an automated quantitation of short echo time mrs spectra in an open source software environment:...

NMR IN BIOMEDICINENMR Biomed. 2007; 20: 493–504Published online 14 December 2006 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/nbm.1112
An automated quantitation of short echo time MRS spectrain an open source software environment: AQSES

Jean-Baptiste Poullet, Diana M. Sima, Arjan W. Simonetti, Bart De Neuter, Leentje Vanhamme,Philippe Lemmerling and Sabine Van Huffel*

ESAT-SISTA, K.U. Leuven, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium

Received 10 January 2006; Revised 14 September 2006; Accepted 17 September 2006

*CorrespondenceKasteelpark ArenE-mail: sabine.vaContract/grant spbers: GOA-AMBing, several PhDContract/grant snumbers: PhD/pSpectral Analysissive brain oxygeContract/grant spContract/grant sptract/grant numbComputation, Ide

Abbreviations udomain signals; FLanczos singulartion; PM, perform0.9 ppm.

Copyright # 200

ABSTRACT: This paper describes a new quantitation method called AQSES for short echo time magnetic resonance spectra.

This method is embedded in a software package available online from www.esat.kuleuven.be/sista/members/biomed/new/

with a graphical user interface, under an open source license, which means that the source code is freely available and easy to

adapt to specific needs of the user. The quantitation problem is mathematically formulated as a separable nonlinear

least-squares fitting problem, which is numerically solved using a modified variable-projection procedure. A macromol-

ecular baseline is incorporated into the fit via nonparametric modelling, efficiently implemented using penalized splines.

Unwanted components such as residual water are removed with a maximum-phase FIR filter. Constraints on the phases,

dampings and frequencies of the metabolites can be imposed. AQSES has been tested on simulated MR spectra with several

types of disturbance and on short echo time in vivo proton MR spectra. Results show that AQSES is robust, easy to use and

very flexible. Copyright # 2006 John Wiley & Sons, Ltd.

KEYWORDS: quantitation; MR spectroscopy; short echo time; metabolites; open source software

INTRODUCTION

Accurate quantitation of metabolites from short echo timein vivo magnetic resonance spectroscopy (MRS), such asproton spectra from the human brain, may be a veryimportant aid in the correct non-invasive diagnosis ofpathology. For example, magnetic resonance spectroscopicimaging can be of help in brain tumour diagnosis (1), butonly if accurate quantitation of the metabolites of interestcan be performed (2). The development of easy-to-usequantitation software is a challenging task, and veryimportant for the acceptance of spectroscopy in the clinic.This paper is devoted to a new quantitation method calledAQSES (Automated Quantitation of Short Echo time MRS

to: S. Van Huffel, ESAT-SISTA, K. U. Leuven,berg 10, B-3001 Leuven-Heverlee, [email protected]: Research Council KUL; contract/grant num-ioRICS, CoE EF/05/006 Optimization in Engineer-/postdoc and fellow grants.ponsor: Flemish Government, FWO; contract/grantostdoc grants, projects, FWO-G.0321.06 (Tensors/), G.0360.05 (EEG, Epileptic), G.0519.06 (Noninva-nation), research communities (ICCoS, ANMMM).onsor: Flemish Government, IWT; PhD grants.onsor: Belgian Federal Science Policy Office; con-ers: IUAP P5/22 (‘Dynamical Systems and Control:ntification and Modelling’).

sed: AQSES, accurate quantitation of short echo timeIR, finite impulse response; HLSVD-PRO, Hankel–value decomposition with partial reorthogonaliza-ance measure; Lip1, lipids at 1.3 ppm; Lip2, lipids at

6 John Wiley & Sons, Ltd.

Spectra) and its implementation in the software packageAQSES GUI (graphical user interface). The functionalitiesof AQSES GUI are described in the Appendix.

During an in vivo NMR experiment, the measuredtime-domain signal consists of responses from allmetabolites (including macromolecules), noise andpartially suppressed water. Spectra of metabolites thatare visible during in vivo spectroscopy can also bemeasured in vitro or they can be simulated using quantummechanical knowledge, and these signals can be groupedin a database of metabolite profiles. An in vivo time-domain signal has, in theory, the shape of a sum ofcomplex damped exponentials. Instead of modellingthese individual line shapes, the in vivo short echo timeMRS signal can be modelled using (a selection of) theprofiles in the database, such that the prior knowledge thatrelates individual peaks in the in vivo spectrum isimplicitely imposed. The quantities of interest, themetabolite concentrations, can be estimated from theweighting coefficients (amplitudes) of the linearlycombined in vitro profiles. The linear combination shouldallow small corrections in spectral parameters such asfrequency shifts, damping corrections and phase shifts, aswell, since these parameters may vary from measurementto measurement (3).

Any quantitation method should also take into accountthe presence of a partially suppressed water resonanceand the presence of the macromolecular baseline. Thefrequency region where the water is located is known,

NMR Biomed. 2007; 20: 493–504

494 J.-B. POULLET ET AL.

while the macromolecular baseline overlaps with themetabolites of interest. Typically, the quantitationmethods assume that the water resonance is removedin a preprocessing step, using a frequency-selectivemethod. For instance, the Hankel singular valuedecomposition (HSVD) method is based on the idea offirst fitting the whole signal as a sum of complex dampedexponentials and then subtracting all the componentswhose frequencies were estimated in the frequency regionof the water resonance.The use of an alternative technique is proposed for

dealing with the presence of water (and otherresonances with relatively known frequency location).The method is based on finding a maximum-phasefinite impulse response (FIR) filter optimized tosuppress the resonances that are outside the frequencyregion of interest and to keep the region of interest(where the metabolites are visible) with minimal distor-tions. The quantitation algorithm aims then at fitting afiltered model to a filtered in vivo signal. This type of filterwas originally proposed for use in the quantitation of longecho time MRS signals (4). The results show that it can besuccessfully applied to short echo time signals as well.Methods for taking into account the macromolecular

baseline are very diverse: some baseline removal methodsare applied as a preprocessing step (5,6), others duringquantitation (6,7); they can be applied to the time-domainsignal (6) or to the Fourier-transformed frequency-domain signal (7). So far, it is not clear which type ofmethod is the best. A new approach is proposed forestimating the baseline, the main properties of which are:the baseline is estimated during the quantitation itself;the fitting takes place in the time domain, and thus thebaseline is also a time series; the baseline is nonparame-trically reconstructed using penalized splines; thecriterion that is monitored in order to prevent the baselinefrom reconstructing part of the metabolites is the smooth-ness of its Fourier transform. Among the previousmethods for baseline estimation, the present method ismost similar to the one in LCModel (7), but the followingdifferences should be pointed out:

� A

Co

QSES fits the whole complex signal in the timedomain, which is the data acquisition domain; LCMo-del fits the real part of the frequency-domain signal.

� A
QSES uses an FIR filtering technique to removeundesired resonances from specific frequency ranges;the baseline is also passed through this filter.
� T
he baseline is nonparametrically modelled usingsplines: in AQSES, penalized splines are chosen, while,in LCModel, smoothing splines are used. Theadvantage of penalized splines (8) compared withsmoothing splines is the fact that a smaller numberof spline functions are used, simplifying the compu-tational complexity.
Another recent contribution for MRS signal quanti-tation is the QUESTmethod (3,6) provided within jMRUI

pyright # 2006 John Wiley & Sons, Ltd.

(9). It is worth mentioning the new features of AQSEScompared with QUEST:

� A
QSES uses the FIR filtering technique during quan-titation, while QUEST performs water suppression as apreprocessing step.
� Q
UEST models the baseline using heuristic methods,where several steps are involved: truncation, partialfitting, subtraction and final fitting. AQSES uses onlyone common optimization problem for the fitting ofboth the model and the baseline. As for the waterremoval, it is conjectured that AQSES is thus lessprone to accumulated errors, since its method is direct,and not a sequence of operations.
� I
n reference (6), an augmented Fisher informationmatrix [inspired by Spall and Garner (10)] is usedfor the computation of confidence bounds for thevariables of interest, but it is not clear how to choosethe value for the number of effective parametersinvolved. In this respect, the semi-parametric frame-work discussed in reference (11), based on asymptoticnonlinear regression theory, clarifies the way the con-fidence bounds can be automatically estimated for theprocedure in AQSES.
The AQSES method comes with an advanced JAVA-based – platform-independent – user interface, whichallows use in scientific as well as clinical environments. Amajor difference of AQSES compared with LCModel aswell as QUEST is that the source code of AQSES GUI(12) is available under the Lesser Gnu Public License(GPL), an Open Source Initiative (OSI) approved opensource license. This license specifies that changes made tothe framework of AQSES GUI by other parties should bedistributed under the same license. It also allows users tocreate their own plug-ins and distribute them under adifferent license, even as closed source.

The goal of this paper is to introduce the AQSESmethod and the AQSES GUI framework, and to discussthe performance of this quantitation method on simu-lations and real data. The main features of AQSES aredescribed. The specificities of AQSES with respect toother existing quantitation methods are highlighted. Theperformance of AQSES is then presented through variousexperiments on simulated, in vitro and in vivo MR data.Next, the features of AQSES are discussed and someconclusions are drawn. The AQSES GUI is described indetail in the Appendix.

THEORY AND METHODS

Mathematical formulation

The model. Consider a ‘metabolite database’ as a setfvk; for k ¼ 1; . . . ;Kg of complex-valued time seriesof length m, representing in vitro measured NMRresponses. An in vivo measured NMR signal y, which

NMR Biomed. 2007; 20: 493–504DOI: 10.1002/nbm

AN AUTOMATED QUANTITATION OF SHORT ECHO TIME MRS SPECTRA 495

is another complex-valued time series of lengthm, satisfies the model

yðtÞ ¼ byðtÞ þ "t; t ¼ t0; . . . ; tm�1 (1)

byðtÞ ¼ XKk¼1

ak ðzkÞt vkðtÞ þ bðtÞ þ wðtÞ (2)

where ak; zk 2 C are unknown parameters that accountfor amplitudes of the metabolites in the database and forthe necessary corrections of the database signals. Thecomplex amplitudes ak and the complex values zk can bewritten (with j ¼

ffiffiffiffiffiffiffi�1

p) as

ak ¼ ak expðjfkÞ; zk ¼ expð�dk þ j fkÞ (3)

where ak are the real amplitudes, fk are the phase shifts,dk are damping corrections and fk are frequency shifts.The present software implementation allows a moregeneral model to be used: eddy current correction terms,as well as Gaussian or Voigt line shapes, can be specified.For ease of exposition, the description in this paper isrestricted to the classical Lorentzian line shapes, buttechnical reports (13,14) are referred to for details on thefull formulation. In eqn (1), the term "t denotes anunknown noise perturbation with zero mean, and, in eqn(2), bðtÞ denotes the ‘baseline’ and wðtÞ denotes the watercomponent.

Baseline modelling. The ‘baseline’ bðtÞ represents thechemical part corresponding to the unknown macromol-ecular components that are not included in the database;bðtÞ is characterized by the assumption that its Fouriertransformation is a smooth function. For the nonpara-metric modelling of the baseline, a basis of splines isconstructed (8,15) and the discretized splines are put ascolumns in a matrix A. An arbitrary nonlinear functioncan be approximated as a linear combination of splinefunctions. The coefficients in this linear combination areunknowns that must be identified. These linear coeffi-cients are denoted by c1; . . . ; cn (or by c 2 Cn, whenstacked in a column vector). Thus, the discretization of anonlinear function approximated with splines (in thepresent case, the Fourier transform of the baseline b) canbe written in matrix notation as the matrix–vector productA�� c. Since the goal is to reconstruct a smooth baseline inthe frequency domain while still fitting in the timedomain, the spline basis matrix A is transformed to thetime domain, using the discrete inverse Fourier transform.

In order to fit the model and the smooth baseline at thesame time, the regularized nonlinear least-squarescriterion

min1

m

Xtm�1

t¼t0

jyðtÞ � byðtÞj2 þ l2kDck2 (4)

is considered, where by is given in eqn (2), but with thebaseline b replaced by the formula b ¼ A� c, which is theinverse Fourier transformation of the frequency-domain

Copyright # 2006 John Wiley & Sons, Ltd.

baseline A � c. In eqn (4), the whole term l2kDck2 isresponsible for ensuring a certain degree of smoothness tothe baseline b. The regularization matrix D is needed tomeasure the smoothness of the baseline in the frequencydomain. Matrix D can be taken as a (combination of)discrete derivative operator(s) (8). Parameter l is a fixedregularization (penalty) parameter; the value given to lcontrols the degree of smoothness; this value can beautomatically selected using a generalized cross-validation criterion [see reference (11) for more details].

Water removal. The term wðtÞ refers to the residualwater component (as well as other possible unwantedterms), the frequency positions of which are relativelyknown. In AQSES, this term can be filtered out using themaximum-phase pass-band FIR filter from reference (4).However, the region(s) that should be filtered out of thein vivo signal should be specified by the user. Ideally, thisfilter will suppress all the components in the specifiedfrequency region(s) so that the spectrum becomes smallerthan an estimated noise level, while keeping thefrequency region(s) of interest undistorted.

The FIR filter in reference (4) is automaticallyoptimized in order to remove the water component froman in vivo NMR signal. The design of the filter isperformed outside the actual fitting method of AQSES.Such a filter consists of a vector of coefficients; the lengthof the filter and the coefficients are optimized during theautomatic filter design.

An FIR filter is a linear operator that commutes withthe sum; however, it does not commute with the modifiedsum of metabolites, since the shifts and corrections on thespectral parameters involve nonlinear operations. Whensuch an operation is applied to the measured signal, itmust also be taken into account by the fitting model. Inother words, a filtered measured signal will be fitted witha filtered model plus a filtered baseline. Thus, the filter isused explicitly during the iterative minimization inAQSES.

The quantitation method. Assuming that the filter isneglected for the sake of simplicity, the nonlinearleast-squares problem (4) becomes

minak ;zk ;c

1

m

Xm�1

i¼0

yðtiÞ �XKk¼1

ak ðzkÞti vkðtiÞ � ðAcÞi

��2

þl2kDck2

¼ mina;z;c

1

my�FðzÞa�Ack k2þl2kDck2

(5)

where y is a column vector containing yðt0Þ; . . . ; yðtm�1Þ,a and z are defined asK-dimensional columnvectors fromthe respective variables ak; zk, and them� K matrixFðzÞhas elements of the form

Fik ¼ ðzkÞtivkðtiÞ ¼ exp ð�dk þ j fkÞtið Þ � vkðtiÞ (6)



Problem (5) is a separable problem, where linearparameters a and c can be projected out of theleast-squares problem, and only a smaller-sized nonlinearleast squares problem remains to be solved for thenonlinear variables z, via an iterative minimizationalgorithm of the Levenberg–Marquardt type (16). Thistechnique is called variable projection [VARPRO(17,18)]. The VARPRO method has already been usedin MRS problems (19,20); a historical note on theapplication of VARPRO to MRS data quantitation isgiven in Section 17 of the review paper by Golub andPereyra (18). The previous use of VARPRO in theabove-mentioned papers was restricted to long echo timeMRS signals and models of the ‘sum of complex dampedexponentials’ type.In the AQSES framework, the classical VARPRO

method is modified (14) such that it is possible to imposeprior knowledge in the form of upper and lower bounds onthe nonlinear parameters, linear equalities between somevariables of the same sort among dk or fk or even someconstraints on the linear parameters (non-negativeamplitudes and equal phases). Normally, VARPROallows the complex amplitudes ak to take any complexvalue such that the residual fit is minimized. In terms ofthe real parameters, this means that the real amplitudes akcould take any non-negative value, while the phasecorrections fk would be unconstrained between �p andp. AQSES allows an option of equal phase corrections foreach metabolite, since it assumes that the database ofmetabolites is already constructed to have metabolites inphase. In terms of the VARPRO implementation, theequal phase constraint is a difficult constraint, since itinvolves part of the linear variables. Sima and Van Huffel(14) deal with this problem by adding one common phasecorrection variable to the nonlinear set of variables, andeffectively imposing a non-negativity condition on thereal-valued amplitudes ak. The solution is numericallycomputed using a non-negative least-squares methodinstead of closed-form least squares.The VARPRO method implemented in AQSES is much

more efficient than optimizing the nonlinear least-squaresproblem (4) directly, over all linear and nonlinearparameters without separation. This improvement incomputation efficiency is more important than in theprevious use of VARPRO for long echo time MRS (19),since there aremanymore linear parameters than nonlinearones, as many as there are spline coefficients. The numberof spline coefficients is typically one-tenth of the numberof data points. Another advantage of VARPRO is that itdoes not encounter numerical problems when someamplitudes ak are nearly zero. Moreover, the Levenberg–Marquardt algorithm needs good initial values for itsvariables; it was found that good initial values for all thenonlinear parameters – frequency and damping correc-tions – are zeros, which means that the optimization isstarted with no spectral corrections to the signals in thedatabase. In the equal phase case, an initial guess for the


common phase corrections is estimated from a preliminaryoptimization round of the free phase algorithm.

Cramer–Rao bounds, specially adapted for semi-parametric nonlinear regression (11), can also becomputed as a byproduct of the quantitation procedure.They correspond to all the spectral parameters for themetabolites of interest (linear and nonlinear parameters aswell) and give an indication about the uncertainty of thefinal quantified parameters. If the given bounds are smallenough relative to the corresponding parameter value,then the computed value is reliable. If a large bound isfound for a certain component, then the computedparameters might be unreliable. This is not due to a faultyminimization process; instead, it is due to a poorsignal-to-noise ratio, an incomplete database of metab-olites or the inclusion of metabolites having similarspectra, resulting in convergence problems. The risk ofconverging to local minima instead of global minima isindeed higher with a poor signal-to-noise ratio. TheCramer–Rao bounds estimated in AQSES are pro-portional to the variance of the residue plotted in AQSESGUI. Therefore, it might also be helpful to inspect theresidue to detect convergence problems.

Simulated examples and in vivoquantitation

The in vitro database used in this paper is described in theAppendix.

Five experiments have been designed to test therobustness and the accuracy of AQSES. The firstexperiment emphasizes the accuracy level that can bereached for the parameter estimation. A large number ofsimulated signals were created for that purpose. Eachsimulated signal consisted of a linear combination ofeight metabolite profiles (six metabolite profiles þ twosimulated lipid profiles) in the basis set, i.e. myo-inositol(Myo), creatine (Cr), phosphocholine (PCh), glutamate(Glu), NAA, lactate (Lac), lipid at 1.3 ppm (Lip1) andlipid at 0.9 ppm (Lip2). These metabolites were chosensince they have been found to be important in thedetection of many pathologies. Note that no disturbancecomponents such as baseline, noise or water were addedto the simulated signals. The parameters for amplitude,damping, phase and frequency for each simulated signalwere chosen in the following way. Firstly, meaningfulparameters were estimated from a set of 98 short echotime in vivo MRSI spectra acquired from normal braintissue. Estimations were obtained using AQSES in acontrolled way in which results were visually inspectedand outliers removed. This was done to mimic areal-world situation and to obtain sensible mean valuesand standard deviations (SD) for all parameters. Then, forthe simulated signals, the amplitudes were restricted tothe mean �3SD (only positive), and the dampingperturbation was restricted to the mean �10Hz. Thephases were set variable between �458 and þ458, but



were the same for all profiles in one simulated signal. Thefrequency shifts were restricted to 0� 4.5Hz. Thisresulted in a set of data (set 1) with 200 simulated spectra.

For each metabolite k in the simulated signal l, the trueamplitudes, ak;l, were compared with the estimatedamplitudes, ~ak;l, obtained with AQSES by means of aperformance measure (PM) defined as

PMk ¼ 100

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPLl¼1ðak;l � ~ak;lÞ2PL

l¼1 a2k;l

vuut (7)

where L is the number of simulated signals in each set. Alow PM reflects a high performance, and is a percentagemeasure of the difference between estimated and trueamplitudes.

The second experiment extends the results of the firstexperiment to larger databases, i.e. with more metaboliteprofiles. The same simulated spectra (set 1) were taken asin the first experiment, but three more metabolite profileswere added to the basis set: taurine (Tau), alanine (Ala)and glucose (Glc). These metabolites were chosenbecause they were known to be important metabolitesthat did not have strong correlation with the metabolitesthat were already inside the basis set.

The third experiment shows the influence of water,baseline and noise on the estimated amplitudes. The samebasis set was considered as in the first experiment (usingeight metabolite profiles in AQSES). Five sets ofsimulated signals were constructed:

Set 2¼ set 1 with water resonance at 4.7 ppm;Set 3¼ set 1 with low white noise (SNR¼ 25);Set 4¼ set 1 with high noise (SNR¼ 7);Set 5¼ set 1 with baseline distortion;Set 6¼ set 1 with water, baseline and high noise.

The baseline distortion was based on information fromTable 1 in reference (21); the baseline is the sum ofgaussians referred to as lip3, lip4, lip5, mm2, mm3 andmm4 in that paper. The water profile has been extractedfrom an in vivo spectrum by means of HLSVD-PRO. TheSNR is defined as the ratio of the reference peak height at8.44 ppm and the standard deviation of the circular (equalvariances for the real and imaginary parts) white gaussian

Table 1. Percentages of cases (for eachmetabolite) forwhich the relative differences between the true andthe estimated metabolite amplitudes is smaller than1% (based on 200 signals for each set). The top tworows correspond to the equal phase constraint, (andthe bottom two rows correspond to no constraints onthe phases). The notations are explained in the ‘simu-lated examples and in vivo quantitation’ section

Myo PCh Cr Glu NAA Lac Lip1 Lip2

Exp. 1, set 1 98.5 99 98.5 98.5 100 96 96.5 97Exp. 2, set 1 92.5 95 95.5 97 98.5 93.5 94.5 96Exp. 1, set 1 98.5 97.5 98 98 99.5 96 96 97Exp. 2, set 1 94 94.5 97.5 95 98.5 93.5 94 95


noise, both in the frequency domain. To determine theinfluence of water, baseline and noise, the PM has beenstudied. As an illustration, simulated spectra from set 4and from set 6 are plotted in Fig. 1.

In the fourth experiment, AQSES was validated usingan in vitro sample. This test solution contained ninemetabolites of known concentrations: Cr, NAA, Glu, Gln,Myo, PCh, glycerphosphocholine (GPCh), Tau and Lac.The basis set used in AQSES was: Cr, NAA, Glu, Myo,PCh, Tau and Lac. Glu was selected to fit the combinationof Glu and Gln, since Glu and Gln have similar profilesand are highly correlated. Glu will be denoted by Glx inthis experiment and in the fifth experiment to indicate thatit fits the combination of Glu and Gln. The combination ofPCh and GPCh was fitted similarly with PCh. The trueand estimated proportions of metabolites have beencompared, the proportion of metabolite k being the ratioof the concentration of metabolite k and the totalconcentration (all metabolites).

In the fifth experiment, in vivo NMR signals from adatabase containing MRSI spectra from normal tissue(122 spectra selected from data of four volunteers),gliomas of grade II (GII, 90 spectra selected from data ofsix patients) and glioblastoma multiforma (GBM, 59spectra selected from data of five patients) wereprocessed. The goal of this part is to show that AQSESprovides results in accordance with the literature. For thespecific acquisition procedure and settings, see reference(22). The basis set was identical to the one in the firstexperiment. Metabolic images obtained from a patientwith a GBM [I-1285 from the INTERPRET database(23)] that underwent spectroscopic imaging are alsodisplayed. The metabolic images have been obtained byprocessing all spectra of the patient in batch mode byAQSES, using the same basis set as before.

The first three experiments are carried out assumingeither no prior knowledge of the phases or that themetabolites are in phase. The last two experiments did notassume any prior knowledge of the metabolite phases.

RESULTS

Robustness of AQSES

Figure 2 shows a box plot of the distribution of theamplitudes found by AQSES for the in vivo spectra ofhealthy tissue that were used to estimate meaningfulvalues for the simulated signals. The means are sensiblevalues with respect to the literature [see, for example,reference (24)]. The large variances may result from thefact that the spectra of healthy tissue originate fromdifferent brain locations, which have an influence on themetabolite concentration as shown in reference (24).

The first experiment shows that, in 95.5% of cases, theparameter estimates are almost perfect (i.e. the relativedifference between the true and the simulated metabolite


Figure 1. Simulated spectra from sets 4 and 6. The amplitudes are in arbitrary units.

Figure 2. Box plot showing the quantitated amplitudes ofin vivo spectra from healthy volunteers.


amplitudes is under 10�6%). This result holds whether themetabolites are assumed to be in phase or not. Looking ateach metabolite separately, the percentages of caseswhere the relative errors are higher than 1% are quitesimilar for both assumptions (rows 1 and 3 in Table 1).Table 1 indicates that Lac is misfit in most of theremaining cases (4% out of 4.5%). In the cases ofimperfect parameter estimates, the relative error for NAAnever exceeds 1% when equal phases are assumed. In 4%out of 4.5% cases, the estimation is corrupted by the valueof Lac which overlaps Lip1, resulting in larger amplitudeestimation errors. Tables 2 and 3 report the PMcorresponding to each set and to each metabolite,

able 2. Performance measure (PM) for each metabolite of each simulation set [in percentage, see eqn (7) with¼ 191]. Equality of all metabolite phases has been imposed


xp. 1, set 1 4.1E-12 1.4E-12 1.9E-12 1.35E-11 1.5E-12 1.81E-11 1.6E-12 1.08E-10xp. 2, set 1 1.72 1.21 0.07 0.09 0.01 0.65 0.77 0.19xp. 3, set 2 1.24 0.93 0.39 0.67 0.20 6.59 7.91 0.81xp. 3, set 3 5.76 4.04 2.87 4.33 2.48 15.18 19.85 6.89xp. 3, set 4 8.66 7.07 4.95 6.65 5.67 20.10 29.25 14.74xp. 3, set 5 9.51 2.67 1.76 24.39 6.25 10.79 14.01 6.26xp. 3, set 6 14.73 8.36 6.44 25.04 9.81 23.53 29.14 17.34

TL

EEEEEEE


imposing respectively equal phases for all metabolites orletting the phases free. These values are obtained afterdiscarding the signals that do not provide perfectparameter estimates (defined above), i.e. nine signalsout of 200 (same signals in both tables). The first row ofthese tables shows that a higher degree of accuracy can bereached when equal phases are assumed.

The second simulated example shows the results whenthe number of metabolites in the basis set and in thesimulated spectra are not the same. The percentage ofalmost perfect parameter estimates decreases to 92%when assuming the metabolites in phase, while itdecreases to 92.5% when no assumptions about thephases are made. However, imposing equality of phasesimproves the accuracy of the fit (Tables 2 and 3, rows 2)when considering the 191 signals that provide perfectparameter estimates in the first experiment. The goodnessof the fit is now complicated by the overlap of metabolitessuch as Myo, Glc, PCh and Tau. Rows 2 and 4 in Table 1illustrate the loss in accuracy compared with rows 1 and 3when Glc, Ala and Tau are added to the basis set. Theother metabolites, located at other frequency ranges, areless affected by the addition of Tau, Ala and Glc to thebasis set. This shows that AQSES is not very sensitive tothe choice of the basis set, provided its components arenot strongly correlated.

The third experiment investigates the robustness ofAQSES against the addition of disturbance componentssuch as noise, baseline and water resonances. The PMsare reported in Tables 2 and 3 for each simulation set (lastfive rows).


Table 3. Performance measure (PM) for each metabolite of each simulation set [in percentage, see eqn (7) withL ¼ 191]. No prior knowledge has been imposed


Exp. 1, set 1 6.95E-07 1.92E-07 1.01E-07 6E-07 2.07E-07 8.12E-07 8.51E-07 6.31E-07Exp. 2, set 1 2.67 3.53 0.44 0.14 0.07 1.34 1.24 0.30Exp. 3, set 2 1.20 1.40 0.35 0.67 0.46 10.47 6.48 1.26Exp. 3, set 3 7.37 5.88 4.25 4.27 3.23 19.17 20.01 7.71Exp. 3, set 4 10.81 9.77 6.22 7.74 5.97 23.00 34.44 15.32Exp. 3, set 5 10.06 7.68 2.90 29.41 7.97 19.15 14.07 9.76Exp. 3, set 6 13.45 11.00 7.41 29.71 10.44 24.65 32.44 18.28


The extreme values are mainly present in theoverlapping peaks, i.e. Lac and Lip1. The maximum-phase filter removes satisfactorily the water component, ifthe PM in set 2 in Tables 2 and 3 (row 3) is inspected. ThePMs for different noise levels confirm the stability ofAQSES against noise. At low noise values, the PM doesnot increase dramatically for any metabolites, except forLac, Lip1 and Lip2. At high noise, the PMs of Lip1 andLip2 keep increasing strongly, while the PM of Lac ismore stable. The fact that these metabolites are estimatedwith a lower accuracy may be explained by their lowmagnitude level. They are more embedded in noise thanthe other ones, or, in other words, they have a smallerrelative signal-to-noise ratio. The PMs of the five mainmetabolite profiles show stability against noise (columns1 to 5 in Tables 2 and 3). The baseline affects eachcomponent, but mainly Myo and Glu. Myo and Glu arewider and therefore are more likely to be fitted by thebaseline. Cr is less affected by the baseline. The PMs ofNAA, Cr and PCh remain under 10% in all sets with theassumption of equal phases (Table 2) and under 11%without this assumption (Table 3). The largest PM value iskept under 30% in Table 2 and under 33% in Table 3. Inmost of the cases, a slightly better accuracy is obtained byassuming that the metabolites are in phase.

Since these three experiments involve different models,the computation time required for each type of model isstudied. The results are reported in Table 4. Forexperiments 1 and 3 (sets 2, 3 and 4) the baseline inthe model is not considered and the number of metaboliteprofiles in the basis set equals 8 (model 1 in Table 4). Forexperiment 2, the baseline is still not included in themodel but the number of metabolite profiles in the basisset increases to 11 (model 2). For experiment 3 (sets 5 and

Table 4. Average computation times (s) per spectrumfor each model, imposing equal phases for all metab-olites or letting them free

Models, prior knowledgeEqualphases

Freephases

Model 1: exp. 1, exp. 3 (sets 2, 3, 4) 1.39 0.87Model 2: exp. 2 4.03 2.74Model 3: exp. 3 (sets 5, 6) 3.29 3.32


6), the baseline is incorporated in the model which takesinto account the contribution of eight metabolite profiles.The computation times of AQSES using two differentassumptions have been compared: imposing equal phasesfor all metabolites or letting the phases free. The valuesreported in Table 4 are the average computation times forone spectrum. AQSES has been run on a Windows XPplatform with a Pentium 4 (3GHz CPU, 1Gb RAM). Thesimplest case in terms of computation time is for model 1when the phases are free with an average quantitationtime per spectrum of 0.87 s (204500 for 191 spectra).Assuming equal phases for all metabolites increases thecomputation time if the baseline is not considered in themodel. This was expected since one variable (commonphase) is added to the K real variables used for theamplitudes, while K complex variables are used for thecomplex amplitudes when the phases are free. Moreover,the amplitudes are restricted to positive numbers sincenegative amplitudes would mean a metabolite in oppositephase, contradicting the ‘equal phase’ constraint [seereference (13) for more information]. In the slowest case,i.e. the case when the database of metabolites is larger (11metabolites), the computation time per spectrum is 4.03 s(1204900 for 191 spectra), which remains relatively small.

For the fourth experiment, the true and estimatedproportions of the amplitudes of the metabolites in the testsample are reported in Fig. 3. The relative errors betweenthe true and the estimated proportions are relatively small(all <26%), especially for the metabolites in higherconcentration (<8%). Note that the estimation of Glx isquite good (�6%) while the individual estimates of Gluand Gln are not as good if we include their correspondingmetabolite profile in the database (�25%, data notshown). This is due to the high degree of correlationbetween these two metabolite profiles. On the contrary,summing up the contributions of Glu and Gln forestimating Glx yields good results (also �6%, data notshown).

For the fifth experiment, Fig. 4 shows the averagedestimated amplitudes obtained with AQSES, for eightmetabolites of the three classes normal, grade II andGBM. NAA and Cr decrease with the grade of the tumour,in agreement with reference (25). A large differenceoccurs between the concentration of NAA in normal and



Figure 3. In vitro test sample results.

Figure 4. Averaged estimated amplitudes for normal tis-sues, GII and GBM, in arbitrary units.

Figure 5. Metabolic maps of a patient with a glioblastoma. The ellipsoids in (c), (g) and (i) indicate regionswhere a substantial increase in the corresponding metabolites is noted compared with a region withnormal tissue (high concentrations in red and low concentrations in blue with a linear scale). Thisinformation may be particularly useful since it barely appears on the T2-weighted image. The concen-tration of Glu is lower in the ventricles [one of the ventricle regions is indicated by the left ellipsoid in (e)].The ellipsoid on the right-hand side in (e) encircles the region that lies between the ventricles.


glioma tissues. Myo, PCh and Glx exhibit much lessvariations. A small increase in Glx and PCh with thegrade of glioma is noted. Ordering comparable metab-olites (i.e. without Lip1 and Lip2, see the ‘simulatedexamples and in vivo quantitation’ section) from thehighest to the lowest in concentration yields thefollowing:

For normal brain: NAA, Glx, Cr, Myo, Lac and PCh;For GII: Glx, Lac, Cr, NAA, Myo, PCh;For GBM: Lac, Glx, PCh, Cr, NAA and Myo.

Note that Lac, Lip1 and Lip2 strongly increase with thegrade of the tumour.

Metabolic images such as in Fig. 5 can also bedisplayed. The computation time required by AQSES toprovide the quantitation results is 205000 (Windows XP,1Gb RAM, 3GHz CPU). In this example, the affectedregion is clearly visible on the T2-weighted image[Fig. 5(a)]. The tumour region can also be identified fromalmost all metabolic images [see Figs 5(d), (f), (g), (h),and (i)]. The concentrations of NAA and Cr are lower inthe tumour region, while the concentrations of Lac, Lip1and Lip2 are larger in that region, which agrees withFig. 4 and with the literature [see, for example, references(1) and (26)]. Myo decreases in the tumour, but thiscontrast is less apparent than in the case of NAA or Cr.Also noticeable is the low Glx concentration in the regionof the ventricle compared with the central part of the brain[ellipsoid in Fig. 5(e)]. An increase in PCh, present in theboundary between the malignant and healthy areas[ellipsoid in Fig. 5(e)], could reflect an increase inmembrane synthesis and accelerated cell proliferation[see, for example, reference (26)]. The ellipsoids inFigs 5(g) and (i) correspond to a region that is slightly



higher in intensity in the T2-weighted image. This regionhas also an increased concentration for Lip2 and Lac. Thepresence of Lip is thought to correspond to cellular andmembrane breakdown corresponding to necrosis (1). Lacis usually detected only under pathologic conditions,when energy metabolism is affected severely (27). Thisshows that pathologic information, which is barely visibleon MRI images, can be successfully extracted frommetabolic maps.

DISCUSSION

The VARPRO implementation of AQSES, using amodified Levenberg–Marquardt minimization algorithm,is important for fast convergence and reliable numericalcomputations and is less affected by local minima, sinceno starting values are needed for the linear parameters(including the parameters of the baseline). The nonlinearparameters (e.g. frequency shifts or damping corrections)are initialized with zeros, which is the most reasonablechoice in the context of short echo time quantitation. Theclassical VARPRO method leaves the linear part of themodel completely free such that no constraints can beimposed on the amplitude and phase. However, in theory,the phases of the metabolites are equal. Constraining thephases to be equal implies some modifications of theclassical VARPRO implementation as described in the‘mathematical formulation’ section. The results showthat, in spite of large variations in all the variables toconstruct the simulations, a high accuracy level can bereached by this algorithm (95.5% of the cases are almostperfect for noise-free signals).

Another important aspect is the choice of the basis setin AQSES. The basis set should contain the metabolitesactually visible in the spectrum except for those that aretoo correlated with each other. Indeed, equivalentmetabolite profiles can ruin their own individualparameter estimates, as has been seen in experiment 4when Glu and Gln were both in the database. When thebasis set contains more metabolites than are actuallycontained in the spectrum, it has been shown that theamplitude estimates of the metabolites not actually in thesignal (i.e. Tau, Ala and Glc) are often close to zero (seeexperiment 2). These results indicate an added value ofthe VARPRO method implemented in AQSES over othermethods. However, adding more metabolites in the basisset will increase the complexity of the algorithm andconsequently the computation time. The results show thatthe latter could be more than doubled by adding threemetabolite profiles to the basis set of eight profiles.Furthermore, the parameter variances will also increase,limiting the accuracy of the algorithm. In case of doubtabout the presence of some metabolites, it is recom-mended that they be added to the basis set if they do notexhibit profiles too similar to the metabolite profilesalready entered in the basis set. Large Cramer–Rao


bounds displayed in AQSES GUI or the presence ofobvious peaks in the plot of the residue may be anindicator of an incomplete basis set. In this respect, thebasis set of eight metabolite profiles used in this paperprovides a good compromise, although it is not beingclaimed that it is the best choice for any type of MRSspectra to be fitted. The protocol of the basis set should besimilar to the one used to acquire the spectra to be fittedsuch that the parameter corrections (dk, fk) can beassumed as small, reducing the risk of convergence to alocal minimum.

One of the underlying goals of a quantitation method isto separate the signal from the disturbance components.In this respect, the maximum-phase FIR filter providessatisfactory results. Its high efficiency allows its embed-ment in the iterative minimization in AQSES, resulting inmore accurate parameter estimates. This filter, in additionto filtering out the unwanted components (including thenoise) in the frequency region of no interest, partiallyremoves the baseline. This reduces the importance ofthe regularization parameter, l, which may influence theresults substantially. The use of a semi-parametric modelreduces the number of steps to obtain the parameterestimates, decreasing their variances and thus increasingthe reliability of the results. The baseline remains acrucial issue during fitting due to its large correlation withthe other metabolites. The present results show that(compared with the results of dataset 1) the errors for allmetabolites increase substantially, with a smaller increasefor Cr. This seems to be in agreement with the observationof Ratiney et al. (6), who noted that the backgroundamplitude was correlated with all metabolite amplitudesexcept that of Cr. The algorithm used in this paper isrobust against noise since the least-squares problem thatis solved is restricted to a linear combination of correctedmetabolite profiles present in the signal; using metaboliteprofiles instead of individual peaks implies an increasedrobustness against noise, because correlations betweenspectral regions that are relatively far apart are taken intoaccount.

CONCLUSION

This paper has described a new short echo time MRquantitation method AQSES embedded in a user-friendlysoftware package. It provides more flexibility inexploiting prior knowledge than the classical VARPROmethod without sacrificing its advantages in numericalaccuracy and computational efficiency. The use of themaximum-phase FIR filter allows more robustnessagainst disturbance components such as water, noise orbaseline. The new method generates fast and accurateresults on simulated data and in vitro samples. The resultsof batches of in vivo data containing spectra from healthy,grade II gliomas and glioblastomas are in line withresults described in literature. The results of a set of



spectroscopic imaging data are in accordance with MRIimages obtained from the same slice. Since the GUI isopen source and written in a flexible language, it has thepotential to grow rapidly and be of high importance forthe medical MR community.

Acknowledgments

The Biomedical Magnetic Resonance Research Group,Radboud University Nijmegen, Medical Centre (http://get.to/mrs), and the EU-funded projects BIOPATTERN(EU network of excellence; Contract No. FP6-2002-IST508803), INTERPRET (EU shared-cost RTD project;Contract No. FP5-IST-1999-10310), eTUMOUR (FP6-2002-LIFESCIHEALTH; Contract No. 503094) andHEALTHagents (IST200427214) are gratefully acknowl-edged. Arend Heerschap and his group (Radboud Uni-versity Nijmegen, Medical Centre) are gratefullyacknowledged for providing data. Lutgarde Buydensand her group (Radboud University Nijmegen, Facultyof Sciences) are gratefully acknowledged for havingpreprocessed the data.

REFERENCES

1. Nelson SJ. Magnetic resonance spectroscopic imaging. IEEE Eng.Med. Biol. 2004; 23: 30–39.

2. Howe FA, Barton SJ, Cudlip SA, Stubbs M, Saunders DE, MurphyM, Wilkins P, Opstad KS, Doyle VL, McLean MC, Bell BA,Griffiths JR. Metabolic profiles of human brain tumours usingquantitative in vivo1H magnetic resonance spectroscopy. Magn.Res. Med. 2003; 49: 223–232.

3. Ratiney H, Sdika M, Coenradie Y, Cavassila S, van Ormondt D,Graveron-Demilly D. Time-domain semi-parametric estimationbased on a metabolite basis set. NMR Biomed. 2004; 17: 1–13.

4. Sundin T, Vanhamme L, Van Hecke P, Dologlou I, Van Huffel S.Accurate quantification of 1H spectra: from FIR filter design forsolvent suppression to parameter estimation. J. Magn. Reson.1999; 139: 189–204.

5. Golotvin S, Williams A. Improved baseline recognition and mod-eling of FT NMR spectra. J. Magn. Reson. 2000; 146(1): 122–125.

6. Ratiney H, Coenradie Y, Cavassila S, van Ormondt D, Grave-ron-Demilly D. Time-domain quantitation of 1H short echo-timesignals: Background accommodation. MAGMA. 2004; 16:284–296.

7. Provencher SW. Estimation of metabolite concentrations fromlocalized in vivo proton NMR spectra. Magn. Res. Med. 1993;30(6).

8. Eilers PHC, Marx BD. Flexible smoothing with B-splines andpenalties. Stat. Sci. 1997; 11(2): 89–121.

9. Magnetic Resonance User Interface in JAVA (jMRUI). http://www.mrui.uab.es/mrui/

10. Spall JC, Garner JP. Parameter identification of state-space modelswith nuisance parameters. IEEE Trans. Aero. Elec. Sys. 1990;26(6): 992–998.


11. Sima DM, Van Huffel S. Regularized semiparametric modelidentification with application to NMR signal quantification withunknownmacromolecular base-line. J. R. Stat. Soc. B. 2006; 68(3):383–409.

12. De Neuter B, Luts J, Vanhamme L, Lemmerling P, Van Huffel S.Java-based framework for processing and displaying short-echo-time magnetic resonance spectroscopy signals. Comput.Methods Programs Biomed. (to appear).

13. Sima DM, Van Huffel S. AQSESVP – description of a variableprojection implementation for nonlinear least squares with linearbounds constraints, applied to accurate quantification of short-echotime magnetic resonance spectroscopic signals. ESAT-SISTAtechnical report 05-120, ESAT Laboratory, K. U. Leuven, Bel-gium. 2005.

14. Sima DM, Van Huffel S. Separable nonlinear least squares fittingwith linear bound constraints and its application in magneticresonance spectroscopy data quantification. J. Comput. Appl.Math. 2006 (In Press).

15. de Boor C. A Practical Guide to Splines. Springer: Berlin, 1978.16. More J. The Levenberg–Marquardt algorithm: implementation and

theory. In Lecture Notes in Mathematics, Watson GA (ed.).Springer Verlag: Dundee, 1978; 630: 104–116.

17. Golub GH, Pereyra V. The differentiation of pseudo-inverses andnonlinear least squares problems whose variables separate. SIAMJ. Numer. Anal. 1973; 10: 413–432.

18. Golub GH, Pereyra V. Separable nonlinear least squares: thevariable projection method and its applications. Inverse Probl.2003; 19(2): 1–26.

19. van der Veen JWC, de Beer R, Luyten PR, Van Ormondt D.Accurate quantification of in vivo PNMR signals using the variableprojection method and prior knowledge.Magn. Res. Med. 1988; 6:92–98.

20. Vanhamme L, Sundin T, Van Hecke P, Van Huffel S.MR spectroscopic quantitation: a review of time domain methods.NMR Biomed. 2001; 14: 233–246.

21. Seeger U, Klose U. Parameterized evaluation of macromoleculesand lipids in protonMR spectroscopy of brain diseases.Magn. Res.Med. 2003; 49: 19–28.

22. Simonetti AW, Melsen W, van der Graaf M, Postma G, HeerschapA, Buydens LMC. A chemometric approach for brain tumorclasssification using magnetic resonance imaging and spec-troscopy. Anal. Chem. 2003; 75(20): 29–36.

23. International network for pattern of tumours using magneticresonance. http://carbon.uab.es/INTERPRET/interpret_home.shtml

24. Tong Z, Toshiaki Y, Yamaki T, Harada K, Houkin K. In vivoquantification of metabolites in normal brain and brain tumors byproton MR spectroscopy using water as an internal standard.Magn. Reson. Imaging 2004; 22: 1017–1024.

25. Fountas KN, Kapsalaki EZ, Gotsis SD, Kapsalakis JZ. In vivoproton magnetic resonance spectroscopy of brain tumors. Stereot.Funct. Neuros. 2000; 74: 83–94.

26. Fan G, Sun B, Wu Z, Guo Q, Guo Y. In vivo single-voxel protonMR spectroscopy in the differentiation of high-grade gliomas andsolitary metastases. Clin. Radiol. 2004; 59: 77–85.

27. Furuya S, Naruse S, Ide M, Morishita H, Kizu O, Ueda S, Maeda T.Evaluation of metabolic heterogeneity in brain tumors using1H-chemical shift imagingmethod.Neurosurgery 1997; 10: 25–30.

28. Gay DM. A trust-region approach to linearly constrained optim-ization. In Numerical Analysis Proceedings, Griffiths DF (ed.).Springer-Verlag: Dundee, 1983; 72–105.

29. Klose U. In vivo proton spectroscopy in presence of eddy currents.Magn. Res. Med. 1990; 14: 26–30.

30. Laudadio T, Mastronardi N, Vanhamme L, Van Hecke P, VanHuffel S. Improved Lanczos algorithms for blackbox MRS dataquantitation. J. Magn. Reson. 2002; 157: 292–297.



APPENDIX

The AQSES framework

To increase the usability, AQSES has been embedded inan application framework that controls the optimizationmethod (12). In general, an application frameworkprovides a set of abstract classes and interfaces, calledhot spots, that can be combined to create an application.For AQSES GUI, the framework provides hot spots forplug-ins to read or write, to preprocess, to quantitate, toexport and to visualize MRS and MRSI data. Thesoftware is developed in Java and is platform independent(e.g. Windows, Linux, OSX and Solaris). The graphicaluser interface (GUI) of the framework is written using theSwing library. AQSES and the HLSVD-PRO algorithmsare implemented in FORTRAN 77. Both methods havebeen compiled for Windows and Linux and have beenmade accessible to the Java code, to make sure that thesoftware can run on both platforms. The main optimiz-ation part of AQSES is carried out using an extension ofthe Levenberg–Marquardt algorithm, which acceptslinear bound constraints, in the DN2GB implementationwritten by Gay (28). FORTRAN is used since well-testedand optimized numerical libraries (e.g. LAPACK, Blas)exist.

At the moment the AQSES GUI accepts MRS andMRSI data coming from:

� Philips (SDAT/SPAR format);� SIEMENS (RDA format);� Matlab (The MathWorks, Inc., Version 4);� text files.

It is easy to add plug-ins to read or write other formatssuch as DICOM by implementing some of the hot spots.After loading, the data can be visualized in the time orfrequency domain and are presented to the user in a 3Dgraph. It is also possible to work with multiple datasets atthe same time, which are stored in projects.

The AQSES GUI offers two types of projects, one calledAQSES database creator to create personal databases, andanother called MRS to process the signals. Any metaboliteprofile can be loaded in the database. There is no restrictionabout the acquisition protocol or about the number ofmetabolite profiles in the database. All preprocessing toolsare available in both projects, while the quantitationmethods are only available in the MRS project. Thepreprocessing methods included at the moment in AQSESGUI are:

� eddy current correction (29);� HLSVD-PRO (30);� zero filling;� point truncation;� manual phase and frequency correction.

The quantitation methods available in the AQSES GUI atthe moment are:


� AQSES;� HLSVD-PRO.

AQSES and HLSVD-PRO are the only methods inAQSES GUI whose codes are not open source. AQSESincorporates model functions with three possible lineshapes (Lorentzian, Gaussian and Voigt). Although this isimplemented in the FORTRAN code, the user presentlyhas access only via AQSES GUI to the Lorentzian lineshape, since the Gaussian and Voigt line shapes have notbeen fully tested yet. The eddy current correction termdiscussed in ‘mathematical formulation’ section is alsonot available yet in AQSES GUI. Therefore, somepreprocessing methods (phase correction, eddy currentcorrection, etc.) should be used before applying AQSES.However, these preprocessing techniques might not berecommendable if the basis set of metabolite profiles andthe MR spectra were acquired with the same acquisitionprotocol such that it is reasonable to assume that they haveundergone the same pattern of distortions.

The AQSES GUI is template driven, which means thatscripts can be built that contain the settings forpreprocessing and quantitation. Templates can be writtenfrom scratch or generated automatically in AQSES GUIwhen processing the signals. These templates can besaved and used easily to redo experiments or to startprocessing in batch mode. The GUI is intended to run intwo different modes. The clinical mode hides most of thecomplexity by using templates, while the research modeprovides the user with all features. In the clinical mode,the user is restricted to:

� load, read, visualize and save data;� process data using existing templates;� visualize and save results.

The results of the quantitation methods are visualizedin a separate window and can be exported to a Matlab file.

The database used in this paper

The in vitro metabolite profiles in this paper havebeen acquired on a 1.5 T Philips NT Gyroscan using aPRESS sequence with an echo time of 23ms, and aPRESS box of 2� 2� 2 cm. To each sample, tworeference compounds were added, situated at 0.0 ppm(3-trimethylsilyl-1-propane-sulfonic acid or TSPS) and at8.44 ppm (formate). One buffer solution of K2HPO4

and KH2PO4 was made including TSPS, formate andphosphate buffer compounds (except for the cholinemetabolite solutions) and NaOH for pH adjustment(brought to 7.2 pH). The solution was divided into smallidentical quantities, in which the relevant metaboliteswere dissolved. All raw FIDs were eddy current correctedusing Klose’s method in the ‘Database Creator’ of theAQSES GUI, and the spectra were frequency shifted suchthat the second reference peak was at 8.44 ppm. All


Figure 6. NAA profile used in the basis set. The amplitudesare in arbitrary units. At 0.0 and 8.44 ppm, the two referencecompounds are visible. They are effectively removed by theFIR filter during quantitation.


profiles were normalized or scaled with respect to the8.44 ppm resonance in the sample of creatine, to ensurethat absolute comparison between metabolites waspossible. This was done as follows. All spectra werefirst filtered with HLSVD-PRO to keep only the referencepeaks at 8.44 ppm. These were fitted using AQSES withthat of the creatine profile. Each metabolite profile wasthen normalized with respect to the amplitudes obtainedin AQSES since the metabolite profiles should have thesame reference peak at 8.44 ppm, its concentration beingidentical for all metabolite solutions. All spectra werefinally normalized with respect to the concentration in thesample during the acquisition, the metabolite concen-tration being different from one metabolite solution toanother. Metabolite profiles of lipids at 1.3 and 0.9 ppmhave been artificially created from the creatine resonance.Therefore, absolute values of these metabolites cannot becompared with the other metabolites. Their simulationwas performed by removing the creatine signal from thespectrum with HLSVD-PRO, followed by addition of asingle resonance at 1.3 or 0.9 ppm. Finally, all metaboliteprofiles have been processed by HLSVD-PRO (from 4.4to 7.0 ppm) to remove the residual water resonance andsome artefacts within that region. As an example, theN-acetylaspartate (NAA) profile is plotted in Fig. 6.At present, two databases are available online from

www.esat.kuleuven.be/sista/members/biomed/new/:

Database 1: 16 metabolite profiles acquired on a 1.5 TPhilips NT Gyroscan using a PRESS sequence with anecho time of 23ms, and a PRESS box of 2� 2� 2 cmþ simulated profiles for Lip1 and Lip2.


Database 2: 16 metabolite profiles acquired on a 1.5 TSiemens using a STEAM sequence with an echo timeof 20ms, and a STEAM box of 2� 2� 2 cm þsimulated profiles for Lip1 and Lip2.

A document is also available, that describes thegeneration and the preprocessing of these databases. Notethat AQSES can be combined with any other database,either generated via simulation or by in vitro acquisition.The databases given here are just representative examples.


an automated quantitation of short echo time mrs spectra in an open source software environment:...

Documents