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Journal of Chromatography A, 1157 (2007) 358–368

Multiresponse optimization and parallel factor analysis, useful tools in thedetermination of estrogens by gas chromatography–mass spectrometry�

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

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

Received 12 December 2006; received in revised form 18 April 2007; accepted 23 April 2007Available online 29 April 2007

bstract

This paper reports an experimental design optimization of a recently proposed silylation procedure that avoids the introduction of false positivesnd false negatives in the simultaneous determination of steroid hormone estrone (E1) and 17-�-ethinylestradiol (EE2) by gas chromatography–masspectrometry (GC/MS). The figures of merit for several calibration procedures were evaluated under optimum conditions in the silylation step.nternal standardization strategies were applied and global models were constructed by gathering signals recorded on three non-consecutive days.hree calibration models were examined: a univariate model with a sum of six monitorized ions and a three-way PARAFAC-based model (thenalyte scores were standardized on the basis of the scores of the internal standard). The global PARAFAC-based calibration model showed theest performance with detection capabilities of 4.3 �g l−1 and 7.0 �g l−1 for E1 and EE2, respectively, when the probability of false positives wasxed at 1% and that of false negatives at 5%. Mean relative error in absolute terms for E1 and for EE2 was 11.1% and 8.5%, respectively, and

rueness was likewise confirmed. The proposed optimized derivatization procedure using a three-way calibration function was also applied in theetermination of E1, 17-�-estradiol (E2) and EE2 in bovine urine samples: recovery values were 68.5%, 40.4% and 43.4%, respectively, and theetection capability was 18.4, 19.3 and 18.6 �g l−1 when the probability of false positives was fixed at 1% and that of false negatives at 5%. Meanelative error in absolute terms for E1, E2 and EE2 was 7.4%, 9.4% and 8.6%, respectively, and trueness was likewise confirmed.

2007 Elsevier B.V. All rights reserved.

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eywords: Estrogens; GC/MS; Doehlert design; Desirability; PARAFAC; PAR

. Introduction

Estrogens, in particular synthetic 17-�-ethinylestradiol (EE2)nd natural estrone (E1) are of interest because their use inhe promotion of livestock growth leaves increasingly highrace levels in the environment. Their presence is growing inurface and underground waters, effluents [1–8] and sludge9], subsequently used as agriculture fertilizer that is takenrom waste treatment works. They are also frequently foundn organic hair samples, urine, and animal [10,11] and human

lood plasma [12] and they pose significant health risk anday be dangerous even at low concentrations to humans andildlife.

� Presented at the 6th Meeting of the Spanish Society of Chromatography andelated Techniques, Vigo, Spain, 8–10 November 2006.∗ 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 © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.chroma.2007.04.056

2; Decision limit; CC�; Capability of detection; CC�; Trueness; Precision

Thus, in February 1998, a study [13] was initiated to eval-ate the side effects of substances with estrogenic, androgenicr gestagenic action. The final report was published in April999 on the potentially adverse effects to human health of hor-one residues and their metabolites. It was proven that the

ubstances in question can have developmental, immunologi-al, neurobiological, immunotoxic, genotoxic, and carcinogenicide effects. Children constituted the at-risk group of greatestoncern.

As a consequence, European Union (EU) Directives996/22/EC and 2003/74/EC [13] prohibited the use of sub-tances with estrogenic, androgenic or gestagenic side-effectsrom being administered to livestock or used in the aquacul-ure industry. Their use is solely authorized for therapeuticalurposes or zootechnical treatment.

Hence, there is a need to correctly evaluate the probabil-ty of false-positive and false-negative results in the analytical

ethod. The EU [14] establishes that the decision limit, CC�, forrohibited substances must be determined with a false-positive

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robability, �, equal to 1% and a detection capability, CC�, withfalse-negative probability, �, of 5%.

GC/MS and GC/MS/MS techniques may be used for theimultaneous determination of the steroid hormones E1, E2 andE2. The most common silylation procedure uses N-methyl--trimethylsilyltrifluoroacetamide (MSTFA) which leads to

he formation of trimethylsilyl (TMS) derivatives. Silyla-ion of EE2 using MSTFA in ethyl acetate, acetonitrile andichloromethane solvents produced 3-mono-TMS-EE2, whichs indicated by Shareef et al. [15] is unstable, due to a rup-ure process that leads to the formation of TMS-E1. This is aerious problem in the systematic control of prohibited sub-tances in animal products destined for human consumption,ecause the formation of TMS-E1 from 3-mono-TMS-EE2eads to false positives of E1 and false negatives of EE2,hich complicates quantification when EE2 is present in the

ample.To prevent the formation of 3-mono-TMS-EE2, Shareef et al.

16,17] and Zuo et al. [1,18,19] proposed various alternatives,hich involve varying the silylation reagent and the catalyst,

nd they concluded that N,N′-dimethylformamide (DMF) oryridine must be used as the dissolvent.

The effect of time and temperature on the derivatizationeaction was studied, although not systematically, in references16,19]. Thus, our first objective was to optimize the silylationrocedure by using MSTFA as the silylation agent, DMF as theissolvent and without using catalysts. Using a Doehlert design,he MSTFA volume was determined as well as the time andemperature of the derivatization reactions that give the great-st standardized peak area for E1 and for EE2. The optimumas obtained for each analyte under different experimental con-itions and conflicts were resolved by using the desirabilityunction.

Mass spectrometry used as a detector in GC [20,21,12]rovides multivariate information (second order signals) butew [22,23] papers have been published using the advantagesf three-way calibration. However, international organizationsequire the presence of these analytes to be confirmed by record-ng various m/z fragments in either single ion monitoring (SIM)

ode or full scan mode [14,24], thereby ensuring that three-wayata is obtained in practice.

Calibration in residue analysis is time consuming, for whicheason once the model has been validated, it is of interest touarantee its stability with time. Internal standardization of theeak area is an efficient technique to improve the reproducibil-ty of GC/MS results in the case of univariate calibration model.everal alternatives have been used to build robust and stable

wo-way calibration models and to correct multivariate signalnstability in mass spectrometry without a complete recalibra-ion stage. In ref. [25] internal standardization of multivariateignals (mass spectra) was carried out with the intensity of aole ion. However, in ref [23], the standardization of the analyteoadings estimated by PARAFAC2 was carried out using the

oadings computed for the internal standard. As the whole masspectra was taken into account to compute the loadings of bothhe analyte and the internal standard any subsequent correctionsere more effective.

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. A 1157 (2007) 358–368 359

Following optimization of the silylation procedure, we com-ined the PARAFAC or PARAFAC2 calibration model withecond order signals and the global calibration in order to obtainobust analytical procedures to identify and quantify E1 and EE2n a single analysis. The different calibration strategies (univari-te, multivariate, PARAFAC regression models together withhe global approach) were compared using the figures of meritstablished by Decision 2002/657/EC for the validation of ana-ytical methods, particularly the decision limit, CC�, detectionapability, CC�, trueness and precision.

Finally, this three-way approach was applied to bovine urineamples to quantify E1, E2 and EE2 obtaining the method’secovery values and the above-mentioned figures of merit.

. Experimental

.1. Chemicals

Ethyl acetate, HPLC-grade methanol, cyclohexane,nalytical-reagent grade sodium acetate anhydrous and glacialcetic acid were obtained from Merck (Darmstadt, Ger-any) and DMF and MSTFA were purchased from Fluka

Neu-Ulm, Germany). Analytical standards of E1, E2, EE2,-glucoronidase and [2H3]testosterone (TES-d3) were pur-hased from Sigma–Aldrich (Steinheim, Germany). Deionisedater was obtained by using the Milli-Q gradient A10 waterurification system of Millipore (Bedford, MA, USA).

.2. Standard solutions and derivatization

Stock solutions at 100 mg l−1 of E1, E2 and EE2 were pre-ared in ethyl acetate. Diluted solutions of 10 mg l−1, werebtained by dilution in the same dissolvent and were then storedt 4 ◦C in the dark. Individual diluted solutions, in DMF, madep every day until the concentrations of E1, E2 and EE2 wereespectively 0.25 mg l−1, 0.25 mg l−1 and 1 mg l−1.

The silylation products obtained in the derivatizationeactions were named TMS-E1, 3,17-di-TMS-E2 and 3,17-di-MS-EE2 for E1, E2 and EE2, respectively.

The reactions were carried out in a vial of 1.5 ml containing00 �l of a mixture of the three estrogens in DMF added to theppropriate amount of MSTFA, and the temperature was set atalues specified in the experimental design. The three optimiza-ion factors in the derivatization reaction were the quantity of

STFA (VMSTFA), reaction time (tREACTION) and temperatureTREACTION).

.3. Urine samples procedure

Stock solutions (2 g l−1) of E1, E2 and EE2 were prepared inethanol. A solution (1 mg l−1) containing all the analytes was

repared by dilution in the same solvent. The internal standardolution of TES-d3 (10 mg l−1) was prepared in methanol from

commercial solution of 100 mg l−1. All solutions were stored

n amber bottles at 4 ◦C in the dark.The spiked urine samples to be quantified were prepared with

nal concentrations of 0, 5, 10, 20, 30, 50 and 100 �g l−1 on a

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aily basis, and the samples at 5, 20 and 50 �g l−1 were repli-ated. Two types of spiked samples (A and B) were prepared andn order to evaluate the recovery, sample of type B were spikedefore and samples of type A after the extraction procedure. Inoth cases, the internal standard was added before the extractiontep.

A suitable volume of urine was centrifuged at 6000 rpm for5 min. Ten millilitres of this urine, 1 ml of sodium acetate bufferM (pH 4.8), 50 �l of I.S. solution and 40 �l of �-glucoronidaseere added to centrifuge tubes and placed in a heater at 37 ◦C for8 h. The samples were centrifuged at 6000 rpm for 15 min andhen loaded and passed across a Sep-Pack Plus 3 ml (500 mg)-18 cartridge from Waters (Milford, MA, USA) that had been

equentially pre-conditioned with 2 ml of methanol and 10 mlf Milli-Q water. The cartridges were washed with 10 ml ofilli-Q water and then with 8 ml of methanol/water (55/45,

/v).Analytes were eluted from the cartridge with 4 ml of

ethanol/water (80/20, v/v). The extracts were reduced topproximately 0.4 ml in a rotatory evaporator (SPD121P Speed-ac, Thermo Electron Corp., Ecublens, Switzerland) and were

aised to 1 ml by adding hydrochloridric acid 0.5 M with sodiumhloride (20%).

A liquid–liquid extraction was performed three times withml of cyclohexane by shaking during 30 s and centrifuging at500 rpm for 2 min. The combined extracts were evaporated toryness at 60 ◦C and then dissolved with 175 �l of methanol andisposed into amber autosampler vials. This extract was againvaporated to dryness.

The derivatization reaction (under optimal Doehlert designonditions) obtained the following silylated compounds:MS-E1, 3,17-di-TMS-E2, 3,17-di-TMS-EE2 and 3,17-di-MS-TES-d3 for E1, E2, EE2 and TES-d3, respectively.

.4. Instrumental analysis

Analyses were performed with the Agilent 6890N gas chro-atograph from Agilent Technologies, coupled with an MSgilent 5975 detector and an Agilent 7683 automatic injector.eparation was achieved with the J and W DB-5MS column fromgilent, J and W Scientific, Folsom, CA, USA, bonded-phasehenyl arylene (equivalent to 5% phenyl-methyl polyxilox-ne), with a film thickness of 0.25 �m, and dimensions of0 m × 0.25 mm I.D.

Injections were performed in splitless mode with a solventelay of 11 min, sample injection volume was 2 �l and heliumas used as the carrier gas at 1 ml min−1. The injector was kept atconstant temperature of 200 ◦C, the ion source was 230 ◦C and

he transfer line 270 ◦C. The oven temperature was programmedt an initial temperature of 150 ◦C for 1 min, and then increasedrom 150◦ to 220◦ at 30 ◦C min−1, held at 220 ◦C for 1 min,hen raised to 250 ◦C at 15 ◦C min−1, held at this temperatureor 3 min, subsequently raised to 270 ◦C at 8 ◦C min−1 and held

or 3 min. The oven equilibration time was set at 0.5 min.

Analyses were performed in the electron impact ionizationode at 70 eV operating in SIM mode, the electron multiplieras fixed at 1294 V and the source vacuum at 10−5 Torr.

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. A 1157 (2007) 358–368

Five groups of ions were registered. Group 1, for TMS-E1,ad a start time of 11 min and registered the following ionragments: 218, 231, 244, 257, 285 and 342. Group 2, for 3,17-i-TMS-E2, had a start time of 12.02 min and registered theollowing six ions 129, 218, 232, 244, 285 and 416. Group 3,hich is a control group for 3-mono-TMS-EE2 to ensure that

his sub-product is not formed in the derivatization reaction,tarted at 12.5 min and registered the following ion fragments18, 232, 244, 285, 300 and 368. Group 4, for 3,17-di-TMS-E2, had a start time of 13.40 min and registered the following

on fragments: 218, 232, 244, 285, 425 and 440. Group 5, for,17-diTMS-TES-d3, started at 12.02 min and registered ions35, 436 and 437. The dwell time per ion was 100 ms in allroups.

For the univariate calibration models, the ions were 342, 416,25 and 368 for TMS-E1, 3,17-di-TMS-E2, 3,17-di-TMS-EE2nd 3-mono-TMS-EE2, respectively. For multivariate calibra-ion the ions mentioned above are considered as both the sum ofreas and as a three-way calibration.

.5. Software

NEMRODW [26] was used for building and analyzing thexperimental design and the desirability function and for findinghe optimum conditions for the derivation procedure.

PARAFAC and PARAFAC2 models were constructed withLS-Toolbox [27] for use with MATLAB version 6.1 (TheathWorks).Decision limit and detection capability for the univariate and

he three-way calibration models were determined using theETARCHI [28] and the NWAYDET programs, respectively,

available from the authors). These programs display the detec-ion capability for any given false-positive � or false-negative �robability as laid down by European Directive 657/2002 andSO 11843.

The univariate regression models (estimated concentrationersus true concentration in the validation of trueness and signalersus concentration in univariate calibrations) were performedith the PROGRESS program [29] that applies the least medianf squares (LMS) regression, a robust regression technique thatetects outliers. The tests for the validation of the univariateegression models were performed with STATGRAPHICS [30].

. Theory

.1. PARAFAC and PARAFAC2 decomposition

GC/MS data are arranged in a three-way array, X, and ana-yzed with PARAFAC or PARAFAC2. A comparison betweenertain three-way models may be consulted in refs. [31–33], aecent review about applications in analytical chemistry is con-ained in ref. [34] and another more specific for chromatographyan be seen in ref. [35]. The two models are briefly described

elow.

The PARAFAC (parallel factor analysis) model is a decom-osition method which decomposes the original data X intoriads or trilinear factors [36,37], each consisting of three loading

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ectors. The PARAFAC structural model [38] is as follows:

ijk =F∑

f=1

aifbjfckf + eijk (1)

here, F is the number of factors, aif, bjf and ckf are the elementsf the loadings matrices, and eijk the experimental error.

The PARAFAC model is highly affected by deviations fromhe trilinear structure. Changes in the retention time betweenuns are habitual in chromatography which can cause theARAFAC model to fail due to the assumption of invariant pro-les in each sample. If we consider the slab matrix Xi, of data

ensor X, PARAFAC2 [39] overcomes this difficulty by mod-ling XiXi

T instead of Xi which allows some deviation in thehromatographic profiles.

.2. Detection capability

The detection capability or minimum detectable net concen-ration has been defined [40,41,14] for a given false-positiverobability, α, as “the true net concentration of the analyte inhe material to be analyzed which will lead, with probability− β, to the correct conclusion that the concentration in thenalyzed material is different from that in the blank material”.he application of this figure of merit to chemical analysis withero-order signals and univariate calibration models is detailedn the second part of the standard ISO 11843 [42] and is obtainedy means Eq. (2)

C� = �(α, β)w0σ

b(2)

In the case of first and higher-order signals modeled by twond superior-order calibrations, the capability of detection canlso be determined through both probabilities α and β. Theetails of generalization can be seen in ref. [43].

4

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able 1xperimental matrix and Doehlert design responses with two replicates at the centre

xperimental plan Experimental matrix

MSTFA (�l) tREACTION (min) TREACTION (◦C) X1 X2

25.0 40.0 50 1.0 0.0075.0 40.0 50 −1.0 0.0012.5 53.0 50 0.5 0.8787.5 27.0 50 −0.5 −0.8712.5 27.0 50 0.5 −0.8787.5 53.0 50 −0.5 0.8712.5 44.3 75 0.5 0.2987.5 35.7 24 −0.5 −0.2912.5 35.7 24 0.5 −0.2900.0 48.7 24 0.0 0.5887.5 44.3 75 −0.5 0.2900.0 31.3 75 0.0 −0.5800.0 40.0 50 0.0 0.0000.0 40.0 50 0.0 0.00

he two responses were the ratio of areas against I.S. TMS-E1 (m/z 342), 3,17-di-TM

. A 1157 (2007) 358–368 361

. Results and discussion

.1. Optimization of the derivatization reaction with aoehlert design

Three factors in the reaction were explored: the quantityf the silylation agent, VMSTFA; time, tREACTION and temper-ture, TREACTION. The experimental design for the three factorsn experimental and coded variables can be seen in Table 1.he responses under analysis were the base peak area of eacherivatized analyte (m/z 342 for TMS-E1 and m/z 425 for,17-di-TMS-EE2) standardized by the base peak area of 3,17-i-TMS-E2 (m/z 416).).

Doehlert experimental design is suitable for fitting a two-egree polynomial in a spherical domain [44,45]. The completeesign was repeated twice with a 6-h time lapse between anxperiment in the first series and the same experiment in theecond series to evaluate possible changes that might be dueo the working time. As a consequence, in Eq. (3) we con-idered the codified variable of the block factor, xB, whichakes a value of 1 for the first experimental series and 2or the second. The model put forward for each experimentalesponse is

= β0 + βBxB + β1x1 + β2x2 + β3x3 + β11x21 + β22x

22

+β33x23 + β12x1x2 + β13x1x3 + β23x2x3 (3)

The experiments were performed in a random order and theesults are shown in Table 1. Each experiment was checked tonsure that no 3-mono-TMS-EE2 was formed.

.1.1. Analysis and optimization of each response surfaceData from the Doehlert design shown in Table 1 were fitted

y least squares to the model of Eq. (3). The model estimated

point

Experimental responses

X3 ATMS-E1/Adi-TMS-E2 Adi-TMS-EE2/Adi-TMS-E2

First Second First Second

0.00 63.142 65.156 33.640 33.8120.00 67.013 63.974 30.138 32.1820.00 58.756 60.347 29.496 28.7380.00 70.233 70.133 32.201 32.9980.00 62.501 64.983 31.335 34.6090.00 59.794 61.037 27.369 30.2730.82 71.753 62.060 30.855 31.621

−0.85 56.928 63.477 29.477 32.061−0.85 69.411 66.018 29.842 30.789−0.85 49.825 56.247 28.142 29.070

0.82 65.000 66.371 31.326 33.5680.82 57.901 63.735 31.300 43.2920.00 64.940 63.433 31.210 33.9540.00 54.295 57.839 29.228 28.679

S-EE2 (m/z 425) and 3-17-di-TMS-E2 (m/z 416).

362 D. Arroyo et al. / J. Chromatogr. A 1157 (2007) 358–368

F S-E1/As f plot( e left

f

y

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ig. 1. (a) Optimum path of the response surface fitted to the ratio of areas ATM

pheres for radius R indicated in abscissa axis; (b) coordinates of the points oTREACTION). The right part of both plots refers to maximum of response and th

or the ratio of areas ATMS-E1/Adi-TMS-E2 is:

= 59.36 − 2.50xB − 1.06 x1 − 4.26 x2 + 1.19 x3 + 6.71 x21

+4.92x22 + 1.76x2

3 + 3.23x1x2 − 9.01x1x3 + 8.36x2x3

(4)

The model for Adi-TMS-EE2/Adi-TMS-E2 is:

= 32.63 − 1.74xB − 0.52x1 − 2.02x2 + 1.26x3 + 0.69x21

−1.40x22 − 0.91x2

3 − 0.06x1x2 − 0.39x1x3 + 0.15x2x3 (5)

here xB, x1, x2 and x3 are the block values and factors in codedariables (Table 1).

If the significance level is set at 0.05, both models are signifi-

ant (p-value equal to 0.0005 and 0.0019 for ATMS-E1/Adi-TMS-E2nd Adi-TMS-EE2/Adi-TMS-E2, respectively) and do not have lackf fit (p-value equal to 0.85 and 0.76 for ATMS-E1/Adi-TMS-E2 anddi-TMS-EE2/Adi-TMS-E2, respectively). The coefficient of deter-

pfmt

ig. 2. (a) Optimum path of the response surface fitted to the ratio of areas Adi-TMS-E

uilt spheres for radius R indicated in abscissas; (b) coordinates of the points of ploTREACTION). The right part of both plots refers to maximum of response and the left

di-TMS-E2 where ordinates represent the optimum response reached on the built(a) for each factor in codified variables X1 (VMSTFA), X2 (tREACTION) and X3

with the minimum.

ination, R2, is 0.82 and 0.80 for Eqs. (4) and (5), respectively.herefore, both models adequately reproduce the experimen-

al data. The block effect is significant because the coefficientf xB is statistically different from zero in the two modelsp-value equal to 0.032 and 0.002 for ATMS-E1/Adi-TMS-E2 anddi-TMS-EE2/Adi-TMS-E2, respectively).

As the response surfaces of Eqs. (4) and (5) depend onhe three factors it is impossible to make a level-curve anal-sis to understand how the response surface changes. Thelternative is the optimum path of the response surface thats determined by tracing spherical surfaces, focused on theentre point of the experimental domain and with a growingadius, and calculating on each of these the maximum andhe minimum of the response surface [44,45]. The optimum

aths of the response surface are shown in Figs. 1a and 2aor both individual models. It is clear in Fig. 1a that theaximum ATMS-E1/Adi-TMS-E2 is reached at the boundary of

he experimental domain, at distance 1 (right). The coordi-

E2/Adi-TMS-E2 where ordinates represent the optimum response reached on thet (a) for each factor in codified variables X1 (VMSTFA), X2 (tREACTION) and X3

with the minimum.

atogr. A 1157 (2007) 358–368 363

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(i) Univariate: the signal being the relation of areas of eachanalyte with that of the I.S. (ATMS-E1/Adi-TMS-E2 andAdi-TMS-EE2/Adi-TMS-E2) obtained with the m/z ratio of eachanalyte peak base.

Table 2Standard samples, in all the cases the I.S. is at 3 �g l−1

Name of samples E1 (�g l−1) EE2 (�g l−1)

M1-1, M1-2 1.5 4.0M2-1, M2-2 2.5 6.5M3 3.5 9.0M4 5.0 11.0M5-1, M5-2 7.0 14.0

D. Arroyo et al. / J. Chrom

ates for this maximum, Fig. 1b, are x1 = −0.83, x2 = −0.44nd x3 = 0.31 which, transformed into experimental vari-bles, correspond to VMSTFA = 79.2 �l, tREACTION = 33.40 minnd TREACTION = 59.5 ◦C. However, Fig. 2a shows that theaximum Adi-TMS-EE2/Adi-TMS-E2 is also reached at distance(right), although the coordinates (Fig. 2b) are x1 = 0.86,

2 = −0.43 and x3 = 0.25 correspond to VMSTFA = 121.5 �l,REACTION = 33.55 min and TREACTION = 57.6 ◦C, when trans-ormed into real variables.

Similar tREACTION and TREACTION values reach the maximumf both peak areas, but the VMSTFA values differ in each case.

greater volume of MSTFA was needed because silylation ofE2 occurs at two positions of its molecule and there are alsoteric impediments.

Close to the maximum, Figs. 1b and 2b show that the TMS-E1eak area is more sensitive to variations in temperature than theeak area of di-TMS-EE2. But the peak area for both analytess very sensitive to changes in the volume of MSTFA. In ordero find a set of values for the three factors that is suitable foroth analytes, the multiresponse optimization method based inesirability function [44] was applied.

.1.2. Multiresponse optimization: desirability functionEach response is transformed over the experimental domain

nto an individual desirability function, varying from zero (unde-irable response) to 100 (optimal response). Our work considersdesirability function with a value of zero for response valueselow a threshold value and 100 above another target. A lin-ar function between the two latter values was chosen for bothesponses.

For the response ATMS-E1/Adi-TMS-E2, desirability, dE1, wasero for areas less than 60, while it was 100 for areas greaterhan 65. The threshold value was 28 for Adi-TMS-EE2/Adi-TMS-E2nd the objective value was 31. The desirability function of thisnalyte is denoted by dEE2. These values take account of theifference between the threshold value and the objective valuen each di, which is greater than the coefficient of the block factorf the response (in absolute value).

Subsequently, the overall desirability function D was cal-ulated as the weighted geometric mean of the individual

esirability functions (D = 4√

dE1d3EE2). The greater weight

ttributed to the function dEE2 with respect to dE1 (relation 3:1)s because the TMS-EE2 peak area was smaller than that of theMS-E1.

Fig. 3 shows the level curves of surface D maintaining axed reaction time at 32 min, which is the second coordinate of

he point at which the optimum for D has been obtained [26].he black area of Fig. 3 denotes 0% desirability and the greyreas, 100% desirability. There are two areas with 100% desir-bility, one for high VMSTFA and low TREACTION values, andnother for low VMSTFA and high TREACTION values. The lowMSTFA area was considered as a way of reducing MSTFA con-

umption in which the optimum was identified at coordinates1 = −0.73, x2 = −0.53 and x3 = 0.33, the experimental variablesor which correspond to VMSTFA = 81 �l, tREACTION = 32 minnd TREACTION = 60 ◦C.

MMMM

MSTFA, and TREACTION (tREACTION was fixed at 32 min in the plot). Black zoneorresponds to zero desirability whereas grey zones correspond to 100% ofesirability.

.2. Comparison of several calibrations functions

The optimized derivatization reaction was used in the jointetermination of E1 and EE2. The elution times of each analyteere 11.71, 12.26 and 13.77 min for TMS-E1, 3,17-di-TMS-E2

nd 3,17-di-TMS-EE2.Fourteen standards were prepared as indicated in Section 2.2.

able 2 shows the nine concentration levels and the distributionf the samples, in which E2 is at a fixed concentration of 3 �g l−1

n all of them. This calibration set was prepared and analyzedn three different days (D1, D2 and D3). G denotes the data setor the three days (D1 + D2 + D3).

Three calibration models were applied to the recorded datas indicated in Section 2.4:

6 9.0 17.07 10.5 19.08-1, M8-2 11.5 21.59-1, M9-2 12.5 24.0

364 D. Arroyo et al. / J. Chromatogr

Fa

(

EPt(

e

(((

(

(

olKi

bsts

dfcttAtmb

CodvfiaEwcg

mamwsoeiwbs

rTswimicc

ig. 4. Chromatographic peaks of 3,17-di-TMS-EE2 (recorded at m/z 425) forll the standards of calibration (Table 2) of day 1.

(ii) Sum of areas (∑

AREAS): the peak areas of the six m/z ratiosrecorded for each analyte are added up and the result isdivided by the sum of the internal standard peak area ratios.This procedure is multivariate in the sense that it uses var-ious signals (areas of several m/z) of each analyte, but themathematical treatment is univariate.

iii) PARAFAC: The original chromatogram is divided intothree parts around the retention times of each estrogen,such that the chromatographic peaks of each estrogen aremodeled separately. For each analyte there is a tensor X ofdimensions (14 × 26 × 6) in the models for each day andof (42 × 26 × 6) in the overall model (G). The first dimen-sion refers to the number of standards, the second to thechromatographic profile (number of scans or elution timesrecorded at each peak), and the third to the mass spectra(number of m/z fragments recorded).

As may be seen in Fig. 4, the peak of the 3,17-di-TMS-E2 showed shifts in the retention time, which meant that aARAFAC2 decomposition was appropriate. In this case, theensor dimension was (26 × 14 × 6) in the daily models and26 × 42 × 6) in the overall model.

Steps in calibration of the PARAFAC and PARAFAC2 mod-ls:

a) Decomposition of the data tensor X.b) Selection of an appropriate number of factors.c) Standardization of the sample mode loadings of the analyte

with the sample mode loadings of the 3,17-di-TMS-E2 [23].d) Construction of a univariate regression between the stan-

dardized sample mode loadings and the true concentrationof the standards.

e) Elimination of outlier data from the above-mentioned

regression using LMS. Data with standardized LMS residualerror greater than 2.5 in absolute value were removed andthe least-squares regression was performed and validatedwith the remaining data (RLS).

ata1

. A 1157 (2007) 358–368

The RLS regression line in step (e) was validated by vari-us hypothesis tests: the significance test of the model’s fit, theack-of-fit test, Bartlett and Cochran’s homoscedasticity test, theolmogorov test of normality of residuals and analysis of the

ndependence of the residuals (Durbin-Watson statistic).All the PARAFAC and PARAFAC2 models were constructed

y applying the ALS algorithm with no restrictions and with aingle factor that was coherent with the absence of interferentshat might be modeled by other factors in accordance with theecond-order property.

Univariate calibration regression for E1 with the data fromay 1 was not significant. The same was true for days 1 and 3 andor the

∑AREAS calibration from day 1 for EE2. In the remaining

ases, all models pass the statistical validation requirements:hey were significant (all the p-values are smaller than 0.05) andhey did not present lack of fit (p-values between 0.07 and 0.65).ll the homoscedasticity tests gave p-values above 0.18 while

he normality tests gave values above 0.47. However, calibrationodels based on PARAFAC and PARAFAC2 always show a

etter statistical fit to the experimental data.Table 3 shows the results of CC� (capability of detection),

C� (decision limit) and mean relative error in absolute valuesbtained from the calibrations on the different days and withifferent calibration functions. It may be observed that for uni-ariate calibration the worst results were obtained in the threegures of merit. The results obtained with the sum of the areasnd PARAFAC or PARAFAC2 were similar on days 2 and 3 for1 and on day 3 for EE2. In some cases, the interday variabilityas noteworthy. For example, the relative error with

∑AREAS

alibrations for E1 varies between 3.95 and 9.10, although thisap is smaller with the three-way calibrations.

The PARAFAC and PARAFAC2 decompositions take theultivariate structure of the information (six m/z ratios for each

nalyte) into account as well as their variation with time (chro-atogram). In addition, a common factor in each of the analytesas identified in the data over the 3 days to a certain extent is a

tandardization of the signals because the uniqueness propertyf the solution guarantees the most adequate assignation of thexperimental variability that is not attributable to the variationn concentration. The PARAFAC and PARAFAC2 calibrationsith no internal standardization had the best figures of meritoth for E1 and for EE2 in relation to the univariate and

∑AREAS

trategies.For each calibration model, trueness was validated using a

egression of estimated concentration versus true concentration.able 4 shows the equation, the standard deviation of regression,yx, and the coefficient of correlation, ρ, for each calibration asell as the number of outliers detected by means of LMS, as

ndicated in step (e). It is interesting to observe that in globalodels the proportion of outliers was smaller than that for the

ndividual ones. The interday variability was noteworthy: in thease of E1, syx varied between 0.62 and 1.07 in the

∑AREAS

alibration, between 0.91 and 1.64 in the univariate calibrations

nd between 0.26 and 1.26 in the PARAFAC calibrations. Some-hing similar happens in the case of EE2: syx varies between 1.49nd 1.99 in the PARAFAC calibrations and between 1.02 and.80 in the

∑AREAS calibrations. It is also observed that the

D. Arroyo et al. / J. Chromatogr. A 1157 (2007) 358–368 365

Table 3Results for different calibration models obtained over 3 days

E1 EE2

Univariate Sum areas PARAFAC Univariate Sum areas PARAFAC2

Day 1CC� a 2.2 0.8 a a 5.1CC� a 3.6 1.5 a a 8.6Error a 4.0 6.4 a a 7.5

Day 2CC� 4.9 3.4 3.8 11.5 3.7 6.5CC� 8.3 5.6 6.5 19.3 6.1 10.9Error 13.1 7.5 10.4 13.2 4.9 8.9

Day 3CC� 2.8 2.6 3.1 a 5.7 5.6CC� 4.7 4.3 5.3 a 9.6 9.4Error 8.3 9.1 10.3 a 9.4 9.1

GlobalCC� 2.9 3.3 3.1 (2.5) 13.2 7.9 5.9 (4.1)CC� 4.8 5.5 5.2 (4.3) 22.4 13.3 10.0 (7.0)Error 12.8 14.1 13.7 (11.1) 20.2 13.6 12.2 (8.6)

C errorr pears

sf

ctcbas

sswrc

TA

C

D

D

D

G

C� (�g l−1), decision limit; CC� (�g l−1), detection capability and relativeespectively. The global calibration function without internal standardization ap

a CC� value outside calibration range.

tandard deviation is greater for the 17-�-ethinylestradiol thanor the estrone.

To guarantee trueness, the composite hypothesis must behecked: the slope is one and the intercept is zero. Fig. 5A showshe joint confidence regions for this hypothesis at a 5% signifi-

ance level for E1. The point (0,1) lay inside of the ellipse definedy each calibration which guarantees that the procedure is true at95% confidence level. However, the size of the ellipse demon-

trated a great degree of variability in the daily calibrations. The

b

ai

able 4nalysis of trueness by using regressions based on calculated concentration vs. true c

alibration E1

model syx ρ Ratio of out

ay 1Univariate a a a a∑

AREAS 0 + 1.00000x 0.617 0.982 5/14Three-way 3 × 10−5 + 0.99994x 0.258 0.998 5/14

ay 2Univariate 0 + 1.00002x 1.638 0.937 0/14∑

AREAS −2 × 10−5 + 1.00007x 1.071 0.970 2/14Three-way 2 × 10−5 + 0.99992x 1.261 0.964 1/14

ay 3Univariate −4 × 10−5 + 1.00001x 0.908 0.978 1/14∑

AREAS 0 + 1.00000x 0.853 0.981 0/14Three-way −2 × 10−5 + 1.00000x 1.041 0.973 0/14

lobalUnivariate 0 + 1.00003x 1.115 0.967 6/42∑

AREAS −7 × 10−5 + 1.00002 x 1.267 0.958 5/42Three-way −0.1 × 10−5 + 1.00000x 1.196 0.958 8/42Three-wayb −0.5 × 10−5 + 1.00002x 0.985 0.974 8/42

a Regression not significant.b Without internal standardization.

in %. False-positive, �, and false-negative, �, probabilities at 1% and 5%,in brackets.

ame experimental data with global calibrations showed veryimilar ellipses, particularly the overall PARAFAC calibrationith no internal standard, which has the smallest joint confidence

egion, except for the ellipse that corresponds to the PARAFACalibration from day 1, the standard deviation for which is far

elow the rest.

Fig. 5B shows the confidence regions for EE2. Once again,ll the procedures are true, but the global PARAFAC2 withoutnternal standardization has the smallest-sized ellipse. It can be

oncentration

EE2

liers model syx ρ Ratio of outliers

a a a a

a a a a

−70 × 10−5 + 1.00023x 1.486 0.977 3/14

8 × 10−5 + 1.00009x 3.521 0.900 1/140 + 1.00000x 1.022 0.989 4/14−80 × 10−5 + 1.00054x 1.994 0.964 1/14

a a a a

0 + 1.00000x 1.801 0.974 1/1480 × 10−5 + 1.00131x 1.668 0.970 3/14

3 × 10−5 + 1.00002x 5.136 0.817 3/422 × 10−5 + 1.00004x 3.061 0.923 2/4212.5 × 10−5 + 0.99882x 2.280 0.956 6/42−9 × 10−5 + 0.99995x 1.611 0.976 3/42

366 D. Arroyo et al. / J. Chromatogr. A 1157 (2007) 358–368

Fig. 5. Ellipse of confidence at 95% for the slope and intercept of the regressions“estimated concentration vs. true concentration” of Table 4 (A) for TMS-E1 (B) for 3,17-di-TMS-EE2. The calibrations models are: (a) PARAFAC orPARAFAC2 day 1. (b) PARAFAC or PARAFAC2 day 3. (c) PARAFAC orPARAFAC2 day 2. (d) Global PARAFAC or PARAFAC2. (e) Global univari-as

scas

4

idt1d

itt

F −1

Tm

Ipn

aptotT

taetA1

frb

te. (f) Global �AREAS. (g) Global PARAFAC or PARAFAC2 without internaltandardization.

een that the ellipses of EE2 have a greater surface area than thoseorresponding to E1 due to the greater syx of this second analyte,lthough the global three-way calibrations revealed ellipses ofimilar size and shape.

.3. Validation in urine samples

The chromatograms for the bovine urine samples were reg-stered under the same optimal conditions obtained for theerivatization procedure (Section 4.1.2), as described in Sec-ions 2.3 and 2.4. The elution times of each analyte are 11.70,2.23, 12.24 and 13.75 min for TMS-E1, 3,17-di-TMS-E2, 3,17-i-TMS-TES-d3 and 3,17-di-TMS-EE2, respectively.

Fig. 6 shows the chromatograms of one of these samples reg-stered at the base peak of each analyte. The dimensional dataensors 17 × 4 × 24, 16 × 6 × 19 and 18 × 6 × 19 are respec-ively considered for each of the three analytes E1, E2 and EE2.

p

f7

ig. 6. Chromatograms of a urine sample spiked at 50 �g l recorded for (a)MS-E1 at m/z 342. (b) 3,17-diTMS-E2 at m/z 416. (c) 3,17-diTMS-TES-d3 at/z 435 and (d) 3,17-diTMS-EE2 at m/z 425.

n all cases, the first index corresponds to the chromatographicrofile, the second to the mass spectrum and the third to theumber of samples.

PARAFAC decomposition was performed jointly on type And type B samples. In the case of E1, five samples of this analyterepared in methanol were also included to facilitate extrac-ion of the spectral and chromatographic profiles. The numberf factors in the construction of the PARAFAC decompositionogether with the validated calibrations models are shown inable 5.

The results of the regression loading samples versus concen-ration for type A and type B samples are shown in columns 4, 5nd 6, and columns 10, 11 and 12, respectively. The recovery forach analyte was obtained by means of the coefficient betweenhe slope of the type B calibrated model and the slope of the type

calibrated model, the values for which are shown in column7 of Table 5.

The decision limit and the detection capacity were calculatedor the spiked samples, both before and after extraction, shownespectively in columns 13 and 14 and in columns 7 and 8. It maye seen that the values are worse when the complete analytical

rocedure was applied.

The mean absolute relative error values are 7.2, 4.8 and 4.3%or E1, E2 and EE2, respectively, for the type A samples and.4, 9.4 and 8.6% for the type B samples.

D. Arroyo et al. / J. Chromatogr

Tabl

e5

Mod

els

and

para

met

ers

ofth

ere

gres

sion

load

ings

ofth

ean

alyt

ean

dth

etr

ueco

ncen

trat

ion,

imm

edia

tely

afte

rth

eur

ine

sam

ples

wer

esp

iked

(typ

eA

)an

dpr

ior

toth

eex

trac

tion

step

(typ

eB

)

Ana

lyte

Tens

ordi

men

sion

PAR

AFA

C2

fact

ors

Uri

nesa

mpl

esA

Uri

nesa

mpl

esB

Rec

over

y(%

)Sp

ectr

alco

rrel

atio

na

Mod

elρ

s yx

CC

�

(�g

l−1)

CC

�

(�g

l−1)

Err

or(%

)M

odel

ρs y

xC

C�

(�g

l−1)

CC

�

(�g

l−1)

Err

or(%

)

E1

17×

4×

242

0.15

8+

0.01

7x0.

995

0.05

510

.818

.17.

20.

059

+0.

012x

0.99

70.

031

11.0

18.4

7.4

68.5

0.99

4E

216

×6

×19

20.

025

+0.

028x

0.99

90.

040

4.7

7.8

4.8

0.04

0+

0.01

1x0.

995

0.03

711

.519

.39.

440

.40.

999

EE

218

×6

×19

1−0

.009

+0.

028x

0.99

90.

041

4.7

7.9

4.3

0.00

4+

0.01

2x0.

995

0.03

811

.118

.68.

643

.40.

985

ρ,c

orre

latio

nco

effic

ient

;syx

stan

dard

devi

atio

nof

regr

essi

on;C

C�

,dec

isio

nlim

it;C

C�

dete

ctio

nca

pabi

lity.

aC

orre

latio

nbe

twee

nth

esp

ectr

allo

adin

gin

the

PAR

AFA

C2

and

the

mas

ssp

ectr

aof

the

anal

yte.

4

fi9spwuti

4

emttas0pct

4

ett

5

omcIdr

Tn

epntwwiTf7fiaE

. A 1157 (2007) 358–368 367

.4. Identification

A minimum of four identification points are required for con-rmation of substances listed in Group A of Annex I of Directive6/23/EC. The selected diagnostic ions should not originateolely from the same part of the molecule so that they willrovide independent information. This can be done by three-ay models such as PARAFAC or PARAFAC2 in which theniqueness property allows the true chromatographic and spec-ral profiles to be obtained even in the presence of unknownnterferences.

.4.1. Standard samplesThe spectral and chromatographic estimated profiles of

strone can be compared with a reference spectrum and chro-atogram (retention time). The correlation coefficient between

he reference and the estimated spectrum is 0.99. The reten-ion time of 11.72 min of the estimated chromatographic profilelmost coincides with that of the chromatogram of a standardample of E1, the difference between the two being less than.5% of the retention time of the reference sample, thus com-lying with the requirements of Decision 657. For EE2, theorrelation coefficient between the PARAFAC2 estimated spec-rum and the reference spectrum is equal to 0.99.

.4.2. Urine samplesThe correlation coefficients between the reference and the

stimated spectrum for E1, E2, EE2 and TES-d3 are shown inhe last column of Table 5 and correlation is in all cases greaterhan 0.985.

. Conclusions

An experimental design-based silylation procedure has beenptimized for the simultaneous determination of steroid hor-ones estrone (E1) and 17-�-ethinylestradiol (EE2) by gas

hromatography with mass spectrometry detection (GC/MS).t was established that the conditions of the silylation proce-ure for the two analytes did not coincide; a problem that wasesolved by means of the desirability function.

Under optimum conditions, the only product formed is di-MS of EE2. Thus, neither false positives for E1 nor falseegatives for EE2 arise as a result of the analytical procedure.

The effects on the figures of merit (CC�, CC�, mean relativerror and trueness) of the calibration type (univariate, sum ofeak areas, PARAFAC and PARAFAC2 with or without inter-al standard) and of day-to-day variability were evaluated whenhe pure standard had been determined. The greatest stabilityith regard to day-to-day changes and the best performancesere obtained with an overall three-way PARAFAC-based cal-

bration for E1 and a PARAFAC2-based calibration for EE2.he decision limits were respectively 2.5 �g l−1 and 5.9 �g l−1

or E1 and EE2, and the detection capabilities 4.3 �g l−1 and

.0 �g l−1 for E1 and EE2, when false-positive probability wasxed at 1% and false-negative probability at 5%. The mean rel-tive error in absolute values was 11.1% for E1 and 8.5% forE2 and trueness was likewise established.

3 atogr

1a1faf

a

Prc

A

o0BtAda

R

[

[

[[

[

[

[

[[[[

[

[

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[

[

[

[

[[

[[[

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[44] G.A. Lewis, D. Mathieu, R. Phan-Tan-Luu, Pharmaceutical ExperimentalDesign, Marcel Dekker, New York, 1999.

68 D. Arroyo et al. / J. Chrom

The decision limits for the urine samples were 11.0 �g l−1,1.5 �g l−1 and 11.1 �g l−1 for E1, E2 and EE2, respectively,nd the capability of detection was 18.4 �g l−1 19.3 �g l−1 and8.6 �g l−1 for E1, E2 and EE2, respectively (probability ofalse-positive at 1% and that of false-negative at 5%). The aver-ge of absolute values of relative error was 7.4% for E1, 9.4%or E2 and 8.6% for EE2.

This procedure unequivocally identifies and quantifies thenalytes in a single step.

In summary, the work shows the advantage of applyingARAFAC and PARAFAC2 calibrations to multiway dataecorded in the determination of E1, E2 and EE2 by gashromatography–mass spectrometry.

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 (ProjectU06/04). Particular thanks are expressed by David Arroyo for

he FPI Grant also provided by the Junta de Castilla y Leon.uthors thank F. Palacios and J.C. Burillo of Departamentoe Salud y Consumo de la Diputacion General de Aragon thevailability to urine samples.

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