Calibration Transfer for Solving the Signal Instability in Quantitative

Anal. Chem. 2003, 75, 6361-6367

Calibration Transfer for Solving the Signal Instability in Quantitative Headspace-Mass Spectrometry Jose´ Luis Pe´rez Pavoń,* Miguel del Nogal Sańchez, Carmelo Garcıá Pinto, Ma Esther Fernańdez Laespada, and Bernardo Moreno Cordero

Departamento de QuıÄmica AnalıÄtica, Nutricio´ n y BromatologaıÄa, Facultad de Ciencias Quı´micas, Universidad de Salamanca, 37008 Salamanca, Spain

It is reported that calibration transfer is able to compensate the variations in sensitivity in direct coupling of a headspace sampler to a mass spectrometer when used for quantification purposes using multivariate calibration techniques. This strategy of signal stability compensation allows the use of models constructed from large calibration standard sets without having to repeat their measurement even though variations occur in sensitivity, which may or may not be constant along the mass range. This technique offers advantages over the use of internal standards in this methodology and only requires the measurement of a small number of transfer samples with each set of unknown samples. The results obtained in the determination of six volatile organic compoundssbenzene, toluene, ethylbenzene, and m-xylene (BTEX), methyl tertbutyl ether (MTBE), and mesitylenesare reported. To obtain an appropriate calibration set, a Plackett-Burman design with five levels of concentration for each component was employed. A PLS multivariate calibration model was constructed with a group of 25 samples. For selection of the optimum number of principal components, an external validation set (5 samples) was used and the prediction capacity of this set was checked with an additional group of samples that had not been used either in the construction or in the validation of the model. The results obtained can be considered highly satisfactory, and the methodology was successfully tested with natural matrixes (river and tap water). The process used in the solving of many analytical problems involves obtaining information about isolated compounds. Sample treatment is the most costly and time-consuming part of the process and one of the most frequent sources of errors.1 However, sometimes it is not necessary to obtain information about individual compounds and some kind of profile signal is sufficient to make decisions about the proposed problem. Within this strategy of collecting signals from groups of compounds are techniques such as near-infrared (NIR) spectroscopy,2,3 membrane * Corresponding author: (fax) +34-923-294483; (e-mail) [email protected]. (1) Flo´rez Meneńdez, J. C.; Fernańdez Sańchez, M. L.; Sańchez Urıá, J. E.; Fernańdez Martıńez, E.; Sanz-Medel, A. Anal. Chim. Acta 2000, 415, 9-20. (2) Wang, Z.; Dean, T.; Kowalski, B. R. Anal. Chem. 1995, 67, 2379-2385. 10.1021/ac034543d CCC: $25.00 Published on Web 10/04/2003

© 2003 American Chemical Society

inlet mass spectrometry,4,5 and pyrolysis mass spectrometry,6,7 among others. It is also within this context that electronic noses have been used to measure the volatile fingerprint profiles of samples. Sample treatment is eliminated or reduced to a minimum, and chemometric techniques are used to extract the information contained in the profile signals. Electronic noses based on sets of gas sensors have been used to resolve classification and quantification problems.8-11 As an alternative to gas sensor electronic noses, a methodology based on the direct coupling of a headspace sampler with a mass spectrometer (HS-MS) has been proposed.12-17 One advantage of the use of a mass analyzer as an alternative to the array of solid-state sensors is that its functioning is less affected by the typical problems found with conventional electronic noses (sensor poisoning, profile masking by some major constituents of the sample, the strong influence of humidity and the nonlinearity of signals). On the other hand, one great advantage of mass analyzers is that they can be considered as “open sensor arrays” in which easy choice of the appropriate “set of sensors” for each application is possible. (3) Zhang, L.: Small, G. W.; Arnold, M. A. Anal. Chem. 2002, 74, 4097-4108. (4) Springett, M. B.; Rozier, V.; Bakker, J. J. Agric. Food Chem. 1999, 47, 11251131. (5) Creaser, C. S.; Lamarca, D. G.; Brum, J.; Werner, C.; New. A. P.; dos-Santos, L. M. F. Anal. Chem. 2002, 74, 300-304. (6) Goodacre, R.; Kell, D. B. Anal. Chem. 1996, 68, 271-280. (7) Radovic, B. S.; Goodacre, R.; Auklam, E. J. Anal. Appl. Pyrolysis 2001, 60, 79-87. (8) Gardner, J. W.; Shin, H. W.; Hines, E. L.; Dow, C. S. Sens. Actuators 2000, 69, 336-341. (9) Gonza´lez Martıń, Y.; Cerrato Oliveros, M. C.; Pe´rez Pavoń, J. L.; Garcıá Pinto, C.; Moreno Cordero, B. Anal. Chim. Acta 2001, 449, 69-80. (10) Yinon, J. Anal. Chem. 2003, 75, 99A-105A. (11) Cerrato Oliveros, M. C.; Pe´rez Pavoń, J. L.; Garcıá Pinto, C.; Fernańdez Laespada, M. E.; Moreno Cordero, B.; Forina, M. Anal. Chim. Acta 2002, 459, 219-228. (12) Marcos Lorenzo, I.; Pe´rez Pavoń, J. L.; Fernańdez Laespada, M. E.; Garcıá Pinto, C.; Moreno Cordero, B. J. Chromatogr., A 2002, 945, 221-230. (13) Pe´re`s, C.; Begnaud, F.; Berdague´, J. L. Sens. Actuators 2002, 87, 491497. (14) Marcos Lorenzo, I.; Pe´rez Pavoń, J. L.; Fernańdez Laespada, M. E.; Garcıá Pinto, C.; Moreno Cordero, B.; Henriques, L. R.; Peres, M. F.; Simo ˜es, M. P.; Lopes, P. S. Anal. Bioanal. Chem. 2002, 374, 1205-1211. (15) Pe´rez Pavoń, J. L.; del Nogal Sańchez, M.; Garcıá Pinto, C.; Fernańdez Laespada, M. E.; Moreno Cordero, B.; Guerrero Pen ã, A. Anal. Chem. 2003, 75, 2034-2041. (16) Dittmann, B.; Nitz, S. Sens. Actuators 2000, 69, 23-257. (17) Dittmann, B.; Zimmermann, B.; Engelen, C.; Jany, G.; Nitz, S. J. Agric. Food. Chem. 2000, 48, 2887-2892.

Analytical Chemistry, Vol. 75, No. 22, November 15, 2003 6361

Even though the problem is less pronounced than with conventional electronic noses, the question of signal stability is still important with mass spectrometric instruments. Many factors contribute to signal instability, and their origin can be found in the two main components of the system, the headspace sampler, on one hand, andson the othersthe mass spectrometer itself: the gradual fouling of the ion source in the device, vacuum instability, and aging of the ion multiplier all contribute to signal instability. When no corrections are made, the effects may lead to a high irreproducibility for replicate measurements, gradual drift, and changes in sensitivity. Three common strategies to correct signal instability are internal normalization, internal standardization, and calibration transfer. Internal normalization involves expressing each mass intensity as a percentage of the total sum of intensities. This type of data treatment corrects the irreproducibility of the headspace sampler and sensitivity changes, provided they are constant along the mass axis.15,18 No additional sample manipulation is needed, but the quantitative information is lost. It is appropriate for many characterization problems in which the “shape” of the profile signals and not the intensityscontains the relevant information. A different approach is internal standardization. Each mass intensity is divided by the intensity of one fragment of an added internal standard. The effect of this type of correction is similar to that of internal normalization, but the quantitative information remains in the signal.19 Nevertheless, additional sample manipulation is necessary (the addition of the internal standard). Moreover, suitable internal standards are hard to find because they must afford a fragmentation pattern that will not interfere with the sample profile. Furthermore, internal standardization is very difficult in the case of solid samples. Recently, a different approach has been proposed to overcome some of the drawbacks of internal standardization.20 Calibration transfer is another alternative for rectifying drift and sensitivity changes and is based on the signal variation observed for a set of reference samples. This procedure has been used in NIR spectroscopy to correct spectral variations,21,22 but it has not been applied for the correction of signal instability in mass spectrometers. The main advantage of calibration transfer is that it corrects sensitivity changes even when they are not constant along the mass axis. The main disadvantage of the technique is that an additional set of samples must be analyzed at regular intervals. However, this is not a big drawback for a rapid technique such as HS-MS. One of the greatest problems involved in the determination of multicomponent systems is the generation of a suitable calibration set able to predict any type of combination of concentrations of compunds.23-25 Appropriate calibration sets can be obtained by using a Plackett-Burman experimental design.26,27 Here we propose the use of multiplicative calibration transfer for the generation of multivariate calibration models that are valid (18) (19) (20) (21) (22)

Pe´re`s, C.; Viallon, C.; Berdague´, J. L. Anal. Chem. 2001, 73, 1030-1036. Marsili, R. T. J. Agric. Food Chem. 1999, 47, 648-654. Pe´re`s, C.; Begnaud, F.; Berdague´, J. L. Anal. Chem. 2002, 74, 2279-2283. Geladi, P. Chemom. Intell. Lab. Syst. 2002, 60, 211-224. Feundale, R. N.; Woody, N. A.; Tan, H.; Myles, A. J.; Brown, S. D.; Ferre´, J. Chemom. Intell. Lab. Syst. 2002, 64, 181-192. (23) Brereton, R. G. Analyst 1997, 122, 1521-1529. (24) Brereton, R. G. Analyst 2000, 125, 2125-2154.

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Analytical Chemistry, Vol. 75, No. 22, November 15, 2003

over long periods of time, in which significant modifications occur in the sensitivity of the HS-MS device. The possibilities of the proposed methodology were checked using a set of volatile organic compounds (VOCs) comprising the species benzene, toluene, methyl tert-butyl ether, ethylbenzene, m-xylene, and mesitylene. All show overlapping mass spectra, which allows them to be used to check the methodology under complex situations. EXPERIMENTAL SECTION Apparatus. The apparatus used to measure the patterns of volatiles of the samples was a Gerstel ChemSensor 4440 (Mu¨lheim an der Ruhr, Germany). This comprises a headspace sampler (HP 7694) with a tray for 44 consecutive samples; an oven with six positions, where the headspace is generated; and a sampling system comprising a stainless steel needle, a 316-SS six-port valve with a nickel loop, and two solenoid valves (for pressurization and venting). The headspace sampler is coupled to a quadrupole mass spectrometer (HP 5973 N) by a transfer line. Data collection was performed with Pirouette 3.0 software28 from Infometrix Inc. on a Hewlett-Packard PC computer that also controlled the MS detector parameters. Reagents and Standards. Benzene, toluene, ethylbenzene, m-xylene, methyl tert-butyl ether (MTBE), and mesitylene (∼99% purity) were supplied by Acros Organics (Geel, Belgium). Standard solutions of these compounds were prepared by dilution of the commercial products with methanol (J. T. Baker, Deventer, Holland). The internal standardsdichloromethaneswas purchased from Scharlau (Madrid, Spain). These stock solutions were stored at 4 °C. Safety Precautions. Several of the compounds studied are suspected carcinogens and caution must be exercised with them. All handling of the solutions should be performed in a ventilated hood using latex gloves, and inhalation or skin contact must be avoided. Sample Sets. Sample set 1 comprised 35 samples and was used for the construction and validation of the PLS models. The concentrations of this sample set are shown in Table 1. The set consisted of three sample subsets: a calibration subset (samples 1-25, prepared according to a Plackett-Burman design); an external validation subset (samples 26-30, used to select the optimum number of principal components for each compound, using the minimum root-mean-square error of validation (RMSEV) values as a criterion), and test set 1 (samples 31-35, used to assess the prediction capacity of the model). Another two sets of 35 samples (sample sets 2 and 3) with the same concentrations as those used in set 1 were prepared and evaluated one month and one year, respectively, after the model had been constructed. Five of the samples from these sets were used as transfer samples (transfer sets 2 and 3, samples 12, 15, 17, 22, and 24), and the rest (30 samples) formed the prediction sets (prediction sets 2 and 3). It should be stressed that over the one-year period the equipment had undergone several modifications including the replacement of the turbomolecular pump. (25) Devos, O.; Fanget, B.; Saber, A.; Paturel, L.; Naffrechoux, E.; Jarosz, J. Anal. Chem. 2002, 74, 678-683. (26) Plackett, R. L.; Burman, J. P. Biometrika 1946, 33, 305-325. (27) Araujo, P. W.; Brereton, R. G. Trends Anal. Chem. 1996, 15, 156-163. (28) Pirouette: Comprehensive Chemometrics Modeling Software. Ver. 3.0; Infometrix, Inc.: Woodinville, WA, 2000.

Table 1. Concentration Data for the Six VOCs in the Sample Sets concentration (µg/mL) sample no.

benzene

toluene

ethylbenzene

m-xylene

MTBE

mesitylene

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

6.32 6.32 0.70 0.70 11.9 3.51 11.9 6.32 3.51 3.51 9.12 11.9 9.12 6.32 11.9 11.9 0.70 9.12 0.70 6.32 9.12 9.12 3.51 0.70 3.51 0.70 0.70 6.32 6.32 11.9 11.9 9.12 9.12 3.51 3.51

2.06 0.69 0.69 3.43 1.37 3.43 2.06 1.37 1.37 2.75 3.43 2.75 2.06 3.43 3.43 0.69 2.75 0.69 2.06 2.75 2.75 1.37 0.69 1.37 2.06 1.37 3.43 0.69 1.37 0.69 3.43 2.06 2.75 2.75 2.06

10.6 20.4 5.75 20.4 10.6 5.75 5.75 15.5 20.4 15.5 10.6 20.4 20.4 0.86 15.5 0.86 10.6 15.5 15.5 5.75 0.86 5.75 10.6 0.86 0.86 10.6 20.4 10.6 0.86 0.86 20.4 15.5 5.75 5.75 15.5

1.89 1.03 3.61 1.89 1.03 1.03 2.75 3.61 2.75 1.89 3.61 3.61 0.17 2.75 0.17 1.89 2.75 2.75 1.03 0.17 1.03 1.89 0.17 0.17 3.61 3.61 1.89 1.89 3.61 0.17 0.17 2.75 1.03 2.75 1.03

1.77 0.59 2.96 1.18 2.96 1.77 1.18 1.18 2.36 2.96 2.36 1.77 2.96 2.96 0.59 2.36 0.59 1.77 2.36 2.36 1.18 0.59 1.18 1.77 0.59 2.96 1.18 1.18 0.59 2.96 0.59 2.37 2.37 1.77 1.77

3.46 6.23 3.46 2.08 2.08 4.85 6.23 4.85 3.46 6.23 6.23 0.69 4.85 0.69 3.46 4.85 4.85 2.08 0.69 2.08 3.46 0.69 0.69 6.23 2.08 2.08 2.08 6.23 0.69 6.23 0.69 3.46 4.85 4.85 3.46

Procedure. Aliquots of 5.0 mL of samples, containing dichloromethane (4.00 µg/mL) as internal standard, were placed in 10-mL vials sealed hermetically with a silicone septum and a cap. The experimental conditions of the headspace sampler were as follows: oven temperature, 80 °C; loop temperature, 120 °C; transfer line temperature, 130 °C; headspace generation time, 40 min. The carrier gas was helium N50 (99.995% pure; Air Liquide) at an approximate flow rate of 20 mL/min. The mass range measured in the mass spectrometer was 45-150 u. Injection and data acquisition times were 1 and 4 min, respectively. Data Analysis. Partial least-squares multivariate calibration was performed using the Unscrambler v7.829 statistical package. For calibration transfer, the Pirouette v3.0 program was used. Internal Standardization. Dichloromethane was added to all the samples, the raw spectra were divided by the mass/charge 84 ratio, and the corresponding calibration models were constructed. None of the compounds studied shows appreciable intensity for this m/z ratio of the internal standard. To check whether correction with the internal standard depended on the zone of the spectrum selected for the correction, the same calibrations were constructed with internal standard using the m/z 49 ratio, the most abundant one of dichloromethane. For this m/z ratio, benzene represented an interference of 4% while there was no interference with the other compounds studied. (29) The

Unscrambler

v7.8; Camo Process AS: Oslo, Norway, 2002.

Calibration Transfer. The multiplicative calibration transfer algorithm included in the Pirouette 3.0 software selected the transfer set of samples used to obtain the best results. The proposed model uses a transfer set of five samples to transform the new responses of data sets 2 and 3. From among the different calibration transfer processes, the multiplicative method was used because it provided the best results. The intensity for each m/z ratio of the prediction set samples was multiplied by the numbersobtained as a means that best approached the intensities of the transferred sample set to those corresponding to the calibration model. In the case of using five transfer samples, the intensity value of one of the m/z variables undergoing this multiplicative fitting is

( ) 1n)5

∑I

I(m/z)tr ) I(m/z)dayb

5n)1

(m/z)day0

1n)5

(1)

∑I

5n)1

(m/z)dayb

where I(m/z)tr is the intensity resulting from applying the transfer process, I(m/z)day0 corresponds to the intensity at the time of constructing the calibration model, I(m/z)dayb is the intensity measured “b” days after the model has been constructed, and n is the number of transfer samples, identical to the model, measured on day b. The term in parentheses is the multiplicative factor R (which depends on the m/z value) that is applied to transform the data. RESULTS AND DISCUSSION Partial Least-Squares (PLS) Calibration. The calibration standards set in ultrapure water was designed using an extended six-component Plackett-Burman experimental design (the six VOCs studied) at five uniformly distributed concentration levels. Thus, the calibration set comprised 25 standards with uncorrelated concentrations.23 The 5-concentration level design with 25 mixtures leads to maximum efficiency.25 The complete design was obtained by using a cyclic generator (-2, 1, 2, 1, -2), a repeater of 0, and a difference vector (0 2 3 1).23 Because the number of variables recorded (106) was relatively high, before establishing the PLS models, a selection was made including the zones of the spectra where the VOCs studied showed the highest intensity. Twenty-four variables were selected and correspond to the m/z ratios of 72-80, 89-94, 103-108, and 120-122. Using the 25 samples of the calibration subset, PLS models were obtained for each compound. The minimum RMSEV value for the external validation set predictions occurred at 3, 6, 6, 8, 11, and 6 principal components (PCs) for benzene, toluene, ethylbenzene, m-xylene, methyl tert-butyl ether, and mesytilene, respectively. The values of the root mean standard error (RMSE) for each set of samples and for each analyte studied were calculated as

x

m

∑(c - cˆ )

RMSE )

2

i

i

i)1

m


(2) 6363

Table 2. Calibration and Prediction Results without Any Calibration Standardization calibration step calibration subseta

prediction step

external validation subseta

test set 1a

prediction set 2b

compound

PCs

RMSEC (µg/mL)

EC (%)

RMSEV (µg/mL)

EV (%)

bias (µg/mL)

RMSEP (µg/mL)

EP (%)

bias (µg/mL)

RMSEP (µg/mL)

EP (%)

bias (µg/mL)

benzene toluene ethylbenzene m-xylene MTBE mesytilene

3 6 6 8 11 6

0.18 0.07 0.26 0.06 0.02 0.21

2.8 3.4 2.4 3.2 1.1 5.2

0.25 0.05 0.39 0.30 0.12 0.38

4.8 3.3 4.5 8.5 6.8 2.0

0.15 -0.02 0.13 -0.06 0.05 0.28

0.19 0.10 0.38 0.24 0.07 0.19

2.6 3.8 3.0 12.9 3.9 5.5

0.07 0.08 0.32 0.07 -0.10 0.19

2.40 0.78 4.19 0.78 0.12 1.26

38.6 38.7 39.4 40.6 6.3 35.9

2.41 0.83 4.23 0.56 -0.01 1.30

a The calibration subset (25 samples), the external validation subset (5 samples), and the test set 1 (5 samples) were run together. b Prediction set 2 (30 samples) was measured one month after the model was built.

where ci is the added analyte concentration, cî is the predicted analyte concentration, and m is the number of samples. RMSEC, RMSEV, and RMSEP correspond to the root mean standard error of calibration, validation, and prediction of the model, respectively, whereas m stands for the number of calibration, validation, or prediction samples, depending on the case. In addition to these absolute values, it is possible to use the relative values (E %) expressed as

E (%) )

RMSE × 100 jc

(3)

where jc is the average of the true (added) concentrations. In the same way, bias was obtained from the expression m

∑(cˆ - c ) i

bias )

i)1

m

i

(4)

where ci and cî are the same as in eq 2, while m is the number of validation and test samples, respectively. The results in Table 2 show that the calibration models work very satisfactorily when calibration standards and test samples are run together. The RMSEP values ranged between 0.07 and 0.38 µg/mL, whereas the relative values were lower than 6%, except for m-xylene, whose prediction error was 12.9%. The bias values ranged between -0.10 and 0.32 for methyl tert-butyl ether and ethylbenzene, respectively. These values are considered to be sufficiently good, and hence, the models were validated in both trueness and precision. However, the model was unable to predict the samples measured one month later correctly (prediction set 2). Accuracy, in terms of relative RMSEP, lies at ∼40%. An interesting exception is the prediction of the concentration of methyl tert-butyl ether, with an error of only 6.3%. These results can be seen graphically in Figure 1a, which shows the positive deviation of the predictions toward higher benzene and ethylbenzene concentrations (toluene, m-xylene, and mesitylene show the same kind of behavior) and the good results obtained for MTBE. These results and the high bias values listed in Table 2 point to the impossibility of predicting the concentrations of most of these analytes in new samples with the calibration model built one month before. 6364


Internal Standardization. To overcome this lack of calibration stability, the internal standardization approach was used, as a first choice, using dichloromethane as internal standard and dividing each mass intensity by the intensity of an m/z fragment of the internal standard, which did not interfere with any of the m/z ratios of the volatiles studied. Table 3 shows the results obtained with internal standardization by using the m/z 84 of dichloromethane. As can be seen, the calibration model worked very satisfactorily in prediction when the test samples were run together with the calibration ones. The absolute and relative errors and the bias values are similar to those obtained without any calibration standardization, both in calibration and in validation and prediction. However, the use of internal standardization did not provide satisfactory values when the prediction of the samples of prediction set 2 was performed. As can be seen in Table 3 and Figure 1b, positive deviations continued to appear (with the exception of MTBE), although their magnitude was slightly reduced with respect to calibration without internal standard. The same results were obtained when the m/z 49 of the internal standard was used. The lack of efficiency of the internal standard in correcting the changes in sensitivity can be attributed to the fact that such changes are not constant along the mass axis. Calibration Transfer. A multiplicative calibration transfer algorithm was employed to perform calibration standardization. Five samples from sample set 2 (transfer set 2) were used as a transfer set to be measured, together with the samples from prediction set 2 (Figure 2a). In this way, it was possible to obtain a mean of the spectra for this sample set on the two days on which the measurements were carried out (Figure 2b), and the ratio between those measurements (Figure 2c) was used to transform the data of the samples measured one month after the calibration models had been constructed. The instability of the signal in HSMS systems is corrected independently for every m/z ratio, and the poor results obtained when internal standard was used to correct this lack of signal instability are explained. Table 4 shows the RMSEP and Ep values and the bias values for the samples from prediction set 2 measured one month after the calibration models had been built. It may be seen that upon using the multiplicative calibration transfer algorithm the prediction results are highly satisfactory. The relative prediction errors are similar to those obtained for the generation of the model. The bias values lay between -0.38 and 0.04 and no trend was observed.

Figure 1. Correlation plots of predicted vs added analyte concentrations for the 30 samples of sample set 2 without calibration standardization (a), with internal standardization (b), and with multiplicative calibration transfer (c). Table 3. Calibration and Prediction Results with Internal Standardization calibration step calibration subseta

prediction step

external validation subseta

test set 1a

prediction set 2b

compound

PCs

RMSEC (µg/mL)

EC (%)

RMSEV (µg/mL)

EV (%)

bias (µg/mL)

RMSEP (µg/mL)

EP (%)

bias (µg/mL)

RMSEP (µg/mL)

EP (%)

bias (µg/mL)


3 6 6 8 11 6

0.17 0.08 0.34 0.10 0.08 0.19

2.7 3.9 3.2 5.3 4.5 5.5

0.26 0.04 0.28 0.21 0.10 0.31

5.0 2.6 3.2 9.4 5.6 8.9

0.18 0.02 0.15 0.07 -0.08 0.23

0.13 0.07 0.32 0.16 0.09 0.25

1.7 2.7 2.5 10.3 4.5 7.2

-0.07 0.02 0.07 0.078 -0.08 0.11

1.11 0.39 1.86 0.44 0.28 0.65

17.8 19.4 17.5 22.9 9.5 17.1

1.08 0.41 1.90 0.13 -0.30 0.61

a The calibration subset (25 samples), the external validation subset (5 samples), and the test set 1 (5 samples) were run together. b Prediction set 2 (30 samples) was measured one month after the model was built.

Figure 1c shows the concentration correlation plots for prediction set 2 after applying the calibration transfer algorithm. It clearly illustrates the improvement in prediction performance obtained as compared with the results without any calibration standardization (Figure 1a) and with internal standardization (Figure 1b). The behavior of MTBE (almost the same results were obtained with and without calibration transfer) can readily be understood by taking into account that the mass/charge ratio used for its quantification was mainly m/z 73. The number with which this variable was multiplied after the calibration transfer process was 0.98, i.e., close to unity.

To check the validity of the calibration model built at longer term, the multiplicative calibration transfer algorithm was applied to the samples from sample set 3. These samples were measured one year after the model had been built and under very different experimental conditions (for details, see Experimental Section). Table 5 shows the results obtained for prediction set 3 using the calibration models without standardization and applying the multiplicative transfer algorithm. In the first case, the relative prediction errors reached values ranging between 41.2% for MTBE and 184% for m-xylene. Similarly, the bias values showed a clear positive trend, with magnitudes ranging between 0.69 and 10.6 Analytical Chemistry, Vol. 75, No. 22, November 15, 2003

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Figure 2. (a) Recordings of the five samples corresponding to the five patterns selected as the transfer set measured on day 0 and on day b; (b) measurements of the spectra of these samples on the two days on which the measurements were carried out; (c) relationship between measurements (R) corresponding to the two days on which the measurements were carried out. Table 4. Prediction Results of Prediction Set 2 after Multiplicative Calibration Transfer prediction stepa compound

RMSEP (µg/mL)

EP (%)

bias (µg/mL)


0.26 0.08 0.56 0.23 0.11 0.20

4.2 4.0 5.3 12.0 5.8 5.7

-0.19 0.05 -0.38 0.04 -0.07 -0.01

a Prediction set 2 (30 samples) was measured one month after the model was built.

Table 5. Prediction Results of Prediction Set 3 without Any Calibration Standardization and after Multiplicative Calibration Transfer prediction stepa without calibration transfer compound

RMSEP (µg/mL)

EP (%)

benzene toluene ethylbenzene m-xylene MTBE Mesytilene

5.00 1.66 10.4 3.54 0.78 5.80

80.3 82.4 97.7 184 41.2 165

with calibration transfer

bias RMSEP EP bias (µg/mL) (µg/mL) (%) (µg/mL) 5.31 1.80 10.6 3.88 0.69 6.18

0.43 0.14 0.69 0.47 0.19 0.26

6.9 7.0 6.5 24.4 9.9 7.4

-0.18 -0.04 -0.18 0.08 0.14 0.06

a Prediction set 3 (30 samples) was measured one year after the model was built.

µg/mL. However, application of the calibration transfer algorithm afforded highly satisfactory prediction results, with errors lower than 10% in all cases, except for m-xylene, whose error was 24.4%. Additionally, the bias values are similar to those obtained for the calibration model and no trend is observed. The efficiency of the calibration transfer process can be seen in Figure 3. This figure (part a) reveals the large differences in intensity between the mass spectra of the same sample recorded the first day (day 0) and one year later (day b). Figure 3 (part b) shows the two recordings after applying multiplicative calibration transfer to the sample measured one year later. It may be seen that the two recordings are almost identical. These results can be considered acceptable and point to the validity of the model even though the experimental measurement conditions had varied considerably. Determination of VOCs in Different Water Matrixes. To evaluate the multiplicative calibration transfer algorithm proposed 6366 Analytical Chemistry, Vol. 75, No. 22, November 15, 2003

here, the PLS models obtained were used to predict concentrations in tap and river water to which the six compounds studied had been added. Again, the calibration transfer algorithm was used, with the five transfer standards prepared in ultrapure water, since these samples were measured one month after the model had been built. Table 6 shows the results together with the deviation in prediction values calculated using the equation included in the Unscrambler v7.8. This deviation is an empirical measure based on the model error, the sample leverage, and the sample residual x-variance.30 These results reveal the applicability of the proposed methodology for simultaneous quantification of these compounds in real matrixes. (30) Moberg, L.; Karlberg, B. Anal. Chim. Acta 2002, 450, 143-153.

Table 6. Concentrations Added, Predicted, and Deviation in Prediction of the Analytes in Tap and River Water Samples concentration (µg/mL) tap water

added

1 2 3

0.70 9.12 3.51

river water

added

1 2 3

6.32 9.12 3.51

a

benzene found 0.62 9.91 3.21

benzene found 6.58 8.86 3.49

da

added

0.12 0.06 0.06

1.37 2.06 2.75

da

added

0.11 0.08 0.04

3.43 2.75 2.06

toluene found 1.46 2.36 2.85

d 0.13 0.08 0.11

toluene found 3.62 2.91 2.13

d 0.12 0.07 0.11

ethylbenzene added found d 10.6 15.5 5.75

11.9 17.9 5.83

0.73 0.50 0.15

ethylbenzene added found d 20.4 5.75 15.5

21.7 6.38 16.8

0.72 0.42 0.60

m-xylene added found 3.61 2.75 2.75

4.17 3.40 2.67

m-xylene added found 3.61 1.03 1.03

4.28 0.99 1.09

d

added

0.68 0.57 0.28

2.96 2.36 1.77

d

added

0.27 0.46 0.58

1.18 2.36 1.77

MTBE found 3.05 2.53 1.65

MTBE found 1.11 2.24 1.65

d 0.18 0.09 0.12

d 0.20 0.17 0.06

mesitylene added found 2.08 3.46 4.85

2.64 4.63 5.24

mesitylene added found 2.08 4.85 3.46

2.14 5.53 3.90

d 0.21 0.14 0.13

d 0.22 0.11 0.12

Deviation in prediction (for details see text).

Figure 3. Recordings obtained for two identical samples run on day 0 and on day b (one year later) before (a) and after (b) multiplicative calibration transfer.

CONCLUSIONS The signal instability associated with HS-MS systems has been corrected using a multiplicative calibration transfer algorithm, allowing prediction of the contents of the compounds studied in samples measured under different experimental conditions and up to one year after the calibration model had been built. Use of a Plackett-Burman experimental design permits the construction of a stable calibration model using a high number of standards (25 mixtures of the 6 VOCs studied) such that the concentrations of all of them are uncorrelated, thus obtaining the

best prediction results possible. The use of only five samples as a transfer set allows one to correct the lack of stability of the MS system. The incorporation of this calibration transfer process represents an important improvement and an increase in the analytical possibilities of this technique based on the rapid collection of information about the volatile set of a sample for both qualitative and quantitative purposes. The results have been compared with those obtained without any calibration standardization and with internal standardization. This latter approach afforded results that were not satisfactory because the signal instability is not constant for the different mass/ charge ratios. The proposed methodology has been successfully applied in the quantification of mixtures of the six VOCs in two real water matrixessriver and tap watersusing the model constructed with ultrapure water. These results show that HS-MS coupling with multivariate calibration constitutes a reliable technique for simultaneous determination in mixtures, with a high sampling throughput. ACKNOWLEDGMENT We acknowledge the DGICYT (Project BQU2001-1858) and the Consejerıá de Educacioń y Cultura of the Junta de Castilla y Leoń y la Unioń Europea (Fondo Social Europeo. Project SA079/ 02) for financial support for this research. M.N.S. acknowledges the grant awarded by the Junta de Castilla y Leoń. The authors thank Dr. C. Raposo for helpful discussions about the practical aspects of mass spectrometric measurements. Received for review May 22, 2003. Accepted September 3, 2003. AC034543D


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Calibration Transfer for Solving the Signal Instability in Quantitative

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