Page 1

Magn Reson Mater Phy (2007) 20:143–155

DOI 10.1007/s10334-007-0076-0

RESEARCH ARTICLE

Estimation of metabolite T1relaxation times using tissue

specific analysis, signal averaging and bootstrapping from

magnetic resonance spectroscopic imaging data

H. Ratiney · S. M. Noworolski · M. Sdika ·

R. Srinivasan · R. G. Henry · S. J. Nelson ·

D. Pelletier

Received: 2 March 2007 / Revised: 20 April 2007 / Accepted: 26 April 2007 / Published online: 30 June 2007

© ESMRMB 2007

Abstract

Object A novel method of estimating metabolite T1relax-

ation times using MR spectroscopic imaging (MRSI) is pro-

posed. As opposed to conventional single-voxel metabolite

T1estimationmethods,thismethodinvestigatesregionaland

graymatter(GM)/whitematter(WM)differencesinmetabo-

lite T1by taking advantage of the spatial distribution infor-

mation provided by MRSI.

Materialandmethods Themethod,validatedbyMonteCarlo

studies, involves a voxel averaging to preserve the

GM/WM distribution, a non-linear least squares fit of the

metabolite T1andanestimationofitsstandarderrorbyboot-

strapping.ItwasappliedinvivotoestimatetheT1ofN-acetyl

compounds (NAA), choline, creatine and myo-inositol in

eight normal volunteers, at 1.5 T, using a short echo time

2D-MRSI slice located above the ventricles.

Results WM-T1,NAAwas significantly (P < 0.05) longer in

anterior regions compared to posterior regions of the brain.

The anterior region showed a trend of a longer WM T1com-

pared to GM for NAA, creatine and myo-Inositol. Lastly,

accounting for the bootstrapped standard error estimate in a

group mean T1calculation yielded a more accurate T1esti-

mation.

Conclusion

The method successfully measured in vivo

metaboliteT1usingMRSIandcannowbeappliedtodiseased

brain.

H. Ratiney · M. Sdika · D. Pelletier (B )

Department of Neurology, University of California,

185 Berry Street, Box 0946, San Francisco,

94107 CA, USA

e-mail: daniel.pelletier@ucsf.edu

S. M. Noworolski · R. Srinivasan · R. G. Henry · S. J. Nelson

Department of Radiology, University of California,

San Francisco, CA, USA

Keywords

T1estimation · Bootstrap · Monte Carlo simulation

MR spectroscopic imaging · Relaxation time

Introduction

Magnetic resonance imaging and spectroscopy is a power-

ful tool for non-invasively assessing anatomic and metabolic

changesthatoccurinbraindiseases.Inclinicalspectroscopic

studies and especially for magnetic resonance spectroscopic

imaging(MRSI)dataacquisition,shortrepetitiontimes(TR)

are often required to meet scan time constraints, but accu-

rate metabolite longitudinal relaxation time values (T1) are

then needed to correct the metabolite concentrations for the

T1-weighted effect. The metabolite T1values are likely to

be important for quantifying results that make comparisons

between patients and normal controls. Moreover, the knowl-

edge of1H metabolite longitudinal relaxation times can by

itself give insight into the properties of a given region of

interest.

In many previous studies, the estimations of the metabo-

liteT1swereperformedusingsinglevoxelacquisitions.Short

echo time spectra coming from either progressive saturation

[1–3]orinversionrecoveryexperiments[4–6]werecollected

and T1valueswereusuallyderivedfromamono-exponential

fit. The inversion recovery experiments typically used long

repetition times (TRs are usually equal to 6 s) with varying

inversion times [4–6], which is prohibitively long for MRSI

experiments. These single voxel approaches assume a single

T1over the whole voxel regardless of its tissue composition.

To obtain white matter or gray matter T1values and good

SNR, large (usually greater than or equal to 8 cc), and rela-

tively heterogeneous single voxels were typically acquired.

In most cases, gray matter (GM)-T1results were obtained

123

Page 2

144Magn Reson Mater Phy (2007) 20:143–155

from voxels containing 60–70% of GM, while white mat-

ter were obtained from voxels containing 70–90% of WM.

At the same time, different MRSI studies [7–10] using linear

regressiondemonstratedhowmetaboliteconcentrations(and

thus metabolite signal intensities) can be different according

to their tissue origin. Thus a common concern about the sin-

gle voxel studies is whether the content of GM and WM in

the examined voxel has an influence on the metabolite T1

results. Moreover attempting to reduce the size of the single

spectroscopic voxel to reduce the voxel tissue heterogeneity

would result in increasing the number of averages and the

scan time. In contrast, MRSI techniques offer the possibility

to acquire simultaneously several spectra over a wide brain

region and at a resolution allowing tissue analysis. The first

goal of this paper was, therefore, to develop a MRSI post-

processingmethodtoestimatemetabolite T1swhileaccount-

ing for the voxels’ tissue content. To date, no published

studies investigated the use of MRSI data to estimate

metabolite T1relaxation times.

Then,asforanyquantitativemeasurementbasedonmodel

fitting, an assessment of the precision of the T1estimation

is desirable. A benefit of MRSI is that it provides several

spectra and thus several data points for the metabolite T1fit

which can be resampled in a bootstrap manner to estimate

standard error. Therefore, a second goal of this study was to

develop an approach to obtain metabolite T1standard error

by bootstrapping.

The last contribution of the paper was to apply the new

techniquestomeasuremetaboliteT1sindifferentregionsand

tissues of the brains of healthy subjects.

The proposed method estimates metabolite T1relaxation

times by using 2D MRSI data at different repetition times.

The progressive saturation method was chosen instead of

inversionrecoverymethodforscantimeconcern.Whilecon-

ventional techniques spend time in averaging single voxel

acquisitions to obtain good SNR, we use this time to acquire

multi-voxel data and investigate regional and tissue specific

metabolite T1differences. The post-processing takes advan-

tage of the combination of segmented MRI and spatially dis-

tributed spectroscopic data to investigate either WM versus

GM metabolite T1values and/or regional differences in lon-

gitudinal relaxation times. The proposed method relies on

three major concepts:

1. Increasing the SNR by averaging voxels according to

their WM/GM content and their location (for example

anterior vs. posterior) since the SNR of the metabolite

signals is very low using the proposed acquisition para-

meters(numberofexcitations(NEX)andnumberofvox-

els in the slice) at 1.5 T.

2. EstimatingmetaboliteT1forgrayandwhitematterusing

a non-linear least squares algorithm. The underlying

model function used in the fitting procedure associates

WM/GM content of a voxel to the metabolite signal

intensity.

3. Using a bootstrap technique to assess uncertainty on the

metabolite T1s and taking into account this confidence

when calculating a group mean value.

This paper presents the techniques developed to utilize

MRSI data for metabolite T1measurement. A validation of

these techniques is then proposed through Monte Carlo data

simulations, demonstrating the statistical performance of the

proposed method. Finally the fitting procedure is applied to

2D conventional MRSI data acquired at 1.5 T from eight

healthy subjects.

MR data acquisitions

Study subjects

A total of eight healthy volunteers (five females and three

males, mean age 31.5±9.5years) were examined to validate

ourmethod.Writtenandinformedconsentwasobtainedfrom

all participating subjects. The study was approved by the

UCSF Committee on Human Research.

MR parameters

The healthy volunteers were scanned on a Signa 1.5 T clini-

cal imager from GE Medical Systems (GE Healthcare Tech-

nologies,Waukesha,WI,USA)usingaquadratureheadcoil.

Short echo time (TE = 35ms) 2D MRSI data sets (12×12,

1 cc resolution) were acquired using a PRESS volume selec-

tionatfivedifferentTRs(TE = 0.850,1,2,4,8s).Thenum-

ber of excitations (NEX) acquired were as follows: NEX=3

for TE = 0.850s, NEX=2 for TR = 1s, NEX=1 for

TR = 2,4and8s.ObliqueFastSpinEchoimageswereused

toguidethepositioningofthespectroscopicacquisition.Care

wastakenthatthePRESSboxavoidedtheventriclesandwas

centered in the anterior-posterior middle of the corpus callo-

sumbody. T1-weighted3Dspoiledgradientrecalled(SPGR)

images were also acquired for segmentation of the anatomic

images. The setup and data acquisition time for the anatomic

and spectroscopic imaging was approximately 55min.

Methods

The first goal of the analysis was the formulation of an

approach to estimate regional metabolite T1s in cortical gray

matter and white matter.

The model function

With the assumption made by several previous MRSI stud-

ies [7–9] of a linear relationship between the voxel WM/GM

123

Page 3

Magn Reson Mater Phy (2007) 20:143–155145

content and the metabolite peak signal intensity, we applied

thefollowingsimplifiedmodelforthemeasuredsignalinten-

sity S (for example S=signal amplitude of NAA) in the nth

MRSI voxel

Sn(TR) = pWM

n

SWM

0

SGM

0

f (TR,TWM

f (TR,TGM

1

)

+pGM

n

1

),

(1)

wherenrunsthroughallthevoxelsinagivenbrainregion(for

exampleanteriorandposterior). pWM

lated fraction of WM and GM, respectively within

the nth spectroscopic voxel, SWM

the signal intensity of a fully relaxed (TR ? 10s) reso-

nance pertaining to assumed pure WM and pure GM, f

is a function that characterizes the T1-weighting at a cer-

tain TR. We used the usual mono-exponential function [2],

f (TR,T1) = 1 − e−TR/T1. S denotes either a resonance

intensity corresponding to only a part of a metabolite or a

whole metabolite signal intensity depending on whether T1

values are assumed to differ between different parts of the

molecule. We then, for example, split the creatine signal into

two parts, assuming that the CH3singlet at 3.02ppm has a

different T1than the CH2singlet at 3.91ppm. Note that this

model does not necessarily require the WM and GM T1s to

be distinct, but rather relaxes the constraint of having only

one T1independent of the tissue type.

n

and pGM

n

arethecalcu-

0

and SGM

0

are respectively

The T1estimation procedure

Metabolite T1s are obtained after the following steps:

Step 1. Calculation of pWM

n

and pGM

n

To compute the fraction of WM and GM, pWM

of Eq. 1, for each spectroscopic voxel, the anatomic T1-

weightedimages(SPGR)weresegmentedintoGM,WMand

cerebrospinalfluid(CSF)

Automated Segmentation Tool, FAST [11]. Then these seg-

mentation masks were resampled using nearest neighbor

interpolation into the coordinate system of the T2-weighted

image used for the prescription of the spectroscopic grid.

The transformation used was calculated from the position

n

and pGM

n

compartments using the

and orientation of the T1and T2images, assuming there was

nomotionbetweenthescans.Finally,foreachvoxel,thefrac-

tionofWMandGMwithinavoxelwascomputedfromthese

segmentation masks by counting the number of WM or GM

pixels within a spectroscopic voxel. Thus, the WM and GM

proportionmapsareatthespectroscopicresolutionasshown

inFig.1.Thechemicalshiftdisplacementwasminimizedby

exciting a larger region than desired (using a larger PRESS

selectedvolumethanusual)andthenusingveryselectivesat-

uration (VSS) pulses to eliminate extra signals and to obtain

the final, desired selected region [12].

Step 2. Voxel averaging

At 1.5 T, the SNR (defined for example as the ratio of NAA

time-domain singlet amplitude to the standard deviation of

the time domain noise) of our acquisition was very low, typi-

cally between 1.5 and 2.8. Consequently the estimation of

the metabolite intensity S is not accurate. For each TR, we

proposed to generate Ngennew signals from the Ntotalorigi-

nal signals of the MRSI grid by averaging Navgchosen sig-

nals to increase the SNR. The Navgsignals are randomly

selected among the nearest neighbors of the voxel in terms

of WM/GM content to track the original WM/GM distribu-

tion while reaching a greater SNR. For each averaged sig-

nal k, the new fractions pWM

k

by averaging the fractions corresponding to the Navgchosen

signals, see Fig. 2. It is possible, with this technique to have

more voxels than originally, Ngen≥ Ntotalas we can draw

several sets of Navgvoxels for one original voxel. Figure 2b,

cshowtheSNRgainbetweentheoriginalinvivospectraand

the averaged spectra.

Notethattoperformregionalanalysis,thisaveragingpro-

cedure is applied on a specific part of the spectroscopic grid

(forexampleintheanteriorpartoftheslice)byworkingonly

with the voxels belonging to the region of interest.

and pGM

k

are also calculated

Step 3. Quantification of S

The signal intensity S of Eq. 1 has to be estimated for each

metabolite of interest, at each TR value, and for n running

Fig. 1 a Segmentation of the white matter, b Percentage of white matter at the spectroscopic resolution, c Segmentation of the gray matter, d

Percentageofgraymatteratthespectroscopicresolution,eExampleoforiginalspectracomingfromthefourhighlightedvoxelsTR = 1s,NEX=2,

SNRNAA≈ 2

123

Page 4

146Magn Reson Mater Phy (2007) 20:143–155

Fig. 2 a Graph showing the WM-GM percentage distribution of the original Ntotalvoxels (black) as well as the Ngenaveraged voxels. b Example

of four spectra coming from the original voxels (Navg= 0,SNRNAA≈ 2). c Example of four spectra coming from the averaged voxels (Navg=

6, SNRNAA≈ 4.4)

through all the Ngen averaged voxels. A quantification or

a peak picking method can be used as is done for single

voxelstudies.Weappliedthetime-domainalgorithmQUEST

[13] using a simulated basis set suitable to the acquisition.

In a preprocessing step, the residual water was eliminated

using the HLSVD method [14]. At 1.5 T, six metabolite

patterns were estimated: the whole metabolite pattern for

N-Acetyl compounds (NAAt = NAA + NAAG, mainly

located at 2.02ppm that we will call summarily NAA),

choline compounds (3.21ppm), glutamate (Glu, ∼2.3ppm),

and myo-Inositol (mI, ∼ 3.6ppm), and the two patterns

for creatine (Cr–CH3, 3.03ppm, Cr-CH2, 3.91ppm). The

metabolitesweresimulatedusingtheNMR-SCOPE[15]pro-

gram of the jMRUI software package [16]. The background

contamination coming from broad macromolecules, lipids

and surrounding broad pattern of metabolites of low concen-

tration were automatically modeled and taken into account

in the semi-parametric approach utilized in QUEST [17].

The T1s of the NAA singlet (T1,NAA), Cr–CH3(T1,Cr−CH3),

Cho (T1,Cho) and mI (T1,mI) were investigated. Note that the

T1of Cr–CH2was not estimated because of its poor signal

quality due to its proximity to the water in the spectrum. To

ensure the quality of the four-parameter fit, good quantifica-

tion results were selected prior to step 4. Voxel results were

selected following these two criteria:

1. estimated relative Cramér–Rao lower bound [18] of the

metabolite amplitude, (rCRB) < 15%.

2. metabolite peaks that had smaller than 9Hz linewidth at

half peak height.

After this selection, we have Nfinal,TRpoints at each TR for

the metabolite T1fit.

Step 4. Four-parameter fit

The four parameters SWM

fittedusinganon-linear leastsquaresalgorithm.Weusedthe

lsqnonlin method from the Optimization Toolbox of Matlab

0

, SGM

0

,TWM

1

,TGM

1

of Eq. 1 were

Fig. 3 Map showing an in vivo example of the four parameter fit for

NAAcompounds.Inthiscase?NTRNfinal,TR= 480datapoints(5TR,

96 points per TR) were available for the four parameters fit

(The MathWorks, Natick, MA, USA). See Fig. 3. If there

are Nfinal,TRselected results and there is a number NTRof

repetition times, one has?NTRNfinal,TR(usually 100–300)

data points to fit the four parameters.

Estimating metabolite T1uncertainties using bootstrap

Bootstrap is an empirical, non-parametric statistical tech-

nique based on data resampling. It is used to make statistical

inference such as the variance estimate of some fitted para-

meters. Although well-known and used in other MR modal-

ities such as fMRI [19] or diffusion tensor MRI [20], it has

rarely been applied, to our knowledge, to MRS parameters

[21]. This computer-based method relies on the drawing of

somebootstrap samples [22].Inour case, abootstrapsample

consists, for each TR, in a random sample of size Nfinal,TR,

say S∗

with replacement from the original data points Sj(TR). To

avoid some downward bias on the estimated standard error,

we applied a bootknife approach [23] which is a resampling

j(TR),1 ≤ j ≤ Nfinal,TR, where S∗

j(TR) is drawn

123

Page 5

Magn Reson Mater Phy (2007) 20:143–155147

Fig. 4 The bootstrap algorithm

adapted from [22] for estimating

standard error of metabolite T1;

The T1estimate is fitted from

the original sample and can be

either WM or GM T1. The

bootstrap replicationsˆTb

b=1 ... B, are used to calculate

its standard error estimate (SE).

B is usually between 25 and 200

1,

techniquecombiningthefeaturesofjackknifeandbootstrap.

For each TR, one point is first randomly omitted from the

original sample of size Nfinal,TR(jacknife), then, from the

remaining sample with size Nfinal−1, a bootstrap sample of

size Nfinal,TRwith replacement (bootstrap) is drawn. This is

done at each TR and the four parameter fitting procedure is

then applied to the bootknife samples to obtain aˆTWM

ˆTGM

1

we used B = 200), see Fig. 4, and a standard error (SE) can

be estimated as follows:

⎛

⎝

where ¯T1 is the mean value of the estimates over the B

bootknife samples and ˆTb

replication) fitted from the bth bootknife sample set.

To take into account the confidence in the T1value esti-

mation from a subject when calculating the mean T1value

over a group of subjects, we proposed using the estimated

standard errors in a weighted average calculated as

follows:

1

and a

replications. This operation is done B times (typically

? SET1=

⎜

?B

b=1

?

B − 1

ˆTb

1−¯T1

?2

⎞

⎠

⎟

1/2

,

(2)

1is the bth estimation of T1(or

Weighted sample mean:

T∗

1=

?nbofscans

i=1

i=1

?nbofscans

wiTi

1

wi

with wi=

1

? SE2

i

,

(3)

where nbofscans corresponds to the number of subjects

scanned in the study and contributing to the group mean

value.

The corresponding individual standard deviation of this

mean value is estimated with:

stdev(Ti

1)=

?

?

?

?

?

?nbofscans

i=1

i=1

(Ti

1−T∗

wi−

1)2∗ wi

?nbofscans

i=1

?nbofscans

i=1

w2

i

?nbofscans

wi

with wi=

1

? SE2

i

,

(4)

where Ti

jecti,? SEiisthebootstrapestimateofthestandarderrorofthe

used in the proposed method for the case of noisy signals.

1is the estimated T1for a given metabolite and sub-

T1estimationforthesubjecti.Figure5summarizesthesteps

123

Page 6

148Magn Reson Mater Phy (2007) 20:143–155

Fig. 5 Scheme of the proposed procedure for a metabolite T1fitting

where “SE” stands for bootstrap standard error estimates

Monte carlo simulations

Simulations were conducted to validate the method. The

bias and standard deviation of metabolite T1estimates were

determined using Monte Carlo studies for different Navg,

with or without a macromolecular background contamina-

tion. We show the ability of the bootstrap technique to esti-

mate the metabolite T1standard error. We used previously

describedMRSIdatasimulationprograms[24].Inthissimu-

lationtechnique,aMRSIk-spaceisgeneratedbyperforming

theproductofthek-spacedistributionofagivenobjectandits

correspondingspectroscopicsignal.TheeffectofthePRESS

box selection is also taken into account. For our simula-

tions, one object for WM and one for GM were generated

and the results summed. A short echo time signal contain-

ing NAA, choline, creatine, Glu, and mI was created for

each TR and each WM or GM object. A background sig-

nal reproducing the effect of macromolecular contamination

intheshortechotimesignalandmimicking,inthemetabolite

region, the macromolecule baseline signal found in [3] was

also added to the signal. The metabolite relative amplitudes,

T1, SNR and the background components that were used in

the Monte Carlo studies are summarized in Table 1. Without

noise, for one voxel with a certain WM/GM content and one

TR,thesimulatedmetabolitesignalamplitudewassetexactly

toEq.1.WhiteGaussiandistributednoisesignalswereadded

to each noise-free signal of the simulated MRSI grid. These

steps were repeated to obtain a total of NMC = 100 noisy

MRSI sets of signals. Metabolite T1values were obtained

using the proposed method for those 100 realizations. For

each metabolite, we obtained a gold standard SE (standard

error)on T1bycalculatingthestandarddeviationofallofthe

T1estimations. This gold standard SE was compared to the

mean value of the standard errors calculated by the proposed

bootstrap approach for each realization.

Study 1: Effects of averaging

In the first Monte Carlo study, we evaluated the statistical

performance of the method in terms of bias and standard

deviation for SNR = 2 along with an increasing number of

voxels in an average, Navg= 2, 4 and 6, and the macromole-

cular background signal (see Table 1) added to the simulated

short echo time signals. For each TR, Ngen= 120 voxels are

created by the proposed averaging method from the origi-

nal MRSI grid. We also tested our method in the case of no

averaging. In this case, designated by Navg= 0, only the 48

voxels (Ngen = Ntotal) in the MRSI grid contribute to the

fitting method.

Study 2: Macromolecular background effect

We tested the macromolecular background effect on the T1

estimation in the second Monte Carlo study. We compared

the statistical results obtained with Navg= 6 with and with-

out a macromolecule signal in the simulation. The weighted

average using the bootstrapped standard error estimation is

tested in these two cases.

Results

Monte Carlo studies

Results of the Monte Carlo simulation are shown in Figs. 6,

7 and Table 2. SE, bootstrap estimates of the SE and bias are

expressed as a percentage of the true T1value.

Study1: Effects of averaging

Figure 6 shows the mean and the standard deviation of the

bootstrap estimates, as well as the gold standard of the SE

for each metabolite, for a range of Navg,SNRNAAequals 2,

and the set of 5 TRs. (*) indicates cases where the bootstrap

estimate is biased by more than 100 % from the actual value.

123

Page 7

Magn Reson Mater Phy (2007) 20:143–155149

Table 1 Parameters used in the Monte Carlo simulation studies

WMGM

Metabolite Concentration

(a.u.)

T1(s)SNR at

TR = 8s

Concentration

(a.u.)

T1(s) SNR at

TR = 8s

NAA singlet (3 equivalent protons)

Cho (9 equivalent protons)

Cr–CH3(3 equivalent protons)

mI

Glu (T1not estimated)

7.5

1.8

5.2

3.8

7

1.55

1.2

1.3

1.1

1.3

2

1.44

1.39

0.91 (at 3.56ppm)

/

9

1.5

7.7

5

9

1.45

1.2

1.4

1.1

1.3

2

1

1.71

0.99

/

Background signalWM/GM

a

ω (ppm) SNR at TR = 8s

Nine gaussian components, time domain model:

?9

2.51.88 0.21

i=1aiexp(jωt)exp(−β2t2)T1= 0.2s

and β =50Hz for all the components

15

2.5

2.5

2.5

10

5

5

10

2.08

2.39

2.55

2.71

3.09

3.5

3.66

3.91

1.29

0.86

0.43

The macromolecular background components were chosen to make the background signal resemble the patterns shown in Ref. [3]

a.u. arbitrary unit, WM white matter, GM gray matter

For the four metabolites of interest (NAA, Cr–CH3, Cho,

mI), higher SE were found in the GM than in WM consis-

tent with the discrepancy between the number of GM voxels

versus the number of WM voxels available in the masks we

used in the simulation. The SE globally decreases with the

number of voxels used in an average Navg. For Navg= 6, the

gold standard SE is below 20% of the true T1for NAA, Cho

and Cre in the WM.

Fig. 6 From Monte Carlo simulations, gold standard standard errors

of metabolite T1s compared against standard errors estimated by the

bootstrap technique with varying numbers of voxels used for sig-

nal averaging Navg. The sign (*) indicates cases where the standard

deviation of the bootstrap estimate is larger than its mean value or

where the bootstrap estimate is biased by more than 100% from the

actual value. Note the general decrease of the SE with Navg

123

Page 8

150Magn Reson Mater Phy (2007) 20:143–155

Fig. 7 The bias (b) on metabolite T1and the bias for a weighted average (bw) calculated with Eq. 3. b and bware displayed as percentage of the

true metabolite T1value

Table 2 From Monte Carlo simulations (NMC= 100), gold standard standard errors (SE), standard error (SEw) corresponding to the weighted

average and calculated with Eq. 4, bias (b) and bias for a weighted average (bw) calculated with Eq. 3

MetaboliteSE (%) SEw(%)

b (%)

bw(%)

w/o

w/w/o

w/ w/o

w/w/o

w/

NAA-WM

NAA-GM

tCho-WM

tCho-GM

tCr-WM

tCr-GM

mI-WM

mI-GM

7.51

9.28

12.14

25.44

12.84

14.83

14.57

25.18

12.84

17.65

14.99

42.47

14.08

18.38

34.25

59.20

6.94

9.12

10.18

24.60

12.06

13.46

13.51

20.95

11.58

15.96

14.97

37.31

13.32

17.28

30.14

42.59

1.96

1.95

1.83

6.21

2.31

2.74

2.63

3.97

5.33

0.82

−5.26

13.82

−8.04

−3.01

9.95

15.30

0.54

2.02

0.14

3.37

1.93

−0.70

0.93

−1.50

0.41

0.73

−8.20

9.74

−7.63

−6.83

3.26

−1.75

Results shown with (“w/”) and without (“w/o”) a background contamination, SNRNAA= 2, Navg= 6

For all of the considered metabolites in the WM and the

GM and for Navg ≥ 4, the SE estimated by the bootstrap

techniquewaswithin50%oftheactualSEvalue.Lessbiased

bootstrap estimates were generally obtained for Navg = 2

and the bias between the bootstrap estimates and the actual

SEvalueincreasedwith Navg.FormI,thebootstrapapproach

successfullyestimatedtheSEwithalargestandarddeviation

in the WM and only for Navg= 6 in the GM. For Navg= 0,

the bootstrap estimates have reasonable values in WM for

NAA, Cho and Cre and failed to estimate the SE in the other

cases.

Figure7showsthebias(denotedbyb)onT1valuesforthe

fourmetabolitesofinterestandforaweightedaveragecalcu-

lated by Eq. 3 and denoted by bw. b and bware displayed as

percentages of the true metabolite T1value. For (WM/GM)-

T1,NAA (WM/GM)-T1,Cr−CH3 and WM-T1,Cho the bias is

below ±10% of the true T1value. We note that, in the case

of our simulation, increasing the Navgdid not reduce the

bias for WM-T1,Cr−CH3. As seen in the next study, we think

that this bias is more due to the interaction with the macro-

molecules than to a lack of SNR. Increasing Navg seems

to reduce the bias for (WM/GM) T1,NAA, GM-T1,Cho,

GM-T1,Cre, and (WM/GM) T1,mI. For WM and GM-T1,mI,

theweightedaveragemakesthebiasbelow10%oftheactual

value for Navg≥ 2.

The best bias and standard deviation trade-off is obtained

for Navg = 6 at the expense of slightly biased bootstrap

estimates.

123

Page 9

Magn Reson Mater Phy (2007) 20:143–155151

Study 2: Macromolecular background effect

Table 2 shows the statistical results (regular SE, SEwcalcu-

lated with Eq. 4, b and bw) of the T1estimation procedure

for Navg = 6, SNR = 2, with and without a background

contamination in the signals to process. All the metabolite

T1estimations show the same trend with a larger standard

deviation and a bigger bias in the case of macromolecular

contamination as compared to the absence of a background

signal. In the absence of a macromolecular background, the

weighted average that takes into account the bootstrapped

standarderrorsuccessfullyreduces thebias(bwascompared

to b) on the metabolite T1.

Inthepresenceofthesimulatedbackgroundsignal,theSE

oftheT1estimateincreasedby10%(forWM-T1,Cr−CH3)and

more than doubled for the T1,mI. The bias was also affected

(but usually reduced) by using a weighted average. The GM-

T1,Cr−CH3and WM-T1,Choestimation were more downward

biased in the presence of a background signal when using a

weighted average than when using the standard mean calcu-

lation.

Metabolite T1estimation on in vivo data

For the eight subjects, the anterior–posterior center of the

PRESS Box (12 × 12, 1 cc) was centered in the anterior–

posterior middle of the corpus callosum body visualized in

a sagittal plane. Voxels anterior to the center of the PRESS

Box were analyzed as part of the anterior brain region (Ant.)

and the rest of the voxels were evaluated as posterior voxels

(Post.).

The bootstrap estimate of standard error on in vivo data

Figure 8 shows, for each subject of the study, a histogram

of B = 200 bootstrap replications of ˆTWM

in the posterior part of the PRESS box. For each subject

i(i = 1,..., 8), these replications are used to estimate stan-

dard error SEi. In this example, subject 3 presents a small

standard error and thus will have a larger weighting in the

proposed weighted average in Eq. 3 while the results from

subject 2 or 5 will have smaller weighting due to their big-

ger bootstrap estimated standard error. This bootstrap stan-

dard error estimate gives good insight about the reliability

of the fitted metabolite T1. In the case of subject 8, the boot-

straphistogramrevealsapeakquitedistinctfromtheaverage

whenfittingˆTWM

indicates the estimated T1when all the selected voxels are

considered while the bootstrap histogram is calculated with

the bootknife approach that randomly removes one voxel at

eachcalculation.Therefore,thiscaseshowsthatsomevoxels

were essential in determining the T1.

1,NAAcalculated

1,NAAfromtheselectedvoxels.Thedottedline

Fig. 8 Histograms of B = 200 bootstrap replications of WM-T1,NAA,

calculatedfrominvivodata(posteriorregion)ofeighthealthysubjects.

A broken line is drawn at the parameter T1estimate

Anterior versus posterior metabolite T1

The estimated in vivo T1relaxation times (mean±SD) for

“pure” WM and “pure” GM at 1.5 T for Navg= 6 and com-

puted from the anterior region (Ant.) or from the posterior

region (Post.) are given in Table 3. These results are cal-

culated with Eqs. 3 and 4 using the bootstrap standard error

estimatesandaregivenasweightedmeans±thecorrespond-

ing standard deviations. For statistical analysis, a two-tailed

paired t-test was used. See Appendix.

The standard deviation in the GM was larger than in the

WM,formostofthetime,asintheMonteCarlosimulations.

From these results, no significant differences were found in

metabolite T1sbetweenGMandWMintheposteriorregion.

In anterior region WM-T1,NAA, WM-T1,Cr−CH3, and WM-

T1,mItend to be higher than GM-T1s but this trend did not

reach statistical significance (0.1 < P < 0.2). The T1of

NAA in the anterior part of the WM was significantly longer

than in the posterior part of the WM (P < 0.05).

123

Page 10

152 Magn Reson Mater Phy (2007) 20:143–155

Table 3 From eight healthy volunteers, estimated T1-relaxation times

(in seconds) of NAA, Cho, Cr–CH3, mI at 1.5 T, in pure WM and pure

GM, using MRSI data, (Navg= 6)

Metabolite

T1, Navg= 6

Ant. Post.

NAA

WM

GM

Cho

WM

GM

Cr–CH3

WM

GM

mI

WM

GM

1.38 ± 0.15

1.23 ± 0.36

1.28 ± 0.10**

1.31 ± 0.20

1.20 ± 0.13

1.18 ± 0.20

1.20 ± 0.05

1.20 ± 0.10

1.26 ± 0.09

1.19 ± 0.12

1.23 ± 0.08

1.22 ± 0.06

1.29 ± 0.09

1.19 ± 0.12

1.23 ± 0.10

1.22 ± 0.09

Note the anterior and posterior difference (P < 0.05) found with a

paired t-test in NAA T1in the WM as well as a trend, not statistically

significant, of a WM/GM difference for NAA, Cr–CH3and mI T1in

the anterior part

** Anterior WM- T1> posterior WM T1with P < 0.05

Discussion

This work presents a novel method for estimating metabo-

lite T1s using MRSI data, enabling estimates within tissue

types (GM and WM) and across different regions (anterior

and posterior were demonstrated here). The smaller voxel

size of the MRSI data versus previous single voxel studies

partially addresses the issue of large partial volume artifacts

between gray matter and white matter. Additionally, incor-

porating the information regarding tissue type composition

obtainedfromhigherresolutionMRimagesandthemultiple

voxel data obtained with MRSI allows better correction of

partial volume artifacts than possible with the previous sin-

gle voxel data. This method has been validated and tested on

simulations and applied in vivo. We also proposed assessing

a confidence interval in the fitted T1results by introducing a

bootstrapapproach.Weshowedthataweightingaveragethat

takes into account the confidence assessment can reduce the

bias on the estimated T1value for a metabolite with a small

SNR. This method relies upon a group mean metabolite T1

approach. The proposed algorithm yielded results that are in

agreement with the literature and support the hypothesis of

regional differences in T1in the brain.

Methodology

The important parameters in the proposed method are the

SNRoftheconsidered metabolitesignal,thenumber ofvox-

els used in an average, Navg, and the number of available,

mostly GM or mostly WM voxels in the MRSI grid.

1. The SNR, as expected, appeared to clearly play a role

bothonthebiasandthestandarddeviationofthe T1esti-

mation. In Figs 6 and 7 the results for NAA and Cr-CH3

which have the greatest SNR in our simulation, present

good biases and standard deviations on T1estimation

comparedtotheonesforCho(especiallyinGM)andmI.

In order to realize a robust four-parameter fit with low

SNR, non-reliable voxel quantification results should be

rejected from the analysis. The use of criteria, such as

Cramér-Rao lower bounds [18] or linewidth thresholds,

is necessary to determine the quality of the metabolite

amplitude quantification and to perform voxel selection.

2. Increasingthenumberofvoxelsusedinanaverage Navg,

improves SNR and so typically reduces both bias and

standard deviation. Note that, by averaging the voxels,

theindependencebetweentheaveragedvoxelsisreduced

and the bootstrap technique can tend to underestimate

the real standard error. Also note that this averaging is

performedwhiletakingintoaccounttheWM-GMdistri-

bution and the introduced dependence tracks the initial

tissue content. It was also shown by the Monte Carlo

simulation results that, for an original SNR of two, the

use of six voxels in an average corresponds to a good

trade-off between the SNR gain and the lost of voxel

independence and leads to reliable metabolite T1esti-

mations. Furthermore, this voxel averaging introduces

some partial voluming with CSF to the generated vox-

els, especially for mostly GM voxels originating from

the thin cortical ribbon at the midline. Nevertheless, as

the percentage of GM and WM (and thus, CSF) in the

voxel are explicitly taken into account during the fitting

procedure, the regression presented in Eq. 1 enables a

correction of this partial voluming effect.

3. The number of voxels available for a specific tissue type

influences the standard deviation of the T1estimation.

Consequently, the dispersion of the results is larger for

theGMthanfortheWMvaluesfrombothoursimulation

and the in vivo data.

ThefirstMonteCarlosimulationsshowedthatforanorig-

inal SNRNAAof 2 in the MRSI data, an almost unbiased

estimation of the T1,NAA, T1,Cho, T1,Cr−CH3is possible. A

weightedaverage,takingintoaccountthebootstrapestimates

of the uncertainty on T1could also yield to an unbiased esti-

mationof T1,mI.Thisapproachtendstoreducethedispersion

due to bad data points and makes a group mean value more

accurate.

We conclude from the second Monte Carlo study that

the presence of a macromolecular background signal has an

important effect on the dispersion and the bias of the results

123

Page 11

Magn Reson Mater Phy (2007) 20:143–155153

andshouldbeconsideredasanothereffect,besidesthesetand

number of TRs and the type and parameters of the sequence

used [25], leading to the discrepancy between the different

published T1values.Thebootstrappedstandarderrorestima-

tion is also hampered by the macromolecular contribution.

Intheproposedsimulation,allthevoxelswerecontaminated

inthesamewayandthebackground signalwasarbitraryand

particularly elevated under the mI making its T1estimation

harder.

Finally, the proposed bootstrap procedure is a novel

method to estimate metabolite T1 standard error and is

enabled in this study by the use of MRSI data. The bootstrap

technique is a non-parametric method that does not require

a complex implementation. This approach may be benefi-

cial in future uncertainty and/or bias estimation studies of

spectroscopic quantification.

In vivo results

The range of our results for the four metabolites is in good

agreement with existing literature [1–4], when using the

weighted average and Navg= 6. The method gives reliable

results,foranoriginalSNRaround2,whenprocessingequiv-

alent 6 cc voxels, which corresponds to an SNR around 4.9

for NAA. Voxel averaging combined with the quantification

procedure, which constrained the additional damping fac-

tor allowed for each metabolite, was required to achieve the

accuracy of the results.

We found significantly greater WM-T1,NAAvalues in the

anterior (frontal) part (1.38 ± 0.15, mean ± SD) than in the

posterior part of the slice(1.28± 0.10),but wewere not able

to see this result for the GM or for the other metabolites.

Brief et al. [1] also reported similar results between WM

frontal (1.59 ± 0.10), and WM parietal (1.35) regions. In

the literature, WM-T1,NAAvalues can differ to some extent.

Our anterior WM T1,NAAis lower than the one reported by

Brief et al. or Kreis et al. [3] (1.88 ± 0.09), but still higher

than others, as for example the value reported by Ethofer [2]

(1.19±0.09 in the fronto-parietal region). This discrepancy

maybepartlyduetothewaythemacromolecularbackground

signal was fitted.

The effect of regional variation in metabolite T1values

may be necessary to take into account in the estimated

metabolite concentration, depending on the ratio of TR/T1

used, on the ratio of the regional T1s, and on the accuracy of

the metabolite amplitude estimation. In our study, a regional

T1variation for NAA of 7.8% would result in a difference

of only 5% in the NAA signal amplitude for a short TR of

1 s. Considering the biological variability and the accuracy

achievable for the NAA signal amplitude estimation, this

difference mightbenegligible foraconcentration estimation

point of view. In the case of healthy versus diseased brain,

the metabolite T1difference may be larger than 7%. The

measured NAA signal amplitudes could have important dif-

ferences (greater than 5%), due solely to the T1variation and

not to a tissue concentration difference. Conversely, the T1

differences could mask the concentration changes due to the

disease. Of course, when the repetition time exceeds three

expected T1(TR > 3T1), the difference in regional T1can

range from 0 to as much as 50%, and the difference (due

to the T1weight) in metabolite signal amplitude will remain

below5%oftheactualconcentrationvalue.Thentheregional

T1variation will have effectively no effect on the estimated

concentrations. In practice, the use of a long TR increases

scan time, especially for MRSI acquisition and is therefore

avoided.

The T1value found for NAA in the WM of the posterior

part of the slice (1.28 ± 0.10) is close to the values reported

by Rutgers et al. [5,26] (1.30 ± 0.14) in the centrum semi-

ovale.TheT1relaxationtimesfoundfortheothermetabolites

Cho,CrandmI,arealsoessentiallythesameasotherreported

values [2,5,26].

Especially in gray matter, where the glutamate signal is

higher, the macromolecular signal, the NAA and the gluta-

mate signals and some contribution from metabolite present

at low concentration such as GABA are unknowingly entan-

gled at 2ppm. Moreover, the amount of macromolecule sig-

nal compared to the metabolite signal differs at each TR,

as macromolecules have a shorter T1than metabolites. As

a consequence, the variability of the quantification results

increases. We think that the higher standard error found for

theGM-T1,NAAispartlyduetothisvariabilityandpartlydue

to the few number of available gray matter voxels.

Wealsoobserved withoutreaching statisticalsignificance

that, as opposed to water T1, the T1for NAA, Cr–CH3and

mI could be greater in the white matter than in the gray mat-

ter in the anterior part while no difference was seen in the

posterior part. Although a difference of WM/GM voxel dis-

tribution in the anterior and posterior regions (see Fig. 1)

might have influenced this result, this observation supports

theassumptionofdifferentunderlyingmechanismsforwater

and metabolite relaxation times. While tissue composition

and difference in anisotropy may be involved in water T1

relaxation process, the intra-cellular metabolite T1, may be

more dependent, as suggested by Ethofer et al., on micro-

structural characteristics and viscosity properties.

Conclusion

Brain metabolite T1measurements were calculated using a

novel MRSI voxel averaging and bootstrapping approach.

The proposed method takes advantage of the multi-voxel

acquisition provided by MRSI and enables the investigation

of regional variations in metabolite T1values. It also intro-

ducesabootstraptechniqueforestimatingastandarderroron

123

Page 12

154Magn Reson Mater Phy (2007) 20:143–155

metabolite T1s. Significant differences were found between

anterior WM-T1,NAAand posterior WM-T,1,NAA. This result

emphasizes the need to take into account tissue and regional

T1differences in MRSI metabolite quantification. Finally,

the method only requires a multi-WM/GM voxel acquisition

and is not restricted to short echo time 2D MRSI acquisi-

tion. The presence of a macromolecular background made

the metabolite T1estimation less accurate and substantially

increased the dispersion. The principle of the method can be

applied and extended to other field strengths (to increase the

SNR) or to other types of data acquisition that present less

macromolecular contamination such as TE-averaging [27],

longerTEacquisitionortousinglocalizationinathirdspatial

dimension (3D-CSI).

Acknowledgements

Residence of Radiology and Biostatistics at UCSF, for his expert assis-

tance in the statistical aspects of this project and are grateful to Sung

Won Chung and Yan Li for helpful discussions. This study was sup-

ported in part by Research Grant RG-3517A2 from the National Mul-

tiple Sclerosis Society (PI: Daniel Pelletier). Dr. Daniel Pelletier is a

recipient of the Harry Weaver Neuroscholar Award from the National

Multiple Sclerosis Society (JF-2122-A).

We thank Dr. Ying Lu, Associate Professor in

Appendix

Paired t-test in the case of weighted combinations

To compare the WM versus GM, or anterior versus posterior

metabolite T1s, we used a paired t-test analysis that took

into account the uncertainties estimated by bootstrapping.

To perform the statistical analysis, we modified the usual

paired t-test with the following steps:

1. Calculate the weighted sample mean of the variable

“difference”

⎧

⎪⎪⎪⎪⎩

X1,iand X2,iareeithertheestimated T1intheWMversus

in the GM or the estimated T1in the anterior region versus

in the posterior region for a given metabolite.

wishouldreflecttheconfidenceinthedifferencevalueand

is set to the inverse of the bootstrap estimate of the variance

of di.

For comparisons between WM and GM T1values:

1

? SE2

the same set of data, they can be correlated and the covari-

ance between the two variables has to be taken into account.

d∗=

?n

i=1widi

?n

i=1wi

where

⎪⎪⎪⎪⎨

di= X1,i− X2,i

wi=

? SE2

1

di

n = number of experiments (scans)

,

wi=

X1,i+? SE2

X2,i− 2c? ov(X1,i, X2,i).

Indeed, as WM and GM T1 values were estimated on

? SE2

anterior versus WM posterior T1, we assume no correlation

(cov(X1,i, X2,i) = 0) as the values are calculated from a

different data set.

2. Calculate the standard error of the weighted sample

mean

?

i=1wi

3. Get the current value of the statistic t and its degree of

freedom ν

t =d∗− 0

X1,i,? SE2

X2,i,c? ov(X1,i, X2,i) are estimated using the pro-

posed bootstrap approach. For comparison between WM

SEd∗ =

?

?

?

?n

i=1(di− d∗)2∗ w2

??n

i

?2−?n

i=1w2

i

.

SEd∗,

Note that if wi= 1 for i = 1,..,n, we retrieve the usual

t statistic with ν = n − 1.

4. Determine the two-tailed P value from the Student’s t

cumulative distribution function f (t,ν)

ν =

?n

i=1wi−

?n

i=1w2

?n

i

i=1wi

.

P = 2 ∗ (1 − f (|t|,ν)).

References

1. Brief EE, Whittall KP, Li DK, MacKay A (2003) Proton T1 relax-

ation times of cerebral metabolites differ within and between

regions of normal human brain. NMR Biomed 16:503–509

2. EthoferT,MaderI,SeegerU,HelmsG,ErbM,GroddW,Ludolph

A, Klose U (2003) Comparison of longitudinal metabolite relax-

ation times in different regions of the human brain at 1.5 and 3

Tesla. Magn Reson Med 50:1296–1301

3. KreisR,SlotboomJ,HofmannL,BoeschC (2005) Integrateddata

acquisitionandprocessingtodeterminemetabolitecontents,relax-

ation times, and macromolecule baseline in single examinations of

individual subjects. Magn Reson Med 54:761–768

4. Mlynarik V, van der Gruber S, Moser E (2001) Proton T (1) and

T (2) relaxation times of human brain metabolites at 3 Tesla. NMR

Biomed 14:325–331

5. Rutgers DR, van der Grond J (2002) Relaxation times of choline,

creatine and N-acetyl aspartate in human cerebral white matter at

1.5 T. NMR Biomed 15:215–221

6. Traber F, Block W, Lamerichs R, Gieseke J, Schild HH (2004) 1H

metabolite relaxation times at 3.0 tesla: measurements of T1 and

T2valuesinnormalbrainanddeterminationofregionaldifferences

in transverse relaxation. J Magn Reson Imaging 19:537–545

7. Hetherington HP, Mason GF, Pan JW, Ponder SL, Vaughan JT,

Twieg DB, Pohost GM (1994) Evaluation of cerebral gray and

white matter metabolite differences by spectroscopic imaging at

4.1 T. Magn Reson Med 32:565–571

8. Maudsley AA, Darkazanli A, Alger JR, Hall LO, Schuff N,

Studholme C, Yu Y, Ebel A, Frew A, Goldgof D, Gu Y, Pagare R,

Rousseau F, Sivasankaran K, Soher BJ, Weber P, Young K, Zhu

X (2006) Comprehensive processing, display and analysis for in

vivo MR spectroscopic imaging. NMR Biomed 19:492–503

9. Noworolski SM, Nelson SJ, Henry RG, Day MR, Wald LL,

Star-Lack J,Vigneron DB (1999) High

1H-MRSI and segmented MRI of cortical gray matter and

subcortical whitematterinthree regionsof thehuman brain.Magn

Reson Med 41:21–29

spatial resolution

123

Page 13

Magn Reson Mater Phy (2007) 20:143–155155

10. Schuff N, Ezekiel F, Gamst AC, Amend DL, Capizzano AA,

Maudsley AA, Weiner MW (2001) Region and tissue differences

ofmetabolitesinnormallyagedbrainusingmultislice1Hmagnetic

resonance spectroscopic imaging, pp 899–907

11. Zhang YMB, Smith S (2001) Segmentation of brain MR images

through a hidden Markov random field model and the expectation

maximization algorithm. IEEE Trans Med Imaging 20(1):45–57

12. Tran TK, Vigneron DB, Sailasuta N, Tropp J, Le Roux P,

Kurhanewicz J, Nelson S, Hurd R (2000) Very selective suppres-

sion pulses for clinical MRSI studies of brain and prostate cancer,

pp 23–33

13. Ratiney H, Sdika M, Coenradie Y, Cavassila S, van Ormondt D,

Graveron-Demilly D (2005) Time-domain semi-parametric esti-

mation based on a metabolite basis set. NMR Biomed 18:1–13

14. Pijnappel WWF, van den Boogaart A, de Beer R, van Ormondt

D (1992) SVD-basedquantificationofmagneticresonancesignals.

J Magn Reson 97(1):122–134

15. Graveron-Demilly DAD, Briguet A, Fenet B (1993) Product-

operator algebra for strongly coupled spin systems. J Magn Reson

Ser A 101(3):233–239

16. NaressiA,CouturierC,DevosJM,JanssenM,MangeatC, deBeer

R, Graveron-Demilly D (2001) Java-based graphical user inter-

face for the MRUI quantitation package. Magn Reson Mater Phy

12:141–152

17. Ratiney H, Coenradie Y, Cavassila S, van Ormondt D, Graveron-

Demilly D (2004) Time-domain quantitation of 1H short echo-

timesignals:backgroundaccommodation.MagnResonMaterPhy

16(6):284–296

18. Cavassila S, Deval S, Huegen C, van Ormondt D, Graveron-

Demilly D (2001) Cramer-Rao bounds: an evaluation tool for

quantitation. NMR Biomed 14:278–283

19. Auffermann WF, Ngan SC, Hu X (2002) Cluster significance test-

ing using the bootstrap. Neuroimage 17:583–591

20. Chung S, Lu Y, Henry RG (2006) Comparison of bootstrap

approaches for estimation of uncertainties of DTI parameters.

Neuroimage 24(2):531–541

21. Bolan PJAW, Henry P-G, Garwood M (2004) Feasibility of

computer-intensive methods for estimating the variance of spec-

tral fitting parameters. In: Proceedings of the 12th annual meeting

ISMRM (abstract 304). Kyoto

22. Efron B, Tibshirani R (1993) An introduction to the bootstrap.

Chapman and Hall, New York

23. Hesterberg T (2004) Unbiasing the bootstrap-boot knife sampling

vs. smoothing. Section on Statistics and the Environment: Ameri-

can Statistical Association, pp 2924–2930

24. Nelson SJ (2001) Analysis of volume MRI and MR spectroscopic

imagingdatafortheevaluationofpatientswithbraintumors.Magn

Reson Med 46:228–239

25. Knight-Scott J, Li SJ (1997) Effect of long TE on T1 measure-

ment in STEAM progressive saturation experiment. J Magn Reson

126:266–269

26. Rutgers DR, Kingsley PB, van der Grond J (2003) Saturation-

corrected T 1 and T 2 relaxation times of choline, creatine and

N-acetyl aspartate in human cerebral white matter at 1.5 T. NMR

Biomed 16:286–288

27. SrinivasanR,CunninghamC,ChenA,VigneronD,HurdR,Nelson

S, Pelletier D (2006) TE-averaged two-dimensional proton spec-

troscopic imaging of glutamate at 3 T. Neuroimage 30:1171–1178

123