lesion relaxation parameters can be assumed to lie between the relaxation times of healthy WM as lower bound (model 1: T2f* = 4.2 milliseconds, T2s* = 34.4 milliseconds, T1 = 37.1 milliseconds) and the relaxation times of CSF as upper bound (model 2: T2* = 54.4 milliseconds, T1 = 64 milliseconds).14 Partial volume effects were corrected using the geometric transfer matrix method26 based on binary masks assuming the same relaxation behavior as described previously for simulation of the point-spread function. In contrast to MS lesions, the resulting differences in the aTSC values determined for NAWM and NAGM between the 2 lesion models are negligible as they only are second-order effects via PVC.14; Nevertheless, in this work, the results for both models will be presented. As a result of the PVC, region-wise partial volume corrected average signal intensities for every tissue compartment were obtained. These average signal intensities were then normalized to the CSF sodium concentration of 147.6 mmol/L,14 which served as single upper reference (see Supplemental Content 2, https://links.lww.com/RLI/A805) in order to get aTSC values for NAWM and NAGM, as well as for MS lesions. In the following, the aTSC values determined using the DA-3D-RADStd sequence are labeled aTSCStd, and the aTSC values determined using the DA-3D-RADSP sequence are labeled aTSCSP.

The aTSC values were determined for 21 HCs (10 male, 11 female; age, 38 ± 14 years; range, 23–65 years), 25 RRMS patients (11 male, 14 female; age, 37 ± 8 years; range, 22–57 years), 14 SPMS patients (6 male, 8 female; age, 50 ± 7 years; range, 36–59 years), and 11 PPMS patients (6 male, 5 female; age, 50 ± 14 years; range, 30–83 years). All MS patients had a confirmed MS diagnosis respecting the revised McDonald criteria.31

Anatomical 1H MRI and Segmentation

For all examined subjects, anatomical information was obtained by acquiring high-resolution 1H 3D T1-weighted magnetization-prepared rapid acquisition gradient echo (MPRAGE) (TR = 2500 milliseconds, TE = 2.92 milliseconds, TI = 1100 milliseconds, nominal spatial resolution (Δx3) = 0.65 × 0.65 × 0.65 mm3, nominal FA = 7 degrees, TAQ = 7 minutes 59 seconds) and fluid-attenuated inversion recovery (FLAIR) (TR = 9000 milliseconds, TE = 269 milliseconds, TI = 2600 milliseconds, nominal spatial resolution Δx3 = 0.8 × 0.8 × 0.8 mm3, TAQ = 7 minutes 14 seconds) data sets using a 1Tx/32Rx 1H head coil (Nova Medical, Wilmington, MA). The anatomical 1H MRI scans were used for segmentation and creation of binary tissue masks for CSF, NAWM, NAGM, and MS lesions, which were used in the postprocessing and analysis of the 23Na MRI data. The SPM12 software (Wellcome Trust Centre for Neuroimaging, London, United Kingdom) was used to automatedly obtain tissue probability maps by segmenting the MPRAGE data set. The binary masks were generated from these tissue probability maps by comparing the tissue contributions for each voxel and choosing the maximum value as corresponding tissue. The lesion mask was created using the FLAIR image and the AI-based segmentation software mdbrain (Mediaire GmbH, Berlin, Germany).32 All voxels characterized as lesions by mdbrain were excluded from the NAWM, NAGM, and CSF masks. Lesion masks were created not only for MS patients but also for HC to account for lesion-like FLAIR hyperintensities arising from aging or other processes. For all analyses, the 23Na MRI data set was co-registered to the MPRAGE data set to match the masks.33

Simulation of 23Na Spin Dynamics

The spin dynamic simulations of the spin-3/2 23Na nuclei were performed with a custom-written MATLAB R2019b software tool,16,34,35 which is based on the differential equations describing the evolution of the density operator expressed by irreducible spherical tensor operators.17,18 The simulated MR pulse sequence is separated into arbitrary time intervals, and for every time step, the matrix equation determining the spin dynamics of the systems is solved by matrix diagonalization.18 The simulation therefore enables the calculation of the theoretical magnetization values for both sequences DA-3D-RADStd and DA-3D-RADSP at any time point. Beside the sequence characteristics, the spectral densities J0, J1, and J2 and the distribution of the residual quadrupolar interaction ωQ¯ served as input parameters to determine the relaxation behavior. The spectral densities were chosen to fit the relaxation times used for correction of relaxation bias and PVE in the postprocessing of the measurement data. In general, spin-3/2 theory provides biexponential longitudinal relaxation depending on J1 and J2. However, as it is common in the literature to assume monoexponential T1 and this was also done in this work to correct for relaxation bias of NAWM and NAGM, a monoexponential estimate resulting from Taylor expansion as described by Kratzer et al36 was used to calculate the corresponding spectral densities. The spectral densities used in the simulations were the following: J0 = J1 = J2 = 7.8 Hz for CSF and J0 = 221.4 Hz, J1 = 16.7 Hz, and J2 = 12.4 Hz for NAWM and NAGM. For NAWM, a hypothetical model similar to the one suggested by Stobbe and Beaulieu16 was assumed, which consists of 2 different pools of sodium nuclei: one pool of 23Na nuclei not experiencing residual quadrupolar splitting ωQ¯=0 and a second pool with equal relaxation times but a Gaussian distribution of ωQ¯ with zero mean and a standard deviation of 625 Hz. The simulated transverse magnetization values at the beginning of the acquisition were corrected for relaxation bias in the same way as the measurement results:

crelaxation,T2=10.6exp−TET2f+0.4exp−TET2s

crelaxation,T1=1−cosFAexp−TRT11−exp−TRT1

crelaxation=crelaxation,T2·crelaxation,T1

Finally, the simulated magnetization values were normalized to the value obtained for the CSF model, and the ratio between the 2 sequences was calculated to compare it to the measurement results.

Statistical Analysis

All statistical analyses were done with MATLAB R2019b, and results were considered statistically significant for P values <0.05.

The differences between the mean concentrations aTSCStd and aTSCSP obtained by the different sequences were tested for significance using the paired samples Wilcoxon signed rank test for all cohorts and brain compartments.

For all examined brain compartments (NAWM, NAGM, MS lesions) and both sequences (aTSCStd, aTSCSP), the differences between the determined mean aTSC values of the 4 cohorts (HC, patients with RRMS, patients with SPMS, patients with PPMS) were analyzed using a 1-way analysis of variance with post hoc Bonferroni correction for multiple comparisons. The ratios between the 2 sequences aTSCSP/aTSCStd were also analyzed using a 1-way analysis of variance with post hoc Bonferroni correction for multiple comparisons for all 3 brain compartments. Only statistically significant P values are presented in the text, and the given values have already been corrected for multiple comparisons.

RESULTS aTSC Values Determined by 23Na MRI

Exemplary 23Na MR images acquired with the 2 different 23Na pulse sequences for aTSC determination as well as the ratio between the images are shown in Figure 1 for 1 healthy volunteer. Both images were normalized to the corrected signal intensity of CSF obtained in the postprocessing for aTSC quantification. The ratio DA-3D-RADSP/DA-3D-RADStd was calculated by dividing both images after Gaussian filtering with a standard deviation of 5 voxel to suppress noise. In WM regions around the ventricles with an expected high microstructure order due to fiber tracts with myelin wraps, a clear increase in signal intensity is apparent in the DA-3D-RADSP image compared with the DA-3D-RADStd image. This is particularly the case in regions with a high density of fiber tracts running superior-inferior and therefore parallel to the main magnetic field. Regions with a lower expected fiber tract density and different orientation in contrast present a lower ratio DA-3D-RADSP/DA-3D-RADStd, which even leads to heterogeneity along tracts, for example, the corticospinal tract or the corpus callosum. In parts of the brain other than the centrum semiovale and in the ventricles, that is, mainly gray matter (GM) and CSF regions, both sequences result in similar signal intensities.

FIGURE 1:

Exemplary images of 1 healthy control acquired with the DA-3D-RADStd (left) and DA-3D-RADSP (middle) sequence as well as the ratio DA-3D-RADSP/DA-3D-RADStd (right), which was obtained by dividing both images after Gaussian filtering with a standard deviation of 5 voxels in order to suppress noise. The red arrows mark dark regions with lower signal intensity in the DA-3D-RADStd image, which display higher signal intensity in the DA-3D-RADSP image.

The means with corresponding standard deviation of the determined aTSCStd and aTSCSP for the different brain compartments as well as the corresponding ratios aTSCSP/aTSCStd can be found in Table 2 for all examined subject cohorts. Furthermore, the results of the aTSC measurements are depicted in boxplots in Figure 2.

TABLE 2 - Overview of the Means With Corresponding Standard Deviation for the aTSCStd and aTSCSP of the Examined Brain Compartments for HC as Well as RRMS, SPMS, and PPMS Patients Brain Compartment Subject Group aTSCStd, mmol/L aTSCSP, mmol/L Ratio aTSCSP/aTSCStd Model 1 Model 2 Model 1 Model 2 Model 1 Model 2 NAWM HC 43.7 ± 3.6 43.7 ± 3.6 53.0 ± 3.9 53.0 ± 3.9 1.21 ± 0.03 1.21 ± 0.03 RRMS 44.2 ± 4.1 44.4 ± 4.1 53.0 ± 4.7 53.2 ± 4.7 1.20 ± 0.03 1.20 ± 0.03 SPMS 44.5 ± 4.9 44.8 ± 5.0 53.3 ± 5.2 53.7 ± 5.3 1.20 ± 0.03 1.20 ± 0.03 PPMS 48.7 ± 5.1 48.9 ± 5.2 57.3 ± 6.0 57.5 ± 6.1 1.18 ± 0.04 1.18 ± 0.04 NAGM HC 64.8 ± 5.6 64.8 ± 5.6 66.7 ± 4.8 66.7 ± 4.8 1.03 ± 0.03 1.03 ± 0.03 RRMS 61.3 ± 6.5 61.2 ± 6.5 63.4 ± 6.4 63.4 ± 6.4 1.04 ± 0.03 1.04 ± 0.03 SPMS 60.0 ± 6.9 59.9 ± 6.8 62.3 ± 5.9 62.3 ± 5.9 1.04 ± 0.04 1.04 ± 0.04 PPMS 66.9 ± 5.4 66.9 ± 5.4 68.1 ± 6.7 68.0 ± 6.7 1.02 ± 0.03 1.02 ± 0.03 MS lesions RRMS 101.6 ± 15.6 82.5 ± 12.8 108.1 ± 15.9 90.2 ± 13.4 1.07 ± 0.07 1.10 ± 0.07 SPMS 96.7 ± 19.6 79.1 ± 17.4 104.0 ± 17.3 87.3 ± 15.9 1.09 ± 0.09 1.12 ± 0.10 PPMS 103.6 ± 29.8 84.6 ± 24.3 106.2 ± 25.4 89.1 ± 22.2 1.05 ± 0.16 1.08 ± 0.16

aTSC, apparent tissue sodium concentrations; HC, healthy control; RRMS, relapsing-remitting multiple sclerosis; SPMS, secondary progressive multiple sclerosis; PPMS, primary progressive multiple sclerosis; NAWM, normal-appearing white matter; NAGM, normal-appearing gray matter; MS, multiple sclerosis.

FIGURE 2:

Boxplots of the aTSCStd and aTSCSP values of the different examined brain compartments (NAWM, normal-appearing white matter; NAGM, normal-appearing gray matter, MS lesions) for healthy controls (HCs) and MS patients of all subtypes (RRMS, SPMS, PPMS) and for both considered lesion models (model 1: assuming relaxation parameters of healthy WM for MS lesions; model 2: assuming relaxation parameters of CSF for MS lesions).

In NAWM, for all subject cohorts, the aTSCSP values were significantly higher than the aTSCStd values (P < 0.001). In NAGM, this was also the case for HC, RRMS, and SPMS patients (P < 0.002); however, no significant difference was found for PPMS patients. Similarly, in MS lesions, aTSCSP values were significantly higher than the aTSCStd values for RRMS and SPMS patients (P < 0.001), but not for PPMS patients.

In NAWM, aTSCStd values were significantly higher in PPMS patients compared with HC (P = 0.01) as well as RRMS patients (P = 0.03). In contrast, no significant differences in NAWM between the subject cohorts were found for aTSCSP. In NAGM, aTSCStd values were significantly higher in PPMS patients compared with SPMS patients (P = 0.04). Again, no significant differences between the subject cohorts were found for aTSCSP. In MS lesions, neither for aTSCStd nor aTSCSP significant differences were detected.

For both lesion models and for all MS subtypes, aTSCStd (86%/130% for RRMS, 77%/118% for SPMS, and 73%/113% for PPMS, respectively, for lesion model 1/2) as well as aTSCSP (70%/104% for RRMS, 63%/95% for SPMS, and 55%/85% for PPMS, respectively, for lesion model 1/2) were higher in MS lesions than in NAWM.

In addition, the ratio aTSCSP/aTSCStd was analyzed for all subject cohorts and examined brain compartments. The means with corresponding standard deviation can be found in Table 2, and the results are also depicted in boxplots in Figure 3. For all subject cohorts, HC as well as all MS subtypes, the ratio aTSCSP/aTSCStd was significantly higher in NAWM than in NAGM (P < 0.002). Furthermore, in RRMS and SPMS patients, the ratio in NAWM was also significantly higher than in MS lesions (P < 0.004); in PPMS, this was only the case for MS lesion model 1 (P = 0.02/0.09 for lesion model 1/2). The ratio in MS lesions was significantly higher than in NAGM for RRMS patients independent of the lesion model (P = 0.04/P < 0.001 for lesion model 1/2) and for SPMS patients for MS lesion model 2 (P = 0.17/P = 0.008 for lesion model 1/2). No significant differences were found between the ratios of NAGM and MS lesions in PPMS patients.

FIGURE 3:

Boxplots of the ratio aTSCSP/aTSCStd of the different examined brain compartments (NAWM, normal-appearing white matter; NAGM, normal-appearing gray matter, MS lesions) for healthy controls (HCs) and MS patients of all subtypes (RRMS, SPMS, PPMS). As for NAWM and NAGM, the differences between the 2 MS lesion models (M1: relaxation parameters of healthy WM were assumed for the relaxation behavior of MS lesions; M2: relaxation parameters of CSF were assumed for the relaxation behavior of MS lesions) were negligible, only for MS lesions the results of both models are presented separately.

For NAWM, the ratio for PPMS patients was significantly lower than for HC (P = 0.006). For NAGM and MS lesions, no significant differences were found between the subject cohorts.

Simulation Results on 23Na Spin Dynamics

First, only the excitation pulse and the following free relaxation were simulated assuming no transverse magnetization Mxy = 0 and fully relaxed longitudinal magnetization Mz = M0 before the RF pulse. No steady-state effects resulting from incomplete T1 relaxation were considered. This allowed to specifically analyze the influence of the different pulse parameters. The simulation results for the evolution of the transverse magnetization during the excitation pulses of the 2 sequences are shown in Figure 4. The relative transverse magnetization values right after the excitation pulse are furthermore given in Table 3.

FIGURE 4:

Simulated evolution of 23Na transverse magnetization during the standard excitation pulse with pulse length TP = 0.6 milliseconds and flip angle (FA) = 90 degrees (A) and the short excitation pulse optimized for minimal residual quadrupolar signal loss with TP = 0.15 milliseconds and FA = 35 degrees (B). The dashed vertical line marks the end of the excitation pulse. The horizontal dotted line marks the maximal possible magnetization sin(FA).

TABLE 3 - Overview of the Simulated Relative Transverse Magnetization Values at the End of the Excitation Pulse Excitation Pulse Standard (TP = 0.6 ms, FA = 90 degrees) Short (TP = 0.15 ms, FA = 35 degrees) CSF 99.7 (99.7) 57.3 (99.9) GM, WM (

ωQ¯=0

) 95.7 (95.7) 56.7 (98.9) WM (

ωQ¯≠0

) 63.6 (63.6) 54.8 (95.5) WM (50%

ωQ¯=0

, 50%

ωQ¯≠0

) 79.7 (79.7) 55.7 (97.2)

The parenthesized values are the percentage of the maximal possible magnetization sin(FA).

TP, pulse length; FA, flip angle; CSF, cerebrospinal fluid; GM, gray matter; WM, white matter.

For the CSF model, relaxation effects during the pulse are negligible, and the maximal achievable transverse magnetization (sin[FA] M0) is reached for both excitation pulses. For the model of GM and WM without residual quadrupolar interaction, there already are small differences between the pulses; approximately 4% of the magnetization is lost during the standard pulse, and approximately 1% of the magnetization is lost during the short pulse. For the model of WM with a residual quadrupolar interaction following a Gaussian distribution with zero mean and standard deviation of 625 Hz, the relaxation effects during the standard pulse are very strong, and only approximately 64% of the possible transverse magnetization are accessible at the end of the pulse. In contrast, more than 95% are reached for the short pulse. After the pulse, the CSF model shows a monoexponential, and the model for GM/WM with ωQ¯=0 shows a biexponential magnetization decay, as expected. The model of WM with ωQ¯≠0 presents a very rapid signal de