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Journal of Chromatography A, 1216 (2009) 5472–5482

Contents lists available at ScienceDirect

Journal of Chromatography A

journa l homepage: www.e lsev ier .com/ locate /chroma

etermination and identification, according to European Union Decision002/657/EC, of malachite green and its metabolite in fish by liquidhromatography–tandem mass spectrometry using an optimizedxtraction procedure and three-way calibration

avid Arroyoa, M. Cruz Ortiza,∗, Luis A. Sarabiab, Francisco Palaciosc

Department of Chemistry, Faculty of Sciences, University of Burgos, Pza. Misael Banuelos s/n, 09001 Burgos, SpainDepartment of Mathematics and Computation, Faculty of Sciences, University of Burgos, Pza. Misael Banuelos s/n, 09001 Burgos, SpainDepartment of Health and Consumption, Diputación General de Aragón, C/Ramón y Cajal 68, 50004 Zaragoza, Spain

r t i c l e i n f o

rticle history:eceived 12 March 2009eceived in revised form 20 May 2009ccepted 25 May 2009vailable online 2 June 2009

eywords:uropean Union Decision 2002/657/ECalachite green

iquid chromatographyass spectrometryesirabilityARAFAC

a b s t r a c t

This paper reports a multiresponse optimization of an extraction procedure in the simultaneous deter-mination of malachite green (MG) and its metabolite (leucomalachite green, LMG) in fish by liquidchromatography with triple quadrupole mass spectrometry (LC–MS/MS). Prior to optimization, the activefactors of the extraction procedure were determined by a screening experimental design. Then, in theoptimal experimental conditions of the extraction, MG and LMG have been determined by using a three-way calibration model based on parallel factor analysis (PARAFAC). The procedure fulfils the performancerequirements for a confirmatory method established by the European Union Decision 2002/657/EC. Thisnorm establishes maximum permitted tolerances for relative abundance of the precursor/product ionpairs. There is a reported contradiction in the literature related to the fact that there are standard sampleswhose concentration is greater than CC˛ but the maximum permitted tolerances are not fulfilled in theidentification of the analytes. In this work, it is shown that with the information provided by PARAFACthis contradiction is avoided. The figures of merit for PARAFAC and univariate calibration procedures wereevaluated under optimal conditions in the extraction step. The figures of merit obtained were in the range

−1 −1

of 0.13–0.23 �g kg for the decision limit, CC˛, (˛ = 0.01) and 0.22–0.39 �g kg for the detection capa-bility, CCˇ, (ˇ = 0.05), whereas mean relative errors in absolute value were in the range of 2.8–4.6% forMG and LMG with PARAFAC calibration. The proposed optimized extraction procedure using a PARAFACcalibration was also applied in the determination of MG and LMG in gilthead bream samples: the decisionlimit was in the range of 0.45–0.55 �g kg−1, the detection capability was in the range of 0.76–0.92 �g kg−1

s was.2%.

for MG and LMG. Trueneswere between 4.2% and 7

. Introduction

Malachite green (MG) is used as fungicide and antiseptic in aqua-ulture and fisheries. Lately, presence of MG in fisheries productsas been reported (cf. EC Rapid Alert Reports for Food and Feed003–2006). In 2007 and 2008, the US Food and Drug Administra-ion (FDA) initiated an import alert [1] against seafood from Chinaecause of numerous cases of contamination with MG and other

eterinary drugs [2].

MG is a triphenylmethane dye and it has been found that dyesf this family can induce hepatic and renal tumors in mice [3] andeproductive abnormalities in fish [4]. It is readily absorbed by fish

∗ Corresponding author. Fax: +34 947 258 831.E-mail address: mcortiz@ubu.es (M.C. Ortiz).

021-9673/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2009.05.076

likewise confirmed and the mean of the absolute values of relative errors

© 2009 Elsevier B.V. All rights reserved.

and metabolically reduced to the lipophilic leucomalachite green(LMG), which is known to have a long residence time in edible fishtissues with a half-life of about 40 days [5,6]. MG and LMG havepotential health and environmental hazards.

MG is not permitted for veterinary treatment, due to its car-cinogenic and mutagenic properties in USA, Europe [7] and othercountries. However, the increasing demand in the consumption ofseafood coupled with the decrease of captures of these productshas provided a very fast growth of the aquaculture industry in thelast years, where MG is still used due to low cost, easy availabilityand its high efficacy. The European Commission has established a

−1

minimum required performance limit (MRPL) of 2 �g kg for thesum of MG and LMG [8,9].

Although, there are recently analytical methods based on spec-trophotometric [6,10–14] or electrochemical detection [15], most ofthe analytical methods for the determination of these residues are

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D. Arroyo et al. / J. Chroma

ased on mass spectrometry (MS) detection, because this detectionethod provides greater sensitivity, specificity and with better val-

es of the figures of merit. Liquid chromatography in combinationith triple quadrupole (LC–QqQ-MS) or with ion trap (LC–IT-MS)S detection are the preferred methods for determination and con-

rmation of MG and LMG [16–26].The experimental design methodology is not used in any of the

revious references to carry out the optimization of the extractionrocess. Only in Ref. [24] and in the papers performed by Europeanroups [18–20] the decision limit (CC˛) and detection capabilityCCˇ) are evaluated. Moreover, in these four papers, the identi-cation of the analytes is according to European Union Decision002/657/EC, based on the concept of identification points (IPs) andaximum permitted tolerances for relative abundance between

hese IPs, but these papers have not shown the intervals of max-mum permitted tolerances and how they are calculated.

The fish species at study in this work (bass, trout, gilthead breamnd turbot) are easy to produce in aquaculture and due to highuality/cost relation are in high demand by consumers.

The residue extraction and analysis method used for MG andMG determination in fish were developed by community referenceaboratory AFSSA-LERMVD (Fougères, France) [27].

In the present paper, the AFSSA-LERMVD extraction procedureas optimized by means of experimental design methodology.

rior to the optimization, the active factors of the extraction pro-ess were determined by means of an optimal screening design andfter that, by means of a central composite design, the conditionshat gave the greatest standardized peak area for MG and LMG wereetermined. The optimum was obtained for each analyte under dif-erent experimental conditions and conflicts were resolved by usingdesirability function.

After the optimization, three-way calibration models based onarallel factor analysis (PARAFAC) were applied to the second orderignals recorded, in order to obtain a robust analytical procedureo identify and quantify MG and LMG in a single analysis. Twoalibration strategies (univariate and PARAFAC) were comparedsing the figures of merit established by European Union Decision002/657/EC for the validation of analytical methods, mainly theecision limit, detection capability, trueness and precision.

In addition to the general performance requirements, additionalnes are described in the European Union Decision 2002/657/ECor confirmatory methods, based on the concept of identificationoints, minimum trueness demanded and maximum permitted tol-rances for relative abundance of the precursor/product ion pairs.ith PARAFAC calibration the additional requirements described

re fulfilled, whereas with univariate calibration there are manytandards of calibration samples that do not fulfil these require-ents. The calibration based on the PARAFAC decomposition needsdata matrix for each sample. For the case of LC–MS/MS, thisatrix is made by the mass spectrum of the product ions in each

lution time. However, to obtain this matrix do not add any addi-ional experimental effort because the European Union Decision002/657/EC demands the recording of these data to unequivocally

dentify the analyte.

. Experimental

.1. Chemicals and standard solutions

All the chemicals used were of analytical grade or higher. Ana-ytical standards of malachite green oxalate (>90%), leucomalachite

reen (>90%) and crystal violet (>90%, CV) were supplied fromldrich (Steinheim, Germany). [2H5]Leucomalachite green (98%,MG-d5) was obtained from WITEGA Laboratorien (Berlin, Ger-any). CV and LMG-d5 were used as internal standards for MG

nd LMG, respectively. A previous work [28] showed the viability of

1216 (2009) 5472–5482 5473

using CV as internal standard for MG due to the fact that the area ofCV is constant for all the calibration samples independently of theadded amount of MG.

Methanol, acetonitrile, glacial acetic acid (99.8%) and ammo-nium acetate (≥98%) were purchased from Merck (Darmstadt,Germany). Hydroxylamine hydrochloride (≥98%) was supplied byFluka (Neu-Ulm, Germany) and deionized water was obtained withMilli-Q gradient A10 water purification system of Millipore (Bed-ford, MA, USA).

Stock solutions of MG, LMG, CV and LMG-d5 at 1000 mg L−1 wereprepared in methanol and were stored at −20 ◦C for 6 months.Individual intermediate solutions (20 mg L−1) were prepared bydiluting the stock solution with mixture of ammonium acetate(0.1 M, pH 4.5) and acetonitrile (30:70, v/v) for MG or with ace-tonitrile for LMG, CV and LMG-d5. These solutions were stored at4 ◦C for less than 3 months.

Combined solutions at 2 mg L−1 of MG plus LMG and CV plusLMG-d5 were prepared prior to use in a mixture of hydroxylamine(5 g L−1) and acetonitrile (20:80, v/v). Working solutions (10 �g L−1)were prepared by the dilution of the combined solutions at the sameconditions. All standard solutions were stored in amber bottles andprotected from light.

2.2. Fish samples treatment

Fish samples were processed as described in a previous work ofour research group [28]. Various fish species (bass, trout, giltheadbream and turbot) were studied. The fishes were filleted, the skinand bones were removed and the muscles were blended in a lab-oratory blender and frozen at −20 ◦C, before analysis. Fish tissueswere previously tested and shown to contain no detectable residuesof MG, LMG and CV and can be used as negative controls. In Ref.[28], the viability of the internal standards with the experimentalprocedure used is shown.

One gram of homogenized edible tissue was placed into 15 mLpolypropylene centrifuge tube, and spiked samples were preparedby the addition of 100 �L of the working solution of the internalstandards (corresponding to spiking level of 1.0 �g kg−1) and of theappropriate amount of the MG plus LMG working solution. Then,the spiked samples were homogenized using a vortex-mixer (VelpScientifica, Milan, Italy) during 30 s and were incubated t minutes(tincub) in darkness. Next, V mL (VNH2OH) of hydroxylamine solution(5 g L−1) was added. The tubes were shaken on a vortex-mixer dur-ing 30 s and incubated again during t minutes (tincub) in darkness.After that, V mL of acetonitrile (VACN) was added and tissues wereextracted for t minutes (tshaking) on a platform shaker (J.P. Selecta,Barcelona, Spain) operating at 210 rpm. The samples were then son-icated for t minutes (tsonic).

Finally, the samples were centrifuged at 3000 rpm for 15 min at4 ◦C. The supernatants were transferred into 2 mL vials using a filtersyringe of 0.45 �m (Pall, East Hills, NY, USA).

The variables VNH2OH , tincub, VACN, tshaking, tsonic and the kind of fish(FISH) were the experimental factors to study with the experimentaldesign methodology and its values are not fixed previously.

2.3. Instruments and apparatus

Analyses were performed with the Waters Alliance 2790 liquidchromatograph (Waters, Milford, MA, USA) coupled to a Micro-mass Quattro Micro-tandem mass spectrometer (Micromass UKLtd., Altrincham, UK) with atmospheric pressure ionization source

operating in the positive ion electrospray (ESI+) mode. LC separa-tion was achieved with the Synergi MAX-RP 80A analytical column(4 �m, 150 mm × 2.0 mm I.D., Phenomenex, Macclesfield, UK) witha MAX-RP guard column (4 mm × 2.0 mm I.D.) at a flow rate of400 �L min−1.

5474 D. Arroyo et al. / J. Chromatogr. A

Table 1MS/MS parameters for the determination of the analytes (MG and LMG) and theinternal standards (CV and LMG-d5).

Compound Precursor/production pairs (m/z)

Conevoltage (V)

Collisionenergy (eV)

Retentiontime (min)

MG 329/313a 55 35 2.59329/208b 55 35 2.59

LMG 331/239a 40 30 5.26331/316b 40 20 5.26

CV 372/356a 55 35 3.34372/340b 55 40 3.34

LMG-d5 336/321a 40 20 5.24

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336/239b 40 30 5.24

a Strong precursor/product ion pair.b Weak precursor/product ion pair.

Two mobile phases were used in a gradient program, in whichobile phase A consists of 0.1 M ammonium acetate (pH 4.5) andobile phase B consists of acetonitrile. The gradient program starts

rom 50%A/50%B increased to 100%B (linear ramp) at 3 min; keep-ng at these conditions for 4 min; returned instantly to 50%A/50%Bnd keeping at these conditions for 3 min (10 min in total). Thenjection volume was 25 �L. Oven and injector temperatures werexed at 30 and 15 ◦C, respectively. Data acquisition was performedsing MassLynx version 4.0 chromatographic management soft-are (Waters).

The ESI interface was operated at positive ion mode at anonization voltage of 3.0 kV. Tandem MS analysis was performedsing the multiple reaction monitoring (MRM) mode. The follow-

ng conditions were used: source temperature, 120 ◦C; desolvationemperature, 400 ◦C; N2 cone gas flow, 50 L h−1; N2 desolvationas flow, 650 L h−1. Argon was used as collision gas. According touropean Union Decision 2002/657/EC, for the confirmation of theresence of an illegal veterinary drug at least 4 identification pointsre necessary. The precursor and two product ions per compound4 IPs) and the spray and collision voltages used are shown inable 1.

.4. Software

NEMRODW [29] was used for building and analyzing the designsthe initial screening design and the later central composite design)nd the desirability function for finding the optimal conditionsf the extraction procedure. PARAFAC decompositions were con-tructed with PLS-Toolbox [30] for use with MATLAB version 7 (TheathWorks). The univariate regressions models (estimated con-

entration vs. true concentration in PARAFAC calibrations and signals. concentration in univariate calibrations) for the validation ofrueness and the statistical test for the validation of regressionsere performed with STATGRAPHICS [31].

Decision limit and detection capability for the univariate and thehree-way calibration models were determined using DETARCHI32] and the NWAYDET programs, respectively. These programsisplay the detection capability for any given false-positive, ˛, or

alse-negative, ˇ, probabilities as it is established by Europeannion Decision 2002/657/EC and ISO 11843 [33].

. Theory

LC–MS/MS data are arranged in a three-way array, X, and ana-

yzed with PARAFAC (a three-way decomposition technique). Aomparison between univariate and three-way calibrations maye consulted in Ref. [28], and two recent reviews about three-wayethod applications to calibration in chromatography can be seen

n Refs. [34,35].

1216 (2009) 5472–5482

There are several ways of introducing the PARAFAC decomposi-tion for the analysis of chromatographic data. This section shows theparallelism that exists between the PARAFAC decomposition and aphysical model of LC–MS/MS data under some common assump-tions.

Considering an analyte, its signal (abundance) xk recorded by aMS/MS spectrometer at the kth m/z of the product ion is

xk = �εk, k = 1, 2, . . . , K (1)

where εk is a coefficient of proportionality between the analyteconcentration and the abundance. εk depends on the kth m/z ofthe product ion and the vector of these coefficients made up thespectral profile.

In LC–MS/MS, a MS/MS spectrometer is coupled to a chromato-graph and the signal (abundance) depends not only on the m/z ofthe product ion and the concentration of the analyte in the solu-tion, but also on the elution time because the fraction of analyteeluting from the column changes over time. Thus at the jth timethe recorded abundance becomes:

xjk = ��jεk, j = 1, 2, . . . , J; k = 1, 2, . . . , K (2)

where �j can be seen as the fraction of the analyte that is goingthrough the detector at time j. The vector of all �j’s forms the chro-matographic profile.

If F spectrally actives substances coelute, the recorded abun-dance is the sum of the contributions of these F differentcompounds:

xjk∼=

F∑

f =1

�f �jf εkf , j = 1, 2, . . . , J; k = 1, 2, . . . , K (3)

where F is the total number of analytes coeluting.Assuming that analyte fth has the same retention time in all

chromatographic runs, the abundance measured at the kth m/z ofthe product ion, the jth retention time and the ith sample can bewritten as

xijk∼=

F∑

f =1

�if �jf εkf , i = 1, 2, . . . , I, j = 1, 2, . . . , J;

k = 1, 2, . . . , K (4)

In the case of three-way data X =(

xijk

), the PARAFAC model of rank

F can be expressed [36,37] as

xijk =F∑

f =1

aif bjf ckf + eijk, i = 1, 2, . . . , I, j = 1, 2, . . . , J;

k = 1, 2, . . . , K (5)

where eijk are the residual errors of the model. It can be observedthat the PARAFAC decomposition of model (5) corresponds to thephysical model in Eq. (4). That is, under the conditions just men-tioned, a PARAFAC model of F components can be used to estimatewith cf = (c1f, c2f, . . ., cKf) the coefficients of proportionality for eachanalyte at all m/z product ions (i.e. its mass spectral profile); bymeans bf = (b1f, b2f, . . ., bJf) the fraction of analyte that exits thecolumn along the chromatographic run (i.e. the chromatographicprofile or chromatogram of each analyte) and the relative concen-tration of every analyte (i.e. the sample profile) in all I samples bymeans af = (a1f, a2f, . . ., aIf). The coordinates of vectors cf, bf and af are

called spectral, chromatographic and sample loadings, respectively.

The PARAFAC model has been fitted by means of the alterna-tive least square (ALS) algorithm, which works sequentially in eachof the ways in every step of the iteration in order to fit the datato the model of the Eq. (5). For the identification of a forbidden

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Table 3Screening design with 16 experiments for the standardized area of the analytes cal-culated with the strong precursor/product ion pair for each of them (see Table 1).For the codification of factors (Xi , i = 1, . . ., 6) see Table 2.

Experiment number Levels of the factors Responses

X1 X2 X3 X4 X5 X6 AMG/ACV ALMG/ALMG-d5

1a 1 1 1 1 1 1 0.64 2.032 1 1 1 2 1 2 0.98 2.703 1 1 1 1 2 3 0.92 2.684 1 1 1 2 2 4 0.88 3.185 2 1 2 1 1 2 1.01 2.706 2 1 2 2 1 1 0.84 3.237 2 1 2 1 2 4 0.87 3.178 2 1 2 2 2 3 0.75 2.949 1 2 2 1 1 3 0.87 3.17

10 1 2 2 2 1 4 0.84 3.4711 1 2 2 1 2 1 0.99 3.5212 1 2 2 2 2 2 0.99 2.9613 2 2 1 1 1 4 0.86 3.3014 2 2 1 2 1 3 0.75 3.1815 2 2 1 1 2 2 0.90 2.96

D. Arroyo et al. / J. Chroma

nalyte in LC–MS/MS, it is only necessary to record the abundancef two product ions from a given precursor ion. In this case, thepectral profile of the data array to be modeled by PARAFAC hasnly 2 variables, K = 2 in Eq. (5). As consequence, other models (e.g.eneralized Rank Annihilation Method, GRAM) could be used and

ndeed may appear to be more parsimonious in fitting the data.owever, even in this case, PARAFAC (using ALS) may be the best

hoice because of the ability to impose realistic and appropriateonstraints to the model, such as the non-negativity (which is ade-uate for both the chromatographic and spectral profiles).

Ref. [28] shows a brief explanation to Q and T2 statistics of theultivariate analysis of data, which allows to detect outliers and

n Ref. [38] the generalization in the calculation of the detectionapability (CCˇ), according to ISO 11843, with second order signalsodeled with three-way calibrations, is shown.

. Results and discussion

The first step of the experimental work involves a screeningesign in order to known the active factors in the experimentalesponses selected and to get a preliminary idea about their effects39].

In the pretreatment step the factors related to the stability ofhe analytes (MG and LMG) are studied. The degradation of MG intoMG and other subproducts is fast, thus when preparing the spikedamples, the incubation time should be short though enough so thathe analyte gets into the fish tissue. Therefore, the incubation timen darkness, tincub, the time the sample is shook during extraction,shaking, the time it is sonicated, tsonic, and the volume of stabilizerhydroxylamine), VNH2OH , were chosen to experimentally decide ifheir effect is important (whether they are active or not) and, in theffirmative case, to go into their optimization.

The fish type was also considered as a factor, FISH, because it issual (to reduce the experimental effort in routine analysis) to pre-are the calibration samples as samples made by tissue of severalshes spiked with MG and LMG. This way of acting assumes thatach individual component of the mixture has the same calibrationodel. Nevertheless, if the amount of fat in the tissues were not

imilar (and there is not guarantee about this), the above assump-ion would be not true and individual calibration models would beeeded for each tissue.

Finally, the volume of extractant (acetonitrile, VACN) has alsoeen considered as a factor in the screening design.

.1. Optimal screening design for selecting the active factors

Table 2 shows the six factors to be studied as described in Section.2, five of them at two levels (VNH2OH , tincub, VACN, tshaking and tsonic)

nd one of them at four levels (FISH). The screening designs basedn factorial designs (as Hadamard) cannot be applied because allactors are not at two levels, therefore, an asymmetrical design withnly 16 experiments [40] has been used, whereas with a completeactorial design 128 experiments would be necessary.

able 2actors of the extraction process to study and its codification in the screening design.

actor (units) Associatedvariable

Levels

1 2 3 4

NH2OH (mL) X1 1 0.5 – –incub (min) X2 10 5 – –ACN (mL) X3 4 3 – –

shaking (min) X4 10 5 – –sonic (min) X5 15 10 – –ISH X6 Bass Trout Gilthead bream Turbot

16 2 2 1 2 2 1 0.85 3.65

a Outlier experiment (standardized residual error greater than 2.5 in absolutevalue).

The 16 experiments (coded by level) and the experimentalresponses obtained are shown in Table 3. The responses under anal-ysis are the area of each analyte (AMG and ALMG) standardized bythe area of its corresponding internal standard (ACV and ALMG-d5,respectively), calculated with the strong precursor/product ion pairof each one of them (see Table 1).

The following mathematical model is proposed to explain thevariation of the responses due to level changes in the experimentalfactors:

Y = b0 + b1AX1A + b2AX2A + b3AX3A + b4AX4A + b5AX5A

+ b6AX6A + b6BX6B + b6CX6C (6)

where Xij (i = 1, . . ., 6, j = A,B,C) are indicator variables which takevalue one when the ith factor is at level jth, and zero in other case,and bij are the coefficients of the model estimated by least squares(b0 is the intercept). These coefficients indicate the effect on theresponse, when the factor changes from the reference level (level 2in the factors with two levels and level 4 in the factor FISH [29,39])to the rest of levels. For this reason the model of Eq. (6) has a singlebiA coefficient in the factors at two levels, but three coefficients, b6A,b6B and b6C in the factor at four levels.

If the model of Eq. (6) adequately fits the experimental results,the interpretation is as follows: the ith factor is active if the coef-ficient that estimates the effect of the change in the level of thisfactor is statistically significant. For example, if coefficient b1A issignificant one can say that the change from 0.5 mL to 1.0 mL in thevolume of hydroxylamine influences the responses (standardizedareas of MG and LMG). Analogously, if at least one of the coeffi-cients b6A, b6B or b6C is statistically significant the conclusion willbe that to change the matrix (type of fish tissue) has effect on thestandardized areas and, thus, the factor FISH is active.

On the other hand, the significance of the factors and there-fore their influence on the responses is checked by the followinghypothesis test: null hypothesis “the coefficient is zero, the factoris not active”; alternative hypothesis “the coefficient is differentfrom zero, there is factor effect”. At the usual 5% significance level,that means that the null hypothesis will be rejected if the p-value

is less than 0.05.

The proposed model has 9 independent coefficients, which areestimated with 16 experiments. There are enough degrees of free-dom, and the significance of the model and the coefficients can beevaluated. The first experiment of Table 3 is an outlier (with stan-

5476 D. Arroyo et al. / J. Chromatogr. A

Table 4Estimates of the coefficients of the model built for the experimental responses(AMG/ACV and ALMG/ALMG-d5) and the p-values of the hypothesis test for checking thesignificance of the coefficients (H0: the coefficient is zero).

AMG/ACV ALMG/ALMG-d5

Coefficient p-value Coefficient p-value

b0 0.775 <0.01* 3.524 <0.01*

b1A 0.081 <0.01* −0.045 0.33b2A 0.025 0.22 −0.318 <0.01*

b3A 0.001 0.94 −0.056 0.23b4A 0.066 0.01* −0.079 0.11b5A 0.002 0.89 −0.016 0.71bbb

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6A 0.060 0.07 0.115 0.126B 0.108 <0.01* −0.439 <0.01*

6C −0.040 0.15 −0.275 <0.01*

* Significant factor at confidence level of 95%.

ardized residual error greater than 2.5, in absolute value, in thewo responses) and was removed to estimate the model.

If the confidence level is set at 95%, the fitted models forhe experimental responses are significant (p-values of 0.008 and.0005) with correlation coefficients, �, of 0.96 and 0.98 for AMG/ACVnd ALMG/ALMG-d5, respectively. Therefore, both models reproducedequately the experimental data.

Table 4 shows the value of the coefficients and their significancep-value) on each experimental response.

Coefficients b1A, b4A and b6B are significant for MG as it can bebserved in Table 4. As b1A and b4A represent the change of theactors X1 and X4, respectively, from level 2 to level 1 and both coef-cients are positive, higher AMG/ACV values will be obtained at levelof each factor (1 mL of NH2OH and 10 min shaking). Analogously,

oefficients b2A, b6B and b6C are significant for LMG. b2A representshe change of factor X2, from level 2 to level 1. In this case, its values negative and so higher ALMG/ALMG-d5 values will be obtained atevel 2 (5 min incubating).

For the factor X6 (FISH), the coefficients b6B (for MG and LMG)nd b6C (for LMG) are significant, and the rest of coefficients b6jave p-values greater than 0.05. For this reason, the factor FISH isonsidered significant for both analytes. A more detailed analysis

f the significance of the coefficients b6A, b6B and b6C in the modelor the MG indicates that when the matrix is turbot, the resultsre significantly different than those obtained when the fish type isrout (p-value for b6B is 0.01), nearly significant when the fish type isass (p-value for b6A equal to 0.07), whereas there is not significant

able 5xperimental matrix of a central composite design for three factors with three replicates ahe area of the analytes has been calculated with the strong precursor/product ion pair o

xperiment number Experimental plan

VNH2OH (mL) tincub (min) tshaking (min)

1 0.50 5.20 7.002 1.50 5.20 7.003 0.50 8.80 7.004 1.50 8.80 7.005 0.50 5.20 13.006 1.50 5.20 13.007a 0.50 8.80 13.008 1.50 8.80 13.009 0.16 7.00 10.00

10 1.84 7.00 10.0011 1.00 4.00 10.0012 1.00 10.00 10.0013 1.00 7.00 4.9514 1.00 7.00 15.0515 1.00 7.00 10.0016 1.00 7.00 10.0017 1.00 7.00 10.0018 1.00 7.00 10.00

a Outlier experiment (standardized residual error greater than 2.5, in absolute value).

1216 (2009) 5472–5482

effect to change to gilthead bream. According to these results, amatrix with turbot and gilthead bream could be spiked with MGto make the calibration samples. However, the results for the otheranalyte, LMG, indicate a significant difference between turbot andtrout (b6B) and turbot and gilthead bream (b6C). Consequently, asthe determination of MG and LMG in the fish samples is made in aunique analysis, a calibration model for each fish type is necessary.

In global, these results suggest that the active factors in theextraction process are VNH2OH , tincub, tshaking and FISH.

Once the most important factors have been identified and sincetheir changes in the levels affect both responses, the next stepis to fit the response to a more complex model (second-orderpolynomial) for subsequent optimization. The aim is to maximizethe standardized areas of both analytes (multiresponse optimiza-tion).

4.2. Central composite design for optimizing the extractionprocess

The non-active factors were fixed at the recommended valuesof Ref. [27], level 1 of Table 2, VACN = 4 mL and tsonic = 15 min. Theoptimization study was only carried out in gilthead bream. Theexperimental design in experimental and coded variables is shownin Table 5.

The central composite designs are suitable for fitting a second-order polynomial in a spherical domain [39,41]. The experimentswere performed in a random order. The fitted responses were theoptimal Box-Cox transformations of the standardized areas of theanalytes to study (see Table 5): log(AMG/ACV) and 1/(ALMG/ALMG-d5)2.These Box-Cox transformations ensure a more suitable fit of theresponse surface, but the position of the optimum is not altered,which is the aim of the study.

4.2.1. Analysis and optimization of each response surface fittedData were fitted to a complete second-order polynomial of three

factors by least squares. The seventh experiment of the Table 5 isoutlier (with standardized residual error greater than 2.5, in abso-lute value) and was removed to obtain the response surface. The

model estimated for MG is

Y = −0.036 + 0.048X1 − 0.018X2 − 0.057X3 − 10−5X21 + 0.005X2

2

−0.058X23 + 0.063X1X2 + 0.054X1X3 − 0.027X2X3 (7)

t the central point and the Box-Cox transformations of the experimental responses.f each one of them (see Table 1).

Experimental matrix Experimental responses

X1 X2 X3 log(AMG/ACV) 1/(ALMG/ALMG-d5)2

−1 −1 −1 0.028 0.0821 −1 −1 −0.104 0.018

−1 1 −1 −0.096 0.0701 1 −1 −0.022 0.019

−1 −1 1 −0.080 0.0571 −1 1 −0.043 0.089

−1 1 1 −0.040 0.0141 1 1 −0.021 0.081

−1.68 0 0 −0.144 0.0781.68 0 0 0.063 0.0040 −1.68 0 −0.041 0.0450 1.68 0 −0.013 0.0600 0 −1.68 −0.067 0.0470 0 1.68 −0.344 0.0770 0 0 −0.075 0.0660 0 0 −0.071 0.0490 0 0 0.009 0.0490 0 0 −0.007 0.046

D. Arroyo et al. / J. Chromatogr. A 1216 (2009) 5472–5482 5477

F rdinati eachb ion.

w

Y

wf

ifinseoa

(e

Frp

ig. 1. (a) Optimum path of the response surface fitted to log(AMG/ACV) where the ondicated as distance in the abscissa axis; (b) coordinates of the points of plot (a) foroth plots refers to maximization of the response and the left part to the minimizat

here Y is log(AMG/ACV) and the model estimated for LMG is

= 0.052 − 0.014X1 + 0.001X2 + 0.011X3 − 0.002X21 + 0.002X2

2

+ 0.005X23 − 0.0002X1X2 + 0.021X1X3 + 0.001X2X3 (8)

here Y is 1/(ALMG/ALMG-d5)2. In both models X1, X2 and X3 are theactors in coded variables (see Table 5).

The models were validated with two hypothesis test (for check-ng the significance of the model and for assessing the lack oft). The first test is as follows: null hypothesis “the model can-ot explain the experimental variation, that is, the model is notignificant” and alternative hypothesis “the model explains thexperimental variation, that is, the model is significant”. In the sec-

nd test the null haypothesis is “the proposed model is suitable”nd alternative hypothesis “the model is biased”.

If the confidence level is set at 95%, both models are significantp-value equal to 0.046 and 0.027), do not have lack of fit (p-valuequal to 0.278 and 0.176) and with correlation coefficients, �, of

ig. 2. (a) Optimum path of the response surface fitted to 1/(ALMG/ALMG-d5)2 where the oadius indicated as distance in the abscissa axis; (b) coordinates of the points of plot (a) foart of both plots refers to maximization of the response and the left part to the minimiza

es represent the optimum response values achieved on the built spheres for radiusfactor in codified variables: X1 (VNH2OH), X2 (tincub) and X3 (tshaking). The right part of

0.91 and 0.93 for log(AMG/ACV) and 1/(ALMG/ALMG-d5)2, respectively.Therefore, both models reproduce adequately the experimentaldata.

As the response surfaces of Eqs. (7) and (8) depend on threefactors, it is impossible to make a graphical level-curve analysisto understand how the response surface changes and like this todetermine the optimum position. The alternative is the optimumpath of the response surface that is determined by tracing sphericalsurfaces, focused on the centre point of the experimental domainwith a growing radius, and estimating on each of these sphericalsurfaces, the maximum and the minimum values [39]. The optimumpaths of the response surface for each individual model are shownin Figs. 1a and 2a, respectively. As can be observed, maximum values

are placed on the right and minimum values on the left. The unionof all points indicates the response evolution with the experimentalfactors.

In Fig. 1a right, it is clear that the maximum log(AMG/ACV),and therefore maximum AMG/ACV, is reached at the boundary of

rdinates represent the optimum response values achieved on the built spheres forr each factor in codified variables: X1 (VNH2OH), X2 (tincub) and X3 (tshaking). The righttion.

5 togr. A 1216 (2009) 5472–5482

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as it has been explained in the theory section.

Fig. 4 shows the chromatograms of a fish sample spiked with2 �g kg−1 of each analyte and 1 �g kg−1 of each internal standard.

478 D. Arroyo et al. / J. Chroma

he experimental domain, at distance 1.68. The codified values ofhe factors for this maximum, Fig. 1b right, are X1 = 1.31, X2 = 0.95nd X3 = −0.10 which, transformed into experimental values, corre-pond to VNH2OH = 1.70 mL, tincub = 8.70 min and tshaking = 9.70 min.nalogously, Fig. 2a left shows that the minimum 1/(ALMG/ALMG-d5)2,nd therefore maximum ALMG/ALMG-d5, is reached at distance 1.68,hose coordinates (see Fig. 2b left) are X1 = 1.30, X2 = 0.0 and

3 = −0.90 which correspond to VNH2OH = 1.70 mL, tincub = 7.0 minnd tshaking = 7.30 min. Similar VNH2OH values reach the maximum ofoth peak areas, but the tincub and tshaking values differ in each case.

n order to select an only set of values for the three factors that isuitable for both analytes, the multiresponse optimization methodased on desirability function [42] was applied.

.2.2. Multiresponse optimizationEach response, log(AMG/ACV) and 1/(ALMG/ALMG-d5)2, is trans-

ormed over the experimental domain into an individual desir-bility function, d, which varies between 0 (undesirable response)nd 100% (optimal response), depending on the closeness of theesponse to the threshold and the target value, respectively.

The aim of this paper is that the standardized area of thenalytes is as great as possible, therefore log(AMG/ACV) must beaximized and 1/(ALMG/ALMG-d5)2 must be minimized. A linear

unction between the threshold and target values was chosen foroth responses.

For the response log(AMG/ACV), desirability, dMG, is 100% for val-es greater than −0.034 (target value, greater than 0.924 in theesponse AMG/ACV) whereas values less than −0.237 (thresholdalue, lower than 0.579 in the response AMG/ACV) are unaccept-ble (desirability 0%). However, for the response 1/(ALMG/ALMG-d5)2,esirability, dLMG, is 100% for values less than 0.027 (target value,reater than 6.08 in the response ALMG/ALMG-d5) and is 0% for val-es greater than 0.071 (threshold value, lower than 3.752 in theesponse ALMG/ALMG-d5). In this case, the threshold and target val-es are fixed at 50 and 80%, respectively, of the best experimentalesult in each of them responses.

After that, a global desirability function, D, is calculated ashe geometric mean of the individual desirability functions (D =

dMG × dLMG). The global desirability function is then examinedike an individual response. Fig. 3 shows the level curves of surface

maintaining a fixed extraction time (tshaking) at 8.11 min, whichs the third coordinate of the point at which the optimum for Das been obtained. The black area of Fig. 3 denotes 0% desirabil-

ty, and consequently, the analysis should not be performed underhose conditions. The grey area denotes 100% desirability, this areaisplays the best conditions of the factors for both responses athe same time. The optimum is achieved at coordinates: X1 = 1.06,2 = 0.25 and X3 = −0.63 which correspond to VNH2OH = 1.50 mL,

incub = 7.45 min and tshaking = 8.11 min in the experimental vari-bles.

.3. Validation of the optimized extraction method

Under the optimal conditions in gilthead bream, the optimizedethod has been applied and validated [8] in the joint determina-

ion of MG and LMG. Eighteen pure standards and fourteen spikedilthead bream samples were prepared as indicated in Section 2.2.he pure standards were distributed at 9 concentration levels (alleplicated) with concentrations between 0 and 5 �g kg−1 and thepiked-fish samples were distributed at 7 concentration levels (also

ll replicated) with concentrations between 0.5 and 5 �g kg−1. Inll samples (pure standards and spiked-fish) CV and LMG-d5 werexed at a concentration of 1 �g kg−1.

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

Fig. 3. Contour plot of the global desirability function D in the space of the factorsVNH2OH and tincub (tshaking fixed at 8.11 min in the plot). Black zone corresponds to 0%of desirability whereas grey zone to 100% of desirability.

(i) Univariate: the signal employed was the relation of areas of eachanalyte standardized with its corresponding internal standard(AMG/ACV and ALMG/ALMG-d5) obtained with the strong precur-sor/product ion pair (see Table 1) of each substance.

(ii) PARAFAC: the original chromatogram was divided into fourintervals around the retention times of each substance, mod-eling separately the chromatographic peaks. The dimensions oftensors X for each substance were 32 × 41 × 2. The first dimen-sion refers to sample profile (pure standards plus spiked-fishsamples), the second corresponds to the chromatographic pro-file (number of elution times recorded at each peak) and thethird one to the precursor/product ion pairs (MS/MS spectrum)

Fig. 4. Chromatograms of a gilthead bream sample spiked at 2 �g kg−1 of each ana-lyte and at 1 �g kg−1 of each internal standard, recorded for (a) MG, (b) CV, (c) LMG-d5

and (d) LMG at the strong precursor/product ion pair of each of them (see Table 1).

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s it can be observed, the chromatographic separation between MGFig. 4a) and LMG (Fig. 4d) is complete; therefore, the figures of

erit obtained from the univariate calibration for both analytesre used as a reference for the posterior evaluation of the PARAFACalibration models.

The steps in the PARAFAC calibration [34] were

a) Decomposition of the data tensor X.b) Identification of the factors related to the analytes present in the

sample according to the retention time and relative abundancesbetween the precursor/product ion pairs for each analyte, inagreement with the European Union Decision 2002/657/EC.

(c) Standardization of the sample mode loadings of the analyteswith the sample mode loadings of their corresponding internalstandards.

d) Construction of a univariate regression, by least squares,between the standardized loadings of sample mode and the trueconcentration.

e) Elimination of outlier data from the previous regression. Datawith standardized residual error greater than 3 in absolute valuewere removed and a new least square regression was performedwith the rest of data.

All PARAFAC calibrations were constructed by applying thelternative least squares (ALS) algorithm with non-negativity con-traints in the chromatographic and MS/MS spectral profile, andnly a single factor was needed.

Table 6 shows the pure standard and fish-spiked cali-ration lines signal vs. true concentration, where signal isANALYTE/AI.S recorded with the strong precursor/product ion pairnd loadingsANALYTE/loadingsI.S for univariate and PARAFAC cali-ration lines, respectively. If the intercept (b0) of these equationsan be considered statistically equal to zero, the recovery (in

ercentage) of the method in gilthead bream can be estimatedy dividing the slopes (fish-spiked line slope/pure standard linelope) × 100.

As can be observed in Table 6, in all PARAFAC based calibra-ion models, b0 can be considered equal to zero because all the

able 6esults of the figures of merit for MG and LMG for different calibration models and analoncentration (CTRUE). sy.x is the residual standard deviation of the CCALCULATED vs. CTRUE regr

Pure standard calib

Univariate

odel signala vs. CTRUE

quation MG −0.005 + 0.87xLMG 0.130 + 1.17x

5% confidence level interval for intercept, b0 MG (−0.058,0.048)LMG (0.107,0.153)

odel CCALCULATED versus CTRUE

quation MG −2.06 × 10−6 + 0.99LMG 7.21 × 10−5 + 1.0x

y.x MG 0.075LMG 0.025

5% confidence level interval for intercept MG (−0.06,0.06)LMG (−0.02,0.02)

5% confidence level interval for slope MG (0.97,1.03)LMG (0.99,1.01)

atio outliers MG 2/18LMG 2/18

C˛b (�g kg−1) MG 0.21LMG 0.07

Cˇb (�g kg−1) MG 0.35LMG 0.12

(%) MG 4.57LMG 2.10

a AANALYTE/AI.S recorded with the strong precursor/product ion pair (see Table 1) and loab False-positive, ˛, and false-negative, ˇ, probabilities at 1% and 5%, respectively.

1216 (2009) 5472–5482 5479

confidence intervals for b0 contains zero. Taking this into account,the recovery determined with PARAFAC models were 48.1% (MG)and 92.1% (LMG). For MG in the univariate calibration model therecovery is 45.9% and for LMG is 82.0% although in the latter theconfidence interval does not contain zero though it is near to.

Furthermore, for each calibration model, trueness was validatedusing a regression of calculated concentration vs. true concentra-tion. Table 6 shows the equation, the residual standard deviation ofregression, sy.x, the number of outliers detected as has been indi-cated in step (e) of procedure, the results of decision limit (CC˛),capability of detection (CCˇ) and the mean of the absolute valueof relative errors. The probabilities of false-positive, ˛, and false-negative, ˇ, were fixed at 1 and 5%, respectively. In all calibrationmodels, the coefficient of linear correlation, �, was 0.99 or higher.

It can be observed that the results obtained with univariateand PARAFAC calibration functions are very similar in the figuresof merit, but univariate models had more outliers than PARAFACmodels for LMG. All calibration models fulfil the trueness, that is,when looking at the model CCALCULATED versus CTRUE, there is neitherconstant nor proportional bias because at 5% significance level thevalues zero and one are in the confidence intervals for intercept andslope, respectively.

In fish samples, the mean of the absolute value of relative errorsare less than 7.3%. CC˛ is 0.45 and 0.55 �g kg−1 whereas CCˇ is0.76 and 0.92 �g kg−1, respectively for MG and LMG. In both cases,the values are less than the MRPL established for these analytes(2 �g kg−1).

4.4. Confirmation of the analytes according to European UnionDecision 2002/657/EC

In the confirmation of these illegal veterinary drugs, is wherethe advantages of PARAFAC calibration above univariate calibration

are shown. At page 17 of European Union Decision 2002/657/EC itcan be read “When mass fragments are measured using other thanfull-scan techniques, a system of identification points shall be used tointerpret the data. For the confirmation of substances listed in Group Aof Annex I of Directive 96/23/EC, a minimum of 4 identification points

ysis of trueness by using regressions calculated concentration (CCALCULATED) vs. trueessions. E is the mean of the absolute value of relative errors.

ration Spiked-fish calibration

PARAFAC Univariate PARAFAC

−0.012 + 0.45x 0.021 + 0.40x −0.005 + 0.22x0.022 + 0.37x 0.234 + 0.96x 0.033 + 0.34x(−0.043,0.018) (−0.055,0.098) (−0.042,0.031)(−0.0005,0.0451) (0.058,0.410) (−0.036,0.103)

9x −1.62 × 10−5 + 1.0x 7.91 × 10−6 + 1.0x −2.87 × 10−5 + 1.0x2.59 × 10−3 + 1.0x 8.88 × 10−5 + 1.0x 1.52 × 10−5 + 1.0x0.083 0.164 0.1450.049 0.154 0.181(−0.07,0.07) (−0.19,0.19) (−0.15,0.15)(−0.04,0.04) (−0.18,0.18) (−0.20,0.20)(0.96,1.03) (0.93,1.06) (0.95,1.05)(0.98,1.02) (0.93,1.07) (0.93,1.07)2/18 2/14 2/141/18 2/14 1/140.23 0.51 0.450.13 0.48 0.550.39 0.86 0.760.22 0.81 0.924.65 4.82 4.192.81 8.41 7.24

dingsANALYTE/loadingsI.S for univariate and PARAFAC calibration, respectively.

5 togr. A 1216 (2009) 5472–5482

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480 D. Arroyo et al. / J. Chroma

hall be required.” MG and LMG are included in the Group A ofnnex I of European Union Directive 96/23/EC, and in LC–MS/MS 4

dentification points (multivariate data) are earned by two precur-or/product ion pairs, that is one precursor and two products ionssee Table 6 at page 17 of European Union Decision 2002/657/EC8]).

In addition, the European Union Decision 2002/657/EC demandshat the difference between the retention times of the analytes inhe spiked-matrix samples and those of a pure standard (reference)ample are less than 2.5%. The PARAFAC estimated chromatographicrofile fulfils this requirement for both analytes.

Furthermore, in all spiked-fish samples the relative abundanceetween the two precursor/product ion pairs must be included

n the interval of maximum permitted tolerances. This intervalust be calculated with the relative abundance between the same

recursor/product ion pairs of a reference sample, according touropean Union Decision 2002/657/EC.

Sometimes, samples with concentration of MG or LMG greaterhan the decision limit CC˛ or even greater than the detectionapability, CCˇ, do not fulfil the identification criterion based onhe maximum permitted tolerances for relative abundance of therecursor/product ion pairs. This contradiction between the confir-atory criterion based on the amount of analyte in the sample and

he one based on the signals has been already shown in Refs. [43,44].ne of the possible causes of the observed discrepancy in the uni-ariate case is that the criterion based on relative abundance useshe multivariate structure of the signals, whereas in the determina-ion of CC˛ and CCˇ with univariate calibration use an univariateignal. Moreover, in both cases a level of concentration must behosen to establish the interval where the signals are considereddetected” and thus to confirm the presence of the analytes. Bothroblems are solved with the calibration models based on PARAFAC.

Table 7 shows the ratios of the relative abundance betweenhe two precursor/product ion pairs and the intervals permittedy European Union Decision 2002/657/EC for the pure standardsf MG and LMG. Both values have been calculated at three levelsf concentration (0.2, 2 and 5 �g kg−1) with the maximum peakbundances (univariate) and with the estimated spectral loadingsf the PARAFAC decomposition built with only the pure standards.n a sample of gilthead bream, the presence of MG or LMG will beonfirmed if the relative abundance between precursor/product ionairs belongs to the intervals permitted by the mentioned Decision,

ntervals that are written in the last row of Table 7. These inter-als depend on the concentration of the pure standard samples.hen using the PARAFAC decomposition, a unique spectral profile

s computed that is common to all the pure standard samples. Theorresponding ratios of these loadings are 17.6% and 94.1% for MGnd LMG, respectively. Also, the last row of Table 7 contains thentervals calculated with the ratios between the PARAFAC loadings.

The relative abundances estimated by the PARAFAC models forll spiked-fish samples for MG and LMG are 17.7% and 94.1%, respec-ively. As can be observed these values almost coincide with thenes calculated for the pure standards. Therefore, we can concludehat the spectral loadings obtained for fish samples correspond to

G and LMG, so that the presence of the analytes in fish sampless confirmed. The amount of MG and LMG added in the samples ofilthead bream varies between 0.5 and 5.0 �g kg−1 and these quan-ities are greater than the CC˛ calculated by using PARAFAC (0.45nd 0.55 �g kg−1 for MG and LMG, respectively). Consequently,here is not contradiction between both procedures when usinghe PARAFAC decomposition.

However, when these relative abundances are obtained takinghe maximum peak abundance (univariate) there is a high numberf spiked-fish samples whose ratios do not fulfil the requirementss can be seen in Table 8. These samples are false non-compliantecause their concentrations are greater than the univariate CC˛ in Ta

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D. Arroyo et al. / J. Chromatogr. A 1216 (2009) 5472–5482 5481

Table 8Ratios of the relative abundance between the two precursor/product ion pairs for the spiked-fish samples with MG and LMG calculated with the maximum peak abundances(univariate).

Spiked-fish concentration(�g kg−1)

Malachite green (MG) Leucomalachite green (LMG)

Maximum peak abundance ofspiked-fish sample atprecursor/product ion pair (counts)

Ratio of counts (%)329/208329/313 · 100

Maximum peak abundance ofspiked-fish sample atprecursor/product ion pair (counts)

Ratio of counts (%)331/316331/239 · 100

329/208 329/313 331/316 331/239

0.5 436 2,482 17.6a 2,794 2,522 110.8c

0.5 564 2,450 23.0ac 1,164 1,934 60.2abc

1.0 821 4,043 20.3a 2,260 2,651 85.31.0 1,023 3,869 26.4bc 1,740 2,287 76.1ab

1.5 746 6,178 12.1ab 2,806 3,257 86.21.5 1,238 5,737 21.6a 3,176 3,275 97.02.0 1,360 9,792 13.9a 3,506 4,322 81.1ab

2.0 1,748 9,368 18.7a 3,340 3,881 86.13.0 2,211 13,052 16.9a 5,852 5,049 115.9c

3.0 2,660 12,632 21.1a 5,476 5,912 92.64.0 3,294 18,956 17.4a 7,422 9,024 82.2b

4.0 3,220 16,424 19.6a 7,221 7,936 91.05.0 4,567 25,280 18.1a 9,728 10,096 96.45.0 4,773 25,196 18.9a

Non-compliant sample when the permitted interval has been calculated with the pureTable 7 for the permitted interval at each level of concentration.

Table 9Number of spiked-fish samples that do not fulfil the criteria of the relative abundancebetween the two precursor/product ion pairs with the maximum peak abundances(univariate).

Concentration of the pure standard considered Analyte

MG LMG

025

fiMa

aala

5

poctoTb(

pr

fgtus

p

non-compliant, even though a compliant measurement has been

.2 �g kg−1 13/14 3/14

.0 �g kg−1 2/14 4/14

.0 �g kg−1 2/14 3/14

sh samples (0.51 and 0.48 �g kg−1 for MG and LMG, respectively)oreover, this false non-compliance depends on the concentration

t which the interval has been determined.The number of samples by analyte that do not fulfil the relative

bundance ratio criterion are shown in Table 9. These samples havenalyte concentration greater than CC˛ (thus the presence of ana-yte is confirmed) but they are false non-compliant with the relativebundance ratio criterion.

. Conclusions

By using a central composite experimental design an extractionrocedure has been optimized for the simultaneous determinationf malachite green (MG) and leucomalachite green (LMG) by liquidhromatography with triple quadrupole mass spectrometry detec-ion (LC–MS/MS) in fish. Prior to the optimization, the active factorsf the extraction procedure are determined by a screening design.he active factors are: volume of hydroxylamine (VNH2OH), the incu-ation time (tincub), the extraction time (tshaking) and the type of fishFISH).

It was established that the optimum conditions of the extractionrocedure for both analytes did not coincide and this problem wasesolved by means of a desirability function.

Next, the optimized method has been applied and validatedor the analysis of MG and LMG in gilthead bream. All the dataenerated by the instrument, which are already in three-way struc-ure, are employed in the PARAFAC decomposition. This calibration

nequivocally identifies and quantifies the analytes in a singletep.

With PARAFAC calibration models, the requirements of Euro-ean Union Decision 2002/657/EC, above all the maximum

9,840 10,136 97.1

standard reference sample at: (a) 0.2 �g kg−1; (b) 2 �g kg−1 and (c) 5 �g kg−1. See

permitted tolerances for relative abundance of the precur-sor/product ion pairs, were fulfilled. With the three-way approachthere is not disagreement about detection with CC˛ and identifica-tion with the relative abundance ratio for each analyte.

Acknowledgments

The authors gratefully acknowledge the financial support ofthe European Union (FEDER funds), the Ministerio de Ciencia eInnovación (Project CTQ2008-02264) and the Junta de Castilla yLeón (Project BU024A07). Particularly, David Arroyo thanks Span-ish Ministerio de Ciencia e Innovación for his FPU Grant (referenceAP2007-01313).

Appendix A.

This appendix describes some of the terms used in themanuscript that appear in the European Union Decision2002/657/EC.

Decision limit (CC˛): the limit at and above which it can beconcluded with an error probability of ˛ that a sample is non-compliant.

Alpha (˛) error: the probability that the tested sample is compli-ant, even though a non-compliant measurement has been obtained(false non-compliant decision). For substances for which no permit-ted limit has been established, ˛ is fixed at 1%.

Detection capability (CCˇ): the smallest content of the substancethat may be detected, identified and/or quantified in a sample withan error probability of ˇ. In the case of substances for which nopermitted limit has been established, the detection capability is thelowest concentration at which a method is able to detect truly con-taminated samples with a statistical certainty of 1 − ˇ. In the caseof substances with an established permitted limit, this means thatthe detection capability is the concentration at which the methodis able to detect permitted limit concentrations with a statisticalcertainty of 1 − ˇ.

Beta (ˇ) error: the probability that the tested sample is truly

obtained (false compliant decision). For substances for which nopermitted limit has been established, ˇ is fixed at 5%.

Minimum required performance limit (MRPL): minimum contentof an analyte in a sample, which at least has to be detected and

5 togr. A

coe

rim

MmRnftGsTsmrit

R

[

[

[

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[[

[

[[

[[

[

[

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482 D. Arroyo et al. / J. Chroma

onfirmed. It is intended to harmonize the analytical performancef methods for substances for which no permitted limit has beenstablished.

Identification points (IP): confirmatory methods for organicesidues or contaminants shall provide information on the chem-cal structure of the analyte. For this reason, mass spectrometric

ethods are suitable for consideration as confirmatory method.Mass spectrometric detection shall be carried out by employing

S techniques such as recording of full mass spectra or selected iononitoring (SIM), as well as MS-MSn techniques such as Selected

eaction Monitoring (SRM), or other suitable MS or MS-MSn tech-iques. When mass fragments are measured using other than

ull-scan techniques, a system of identification points shall be usedo interpret the data. For the confirmation of substances listed inroup A of Annex I of European Union Directive 96/23/EC (forbiddenubstances), a minimum of four identification points are required.able 5 in page 17 of European Union Decision 2002/657/EC [8]hows the number of identification points that each of the basicass spectrometric techniques can earn per ion (m/z ratio). In low

esolution tandem mass spectrometry techniques (LR-MSn) onedentification point is earned with the precursor ion and 1.5 iden-ification points are earned with each of the products ions.

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