Nonexponential T2* decay in white matter

Nonexponential T2* Decay in White Matter*

Peter van Gelderen,1* Jacco A. de Zwart,1 Jongho Lee,1,2 Pascal Sati,3

Daniel S. Reich,3 and Jeff H. Duyn1

Visualizing myelin in human brain may help the study of dis-

eases such as multiple sclerosis. Previous studies based on

T1 and T2 relaxation contrast have suggested the presence of

a distinct water pool that may report directly on local myelin

content. Recent work indicates that T2* contrast may offer par-

ticular advantages over T1 and T2 contrast, especially at high

field. However, the complex mechanism underlying T2* relaxa-

tion may render interpretation difficult. To address this issue,

T2* relaxation behavior in human brain was studied at 3 and 7

T. Multiple gradient echoes covering most of the decay curve

were analyzed for deviations from mono-exponential behavior.

The data confirm the previous finding of a distinct rapidly

relaxing signal component (T2* ~ 6 ms), tentatively attributed

to myelin water. However, in extension to previous findings,

this rapidly relaxing component displayed a substantial reso-

nance frequency shift, reaching 36 Hz in the corpus callosum

at 7 T. The component’s fractional amplitude and frequency

shift appeared to depend on both field strength and fiber ori-

entation, consistent with a mechanism originating from mag-

netic susceptibility effects. The findings suggest that T2*

contrast at high field may be uniquely sensitive to tissue mye-

lin content and that proper interpretation will require modeling

of susceptibility-induced resonance frequency shifts. Magn

Reson Med 67:110–117, 2012. VC 2011 Wiley Periodicals, Inc.

Key words: T2* relaxation; high field imaging; myelin waterfraction; white matter imaging

Loss of axonal myelin in human brain white matter

(WM) may lead to impaired brain function. Such loss

may result from normal aging as well as a number of

neurological diseases, most notably multiple sclerosis

(MS). For this reason, the measurement of local myelin

content has been a longstanding goal of MRI technique

development. Most of the current techniques aim at

measuring the relative concentration of myelin water

based on its characteristic relaxation properties. The

term ‘‘myelin water’’ is used here as a loosely defined

entity which includes all water that is in close vicinity

to myelin. It is often assumed that the myelin water may

be physically restricted to the spaces between myelin

sheets surrounding axons and may experience acceler-

ated relaxation due to reduced mobility.

Several methods have been proposed to distinguish

myelin water from other water signals, based on various

contrast mechanisms. Magnetization transfer (MT) effects

(1) can be exploited to selectively saturate water in con-

tact with macromolecules or myelin (e.g., Ref. 2). Sub-

traction of MT-saturated images from unsaturated images

may thus provide an estimate of myelin water content.

T2 relaxation measurements can be used to identify fast

and slow T2 components (3,4), with the fast component

interpreted as myelin water. Simultaneous T1 and T2 in-

formation may be obtained with the DESPOT1 and DES-

POT2 techniques (5) (Driven Equilibrium Single Pulse

Observation of T1 and T2). Inclusion of T1 information

may improve the reliability of the estimated fast T2 frac-

tion and, under some conditions, allow estimation of

exchange rates between the differentially relaxing puta-

tive compartments or ‘‘pools.’’ More quantitative meth-

ods, based on MT measurements at a range of saturation

frequencies and T1 measurements, and analyzed with a

two-pool model of magnetization (6), have been pro-

posed as well. These methods allow estimation of the

size of the rapidly decaying proton fraction and its

exchange rate (7–9), resulting in a measure of a bound

proton pool, generally assumed to be representative of

larger molecules, such as those forming myelin. How-

ever, a comparison between quantitative MT and T2 data

in multiple sclerosis patients showed little correlation

between the myelin water fractions derived with these

methods (10), indicating that the underlying contrast

mechanisms are still poorly understood.

Although promising, current myelin water measure-

ment methods generally suffer from long measurement

time, poor signal-to-noise ratio (SNR), and limited speci-

ficity to myelin water. Some of the methods furthermore

lack the ability to provide reproducible quantitative

numbers. The hope is, therefore, that further improve-

ments in MRI measurement of myelin water will arise

from novel methods.

One very recent and particularly promising technique

to measure myelin associated water is the use of T2* con-

trast (11,12). Similar to the T1 or T2 based methods, the

premise is that the myelin associated water has a dis-

tinctly reduced T2* and that the exchange between the

free and myelin water pools is slow enough to observe

multiexponential T2* decay as function of echo time (TE)

for myelin containing tissue.

Potential advantages of using T2* contrast over alterna-tive methods are its rather strong (relative to other con-trasts) amplification at high field strength and the factthat the relatively simple gradient echo (GRE) pulse

1Advanced MRI Section, Laboratory of Functional and Molecular Imaging,National Institute of Neurological Disorders and Stroke, National Institutes ofHealth, Bethesda, Maryland, USA.2Department of Radiology, University of Pennsylvania, Philadelphia,Pennsylvania, USA.3Translational Neuroradiology Unit, Neuroimmunology Branch, NationalInstitute of Neurological Disorders and Stroke, National Institutes of Health,Bethesda, Maryland, USA.

This work was supported by the Intramural Research Program of theNational Institutes of Neurological Disorders and Stroke.

*Correspondence to: Peter van Gelderen, Ph.D., Bld 10, Rm B1D-725, 10Center Drive, Bethesda, Maryland 20892. E-mail: [email protected]

Received 10 January 2011; revised 8 April 2011; accepted 12 April 2011.

DOI 10.1002/mrm.22990Published online 31 May 2011 in Wiley Online Library (wileyonlinelibrary.com).

Magnetic Resonance in Medicine 67:110–117 (2012)

VC 2011 Wiley Periodicals, Inc. 110

sequence can be used. Moreover, GRE pulse sequenceshave low radiofrequency power deposition. This is im-portant, because radiofrequency power depositionincreases quadratically with field strength, and thus maylimit the field strength at which T1 and T2 measurementsare practical. The goal of this study, therefore, was toinvestigate whether T2* decay at 7 T can be used to detectand further characterize myelin water. For this purpose,multiecho GRE data were acquired in a number of nor-mal volunteers at 7 T. For comparison, similar data wereacquired at 3 T as well in a smaller group of subjects.

MATERIALS AND METHODS

Seven healthy volunteers (3 female, 4 male, ages 33–54,average age 41) were studied at 7 T, one of whom wasscanned twice. Four volunteers (1 female, age 24–45, av-erage 36 years) were scanned at 3 T, three of which alsoparticipated in the 7 T study. Both scanners were Gen-eral Electric (GE, Milwaukee, Wisconsin) systems,equipped with standard clinical gradients (maximumamplitude 40 mT/m, slew rate 150 T/m/s). For the 7 Tstudy, a Nova Medical (Wilmington, MA) birdcage trans-mit coil was used in combination with a 32-channelreceive coil, for the 3 T study the GE body coil was usedfor transmission and a 16-channel Nova Medical coil forreception. All studies were performed under an InternalReview Board approved human protocol.

The pulse sequence was an in-house developed multiGRE acquisition for mapping the T2* decay. A train ofechoes was produced by alternating the acquisition gra-dient, similar to an echo planar imaging acquisition, butomitting the phase encoding blips between echo acquisi-tions. Only the positive gradient lobes were used toavoid misalignment between positive and negative ech-oes due to local off resonance effects, and the negativegradient lobes were maximized for minimum inter echospacing (13). The acquisition time of the first echo wasminimized by using a short (1.6 ms) radiofrequency exci-tation pulse and combining the slice rephrasing, phaseencoding, and acquisition dephasing gradients. A single2 mm slice was measured per scan, with an in plane re-solution of 256 � 96 voxels and a field of view of 240 �180 mm. The repetition time was 70 ms, and the flipangle (as estimated at the center of the slice) was 30degrees. The single slice acquisition was repeated 50times for a total scan time was 336 s. The repetitionswere selectively averaged (see below) for improved SNRand stability. The shortest TE was 2.7 ms, the longestone 45.0 ms, for a total of 19 echoes spaced at 2.35 ms.The 10th echo was programmed to be used as a naviga-tor; for this purpose, the phase encoding was rewoundbefore the echo and reapplied immediately after. Thisnavigator was intended to help improve the stability, butnot used in the final analysis. Two slices were scannedin separate experiments, in a close to axial orientationparallel to the anterior and posterior commissure line.One slice was positioned a few millimeters above ante-rior and posterior commissure to capture a section of thecorpus callosum, and a second slice was acquired at aposition �25 mm higher to capture WM outside themajor fiber bundles.

The images from individual receiver channels werecombined using a sensitivity encoding (SENSE) (14) typecalculation without external reference (15) based on thefirst echo of the first repetition. For each repetition andeach voxel, the signal across TEs was fitted to a single-exponential decay using a Levenberg-Marquardt nonlin-ear least squares algorithm. The results were averagedover repetitions after excluding outliers. The outlierswere identified by analyzing the fluctuations of the fittedamplitudes over the repetitions. These amplitudes wereaveraged over the repetitions. Subsequently, the differ-ence of the amplitudes with this average was calculatedand normalized by its standard deviation (SD), and thensummed over all voxels. The repetitions for which thesummed deviation from average was more than twice theSD were excluded from further analysis.

Subsequent analysis was geared toward investigatingthe potential presence of multiexponential relaxation, aspreviously found at 3 T (11,12), by looking at the devia-tion from single exponential relaxation. To determinethis deviation, the averaged fit results were comparedwith the averaged echo signals, resulting in average dif-ference maps for each TE measured. These maps werethen further analyzed in selected regions of interest(ROIs). Using the average R2* map as a guide, ROIs wereselected in posterior part (the splenium) of the corpuscallosum (SCC), in the posterior internal capsule and inthe WM surrounding the posterior part of the CC, notassociated with any major fiber bundle. In the following,the last of these is referred to as general white matter(GWM).

After region selection, ROI averaged signals were usedto derive quantitative estimates of a potential fast relax-ing component. For this purpose, a single exponential,slow relaxation component was estimated by performinga single exponential fit to ROI-averaged data after exclu-sion of data from the first two TEs for the 7 T data andexclusion of the first 4 echoes for the 3 T data. Thisexclusion was designed to select the slow component inthe data. The difference with this fit was used to studythe deviation from single exponential decay resultingfrom a putative fast component.

The choice of the ROIs was informed by comparisonof the R2* maps with diffusion derived fiber orientationand anisotropy maps acquired in a previous, unrelatedstudy. Two of the subjects in the current study had alsoparticipated in that diffusion study and a closely corre-sponding slice position and orientation could be selectedin one of these two volunteers to allow identification ofseveral structures in the R2* data using the diffusionmaps as a guide. The fiber orientation in the threeselected ROIs (SCC, posterior internal capsule, andGWM) was predominantly perpendicular to the mainmagnetic field, parallel to it and mixed, respectively.Susceptibility effects in structured tissue, such as paral-lel fiber bundles, are dependent on the angle of thestructure with respect to the main magnetic field (16,17).As a result, the T2* decay may show a deviation from sin-gle exponential behavior that is orientation dependent.

Further analysis revealed that a three-componentmodel, as suggested in (18), may produce a better fit tothe data, provided that a variable offset frequency is

Nonexponential T2* decay in White Matter 111

allowed for the components. This analysis is analogousto the model proposed previously for the separation ofgray matter, cerebrospinal fluid, and intravascular sig-nals (19), and that for the separation of tissue water andcerebrospinal fluid (20). In WM, compartment-specificresonance frequency shifts may occur due to the mag-netic susceptibility effects of the distribution of myelin-associated lipids and iron (21). If one assumes that thereis one dominant component and two components of rela-tively small amplitude, then only the frequency differen-ces between the two smaller components and the domi-nant term are relevant when considering magnitude data.The phase of the total signal will be set by the dominantcomponent, and this phase is removed by taking themagnitude of the signal. The resulting model is:

SðtÞ ¼ jjA1e�tR�

2;1�i2pf1t þA2e�tR�

2;2 þA3e�tR�

2;3�i2pf3t jj ½1�

where S is the magnitude signal as function of time, jj�jjindicates the magnitude operator, and Ai is the amplitude,fi the frequency difference with the main component (inHz), and R*2,i the relaxation rate of component i. Themodel has eight free parameters (f2 is zero and thereforenot included in the model, as this component is assumedto be on resonance). All components start in-phase at t ¼0. The first (fast) component is tentatively assigned tomyelin water, the second component represents the domi-nant, larger signal of the on-resonance tissue water, andthe third and longer component represents mobile waterin cerebrospinal fluid and extracellular spaces.

As the fitting of such a model to data acquired in a rel-atively short range of TEs is inherently an ill-conditionedproblem, a simple (and slow) fitting procedure was fol-lowed in which in successive iterations every compo-nent in the model was optimized by minimizing the sumof squares the residue of the fit for a given range of itsparameters. The search was limited to positive values forthe amplitude and relaxation rates. After each iteration,the range was reduced by a factor of two to refine thesearch if an optimum was found within the given range;otherwise the range was increased by a factor two. Theinitial search range was 70–130% of the initial guess foreach parameter. The optimization was halted when fur-ther reduction of the residue was no longer significant.This fitting procedure was only applied to the 7 T ROIaveraged signal in the SCC and GWM areas, as the poste-rior internal capsule data did not give reproducibleresults.

On the 3 T data the fitting of the three componentsdid not result in reproducible results, so those data werefitted with a comparable two-component model:

SðtÞ ¼ jjA1e�tR�

2;1�i2pf1t þA2e�tR�

2;2 jj ½2�

leaving out the third, slow component, reducing thenumber of parameters to five.

RESULTS

The SNR in the coil-combined images for the first echo(TE 2.7 ms) was 30–90 at 3 T and 70–180 at 7 T (before

averaging). The large range at each field is attributed tothe highly inhomogeneous B1 profile of the receive coilarrays. The temporal stability, expressed as mean di-vided by the SD of the fitted amplitude over time, was20–60 for both field strengths before the rejection ofdeviating repetitions (see Materials and Methods). Afterthis rejection, the stability was 50–90 for the 3 T scansand 60–150 for the 7 T scans. In the majority of studies,the fraction of rejected repetitions was below 20%.

Figure 1 shows an example of the average differencemaps (the difference between data and the mono-expo-nential fit) at selected TEs, calculated from 46 repeti-tions. Substantial difference signal is observed at theshortest TE (2.7 ms), which is most pronounced in themyelin-rich SCC. Interestingly, substantial difference sig-nal remains visible at longer TEs, both in gray and WMregions. Even at TE ¼ 45 ms, significant deviation fromthe single-exponential fit is observed. This observed con-trast evolution with TE appears inconsistent with thedifference of a previously suggested multiexponentialdecay (12) and a mono-exponential fit (see Appendix A).

Results of the ROI-based T2* decay analysis are shownin Figs. 2 and 3. Figure 2 shows an example of ROIselection; ROI- and subject-averaged differences betweenthe data and the mono-exponential fit for the 7 T dataare shown in Fig. 3. The error bars in the plot, derivedfrom the SD over the subjects, show that the shape of thedecay curves is very reproducible. Across ROIs,

FIG. 1. The difference between a mono-exponential model andthe T2*-weighted data at four selected echo times, as fraction of

the fitted amplitude for echo time zero. The echo times are indi-cated below each image. The images show that the deviationfrom exponential behavior is not limited to the contribution of a

fast component and notably different in contrast for different ana-tomical structures.

112 van Gelderen et al.

substantial differences in amplitude and shape areobserved. An illustration of the field dependence of thenonexponential T2* decay is shown in Fig. 4, showingthe subject averaged differences with a mono-exponen-tial fit for the SCC ROI data at 3 T. The error bars reflectthe standard error of the averages. The shape is notablydifferent than the residue for the 7 T data, plotted in thesame figure for comparison (it is the same curve as inFig. 3b). The 3 T curve is expanded in time comparedwith the 7 T curve and lower in amplitude.

The deviation from single exponential decay appearsto be inconsistent with a multicompartment model with-out frequency offsets, as discussed Appendix A. A modelincluding a frequency offset for the two smaller compo-nents (Eq. 1), however, fits the data very well, as shownin Fig. 5. The adjusted coefficient of determination (R2)improved from 1 � R2 ¼ 1.8 � 10�4 for the model with-out frequency offsets to 1 � R2 ¼ 1.6 � 10�6 for themodel with the offsets. The average of the fit parametersfor the 7 T and 3 T data is presented in Table 1. As dem-onstrated by the SD of the fit parameters, the 7 T resultsare reproducible over subjects. However, the results ofthe fit of the three-compartment model to the 3 T datawere not reproducible between subjects and, therefore,only the results of fit with the two-compartment model(Eq. 2) are shown.

The triple-exponential model could not be fitted reli-ably to the data on a voxel by voxel basis. To create amap of the fast component, the model was modified by

FIG. 2. ROI selection based on R2* maps using diffusion data toidentify the structures of interest. The diffusion data were proc-essed to show fractional anisotropy (FA) and a color-coded pre-

dominant fiber orientation with green for left–right, red foranterior–posterior and blue for the superior–inferior direction. The

three ROIs represent the posterior corpus callosum (CC, red) withpredominantly left–right fibers, the posterior internal capsule (PIC,brown) with mostly up–down fibers and a mixed WM area (GWM)

in green containing fibers of various orientations and, therefore,has a lower FA. The scale for the R2* images is in Hz.

FIG. 3. a: An example of the decay curve, averaged over a ROI inthe splenium of the corpus callosum (SCC), and the correspond-

ing mono-exponential fit for one subject. b: Plots of the subject-averaged differences between the ROI averaged T2* weighted data

and a mono-exponential fits. The curves show the mean overeight studies at 7 T with error bars indicating the standard error ofthe mean for the three ROIs (see Fig. 2 for locations).

FIG. 4. Plot of the subject averaged difference between the sple-nium of the corpus callosum (SCC) ROI data and a mono-expo-

nential fit for 3 T. The error bars reflect the standard error of themean. The 7 T data is repeated from Fig. 3b for comparison.


fixing the relaxation and frequency parameters to the val-ues determined in the fit to the SCC ROI averaged data.This reduced the fitting problem to a three parameter lin-ear least squares optimization to find the amplitudes ofthe three components. The resulting map of the ampli-tude of the fast component is shown in Fig. 6, togetherwith the difference between the data at TE 2.7 ms and amono-exponential model, fitted excluding the first twoechoes. For comparison, the map of the fast component

reflects the amplitude of this component at the same 2.7ms TE, not directly the fitted amplitude parameter in theexponential model (which would be the amplitude at TE0 ms).

DISCUSSION

In the experiments described above, extensive signalaveraging was performed to investigate a previouslyreported multicomponent T2* relaxation in WM of humanbrain (12). Using 40–50 averages, the SNR was sufficientto accurately observe small (<8%) deviations from singleexponential decay in various areas of WM on a singlevoxel level. The most pronounced deviations were foundat the shortest TE (2.7 ms). The deviations varied acrossWM and were different between major fiber bundlessuch as the corona radiata and optic radiation. The high-est amplitude of deviation was found in the posteriorpart of the SCC. This appears inconsistent with the find-ings of Hwang et al. (12), who concluded that the fastcomponent is almost uniform throughout the WM. Also,our values for the deviation at TE ¼ 2.7 ms are lowerthan those reported for the fast component in (12), inparticular for the 3 T SCC data: 5.4% found in this studyversus 13% reported in (11,12). The discrepancy withresults reported by Hwang et al. (11,12) may be partydue to the differences in processing. In this study, onlythe deviation from a mono-exponential model was con-sidered, without further filtering or processing. Hwanget al. used a nonlinear spatial filter that tends to elimi-nate contrast in areas that do not have sharp edges, andthey used a triple exponential model to fit their data.The high degree of interdependence of the exponentialfunctions (their nonorthogonallity) makes it hard toassign accurate amplitudes to the three decay functionsin such a model.

The three-compartment model with offset frequenciesappears to explain the data better than a model withoutthese, as shown in Appendix A. It should be noted thatfitting a model with eight parameters to a decay of 18echoes, with a limited range of TEs, is an inherently ill-conditioned problem. Fitting the model to single voxeldata did not produce stable and meaningful results,therefore only the ROI averaged signals in the SCC andthe GWM were analyzed with this model. For the samereason, the results of the 3 T fit were not very reliable.When comparing the 3 T and 7 T results in Fig. 4, itappears the short component is decaying slower at 3 T,which is reflected in both the decay rate and offset

FIG. 5. Results of a three-compartment model fit (Eq. 1) for the

same data as in Fig. 3a (SCC ROI), (a) data with the fitted model,(b) the residue, scaled up 1000 fold.

Table 1

Results of Multicompartment Model

B0 (T) ROI A1 R*2,1 (Hz) f1 (Hz) A2 R*2,2 (Hz) A3 R*2,3 (Hz) f3 (Hz)

7 SCC AV 0.130 159 35.8 0.776 36.5 0.094 22.8 7.0SD 0.020 12 2.9 0.018 1.0 0.011 6.4 0.7

7 GWM AV 0.077 169 31.8 0.809 36.0 0.114 10.8 5.9SD 0.009 11 3.3 0.008 1.4 0.011 2.01 0.7

3 SCC AV 0.054 92 19.4 0.946 21.2SD 0.019 10 2.6 0.019 0.7

The average (AV) and SD (over subjects) of multicompartment model parameters (Eq. 1 for 7 T and Eq. 2 for 3 T) fitted to the SCC ROIaveraged signal decays for two field strengths. The corresponding GWM data for 7 T are also shown.


frequency of the fitted results in Table 1. The suscepti-bility induced frequency offset and decay scale withfield strength, confirming a susceptibility related sourcefor the observed components reported in Table 1. Notethat the susceptibility induced frequency differences cancontribute to both a higher decay rate and an observableoffset frequency, depending on the homogeneity of thefrequency distribution in the compartment in question.The fact that the amplitude of the short componentappears lower at 3 T compared with 7 T may have sev-eral reasons: lower SNR, differences in T1 saturation anddifferences the separation between the short and maincomponents in the decay. The T1 tends to go up withfield strength, which means the 7 T had relatively moreT1 saturation than the 3 T experiments. This may be rele-vant if the main component of the GRE (T2*) decay is sat-urated more than the short component, due to differen-ces in their respective T1 relaxation rates, resulting in arelative enhancement of this short component. At 3 T,all the T1s are shorter, resulting in less saturation andless enhancement, hence, a lower relative signal ampli-tude for the short component at 3 T. The difference inseparation from the main component is related to theinfluence of the T2 on the GRE decay. The T2 does notchange much with field strength, while the susceptibilityinduced dephasing scales linear with field. As a conse-quence, the T2* of the main signal component is limitedby the T2 at 3 T, resulting in a less than linear scaling ofthe decay constants with field strength (see R*2;2 in Table1). This results in less separation between the short andmain components, which in turn, together with thelower SNR, makes the fitting of multiple componentsless reliable and could cause an underestimation of therelative amplitude of the short component at 3 T.

To investigate the possibility that microscopic mag-netic susceptibility variations indeed could underlie theobserved relaxation behavior, we simulated the signaldecay of spins surrounding a cylindrical susceptibilityperturber. The results suggest that the signal decay canbe distinctly different from mono-exponential behavior,as illustrated in Appendix B. Not enough detail is

known about the exact distribution of susceptibility sour-ces in brain tissue to create an accurate and realisticmodel, but this simulation shows it is at least plausiblethat the T2* decay is partly shaped by the susceptibilityvariations on a microscopic scale.

The dependence of amplitude of the short componenton fiber orientation with respect to the B0 field and theresulting strong contrast within the WM also support asusceptibility-related source, the effects being the strong-est in highly oriented fibers perpendicular to the mainfield (SCC), small in oriented fibers parallel with thefield (posterior internal capsule) and in between for amore mixed source (GWM). The GWM ROI contains amix of fibers types and orientations, which may explainthe results shown in Table 1. The fibers oriented parallelwith the magnetic field and those with a more randomorientation would not contribute to the fast component,whereas bundles with an orientation predominantly per-pendicular to the field may show a frequency effect simi-lar to the SCC, or perhaps a somewhat smaller effect ifthe local fibers have a different structure. Averagingthese various orientations together could result in theobserved lower amplitude and frequency for the shortcomponent in the GWM ROI. The susceptibility inducedfield changes in and around elongated structures in gen-eral have a sin2y dependence for their orientation withrespect to the main magnetic field (17), which can easilybe derived from the 2-fold rotation symmetry, meaningthe largest difference in orientation effects will be foundbetween parallel and perpendicular fibers. Although itcannot be proven to be the sole source of the observedsignal decay behavior, it appears likely that the micro-scopic susceptibility distribution is responsible for most,if not all, of the observed deviations from mono-expo-nential decay. It may be possible to exploit these effectsand use T2* based measurements to study the micro-scopic structure of brain tissue. T2* data are easier to ac-quire and could provide a higher spatial resolution thanalternative MR contrasts. It should be pointed out that itis not proven here that the short component is indeed amyelin water fraction; although this seems plausible,there maybe other sources of susceptibility associatedwith myelin that could produce similar results.

One obvious feature in the residue images (see Fig. 1)is a region in the anterior part of the brain that shows asmaller effect and generally a negative deviation from ex-ponential decay for the shorter TE. This negative devia-tion is likely related to macroscopic susceptibilityeffects, which are strongest in orbito-frontal areas. Com-parison with B0 field maps (not shown) indeed con-firmed that the areas of poor B0 homogeneity correspondto the darker areas for the short and long TEs in Fig. 1,and the brighter areas for the intermediate TEs. A calcu-lation based on the 2D phase map did show that shim-ming could explain a large part of the observed effects.The amplitude map of the fast component of the triple-exponential fit (Fig. 6) appears less sensitive to this prob-lem, which may be explained by the fact that the poor(macroscopic) B0 homogeneity primarily changes theslower component in the signal and not the amplitude ofthe fast one. Fitting a mono-exponential function asdone for Fig. 1 will result in a lower T2* in areas of poor

FIG. 6. Image showing the relative amplitude of the fast compo-nent of a triple-exponential fit on the right and the difference

between the data and a mono-exponential fit at TE 2.7 ms on theleft. The triple-exponential model was fitted with the relaxation

and frequency parameters fixed to the values found for the CCROI averaged signal, the image is scaled to reflect the amplitudeof the fast component at TE 2.7 ms.


B0 homogeneity, bringing the fit closer to the fast compo-nent and reducing the difference signal. Macroscopicsusceptibility effects can also give rise to a more quad-ratic exponential decay (17), which would influencemostly the later echoes. The triple-exponential modelcan account for that effect in the third component,whereas the mono-exponential fit would be adverselyaffected, contributing to the differences between Figs. 1and 6. A double exponential model with a linear andquadratic term in the second (and dominant) exponentresulted in a similar residue after fitting as the presentedtriple exponential model. Based on these data, it cannotbe determined which of these models is the best toexplain the deviation from exponential decay in the lon-ger TEs.

Fiber structure differences in the anterior and posteriorparts of the CC may explain some of the differences indeviation from exponential decay. Interestingly, the con-trast in the deviation map (as in Fig. 1) bears resem-blance to the contrast observed in a balanced SteadyState Free Precession (bSSFP) asymmetry study (22),including the difference between posterior and anteriorCC and orientation dependence. The frequency shiftsobserved in that study (20–25 Hz in the perpendicularCC fibers) appear somewhat higher than expected basedthe frequency of the fast component in the three com-partment fit of the 7 T data (36 Hz), assuming that thefrequency shifts scale with field strength. The deviationmaps from Fig. 1 also resemble the maps of the fastrelaxation water fraction in a cross-relaxation (MT) study[(9), Fig. 2], suggesting again that both methods are sen-sitive to the local fiber density.

A 3D multiecho experiment on a fixed section of braintissue containing the CC, WM, and some gray mattershowed an only very small deviation from mono-expo-nential T2* decay in all tissue types (less than 0.6%, datanot presented here). In contrast, a previous T2 study (23)found a preservation of a fast T2 component after fixa-tion. The short component reported there at 20 ms maybe too close to the main component in the T2* decay tobe observable as a separate fraction in T2* data.

A limitation of the implementation presented here isthe use of a single slice acquisition mode with a longtotal scan time due to the number of repetitions. Thismethod was chosen to maximize the achievable resolu-tion, SNR and stability of the scans. Single image acquis-itions were occasionally degraded by small motion arti-facts. Using a large number of repetitions and rejectingthe outliers from the average resulted in high qualitydata where the small deviations from exponential decaycould reliably be detected and analyzed. Some form of3D acquisition with motion correction (navigators, etc.)is likely of more practical value. This would alsoimprove the available phase information to possiblyallow for a correction of the macroscopic susceptibilityeffects (shimming).

CONCLUSIONS

Multigradient echo data obtained at 7 T suggest nonex-ponential T2* decay in WM fiber bundles. Multicompo-nent fitting of the decay characteristics confirm earlier

indications of the presence of a short component whoseamplitude and resonance frequency appeared to dependon fiber orientation relative to B0. This phenomenonmay be exploited to investigate the local myelin struc-ture and will need to be taken into account when esti-mating tissue myelin content from T2* data.

ACKNOWLEDGMENTS

The authors thank Dr. M. Fukunaga and Dr. T.Q. Li formaking their diffusion images available for this study.

APPENDIX A: MULTI-EXPONENTIAL MODEL WITHOUTFREQUENCY OFFSETS

Figure A1 shows the residual after fitting a triple-expo-nential model without frequency offsets to the 7 T CCROI averaged and normalized data. The residuals areaveraged over the eight subjects and the standard errorof the average is indicated with the error bars. Althoughthe differences are small (6 1%), they are highly signifi-cant, showing the model does not properly fit the data.The model fit including two offset frequencies Eq. [1]reduces the residue to noise, as shown in Fig. 5b. Theimprovement in the fitting is reflected in the adjusted R2

value: 1 � R2 ¼ 1.8 � 10�4 versus 1 � R2 ¼ 1.6 � 10�6.The R2 values are close to 1, because the signal is domi-nated by the intermediate (main) component, which isfitted well by both models.

APPENDIX B: SIMULATED DECAY FUNCTIONS IN THEPRESENCE OF SUSCEPTIBILITY INDUCEDINHOMOGENEITIES

To illustrate that the presence of susceptibility-inducedinhomogeneities can result in a nonexponential T2*decay, the field around a cylinder of higher susceptibil-ity was calculated and the resulting signal evolution as afunction of TE was simulated. Note this is not intendedto be an accurate model of human brain tissue, merelyan illustration of a mechanism that could contribute to anonexponential decay. Therefore, the simulation is of

FIG. A1. The residue of a ROI averaged decay curve (from the

splenium of the corpus callosum) fitted with a triple-exponentialmodel without frequency offsets.


unrealistic simplicity and lacks for example T2 and dif-fusion effects.

A uniform spin density was assumed outside of thecylinder and zero inside. The phase was calculated asproduct of the field strength and TE, after which thedecay curve was calculated as the complex sum over allpoints outside of the cylinder. The field of view (‘‘voxelsize’’) of the simulation was nine times the diameter ofthe cylinder. The field was calculated using a k-space fil-tering technique (24), assuming the cylinder axis to beperpendicular to the main magnetic field. A plot of theresulting decay is shown in Fig. B1a. A nonexponential,sinc-like behavior can be readily appreciated. In a simi-lar fashion, the decay in the presence of a closely packedset of hollow cylinders, filling the entire field of view,was calculated. The size of each cylinder was again 1/9th of the field of view. The result is shown in Fig. B1b.Again a nonexponential decay is observed, albeit with arather different temporal evolution than the signal inFig. B1a.

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FIG. B1. Simulations of the dephasing effects of the susceptibil-ity-induced field inhomogeneity around (a) one solid cylinder and

(b) in and around a bundle of hollow cylinders, all perpendicular tothe main field.


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Nonexponential T2* decay in white matter