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Sample diagnosis using non-analyte signals for inductively coupled plasma mass spectrometry
Spectrochimica Acta Part B 57 (2002) 277–290
Sample diagnosis using non-analyte signals for inductively coupled plasma mass spectrometry Hai Ying, Margaret Antler, John W. Tromp, Eric D. Salin* Department of Chemistry, McGill University, 801 Sherbrooke St. W, Montreal, Quebec, Canada H3A 2K6 Received 3 January 2001; accepted 11 November 2001
Abstract A sample diagnosis procedure that uses non-analyte signals to predict matrix effects in inductively coupled plasmamass spectrometry (ICP-MS) is presented. Non-analyte signals are those of other species which are present in the plasma (e.g. Arq 2 ), and monitoring them can indicate changes in the instrument or sample. Matrix effects of Na, Al, K, Cs, and Ba on 19 non-analyte signals were studied. Non-analyte signals changed significantly in the presence of the matrices. The heavier matrices, Cs and Ba, caused more interference. Stagewise regression was applied to build prediction models. The results showed that matrix effects caused by matrices of various concentrations could be predicted, with the predictions of the model well correlated with the test experimental results. In previous work, we introduced a total interference level (TIL) model, which predicted interferences based on previous experiments, and tested it in terms of analytical decision making. The current model is tested in the same way, and gave excellent results. In terms of guaranteeing a desired accuracy, the predictions were at least 80% correct for test solutions with overall matrix effects that varied from 10 to 50%. The key prediction factors were also determined. The main conclusion of this study was that the presence of matrix effects could be detected by online monitoring of only nonanalyte signals. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Inductively coupled plasma mass spectrometry; Diagnosis; Non-analyte signals
1. Introduction Inductively coupled plasma mass spectrometry (ICP-MS) has been widely accepted as a sensitive and accurate technique for trace element determination w1–4x; however, since the inception of ICPMS, spectral and non-spectral interferences have * Corresponding author. E-mail address: [email protected] (E.D. Salin).
been a challenge for practical analysis w2–4x. Much research has been dedicated to solving these problems, such as the use of concomitantsymatrices separation w5,6x, alternative calibration methods w7,8x, different operating conditions w9,10x, mixed gas plasmas w11x, mathematical correction procedures w12,13x, high resolution MS w14x and dynamic reaction cells w15x. The understanding of matrix effects has been also probed through more fundamental experiments, for example the effect
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of a matrix element on measured ion distributions in the plasma w16x, including experiments on single droplets by several groups w17–20x. When analyzing a complex sample, the choice of a proper analytical methodology is difficult and time-consuming, especially for non-experts. Therefore, there is an increasing need to establish an intelligent system to help users make the right choice of analytical methodology and thus to ensure the quality of the final analytical results w21x. While spectral interferences continue to be a problem, and are likely to be completely avoided only by pre-separation or advanced instrumental designs (e.g. high resolution MS w14x or a dynamic reaction cell w15x), this work focuses on nonspectral interferences (matrix effects). Our laboratory has been pursuing the Autonomous Instrument project for the last decade to develop software to allow more autonomous and operator independent operation of both ICP-AES w22,23x and ICP-MS w8,21,24,25x instruments. The design was outlined in previous papers w22,24x. Different modules were studied and related software systems were demonstrated. In its present design, the system first obtains semi-quantitative data from a full mass scan, which is used to determine the total interference level (TIL). The TIL, as described in a recent paper w24x for ICP-MS, is a critical module for the Autonomous Instrument project. If the TIL is above a certain threshold, which means a simple calibration method would not work well, an appropriate calibration methodology (e.g. internal standardization) andy or specific operating conditions (e.g. robust conditions w10x) is selected. Two important assumptions, linearity of matrix effects with matrix concentrations w24x and additivity of matrix effects of different matrices w25x, were tested with satisfying results. The TIL model is a direct method, which uses the full scan spectra to identify and roughly quantify the major components and estimates the total interference level using the estimated major component concentrations and predetermined interference coefficients. These interference coefficients are determined empirically, so the model must be calibrated for each potential interferent, potentially a tedious process. Here, we present a simple, indirect and more universal method, using non-analyte signals
(NAS), for evaluation of overall matrix effects for unknown samples in ICP-MS. Non-analyte signals have been of concern because of their potential to cause spectroscopic interferences, with the overlap of 40Ar16O with 56 Fe being a well-known example. However, nonanalyte signals have also been used for signal calibration and instrument diagnostics. An early application was the use of non-analyte lines as internal standards to compensate for the occurrence of matrix effects. Beauchemin et al. w26,27x investigated the use of the species 12Cq and 80(Arq 2 ) as internal standards in the analysis of marine sediments. They found that an accurate correction was realized in most cases, with the exception of the heavier elements Cd and Pb. Chen and Houk w28x extended this concept to a variety of other polyatomic ions. They used several strong polyaq q q tomic ion signals (Nq 2 , ArO , ClO , and MO ) as internal standards to correct for matrix interferences. This approach avoids the extra manipulation of adding an internal standard element, as well as the risk of accidental contamination. However, as was pointed out w2x, one must be careful in the application of non-analyte signals as internal standards since the mechanism of polyatomic ion formation in the plasma is different from that of the analyte ions. The argon dimer has also been used as a diagnostic tool in slurryysolid sampling ETV-ICP-MS for the optimization of operating conditions and the correction for non-linearity of signals caused by matrix effects w29,30x. We reported an instrument diagnosis system for ICPMS w21x which uses non-analyte (background) species monitored while measuring blank solutions (i.e. water or 0.5% HNO3). In the present work, non-analyte signals were used to predict average matrix effects. Implementing the model involves monitoring several nonanalyte signals during analysis. It is shown to be a simple, universal, and relatively accurate method to evaluate matrix effects on-line. 2. Algorithms In general, it is desirable to develop the simplest model that can make accurate predictions. Thus, a modeling method with feature selection is preferred. Only those non-analyte signals determined
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Table 1 ICP-MS operating conditions and experimental parameters Instrument Skimmer cones Nebulizer
PE-SCIEX Elan 6000 ICP-MS Nickel Cross-flow with Scott-type spray chamber
ICP RF power Auxiliary gas flow Sample liquid uptake Nebulizer gas flow rate
1.0 kW 15 lymin 1.0 mlymin 0.825 lymin
Mass spectrometer Detector
Dual
Ion lens voltage Auto lens
7.5 V Off
Peak scan parameters Basic mass range Scan mode Replicates Dwell time Resolution Sweeps per reading Reading per replicate
2–15, 17–39, 42–250 (amu)a Peak hopping 3 25 ms 0.1 (amu) 15 1
a
The real mass range for data collection was determined with different matrices as well. When doing experiment for a specific matrix element, all isotopes of this element were avoided.
to be essential for prediction are retained in the model. Based on our previous work w21x, and the problems encountered, we chose a common, powerful regression method, stagewise linear regression. It is a supervised learning method, which means ‘solved problems’ are needed in the training process. Using the data from many non-analyte signals, models were constructed with the most important spectral information. The selection of the variables (spectral features) that provide the most information is a critical process. Variable selection methods have been developed which identify good (although not necessarily the best) variables, with considerably less computing than is required for all possible regressions w31x. These methods are referred to as stepwise regression methods and have not been commonly used in ICP spectroscopy. Stagewise linear regression is very similar to stepwise linear regression, but the calculations are simplified. For both stepwise and stagewise linear regression, the variables are identified sequentially by addition (forward selection) or deletion (backward elimination). Forward stagewise selection, used in the current work, starts by choosing the
independent variable (intensity of a certain nonanalyte species) that has the highest correlation with the dependent variable, the matrix effect. At the second step, the independent variable that causes the largest decrease in the residual sum of squares is chosen from the subset of independent variables not already in the model. This will be the variable that has the highest correlation with the residuals from the first model (which contains one independent variable). This second independent variable is added to the model, and the step is repeated. The procedure terminates either when a criterion is reached, e.g. a partial F-statistic at a particular step does not exceed a preset value Fin, or when the desired number of candidate regressors have been added to the model. Related procedures can be found elsewhere w31x. 3. Instruments, experiments, and method development process 3.1. Instruments and experiments A conventional PE-SCIEX Elan 6000 ICP-MS with a cross-flow nebulizer and a Scott-type spray
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chamber was used for this study. The operating conditions and experimental parameters are given in Table 1. The standard daily optimization procedure suggested by the manufacturer was applied to determine nebulizer gas flow rate and ion lens voltage. The detector was set in dual mode. In the following data processing section, the analyte signals were in pulse mode (counts per second) while the analog values of non-analyte signals were used, since they tended to be of higher intensity and could saturate in pulse count mode. The Auto Lens is a function of the Elan 6000 ICP-MS which adjusts the ion lens voltage dynamically with analyte mass and may improve results in the presence of matrices w32x. To minimize experimental variables we did not use the Auto Lens, so the ion lens voltage was fixed at the value that maximized the 103Rhq signal. In order to have adequate information for data processing, full scan spectra were obtained in peak hopping mode, skipping masses 16O and 40Ar. In addition, when doing an experiment for a specific matrix element (interferent), all isotopes of the matrix element were skipped in the data acquisition. All samples described herein were prepared in distilled de-ionized water (Milli-Q water system, Millipore Corp., Bedford, MA, USA) by sequentially diluting multi-element standards (SCP Science, St. Laurent, Quebec, Canada) and trace metal grade nitric acid (Baker Instra-Analyzed, J.T. Baker, Phillipsburg, NJ, USA). There were 15 analytes, Cu, Fe, Mg, Ni, Pb, Pt, Y, Zn, Be, La, Li, Mo, P, Sb and Sr. Based on previous work w24x, five matrices were selected for this study, Na, K, Al, Cs and Ba. Single matrix solutions were made from solid nitrate salts (Alfa Aesar, Ward Hill, MA, USA). Matrix effects depend on the absolute amount of the matrix element rather than on the molar ratio of matrix element to analyte w2x, so absolute concentrations of matrices in mgyml are used. In total, there were five ‘clean’ solutions which did not contain matrices: water, 0.5% HNO3 and three multi-element standard solutions (5 ngyml, 10 ngyml, 20 ngyml). For each matrix solution except Cs, there are six matrix blank solutions (i.e. containing only the interferent) in different concentrations (10 mgyml, 30 mgyml, 100 mgyml, 300 mgyml, 400 mgyml, and 1000
mgyml) and six other solutions with the same matrix and with 10 ngyml of multi-element standards. The matrix blanks are used for blank subtraction, and compensate for spectrometric interferences due to the matrix. Since Cs was known to cause more serious matrix effects than the others w24x, five concentrations were used, 10 mgyml, 30 mgyml, 100 mgyml, 200 mgyml, and 500 mgyml. The data for the two highest matrix concentrations were collected on one set of days, and the data for the other matrix concentrations were collected on different days. The experiments during a day were performed in the sequence: MilliQ water, 0.5% HNO3, standard solutions (5, 10 and 20 ngyml), lower matrix blank, lower matrix solution with standards, higher matrix blank, and higher matrix solution with standards. The washout time was selected to ensure that there was no residual contamination in the instrument from the matrices. Full scan spectra of Milli-Q water were used to monitor the background before and after experiments each day. 3.2. Diagnosis process The diagnosis development process is illustrated in Fig. 1. In general, there are two steps, model building and model testing. Two different sets of data were collected. The data sets consisted of non-analyte signals for water, 0.5% HNO3, the three multi-standard solutions (5 ngyml, 10 ngy ml and 20 ngyml) and matrix solutions with and without standards at 10 ngyml. The data sets differ in the concentrations of the matrix solutions that were used to generate them. Dataset 1, on the left of Fig. 1, included data for matrix solutions of three concentrations (30, 100, 500 mgyml for Cs and 30, 100, 1000 mgyml for the other four matrices). Seventy percent of the data set were randomly chosen to build a prediction model. The remaining 30% of the data were used to test the model. This was repeated five times as a crossvalidation of the diagnosis process. In addition, Dataset 2 contained independent data for solutions with matrices of different concentrations (10, 300 and 400 mgyml, 10 and 400 mgyml for Cs), and was used as a more difficult blind test.
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variation of signals obtained under the same operating conditions as the non-analyte matrix effect, formulated as: MENASs
Fig. 1. Flow chart of the model development process.
A Visual Basic subroutine was compiled to read and convert the Elan 6000 report files to the desired format for processing. The programs for the data processing were written in MATLAB. 4. Results and discussions 4.1. Matrix effects on analyte and non-analyte signals Matrix effects may be defined as matrix-induced signal variations, either suppression or enhancement w3x. In this paper, the matrix effect for an analyte was calculated as the variation of the net intensities using the following formula: MEs
ŽIMyIMBl. y1 ŽIyIBl.
(1)
where IBl and IMBl represent the blank signal at a given mass with no matrix and the blank with matrix, respectively, while I and IM stand for the intensity with no matrix and that with a matrix for a specific analyte at a same concentration. An average overall matrix effect for a particular matrix at a certain concentration is defined as the average of the absolute value of the matrix effect for every analyte, computed as: NA
OMEs8)MEi) yNA
(2)
i
where NA is the number of analytes measured. For non-analyte signals, we also define the
IM y1 I
(3)
where I and IM represents the intensity of nonanalyte species without and with a matrix, respectively. Table 2 lists all the masses used in the present work in bold font, ignoring those analytes used as matrices. Information about all mass species was extracted from a useful ICP-MS database, the MS INTERVIEW software w33x for a nitric acid environment. Fifteen analytes were used to determine the overall matrix effects on analytes while 19 nonanalyte species were initially chosen to develop the methods for matrix effect prediction. Several non-analyte species, 56wArOx, 76wAr2 x, 78wAr2 x and 80w Ar2x, were overlapped with isotopes of analytes; however, since these non-analyte signals originate from the major component of the plasma, Ar, we assume that their signals are much stronger than those of the analytes. Non-analyte species were important in instrument diagnosis w21x, and we wanted to determine whether they were also important factors for matrix effect prediction. In the following results, it is seen that the various non-analyte lines displayed showed considerable matrix effects. Fig. 2 illustrates variations of every studied non-analyte signal with different solutions. In our notation, Bg indicates background, Std5, Std10, Std20 stand for standard solutions (5 ngyml, 10 ngyml and 20 ngyml), and MLow, ML S, MHigh, MH S represent lower matrix, lower matrix with multi-element standards (10 ngyml), higher matrix, and higher matrix with multi-element standards (10 ngyml), respectively. Note that the results are from Dataset 1 so the concentrations for the matrices are the two highest (200 mgyml and 500 mgyml for Cs, 400 mgyml and 1000 mgyml for the other four matrices). Fig. 2 shows clearly that the non-analyte signals changed in the presence of matrices, which is the basic requirement for the current work. The Cs matrix caused suppression for all non-analyte signals except mass 4. Mass 4 is an exception because
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Table 2 All masses used in the current study (in nitric acid environment) Mass Analyte signals 7 9 24 31 54 58 63 64 88 89 98 121 139 195 208
Background species (non-analyte signals)
N2H, NOH, NO, CO ArN, ArO ArO, ArOH ClN2
Non-analyte signals H2, H 2 H3 3 4 12 C 13 C 14 N 15 N OH, NH3, O 17 O, OH, H2O, NH4 18 OH, H2O, H3O 19 H2O, H3O 20 H 3O 21 36 Ar ArH, H3O(H2O) 37 38 Ar, ClH 56 ArO, ArNH Ar2 76 Ar 78 2 Ar2 80 a
Isobarics
Li Be Mg P Fe, Cra Ni, Fea Cu Zn, Nia Sr Y Mo, Rua Sb La Pt Pb
Doubly charged ions
Matrix dependent or oxidesyhydrides
Ca, Ti
C2(organics)
Cd Cd
Lu, Yb
NaCl, CaO PO2, NaAr, MgCl HPO2, CaO, TiO, Na2O GeO, MnO2H GeO NiAr, CuCl SbO HfO
H He C C N N O O F Ne Ne S, Ar Cl Ar Fe Ge, Se Se, Kr Se, Kr
Mg Mg
CH(organics) CH(org.), CH2(org.) NH(org.)
Ca Ca
Cd Eu, Sm, Gd Gd, Dy Tb, Gd, Dy
CaO AsH, NiO NiO, TiO2 NiO, TiO2
These isobarics were regarded as spectral interferences here.
there is only one species at mass 4, He, and the variation of that signal was less than 5% in all the solutions. The Ba matrix behaved differently, suppressing non-analyte signals in the lower and higher mass ranges and enhancing those of masses 18–21 which are all water based peaks (see Table 2). It is not surprising to see that each of the other four matrices showed some similarities for these
four masses because there is a strong abundance 20 co-relationship between 18(H16 (H18 2 O) and 2 O), 19 16 21 18 and between (H3 O) and (H3 O). The Na matrix caused enhancement for all species except two C-based species, 12C and 13C. Like Na, K mainly enhanced non-analyte signals except that it suppressed intensities of 12C and 13C more than Na did. In most cases (mass 2, 3, 14, 15, 17, 36,
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Fig. 2. Fractional signal variations of non-analyte signals with different solutions with or without matrices. (M low and M high are two matrix blanks with different concentrations, 200 mgyml and 500 mgyml for Cs, 400 mgyml and 1000 mgyml for Na, Al, K and Ba. ML S and MH S are the same but with multi-standards.) If the signal in the indicated solution is the same as in the background, then the relative signal variation is zero. If there is 20% signal enhancement with respect to the background, then the relative signal variation is 0.2. If there is 20% signal suppression, then the relative signal variation is y0.2.
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Fig. 2 (Continued).
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Fig. 2 (Continued).
37, 38, 56, 76, 78, 80), Cs and Ba had a similar effect, Na and K were similar, and only Al was quite different from the others. Al suppressed the intensities of 12C, 18H2O and 20H2O while only the highest concentration Al (1000 mgyml) caused decreases of the intensities of Ar dimer species (mass 76, 78, 80). The other non-analyte signals increased with a high concentration of Al. Another important point from Fig. 2 concerns the standard solutions. In contrast to our initial assumption, the non-analyte signals did vary slightly with the different concentrations of the standards in the solutions. In addition, except for several N based species (mass 14, 15, 17), the day-to-day variations of the other non-analyte signals for the standard solutions were considerable. Several previous studies about matrix effects on analytes have obtained different results. Gregoire w34x observed only suppression while Beauchemin
w26x found enhancements due to Na, K, Cs, Mg and Ca. While space charge effect theory w35x only explains suppressions, it has been widely accepted to explain the difference in matrix effects in ICP-MS compared to ICP-AES. Fig. 3 displays the results obtained in the current study. Fig. 3a shows the matrix effects on 15 analytes with Na, K and Al while Fig. 3b shows those with Cs and Ba. Fig. 3c shows the overall matrix effects for every matrix at the highest two concentrations. For most analytes (see related masses in Table 2), existence of these matrix effects caused suppression, some quite serious. Heavier matrices (Cs and Ba) caused more serious matrix effects than the lighter ones except Al at 1000 mgyml. Neither Na nor K seemed to have a significant effect on several analytes at the medium mass range, e.g. 88Sr, 89Y, 98Mo. Al was different from other matrices in its effect on non-analyte
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and correction equations provided in Elan 6000 software were not used. 4.2. Matrix effect prediction Three different types of interference prediction models were constructed for comparison. For simplicity, we examined models that would predict the average overall matrix effect (OME) as defined by Eq. (2). The model designated as ‘raw’ chooses variables from among the set of non-analyte signals, and predicts interference as a linear combination of the important selected non-analyte signals. An example of a model using ‘raw’ variables is OMEsaSw18ŽH2O.xqbSw76ŽAr2.xqc where Swx denotes the signal at the mass and the likely species responsible, and a, b and c are the model coefficients. A ‘ratio’ model chooses from all possible ratios of the raw signals, so if there are N raw variables i.e. non-analyte signals, there are ;N 2 ratio variables. An example of a model with ratio variables is OMEsaSw17ŽOH.x ySw12CxqbSw12Cx ySw15Nxqc
Fig. 3. Matrix effects on different analytes. (a) Matrix effects caused by Na, Al and K. (b) Matrix effects caused by Cs and Ba. (c) Overall matrix effects for different solutions. (The xaxis was represented by matrix element plus its concentrations, e.g. Al400 means Al 400 mgyml.)
signals. It enhanced analyte signals at the lower mass range, e.g. 7Li, 9Be, 24Mg, 31P. Among analytes, Pt is special, exhibiting only minor suppression or even enhancement in many cases. When viewing these results, recall that the AutoLens function on the Elan 6000 was not used
Finally, the ‘total’ data set consists of all raw signals and all ratio signals, and so could have terms as in either of the models above. In order to determine whether this matrix prediction method works successfully, a cross-validation process was done. As shown in Fig. 1 70% of Dataset 1 was randomly chosen to build the model, and the remaining 30% was used to test the model. To correct for day-to-day signal variations, all of the raw non-analyte signals were normalized by their percent changes from the average ones obtained with water on the same day. It had been previously found that ratios were better indicators of instrument malfunction w21x so the percent changes of non-analyte signal ratios were also used in the method development in this work. Stagewise regression method was applied to build prediction models. Fig. 4 demonstrates the relationship between experimental measurements of overall matrix effect, and predictions based on non-analyte signal
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Fig. 4. Comparison of the predictions of a stagewise regression model based on ratios of non-analyte lines with actual overall matrix effect. (a) for the test data set; (b) for the cross-validation; (c) for the blind test.
ratio models. The ideal correlation result is that both slope and correlation coefficient R 2 equal to 1. Fig. 4a shows the correlation achieved in the training set, while Fig. 4b displays the crossvalidation correlation, and Fig. 4c shows the correlation between the prediction model and the independent blind data from Dataset 2. The linear-
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ity of the three processes is good and comparable with similar values of R 2, but the blind test is slightly worse, which is reasonable, given that the model had been trained with different concentrations. These graphs are the basic justification of the method in that they show that our hypothesis is correct. It is possible to build models based on non-analyte signals that correlate well with overall matrix effect. Table 3 lists the five most important factors in the prediction models for different data sets, selected by stagewise regression. For different instances of cross-validation, the selection of these key variables was slightly different, mostly in sequence. They are listed in order of frequency of selection. Consistent with previous results w21x, not only was the best prediction accuracy obtained with the ratio-only data set, but most of the factors selected for the total data sets were exactly the same as those chosen for the ratio-only data set. In our previous instrument diagnosis study w21x, the masses or mass ratios selected were mainly Ar and water based species. In contrast, for the present work, N and C based species appear to be more important for ratio data sets. These results are not inconsistent, since the instrument diagnosis was mainly for prediction of the malfunction of the ICP part of the instrument (power, nebulizer gas flow rate, and liquid uptake rate) where the principle species, Ar and water, would be affected more. Since ICP-MS matrix effects have major contributions from the ion extraction process w35x, it is not surprising that different species were selected in the current study. Considering Fig. 2 again, we find that the signals of Ar and water species (masses 18–21, 37, 56, 76, 78, 80) varied Table 3 Important variables for the matrix effect prediction selected by stagewise regression method Raw data set 18
76w Ar2x wH2O;NH4;OH;Ox 56w ArO;ArNHx 2w H2;Hx 17w OH;NH3;Ox
Ratio data set or total data set 17
wOH;NH3;Ox y 12 wCx 12w x 15w x C y N 18w H2O;NH4;OH;Ox y 19 wH3 O;OH;H2 Ox 36w Arx y 14wNx 56w ArO;ArNHx y 18 wH2 O;NH4 ;OH;Ox
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considerably with the differing concentrations of standard solutions. In some cases, the different concentrations of standards caused more variation than changes in the concentrations of the matrix solutions (e.g. Na, K), indicating that those species were too unstable to be used in an interference prediction model. As in the validation of the TIL model in previous work w24,25x, the question is: how often will the prediction model make the correct decision if accuracy is desired at a certain threshold or bound (e.g. less than 10% error). Thus, if the interference is less than the bound and the model predicts it is less, it is correct. Similarly, if the interference is greater than the bound and the model predicts it is greater, it is also correct. Incorrect predictions are those where the model predicts interference greater than the bound while it is less, or vice versa. The first situation results in over-calibration, where a more elaborate technique than necessary is used, wasting time, while the second situation results in under-calibration, causing errors. Fig. 5 is the illustration of the fraction of correct analytical decisions as a function of the desired accuracy for the training set in Fig. 5a, the crossvalidation in Fig. 5b and the blind test in Fig. 5c. We assume that we want to measure analytical samples and be guaranteed a maximum error, which we call the desired accuracy, or threshold. Thus, if the threshold is 10%, we want to ensure that the reported concentrations are within 10% of the true values. Fig. 5 shows how often the predictions of our models will guarantee the desired accuracy. The results were the average of a five-fold modeling and testing process. Errors for training and cross-validation are lower at the higher thresholds. The intermediate range was more difficult, with training errors of the order of 10–15%, reflecting the fact that making the correct decision is difficult when the average interference is around the bound desired. Low thresholds (5%) were the most difficult for the model to classify, due to similarities between the blank and samples that were slightly suppressed (10 mgyml matrix concentration). The standard deviation of the raw non-analyte signals was 2–3%, so some overlap between the blank and sample is possible. How-
Fig. 5. Test of the decision-making ability of the model, with error displayed as a function of desired accuracy. (a) for the test data set; (b) for the cross-validation; (c) for the blind test.
ever, the fact that Fig. 5c is very similar to Fig. 5a is encouraging, indicating that the error rate in the blind test is only slightly greater than that in the training data, and, in the worst case, 80% success in the blind test is a good result.
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5. Conclusions In this work, a simple sample diagnosis procedure to predict matrix effects in ICP-MS based on non-analyte signals is demonstrated. The heavier matrices, Cs and Ba, caused similar effects, severe suppression, except that Ba strongly enhanced the water based signals (mass 18–21). The observations with lighter matrices were more complex. The Na and K matrices were found to have similar effects on non-analyte signals. The Al matrix had a larger effect on lower mass species. In addition to the effects of the matrices, the introduction of analytes also caused considerable changes to nonanalyte signals, especially in matrix solutions, which implies that the matrix blank might not fully compensate for the variations of the real blank. The results show that matrix effects could be predicted with models based on stagewise regression, suggesting that this type of model could be used in an autonomous instrument to make analytical methodology decisions. In terms of guaranteeing a desired accuracy, the predictions were at least 80% correct for test solutions with overall matrix effects that varied from 10 to 50%. The key prediction factors e.g. 12wCx y 15wNx were also determined. Acknowledgments The authors wish to thank the Natural Sciences and Engineering Research Council of Canada (NSERC), the National Research Council of Canada (NRC) and SCIEX Canada for their financial support under the Strategic Grants Partnership Program, and Michael Rybak and Beth Brown for valuable discussions. References w1x A. Montaser, Inductively Coupled Plasma Mass Spectrometry, Wiley-VCH, New York, 1998. w2x E.H. Evans, J.J. Giglio, J. Anal. At. Spectrom. 8 (1993) 1–18. w3x R.F.J. Dams, J. Goossens, L. Moens, Mikrochim Acta 119 (1995) 277–286.
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w4x N. Jakubowski, D. Stuewer, New Instrumental Developments and Analytical Applications in ICP-MS, in: G Holland, S.D. Tanner ŽEds.., Plasma Source Mass Spectrometry: Developments and Applications, The Royal Society of Chemistry, Cambridge, 1999, pp. 298–312. w5x J.W. McLaren, A.P. Mykytiuk, S.N. Willie, S.S. Berman, Anal. Chem. 57 (1985) 2907. w6x D. Beauchemin, S.S. Berman, Anal. Chem. 61 (1989) 1857. w7x J.J. Thompson, R.S. Houk, Appl. Spectrosc. 41 (1987) 801. w8x P. Abbyad, J.W. Tromp, J. Lam, E.D. Salin, J. Anal. At. Spectrom. 16 (5) (2001) 464–469. w9x S.D. Tanner, M. Paul, S.A. Beres, E.R. Denoyer, At. Spectrosc. 16 (1995) 16–18. w10x J.W. Tromp, M. Pomares, M. Alvarez-Prieto, A. Cole, H. Ying, E.D. Salin, Spectrochim. Acta Part B (2000) submitted. w11x G. Xiao, D. Beauchemin, J. Anal. At. Spectrom. 9 (4) (1994) 509–518. w12x W. Zhu, E.W.B. De Leer, M. Kennedy, P. Kelderman, G.J.F.R. Alaerts, J. Anal. At. Spectrom. 12 (1997) 661–665. w13x M.A. Vaugham, D.M. Templeton, Appl. Spectrosc. 44 (1990) 1685–1689. w14x L. Moens, F. Vanhaecke, J. Riondato, R. Dams, J. Anal. At. Spectrom. 10 (1995) 569–574. w15x U. Vollkopf, V.I. Baranov, S.D. Tanner, ICP-MS Multielement analysis at sub-ppt levels applying new instrumental design concepts, in: G Holland, S.D. Tanner ŽEds.., Fundamentals of Plasma Source Mass Spectrometry — New Development and Applications, The Royal Society of Chemistry, Cambridge, 1999, pp. 63–79. w16x M.M. Fraser, D. Beauchemin, Spectrochim. Acta Part B 55 (2000) 1705–1731. w17x J.W. Olesik, I.I. Stewart, J.A. Hartshome, C.E. Hensman, Spec. Publ. R. Soc. Chem. (Plasma Source Mass Spectrometry) 241 (1999) 3–19. w18x J.W. Olesik, C. Hensmen, S. Rabb, D. Rago, Spec. Publ. R. Soc. Chem. 267 (2001) 3–16. w19x A.C. Lazar, P.B. Farnsworth, Appl. Spectrosc. 53 (1999) 457–464. w20x A.C. Lazar, P.B. Farnsworth, Appl. Spectrosc. 53 (1999) 465–470. w21x H. Ying, J. Murphy, J.W. Tromp, J.-M. Mermet, E.D. Salin, Spectrochim. Acta Part B 55 (2000) 311–326. w22x W. Branagh, C. Whelan, E.D. Salin, J. Anal. At. Spectrom. 12 (1997) 1307–1315, wand references thereinx. w23x C. Sartoros, E.D. Salin, Spectrochim. Acta Part B 53 (1998) 741–750, wand references thereinx. w24x J.W. Tromp, R.T. Tremblay, J.-M. Mermet, E.D. Salin, J. Anal. At. Spectrom. 15 (2000) 617–625.
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w25x J.W. Tromp, A. Cole, H. Ying, E.D. Salin, Appl. Spectrosc. 55 (2001) 611–620. w26x D. Beauchemin, J.W. McLaren, S.S. Berman, Spectrochim. Acta Part B 42 (1987) 467–490. w27x J.W. McLaren, D. Beauchemin, S.S. Berman, Spectrochim. Acta Part B 43 (1988) 413–420. w28x X. Chen, R.S. Houk, J. Anal. At. Spectrom. 10 (1995) 837–841. w29x F. Vanhaecke, G. Galbacs, S. Boonen, L. Moens, R. Dams, J. Anal. At. Spectrom. 10 (1995) 1047–1052. w30x D.C. Gregoire, R.E. Sturgeon, Spectrochim. Acta Part B 48 (1993) 1347–1364.
w31x J.O. Rawlings, Applied Regression Analysis, Wadsworth & BrooksyCole Advanced Books & Software, Pacific Grove, CA, 1988. w32x E.R. Denoyer, D. Jacques, E. Debrah, S.D. Tanner, Atom. Spectrosc. 16 (1995) 1. w33x L.L. Burton, G. Horlick, Spectrochim. Acta Part B 48 (1993) 1063–1064. w34x D.C. Gregoire, Spectrochim. Acta Part B 42 (1987) 895–907. w35x S.D. Tanner, Spectrochim. Acta Part B 47 (1992) 809–823.
Sample diagnosis using non-analyte signals for inductively coupled plasma mass spectrometry Hai Ying, Margaret Antler, John W. Tromp, Eric D. Salin* Department of Chemistry, McGill University, 801 Sherbrooke St. W, Montreal, Quebec, Canada H3A 2K6 Received 3 January 2001; accepted 11 November 2001
Abstract A sample diagnosis procedure that uses non-analyte signals to predict matrix effects in inductively coupled plasmamass spectrometry (ICP-MS) is presented. Non-analyte signals are those of other species which are present in the plasma (e.g. Arq 2 ), and monitoring them can indicate changes in the instrument or sample. Matrix effects of Na, Al, K, Cs, and Ba on 19 non-analyte signals were studied. Non-analyte signals changed significantly in the presence of the matrices. The heavier matrices, Cs and Ba, caused more interference. Stagewise regression was applied to build prediction models. The results showed that matrix effects caused by matrices of various concentrations could be predicted, with the predictions of the model well correlated with the test experimental results. In previous work, we introduced a total interference level (TIL) model, which predicted interferences based on previous experiments, and tested it in terms of analytical decision making. The current model is tested in the same way, and gave excellent results. In terms of guaranteeing a desired accuracy, the predictions were at least 80% correct for test solutions with overall matrix effects that varied from 10 to 50%. The key prediction factors were also determined. The main conclusion of this study was that the presence of matrix effects could be detected by online monitoring of only nonanalyte signals. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Inductively coupled plasma mass spectrometry; Diagnosis; Non-analyte signals
1. Introduction Inductively coupled plasma mass spectrometry (ICP-MS) has been widely accepted as a sensitive and accurate technique for trace element determination w1–4x; however, since the inception of ICPMS, spectral and non-spectral interferences have * Corresponding author. E-mail address: [email protected] (E.D. Salin).
been a challenge for practical analysis w2–4x. Much research has been dedicated to solving these problems, such as the use of concomitantsymatrices separation w5,6x, alternative calibration methods w7,8x, different operating conditions w9,10x, mixed gas plasmas w11x, mathematical correction procedures w12,13x, high resolution MS w14x and dynamic reaction cells w15x. The understanding of matrix effects has been also probed through more fundamental experiments, for example the effect
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of a matrix element on measured ion distributions in the plasma w16x, including experiments on single droplets by several groups w17–20x. When analyzing a complex sample, the choice of a proper analytical methodology is difficult and time-consuming, especially for non-experts. Therefore, there is an increasing need to establish an intelligent system to help users make the right choice of analytical methodology and thus to ensure the quality of the final analytical results w21x. While spectral interferences continue to be a problem, and are likely to be completely avoided only by pre-separation or advanced instrumental designs (e.g. high resolution MS w14x or a dynamic reaction cell w15x), this work focuses on nonspectral interferences (matrix effects). Our laboratory has been pursuing the Autonomous Instrument project for the last decade to develop software to allow more autonomous and operator independent operation of both ICP-AES w22,23x and ICP-MS w8,21,24,25x instruments. The design was outlined in previous papers w22,24x. Different modules were studied and related software systems were demonstrated. In its present design, the system first obtains semi-quantitative data from a full mass scan, which is used to determine the total interference level (TIL). The TIL, as described in a recent paper w24x for ICP-MS, is a critical module for the Autonomous Instrument project. If the TIL is above a certain threshold, which means a simple calibration method would not work well, an appropriate calibration methodology (e.g. internal standardization) andy or specific operating conditions (e.g. robust conditions w10x) is selected. Two important assumptions, linearity of matrix effects with matrix concentrations w24x and additivity of matrix effects of different matrices w25x, were tested with satisfying results. The TIL model is a direct method, which uses the full scan spectra to identify and roughly quantify the major components and estimates the total interference level using the estimated major component concentrations and predetermined interference coefficients. These interference coefficients are determined empirically, so the model must be calibrated for each potential interferent, potentially a tedious process. Here, we present a simple, indirect and more universal method, using non-analyte signals
(NAS), for evaluation of overall matrix effects for unknown samples in ICP-MS. Non-analyte signals have been of concern because of their potential to cause spectroscopic interferences, with the overlap of 40Ar16O with 56 Fe being a well-known example. However, nonanalyte signals have also been used for signal calibration and instrument diagnostics. An early application was the use of non-analyte lines as internal standards to compensate for the occurrence of matrix effects. Beauchemin et al. w26,27x investigated the use of the species 12Cq and 80(Arq 2 ) as internal standards in the analysis of marine sediments. They found that an accurate correction was realized in most cases, with the exception of the heavier elements Cd and Pb. Chen and Houk w28x extended this concept to a variety of other polyatomic ions. They used several strong polyaq q q tomic ion signals (Nq 2 , ArO , ClO , and MO ) as internal standards to correct for matrix interferences. This approach avoids the extra manipulation of adding an internal standard element, as well as the risk of accidental contamination. However, as was pointed out w2x, one must be careful in the application of non-analyte signals as internal standards since the mechanism of polyatomic ion formation in the plasma is different from that of the analyte ions. The argon dimer has also been used as a diagnostic tool in slurryysolid sampling ETV-ICP-MS for the optimization of operating conditions and the correction for non-linearity of signals caused by matrix effects w29,30x. We reported an instrument diagnosis system for ICPMS w21x which uses non-analyte (background) species monitored while measuring blank solutions (i.e. water or 0.5% HNO3). In the present work, non-analyte signals were used to predict average matrix effects. Implementing the model involves monitoring several nonanalyte signals during analysis. It is shown to be a simple, universal, and relatively accurate method to evaluate matrix effects on-line. 2. Algorithms In general, it is desirable to develop the simplest model that can make accurate predictions. Thus, a modeling method with feature selection is preferred. Only those non-analyte signals determined
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Table 1 ICP-MS operating conditions and experimental parameters Instrument Skimmer cones Nebulizer
PE-SCIEX Elan 6000 ICP-MS Nickel Cross-flow with Scott-type spray chamber
ICP RF power Auxiliary gas flow Sample liquid uptake Nebulizer gas flow rate
1.0 kW 15 lymin 1.0 mlymin 0.825 lymin
Mass spectrometer Detector
Dual
Ion lens voltage Auto lens
7.5 V Off
Peak scan parameters Basic mass range Scan mode Replicates Dwell time Resolution Sweeps per reading Reading per replicate
2–15, 17–39, 42–250 (amu)a Peak hopping 3 25 ms 0.1 (amu) 15 1
a
The real mass range for data collection was determined with different matrices as well. When doing experiment for a specific matrix element, all isotopes of this element were avoided.
to be essential for prediction are retained in the model. Based on our previous work w21x, and the problems encountered, we chose a common, powerful regression method, stagewise linear regression. It is a supervised learning method, which means ‘solved problems’ are needed in the training process. Using the data from many non-analyte signals, models were constructed with the most important spectral information. The selection of the variables (spectral features) that provide the most information is a critical process. Variable selection methods have been developed which identify good (although not necessarily the best) variables, with considerably less computing than is required for all possible regressions w31x. These methods are referred to as stepwise regression methods and have not been commonly used in ICP spectroscopy. Stagewise linear regression is very similar to stepwise linear regression, but the calculations are simplified. For both stepwise and stagewise linear regression, the variables are identified sequentially by addition (forward selection) or deletion (backward elimination). Forward stagewise selection, used in the current work, starts by choosing the
independent variable (intensity of a certain nonanalyte species) that has the highest correlation with the dependent variable, the matrix effect. At the second step, the independent variable that causes the largest decrease in the residual sum of squares is chosen from the subset of independent variables not already in the model. This will be the variable that has the highest correlation with the residuals from the first model (which contains one independent variable). This second independent variable is added to the model, and the step is repeated. The procedure terminates either when a criterion is reached, e.g. a partial F-statistic at a particular step does not exceed a preset value Fin, or when the desired number of candidate regressors have been added to the model. Related procedures can be found elsewhere w31x. 3. Instruments, experiments, and method development process 3.1. Instruments and experiments A conventional PE-SCIEX Elan 6000 ICP-MS with a cross-flow nebulizer and a Scott-type spray
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chamber was used for this study. The operating conditions and experimental parameters are given in Table 1. The standard daily optimization procedure suggested by the manufacturer was applied to determine nebulizer gas flow rate and ion lens voltage. The detector was set in dual mode. In the following data processing section, the analyte signals were in pulse mode (counts per second) while the analog values of non-analyte signals were used, since they tended to be of higher intensity and could saturate in pulse count mode. The Auto Lens is a function of the Elan 6000 ICP-MS which adjusts the ion lens voltage dynamically with analyte mass and may improve results in the presence of matrices w32x. To minimize experimental variables we did not use the Auto Lens, so the ion lens voltage was fixed at the value that maximized the 103Rhq signal. In order to have adequate information for data processing, full scan spectra were obtained in peak hopping mode, skipping masses 16O and 40Ar. In addition, when doing an experiment for a specific matrix element (interferent), all isotopes of the matrix element were skipped in the data acquisition. All samples described herein were prepared in distilled de-ionized water (Milli-Q water system, Millipore Corp., Bedford, MA, USA) by sequentially diluting multi-element standards (SCP Science, St. Laurent, Quebec, Canada) and trace metal grade nitric acid (Baker Instra-Analyzed, J.T. Baker, Phillipsburg, NJ, USA). There were 15 analytes, Cu, Fe, Mg, Ni, Pb, Pt, Y, Zn, Be, La, Li, Mo, P, Sb and Sr. Based on previous work w24x, five matrices were selected for this study, Na, K, Al, Cs and Ba. Single matrix solutions were made from solid nitrate salts (Alfa Aesar, Ward Hill, MA, USA). Matrix effects depend on the absolute amount of the matrix element rather than on the molar ratio of matrix element to analyte w2x, so absolute concentrations of matrices in mgyml are used. In total, there were five ‘clean’ solutions which did not contain matrices: water, 0.5% HNO3 and three multi-element standard solutions (5 ngyml, 10 ngyml, 20 ngyml). For each matrix solution except Cs, there are six matrix blank solutions (i.e. containing only the interferent) in different concentrations (10 mgyml, 30 mgyml, 100 mgyml, 300 mgyml, 400 mgyml, and 1000
mgyml) and six other solutions with the same matrix and with 10 ngyml of multi-element standards. The matrix blanks are used for blank subtraction, and compensate for spectrometric interferences due to the matrix. Since Cs was known to cause more serious matrix effects than the others w24x, five concentrations were used, 10 mgyml, 30 mgyml, 100 mgyml, 200 mgyml, and 500 mgyml. The data for the two highest matrix concentrations were collected on one set of days, and the data for the other matrix concentrations were collected on different days. The experiments during a day were performed in the sequence: MilliQ water, 0.5% HNO3, standard solutions (5, 10 and 20 ngyml), lower matrix blank, lower matrix solution with standards, higher matrix blank, and higher matrix solution with standards. The washout time was selected to ensure that there was no residual contamination in the instrument from the matrices. Full scan spectra of Milli-Q water were used to monitor the background before and after experiments each day. 3.2. Diagnosis process The diagnosis development process is illustrated in Fig. 1. In general, there are two steps, model building and model testing. Two different sets of data were collected. The data sets consisted of non-analyte signals for water, 0.5% HNO3, the three multi-standard solutions (5 ngyml, 10 ngy ml and 20 ngyml) and matrix solutions with and without standards at 10 ngyml. The data sets differ in the concentrations of the matrix solutions that were used to generate them. Dataset 1, on the left of Fig. 1, included data for matrix solutions of three concentrations (30, 100, 500 mgyml for Cs and 30, 100, 1000 mgyml for the other four matrices). Seventy percent of the data set were randomly chosen to build a prediction model. The remaining 30% of the data were used to test the model. This was repeated five times as a crossvalidation of the diagnosis process. In addition, Dataset 2 contained independent data for solutions with matrices of different concentrations (10, 300 and 400 mgyml, 10 and 400 mgyml for Cs), and was used as a more difficult blind test.
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variation of signals obtained under the same operating conditions as the non-analyte matrix effect, formulated as: MENASs
Fig. 1. Flow chart of the model development process.
A Visual Basic subroutine was compiled to read and convert the Elan 6000 report files to the desired format for processing. The programs for the data processing were written in MATLAB. 4. Results and discussions 4.1. Matrix effects on analyte and non-analyte signals Matrix effects may be defined as matrix-induced signal variations, either suppression or enhancement w3x. In this paper, the matrix effect for an analyte was calculated as the variation of the net intensities using the following formula: MEs
ŽIMyIMBl. y1 ŽIyIBl.
(1)
where IBl and IMBl represent the blank signal at a given mass with no matrix and the blank with matrix, respectively, while I and IM stand for the intensity with no matrix and that with a matrix for a specific analyte at a same concentration. An average overall matrix effect for a particular matrix at a certain concentration is defined as the average of the absolute value of the matrix effect for every analyte, computed as: NA
OMEs8)MEi) yNA
(2)
i
where NA is the number of analytes measured. For non-analyte signals, we also define the
IM y1 I
(3)
where I and IM represents the intensity of nonanalyte species without and with a matrix, respectively. Table 2 lists all the masses used in the present work in bold font, ignoring those analytes used as matrices. Information about all mass species was extracted from a useful ICP-MS database, the MS INTERVIEW software w33x for a nitric acid environment. Fifteen analytes were used to determine the overall matrix effects on analytes while 19 nonanalyte species were initially chosen to develop the methods for matrix effect prediction. Several non-analyte species, 56wArOx, 76wAr2 x, 78wAr2 x and 80w Ar2x, were overlapped with isotopes of analytes; however, since these non-analyte signals originate from the major component of the plasma, Ar, we assume that their signals are much stronger than those of the analytes. Non-analyte species were important in instrument diagnosis w21x, and we wanted to determine whether they were also important factors for matrix effect prediction. In the following results, it is seen that the various non-analyte lines displayed showed considerable matrix effects. Fig. 2 illustrates variations of every studied non-analyte signal with different solutions. In our notation, Bg indicates background, Std5, Std10, Std20 stand for standard solutions (5 ngyml, 10 ngyml and 20 ngyml), and MLow, ML S, MHigh, MH S represent lower matrix, lower matrix with multi-element standards (10 ngyml), higher matrix, and higher matrix with multi-element standards (10 ngyml), respectively. Note that the results are from Dataset 1 so the concentrations for the matrices are the two highest (200 mgyml and 500 mgyml for Cs, 400 mgyml and 1000 mgyml for the other four matrices). Fig. 2 shows clearly that the non-analyte signals changed in the presence of matrices, which is the basic requirement for the current work. The Cs matrix caused suppression for all non-analyte signals except mass 4. Mass 4 is an exception because
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Table 2 All masses used in the current study (in nitric acid environment) Mass Analyte signals 7 9 24 31 54 58 63 64 88 89 98 121 139 195 208
Background species (non-analyte signals)
N2H, NOH, NO, CO ArN, ArO ArO, ArOH ClN2
Non-analyte signals H2, H 2 H3 3 4 12 C 13 C 14 N 15 N OH, NH3, O 17 O, OH, H2O, NH4 18 OH, H2O, H3O 19 H2O, H3O 20 H 3O 21 36 Ar ArH, H3O(H2O) 37 38 Ar, ClH 56 ArO, ArNH Ar2 76 Ar 78 2 Ar2 80 a
Isobarics
Li Be Mg P Fe, Cra Ni, Fea Cu Zn, Nia Sr Y Mo, Rua Sb La Pt Pb
Doubly charged ions
Matrix dependent or oxidesyhydrides
Ca, Ti
C2(organics)
Cd Cd
Lu, Yb
NaCl, CaO PO2, NaAr, MgCl HPO2, CaO, TiO, Na2O GeO, MnO2H GeO NiAr, CuCl SbO HfO
H He C C N N O O F Ne Ne S, Ar Cl Ar Fe Ge, Se Se, Kr Se, Kr
Mg Mg
CH(organics) CH(org.), CH2(org.) NH(org.)
Ca Ca
Cd Eu, Sm, Gd Gd, Dy Tb, Gd, Dy
CaO AsH, NiO NiO, TiO2 NiO, TiO2
These isobarics were regarded as spectral interferences here.
there is only one species at mass 4, He, and the variation of that signal was less than 5% in all the solutions. The Ba matrix behaved differently, suppressing non-analyte signals in the lower and higher mass ranges and enhancing those of masses 18–21 which are all water based peaks (see Table 2). It is not surprising to see that each of the other four matrices showed some similarities for these
four masses because there is a strong abundance 20 co-relationship between 18(H16 (H18 2 O) and 2 O), 19 16 21 18 and between (H3 O) and (H3 O). The Na matrix caused enhancement for all species except two C-based species, 12C and 13C. Like Na, K mainly enhanced non-analyte signals except that it suppressed intensities of 12C and 13C more than Na did. In most cases (mass 2, 3, 14, 15, 17, 36,
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Fig. 2. Fractional signal variations of non-analyte signals with different solutions with or without matrices. (M low and M high are two matrix blanks with different concentrations, 200 mgyml and 500 mgyml for Cs, 400 mgyml and 1000 mgyml for Na, Al, K and Ba. ML S and MH S are the same but with multi-standards.) If the signal in the indicated solution is the same as in the background, then the relative signal variation is zero. If there is 20% signal enhancement with respect to the background, then the relative signal variation is 0.2. If there is 20% signal suppression, then the relative signal variation is y0.2.
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Fig. 2 (Continued).
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Fig. 2 (Continued).
37, 38, 56, 76, 78, 80), Cs and Ba had a similar effect, Na and K were similar, and only Al was quite different from the others. Al suppressed the intensities of 12C, 18H2O and 20H2O while only the highest concentration Al (1000 mgyml) caused decreases of the intensities of Ar dimer species (mass 76, 78, 80). The other non-analyte signals increased with a high concentration of Al. Another important point from Fig. 2 concerns the standard solutions. In contrast to our initial assumption, the non-analyte signals did vary slightly with the different concentrations of the standards in the solutions. In addition, except for several N based species (mass 14, 15, 17), the day-to-day variations of the other non-analyte signals for the standard solutions were considerable. Several previous studies about matrix effects on analytes have obtained different results. Gregoire w34x observed only suppression while Beauchemin
w26x found enhancements due to Na, K, Cs, Mg and Ca. While space charge effect theory w35x only explains suppressions, it has been widely accepted to explain the difference in matrix effects in ICP-MS compared to ICP-AES. Fig. 3 displays the results obtained in the current study. Fig. 3a shows the matrix effects on 15 analytes with Na, K and Al while Fig. 3b shows those with Cs and Ba. Fig. 3c shows the overall matrix effects for every matrix at the highest two concentrations. For most analytes (see related masses in Table 2), existence of these matrix effects caused suppression, some quite serious. Heavier matrices (Cs and Ba) caused more serious matrix effects than the lighter ones except Al at 1000 mgyml. Neither Na nor K seemed to have a significant effect on several analytes at the medium mass range, e.g. 88Sr, 89Y, 98Mo. Al was different from other matrices in its effect on non-analyte
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and correction equations provided in Elan 6000 software were not used. 4.2. Matrix effect prediction Three different types of interference prediction models were constructed for comparison. For simplicity, we examined models that would predict the average overall matrix effect (OME) as defined by Eq. (2). The model designated as ‘raw’ chooses variables from among the set of non-analyte signals, and predicts interference as a linear combination of the important selected non-analyte signals. An example of a model using ‘raw’ variables is OMEsaSw18ŽH2O.xqbSw76ŽAr2.xqc where Swx denotes the signal at the mass and the likely species responsible, and a, b and c are the model coefficients. A ‘ratio’ model chooses from all possible ratios of the raw signals, so if there are N raw variables i.e. non-analyte signals, there are ;N 2 ratio variables. An example of a model with ratio variables is OMEsaSw17ŽOH.x ySw12CxqbSw12Cx ySw15Nxqc
Fig. 3. Matrix effects on different analytes. (a) Matrix effects caused by Na, Al and K. (b) Matrix effects caused by Cs and Ba. (c) Overall matrix effects for different solutions. (The xaxis was represented by matrix element plus its concentrations, e.g. Al400 means Al 400 mgyml.)
signals. It enhanced analyte signals at the lower mass range, e.g. 7Li, 9Be, 24Mg, 31P. Among analytes, Pt is special, exhibiting only minor suppression or even enhancement in many cases. When viewing these results, recall that the AutoLens function on the Elan 6000 was not used
Finally, the ‘total’ data set consists of all raw signals and all ratio signals, and so could have terms as in either of the models above. In order to determine whether this matrix prediction method works successfully, a cross-validation process was done. As shown in Fig. 1 70% of Dataset 1 was randomly chosen to build the model, and the remaining 30% was used to test the model. To correct for day-to-day signal variations, all of the raw non-analyte signals were normalized by their percent changes from the average ones obtained with water on the same day. It had been previously found that ratios were better indicators of instrument malfunction w21x so the percent changes of non-analyte signal ratios were also used in the method development in this work. Stagewise regression method was applied to build prediction models. Fig. 4 demonstrates the relationship between experimental measurements of overall matrix effect, and predictions based on non-analyte signal
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Fig. 4. Comparison of the predictions of a stagewise regression model based on ratios of non-analyte lines with actual overall matrix effect. (a) for the test data set; (b) for the cross-validation; (c) for the blind test.
ratio models. The ideal correlation result is that both slope and correlation coefficient R 2 equal to 1. Fig. 4a shows the correlation achieved in the training set, while Fig. 4b displays the crossvalidation correlation, and Fig. 4c shows the correlation between the prediction model and the independent blind data from Dataset 2. The linear-
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ity of the three processes is good and comparable with similar values of R 2, but the blind test is slightly worse, which is reasonable, given that the model had been trained with different concentrations. These graphs are the basic justification of the method in that they show that our hypothesis is correct. It is possible to build models based on non-analyte signals that correlate well with overall matrix effect. Table 3 lists the five most important factors in the prediction models for different data sets, selected by stagewise regression. For different instances of cross-validation, the selection of these key variables was slightly different, mostly in sequence. They are listed in order of frequency of selection. Consistent with previous results w21x, not only was the best prediction accuracy obtained with the ratio-only data set, but most of the factors selected for the total data sets were exactly the same as those chosen for the ratio-only data set. In our previous instrument diagnosis study w21x, the masses or mass ratios selected were mainly Ar and water based species. In contrast, for the present work, N and C based species appear to be more important for ratio data sets. These results are not inconsistent, since the instrument diagnosis was mainly for prediction of the malfunction of the ICP part of the instrument (power, nebulizer gas flow rate, and liquid uptake rate) where the principle species, Ar and water, would be affected more. Since ICP-MS matrix effects have major contributions from the ion extraction process w35x, it is not surprising that different species were selected in the current study. Considering Fig. 2 again, we find that the signals of Ar and water species (masses 18–21, 37, 56, 76, 78, 80) varied Table 3 Important variables for the matrix effect prediction selected by stagewise regression method Raw data set 18
76w Ar2x wH2O;NH4;OH;Ox 56w ArO;ArNHx 2w H2;Hx 17w OH;NH3;Ox
Ratio data set or total data set 17
wOH;NH3;Ox y 12 wCx 12w x 15w x C y N 18w H2O;NH4;OH;Ox y 19 wH3 O;OH;H2 Ox 36w Arx y 14wNx 56w ArO;ArNHx y 18 wH2 O;NH4 ;OH;Ox
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considerably with the differing concentrations of standard solutions. In some cases, the different concentrations of standards caused more variation than changes in the concentrations of the matrix solutions (e.g. Na, K), indicating that those species were too unstable to be used in an interference prediction model. As in the validation of the TIL model in previous work w24,25x, the question is: how often will the prediction model make the correct decision if accuracy is desired at a certain threshold or bound (e.g. less than 10% error). Thus, if the interference is less than the bound and the model predicts it is less, it is correct. Similarly, if the interference is greater than the bound and the model predicts it is greater, it is also correct. Incorrect predictions are those where the model predicts interference greater than the bound while it is less, or vice versa. The first situation results in over-calibration, where a more elaborate technique than necessary is used, wasting time, while the second situation results in under-calibration, causing errors. Fig. 5 is the illustration of the fraction of correct analytical decisions as a function of the desired accuracy for the training set in Fig. 5a, the crossvalidation in Fig. 5b and the blind test in Fig. 5c. We assume that we want to measure analytical samples and be guaranteed a maximum error, which we call the desired accuracy, or threshold. Thus, if the threshold is 10%, we want to ensure that the reported concentrations are within 10% of the true values. Fig. 5 shows how often the predictions of our models will guarantee the desired accuracy. The results were the average of a five-fold modeling and testing process. Errors for training and cross-validation are lower at the higher thresholds. The intermediate range was more difficult, with training errors of the order of 10–15%, reflecting the fact that making the correct decision is difficult when the average interference is around the bound desired. Low thresholds (5%) were the most difficult for the model to classify, due to similarities between the blank and samples that were slightly suppressed (10 mgyml matrix concentration). The standard deviation of the raw non-analyte signals was 2–3%, so some overlap between the blank and sample is possible. How-
Fig. 5. Test of the decision-making ability of the model, with error displayed as a function of desired accuracy. (a) for the test data set; (b) for the cross-validation; (c) for the blind test.
ever, the fact that Fig. 5c is very similar to Fig. 5a is encouraging, indicating that the error rate in the blind test is only slightly greater than that in the training data, and, in the worst case, 80% success in the blind test is a good result.
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5. Conclusions In this work, a simple sample diagnosis procedure to predict matrix effects in ICP-MS based on non-analyte signals is demonstrated. The heavier matrices, Cs and Ba, caused similar effects, severe suppression, except that Ba strongly enhanced the water based signals (mass 18–21). The observations with lighter matrices were more complex. The Na and K matrices were found to have similar effects on non-analyte signals. The Al matrix had a larger effect on lower mass species. In addition to the effects of the matrices, the introduction of analytes also caused considerable changes to nonanalyte signals, especially in matrix solutions, which implies that the matrix blank might not fully compensate for the variations of the real blank. The results show that matrix effects could be predicted with models based on stagewise regression, suggesting that this type of model could be used in an autonomous instrument to make analytical methodology decisions. In terms of guaranteeing a desired accuracy, the predictions were at least 80% correct for test solutions with overall matrix effects that varied from 10 to 50%. The key prediction factors e.g. 12wCx y 15wNx were also determined. Acknowledgments The authors wish to thank the Natural Sciences and Engineering Research Council of Canada (NSERC), the National Research Council of Canada (NRC) and SCIEX Canada for their financial support under the Strategic Grants Partnership Program, and Michael Rybak and Beth Brown for valuable discussions. References w1x A. Montaser, Inductively Coupled Plasma Mass Spectrometry, Wiley-VCH, New York, 1998. w2x E.H. Evans, J.J. Giglio, J. Anal. At. Spectrom. 8 (1993) 1–18. w3x R.F.J. Dams, J. Goossens, L. Moens, Mikrochim Acta 119 (1995) 277–286.
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