Magnetic Resonance in Medicine 73:223–232 (2015)

Comparison of Myelin Water Fraction from Multiecho T2 Decay Curve and Steady-State Methods Jing Zhang,1* Shannon H. Kolind,2 Cornelia Laule,1,3 and Alex L. MacKay1,4 Purpose: Myelin water fraction is conventionally measured from the T2 decay curve. Recently, a steady-state approach entitled multicomponent-driven equilibrium single pulse observation of T1/T2 (mcDESPOT) was employed for myelin water fraction mapping. However, no direct comparison between the established multiecho T2 relaxation method and mcDESPOT has been performed. Methods: Gradient and spin echo (GRASE) acquired T2 decay curve and mcDESPOT measurements were acquired from 10 healthy volunteers using a 3T MRI. We compared myelin water fraction, transmit radio frequency field (B1), and T2’s of intraand extracellular water obtained from both methods. Results: For all brain regions examined, myelin water fractions from mcDESPOT were significantly higher than those from multiecho GRASE. B1 maps were qualitatively similar between GRASE and mcDESPOT, but multicomponent T2 times were significantly different. To investigate the effect of exchange, mcDESPOT data were analyzed with and without exchange. When exchange was turned off, intra- and extracellular T2 times from mcDESPOT were roughly consistent with GRASE results; however, myelin water fractions derived from mcDESPOT were still significantly higher than those derived from GRASE. Conclusion: Myelin water fraction values derived from mcDESPOT cannot be considered to be equivalent to those derived from T2 decay curve approaches. Magn Reson Med C 2014 Wiley Periodicals, Inc. 73:223–232, 2015. V Key words: steady-state imaging; T2 relaxation; myelin water fraction; mcDESPOT

INTRODUCTION Myelin is an electrically insulating material that consists of multiple lipid rich bilayers wrapped around the axons of neuron. It appears mainly in white matter (WM) and to a lesser amount in gray matter (GM) of the peripheral and 1 UBC MRI Research Centre, Department of Radiology, University of British Columbia, Vancouver, BC, Canada. 2 Division of Neurology, Department of Medicine, University of British Columbia, Vancouver, BC, Canada. 3 Department of Pathology & Laboratory Medicine, University of British Columbia, Vancouver, BC, Canada. 4 Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada. Grant sponsor: Cornelia Laule is the recipient of the Women Against MS endMS Research and Training Network Transitional Career Development Award from the Multiple Sclerosis Society of Canada. Alex MacKay has received funding from the Natural Sciences and Engineering Research Council and the Multiple Sclerosis Society of Canada. Shannon H. Kolind is the recipient of a Michael Smith Foundation for Health Research Postdoctoral Fellowship. *Correspondence to: Jing Zhang, M10, Purdy Pavillion, University of British Columbia Hospital, 2221 Wesbrook Mall, Vancouver, BC V6T 1Z9 Canada. E-mail: [email protected] Received 15 October 2013; revised 29 November 2013; accepted 18 December 2013 DOI 10.1002/mrm.25125 Published online 11 February 2014 in Wiley Online Library (wileyonlinelibrary. com). C 2014 Wiley Periodicals, Inc. V

central nervous system of vertebrates. Myelin’s central function is to increase the velocity of electrical signals conducted along the axons (1). Quantitative mapping of myelin would provide significant insight into development as well as the pathophysiology of myelin-related disorders, such as multiple sclerosis (2) and leukoencephalopathies, and could become a useful clinical tool for diagnosis and management of WM diseases. Previous T2 relaxation work has shown that, in human brain in vivo, the water signal can be detected in multiple environments within a single voxel, usually including: 1) a long T2 component (2 s) due to cerebrospinal fluid; 2) an intermediate component (70–100 ms) arising from intra- and extracellular water; and 3) a short T2 component (10–20 ms) thought to be due to water trapped between the myelin bilayers (myelin water) (3,4). In some cases, an additional component between 200 and 800 ms has been observed in healthy and abnormal brain (5–7). Because all of the water in brain contributes to the MR signal (8), the sum of all T2 component amplitudes is proportional to the total water content. The ratio of the myelin water signal (short T2 component) to the total signal is defined as the myelin water fraction (MWF). Myelin water imaging was first demonstrated in human brain in vivo in 1994 (3), when a single-slice 32echo spin-echo sequence was used for acquisition of the T2 decay curve. The data were analyzed using a nonnegative least-squares (NNLS) algorithm (4). NNLS makes no a priori assumption about the number of components, and the NNLS results are usually interpreted with the assumption that exchange between water compartments is negligible on the T2 timescale. MWF obtained from T2 decay curve studies in post mortem fixed brain was found to accurately scale with optical density of luxol fast blue, which stains phospholipids in myelin, thereby providing a validation for the use of the MWF as a measure of myelination in vivo (9,10). However, Dula et al. (11) reported recently that the measured MWF in rodent spine was influenced by intercompartmental water exchange; this effect was accentuated when the myelin sheath thickness was thinner. Therefore, more research is required to assess water exchange in brain to determine what effect it may have on MWF measurements. Several groups have studied MWF in both brain and spinal cord in healthy controls as well as in disease (12–14). In vivo studies have shown that the MWF is significantly larger within WM than within GM, and that there is reduced myelin water in lesions as well as normal appearing WM for various neurological diseases, including multiple sclerosis, schizophrenia, and phenylketonuria (2,5,15). Recently, there has been substantial progress in speeding up T2 decay curve measurements (14,16). One approach is

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to use a multiple combined gradient and spin echo (GRASE) 3D technique that can produce whole cerebrum MWF images in less than 15 minutes (17,18). Multicomponent-driven equilibrium single-component observation of T1 and T2 (mcDESPOT) is a novel approach for measuring multicomponent relaxation in vivo, which has the advantage of being able to collect whole brain data on a clinical imaging timescale of about 10 minutes (19,20). This method derives two-component relaxation information from spoiled gradient echo (SPGR) and fully balanced steady-state free precession (and bSSFP) imaging data acquired over multiple flip angles. mcDESPOT yields T1 and T2 for each of the two predefined components of myelin and intra- and extracellular water pools, as well as a myelin water fraction, fM, and the rate of exchange, 1/tM, between the myelin water and the intra- and extracellular water pools. mcDESPOT has been used to study myelination in controls in both brain (20) and spinal cord (21). In normal development (22), fM has been shown to correspond to expected myelin development patterns. mcDESPOT has also demonstrated significant differences between patient groups and correlations with clinical disability in various neurological diseases (23). However, a direct comparison between mcDESPOT and the more established spin-echo based approach in the same cohort has not yet been performed. The myelin water–related metric has been referred to in many different ways; for clarity, in this study we refer to the myelin water fraction derived from multiecho T2 measurements as MWF, and that estimated from mcDESPOT as fM, as found in respective original publications (3,24). In this study, we implemented both methods on the same 3T MRI scanner and compared B1, MWF/fM, and T2 times in acquisitions from 10 healthy volunteers. Because these techniques involve very different experimental and analysis methods, the goal of this study was to determine whether the two approaches yielded results which were consistent with each other. A secondary goal was to determine if the inclusion of exchange in the mcDESPOT model could account for potential differences between MWF and fM values. METHODS All MRI experiments were performed on a 3.0T whole body MR scanner (Achieva 3.0T, Philips Medical Systems, Best, The Netherlands) using an eight-channel phased-array head coil for reception and the internal quadrature body coil for transmission. Data were collected from 10 healthy volunteers (n ¼ 7 male, n ¼ 3 female; mean age, 39 y [range, 26–64 y]). All examinations were performed with approval from the University of British Columbia Clinical Research Ethics Board, and all subjects provided signed, informed consent prior to participation. Data Acquisition Auto shim with first- and second-order shim coils was conducted for minimization of main magnetic field inhomogeneities before all experiments. After sagittal and

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axial localizer scans, the GRASE sequence was collected (pulse repetition time [TR] ¼ 1000 ms; 32 echoes with echo time [TE] ¼ 10 ms; 20 axial slices acquired at 5-mm slice thickness and reconstructed to 40 slices at 2.5-mm slice thickness; slice oversampling factor ¼ 1.3; in-plane voxel size ¼ 1  1 mm; receiver bandwidth (BW) ¼ 697 kHz; field of view ¼ 230  192  100 cm; acquisition time ¼ 14.4 min) (18). The approximate signal-to-noise ratio for WM voxels (signal at TE 10 ms/standard deviation of decay curve residuals) from this sequence was 300. The mcDESPOT scanning protocol was then performed with the same field of view and voxel size as the GRASE sequence. The mcDESPOT protocol included three series of scans: 1. SPGR (TR/TE ¼ 6.3 ms/1.9 ms, axial, a ¼ [2 , 3 , 4 , 5 , 6.5 , 8 , 10 , 13 , 16 ], BW ¼ 623 kHz); 2. inversion recovery (IR) prepared SPGR (TR/ TE ¼ 7.5ms/3.7ms, inversion time (TI) ¼ 450 ms, a ¼ 8 , Turbo Field Echo (TFE) factor ¼ 64, BW ¼ 623 kHz); and 3. bSSFP (TR/TE ¼ 7 ms/3.5 ms, a ¼ [6 , 11 , 16 , 22 , 30 , 38 , 46 , 54 , 62 ], BW ¼ 667.5 kHz). The bSSFP sequence was run twice, with offresonance frequencies of Dn ¼ 0 and 71.43 Hz in order to better deal with banding artifacts (19). Total acquisition time for mcDESPOT was 7 min. The approximate signalto-noise ratio for WM regions from a ¼ 16 (Ernst angle) images from this sequence was 200. Both sequences used parallel imaging (SENSE) (25) along the left-to-right direction with a SENSE factor of 2 and elliptical K-space filtering. Data Analysis GRASE data were analyzed on a voxel-wise basis using multicomponent T2 analysis with concurrent correction for stimulated echo contamination of decay curves resulting from B1 inhomogeneity. A regularized NNLS algorithm (4) was used to decompose the decay curve into multiple T2 components with no a priori assumptions about the number of contributing T2 components; the stimulated echo correction was applied within NNLS. The input theoretical T2 decay curves were calculated for non-ideal refocusing pulse flip angles using the extended phase graph (EPG) algorithm (26). The actual refocusing flip angle, aestimated, was estimated by comparing theoretical decay curves with different refocusing pulse flip angles to the experimental decay curve and determining which angle gave rise to the best fit to the experimental curve. The B1(k) map was expressed in units of the ratio, k, between the estimated flip angle and the prescribed flip angle at each voxel in the image (k ¼ aestimated/aprescribed). Using the estimated refocusing pulse flip angle, T2 distributions were created using 40 logarithmically spaced T2 values ranging from 0.015 to 2 s. The T2 distributions were obtained using a nonnegative least squares algorithm to minimize the sum of squares of the residuals. In addition, to produce smooth T2 distributions, regularization was performed jointly by also minimizing the sum of the squares of the solution.

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From the T2 distributions, the MWF was calculated as the discrete integral for T2 times from 15 to 40 ms normalized by the total area under the distribution (total proton density). MWF maps were created by determining the MWF at each voxel in the image. The geometric mean T2 was defined by (27): " # M M max max X X GMT2 ¼ exp Sj log ðT2j Þ= Sj ; j¼Mmin

j¼Mmin

where Sj represents the relative signal amplitudes for each partitioned relaxation time T2j. GMT2,M was defined as the short component peak ranging from Mmin ¼ 15 ms to Mmax ¼ 40 ms, while GMT2,IE was defined as the intracellular/extracellular component peak ranging from Mmin ¼ 40 ms to Mmax ¼ 200 ms. T2 maps were created by displaying the GMT2 at each voxel in the image. Images from the mcDESPOT sequence were also analyzed on a voxel-wise basis. The SPGR and IR-SPGR scans were used to first calibrate the transmitted flip angles, and the single-component T1 and the B1(k) field maps were obtained by following Deoni (28); the bSSFP data (acquired with two offset frequencies) and the single-component T1 and B1(k) maps were then used to calculate single-component T2 and B0 field maps (29). Finally, the B0 and B1(k) maps combined with the SPGR and bSSFP data were used to estimate the 6D parameter search space, which included myelin water fraction (fM), myelin water residence time (tM), and the two-pool water T1 and T2 times (T1,F, T1,M, T2,M, T2,F) (24), where M and F represent the myelin water and free water pool, respectively. To fit the multiple flip angle SPGR and bSSFP data, a stochastic region contraction approach was used (30). Following the literature (20), this approach began by defining the expected search-space limits for the 6D space of T1,M, T1,F, T2,M, T2,F, fM, and tM. For this study, the following search space was employed: 200 ms  T1,M  500 ms, 700 ms  T1,F  2500 ms, 2 ms  T2,M  45 ms, 75 ms  T2,F  200 ms, 107  fM  0.3, 50 ms  tM  2 s. Three thousand search space samples were then randomly chosen from uniform distributions for each parameter, and for each combination, the theoretical SPGR and bSSFP signal curves were generated. Both theoretical and experimental data were normalized (with respect to P their mean values), and the sum-of-squares of residuals n ðSntheory  Snexperiment Þ2 was calculated, where n is the number of data points being fitted (n ¼ 18). The stochastic region contraction algorithm was applied as follows: By searching the global minimum residuals, the minimum and maximum sampled values for each parameter were determined from the top 30 searching space combinations that gave rise to the best fits. These values were then used to update the limits of searching space for the next iteration and the algorithm slowly contracted to a globally optimum solution after 10 iterations. To investigate the effect of excluding exchange between myelin and intraand extracellular water on parameter values, the mcDESPOT analysis was also conducted by defining a 5D searching space of T1,M, T1,F, T2,M, T2,F, and fM while setting tM to infinity, effectively turning off exchange. To discriminate this calculation from the previous analysis,

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we labeled it “mcDESPOT without exchange.” The same searching routine was reused to find the optimum solution. In addition, we used the mcDESPOT (with exchange) parameters to estimate the apparent T2,M, T2,F, and myelin water fraction values, which one might expect to measure with a decay curve measurement (31). Region Identification Regions of interest (ROIs) were drawn bilaterally in each subject on the IR-SPGR image obtained from the mcDESPOT protocol in five WM structures (genu and splenium of the corpus callosum, minor and major forceps, and the posterior internal capsules) and six GM structures (head of the caudate nucleus, putamen, thalamus, cingulate gyrus, insular cortex, and cortical GM) (27). ROIs were mapped onto MWF/fM and T2 maps created from the GRASE and mcDESPOT data. All scans had the same resolution and position (i.e., no evidence of movement was observed between the two scans), so image registration was not required. For each ROI, mean MWF and mean fM were determined using the previously created MWF/fM maps, and results were averaged between corresponding left and right hemispheres of the brain and across all subjects for each sequence. Statistical Analysis For the 11 regions of interest, the average MWF and GMT2,M /GMT2,IE from the GRASE sequence were compared with the corresponding average fM and T2,M/T2,F from the mcDESPOT sequence. Two-tailed t tests were performed for the comparisons between the GRASE and mcDESPOT parameters. Intersequence agreement of MWF/fM values was also determined using BlandAltman analysis (32). RESULTS Comparison of Myelin Water Fraction Figure 1 shows B1(k) maps obtained from a representative brain slice using the GRASE and mcDESPOT methods. The flip angle ratio, k, ranged from 0.8 to 1.2 and demonstrated higher intensity at the center of the images and lower intensity at the periphery of the images. For the GRASE approach, k must be 1, because an estimated flip angle of 180 þ a is equivalent to an estimated angle of 180  a. The B1(k) difference map is also shown in Fig. 1. As we can see, the k difference values were around zero over most of the brain. The B1(k) map derived from GRASE showed a few brighter regions, which may have originated from moving spins. The B1(k) map derived from mcDESPOT possessed some structural information, especially in the cortical gray and ventricular regions. Figure 2 shows MWF and fM maps obtained from a representative brain slice using GRASE and mcDESPOT. Both images showed good definition at structure boundaries and WM–GM interfaces; however, the quantitative values were markedly different. The mcDESPOT fM image showed less apparent noise; however, a large proportion of the WM areas exhibited an fM at the upper search space limiting value of 0.30.

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FIG. 1. Representative axially oriented slice of the B1(k) inhomogeneity map from a healthy volunteer with GRASE and mcDESPOT. The difference B1(k) map between the two methods is also shown.

Figure 3 presents average MWF and fM values from GRASE and mcDESPOT for each ROI. The values of MWF and fM for specific ROIs were markedly different between the two sequences. fM obtained from “mcDESPOT without exchange” by setting the exchange rate (1/tM) fitting parameter to zero are also shown in Fig. 3. For a two-component system, the onset of exchange between the two components should cause a reduction in both measured T2 times plus a reduction in the measured myelin water fraction (33). As expected, fM in WM were shifted to slightly lower values when exchange was not included in the mcDESPOT analysis; however, the “mcDESPOT without exchange” fM’s were still generally much higher than MWFs derived from GRASE. P values, which are also shown in Fig. 3, indicate that with the exception of two GM structures, MWF from GRASE and fM from mcDESPOT were significantly different. The apparent fM values (i.e., the MWF values we would expect from the T2 decay curve) which were estimated from the mcDESPOT solution by applying a two-pool exchange correction are also shown in Fig. 3; these fM values were still much higher than MWF derived from GRASE.

Figure 4 shows mean MWF and fM histograms from the ROIs separated into WM, cortical GM (cingulate gyrus, insular cortex, and cortical GM), and internal GM (head of the caudate nucleus, putamen, thalamus) for GRASE and mcDESPOT sequences. MWF and fM values from the two techniques are plotted against each other in Figure 5. As shown in Fig. 5, GRASE MWF values did not vary across GM structures, but the mcDESPOT fM values differed greatly between them; for WM, the GRASE MWF differed greatly between structures, while the mcDESPOT fM’s did not vary across regions and appeared to be constrained by the input search space limit to fM of 0.30. Comparison of Relaxation Times Figure 6 shows T2 maps of a representative brain slice from GRASE and mcDESPOT which demonstrate clear qualitative differences between the sequences. Figure 7 presents the average T2’s for each ROI from GRASE and mcDESPOT. The values of T2 within specific ROIs were generally different between the two sequences; however,

FIG. 2. Representative axially oriented slice of MWF and fM maps from a healthy volunteer with GRASE and mcDESPOT.

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FIG. 3. Mean ROI MWF from GRASE, fM values from mcDESPOT with and without exchange, and the mcDESPOT apparent fM values. Error bars indicate the standard deviation from 10 healthy subjects. *P < 0.05. **P < 0.001. ***P < 0.0001.

T2’s obtained from “mcDESPOT without exchange” were closer to the GRASE results. The almost constant T2,F times and standard deviations for WM structures obtained from “mcDESPOT without exchange” were constrained by the searching space lower limit. Figure 8 shows T2 distributions derived from the GRASE T2 decay curves for different cortical GM, internal GM, and WM regions. Most ROIs in cortical GM gave rise to three T2 components; however, the mcDESPOT analysis assumed only two T2 components. DISCUSSION Quantitative mapping of MWF is a validated indicator of myelination, and although the effect of exchange on in vivo measurements of MWF is still not fully understood, MWF can provide valuable insights into the pathology of focal and diffuse WM diseases, such as in multiple sclerosis. Many different approaches have been employed to

estimate myelin content. Multiple spin echo and steadystate methods for myelin water measurement report markedly different values; this is causing considerable confusion in the field. To better understand the principles and factors that influence measurements of MWF 7and to aid in the design of future studies, we felt that it would be worthwhile to compare results from different techniques under similar experimental situations. In this study, we acquired both GRASE and mcDESPOT data for 10 healthy subjects. The two sequences had the same field of view and voxel size. The acquisition time for GRASE was approximately twice that for mcDESPOT. The two sets of data were analyzed to produce estimates for B1, MWF/fM, and T2. B1 Maps B1 maps from GRASE and mcDESPOT were in reasonable agreement. Three factors contributed to small

FIG. 4. Mean MWF and fM histograms from WM, internal GM, and cortical GM from GRASE and mcDESPOT.

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FIG. 5. a: Correlation plot of mean ROI MWF and fM values from GRASE and mcDESPOT. b: Bland-Altman plot comparing the difference in MWF and fM as a function of the intersequence mean value. In both plots, gray diamonds represent GM ROIs, and white diamonds represent WM ROIs. Error bars represent the standard deviation.

differences in B1 maps: 1) the GRASE B1 algorithm cannot distinguish between flow induced decay curve oscillations and stimulated echo induced decay curve oscillations resulting in artifactually low B1 near vessels; 2) The GRASE B1 algorithm cannot distinguish between 180˚ þ a and 180˚ - a, since these two scenarios give identical stimulated echo patterns; and 3) The mcDESPOT protocol used slightly different values of TE and TR between the SPGR and IR-SPGR resulting in slight relaxation time weighting in the B1 maps. However, substituting the B1 map from GRASE into the mcDESPOT

analysis did not significantly alter mcDESPOT results; therefore, errors in the estimated B1 field inhomogeneity were believed to have negligible effect on estimates of MWF and fM. MWF Maps Although WM appeared brighter on both MWF and fM maps (Fig. 2), maps created from the two methods for the same volunteer were markedly different. Generally, MWFs from GRASE were much smaller than fM’s from

FIG. 6. Representative axially oriented slice of the T2,F, T2,M map from a healthy volunteer from GRASE and mcDESPOT.

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FIG. 7. a: Mean ROI T2,F values from GRASE and mcDESPOT with and without exchange and the apparent T2,F values obtained from mcDESPOT. b: Mean ROI T2,M values from GRASE and mcDESPOT with and without exchange and the mcDESPOT apparent T2,M values of 10 healthy subjects. Error bars indicate standard deviation. *P < 0.05. **P < 0.001. ***P < 0.0001.

mcDESPOT. However, in cortical GM, the two techniques gave rise to somewhat similar MWF/fM histograms. This similarity in MWF results in cortical gray might be attributed to a limitation of the two-pool mcDESPOT model. When mcDESPOT was extended to a three-pool model, it produced higher fM’s for cortical GM (34). In GM, the dynamic range was much smaller for MWF than for fM. In WM, the opposite occurred; GRASE gave quite different MWFs for different structures, while fM’s appeared to be constrained by the searching limits. In summary, the two approaches lead to both qualitative and quantitatively different results between MWF and fM. We note that the fM values reported here from mcDESPOT are slightly higher than fM values in the literature

(20); however, our analysis, which was programmed inhouse, provided solutions with minimum sum-of-squares residuals for the given parameter spaces. The GRASE MWFs reported here are in agreement with previously published work (18). Exchange Effects A strength of the mcDESPOT method is that its analysis includes the possibility of exchange between water pools; therefore, mcDESPOT might have the potential to assess the influence of exchange on MWF values measured from the T2 decay curve. One could interpret the variability of MWF in WM for GRASE as a consequence of water exchange between the

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In addition, using mcDESPOT-derived parameters, we calculated the apparent fM values that one might expect to obtain from a multiecho measurement. These apparent fM values were still much higher than the MWFs obtained from GRASE, demonstrating that exchange cannot account for the differences between MWF and fM. T2 and T1 Values

FIG. 8. Mean T2 distributions for three regions from GRASE across all volunteers: cortical GM, internal GM, and WM.

two pools, since a significant difference between GRASE and mcDESPOT is that the mcDESPOT analysis includes the exchange rate as a fitting parameter, while GRASE numbers are often interpreted with an assumption implicitly of slow water exchange. To better understand this effect, we reanalyzed the mcDESPOT data assuming slow water exchange between compartments. If the aforementioned MWF differences between the T2 decay and mcDESPOT methods were a result of the fact that measured MWF was reduced due to exchange, then eliminating exchange in the mcDESPOT model should result in similar values for MWF and fM. However, surprisingly, while the fM’s from “mcDESPOT without exchange” decreased slightly from the limiting search space value, they were still much higher than the corresponding MWFs from GRASE (Fig. 3). It is possible that the insensitivity of mcDESPOT to exchange effects arises from the large 6D searching space of this method, resulting in nonunique solutions; this issue is investigated in a later section.

We also compared the T2 s obtained from the two methods (Fig. 7). GMT2,M from GRASE were much longer than T2,M from mcDESPOT. Since the GRASE technique has acquisition limits with TE ¼ 10 ms, we would be unable to measure GMT2,M’s much below 10 ms. Also, due to the regularization step in the GRASE analysis, the resulting GMT2,M’s are not expected to be very accurate and are typically not reported in the literature for that reason. However, the T2,M’s from mcDESPOT seem unrealistically short; if the T2,M were actually 3 ms, it would contribute less than 4% of its signal at the first echo time of 10 ms and have negligible contribution to the second echo time at 20 ms. Since it has been shown that multiecho sequences with an echo spacing of 10 ms can measure the entire water signal in brain (27), it seems unlikely that myelin water has a T2 time of 3 ms. GMT2,IE’s from GRASE were smaller than T2,F from mcDESPOT. When exchange was excluded from the mcDESPOT analysis, the estimated T2,F values decreased and T2,M values increased—both cases coming closer to the GRASE numbers. However, the mcDESPOT without exchange T2,F’s were also constrained by their lower search limit. For a two-component system, the onset of exchange between the two components should cause a reduction in both measured T2 times plus a reduction in the measured MWF (33). Surprisingly, removing the possibility of exchange in the mcDESPOT analysis gave the expected results for T2,F and fM but not for T2,M. This might be an effect of limited search space boundaries. Since we examined the effects of removing exchange from the mcDESPOT model on fM and T2, for

FIG. 9. Representative axially oriented slice of fM from a healthy volunteer with mcDESPOT using two different fM searching spaces: 107  fM  0.3 and 107  fM  0.8.

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FIG. 10. a: Plot of sum-of-square of residuals versus fM from one voxel within major forceps region obtained by fitting the other five parameters for each fM within searching spaces. b: Histogram plot of fM within the major forceps.

completeness we also investigated the effect of exchange on T1. T1,M and T1,F did not change significantly except T1,F for WM increased when exchange was excluded as expected. Limitations of the mcDESPOT Analysis Approach Our comparative observations between GRASE and mcDESPOT noted that fM was typically close to the upper searching space limit. Therefore, the effect of the 6D searching space limit choice in the mcDESPOT analysis was preliminarily investigated by expanding the fM searching space. Figure 9 shows the comparison of two fM maps: one created using the search space defined in the Methods, and a second created with the fM upper limit increased from 0.3 to 0.8 but leaving the other five parameter search spaces unaltered. The estimated fM generally increased for the second case, confirming that search space limits have considerable impact on the fM solutions for mcDESPOT. To explore the fM search space in more detail, we sampled a set of data from one voxel from the major forceps in Fig. 9. We fixed fM to values ranging from 0.1 to 0.8, and for each fM the other five parameters were varied within their searching spaces to obtain the minimum sum of squared residuals. This calculated sum-of-square of residuals versus fM is shown in figure 10(a). As we can see, the mcDESPOT method yielded a relatively flat curve between fM ¼ 0.3 and fM ¼ 0.5. In Figure 10b, we show a histogram of fM within the major forceps region.

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This plot demonstrates that the major forceps fM values were approximately Gaussian distributed across the aforementioned “flat residual” range between 0.3 and 0.5. In this preliminary investigation, we only explored changing the search space boundaries for fM. If one of five other parameters were outside of the search space chosen here, it could also influence the choice of solutions. A rigorous exploration of search space boundaries for all parameters was beyond the scope of this study. More research is also required to learn how sensitive the fM values obtained with the mcDESPOT method are to magnetization transfer effects in the SSFP signal, as suggested recently by Lenz et al. (35) and Deoni et al. (20). In this case, the derived myelin fraction estimates would represent not only the magnetization associated with the water pool bound between the myelin sheaths, but also magnetization transfer from nonaqueous myelin protons. On-resonance magnetization transfer effects can be excluded from experiments by choosing long radiofrequency pulse durations. However, the selection of long radiofrequency pulse durations requires the use of a finite pulse correction (36), which must be applied to the derived bSSFP signal equation. Further, computation of fM with the mcDESPOT approach relies on a priori assumptions regarding the number of T2 components present and also requires estimation of six parameters, which is especially challenging given the simple behavior of the bSSFP curves. Recently, Lankford and Does (37) demonstrated, through propagation-of-error analysis, that it is problematic for mcDESPOT analysis to accurately estimate parameters of a two-pool model with exchange without constraining the model. Limitations of the GRASE Analysis Approach For the GRASE technique, we used the NNLS analysis, which has the significant advantage of no a priori assumptions about the number of T2 components. However, regularized NNLS solutions provide less accurate results when the signal-to-noise ratio is low, such as in GM or demyelinated areas (4,38). NNLS may also overestimate the MWF in the internal capsules due to overlap of the myelin water and intracellular/extracellular water T2 peaks (39). CONCLUSIONS Recent studies have demonstrated that mcDESPOT provides low-variance estimates of model parameters in human spinal cord and human infant brain and appears to be sensitive to tissue alterations in development and pathology. However, fM’s from mcDESPOT are considerably higher than MWFs from T2 decay curve–derived results, and T2,M times estimated by mcDESPOT are unrealistically short. This study demonstrates that parameter search space limitations have nonnegligible influence on the mcDESPOT results and also that the explicit incorporation of exchange in mcDESPOT does not account for the differences in results from the two techniques. Until we understand the two techniques sufficiently well to be able to rationalize the differences in myelin-associated parameter estimates, fM values derived

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