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Journal of Chromatography A, 1187 (2008) 1–10

Advantages of PARAFAC calibration in the determination ofmalachite green and its metabolite in fish by liquid

chromatography–tandem mass spectrometry�

David Arroyo a, M. Cruz Ortiz a,∗, Luis A. Sarabia b, Francisco Palacios c

a Department of Chemistry, Faculty of Sciences, University of Burgos, Pza. Misael Banuelos s/n, 09001 Burgos, Spainb Department of Mathematics and Computation, Faculty of Sciences, University of Burgos, Pza. Misael Banuelos s/n, 09001 Burgos, Spain

c Department of Health and Consumption, Diputacion General de Aragon, C/Ramon y Cajal 68, 50004 Zaragoza, Spain

Received 11 December 2007; received in revised form 6 February 2008; accepted 11 February 2008Available online 15 February 2008

bstract

This paper reports the properties and advantages of the three-way calibration models based on parallel factor analysis (PARAFAC) in theimultaneous determination of malachite green (MG) and its metabolite (leucomalachite green, LMG) in trout. A recently method proposed byommunity reference laboratory AFSSA-LERMVD (Fougeres, France) has been used. The method is based on liquid chromatography–tripleuadrupole mass spectrometry (LC–MS/MS) in multiple reaction monitoring (MRM) mode. The validation of the method has been carried outaking into account the Decision 2002/657/EC. The figures of merit for PARAFAC and univariate calibration models of six non-consecutive daysnalyzed during a month were evaluated. With the samples of the first 3 days, calibration models were built and the fish fortification samples ofhe other days were predicted. Decision limits (CCα, α = 0.01), detection capabilities (CCβ, β = 0.05) and mean relative errors in absolute valuein calibration and with test samples) obtained with PARAFAC calibrations were more homogeneous than the ones obtained with the univariate

alibrations, especially in LMG. These figures of merit were in the range of 0.2–0.83 �g kg−1 (CCβ) and 0.2–0.49 �g kg−1 (CCα), whereas meanelative errors in absolute value were in the range of 1.1–7.4% in calibration and 3–12% in test samples for MG and LMG with PARAFACalibrations. The PARAFAC calibrations allow detecting the test samples which are not similar to the calibration samples and in this way theirrong quantification is avoided.

/EC;

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2008 Elsevier B.V. All rights reserved.

eywords: Malachite green; LC–MS/MS; PARAFAC; Fish; Decision 2002/657

. Introduction

Malachite green (MG) is a triphenylmethane dye that haseen used in fish farming industry during many decades becausef its broad anti-microbial, anti-parasitic and anti-fungal spec-rum, its high efficacy in the prevention and treatment of certainsh diseases and its low cost. It has been found that dyes of thisamily (like rosaniline) can induce hepatic and renal tumors in

ice [1] and reproductive abnormalities in fish [2]. Due to its

arcinogenic properties, MG is not authorized by the Europeannion [3] and the US Food and Drug Administration (FDA).

� Presented at the 7th Meeting of the Spanish Society of Chromatography andelated Techniques, Granada, Spain, 17–19 October 2007.∗ Corresponding author. Fax: +34 947 258 831.

E-mail address: mcortiz@ubu.es (M.C. Ortiz).

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021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2008.02.040

Capability of detection; CCβ

MG is readily absorbed by fish and metabolically reduced tohe non-polar and colourless leucomalachite green (LMG). The

ajority of prevalent residues present in fish tissues are thereforen the form of LMG [4]. For this reason, the European Commis-ion requires that methods to be able to determine MG and LMGesidues in the meat of aquaculture products. In addition, theommission has established a minimum required performance

imit (MRPL) of 2 �g kg−1 for the sum of MG and LMG [5,6].Due to strong absorption of MG in the visible range, sev-

ral analytical methods of liquid chromatography with visibleetection for screening and confirmatory purposes have beenmployed. In these examples, post-column oxidations of LMGo MG using lead(IV) oxide [7–10] or another oxidative process

11] are necessary.

However, most of the analytical methods for the determina-ion of these residues are based on liquid chromatography with

ass spectrometry detection (LC–MS). The most common

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D. Arroyo et al. / J. Chro

onization techniques are atmospheric pressure chemicalonization (APCI) [12–15] and electrospray ionization (ESI)16–19]. Compared to visible spectroscopic techniques, masspectrometry (and above all tandem mass spectrometry)ethods provide greater sensitivity and specificity, with smaller

apability of detection.In this paper the advantages of PARAFAC calibration for

imultaneous confirmation and quantification of MG and LMGre shown by using a recently LC–ESI-MS/MS proposedethod by community reference laboratory AFSSA-LERMVD

Fougeres, France) [20].Since PARAFAC calibrations allow the unequivocal iden-

ification of an analyte (second-order property), it is possibleo quantify a problem sample without carrying out again the

easure of new calibration standards, only a new PARAFACecomposition is necessary [21], with the advantage of reduc-ng the analysis time. In this analytical method a stability timeetween measurements greater than the time run is necessary, sony reduction in the number of the calibration samples is impor-ant. In addition, Q and T2 indices, which are characteristics ofhe multivariate calibrations, are useful to decide if a problemample can be predicted with the fitted model. This possibilitys of great interest in the routine laboratories.

As Decision 2002/657 demands to record multivariate datao identify unequivocally the analyte, the approach proposed inhis paper no additional experimental work is needed.

. Experimental

.1. Chemicals and standard solutions

All organic solvents were of HPLC-grade and the rest ofhemicals used were of analytical-reagent grade unless other-ise stated. Methanol, acetonitrile, glacial acetic acid (99.8%)

nd ammonium acetate (≥98%) were supplied by Merck (Darm-tadt, Germany). Hydroxylamine hydrochloride (≥98%) wereurchased from Fluka (Neu-Ulm, Germany) and deionised wateras obtained by using the Milli-Q gradient A10 water purifica-

ion system of Millipore (Bedford, MA, USA).Analytical standards of malachite green oxalate (>90%),

eucomalachite green (>90%) and crystal violet (>90%,V) were obtained from Aldrich (Steinheim, Germany).

2H5]Leucomalachite green (98%, LMG-d5) was purchasedrom WITEGA Laboratorien Berlin-Adlershof GmbH (Berlin,ermany). CV and LMG-d5 were used as internal standards forG and LMG, respectively.Individual stock solutions of MG, LMG, CV and LMG-d5

t 1000 mg L−1 were prepared in methanol and were stored inmber bottles at −20 ◦C in the dark for less than 6 months. Thendividual intermediate standard solutions (20 mg L−1) wererepared by diluting the stock solution with acetonitrile (LMG,MG-d5 and CV) or with a mixture of ammonium acetate (0.1 MH 4.5) and acetonitrile (30:70 v/v) for MG. The intermediate

tandard solutions were stored in amber bottles at 4 ◦C in theark for less than 3 months.

Combined standard solutions (2 mg L−1) of MG plus LMGnd CV plus LMG-d5 were prepared prior to use, with a mixture

toss

r. A 1187 (2008) 1–10

f hydroxylamine (5 g L−1) and acetonitrile (20:80 v/v). Work-ng standard solutions (0.01 mg L−1) were prepared by the dilu-ion of the combined standard solutions at the same conditions.ll solutions containing the dyes were protected from light.

.2. Characterization of the internal standards

Table 1 shows the integrated areas for both internal standardsCV and LMG-d5) and the analytes in three types of fortifiedatrix (the same trout muscle fortified in two different days and

ure standard samples diluted in a mixture of hydroxylamine5 g L−1) and acetonitrile (20:80 v/v).

Table 2 shows the calibration curves of the regressionetween peak area of internal standards (CV or LMG-d5) andeak area of its corresponding analyte (values of the peak areasn Table 1). As can be seen these regressions are not significa-ive (in all of them the test of linearity has p-values greater than.05). Therefore, in the range of calibration carried out, it cane concluded that the responses of the internal standards areonstant, that is, the slope is zero.

The same conclusion can be obtained if the peak areas ofhe internal standards are adequately modeled by a rectangularuniform) distribution. As can be seen in Table 2, all of the p-alues of the three test (Kolmogorov, Cramer-Von Mises andnderson-Darling) are greater than 0.05, and therefore there iso evidence to reject the null hypothesis (H0) at a confidenceevel of 95%. The H0 of these three tests is: The data come fromrectangular distribution.

.3. Fish sample preparation

The trout was filleted, the skin and bones were removed, andhe muscles were homogenized and frozen at −20 ◦C, beforenalysis. One gram of homogenized edible tissue was placednto 15 mL polypropylene centrifuge tube, and fortified samplesere prepared by the addition of 100 �L of the working solu-

ion of the internal standards (corresponding to 1.0 �g kg−1) andf appropriate amount of the MG plus LMG working standardolution (corresponding to final concentrations between 0.2 and.0 �g kg−1 with five concentration levels).

Then, fortified samples were homogenized using a vortex-ixer (Velp Scientifica, Milan, Italy) during 30 s and were

ncubated during 10 min in darkness. After that, 1 mL of hydrox-lamine solution (5 g L−1) was added. The tubes were shakenn a vortex-mixer during 30 s and incubated again during 10 minn darkness. Next, 4 mL of acetonitrile were added and tissuesere extracted for 10 min on a platform shaker (J.P Selecta,arcelona, Spain) operating at 210 rpm. The samples were then

onicated for 15 min.Finally, the tubes were centrifuged at 3000 rpm for 15 min at

◦C. The supernatants were transferred into 2 mL vials using

issues were previously tested and shown to contain no residuesf the analytes (MG and LMG). The second series of Table 1hows one fish sample unfortified with the analytes, as can beeen there is no signal detected for MG and LMG in this sample.

D. Arroyo et al. / J. Chromatogr. A 1187 (2008) 1–10 3

Table 1Characterization of the internal standards used

Type of matrix Concentration (�g kg−1) AMG ACV ALMG ALMG-d5

First series fish sample fortified

0.50 418 1326 658 9110.50 432 1384 649 8661.00 832 1419 1299 9071.00 824 1464 1321 9652.00 1769 1425 2599 9532.00 1679 1409 2667 9412.90 2598 1387 3130 7372.90 2572 1449 3203 7153.90 3411 1311 4997 8873.90 3419 1338 5025 9014.90 4366 1350 5240 7294.90 4389 1345 5143 708

Second series fish sample fortified

0.00 n.d 1424 n.d 7220.50 544 1544 467 6741.00 1105 1441 884 6812.00 2133 1392 1595 6332.90 3123 1418 2549 6853.90 3980 1372 2605 5464.90 5254 1413 4143 672

Pure standard fortified (LMG in brackets)

0.49 (0.54) 654 1429 525 6010.49 (0.54) 640 1375 468 5790.98 (1.09) 1251 1394 921 6051.96 (2.17) 2533 1392 1957 6462.94 (3.26) 3871 1402 2465 6113.93 (4.34) 5000 1403 3120 565

In all the samples, CV and LMG-d5 (internal standards) are at 1 �g kg−1. The column “concentration” shows the fortified concentration for both analytes (MG andLMG). The Aanalyte were calculated with the strong transition of each analyte (see Table 3). n.d, not detected.

Table 2Performance of the internal standards (CV and LMG-d5) with the data of Table 1

Data Analyte/I.S Null hypothesis (H0) p-Value Equation, R2, syx

First series fish sample fortifiedMG/CV

The linear model is notsignificant

0.138 ACV = 1418.71 − 0.015 AMG,R2 = 0.20, syx = 46.87

The data come from arectangular distribution

K testa = 0.912, CVMtestb = >0.1, AD testc = >0.1

LMG/LMG-d5The linear model is notsignificant

0.10 ALMG-d5 = 936.29 − 0.028 ALMG,R2 = 0.25, syx = 90.17

The data come from arectangular distribution

K testa = 0.299, CVMtestb = >0.1, AD testc = >0.1

Second series fish sample fortifiedMG/CV

The linear model is notsignificant

0.140 ACV = 1491.85 − 0.022 AMG,R2 = 0.45, syx = 49.94

The data come from arectangular distribution

K testa = 0.212, CVMtestb = >0.1, AD testc = >0.1

LMG/LMG-d5The linear model is notsignificant

0.749 ALMG-d5 = 662.25 − 0.006 ALMG,R2 = 0.02, syx = 59.01

The data come from arectangular distribution

K testa = 0.149, CVMtestb = >0.1, AD testc = >0.1

Pure standard fortifiedMG/CV

The linear model is notsignificant

0.343 ACV = 1405.25 − 0.004 AMG,R2 = 0.14, syx = 25.91

The data come from arectangular distribution

K testa = 0.591, CVMtestb = >0.1, AD testc = >0.1

LMG/LMG-d5The linear model is notsignificant

0.20 ALMG-d5 = 615.42 − 0.012 ALMG,R2 = 0.25, syx = 33.67

The data come from arectangular distribution

K testa = 0.791, CVMtestb = >0.1, AD testc = >0.1

a Kolmogorov test.b Cramer-Von Mises test.c Anderson-Darling test.

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.4. Chromatography conditions

The LC system consists of a Waters Alliance 2790 separationsodule (Waters, Milford, MA, USA) coupled to a Micromassuattro Micro-tandem mass spectrometer (Micromass UK Ltd.,ltrincham, UK) with atmospheric pressure ionization sourceperating in the positive ion electrospray (ESI+) mode.

The chromatography separation was carried out using a Syn-rgi MAX-RP 80 A analytical column (4 �m, 150 mm × 2.0 mm.D., Phenomenex, Macclesfield, UK) with a MAX-RP guardolumn (4 mm × 2.0 mm I.D.). A gradient program was usedt a flow rate of 400 �l min−1, in which mobile phase A con-ists of 0.1 M ammonium acetate (pH 4.5) and mobile phase Bonsists of acetonitrile. The gradient program was applied as fol-ows: 50%A/50%B increased to 100%B (linear ramp) from 0 tomin; keeping at these conditions for 4 min; returned instantly

o 50%A/50%B; keeping at these conditions for 3 min (10 min inotal). Oven and injector temperatures were fixed at 40 and 15 ◦C,espectively. The injection volume was 20 �L. Data acquisitionas performed using MassLynx version 4.0 chromatographicanagement software (Waters).

.5. MS–MS parameters

The analysis was performed using positive-ion electrosprayESI+) interface with multiple reaction monitoring (MRM)ode. The two transitions per compound (only one for I.S.) and

he spray and collision voltages used are shown in Table 3. Forhe confirmation of the presence of MG and LMG, the identityf these residues could be determined with at least four iden-ification points, according to European Decision 657/2002. Aotal score of 4 identification points was obtained (1 point wasarned with the parent ion and 1.5 points were earned with eachroduct ions). The following conditions were used: source tem-erature 120 ◦C; desolvation temperature 400 ◦C; N2 cone gasow 50 L h−1 and N2 desolvation gas flow 650 L h−1; capillaryoltage 3.0 kV. Argon was used as collision gas.

.6. Software

PARAFAC decomposition was made with PLS-Toolbox [22]or the use with MATLAB version 7 (The MathWorks). Decision

able 3S/MS parameters for the determination of MG and LMG (CV and LMG-d5ere used as internal standards)

nalyte Transition Cone voltage(V)

Collisionenergy (eV)

Retention time(min)

G 329 > 313a 55 35 2.54329 > 208b 55 35 2.54

MG 331 > 239a 40 30 5.35331 > 316b 40 20 5.35

V 372 > 356 55 35 3.32MG-d5 336 > 321 40 20 5.32

a Strong transition.b Weak transition.

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r. A 1187 (2008) 1–10

imit and detection capability for the univariate and PARAFACalibration models were determined by using the DETARCHI23] and the NWAYDET programs (available from the authors),espectively. These programs display the detection capability forny given false-positive α or false-negative β probability as laidown by European Decision 657/2002 and ISO 11843.

The univariate regression models (estimated concentrationersus true concentration in PARAFAC calibrations and signalersus concentration in univariate calibrations for the validationf trueness) and the test for the validation of regression wereerformed with STATGRAPHICS [24].

. Theory

.1. PARAFAC decomposition

LC-MS/MS data are arranged in a three-way array, X, andnalyzed with PARAFAC. A recent review about three-wayethods applications to calibration in chromatography can be

een in Ref. [25].PARAFAC is a methodology which decomposes the orig-

nal data X into triads or factors [26,27], each consisting ofhree loading vectors. The PARAFAC structural model [28] iss follows:

ijk =F∑

f=1

aif bjf ckf + eijk (1)

here, xijk is an element of X, F is the number of factors, aif,jf and ckf are the elements of the loadings matrices and eijk ishe experimental error. In a chromatographic calibration [29],he vectors af, bf and cf are the chromatographic, sample andpectral profiles of fth analyte, respectively.

The PARAFAC model has been fitted by means of the alter-ative least squares (ALS) algorithm, which works sequentiallyn each of the ways in every step of the iteration in order tot the data to the model of the Eq. (1). According to this, theARAFAC model is not limited by the number of ways and itan decompose n-way data for n higher or equal to two. In casef a data matrix with n = 2, the model of the Eq. (1) is that onef the principal components and the algorithm ALS calculateshe loadings and scores as usual.

The PARAFAC fitted model provides the A, B and C matricesormed by the loadings in each way respectively. Leverages andesiduals can be used for influence and residual analysis [30].he leverages, or squared Mahalanobis distance T2, have to bealculated as

A = diag[A(A′A)−1A′] (2)

being replaced with the proper loading matrix (A, B or C) anddiag’ is the diagonal of the matrix. The leverage, or T2, for theth element of af is the ith component of vector hA (the sameor bf and cf). T2 represents the projection of each variable or

ample onto the space spanned by PARAFAC factors.

Residuals are easily calculated by subtracting the model fromhe data. For each i, we have Q(i) = ∑

jk(xijk − xijk)2 where xijk

s the fitted value with PARAFAC model. Similarly, the index

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is defined for the other two ways. Q represents the squaredistance of each variable or sample to the subspace spanned byARAFAC factors.

Habitually a threshold value at 95% (or 99%) confidence levels posed for these two indices. If a sample or variable has thesewo indices larger than the threshold value must be declaredutlier.

.2. Detection capability

The detection capability or minimum detectable net con-entration has been defined [5,31,32] for a given false-positiverobability, α, as “the true net concentration of the analyte in theaterial to be analyzed which will lead, with probability 1 − β,

o the correct conclusion that the concentration in the analyzedaterial is different from that in the blank material”. The appli-

ation of this figure of merit to chemical analysis with zero-orderignals and univariate calibration model is detailed in the secondart of the standard ISO 11843 [33] and is obtained by meansf the following equation:

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b(3)

here �(α,β) is the non-central parameter of t-Student andepends on the probabilities α and β, σ is the residual stan-ard deviation of the regression, b is the estimated slope and ω0s a function of the calibration samples.

In the case of first and higher order signals modeled by twond superior order calibrations, the capability of detection canlso be determined fixing both probabilities α and β. The detailsf this generalization can be seen in Refs. [34] and [35] for firstnd higher order signals, respectively.

. Results and discussion

.1. Recovery

The recovery of the method was determined by the com-arison of the slopes in fish-fortified calibration lines (fortifiedefore extraction) and pure standard calibration line. The twosh-fortified calibration lines and the pure standard calibration

ine (peak area analyte/peak area I.S versus fortified concentra-ion) were made in different days.

Table 4 shows the number of samples used in the calibrationines, the equation of the fitted model, the standard deviation ofhe regression (syx), the interval of the intercept (b0) at 95% ofonfidence level and the obtained recovery for MG and LMG. Asn all equations b0 can be considered statistically equal to zero,ecovery in percentage can be estimated by dividing the slopesfish fortified line slope/pure standard line slope) × 100. In allhe cases, the coefficient of correlation (ρ) was 0.99 or higher.

.2. Comparison of univariate and three-way calibration

unctions

The fortified fish samples were prepared as indicated in Sec-ion 2.3. Table 5 shows the five concentration levels and the Ta

ble

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6 D. Arroyo et al. / J. Chromatogr. A 1187 (2008) 1–10

Table 5Fish samples spiked with MG and LMG, at five concentration levels distributed in the 6 days studied (concentrations at �g kg−1)

Concentration level Day 1 (D1) Day 2 (D2) Day 3 (D3) Day 4 (D4) Day 5 (D5) Day 6 (D6)

1 0.2a 0.2a 0.2 0.2 0.2 0.5a

2 0.5a 0.5a 0.5a 0.5a 0.5a 1.03 1.0a 1.0a 1.0 1.0 1.0 2.04 2.0a 2.0a 2.0b 2.0b 2.0b 3.05 3.0a 3.0a 3.0 3.0 3.0 4.0

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n all the cases CV and LMG-d5 (internal standards) are at 1 �g kg−1

a Two replicates.b Three replicates.

istribution of the samples in the 6 days of analysis. These daysere distributed during a month.Fig. 1 shows the chromatograms of a fish sample spiked at

�g kg−1 of MG and 2 �g kg−1 of LMG (at 1 �g kg−1 of CVnd 1 �g kg−1 of LMG-d5 as internal standards). As it can bebserved, the chromatographic separation is complete; thereforehe figures of merit of the univariate calibration are the referencen the evaluation of the PARAFAC calibration.

Two calibration models were applied to the LC–MS/MSecorded data:

(i) Univariate: the signal employed was the relation of areasof each analyte standardized with its corresponding I.S.(AMG/ACV and ALMG/ALMG-d5) obtained with the strongionic transition (see Table 3) of each analyte.

ii) PARAFAC: the original chromatogram was divided intofour intervals around the retention times of each substance,modeling separately the chromatographic peaks of eachsubstance. The dimensions of tensors X for MG and LMG

were (81 × N × 2) in the models for each day, where N wasthe number of fortified fish samples of each day accordingto Table 5. In the global model (G) the dimensions of X were(81 × 50 × 2). For the internal standards, CV and LMG-d5,

ig. 1. Chromatograms of a fish sample spiked at 2 �g kg−1 of MG and�g kg−1 of LMG (at 1 �g kg−1 of CV and 1 �g kg−1 of LMG-d5 as inter-al standards) recorded for (a) MG at transition 329 > 313, (b) CV at transition72 > 356, (c) LMG-d5 at transition 336 > 321 and (d) LMG at transition31 > 239.

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the dimensions of tensors X were (81 × N × 1) in the modelsof each day and (81 × 50 × 1) in the global model. The firstdimension refers to the chromatographic profile (number ofscans or elution times recorded at each peak), the secondcorresponds to the number of fortified fish samples and thethird one to transitions of the precursor ion to product ion.In the tensors built with the chromatographic data is usualto place in the first-way the chromatographic profile [25], inorder to apply PARAFAC2 if changes in the retention timesare observed.

The details of the procedure to develop a PARAFAC calibra-ion with chromatographic data can be looked up in reference25]. Fig. 2 graphically shows the procedure in the particularase of this work.

The steps in the PARAFAC calibration were:

(a) Decomposition of the data tensor X.b) Selection of an appropriate number of factors.

(c) Identification of the factors related to the analytes presentin the sample according to the retention time and relativeabundances between the precursor/product ion pairs for eachanalyte, in agreement with the Decision 2002/657.

d) Standardization of the sample mode loadings of the ana-lytes with the sample mode loadings of their correspondinginternal standards [21].

(e) Construction of an univariate regression, by least squares,between the standardized loadings of sample mode and theconcentration of the fortified fish samples.

(f) Elimination of outlier data from the previous regression.Data with standardized residual error greater than 3 in abso-lute value were removed and a new least square regression(RLS) was performed and validated with the remaining data.

The RLS regression line of the step (e) was validated byeans of following hypothesis test: the significance test of

he model’s fit, the lack of fit test, Bartlett and Cochran’somoscedasticity test, the Kolmogorov test of normality ofesiduals and analysis of the independence of the residualsDurbin–Watson statistic) [36,37].

All PARAFAC calibrations were constructed by applying thelternative least squares (ALS) algorithm with non-negativityonstraints in the chromatographic and spectral modes, and withsingle factor.

D. Arroyo et al. / J. Chromatogr. A 1187 (2008) 1–10 7

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Fig. 2. Scheme of the step

Table 6 shows the results of decision limit (CCα), capabil-ty of detection (CCβ) and mean relative error in absolute valuebtained from the calibrations of the different days with uni-ariate and PARAFAC calibration functions. The probabilities

f false-positive, α, and false-negative, β, were fixed at 1 and%, respectively. It can be observed that the results obtainedith both functions, were very similar in the three figures oferit.

sscd

e PARAFAC calibration.

For each calibration model, trueness was validated using aegression of estimated concentration versus true concentration.able 7 shows the equation, the standard deviation of regression,yx, and the number of outliers detected as has been indicated in

tep (f) of procedure. Most of the PARAFAC calibration haveyx lower than univariate ones. In all calibration models, theoefficient of correlation (ρ) was 0.99 or higher. The interme-iate precision in the range of concentration is estimated by the

8 D. Arroyo et al. / J. Chromatog

Table 6Results for different calibration models obtained over 6 days

Malachite green (MG) Leucomalachite green (LMG)

Univariate PARAFAC Univariate PARAFAC

Day 1CCα <0.2 <0.2 <0.2 <0.2CCβ 0.26 0.22 0.28 <0.2Error 3.5 2.2 4.1 2.6

Day 2CCα <0.2 <0.2 0.28 <0.2CCβ <0.2 <0.2 0.47 <0.2Error 3.7 3.2 5.9 2.0

Day 3CCα 0.21 <0.2 0.31 0.26CCβ 0.32 0.29 0.53 0.44Error 3.0 2.9 3.6 2.8

Day 4CCα <0.2 <0.2 <0.2 0.24CCβ <0.2 0.23 0.21 0.40Error 2.0 2.1 2.3 3.2

Day 5CCα 0.36 0.49 0.67 0.47CCβ 0.61 0.83 1.12 0.78Error 4.9 6.5 7.4 4.9

Day 6CCα <0.2 <0.2 0.20 0.21CCβ <0.2 <0.2 0.34 0.36Error 1.0 1.1 3.1 3.3

GlobalCCα 0.30 0.21 0.29 0.31CCβ 0.51 0.36 0.50 0.53

C

s[

4

te

cribu

Dwdvtnfis

uwrtb

ttl(but with more samples in the regression line). All the calibrationmodels fulfill the trueness, but only the two univariate modelshave lack of fit (p-values smaller than 0.05). For these reasons,

Fig. 3. Q and T2 indices of the set calibration samples (D1 + D2 + D3) with thetest samples of day 4 (D4) in PARAFAC model for MG. The calibration samplesare indicated by circles and the test samples of D4 by triangles. With dashedlines the 99% limits in the indices are indicated.

Fig. 4. Relative errors in prediction of the samples of days 4, 5 and 6 for MG

Error 6.2 4.6 5.8 7.9

Cα and CCβ in �g kg−1, mean relative error (in absolute value) in %.

yx of the corresponding regression line according to ISO 572538].

.3. Maintenance of calibration models

The first 3 days samples (D1 + D2 + D3) were used as calibra-ion set. The samples of the other 3 days (D4, D5 and D6) weremployed for evaluating the stability of the calibration models.

The PARAFAC decomposition can be carried out with thealibration set adding the samples of each day to predict sepa-ately. In this way, the particular characteristics (minor changesn the sensibility of equipment) of the samples of a day cane introduced in the PARAFAC calibration to be predicted. Innivariate calibration this advantage is not possible.

The calibration regressions based on PARAFAC (loadings1 + D2 + D3 versus fortified concentration) were constructedith standardized loadings of the sample mode obtained with theata of the first 3 days. For each calibration model, trueness wasalidated as it has been mentioned in Section 4.2. Table 8 shows

he equation, the standard deviation of regression as well as theumber of outliers detected. In all calibration models, the coef-cient of correlation (ρ) was 0.99 or higher. Only D1 + D2 + D3amples (28 in total) were used for building the PARAFAC and

a(li

r. A 1187 (2008) 1–10

nivariate calibration models, but PARAFAC decompositionsere carried out with (D1 + D2 + D3) and D4, D5 or D6 samples,

espectively. In relation to the figures of merit, the advantage ofhis procedure to carry out the PARAFAC decomposition haseen shown in Ref. [35].

As can be seen in Table 8, univariate models had more outliershan PARAFAC models for both analytes (one more in LMG andhree more in MG). The syx in PARAFAC models are slightlyower than univariate model for LMG and slightly bigger for MG

nd LMG with univariate and PARAFAC calibrations: ( ) MG PARAFAC,) MG univariate, ( ) LMG PARAFAC, ( ) LMG univariate and ( )

imit established by Decision 2002/657. Spiked samples at 0.2 �g kg−1 are notncluded because they are below of the capability of detection.

D. Arroyo et al. / J. Chromatogr. A 1187 (2008) 1–10 9

Table 7Analysis of trueness by using regressions based on calculated concentration vs. true concentration

Calibration Malachite green (MG) Leucomalachite green (LMG)

Model syx Ratio outliers Model syx Ratio outliers

Day 1Univariate −5.98 × 10−6 + 1.0x 0.044 2/10 −2.60 × 10−7 + 0.9999x 0.047 2/10PARAFAC 2.55 × 10−4 + 1.0x 0.036 2/10 −3.53 × 10−8 + 1.0x 0.028 2/10

Day 2Univariate 8.22 × 10−6 + 1.0x 0.030 1/10 5.51 × 10−7 + 1.0x 0.087 0/10PARAFAC 1.00 × 10−4 + 0.9999x 0.015 2/10 1.17 × 10−7 + 1.0x 0.032 1/10

Day 3Univariate 4.66 × 10−6 + 0.9999x 0.048 1/8 −4.40 × 10−5 + 1.0x 0.085 0/8PARAFAC −7.47 × 10−6 + 0.9999x 0.043 1/8 −1.44 × 10−4 + 1.0x 0.071 0/8

Day 4Univariate 2.53 × 10−6 + 1.0x 0.022 1/8 −1.29 × 10−6 + 1.0x 0.031 1/8PARAFAC −1.50 × 10−7 + 1.0x 0.033 1/8 7.96 × 10−6 + 1.0x 0.064 0/8

Day 5Univariate 1.08 × 10−4 + 1.0x 0.091 1/8 1.24 × 10−6 + 1.0x 0.179 0/8PARAFAC 5.07 × 10−6 + 1.0x 0.133 0/8 −1.10 × 10−5 + 1.0x 0.126 0/8

Day 6Univariate −3.88 × 10−6 + 0.9999x 0.024 0/6 2.53 × 10−6 + 0.9999x 0.043 0/6PARAFAC 6.95 × 10−6 + 1.0x 0.013 0/6 3.30 × 10−6 + 1.0x 0.047 0/6

Global

me

pc(insbcosp

ti−s

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TA

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P

U

Univariate −2.04 × 10−6 + 1.0x 0.122 2/50PARAFAC 1.86 × 10−6 + 1.0x 0.085 2/50

odels based on PARAFAC show a better statistical fit to thexperimental data.

Multivariate calibration techniques (such as PARAFAC)resent a very important advantage with respect to univariatealibrations. PARAFAC decomposition provides two indicescalled Q and T2), which are useful to decide if a new samples similar to those used in the decomposition. Q index determi-ates the variance unexplained by the PARAFAC factors in theignals of the new sample. T2 index determinates the similarityetween the projection of the new sample and the projection ofalibration samples in the space spanned by factors. If the valuesf both indices are higher than 99% at the same time, the newample is considered outlier and therefore, it is not correct toredict it with the fitted model.

Fig. 3 shows the Q and T2 indices of the calibration set and

est samples of day 4 for MG. As can be seen in this figure, theres an outlier test sample with a relative error in the prediction of

15.38 %, which is the highest value, in absolute value, of theamples of day 4.

c

sm

able 8nalysis of trueness by using regressions based on calculated concentration vs. true c

alibration models Malachite green (MG)

Model syx Ratio

ARAFAC(D1 + D2 + D3) + D4 −4.37 × 10−6 + 1.0x 0.091 2/28(D1 + D2 + D3) + D5 −9.84 × 10−7 + 1.0x 0.081 2/28(D1 + D2 + D3) + D6 −6.03 × 10−7 + 1.0x 0.100 2/28

nivariate 8.29 × 10−6 + 1.0x 0.080 5/28

−6.22 × 10−8 + 1.0x 0.117 2/501.32 × 10−8 + 1.0x 0.126 2/50

Fig. 4 shows the relative error in the prediction of the sam-les of days 4, 5 and 6, calculated with univariate and PARAFACalibrations for MG and LMG. As can be seen in this figure, allamples of both calibrations have relative errors which do notxceed the permitted limits by Decision 2002/657, but a singleample of day 4 (sample number 6 in Fig. 4) that exceeds in thenivariate calibrations for both analytes and in the PARAFACalibration for one analyte (LMG). The permitted limits areased on the fortified concentration of the sample (samplesith fortified concentration lower or equal at 1 �g kg−1 haveminimum trueness range between −50 and +20% whereas

amples with fortified concentration between 1 and 10 �g kg−1

ave a range between −30% and +10%). As can be seen inhis figure, errors obtained with PARAFAC calibration vary lessith the change of day than the same errors with the univariate

alibrations, especially for LMG.Mean relative error in prediction (in absolute value) by day is

hown in Table 9. The mean relative errors between days wereore homogeneous with PARAFAC calibrations, above all for

oncentration in the calibration set (D1 + D2 + D3)

Leucomalachite green (LMG)

outliers Model syx Ratio outliers

−1.47 × 10−6 + 1.0x 0.067 2/28−1.69 × 10−7 + 1.0x 0.059 2/28−7.37 × 10−7 + 1.0x 0.066 2/28

2.45 × 10−8 + 0.9999x 0.077 3/28

10 D. Arroyo et al. / J. Chromatog

Table 9Mean prediction relative errors (%) in absolute value for the samples of day 4,5 and 6 with univariate and PARAFAC models

Day Malachite green (MG) Leucomalachite green (LMG)

Univariate PARAFAC Univariate PARAFAC

D4 7.65 (n = 7) 8.70 (n = 6) 4.90 (n = 7) 8.95 (n = 7)DD

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5 14.35 (n = 7) 11.55 (n = 7) 8.40 (n = 7) 7.50 (n = 7)6 4.80 (n = 5) 2.70 (n = 5) 11.40 (n = 5) 8.65 (n = 5)

= number of samples.

MG (this metabolite is the prevalent residue which is presentn the fish treatment tissues).

. Conclusions

The experimental procedure is the one proposed by theuropean reference laboratory AFSSA-LERMVD (Fougeres,rance) with a preparation stage of the sample characterized by

ts simplicity and low volume of generated residues. All the dataenerated by the instrument, maintaining their three-way struc-ure, are employed in the PARAFAC calibration. This allows thedentification and quantification of the analyte of interest in onlyne step, even in the presence of non-calibrated interferents.

In this work the advantages (outliers detection and stabil-ty of calibration models) of applying PARAFAC calibration inhe determination of MG and LMG in trout by LC–MS/MS arehown.

In addition, the possibility of reducing the experimentalffort, building PARAFAC calibrations stable along the times shown. With PARAFAC calibrations, the requirements ofecision 2002/657 (minimum trueness demanded for the quan-

itative methods and maximum permitted tolerances for relativentensities of the precursor/product ion pairs) were fulfilled.

cknowledgments

The authors gratefully acknowledge the financial supportf the Ministerio de Educacion y Ciencia (Project CTQ2004-7216/BQU) and the Junta de Castilla y Leon (ProjectU024A07). Particular thanks are expressed by David Arroyo

or the FPI Grant also provided by the Junta de Castilla y Leon.

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