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Multivariate detection limits for selected ion monitoring gas chromatography — mass spectrometry
Original
Research
Paper
l
Chemometrics and Intelligent Laboratory Systems, 3 (1988) 45-51 Elsevier
Science Publishers
B.V., Amsterdam
-
Printed
in The Netherlands
Multivariate Detection Limits for Selected Ion Monitoring Gas ChromatographyMass Spectrometry MICHAEL
F. DELANEY
Cambridge Analytical Associates, Inc., 1106 Commonwealth Avenue, Boston, MA 02215 (U.S.A.)
ABSTRACT
Delaney,
M.F., 1988. Multivariate
detection
limits for selected ion monitoring
gas chromatography-mass
spectrometry.
Chemometrics and Intelligent L&oratory Systems, 3: 45-51. A multivariate approach is developed for estimating detection limits for selected ion monitoring gas chromatography-mass spectrometry. This technique is directly based on the Hubaux-Vos technique which regresses instrument response onto concentration. The statistics of this regression are used to estimate the detection limit as the lowest true concentration which will, with high probability, be significantly different from a blank and therefore be considered a positive sample. The proposed multivariate approach forms a composite instrument response from all mass channels monitored using the first principal component. The instrument and method detection limits estimates using this approach are shown to be directly comparable to estimates obtained using the conventional univariate approach.
INTRODUCTION
This paper is focussed on an approach to multivariate detection limits (MVDL) which is tailored to analytical results obtained by gas chromatography with selected ion monitoring mass spectrometry (GC-MS-SIM). In this technique only a few mass channels are monitored at any given time [l]. The masses are carefully selected to coincide with the elution times and abundant ions of the compounds which have been selected for analysis. In a conventional GC-MS-SIM analysis, the primary ion data are used for quantitation, while the data for other ions monitored are used to confirm the identification of the target compound and to guard against inaccurate quantitation caused by chem0169-7439/88/$03.50
0 1988 Elsevier Science Publishers
B.V.
ical interferences (co-elution). This is done by ensuring that the ion chromatograms for each mass channel maximize simultaneously and that the relative magnitudes of the signals in each mass channel are in agreement with the relative ion abundances in the mass spectrum of the target compound. GC-MS-SIM data of the type described above can be considered as a special case of the more general “multiple sensor-multiple analyte” situation which has been examined in the chemomettics literature [2]. For multicomponent quantitation, principal components regression [3] and partial least squares [4] approaches have been utilized. In GC-MS-SIM, the confirmation criteria limit the number of compounds to the single target 45
#
Chemometrics and Intelligent Laboratory Systems
molecule. Also, all of the mass channels monitored respond well to the target compound. Our goal was to find an approach for quantitative analysis and detection limits estimation which would employ these multivariate GC-MS-SIM data as fully as possible. Ideally such an approach would not only make maximal use of the available data, but would also give performance that was
superior to the conventional univariate techniques. Other approaches to multivariate detection limits are also being pursued independently [5]. BACKGROUND
Quantitative determinations by GC-MS-SIM are performed using either an averaged response
3
/
,
I
954 Confidence
2
Y
I
/
I
Calibration Line
Largest Signal Consistent with a Concentration of Zero
DL 1
Largest Concentration Consistent with YDL
0 LDL Concentration
( ngl ml)
Fig. 1. Example of the Hubaux-Vos detection limits approach. The squares are individual measurements of standards or spiked samples. The double line is from a regression of instrument signal onto concentration. The dotted lines are the 95% confidence interval for the regression.
46
Original Research Paper
n
factor or a calibration curve which relates the instrumental response (peak area for the primary ion) to the concentration of the target compound. A careful examination of the pertinent analytical chemistry literature indicated that there were three detection limits approaches which warranted further examination. The Currie approach [6] is based on a characterization of the responses of the instrument or analytical method to blanks. In GC-MS-SIM, replicate analyses of many blanks are infeasible due to the lengthy time of the analysis and data processing. We have developed a Currie-type detection limit technique based on using noise-peak areas to characterize the blank response, but will not pursue the technique further here. The U.S. Environmental Protection Agency’s Contract Laboratory Program (CLP) detection limits approach [7] is based on the precision of analysis for low-level samples. The standard deviation of the results of analyzing seven low-concentration replicates is multiplied by the appropriate Student’s t value to give a detection limits estimate. Since this approach also requires a number of replicates, it is not recommended for use with GC-MS-SIM. The Hubaux-Vos (H-V) approach [8] is based on the statistics of a regression of the instrumental response onto the concentration of standards or spiked samples. The Hubaux-Vos method is also used in the U.S. Army Toxic and Hazardous Materials (UASTHAMA) program. In this approach the confidence interval for the regression is used to find the lowest concentration which is consistent with the largest instrument response expected from a blank (zero concentration) sample. This is shown graphically in Fig. 1. When the calibration standards are used in the regression, an instrument detection limit, or more correctly instrument detection concentration (IDC), is obtained. When spiked samples are used in the regression, a method detection limit, or method detection concentration (MDC), is obtained.
[8]. To obtain a MVDL, the instrument responses for all of the mass channels monitored could be combined in an optimal way resulting in a composite instrumental response. This composite response could be used in a H-V regression to yield the MVDL. To get a sense of what this composite response should look like, consider the plot of the instrumental responses (peak areas) for each mass channel for all the samples used to estimate the MVDL. Such a plot for hypothetical data is shown in Fig. 2. In this example three ions of the target compound are monitored resulting in three axes being needed to represent the measurements. If more ions were monitored, correspondingly more axes would be needed. The three peak areas for the target compound from one sample are represented as one point in this plot. In this example we have chosen to use three standards at three different concentrations, each analyzed in triplicate, for a total of nine points. The composite instrument response which best utilizes the information in the ion peak areas can be conveniently obtained by principal components analysis (PCA), one of the most important techniques in chemometrics [2]. The first principal component (PCl) is the line which best fits the data points in a least squares sense (minimizes the sum of squares of the residuals between the points and the line). PC1 is added to our example in Fig. 3. Each of the points if projected onto the line, resulting in a projection coordinate. In PCA this is
THEORY
Primary
The MVDL approach presented here can be considered as an extension of the H-V approach
Tertmry
Fig. 2. Typical multivariate GC-MS-SIM data. Each point corresponds to the instrument response (peak area) for each monitored ion. 47
n
Chemometrics
and Intelligent
Laboratory
Systems
Tertmry
Primary
Fig. 3. The first principal component best fits the measured data.
(PCl)
is the line which
often referred to as a “score” for this object on the first PC. The scores can be plotted against concentration, producing a PC calibration curve. Fitting a line to these scores versus concentration data yields a MVDL using the standard H-V procedure (as in Fig. 1).
EXPERIMENTAL
Capillary gas chromatograms of six chlorinated aromatic compounds and four internal standards were monitored by GC-MS-SIM. Three appropriate ions were monitored for each compound. The mass spectrometer’s quantitation software performed peak detection and integration for each mass channel monitored. Peak areas were read from the instrumental quantitation report. Internal standard corrections were made prior to performing PCA or Hubaux-Vos regression for estimating detection limits. For instrument detection limits, the samples consisted of dilutions of the calibration standards, having final concentrations of 1, 10, and 100 ng/ml. Each standard was analyzed in triplicate. For method detection limits, the samples consisted of spiked soil samples having spiked levels of 5, 20, and 50 ppb. Each spiked sample was processed through the entire analytical method in triplicate and then analyzed by GC-MS-SIM.
48
PCA was performed using the $PRINCO routine provided in RS/l Release 2 (BBN Software Products Corp., Cambridge, MA, U.S.A.). $PRINCO reported the scores for the first PC which were then used with a Fortranprogram which performed the Hubaux-Vos regression calculation. Graphics were performed by RS/l. PCA is a standard statistical tool and is available in many statistical software packages, such as SAS. The linear regression performed by the Fortran-77 program in this study is an implementation of a simple least squares calculation, as would be found in any calibration or curve-fitting program. In addition, the confidence intervals of the regression are needed, which is not routinely provided by most regression programs. Readers interested in the availability of this software should contact the author.
RESULTS
AND
DISCUSSION
Instrument detection concentrations IDCs are based on the analysis of standards. They tend to be significantly lower than MDCs because the sample matrix, which may contain interferences, is not present. Table shows the MVDL obtained using PCA as well as the univariate IDCs for the three ions monitored for each analyte. An IDC of 1 ng/ml corresponds to a concentration of 0.01 ppb in prepared samples. Essentially all of the systematic variation in the data is contained in the first PC. This is due to the high linearity and precision in the measurement technique. The first PC always accounted for more than 99% of the variation in the data. For this reason no other PCs were examined.
Method detection concentrations MDCs are estimated from the analysis of spiked samples. For this process to be successful, a sufficient, amount of homogeneous sample must be available. Also, the amount of analyte present in the unspiked samples must be comparable or lower than the amounts spiked into the samples. Table 2 shows PCA and univariate MDCs for triplicate
Original
TABLE
Compound
and univariate
X Variance
TABLE
instrument
detection
limits and the percent
PCA IDC (ng/mI)
Univariate
1.79 2.02 3.10 4.08 5.14 4.71
99.985 99.989 99.966 99.968 99.612 99.855
1 2 3 4 5 6
Based on triplicate
analyses
and
univariate
method
of spiked samples
detection
of the total variance
captured
in the first
IDC (ng/ml) .-.
primary
secondary
tertiary
2.10 2.18 3.41 4.70 8.44 4.68
1.88 2.32 6.85 3.27 8.61 5.19
2.73 2.64 1.93 8.33 7.13 8.31
limits
and
the percent
of the total
variance
captured
in the first
of 0, 5, 20, and 50 ppb.
Compound
% variance
PCA MDC (ppb)
1 2 3 4 5 6
99.985 99.999 99.988 99.990 99.955 99.921
13.1 6.8 8.8 5.4 17.4 15.7
Univariate
MDC (ppb)
primary
secondary
tertiary
7.9 6.8 6.0 5.4 10.4 9.6
12.9 6.8 6.9 5.2 13.2 12.2
8.3 6.9 9.3 5.6 13.4 14.8
slightly higher than the tertiary ion MDC. This indicates that the multivariate approach is responsive to variation in all three mass channels. The PCA MDC can be regarded as a composite detection limit.
analysis of samples spiked at the 0, 5, 20, and 50 ppb levels. Essentially all of the variation in the data is still explained by the first PC. For this experiment the PCA MDCs are seen to range being as low as the primary ion MDC to being
3
Comparison of multivariate principal component Based on triplicate Compound
2 3 4 5 6
n
2
Comparison of multivariate principal component
1
Paper
1
Comparison of multivariate principal component
TABLE
Research
analyses
and
method
of spiked samples
I Variance
99.992 99.999 99.995 99.971 99.974 99.810
univariate
detection
limits
and
the percent
of the total
variance
captured
in the first
at 0, 5, and 20 ppb.
PCA MDC (ppb)
5.7 2.1 3.7 1.5 13.1 2.7
Univariate
MDC (ppb)
primary
secondary
tertiary
2.5 2.1 1.9 1.5 5.3 1.8
5.7 2.1 2.6 1.5 5.8 2.7
2.5 2.1 3.8 1.8 8.2 5.5
49
n
Chemometrics and Intelligent Laboratory Systems
TABLE 4 Comparison of multivariate and univariate method detection limits and the percent of the total variance captured in the first principal component Based on triplicate analyses of spiked samples at 5, 20, and 50 ppb. Compound
1 2 3 4 5 6
% Variance
99.985 99.998 99.988 99.986 99.955 99.921
PCA MDC (ppb)
13.1 11.2 8.8 8.9 17.4 15.7
Univariate MDC (ppb) Primary
secondary
tertiary
12.9 11.2 8.6 8.9 10.4 9.6
12.9 11.2 8.4 8.6 18.1 16.8
13.5 11.4 9.3 9.3 13.4 14.8
Choice of spiking levels
Unconfirmed detection
As with the univariate H-V approach, the multivariate results are very sensitive to the actual spiking levels used in the experiment. This is demonstrated by comparing Tables 2 and 3. In Table 2, results are given for triplicate spikes at 0, 5, 20, and 50 ppb. When the 50 ppb data are not included (Table 3), the MVDL estimates typically decrease by a factor of 2-3. The same trend is seen in the univariate results. This implies that obtaining low detection limit estimates can be achieved only by making measurements at very low concentrations.
To obtain the lowest possible detection limits requires collecting data at the lowest possible concentrations. The analysis uses several confirmation checks to guard against using the wrong peak (retention time, ion abundance ratios, etc.). At some point the GC-MS-SIM instrument is not able to completely confirm the identity of the peak. Should this result be used in the detection limit calculation? It may be caused by a chemical interferent rather than the target compound. The tendency of the mass spectrometrist is to only use data that have passed all of the confirmation checks. To obtain a low detection limit, data at the lowest possible concentration are needed. The multivariate approach seems to offer a compromise on this issue, since data from all of the monitored ions are included in the detection limits calculation. Low concentration data will have more variability, especially for the less abundant ions, which will broaden the confidence intervals on the H-V regression curve and keep the detection limit from falling too low. Perhaps the way to conduct the experiment is to keep spiking the sample at the progessively lower concentrations until the estimate of the detection limit stops decreasing.
The importance
of blanks
The analysis of blanks (unspiked samples) in the detection limits experiment can also be important. This can be seen by comparing Tables 2 and 4 which is based on results from the analysis of triplicate spikes at 0, 5, 20, and 50 ppb. Table 4 shows what happens to the MDCs when the data for unspiked samples are not used. The results for four of the compounds do not change because those compounds did not have detectable amounts in the unspiked samples. For the other two compounds, the MDC increased by about 60%. Based on these results, it seems advisable to ensure that the effort to obtain quantitative results for target compounds in the unspiked samples is as diligent as for the spiked samples. 50
ACKNOWLEDGEMENTS
The Andrew
author acknowledges Schkuta for providing
Scott Drew and the GC-MS-SIM
Original
data and thanks Bruce Peterson and Forest Gamer for helpful discussions.
REFERENCES 1 W.V. Ligon Jr. and R.J. May, Determination of selected chlorodibenzofurans and chlorodibenzodioxins using two-dimensional gas chromatography/mass spectrometry, Anolyficul Chemistry, 58 (1986) 558-561. 2 M.F. Delaney, Chemometrics, Analyticul Chemistry, 54 (1984) 261R-277R. 3 C.-N. Ho, G.D. Christian and E.R. Davidson, Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons,
Research
Paper
n
Analytical Chemistry, 52 (1980) 1071-1079. 4 W. Lindberg, J.-A. Persson and S. Wold, Partial least-squares method for spectrofluorimetric analysis of mixtures of humic acid and lignin sulfonate, Analytical Chemistry, 55 (1983) 643-648. Evaluation of detection 5 F.C. Garner and G.L. Robertson, limit estimators, Chemometrics and Intelligent Laboratory Systems, 3 (1988) 53-59. 6 L.A. Currie, Limits for qualitative detection and quantitative determination, Analytical Chemistry, 40 (1968) 586-593. I J.A. Glaser, D.L. Foerst, G.D. McKee, S.A. Quave and W.L. Budde, Trace analysis for wastewaters, Environmental Science and Techntilogv, 15 (1981) 1426-1435. 8 A. Hubaux and G. Vos, Decision and detection limits for linear calibration curves, Analytical Chemistry, 42 (1970) 849-855.
51
Research
Paper
l
Chemometrics and Intelligent Laboratory Systems, 3 (1988) 45-51 Elsevier
Science Publishers
B.V., Amsterdam
-
Printed
in The Netherlands
Multivariate Detection Limits for Selected Ion Monitoring Gas ChromatographyMass Spectrometry MICHAEL
F. DELANEY
Cambridge Analytical Associates, Inc., 1106 Commonwealth Avenue, Boston, MA 02215 (U.S.A.)
ABSTRACT
Delaney,
M.F., 1988. Multivariate
detection
limits for selected ion monitoring
gas chromatography-mass
spectrometry.
Chemometrics and Intelligent L&oratory Systems, 3: 45-51. A multivariate approach is developed for estimating detection limits for selected ion monitoring gas chromatography-mass spectrometry. This technique is directly based on the Hubaux-Vos technique which regresses instrument response onto concentration. The statistics of this regression are used to estimate the detection limit as the lowest true concentration which will, with high probability, be significantly different from a blank and therefore be considered a positive sample. The proposed multivariate approach forms a composite instrument response from all mass channels monitored using the first principal component. The instrument and method detection limits estimates using this approach are shown to be directly comparable to estimates obtained using the conventional univariate approach.
INTRODUCTION
This paper is focussed on an approach to multivariate detection limits (MVDL) which is tailored to analytical results obtained by gas chromatography with selected ion monitoring mass spectrometry (GC-MS-SIM). In this technique only a few mass channels are monitored at any given time [l]. The masses are carefully selected to coincide with the elution times and abundant ions of the compounds which have been selected for analysis. In a conventional GC-MS-SIM analysis, the primary ion data are used for quantitation, while the data for other ions monitored are used to confirm the identification of the target compound and to guard against inaccurate quantitation caused by chem0169-7439/88/$03.50
0 1988 Elsevier Science Publishers
B.V.
ical interferences (co-elution). This is done by ensuring that the ion chromatograms for each mass channel maximize simultaneously and that the relative magnitudes of the signals in each mass channel are in agreement with the relative ion abundances in the mass spectrum of the target compound. GC-MS-SIM data of the type described above can be considered as a special case of the more general “multiple sensor-multiple analyte” situation which has been examined in the chemomettics literature [2]. For multicomponent quantitation, principal components regression [3] and partial least squares [4] approaches have been utilized. In GC-MS-SIM, the confirmation criteria limit the number of compounds to the single target 45
#
Chemometrics and Intelligent Laboratory Systems
molecule. Also, all of the mass channels monitored respond well to the target compound. Our goal was to find an approach for quantitative analysis and detection limits estimation which would employ these multivariate GC-MS-SIM data as fully as possible. Ideally such an approach would not only make maximal use of the available data, but would also give performance that was
superior to the conventional univariate techniques. Other approaches to multivariate detection limits are also being pursued independently [5]. BACKGROUND
Quantitative determinations by GC-MS-SIM are performed using either an averaged response
3
/
,
I
954 Confidence
2
Y
I
/
I
Calibration Line
Largest Signal Consistent with a Concentration of Zero
DL 1
Largest Concentration Consistent with YDL
0 LDL Concentration
( ngl ml)
Fig. 1. Example of the Hubaux-Vos detection limits approach. The squares are individual measurements of standards or spiked samples. The double line is from a regression of instrument signal onto concentration. The dotted lines are the 95% confidence interval for the regression.
46
Original Research Paper
n
factor or a calibration curve which relates the instrumental response (peak area for the primary ion) to the concentration of the target compound. A careful examination of the pertinent analytical chemistry literature indicated that there were three detection limits approaches which warranted further examination. The Currie approach [6] is based on a characterization of the responses of the instrument or analytical method to blanks. In GC-MS-SIM, replicate analyses of many blanks are infeasible due to the lengthy time of the analysis and data processing. We have developed a Currie-type detection limit technique based on using noise-peak areas to characterize the blank response, but will not pursue the technique further here. The U.S. Environmental Protection Agency’s Contract Laboratory Program (CLP) detection limits approach [7] is based on the precision of analysis for low-level samples. The standard deviation of the results of analyzing seven low-concentration replicates is multiplied by the appropriate Student’s t value to give a detection limits estimate. Since this approach also requires a number of replicates, it is not recommended for use with GC-MS-SIM. The Hubaux-Vos (H-V) approach [8] is based on the statistics of a regression of the instrumental response onto the concentration of standards or spiked samples. The Hubaux-Vos method is also used in the U.S. Army Toxic and Hazardous Materials (UASTHAMA) program. In this approach the confidence interval for the regression is used to find the lowest concentration which is consistent with the largest instrument response expected from a blank (zero concentration) sample. This is shown graphically in Fig. 1. When the calibration standards are used in the regression, an instrument detection limit, or more correctly instrument detection concentration (IDC), is obtained. When spiked samples are used in the regression, a method detection limit, or method detection concentration (MDC), is obtained.
[8]. To obtain a MVDL, the instrument responses for all of the mass channels monitored could be combined in an optimal way resulting in a composite instrumental response. This composite response could be used in a H-V regression to yield the MVDL. To get a sense of what this composite response should look like, consider the plot of the instrumental responses (peak areas) for each mass channel for all the samples used to estimate the MVDL. Such a plot for hypothetical data is shown in Fig. 2. In this example three ions of the target compound are monitored resulting in three axes being needed to represent the measurements. If more ions were monitored, correspondingly more axes would be needed. The three peak areas for the target compound from one sample are represented as one point in this plot. In this example we have chosen to use three standards at three different concentrations, each analyzed in triplicate, for a total of nine points. The composite instrument response which best utilizes the information in the ion peak areas can be conveniently obtained by principal components analysis (PCA), one of the most important techniques in chemometrics [2]. The first principal component (PCl) is the line which best fits the data points in a least squares sense (minimizes the sum of squares of the residuals between the points and the line). PC1 is added to our example in Fig. 3. Each of the points if projected onto the line, resulting in a projection coordinate. In PCA this is
THEORY
Primary
The MVDL approach presented here can be considered as an extension of the H-V approach
Tertmry
Fig. 2. Typical multivariate GC-MS-SIM data. Each point corresponds to the instrument response (peak area) for each monitored ion. 47
n
Chemometrics
and Intelligent
Laboratory
Systems
Tertmry
Primary
Fig. 3. The first principal component best fits the measured data.
(PCl)
is the line which
often referred to as a “score” for this object on the first PC. The scores can be plotted against concentration, producing a PC calibration curve. Fitting a line to these scores versus concentration data yields a MVDL using the standard H-V procedure (as in Fig. 1).
EXPERIMENTAL
Capillary gas chromatograms of six chlorinated aromatic compounds and four internal standards were monitored by GC-MS-SIM. Three appropriate ions were monitored for each compound. The mass spectrometer’s quantitation software performed peak detection and integration for each mass channel monitored. Peak areas were read from the instrumental quantitation report. Internal standard corrections were made prior to performing PCA or Hubaux-Vos regression for estimating detection limits. For instrument detection limits, the samples consisted of dilutions of the calibration standards, having final concentrations of 1, 10, and 100 ng/ml. Each standard was analyzed in triplicate. For method detection limits, the samples consisted of spiked soil samples having spiked levels of 5, 20, and 50 ppb. Each spiked sample was processed through the entire analytical method in triplicate and then analyzed by GC-MS-SIM.
48
PCA was performed using the $PRINCO routine provided in RS/l Release 2 (BBN Software Products Corp., Cambridge, MA, U.S.A.). $PRINCO reported the scores for the first PC which were then used with a Fortranprogram which performed the Hubaux-Vos regression calculation. Graphics were performed by RS/l. PCA is a standard statistical tool and is available in many statistical software packages, such as SAS. The linear regression performed by the Fortran-77 program in this study is an implementation of a simple least squares calculation, as would be found in any calibration or curve-fitting program. In addition, the confidence intervals of the regression are needed, which is not routinely provided by most regression programs. Readers interested in the availability of this software should contact the author.
RESULTS
AND
DISCUSSION
Instrument detection concentrations IDCs are based on the analysis of standards. They tend to be significantly lower than MDCs because the sample matrix, which may contain interferences, is not present. Table shows the MVDL obtained using PCA as well as the univariate IDCs for the three ions monitored for each analyte. An IDC of 1 ng/ml corresponds to a concentration of 0.01 ppb in prepared samples. Essentially all of the systematic variation in the data is contained in the first PC. This is due to the high linearity and precision in the measurement technique. The first PC always accounted for more than 99% of the variation in the data. For this reason no other PCs were examined.
Method detection concentrations MDCs are estimated from the analysis of spiked samples. For this process to be successful, a sufficient, amount of homogeneous sample must be available. Also, the amount of analyte present in the unspiked samples must be comparable or lower than the amounts spiked into the samples. Table 2 shows PCA and univariate MDCs for triplicate
Original
TABLE
Compound
and univariate
X Variance
TABLE
instrument
detection
limits and the percent
PCA IDC (ng/mI)
Univariate
1.79 2.02 3.10 4.08 5.14 4.71
99.985 99.989 99.966 99.968 99.612 99.855
1 2 3 4 5 6
Based on triplicate
analyses
and
univariate
method
of spiked samples
detection
of the total variance
captured
in the first
IDC (ng/ml) .-.
primary
secondary
tertiary
2.10 2.18 3.41 4.70 8.44 4.68
1.88 2.32 6.85 3.27 8.61 5.19
2.73 2.64 1.93 8.33 7.13 8.31
limits
and
the percent
of the total
variance
captured
in the first
of 0, 5, 20, and 50 ppb.
Compound
% variance
PCA MDC (ppb)
1 2 3 4 5 6
99.985 99.999 99.988 99.990 99.955 99.921
13.1 6.8 8.8 5.4 17.4 15.7
Univariate
MDC (ppb)
primary
secondary
tertiary
7.9 6.8 6.0 5.4 10.4 9.6
12.9 6.8 6.9 5.2 13.2 12.2
8.3 6.9 9.3 5.6 13.4 14.8
slightly higher than the tertiary ion MDC. This indicates that the multivariate approach is responsive to variation in all three mass channels. The PCA MDC can be regarded as a composite detection limit.
analysis of samples spiked at the 0, 5, 20, and 50 ppb levels. Essentially all of the variation in the data is still explained by the first PC. For this experiment the PCA MDCs are seen to range being as low as the primary ion MDC to being
3
Comparison of multivariate principal component Based on triplicate Compound
2 3 4 5 6
n
2
Comparison of multivariate principal component
1
Paper
1
Comparison of multivariate principal component
TABLE
Research
analyses
and
method
of spiked samples
I Variance
99.992 99.999 99.995 99.971 99.974 99.810
univariate
detection
limits
and
the percent
of the total
variance
captured
in the first
at 0, 5, and 20 ppb.
PCA MDC (ppb)
5.7 2.1 3.7 1.5 13.1 2.7
Univariate
MDC (ppb)
primary
secondary
tertiary
2.5 2.1 1.9 1.5 5.3 1.8
5.7 2.1 2.6 1.5 5.8 2.7
2.5 2.1 3.8 1.8 8.2 5.5
49
n
Chemometrics and Intelligent Laboratory Systems
TABLE 4 Comparison of multivariate and univariate method detection limits and the percent of the total variance captured in the first principal component Based on triplicate analyses of spiked samples at 5, 20, and 50 ppb. Compound
1 2 3 4 5 6
% Variance
99.985 99.998 99.988 99.986 99.955 99.921
PCA MDC (ppb)
13.1 11.2 8.8 8.9 17.4 15.7
Univariate MDC (ppb) Primary
secondary
tertiary
12.9 11.2 8.6 8.9 10.4 9.6
12.9 11.2 8.4 8.6 18.1 16.8
13.5 11.4 9.3 9.3 13.4 14.8
Choice of spiking levels
Unconfirmed detection
As with the univariate H-V approach, the multivariate results are very sensitive to the actual spiking levels used in the experiment. This is demonstrated by comparing Tables 2 and 3. In Table 2, results are given for triplicate spikes at 0, 5, 20, and 50 ppb. When the 50 ppb data are not included (Table 3), the MVDL estimates typically decrease by a factor of 2-3. The same trend is seen in the univariate results. This implies that obtaining low detection limit estimates can be achieved only by making measurements at very low concentrations.
To obtain the lowest possible detection limits requires collecting data at the lowest possible concentrations. The analysis uses several confirmation checks to guard against using the wrong peak (retention time, ion abundance ratios, etc.). At some point the GC-MS-SIM instrument is not able to completely confirm the identity of the peak. Should this result be used in the detection limit calculation? It may be caused by a chemical interferent rather than the target compound. The tendency of the mass spectrometrist is to only use data that have passed all of the confirmation checks. To obtain a low detection limit, data at the lowest possible concentration are needed. The multivariate approach seems to offer a compromise on this issue, since data from all of the monitored ions are included in the detection limits calculation. Low concentration data will have more variability, especially for the less abundant ions, which will broaden the confidence intervals on the H-V regression curve and keep the detection limit from falling too low. Perhaps the way to conduct the experiment is to keep spiking the sample at the progessively lower concentrations until the estimate of the detection limit stops decreasing.
The importance
of blanks
The analysis of blanks (unspiked samples) in the detection limits experiment can also be important. This can be seen by comparing Tables 2 and 4 which is based on results from the analysis of triplicate spikes at 0, 5, 20, and 50 ppb. Table 4 shows what happens to the MDCs when the data for unspiked samples are not used. The results for four of the compounds do not change because those compounds did not have detectable amounts in the unspiked samples. For the other two compounds, the MDC increased by about 60%. Based on these results, it seems advisable to ensure that the effort to obtain quantitative results for target compounds in the unspiked samples is as diligent as for the spiked samples. 50
ACKNOWLEDGEMENTS
The Andrew
author acknowledges Schkuta for providing
Scott Drew and the GC-MS-SIM
Original
data and thanks Bruce Peterson and Forest Gamer for helpful discussions.
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