MRS文献

European Journal of Radiology 67(2008)218–229
Review
The principles of quantification applied to
in vivo proton MR spectroscopy
Gunther Helms ∗
MR-Research in Neurology and Psychiatry,Faculty of Medicine,University of G¨o ttingen,D-37075G¨o ttingen,Germany
Received 27February 2008;accepted 28February 2008
Abstract
Following the identification of metabolite signals in the in vivo MR spectrum,quantification is the procedure to estimate numerical values of
their concentrations.The two essential steps are discussed in detail:analysis by fitting a model of prior knowledge,that is,the decomposition of the spectrum into the signals of singular metabolites;then,normalization of these signals to yield concentration estimates.Special attention is given to using the in vivo water signal as internal reference.©2008Elsevier Ireland Ltd.All rights reserved.
Keywords:MRS;Brain;Quantification;QA
Contents
1.Introduction ............................................................................................................219
2.
Spectral analysis/decomposition..........................................................................................2192.1.Principles........................................................................................................2192.2.Statistical and systematic fitting errors ..............................................................................2212.3.Examples of analysis software......................................................................................
2212.3.1.LCModel ................................................................................................2212.3.2.jMRUI...................................................................................................2213.
Signal normalization ....................................................................................................2233.1.Principles........................................................................................................2233.2.Internal referencing and metabolite ratios............................................................................2233.3.External referencing...............................................................................................2233.4.Global transmitter reference........................................................................................2233.5.Local flip angle...................................................................................................2243.6.Coil impedance effects ............................................................................................2243.7.External phantom and local reference ...............................................................................2253.8.Receive only-coils ................................................................................................2253.9.Internal water reference............................................................................................2253.10.Partial volume correction.........................................................................................2264.Calibration .............................................................................................................2275.Discussion..............................................................................................................2286.Experimental ...........................................................................................................2287.
Recommendations.......................................................................................................228Acknowledgements .....................................................................................................229References .............................................................................................................
229
∗
Tel.:+495513913132;fax:+495513913243.E-mail address:ghelms@gwdg.de .
0720-048X/$–see front matter ©2008Elsevier Ireland Ltd.All rights reserved.doi:10.1016/j.ejrad.2008.02.034
G.Helms/European Journal of Radiology67(2008)218–229219
1.Introduction
In vivo MRS is a quantitative technique.This statement is often mentioned in the introduction to clinical MRS studies. However,the quantification of signal produced by the MR imag-ing system is a complex and rather technical issue.Inconsistent terminology and scores of different approaches make the prob-lem appear even more complicated,especially for beginners. This article is intended to give a structured introduction to the principles of quantification.The associated problems and pos-sible systematic errors(“bias”)are explained to encourage a critical appraisal of published results.
Quantification is essential for clinical research,less so for adding diagnostic information for which visual inspection often may suffice.Subsequent to the identification of metabolites,its foremost rationale is to provide numbers for comparison of spec-tra from different subjects and brain regions;and–ideally–different scanners and sequences.These numbers are then used for evaluation;e.g.statistical comparison of cohorts or correla-tion with clinical parameters.The problem is that the interaction of the radio-frequency(RF)hardware and the dielectric load of the subject’s body may lead to rather large signal variations(up to30%)that may blur systematic relationships to cohorts or clinical parameters.One of the purposes of quantification is to reduce such hardware related variation in the numbers.Thus, quantification is closely related to quality assurance(QA).
In summary,quantification is a procedure of data processing. The post-processing scheme may require additional data acqui-sitions or extraction of adjustment parameters from the scanner. The natural order of steps in the procedure is
1.acquisition and pre-processing of raw data,reconstruction of
the spectrum(e.g.averaging and FFT),
2.analysis:estimation of the relative signal for each identified
metabolite(here,proton numbers and linewidth should be taken into account),
3.normalization of RF-induced signal variations,
4.calibration of signals by performing the quantification
scheme on a standard of known concentration.
In turn,these steps yield the metabolite signals
1.for visual inspection of the displayed spectrum on the ppm
scale,
2.in arbitrary units,from which metabolite ratios can be cal-
culated,
3.in institutional units(for your individual MR scanner and
quantification scheme;these numbers are proportional to the concentration),
4.in absolute units of concentration(commonly in
mM=mmol/l);estimated by comparison to a standard of known concentration.
The term quantification(or sometimes“quantitation”)is occasionally used to denote singular steps of this process.In this review,it will refer to the whole procedure,and further differ-entiation is made for the sake of clarity.In practice,some these steps may be performed together.Already at this stage it should be made clear that the numbers obtained by“absolute quantifica-tion”are by no means“absolute”but depend on the accuracy and precision of steps1–4.Measurement and reconstruction(step1) must be performed in a consistent way lest additional errors have to be accounted for in individual experiments.Only in theory it should be possible to correct all possible sources of variation;in clinical practice it is generally is too time consum-ing.Yet the more sources of variation are cancelled(starting with the biggest effects)the smaller effects one will be able to detect.
Emphasis will be put on the analysis(the models and the automated tools available),the signal normalization(and basic quality assurance issues),and the use of the localized water signal as internal reference.
2.Spectral analysis/decomposition
2.1.Principles
The in vivo spectrum becomes more complicated with decreasing echo time(TE):next to the singlet resonances and weakly coupled multiplets,signals from strongly coupled metabolites and baseline humps from motion-restricted macro-molecules appear.Contrary to long-TE spectra short-TE spectra should not be evaluated step-by-step and line-by-line.For exam-ple,the left line of the lactate doublet is superposed onto the macromolecular signal at1.4ppm.The total signal at this fre-quency is not of interest but rather the separate contributions of lactate and macromolecules/lipids.Differences between the two whole resonance patterns can be used to separate the metabolites;
e.g.the doublet of lactate versus the broad linewidth.In visual inspection,one intuitively uses such‘prior knowledge’about the expected metabolites to discern partly overlying metabolites in a qualitative way.This approach is also used to simplify the problem to automaticallyfind the metabolite resonances to order to evaluate the whole spectrum“in one go”.
Comparing the resonance pattern of MR spectra in vivo at highfield and short TE with those of tissue extracts and sin-gle metabolites in vitro at matchedfield strengths hasfirmly established our‘prior’knowledge about which metabolites con-tribute to the in vivo MR spectra[1].Next to TE,thefield strength exerts the second biggest influence on the appearance of in vivo MR spectra.Overlap and degeneration of binomial multiplets due to strong coupling increase at the lowerfield strengths of clinical MR systems(commonly3,2,or1.5T). These effects can be either measured on solutions of single metabolites[2]or simulated fromfirst quantum-mechanical principles,once the chemical shifts and coupling constants(J in Hz)of a certain metabolite have been determined at suffi-ciently highfield[3].Motion-restricted‘macromolecules’are subject to rapid relaxation that blurs the coupling pattern(if the linewidth1/πT∗2>J)and hampers the identification of specific compounds.These usually appear as broad‘humps’that form the unresolved baseline of short-TE spectra(Fig.1).These vanish at longer TE(>135ms).The baseline underlying the metabo-
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Fig.1.Including lipids/macromolecules into the basis set.Without inclusion of lipids/macromolecules in the basis set (A)the broad “humps”at 1.3and 0.9ppm are fitted by the baseline.Inclusion of lipids/macromolecules (B)resulted in a better fit and a lower baseline between 2.2and 0.6ppm.The SNR improved from 26to 30.The signals at 2.0ppm partly replaced the co-resonating tNAA.The 6%reduction in tNAA was larger than the fitting error (3%).This may illustrate that the fitting error does not account for the bias in the model.LCModel (exp.details:6.1-0;12.5ml VOI in parietal GM,3T,STEAM,TE/TM/TR/avg =20/10/6000/64).
lite signals is constituted from all rapidly relaxing signals that have not decayed to zero at the chosen TE (macromolecules and lipids),the “feet”of the residual water signal,plus possible arte-facts (e.g.echo signals from moving spins that were not fully suppressed by gradient selection).
The ‘prior knowledge’about which metabolites to detect and how the baseline will look like is used to construct a math-ematical model to describe the spectrum.Selecting the input signals reduces the complexity of the analysis problem.In con-trast to integrating or fitting singlet lines the whole spectrum is evaluated together (“in one go”)by fitting a superposition of metabolite signals and baseline signals.Thus,the in vivo spec-trum is decomposed into the constituents of the model.Without specifying the resonances this is often too complicated to be per-formed successfully,in the sense that an unaccountable number of ‘best’combinations exist.
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Prior knowledge may be implemented in the metabolite basis set adapting experimental data(like in LCModel[2]),theoretical patterns simulated fromfirst principles(QUEST[4]),or purely phenomenological functions like a superposition of Gaussians of different width to model strongly coupled signals and baseline humps alike(AMARES[5]).The least squaresfit may be per-formed in either time domain[6]or frequency domain or both [7].For an in-depth discussion of technical details,the reader is referred to a special issue of NMR in Biomedicine(NMR Biomed14[4];2001)dedicated to“quantitation”(in the sense of spectrum analysis)by mathematical methods.
2.2.Statistical and systematicfitting errors
Modelfitting yields the contribution of each input signal. Usually Cr´a mer–Rao lower bounds(CLRB)are provided as an estimate for thefitting error or the statistical uncertainty of the concentration estimate.These are calculated from the residual error and the Fisher matrix of the partial derivatives of the con-centrations.In the same way,correlations between the input data can be estimated.Overlapping input signals(e.g.from glutamate (Glu)and glutamine(Gln))are inversely correlated.In this case, the sum has a smaller error than the single metabolites.The uncertainties are fairly well proportional to the noise level(both must be given in the same units).
The models are always an approximate,but never a com-plete description of the in vivo MR spectrum.Every model thus involves some kind of systematic error or“bias”,in the sense of deviation from the unknown“true”concentration.Contrary to the statistical uncertainty,the bias cannot be assessed within the same model.In particular,the CRLB does not account for the bias.Changes in the model(e.g.,by leaving out a minor metabo-lite)may result in systematic differences that soon become significant(by a paired t-test).These are caused by the pro-cess of minimizing the squared residual difference whenfitting the same data by two different models.
Spurious artefacts or“nuisance signals”that are not included in the model will results in errors that are neither statistical nor systematic.It is also useful to know,that for every non-linear function(as used in MRS)there is a critical signal-to-noise (SNR)threshold for convergence onto meaningful values.
2.3.Examples of analysis software
A number of models and algorithms have been published dur-ing the past15years.A few are available to the public and shared by a considerable number of users.These program packages are generally combined with some automated or interactive pre-processing features,such as correction of frequency offset,zero andfirst order,as well as eddy-current induced phase errors.We shall in brief describe the most common programs for analysis of in vivo1H MRS data.
2.3.1.LCModel
The Linear Combination Model(LCModel)[2]comes as stand-alone commercial software(/ lcmodel).It comprises automated pre-processing to achieve a high degree of user-independence.An advanced regularization ensures convergence for the vast majority of in vivo spectra.It was thefirst program designed tofit a basis set(or library)of experimental single metabolite spectra to incorporate maximum information and uniqueness.This means that partly overlap-ping spectra(again such as,Glu and Gln)are discerned by their unique features,but show some residual correlation as mentioned above.Proton numbers are accounted for,even“frac-tional proton numbers”in“pseudo-singlets”(e.g.,the main resonance of mIns).Thus,the ratios provided by LCModel refer to the concentrations rather than proton numbers.The basis set of experimental spectra comprises the prior information on neurochemistry(metabolites)as well as technique(TE,field strength,localization technique).The non-analytic line shape is constrained to unit area and capable tofit even distorted lines (due to motion or residual eddy currents).The number of knots of the baseline spline increases with the noise level.Thus,the LCModel is a mixture of experimental and phenomenological features.Although the basis spectra are provided in time domain, the evaluation is performed across a specified ppm interval.
LCModel comes with a graphical user interface for routine application.Optionally the water signal may be used as quan-tification reference.Recently,lipids and macromolecular signals have been included to allow evaluation of tumour and muscle spectra.An example is shown in Fig.1.
LCModel comprises basic signal normalization(see below) according to the global transmitter reference[8]to achieve a consistent scaling of the basis spectra.An in-house acquired basis set can thus be used to estimate absolute concentrations. Imported basis sets are available for a wide range of scanners and measurement protocols,but require a calibration to match the individual sensitivity(signal level)of the MR system[9]. Owing to LCModel’sflexibility,the basis set may contain also simulated spectra or an experimentally determined baseline to account for macromolecular signals.Such advanced applica-tions require good theoretical understanding and some practical experience.Care must be taken to maintain consistent scaling when adding new metabolite spectra to an existing basis.This is easiest done by cross-evaluation,that is evaluating a reference peak(e.g.,formate)in spectrum to be included by the singlet of the original basis and correcting to the known value.
Caveat:The fact that LCModel converges does not ensure reliability of the estimates;least in absolute units(see Sections 3and4).Systematic difference in SNR may translate into bias via the baseline spline(see Fig.2).The same may be due an inconsistent choice of the boundaries of the ppm interval,partic-ularly next to the water resonance.In particular,with decreasing SNR(lower than4)one may observe more often systematically low or high concentrations.This is likely due to the errors in the feet of the non-analytical line shape,as narrow lines lead to underestimation and broad lines to overestimation.The metabo-lite ratios are still valid,as all model spectra are convoluted by the same lineshape.
2.3.2.jMRUI
The java-based MR user interface for the processing of in vivo MR-spectra(jMRUI)is provided without charge
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Fig.2.Systematic baseline differences between low and high SNR.Single spectrum from an 1.7ml VOI in white matter of the splenium (A)and the averaged spectra of seven healthy subjects (B).Note how the straight baseline leads to a severe underestimation of all metabolites except mIns.Differences were most prominent for Glu +Gln:3.6mM (43%)in a single subject vs.6.7mM (7%)in the averaged spectrum.
(http://www.mrui.uab.es/mrui/mrui Overview.shtml ).It comes with a wide range of pre-processing features and interac-tive graphical software applications,including linear prediction and a powerful water removal by Hankel–Laclosz single value decomposition (HLSVD).In contrast to LCModel,it is designed to support user interaction.Several models for analy-sis/evaluation have been implemented in jMRUI,in particular AMARES [5]and QUEST [4].These focus on time-domain analysis,including line shape conversion,time-domain filter-ing and eddy-current deconvolution.Note that in the context of jMRUI ‘quantitation’refers to spectrum analysis.The pre-processing steps may exert a systematic influence on the results of model fitting.jMRUI can handle large data sets as from time-resolved MRS,two-dimensional MRS,and spatially resolved MRS,so-called MR spectroscopic imaging (MRSI)or chemical-shift imaging (CSI).
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3.Signal normalization
3.1.Principles
The signal is provided in arbitrary units of signed integer numbers,similar to MRI,and then converted tofloating complex numbers.In addition to scaling along the scanner’s receiver line, the proportionality between signal strength and number of spins per volume is strongly influenced by interaction of the RF hard-ware and its dielectric and conductive load,the human body.It is the correction of this interaction that forms the non-trivial part of signal normalization.Signal normalization is mainly applied to single-volume MRS,since spatially resolved MRSI poses addi-tional technical problems that are not part of this review.For sake of simplicity we assume homogeneous conditions across the whole volume-of-interest(VOI).
Normalization consists of multiplications and divisions that render the signal,S,proportional to the concentration(of spins), C.Regardless whether in time domain(amplitude)or frequency domain(area),the signal is proportional to the size V of the VOI and the receiver gain R.
S∼CVR or(1a) S/V/R∼C(1b) Logarithmic(decibel)units of the receiver gain must be con-verted to obtain a linear scaling factor,R.If R can be manually changed,it is advisable to check whether the characteristic of S(R)follows the assumed dependence.If a consistent(often the highest possible)gain used by default for single voxel MRS, one does not have to account for R.Correction of V for partial volume effects is discussed below.
The proportionality constant will vary under the influence of the specific sample“loading”the RF coil.The properties of a loaded transmit–receive(T/R)coil are traditionally assessed by measuring the amplitude(or width)of a specific RF pulse,e.g., a180◦rectangular pulse.This strategy may also be pursued in vivo.The signal theory for T/R coils is given in concise form in [10]without use of complex numbers.Here,we develop it by presenting a chronology of strategies of increasing complexity that have been used for in vivo quantification.
3.2.Internal referencing and metabolite ratios
By assuming a concentration C int for the signal(S int)of ref-erence substance acquired in the same VOI,one has not to care about the influence of RF or scanner parameters:
S
S int
C int=C(2)
When using the total creatine(tCr)signal,internal referencing is equivalent to converting creatine ratios to absolute units.In early quantification work,the resonance of tCr has been assigned to 10mM determined by biochemical methods[11].However,it turned out that the MRS estimates of tCr are about25%lower and show some spatial dependence.In addition,tCr may increase in the presence of gliosis.3.3.External referencing
The most straightforward way is to acquire a reference sig-nal from an external phantom during the subject examination, with C ext being the concentration of the phantom substance [12,13].The reference signal S ext accounts for any changes in the proportionality constant.It may be normalized like the in vivo signal:
S
(VR)
C ext
S ext/(V ext R ext)
=C(3)
If,however,the phantom is placed in the fringefield of the RF receive coil,the associated reduction in S ext will result in an overestimation of C.Care has to be taken to mount the external phantom reproducibly into the RF coil if this bias cannot be corrected otherwise.
3.4.Global transmitter reference
Already in high-field MR spectrometers it has been noticed that by coil load the sample influences both the transmit pulse and the signal:a high load requires a longer RF pulse for a 90◦excitation,which then yields reciprocally less signal from the same number of spins.This is the principle-of-reciprocity (PoR)for transmit/receive(T/R)coils in its most rudimentary form.It has been applied to account for the coil load effect, that is,large heads giving smaller signals than small heads [8].On MRI systems,RF pulses are applied with constant duration and shape.A high load thus requires a higher volt-age U tra(or transmitter gain),as determined during pre-scan calibration.
S/V/R∼
C
tra
or(4a) S U tra/V/R∼C(4b)
Of course,U tra must always refer to a pulse of specific shape, duration andflip angle,as used forflip angle calibration.On Siemens scanners,the amplitude of a non-selective rectangu-lar pulse(rect)is used.The logarithmic transmitter gain of GE scanners is independent of the RF pulse,but has to be converted from decibel to linear units[9].
Normalization by the PoR requires QA at regular intervals,as the proportionality constant in Eqs.((4a)and(4b))may change in time.This may happen gradually while the performance of the RF power amplifier wears down,or suddenly after parts of the RF hardware have been replaced.For this purpose,the MRS protocol is run on a stable QA phantom of high concentration and the concentration estimate C QA(t i)obtained at time point, t i,is used to refer any concentration C back to time point zero by
C→
C C QA(t0)
C QA(t i)(5)
An example of serial QA monitoring is given in Fig.3.
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Fig.3.QA measurement of temporal variation.Weekly QA performed on stable phantom of 100mM lactate and 100mM acetate from January 1996to June 1996.The standard single-volume protocol and quantification procedure (LCModel and global reference)were applied.(A)The mean estimated concentration is shown without additional calibration.The A indicates the state after installation,B a gradual breakdown of the system;the sudden jumps were due to replacement of the pre-amplifier (C and D)or head-coil (E),and retuning of the system (F).Results were used to correct proportionality to obtain longitudinally consistency.(B)The percentage deviation from the preceding measurement in Shewhart’s R-diagram indicates the weeks when quantification may not be reliable (data courtesy of Dr.M.Dezortov´a ,IKEM,Prague,Czech Republic).
3.5.Local flip angle
Danielsen and Hendriksen [10]noted that the PoR is a local relationship,so they used the amplitude of the water suppression pulse,U tra (x ),that had been locally adjusted on the VOI signal.S (x )U tra (x )/V/R ∼C
(6)
The local transmitter amplitude may also be found be fitting the flip angle dependence of the local signal [14].The example in Fig.4illustrates the consistency of Eq.(6)at the centre (high signal,low voltage)and outside (low signal,high voltage)the volume head
coil.
Fig.4.Local verification of the principle of reciprocity.Flip angle dependence of the STEAM signal measured at two positions along the axis of a GE birdcage head-coil by varying the transmitter gain (TG).TG was converted from logarith-mic decibel to linear units (linearized TG,corresponding to U tra ).At coil centre (×)and 5cm outside the coil (+)the received signal,S (x ),was proportional to the transmitted RF,here given by 1/lin TG(x )at the signal maximum or 90◦flip angle.
Like in large phantoms,there are considerable flip angle devi-ations across the human head as demonstrated at 3T in Fig.5a [15].The local flip angle,α(x ),may be related to the nominal value,αnom ,by α(x )=f (x )αnom
(7)
The spatially dependent factor is reciprocal to U tra (x ):f (x )∼1/U tra (x ).The flip angle will also alter the local signal.If a local transmitter reference is used,S (x )needs to be corrected for excitation effects.For the ideal 90◦–90◦–90◦STEAM local-ization and 90◦–180◦–180◦PRESS localization in a T/R coil,the signals are
S (x )STEAM ∼M tr (x )∼C
2f (x )sin 3(f (x )90◦)
(8a)S (x )PRESS ∼M tr (x )∼C f (x )sin 5(f (x )90◦)
(8b)
The dependence of S (x )was simulated for a parabolic RF profile.A constant plateau is observed as the effects of transmission and reception cancel out for higher flip angles in the centre of the head where the VOI is placed.This is the reason why the global flip angle method works even in the presence of flip angle inhomogeneities.Note that the signal drops rapidly for smaller flip angles,i.e.close to the skull.3.6.Coil impedance effects
Older quantification studies were performed on MR systems where the coil impedance Z was matched to 50 [8,10].Since the early 1990s,most volume head coils are of the high Q design and approximately tuned and matched by the RF load of the head and the stray capacitance of the shoulders.The residual variation of the impedance Z will affect the signal by S (x )U tra (x )/V/R ∼CZ
(9)
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225
Fig.5.Flip angle inhomogeneities across the human brain.(Panel A)T1-w sagittal view showing variation in the RFfield.Flip angles are higher in the centre of the brain.The contours correspond to80–120◦localflip angle for a nominal value of90◦.(Panel B)The spatial signal dependence of STEAM and PRESS was simulated for a parabolicflip angle distribution with a maximum of115%relative to the global transmitter reference.This resulted in a constant signal obtained from the central regions of the brain,and a rapid decline at the edges.
Reflection losses due to coil mismatch are symmetric in trans-mission and reception and are thus accounted for by U tra.These are likely to occur with exceptionally large or small persons (infants)or with phantoms of insufficient load.
3.7.External phantom and local reference
When the impedance is not individually matched to50 , the associated change in proportionality must be monitored by a reference signal.In aqueous phantoms,the water signal can be used as internal reference.For in vivo applications,one may resort to an extra measurement in an external phantom[14].An additionalflip angle calibration in the phantom will account for local differences in the RFfield,especially if the phantom is placed in the fringe RFfield:
SU tra(x)/(VR)
S ext U tra(x ext)/(V ext R ext)
C ext=C(10)
This is the most comprehensive signal normalization.The com-bination of external reference and localflip angle method corrects for all effects in T/R coils.The reference signal accounts for changes in the proportionality,while the localflip angle cor-rects for RF inhomogeneity.Note also that systematic errors in S,U tra and V cancel out by division.Calibration of each individual VOI may be sped up by rapid RF mapping in three dimensions.
3.8.Receive only-coils
The SNR of the MRS signal can be increased by using sur-face coils or phased arrays of surface coils.The inhomogeneous receive characteristic cannot be mapped directly.The normaliza-tions discussed above(except Section3.2)cannot be performed directly on the received signal,as the coils are not used for trans-mission.Instead,the localized water signal may be acquired with both the receive coil and the body coil to scale the low SNR metabolite signal to obey the receive characteristics of the T/R body coil[16,17]:
S rec met S body
water
S rec water
=S body
met
(11)
For use with phased array coils it is essential that the metabolite and water signals are combined using consistent weights,since the low SNR of the water suppressed acquisition is most likely influenced by noise.
3.9.Internal water reference
The tissue water appears to be the internal reference of choice, due to its high concentration and well established values for water content of tissues(βper volume[18]):
S
S water
β55mol/litre=C(12)
It should be kept in mind that in vivo water exhibits a wide range of relaxation times,with the main component relaxing consider-able faster than the main metabolites.T2-times range from much shorter(myelin-associated water in white mater T2of15ms)to much longer(CSF,2400ms in bulk down to700ms in sulci with large surface-to-volume ratio).This implies an influence of TE on the concentration estimates.In addition,relaxation time and water content are subject to change in pathologies.Since the water signal is increasing in most pathologies(by content and relaxation),water referencing tends to give lower concentration estimates in pathologies.
Ideally,the water signal should be determined by a multi-componentfit of the T2-decay curve[12].An easy but time-consuming way is to increase TE in consecutive fully relaxed single scans.A reliable way to determine the water sig-nal is tofit a2nd order polynomial through thefirst50ms of the magnitude signal(Fig.6).Thus,determining the amplitude cancels out initial receiver instabilities and avoids linefitting at an ill defined phase.If care is taken to avoid partial saturation by RF leakage from the water suppression pulses,this is consistent with multi-echo measurements using a CPMG MRI sequence [18](Fig.7).。