Prediction of Multiple Matrix Interferences in Inductively Coupled Plasma Mass Spectrometry

Volume 55, Number 5, 2001 APPLIED SPECTROSCOPY 6110003-7028 / 01 / 5505-0611$2.00 / 0q 2001 Society for Applied Spectroscopy

Prediction of Multiple Matrix Interferences in InductivelyCoupled Plasma Mass Spectrometry

JOHN W. TROMP, AMANDA COLE, HAI YING, and ERIC D. SALIN*Department of Chemistry, McGill University, 801 Sherbrooke St. W, Montreal, Quebec, H3A 2K6, Canada

Matrix effects for pairs of interferents (Al, Na, K, Ba, and Cs) wereinvestigated and compared to predictions of the amount of inter-ference determined by single interferent experiments in order totest a model called the total interference level (TIL), which assumesthat the effects of different interferents add linearly. The TIL modelis part of an Autonomous Instrument and is designed to indicatewhen a simple default calibration, such as external calibration orinternal standardization, is inadequate for the desired accuracy ofanalysis. The performance of the TIL model was examined in termsof a daily calibration basis, which should be more accurate, and anoccasional calibration basis, which is more convenient, consideringsimple external standardization and internal standardization as thetechniques to be tested for desired accuracy. The results are en-couraging for multiple interferences and show that the TIL modelcan serve a useful function in predicting calibration errors, evengiven the presence of instrument drift on ICP-MS.

Index Headings: Inductively coupled plasma mass spectrometry;ICP-MS; Instrument automation; Matrix interferences; Sample di-agnosis.

INTRODUCTION

Inductively coupled plasma mass spectrometry (ICP-MS) is an excellent technique for elemental analysis,1–3

but still suffers from interferences.4,5 While spectroscopicinterferences are an important problem, this work focuseson matrix effects, continuing previous work.6 Matrix ef-fects occur when the presence of some species at higherconcentration affects the signal of the analytes of interest.As ICP-MS was developed as an analytical technique,matrix effects were investigated by various groups to de-termine their magnitude, instrument condition depen-dence, and physical origins, thereby aiding in the designof the current generation of instruments.7–10 While thereis no complete understanding of matrix effects in ICP-MS, it is clear that they arise from different stages of theinstrument. There are interferences in the aerosol gener-ation and transport systems,11 plasma effects,7 interfaceeffects as a result of salt deposition on the cones,12 spacecharge effects in the ion extraction,9 and long-term de-position on the ion lens.13 The � rst two sources of inter-ference (sample introduction and plasma) also arise inICP-AES (atomic emission spectrometry), where matrixeffects are generally less of a problem. Thus, it is clearthat the main dif� culty with matrix effects in ICP-MS isdue to the fact that ions, not photons, are extracted. Un-like photons, ions interact with each other during extrac-tion, and can dirty the extraction system, with differenttime scales due to different processes. Thus, instrumentdrift is a fundamental feature of ICP-MS, as the sample

Received 8 May 2000; accepted 22 January 2001.* Author to whom correspondence should be sent.

measured changes the state of the instrument during themeasurement.

Analysis can still be done in the presence of matrixeffects, but a more elaborate calibration than simple ex-ternal standards is needed if quantitative accuracy is de-sired. In ICP-MS this calibration scheme is often externalcalibration with internal standardization using two tothree internal standards to compensate for the various ef-fects mentioned above. In this work, we examine the ma-trix effects of single and pairs of interferents on a modernICP-MS instrument to test a simple model for automati-cally choosing a calibration methodology.

Our laboratory has had a long-term interest in the au-tomation of analytical instrumentation, starting with workon ICP-AES,14–17 where the idea of an Autonomous In-strument was � rst proposed. The Autonomous Instrumentis designed to accurately analyze samples independent ofan operator. We have also explored various aspects of theautomation of analysis using ICP-MS,6, 18–21 including se-lection of internal standards,18 optimization,19 diagnos-tics,20 sample recognition,21 and matrix interferences.6

In a previous paper,6 we investigated single matrix in-terferences in ICP-MS and tested the decision model thattreats them in a proposed Autonomous Instrument. Thatwork tested a simple linear model for total interferencelevel (TIL), which was used to predict whether the sam-ple could be accurately analyzed with a ‘‘simple’’ cali-bration method such as external standardization or inter-nal standardization, or whether it had to be analyzed witha better calibration method such as standard additions, orwith different operating conditions. The TIL model as-sumed that interference was linear with interferent con-centration and that the effects of different interferentsadded linearly. Although the observed behavior of theinterference with interferent concentration was not line-ar,6 a linear model based on the initial slope of the curveat low interferent concentrations proved to be quite usefulin deciding whether the level of interference in the sam-ple would be problematic for a desired analytical accu-racy. In predicting when external standards were inade-quate for the desired accuracy, the TIL model made errorsthat would result in an inaccurate analysis in about 3%of cases. It also made more errors in the other direction,sometimes recommending that a better calibration shouldbe done when it was not necessary. Internal standards 22

are routinely used to compensate for drift and matrix ef-fects in ICP-MS, and the TIL model was also tested forits ability to determine the accuracy of internal standardsas a default method. The TIL model made errors thatwould result in an inaccurate analysis in about 8% ofthese cases, a higher error rate than for external standards.

While this success is encouraging, it tested only one

612 Volume 55, Number 5, 2001

part of the TIL model, which shows that a simple linearmodel for single interferents is useful. It also showed thatthe initial slope of the interference vs. concentrationcurve should be used to predict the accuracy of calibra-tion for single interferents. However, another importantTIL assumption is that multiple interferents add linearly,i.e., that the presence of one interferent will have no ef-fect on the effect of another. The goal of the current workis to test the validity of that aspect of the TIL modelusing multiple interferents. In the single interferent work,we ran experiments on an ICP-MS instrument at standardoperating conditions, with several different single inter-ferents (Na, K, Al, Ba, and Cs) at different concentrationsin a multielement analyte solution. This approach allowedus to determine the effects of these interferents on thevarious analyte signals as a function of interferent con-centration. In the current work we considered the effectsof single and pairwise combinations of the � ve interfer-ents considered previously. We were interested in com-paring the sum of the effects of two single interferentswith the effect of a two-interferent solution. This com-parison allows us to test the assumption of linear addi-tivity of interferences and to determine whether potentialdeviations from linearity were as they had tended to bein the single interferent study—that is, in a direction suchthat a prediction based on measuring only single inter-ferents would be conservative and not lead to analysiserrors.

Total Interference Level. The purpose of the TIL isto � ag samples where the matrix effect is above a certainthreshold so that an inaccurate calibration technique willnot be used. The TIL module of an Autonomous Instru-ment depends on parameters (interference coef� cients foreach matrix on each analyte) which must be experimen-tally determined, by doing a series of experiments witha single multielement standard spiked with each differentinterferent. While the TIL model pessimistically assumesa linear matrix effect with matrix concentration, this is asimpli� cation which our previous work showed to be un-true.6 Where the interference as a function of interferentconcentration is not linear, it generally has a convex rath-er than concave shape. Thus the higher levels of inter-ferent often have less relative suppression than lower lev-els. However, the linear TIL estimate is based on theinitial low concentration part of the curve, and is accuratefor low concentrations and overestimates the error forhigher interferent concentrations.

Explicitly, the TIL model can be written as

n

TIL 5 f (c )Ox m x mm51

where TIL x is the total interference level for analyte x,and n is the total number of interferents. The concentra-tion of the interferent m as determined by the semiquan-titative procedure is cm, and f mx(cm) is the enhancementor suppression of the signal for analyte x caused by in-terferent m. The use of the TIL requires that a semiquan-titative scan be made of all the potential interferents. Infact, our general operating procedure requires that signalsfrom all the matrix constituents be determined so thatthey can be used in other portions of the AutonomousInstrument thought process (e.g., pattern recognition).

This equation assumes linear additivity of interferents,but it is not linear with interferent concentration. How-ever, making the linear assumption,

f mx(cm) 5 Imxcm,

simpli� es the TIL model to the determination of the setof interference correction coef� cients {Imx}, which de-pend on the interferent and analyte.

The TIL model is also implicitly based on the as-sumption that the linear TIL coef� cients stay constant. InICP-MS, instrument drift has frequently been observedfor raw signals, and a method such as the TIL is basedon assuming a constancy of relative signal. This assump-tion is tested in the current work by testing two differentmethods of TIL parameterization. In one method, the TILparameters are determined by an experiment conductedon one day and then the parameters are tested on thatand subsequent days. Another method of TIL parameter-ization, which would be much less convenient in analyt-ical practice, is to calibrate the TIL each day that it isused. Both methods are tested in the current work.

EXPERIMENTAL

A standard PE-SCIEX Elan 6000 ICP-MS with cross-� ow nebulizer and Scott-type spray-chamber was usedfor these experiments. The sampling position was � xedat the manufacturer’s recommendation of 11 mm. Thenebulizer gas � ow was set to maximize Rh signal inten-sity while maintaining the CeO/Ce ratio at less than 3%according to the standard operating procedure. For 1000W power, the optimum was a nebulizer gas � ow of 0.75–0.8 L/min, depending on the day. The liquid uptake ratewas 1.0 mL/min for the experiments, although the dailyoptimization was carried out at a � ow rate of 1.8 mL/min as speci� ed in the manufacturer’s procedure. Theconditions were not re-optimized in the presence of thesample matrix; i.e., different combinations of interferentswere run under the same operating conditions. Signalswere acquired with � ve sweeps per replicate with a dwelltime of 200 ms/amu, for a total integration time of 1 sper replicate, and � ve replicates were averaged to obtainthe reported signals.

In the previous work, we used the AutoLens feature ofthe Elan 6000, which was calibrated with a three-elementsolution containing low- to mid-mass elements. TheAutoLens was designed to maximize the signal by ramp-ing the ion lens potential with the mass � lter of the quad-rupole so that ions would be monitored at the lens voltagethat maximized their transmission.23 A secondary featuremay be a reduction in space charge interferences, sinceinterferent ions would be transmitted with a lower ef� -ciency.24

Before the current work, we performed a preliminaryexperiment that showed that, while the interference of aK matrix was slightly lower with the AutoLens used (anaverage of 15% vs. 17% without the AutoLens), it wasnot signi� cantly better. Thus, we did not use theAutoLens feature, but instead used the single lens voltageobtained through the standard daily optimization processwhich involved maximizing for 103Rh1 sensitivity in amatrix-free solution.

The effect of all possible two-interferent combina-

APPLIED SPECTROSCOPY 613

FIG. 1. Plot of sum of absolute interference for each individual inter-ferent (areas) compared to absolute interference of two-interferent so-lution (bars) for each of the 16 analytes, indicated by their mass. Recallthat by de� nition interference is zero in a matrix-free environment. Theshaded areas in the � gure are cumulative, so the lower curve is theeffect of Cs and the upper curve is the sum of the effects of both Csand Ba. The effect of Ba is the difference between the upper and lowercurve. The three panels are three different experiments run on threedifferent days.

tions—using Na, Al, K, Cs, and Ba as interferents—onthe mass spectroscopic signals of 16 analytes was ex-amined. The relative signals of 16 analytes were calcu-lated for each combination of two interferents. The fouranalytes which were also used as interferents (Na, Al, K,and Ba) were not used, as the concentrations used in theinterferent solutions created problems of memory effect.

From previous work on the concentration effect ofthese � ve interferents,6 interferent concentrations werechosen so that an average signal suppression of 10–20%from each interferent was expected. We wanted to testthe TIL model where it was likely to have problems.Thus, it did not seem useful to run very low or very highmatrix solutions experimentally, since it seemed clear thatthe TIL approach would do well. We chose the experi-ments performed as our test set, and did not correct forthe fact that the TIL was likely to do better at higher orlower concentrations. These concentrations were as fol-lows: Na 230 ppm (mg/L); Al 270 ppm; K 400 ppm; Cs66 ppm; Ba 137 ppm. All interferents were added as highpurity (99.999% pure) nitrates (Alfa Aesar, Ward Hill,MA). The solutions and blanks were prepared in 0.5%nitric acid (trace metal grade, ‘‘instra-analyzed’’, J. T.Baker, Phillipsburg, NJ) with the use of Milli-Q distilleddeionized water (Millipore Corp., Bedford MA). The in-terferents were added to a 10 ppb standard solution (SCPScience, St. Laurent, Quebec) of 21 elements (Li, Na,Be, Mg, Al, K, Fe, Ni, Cu, Zn, Se, Sr, Y, Mo, Ag, Sb,Ba, La, Pt, Pb, and Bi). Solutions with a single interferentwere prepared with the interferent at the above concen-trations and at twice those concentrations. Ten solutionswith two different interferents were prepared, with eachinterferent present at the indicated concentrations.

The experiments were run with matrix-matched blanksto compensate for any potential spurious spectroscopicsignal from the matrix interferent. Note that these spec-troscopic interferences may include polyatomic ions,which depend critically on operating conditions, but thesample and matrix blanks are run successively under thesame operating conditions, so simple subtraction shouldprovide correct compensation. The standard solutionwithout interferent was run six times throughout thecourse of the experiment to correct for possible instru-ment drift. Relative signals (RSs) of each analyte areblank adjusted signals relative to the matrix-free standard,where the matrix-free signal is the average from the two� anking runs:

[standard 1 interferent] 2 [interferent blank]RS 5

[standard] 2 [blank]

where the square brackets denote the signal of the re-spective solutions. By de� nition, without interferent, therelative signal is 1. In the discussion below, we will makeuse of the term ‘‘Interference’’, which will be denoted byInt ( ), and is de� ned as zRS-1z. This is a more convenientterm, since it allows us to ask whether ‘‘interferences’’add. The complete experiment detailed above was runthree times on three different days.

RESULTS AND DISCUSSION

To test the additivity of the TIL model, one comparesthe sum of the interferences of single interferent solutions

to the actual interference in the dual interferent solutions.There are 15 possible combinations of interferents thatcan be tested against the predictions of single interferentexperiments, but to give an idea of the results Figs. 1–3present the results of three runs done on three differentdays of Ba1Cs, K1Cs, and Na1K interferents testedagainst the single interferents. For each individual exper-imental run the signal relative standard deviation (RSD)was 1–3%, depending on the analyte. These three inter-ferent combinations are chosen for display since the in-terferents are either of light (Na, Al, K) or mid-massrange (Ba, Cs), and this choice includes a mid-mid, mid-light, and light-light combination of the masses of theinterferents.

Two clear results stand out at this stage. The � rst isthat, qualitatively, the model seems to work for each run,i.e., usually Int(A) 1 Int(B) ^ Int(A1B), which impliesfavorable calibration decisions. The second is that, whilethe individual results from run to run have qualitativesimilarity, they do not agree quantitatively. Thus, wemust consider closely the question of the frequency of


FIG. 2. Same as Fig. 1, but with Cs (lower) and K as interferents. FIG. 3. Same as Fig. 1, but with Na (lower) and K as interferents.

TIL calibration. We will discuss each of these issues inturn.

Recall that the best situation would be if Int(A) 1Int(B) were approximately Int(A1B), since the single in-terferent coef� cient would then correctly predict the in-terference in a multi-interferent solution. An unfavorablesituation would be if Int(A) 1 Int(B) , Int(A1B), sincethen the multi-interferent solution would actually havemore interference than predicted by the single interferentcoef� cients, and an erroneous prediction of accurate re-sults could be made. Finally, if Int(A) 1 Int(B) .Int(A1B), the TIL estimate would be too conservativeand would recommend a better calibration methodologythan required, but this is considered an acceptable (OK)situation, since an accurate result would be obtainednonetheless.

In general, adding the interferences of the single inter-ferent solutions (lines in Figs. 1–3) overestimated the ac-tual interference in the two-interferent solution (bars inFigs. 1–3). The percentages of predictions that were over-estimates are given in Table IA for all 16 analytes. Asseen from this table, the interference was overestimatedin an average of 80% of the cases.

Of course, in the best case, the additive model wouldclosely approximate the actual interference effect. Theestimated repression was within 5–8% of the actual value,on average. However, there was a fairly large variation

between analytes, with overestimation reaching up to30%.

In our previous paper,6 we tested the validity of theTIL model by using the parameters obtained in one ex-periment to test predictions in subsequent experiments.This was done to simulate the use of the TIL model inlaboratory practice. In that paper, we used a model de-termined at one concentration to make predictions at oth-er concentrations. However, since the actual use of theTIL module would be based on a semiquantitative scanon a sample, the interferent concentrations would only beknown to semiquantitative accuracy. Thus, in our previ-ous work, we assumed that the predictions at other con-centrations assumed a 25% uncertainty in the actual in-terferent concentration. Here, we use a TIL predictionobtained in a single interferent experiment to test the suc-cess of the model in making calibration decisions formultiple-interferent samples, by generating 100 predic-tions with the interferent concentration in a normal dis-tribution with 25% RSD around the actual interferentconcentration.

In the past work, we also tested two models of TILcalibration, one where the TIL was calibrated on one day,and then used in subsequent experiments on followingdays, and another where it was calibrated the same day.The initial calibration was very accurate, leading to only3% inaccurate recommendations as long as the instru-


TABLE IA. Percentage of predictions that overestimate actual in-terference with external standardization.

Mass Day 1 Day 2 Day 3 Avg.

79

245863

67%53%80%93%

100%

53%60%67%73%93%

60%73%87%

100%100%

60%62%78%89%98%

6482888998

100%73%73%53%33%

93%53%67%87%73%

100%67%93%93%93%

98%64%78%78%67%

107121139195

87%60%60%87%

67%87%87%93%

93%100%93%60%

82%82%80%80%

208209Avg.

100%93%76%

93%87%77%

80%93%87%

91%91%80%

TABLE IB. Percentage of predictions that overestimate actual in-terference with Li-Bi internal standardization.

Mass Day 1 Day 2 Day 3 Avg.

924586364

80%80%53%67%87%

53%80%53%73%87%

60%7%

20%67%

100%

64%56%42%69%91%

82888998

107

67%67%73%80%67%

67%53%53%67%73%

47%20%33%20%87%

60%47%53%56%76%

121139195208Avg.

87%93%

100%53%75%

67%73%67%53%66%

27%53%87%87%51%

60%73%84%64%64%

TABLE II. Summary of the different ways that TIL decisions arecategorized, depending on the relationship between the TIL predic-tion, the actual experimental value, and the desired accuracy bound.These categories are used in Tables III–VI to describe the results.

Experiment . Bound Experiment , Bound

TIL prediction. Bound

TIL prediction, Bound

True positive(GOOD)

False negative(BAD)

False positive(OK)

True negative(GOOD)

ment was not modi� ed. Thus, it appears that the TILmodel can be calibrated and the calibration remains valid.

In the current work, in light of the variation in resultsfrom day to day, the same question is re-examined. Inthe discussion above, when we compared the signals ofsingle interferents to multiple interferents, we were con-sidering the daily calibration point of view, which wouldbe less useful operationally due to the higher labor/timerequirements. Thus, in the discussion which follows, wewill determine the prediction rate of the TIL model underfour different analytically relevant scenarios, which areinitial (using only one calibration) and daily calibration,and deciding on the accuracy of either external calibra-tion or internal standardization as the default calibrationmethod.

The TIL model was designed to be used as a ‘‘� ag’’,where samples whose accuracy cannot be guaranteed ata certain level will be subjected to a more robust analyt-ical calibration methodology. We compare the predictionsof the TIL model to the experimental results, accordingto the categories de� ned in Table II, where we assume adesired accuracy, or ‘‘bound’’, and see how effective theTIL is at making decisions that give analytical resultswithin that bound. We de� ne ‘‘GOOD’’ as the total frac-tion of the true positives and true negatives, while ‘‘OK’’is de� ned as the fraction of false positives, and ‘‘BAD’’

is de� ned as the fraction of false negatives as de� ned inTable II.

It would perhaps clarify the discussion if we now giveexamples of the two types of errors that the TIL predic-tion can make. A false positive (OK) will arise if twoconditions are met. The � rst condition occurs when eitherthe matrix concentration is overestimated by the semi-quantitative scan or the actual matrix effect is smallerthan that predicted by the linear and additive TIL model.The second condition occurs when this scenario causesan error in prediction with respect to the desired accuracyor bound. Consider a hypothetical example where TILestimates 12% interference, while the experimental inter-ference is 8%. If the desired accuracy bound was 10%,this would cause a false positive error, while if the desiredaccuracy was 5%, it would be a true positive.

To consider a real example, in the TIL daily calibrationon the second day the TIL coef� cient for Cs interferentacting on Mg analyte was 2.93 3 1023 /ppm Cs, whilethat for Al acting on Mg was 1.98 3 1024 /ppm Al. In asolution with 270 ppm Al and 66 ppm Cs, the TIL pre-diction of interference is (270)(1.98 3 1024) 1 (66)(2.933 1023) 5 0.247. The observed interference was 0.087.Thus, the TIL coef� cients overestimated the matrix effectin this example, and if the desired accuracy was 10% thisresult would be a false positive.

A false negative (BAD) will arise if two conditions aremet. The � rst condition is that either the matrix concen-tration is underestimated by the semiquantitative scan orthe actual matrix effect is larger than that predicted bythe linear and additive TIL model. The second conditionrelates to the bound or desired accuracy, as just discussed.We will give an example when the TIL prediction is afalse negative, using the same experiment as above. TheTIL coef� cient for Na on Se was 8.57 3 1025 /ppm, whilethat for Al on Se was 1.75 3 1024 /ppm. In a solutionwith 230 ppm Na and 270 ppm Al, the TIL prediction is(230)(8.57 3 1025) 1 (270)(1.75 3 1024) 5 0.067. Ac-tually observed was an interference of 0.204, so for a10% desired accuracy, this is a false negative. In both ofthese examples, the error was caused by the TIL coef� -cients, since the interferent concentrations were known.

The results for external standards with initial calibra-tion are presented in Table IIIA, for a 10% desired ac-curacy or bound. The percentages in the table are derivedfrom (3 experiments) 3 (16 analytes) 3 (100 simulationsof 25% RSD error) for each of the 15 two-interferentcombinations in separate rows. Note that we divide theexperiments into two groups, 10 of which involve pairsof interferents and 5 that are single interferents at twicethe concentration used to determine the TIL parameters.This approach allows us to compare the two TIL as-


TABLE IIIA. Results of TIL predictions of accuracy for externalstandards calibration for � ve single interferents at double concen-tration (2 3 ), and the 10 pairwise combinations (XY) of these in-terferents . The TIL was calibrated the � rst day, and those valueswere used that day and in two subsequent days. Results are dis-played in terms of the fraction of time the prediction can beplaced in one of four classes: true positive and true negative,which add to GOOD; false positive, which is OK; and false nega-tive, which is BAD. The desired analytical accuracy was 10%.

Matrix truPOS truNEG GOOD OK BAD

CsBaAlKNaAVG(23)

95.7%100.0%58.0%87.4%70.1%82.3%

0.0%0.0%

12.8%0.0%4.5%3.5%

95.7%100.0%70.8%87.4%74.6%85.7%

4.2%0.0%

22.6%12.5%22.5%12.4%

0.1%0.0%6.6%0.1%2.8%1.9%

Cs1BaCs1AlCs1KCs1NaBa1Al

100.0%85.2%

100.0%74.9%99.8%

0.0%0.2%0.0%0.2%0.0%

100.0%85.4%

100.0%75.1%99.8%

0.0%14.4%0.0%

24.8%0.0%

0.0%0.2%0.0%0.1%0.3%

Ba1KBa1NaAl1KAl1NaK1NaAVG(XY)

100.0%99.9%83.4%78.1%89.3%91.0%

0.0%0.0%0.4%4.3%0.2%0.5%

100.0%99.9%83.8%82.4%89.5%91.6%

0.0%0.0%

12.1%14.5%10.2%7.6%

0.0%0.1%4.1%3.2%0.3%0.8%

TABLE IIIB. Average TIL prediction accuracy using externalstandards calibration with initial TIL calibration for the � ve sin-gle interferents at double concentration (2 3 ) and for the pair-wisecombinations (XY) displayed for 5, 10, and 20% accuracy bounds.

Matrix Bound truPOS truNEG GOOD OK BAD

AVG(23) 5%10%20%

91.5%82.3%50.4%

1.1%3.5%

16.7%

92.6%85.7%67.1%

6.4%12.4%25.4%

1.0%1.9%7.5%

AVG(XY) 5%10%20%

97.5%91.0%57.6%

0.0%0.5%

12.4%

97.5%91.6%69.9%

2.5%7.6%

24.7%

0.0%0.8%5.3%

FIG. 5. Illustration of how the scatter plot is converted into differentcategories of success (GOOD, BAD, OK) in analytical decision making.

TABLE IVA. Results of TIL predictions of accuracy for externalstandards calibration, with the TIL calibrated each day used, asdisplayed in Table IIIA. The desired accuracy was 10%.


CsBaAlKNaAVG(23)

94.9%100.0%51.5%85.5%65.2%79.4%

0.0%0.0%

19.6%5.0%8.6%6.7%

94.9%100.0%71.1%90.5%73.9%86.1%

4.2%0.0%

15.8%7.5%

18.5%9.2%

0.9%0.0%

13.1%2.0%7.7%4.8%


100.0%84.0%99.5%74.5%99.0%

0.0%1.0%0.0%1.3%0.0%

100.0%85.0%99.5%75.8%99.0%

0.0%13.6%0.0%

23.7%0.0%

0.0%1.5%0.5%0.5%1.0%


99.9%99.8%82.5%72.6%89.1%90.1%

0.0%0.0%4.8%7.9%5.6%2.1%

99.9%99.8%87.3%80.5%94.6%92.1%

0.0%0.0%7.7%

10.9%4.9%6.1%

0.1%0.2%5.0%8.7%0.5%1.8%

TABLE IVB. Average TIL prediction accuracy for external stan-dards calibration with the TIL calibrated each day used for the� ve single interferents at double concentration (2 3 ) and for thepair-wise combinations (XY) displayed for 5, 10, and 20% accura-cy bounds.


AVG(23) 5%10%20%

89.7%79.4%51.0%

1.6%6.7%

25.8%

91.3%86.1%76.9%

5.9%9.2%

16.2%

2.8%4.8%6.9%

AVG(XY) 5%10%20%

97.3%90.1%56.5%

0.1%2.1%

21.3%

97.4%92.1%77.7%

2.4%6.1%

15.8%

0.2%1.8%6.5%FIG. 4. Scatter plot presenting the experimentally measured interfer-

ence vs. the TIL prediction for external standards and initial calibration.

sumptions in the same experimental situation. The groupof 10 tests the interferent additivity assumption, while thegroup of 5 tests the linearity with interferent concentra-tion assumption. Our previous paper investigated this sec-ond TIL assumption by conducting experiments at dif-ferent interferent concentrations and found that makingthe assumption of linearity allowed simple parameteri-zation of a model that made reasonable calibration de-cisions. Thus, as we discuss the results, we will look at


FIG. 6. Scatter plot presenting the experimentally measured interfer-ence vs. the TIL prediction for external standards and daily calibration.

FIG. 7. Plot of sum of Li-Bi internally standardized interference foreach individual interferent (areas) compared to absolute interference oftwo-interferent solution (bars) for each of the 14 analytes, indicated bytheir mass. The three panels are three different experiments run on threedifferent days. The interferents are Cs and Ba.

these groups separately to see whether they behave sim-ilarly or differently, which will allow us to determinewhether multiple interferents pose more of a problemthan single ones.

In Table IIIB, we compare the accuracy of the TILpredictions for these two groups for bounds of 5, 10, and20%. The results seem quite good for low thresholds andseem to get poorer as the accuracy threshold is loosened.This is because our measure of GOOD includes both truepositives and true negatives, and at the 5% criterion, mostsamples are true positives and are correctly � agged assuch; i.e., they will not be accurately analyzed with ex-ternal calibration to the 5% level. There are few BADpredictions at the 5% level, since the model and the sam-ple are both over 5% interference. At the 20% level how-ever, there are fewer true positives, since the sample maybe analyzed to that level of accuracy with external cali-bration for some analytes. False positives occur, wherethe model overestimates the error, so that while the erroris under 20%, the model predicts over 20%, and recom-mends a better calibration. There are also more BAD pre-dictions at the 20% level, where BAD is a false negative,a prediction that the error would be under 20% when itwas over. Note the relative similarity between the singleinterferent and mixed interferent results in terms of pre-diction accuracy.

In Fig. 4 we display the scatter plot of experimentalresults vs. TIL prediction, which allows a visual under-standing of the variability. Each point in Fig. 4 representsan analyte in a separate experiment with one of 15 dif-ferent interferent combinations, assuming the known in-terferent concentrations in the TIL prediction, where theTIL coef� cients were obtained from the � rst-day exper-iment.

Figure 5 then shows how the analytical decision cat-egories GOOD, BAD, and OK are obtained from the cor-respondence between the TIL prediction and the experi-mental results.

What we have examined to this point is the analyticalideal, i.e., being able to test whether a routine defaultmethod would yield accurate results based on occasional

calibration. However, it seems possible from the exami-nation of Figs. 1–3 that same-day calibration would bebetter. In Fig. 6 we show the scatter plot of the experi-mental results vs. the TIL predictions for external stan-dards with daily calibration, while the results for the an-alytical decision making validation are presented in TableIV. The prediction error rate seems to be about the sameas it was for occasional calibration, suggesting that, fortesting external standards, occasional calibration couldsuf� ce. However, examination of the scatter plot for dailycalibration in Fig. 6, and comparing it to that for initialcalibration in Fig. 4, shows that such a conclusion is un-justi� ed, and probably fortuitous, since the scatter ismuch less for daily calibration.

One point to note from both of these results with ex-ternal calibration is that often when the sample could beanalyzed to the desired accuracy with external calibra-tion, TIL recommends a better calibration method. Therate of false positives (OK) can be compared to true neg-atives, and over half the time that the sample would beanalyzed correctly, the TIL recommends better calibra-tion. This shows that the TIL is conservative, and in-


FIG. 8. Same as Fig. 6, but with Cs and K as interferents.

FIG . 9. Same as Fig. 6, but with Na and K as interferents.

clined to overanalyze rather than underanalyze a sample,which means that it will often make OK (false positive)errors but does not make many BAD errors.

We now consider the use of internal standards, sinceICP-MS is often run with constant introduction of an in-ternal standard or standards. As in our previous work weconcentrated on a simple version of internal standards inthe context of the TIL, choosing a high mass and lowmass internal standard and interpolating between them.We selected Li and Bi as the two internal standards, sincethey were the highest and lowest mass elements in ourstudy. Inteferences can be reduced with internal standardsif the internal standard partially compensates for the ma-trix effect. In fact, we can compare the average interfer-ence of 16 analytes over the 15 dual interferent combi-nations. With external calibration the average interferencewas 24%, while with internal standardization, the averageinterference of 14 analytes was 10%. Thus, this simpleform of internal standardization reduced the average ma-trix effect by 58% (24%®10%) compared to the matrixeffect seen with external calibration. Figures 7–9 presentthe results of three runs done on three different days forBa1Cs, K1Cs, and Na1K interferents tested against thesingle interferents, similar to Fig. 1–3, but with internallystandardized signals. Table IB shows the fraction of re-sults where the single interferent predictions overestimatethe interference in the dual interferent solutions. Here theassumption is less often correct, with overestimation oc-

curring in only 64% of the cases, as opposed to 80% inTable IA.

The prediction accuracy results for internal standardswith initial calibration are presented in Table V. As be-fore, the error prediction rates are better for the pairs ofdifferent interferents than for single interferents at doubleconcentration, and, as in the previous paper, the internallystandardized prediction rates are in general not as accu-rate as the external calibration prediction rates. Again,this can be understood by considering that there are manyfewer true positives with internal standards (i.e., with in-ternal standards the result is more often adequate), but byrecommending internal standards as adequate, sometimeserrors are made, whereas external standards were rarelyrecommended as adequate by the TIL algorithm.

Finally, we consider daily calibration of TIL with in-ternal standards in Table VI. The daily calibration leadto a higher rate of GOOD predictions, but also a slightlyhigher rate of BAD predictions. Note from Figs. 7–9 that,generally, the matrix effect after internal standardizationseemed to be larger in the � rst experiment (top panel)than in subsequent experiments, so initial TIL calibrationtended to overestimate the matrix effect for subsequentruns. This led to many OK and not very many BADpredictions for initial calibration, while the daily calibra-tion, which was more accurate, lead to more GOOD sit-uations. However, since daily calibration did not over-


TABLE VA. Results of TIL predictions of accuracy for internalstandards calibration, with the TIL calibrated the � rst day used,as displayed in Table IIIA. The desired accuracy was 10%.


CsBaAlKNaAVG(23)

26.2%40.5%21.3%43.0%36.8%33.5%

21.7%20.0%31.6%30.7%36.5%28.1%

47.8%60.5%52.9%73.7%73.3%61.7%

49.8%39.5%30.3%5.0%

23.0%29.5%

2.4%0.0%

16.8%21.3%3.7%8.8%


38.0%15.9%55.5%30.9%38.0%

18.5%15.5%19.7%24.4%13.6%

56.5%31.4%75.1%55.3%51.6%

43.4%67.9%20.8%44.6%48.3%

0.1%0.8%4.0%0.1%0.1%


47.6%35.7%28.5%19.1%33.8%34.3%

19.2%21.5%40.1%37.5%32.0%24.2%

66.8%57.2%68.6%56.6%65.9%58.5%

30.8%42.8%26.6%38.7%18.0%38.2%

2.4%0.0%4.8%4.7%

16.2%3.3%

TABLE VB. Average TIL prediction accuracy with internalstandards calibration, with the TIL calibrated the � rst day usedfor the � ve single interferents at double concentration (2 3 ) andfor the pair-wise combinations (XY) displayed for 5, 10, and 20%accuracy.


AVG(23) 5%10%20%

52.9%33.5%12.8%

13.1%28.1%50.7%

66.0%61.7%63.5%

24.5%29.5%27.3%

9.5%8.8%9.1%

AVG(XY) 5%10%20%

59.3%34.3%9.1%

10.9%24.2%55.8%

70.1%58.5%65.0%

27.2%38.2%34.4%

2.6%3.3%0.6%

TABLE VIA. Results of TIL predictions of accuracy for internalstandards calibration, with the TIL calibrated each day used, asdisplayed in Table IIIA. The desired accuracy was 10%.


CsBaAlKNaAVG(23)

23.3%30.4%14.5%37.2%36.6%28.4%

61.5%49.1%45.6%26.1%39.8%44.4%

84.7%79.5%60.1%63.3%76.4%72.8%

10.0%10.4%16.3%9.6%

19.7%13.2%

5.3%10.1%23.6%27.1%3.9%

14.0%Cs1BaCs1AlCs1KCs1NaBa1Al

24.2%11.9%38.0%29.2%24.0%

51.0%57.5%30.6%49.4%45.5%

75.1%69.3%68.6%78.6%69.6%

11.0%25.9%9.9%

19.6%16.4%

13.9%4.8%

21.6%1.8%

14.1%Ba1KBa1NaAl1KAl1NaK1NaAVG(XY)

42.3%30.7%26.6%15.7%37.1%28.0%

40.8%39.0%49.6%46.1%29.5%43.9%

83.1%69.7%76.2%61.8%66.6%71.9%

9.2%25.2%17.1%30.0%20.5%18.5%

7.7%5.0%6.7%8.1%

12.9%9.7%

TABLE VIB. Average TIL prediction accuracy for internal stan-dards calibration, with the TIL calibrated each day used for the� ve single interferents at double concentration (2 3 ) and for thepair-wise combinations (XY) displayed for 5, 10, and 20% accura-cy.


AVG(23) 5%10%20%

50.6%28.4%12.1%

23.0%44.4%68.0%

73.6%72.8%80.0%

14.6%13.2%10.1%

11.8%14.0%

9.8%AVG(XY) 5%

10%20%

53.3%28.0%8.0%

17.5%43.9%77.7%

70.8%71.9%85.7%

20.6%18.5%12.5%

8.6%9.7%1.8%

estimate the matrix effect, there were situations where itwas insuf� ciently conservative, and hence it made wrongpredictions.

CONCLUSION

In this paper, we have continued the investigation ofthe TIL model in ICP-MS, testing it for pairs of inter-ferents, and comparing the effect with that from doublingthe concentration of single interferents. We have testedboth external calibration and internal standardization asa default calibration method and have considered occa-sional and daily calibration of the TIL parameters. In gen-eral, the TIL model assumption worked as well for mul-tiple interferences as it did for different concentrations ofa single interferent. This outcome is perhaps not surpris-ing, since in the previous single interferent work, we hadseen the nonlinear nature of the interference vs. concen-tration for single interferents. Thus, while the multipleinterferences are also nonlinear, in that 80% of the timethe sum of the two single interferences is bigger than thetotal interference of a two-interferent solution, this non-linearity still works in the context of the TIL model forcalibration recommendations.

One way to summarize the results is in terms of theamount of time that inaccurate calibration recommenda-tions will be made for a two-interferent solution whenthe desired accuracy is 10%. The four methods yieldBAD results 0.8% (initial calibration, external standards),

1.8% (daily calibration, external standards), 3.3% (initialcalibration, internal standards), and 9.7% (daily calibra-tion, internal standards) of the time. With external stan-dards, the decision being made is often easy (i.e., that thesolution cannot be analyzed with external standards ac-curately), while with internal standards, the system moreoften predicts that internal standards are adequate, and isless successful. Also, while it may seem that initial cal-ibration is better, in our experiments, the interferenceswere bigger on the � rst day than subsequent days, so theapparent superiority is fortuitous.

ACKNOWLEDGMENTS

The authors wish to thank the Natural Sciences and Engineering Re-search Council of Canada (NSERC), the National Research Council ofCanada (NRC), and SCIEX Canada for their � nancial support under theStrategic Grants Partnership Program, and Joseph Lam, Scott Tanner,and Michael Rybak for valuable discussions.

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Prediction of Multiple Matrix Interferences in Inductively Coupled Plasma Mass Spectrometry