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Ion band multicomponent resolution method
International Journal of Mass Spectrometry and Ion Processes, 120 (1992)
117-127 117
ElsevierSciencePublishersB.V.,Amsterdam
Ion band multicomponent
resolution method
Anatole Lokshin The Perkin-Elmer Corporation, Applied Science Operation, 2771 North Garey Avenue, Pomona CA 91767 (USA)
(Received 5 March 1992)
ABSTRACT A new gas chromatography-mass spectrometry (GC-MS) data reduction method for resolving coeluting components is developed. The method does not require each component to possess a unique ion but instead relies on a band of ions common to all compounds. The paper provides an expression for band size as a function of signal-to-noise ratio, ion mass numbers, and relative scan rate. The ion band method provides a unified view of the selected ion monitoring technique for GC-MS and the least squares methods for mass spectrometry. Keywords: gas chromatography; method.
mass spectrometry; multimixture separation; least-squares; single-ion
INTRODUCTION Gas chromatography-mass spectrometry GC-MS technology has found wide application in chemical analysis owing to its ability to separate different components, not only by their characteristic mass spectra but also in time. As a result, components with similar mass spectra are separated in time to such a degree that the selected ion monitoring (SIM) method can be used. Unfortunately, it is quite common for complex mixtures to have no unique ions of sufficient intensities to be used for resolving the coeluting components using the SIM algorithm. If component concentrations remain constant during the whole mass scan then a least squares (LS) method of multicomponent resolution can be used [l]. The LS method is commonly used in mass spectroscopy [2]. In contrast to the SIM method, the LS approach uses several masses obtained in one scan to resolve unknown compounds. However, the elution time separation achieved in the chromatography has its price to pay. When the mass scan time is comparable with the GC peak width at half height (PWHH), component concentrations vary significantly during one scan. This prevents the use of the LS technique. to: A. Lokshin, The Perkin-Elmer Corporation, Garey Avenue, Pomona CA 91767, USA.
Correspondence
2771 North
0168-l 176/92/$05.00
0
1992 Elsevier Science Publishers
Applied
Science Operation,
B.V. All rights reserved.
118
A. Lokshinllnt.
J. Mass Spectrom. Ion Processes 120 (1992) 117-127
This paper describes a new GC-MS data reduction method that allows resolution of coeluting components even when there are no unique ions among them. Separation is achieved by simultaneously monitoring several ions with neighboring mass numbers and then resolving a corresponding system of linear equations for each scan. The method’s precision is discussed and its application is illustrated via computer simulation and with an example from the space station air composition monitoring (ACM) GC-MS system. METHOD
In the conventional SIM method the intensities of a set of ions are monitored for each mass spectrometer scan. Each of these ions uniquely represents a particular coeluting component. Let the jth component in a mixture have a characteristic ion with mass M;. that is unique for this component. Then the component’s concentration at time t can be determined as
Here yM,(t) is an observed ion intensity at mass Mj and time ~~~(44~)is the ratio of the nominal intensity of the mass M;. and the base peak for the jth component, and sj is the component’s sensitivity in terms of counts per peak intensity. For notational simplicity we assume that sj = 1 for all components. The resulting intensity-time curve, Cj(t), is integrated to obtain the total component concentration. To improve the accuracy a gaussian curve can be fitted to the computed set {cj(ts)> [3], where s = 1 . . . N stands for scan number. Instead of using a set of unique ions, the ion band method described here employs a narrow band of ions with neighboring mass numbers to characterize the target compound set. Owing to their proximity in the mass spectrum these ions are measured at about the same time. Therefore, there is no significant change in the component concentrations during the time needed to measure the whole band. As a result, a multicomponent resolution can be performed for this narrow band of ions for each sc.an. These solutions provide concentration-time curves (cj(t,)} for each individual component in the mixture similar to those obtained with the SIM method. These curves can be treated in the same way to those obtained by the SIM method. To illustrate the technique, let an unresolved GC peak be composed of components A, B, and C which do not have unique ions, but have common ions with masses k, k + 1, and k + 2. Since these masses are obtained at about the same time we can assume that component concentrations cA, cg, and cc are constant during all three measurements. Therefore, for each scan, s, the
A. Lokshinllnt.
J. Mass Spectrom. Ion Processes 120 (1992) 117-127
119
following system of linear equations can be formulated: Y(&) = X * 44)
(2)
Here vector I corresponds to the observed ion intensities for the corresponding masses and X denotes a matrix of the nominal mass ratios with sensitivity taken into account. System 2 has a full rank and therefore can be resolved to obtain cA(ts), cg(ts), and cc(t,) at each scan. In vector notation: c = x-‘y
(3)
It is clear that various modifications of system 2 are available. For example, if only two components A and B have three common ions of mass k, k + 1, and k + 2, then equations can be resolved by an LS method where X-’ is replaced by a pseudo inverse X + . Another possible situation is when common ions are not sequential but have small separations between them. In this case the principle parameter of the method, the total size K of the band, is larger than the number of ions used in system 2. If masses k, , . . . , k, are used, then the band size K is K=k,-k,+l
(4)
With K = 1 the ion band method becomes a conventional SIM algorithm and with K equal to the total dimension of the mass spectrum, M, the method becomes the LS technique used in mass spectroscopy. The value of K is limited by a requirement that the component concentrations do not change too much between the instants when the masses k, and k,, are detected. The next section describes how a maximum allowable band size, K, can be determined from a desired signal-to-noise ratio (SNR). LIMITATION
ON THE BAND SIZE
The GC elution peaks can be generally approximated [41: c(t) = co * ew (- W - W/Bl’>
by a gaussian curve (5)
where T, is the retention time of the component and fl is a characteristic time scale. In the traditional PWHH units /3 = PWHH/2 (In 2)‘/*. By differentiating eqn. 5 one gets a concentration change rate de/c,=
-2r*exp(-z’).dz
(6)
where r N (t - T,)//?. It is easy to show that the maximum of eqn. 6 is achieved at z P (l/2) ‘I2 . Therefore, the maximum possible change in concentration during time period At is max (ldc/c, I) = (2)‘12- ,-‘I2 dz = (2)“2 - e-“‘At//?
(7)
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
120
For example, for ion energy-scanned magnetic mass spectrometers the time difference between the instants when the masses k, and k,, are detected is At = T,log,,(k,lk,)
(8)
where T, is the time required for one decade scan. By substituting eqns. 5 and 8 into eqn. 7 we obtain the maximal concentration change for a band of size K: max (6) = 0.37(T,/j)
l
In (1 + (K - 1)/k,)
(9a)
where 6 N Idc/c, 1. For linearly-scanning spectrometers At = (K - 1) T,/M, where M is the total number of channels to be scanned during time T,. Correspondingly: l
max (6) = (2)‘j2 * e-II2 * T,//l* (K - 1)/M
(9b)
The maximum admissible change in concentration, a,,,,,, can be related to a desired SNR, since the error resulting from the change in concentration across the band can be regarded as an additional “noise”, a. Indeed, by replacing c in eqn. 2 with c * (1 + S) we obtain: y = (1 + S) * xc = xc + s * xc = xc + & Therefore, the SNR becomes smaller owing to the concentration across the band: SNR = S&N, + 6 . S,) = SNR,,/( 1 + 6 SNR,) l
(10)
averaging (11)
If one desires to keep the SNR above some minimal level of SN~i” then from eqn. 11: 6 < (SNR, - SNRmi,)/(SNR, . SNR,i,) = 8SNR/SNR,i” II 6,,,
(12)
By substituting 6,,, into eqns. 9a and 9b we obtain a direct relation between the maximum band size, K, and the maximum allowable signal degradation, 6mm** K <
1 + 2.703 * k, . (/l/T,)
K<
1 + 1.166*M*(/.I/T,)*6,,,
l
d,,,
(134
(13b)
For example, let a mass spectrometer to scan exponentially a decade between masses 25 and 250 in 2 s. Let the characteristic PWHH for the same GC peak be 12 s. Then for a three-ion band located at masses 25, 26, and 27, 6 can be computed according to eqn. 9a as 6 = 0.03 1. Assuming that the original SNR at these masses is 10 we obtain, according to eqn. 11,24% SNR degradation. The same band located at masses 248, 249, and 250 leads to only 0.0031 relative concentration error and, correspondingly, to 3% SNR degradation at SNR = 10.
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
121
Equations 13 show that the SIM method and the LS approach are particular cases of the ion band monitoring method described here. Indeed, for static mass spectrometry concentration is constant during one scan. Mathematically it is equivalent to /? + co. Therefore, from eqns. 13 the band size can encompass the whole mass spectrum without any loss in SNR. However, if the scan time becomes large compared with the GC peak width, b/T’ + 0, or no SNR degradation can be tolerated, 6,,, --) 0, then, according to eqn. 13, K + 1, which corresponds to the SIM method. Equation 11 shows that the relative signal degradation depends on the strength of the initial signal. This puts an additional constraint on band selection. The ion intensities in the selected band must be strong enough to prevent significant error in the concentration estimate. This is reflected in eqn. 13. Note that, since there are usually many more bands available for analysis than there are unique ions, the ion band method generates more concentration curve points than are available with the SIM. Consequently, the accuracy of the total concentration determination may be higher. This makes the ion band method a strong competitor with the SIM method even in cases when unique ions are available. An additional improvement in accuracy can come from global curve fitting. Indeed, if the pure component chromatogram has a known shape, then after curve fitting the total average error, 6, is reduced about 1/N’j2 times, where N is the number of points of similar intensity used for the fit. Assuming that only the points inside the PWHH are used for the fitting: N x 1.678/T,. By substituting into eqn. 13 we obtain less restrictive bounds on K K < 1 + 1.62 k, - (j3/7’J”2 - d,,, l
K <
1 + 0.7 - A4 (p/Ty l
l
6,,,
(W (14b)
Note that eqns. 14 are approximate since the actual signal strength varies for different scans. EXPERIMENTAL
The algorithm described above has been tested via computer simulation and with actual GC-MS data for the trace contaminant monitor (TCM) system at Perk&Elmer ASO. For the TCM system description see ref. 5. Computer simulations are added to illustrate the algorithm’s performance independent of measurement noise. Computer simulation The computer simulation used propadiene and methyl acetylene. Their standard mass spectra, taken from the NBS library, are listed in Table 1. The
122
A. Lokshin/lnt.
J. Mass Speclrom. Ion Processes 120 (1992) 117-127
TABLE 1 NBS fragmentation
spectra
Compound
Propadiene Methyl acetylene
Mass number 25
26
39
40
41
45 38
41 31
946 182
999 999
23 30
components’ retention times, T,, , were determined on a Perkin-Elmer GCMS system. The component mass spectra are very similar and there are no unique ions. The retention time separation is 5s which is not enough to separate two GC peaks with PWHH values of 12 s each. However, one scan duration is 2 s which is comparable with the PWHH value-namely, a concentration change during one scan time can be quite significant. Therefore, a conventional SIM method cannot resolve these components. However, these components can be resolved using the ion band method described above. There is a band [25,26] of size K = 2, and a band [39-411 of size K = 3. Mass 40, characteristic of argon, is not used to demonstrate a “sparse” band case. The data were simulated with concentrations of propadiene and methyl acetylene of 50ppm and 250ppm respectively. The GC peak profile was assumed to be gaussian with j3 = 7.2 s and retention times differing by 5 s. The mass scan rate was set to 2 s per decade. Figure 1 provides “true” component GC peak profiles (broken curves) as well as the total ion current (TIC) for both components (solid curve). The TIC curve does not give any visual indication that there is a mix of two components. Figure 2 shows how the ion band method resolves concentration-time curves for both components. The solid lines correspond to band 1 (masses 25 and 26) and the broken lines correspond to band 2 (masses 39 and 41). Figure 3 shows the result of the ion band method when 1% random noise was added to the observations. Table 2 summarizes estimation errors (using peak maximum) observed during simulation. The first line for each component gives an estimated error which is purely due to change in concentration inside the band; the second line gives the r.m.s. error with 1% noise. TCM GC-MS DATA
The ion band method has been used to analyze actual GC-MS data collected from the TCM. The compounds used in the test were the p-xylene and ethylbenzene isomers. (This work was reported in ref. 5.) The common base peak of the isomers is at mass 91; however, both compounds have masses 105 and 106 which can be used as an ion band. The relative abundances at
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
123
Total Ion Current 300,
Time in set
Fig.
1.
Ion Band Dcconvolution
: no noise
-
200-
E 8 .E
150-
.I
loo-
! u
using Band 1
50 -
o-
-50 ’ 0
2
4
6
8
10 Scan number
Fig. 2.
12
14
16
18
2c
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
124
Ion Band Deconvolution : 40 db noise
250 -
200E B 5 .s 3 z8
150 -
loo-
g u 50 -
O-501
I
0
2
4
6
8
10
12
14
16
18
20
Scan number Fig. 3.
these masses as determined by the TCM are 16% and 27% for p-xylene and 3% and 31% for ethylbenzene. The first experiment used concentrations of 2.27 ppm for p-xylene and 2.5 1 ppm for ethylbenzene. Shown in Fig. 4 is the reconstructed total ion chromatogram (RTIC) for the coeluting isomers. The PWHH of the peak is approximately 12 s, which is about 3 s wider than that measured for a single peak of either component. The reconstructed ion chromatograms (RIC) for masses 105 and 106 for the same sample are shown in Fig. 5. The data were analyzed by the ion band method and the result of the deconvolution is illustrated in Fig. 6. The resulting errors in concentration determinations are 7% for p-xylene and 14% for ethylbenzene respectively. TABLE
2
Ion band prediction
errors (%)
Compound
Band 1 (K=2)
Band 2 (K=3)
Average of both bands
Propadiene (With noise) Methyl acetylene (With noise)
6.1 21.3 1.02 7.1
5.95 11.1 0.67 3.2
0.1 13.6 0.8 3.8
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
125
RECONSTRUCTED TOTAL ION CHROMATOGRAM 50, 45 40Sample Mix: 35 -
Ethylbenzene + p-Xylcne (2.51 ppm) (2.27 ppm)
30 2520 15 10 50 125
130
135
140
145
150
155
SCAN NO. Fig. 4.
RECONSTRUCTED ION CHROMATOGRAMS
Sample Mix: Ethylbenzene + p-Xylene (2.51 ppm) (2.27 ppm)
SCAN NO. Fig. 5.
18D
126
A. Lokshin/lnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127 COMPONENT RBSOLUTION BY ION BAND METHOD
p-XYLENE
: ETHYLBBNZENE 1.5 :
: :
/
l-
Actual Concentrations: Ethylbenzene - 2.51 ppm
1
-0.5 12.5
130
135
140
145
150
155
160
SCAN NUMBER
Fig. 6.
The method was also applied to a sample of lower concentration, that is 0.40 ppm for ethylbenzene and 0.36 ppm for p-xylene. The results are shown in Fig. 7. For this concentration level the measurement errors are 15% for ethylbenzene and 3% for p-xylene. These results are in good agreement with the conclusions of computer simulation. CONCLUSION
The ion band monitoring method developed in this paper allows one to resolve multicomponent GC (or LC) peaks in cases where no unique ions can be found. This is achieved by monitoring a band of neighboring masses and then resolving a system of linear equations. The choice of maximum band size, K, depends on the scan rate and the SNR degradation that can be tolerated. The exact expression is given by the eqns. 13. The discussion shows that the SIM method of GC-MS and the LS method of mass spectroscopy can be regarded as particular realizations of the ion band monitoring method proposed here, with the band size parameter, K, assuming limit values of 1 and A4 respectively. If a GC curve has a known shape then the restrictions on K can be relaxed owing to the smoothing from the fitting of the sampled curve {cj(t,)}. Equations 14 reflect this relaxation. The ion band method can be used even when the coeluting components have unique ions, when it will provide additional points on the concentration-time curve. This will improve the
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
127
COMPONENTRESOLUTIONBY ION BAND METHOD 0.4 )
:
-0.1 -
:
:, 3’ ’ ;,;’
Actual Concentrations:
Ethylbenzene (.4 ppm) + p-Xylene (136ppm) -0.2 132
134
136
138
140
142
144
146
148
150
SCAN NO. Fig. 7.
overall system accuracy and will give additional’assurance ions are not contaminated by an unexpected compound.
that the selected
ACKNOWLEDGMENT
I thank Dr. Laarni Davidson for providing GC-MS experimental data, Dr. Laarni Davidson and Dr. Robert Hertel for stimulating discussions, and all my colleagues from Perkin-Elmer AS0 who read and commented on this paper. REFERENCES T. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958. J.R. Chapman, Computerized Mass Spectrometry, The Institute of Physics, Bristol, UK, 1980, pp. 365-375. G.H. Weiss and J. Rice, Optimal parameters for the measurement of the half-width of a Gaussian peak, Sep. Sci. Technol., 17 (1982) 1101-l 115. R. Delley, The peak width of nearly Gaussian peaks, Chromatographia, 18 (1984) 374-382. M. Rotheram, L. Davidson, A. Lokshin and P. Chang, Space Station Freedom trace contaminant monitor, Int. Conf. Life Support and Biospherics, Huntsville, AL, February 18-20, 1992.
117-127 117
ElsevierSciencePublishersB.V.,Amsterdam
Ion band multicomponent
resolution method
Anatole Lokshin The Perkin-Elmer Corporation, Applied Science Operation, 2771 North Garey Avenue, Pomona CA 91767 (USA)
(Received 5 March 1992)
ABSTRACT A new gas chromatography-mass spectrometry (GC-MS) data reduction method for resolving coeluting components is developed. The method does not require each component to possess a unique ion but instead relies on a band of ions common to all compounds. The paper provides an expression for band size as a function of signal-to-noise ratio, ion mass numbers, and relative scan rate. The ion band method provides a unified view of the selected ion monitoring technique for GC-MS and the least squares methods for mass spectrometry. Keywords: gas chromatography; method.
mass spectrometry; multimixture separation; least-squares; single-ion
INTRODUCTION Gas chromatography-mass spectrometry GC-MS technology has found wide application in chemical analysis owing to its ability to separate different components, not only by their characteristic mass spectra but also in time. As a result, components with similar mass spectra are separated in time to such a degree that the selected ion monitoring (SIM) method can be used. Unfortunately, it is quite common for complex mixtures to have no unique ions of sufficient intensities to be used for resolving the coeluting components using the SIM algorithm. If component concentrations remain constant during the whole mass scan then a least squares (LS) method of multicomponent resolution can be used [l]. The LS method is commonly used in mass spectroscopy [2]. In contrast to the SIM method, the LS approach uses several masses obtained in one scan to resolve unknown compounds. However, the elution time separation achieved in the chromatography has its price to pay. When the mass scan time is comparable with the GC peak width at half height (PWHH), component concentrations vary significantly during one scan. This prevents the use of the LS technique. to: A. Lokshin, The Perkin-Elmer Corporation, Garey Avenue, Pomona CA 91767, USA.
Correspondence
2771 North
0168-l 176/92/$05.00
0
1992 Elsevier Science Publishers
Applied
Science Operation,
B.V. All rights reserved.
118
A. Lokshinllnt.
J. Mass Spectrom. Ion Processes 120 (1992) 117-127
This paper describes a new GC-MS data reduction method that allows resolution of coeluting components even when there are no unique ions among them. Separation is achieved by simultaneously monitoring several ions with neighboring mass numbers and then resolving a corresponding system of linear equations for each scan. The method’s precision is discussed and its application is illustrated via computer simulation and with an example from the space station air composition monitoring (ACM) GC-MS system. METHOD
In the conventional SIM method the intensities of a set of ions are monitored for each mass spectrometer scan. Each of these ions uniquely represents a particular coeluting component. Let the jth component in a mixture have a characteristic ion with mass M;. that is unique for this component. Then the component’s concentration at time t can be determined as
Here yM,(t) is an observed ion intensity at mass Mj and time ~~~(44~)is the ratio of the nominal intensity of the mass M;. and the base peak for the jth component, and sj is the component’s sensitivity in terms of counts per peak intensity. For notational simplicity we assume that sj = 1 for all components. The resulting intensity-time curve, Cj(t), is integrated to obtain the total component concentration. To improve the accuracy a gaussian curve can be fitted to the computed set {cj(ts)> [3], where s = 1 . . . N stands for scan number. Instead of using a set of unique ions, the ion band method described here employs a narrow band of ions with neighboring mass numbers to characterize the target compound set. Owing to their proximity in the mass spectrum these ions are measured at about the same time. Therefore, there is no significant change in the component concentrations during the time needed to measure the whole band. As a result, a multicomponent resolution can be performed for this narrow band of ions for each sc.an. These solutions provide concentration-time curves (cj(t,)} for each individual component in the mixture similar to those obtained with the SIM method. These curves can be treated in the same way to those obtained by the SIM method. To illustrate the technique, let an unresolved GC peak be composed of components A, B, and C which do not have unique ions, but have common ions with masses k, k + 1, and k + 2. Since these masses are obtained at about the same time we can assume that component concentrations cA, cg, and cc are constant during all three measurements. Therefore, for each scan, s, the
A. Lokshinllnt.
J. Mass Spectrom. Ion Processes 120 (1992) 117-127
119
following system of linear equations can be formulated: Y(&) = X * 44)
(2)
Here vector I corresponds to the observed ion intensities for the corresponding masses and X denotes a matrix of the nominal mass ratios with sensitivity taken into account. System 2 has a full rank and therefore can be resolved to obtain cA(ts), cg(ts), and cc(t,) at each scan. In vector notation: c = x-‘y
(3)
It is clear that various modifications of system 2 are available. For example, if only two components A and B have three common ions of mass k, k + 1, and k + 2, then equations can be resolved by an LS method where X-’ is replaced by a pseudo inverse X + . Another possible situation is when common ions are not sequential but have small separations between them. In this case the principle parameter of the method, the total size K of the band, is larger than the number of ions used in system 2. If masses k, , . . . , k, are used, then the band size K is K=k,-k,+l
(4)
With K = 1 the ion band method becomes a conventional SIM algorithm and with K equal to the total dimension of the mass spectrum, M, the method becomes the LS technique used in mass spectroscopy. The value of K is limited by a requirement that the component concentrations do not change too much between the instants when the masses k, and k,, are detected. The next section describes how a maximum allowable band size, K, can be determined from a desired signal-to-noise ratio (SNR). LIMITATION
ON THE BAND SIZE
The GC elution peaks can be generally approximated [41: c(t) = co * ew (- W - W/Bl’>
by a gaussian curve (5)
where T, is the retention time of the component and fl is a characteristic time scale. In the traditional PWHH units /3 = PWHH/2 (In 2)‘/*. By differentiating eqn. 5 one gets a concentration change rate de/c,=
-2r*exp(-z’).dz
(6)
where r N (t - T,)//?. It is easy to show that the maximum of eqn. 6 is achieved at z P (l/2) ‘I2 . Therefore, the maximum possible change in concentration during time period At is max (ldc/c, I) = (2)‘12- ,-‘I2 dz = (2)“2 - e-“‘At//?
(7)
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
120
For example, for ion energy-scanned magnetic mass spectrometers the time difference between the instants when the masses k, and k,, are detected is At = T,log,,(k,lk,)
(8)
where T, is the time required for one decade scan. By substituting eqns. 5 and 8 into eqn. 7 we obtain the maximal concentration change for a band of size K: max (6) = 0.37(T,/j)
l
In (1 + (K - 1)/k,)
(9a)
where 6 N Idc/c, 1. For linearly-scanning spectrometers At = (K - 1) T,/M, where M is the total number of channels to be scanned during time T,. Correspondingly: l
max (6) = (2)‘j2 * e-II2 * T,//l* (K - 1)/M
(9b)
The maximum admissible change in concentration, a,,,,,, can be related to a desired SNR, since the error resulting from the change in concentration across the band can be regarded as an additional “noise”, a. Indeed, by replacing c in eqn. 2 with c * (1 + S) we obtain: y = (1 + S) * xc = xc + s * xc = xc + & Therefore, the SNR becomes smaller owing to the concentration across the band: SNR = S&N, + 6 . S,) = SNR,,/( 1 + 6 SNR,) l
(10)
averaging (11)
If one desires to keep the SNR above some minimal level of SN~i” then from eqn. 11: 6 < (SNR, - SNRmi,)/(SNR, . SNR,i,) = 8SNR/SNR,i” II 6,,,
(12)
By substituting 6,,, into eqns. 9a and 9b we obtain a direct relation between the maximum band size, K, and the maximum allowable signal degradation, 6mm** K <
1 + 2.703 * k, . (/l/T,)
K<
1 + 1.166*M*(/.I/T,)*6,,,
l
d,,,
(134
(13b)
For example, let a mass spectrometer to scan exponentially a decade between masses 25 and 250 in 2 s. Let the characteristic PWHH for the same GC peak be 12 s. Then for a three-ion band located at masses 25, 26, and 27, 6 can be computed according to eqn. 9a as 6 = 0.03 1. Assuming that the original SNR at these masses is 10 we obtain, according to eqn. 11,24% SNR degradation. The same band located at masses 248, 249, and 250 leads to only 0.0031 relative concentration error and, correspondingly, to 3% SNR degradation at SNR = 10.
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
121
Equations 13 show that the SIM method and the LS approach are particular cases of the ion band monitoring method described here. Indeed, for static mass spectrometry concentration is constant during one scan. Mathematically it is equivalent to /? + co. Therefore, from eqns. 13 the band size can encompass the whole mass spectrum without any loss in SNR. However, if the scan time becomes large compared with the GC peak width, b/T’ + 0, or no SNR degradation can be tolerated, 6,,, --) 0, then, according to eqn. 13, K + 1, which corresponds to the SIM method. Equation 11 shows that the relative signal degradation depends on the strength of the initial signal. This puts an additional constraint on band selection. The ion intensities in the selected band must be strong enough to prevent significant error in the concentration estimate. This is reflected in eqn. 13. Note that, since there are usually many more bands available for analysis than there are unique ions, the ion band method generates more concentration curve points than are available with the SIM. Consequently, the accuracy of the total concentration determination may be higher. This makes the ion band method a strong competitor with the SIM method even in cases when unique ions are available. An additional improvement in accuracy can come from global curve fitting. Indeed, if the pure component chromatogram has a known shape, then after curve fitting the total average error, 6, is reduced about 1/N’j2 times, where N is the number of points of similar intensity used for the fit. Assuming that only the points inside the PWHH are used for the fitting: N x 1.678/T,. By substituting into eqn. 13 we obtain less restrictive bounds on K K < 1 + 1.62 k, - (j3/7’J”2 - d,,, l
K <
1 + 0.7 - A4 (p/Ty l
l
6,,,
(W (14b)
Note that eqns. 14 are approximate since the actual signal strength varies for different scans. EXPERIMENTAL
The algorithm described above has been tested via computer simulation and with actual GC-MS data for the trace contaminant monitor (TCM) system at Perk&Elmer ASO. For the TCM system description see ref. 5. Computer simulations are added to illustrate the algorithm’s performance independent of measurement noise. Computer simulation The computer simulation used propadiene and methyl acetylene. Their standard mass spectra, taken from the NBS library, are listed in Table 1. The
122
A. Lokshin/lnt.
J. Mass Speclrom. Ion Processes 120 (1992) 117-127
TABLE 1 NBS fragmentation
spectra
Compound
Propadiene Methyl acetylene
Mass number 25
26
39
40
41
45 38
41 31
946 182
999 999
23 30
components’ retention times, T,, , were determined on a Perkin-Elmer GCMS system. The component mass spectra are very similar and there are no unique ions. The retention time separation is 5s which is not enough to separate two GC peaks with PWHH values of 12 s each. However, one scan duration is 2 s which is comparable with the PWHH value-namely, a concentration change during one scan time can be quite significant. Therefore, a conventional SIM method cannot resolve these components. However, these components can be resolved using the ion band method described above. There is a band [25,26] of size K = 2, and a band [39-411 of size K = 3. Mass 40, characteristic of argon, is not used to demonstrate a “sparse” band case. The data were simulated with concentrations of propadiene and methyl acetylene of 50ppm and 250ppm respectively. The GC peak profile was assumed to be gaussian with j3 = 7.2 s and retention times differing by 5 s. The mass scan rate was set to 2 s per decade. Figure 1 provides “true” component GC peak profiles (broken curves) as well as the total ion current (TIC) for both components (solid curve). The TIC curve does not give any visual indication that there is a mix of two components. Figure 2 shows how the ion band method resolves concentration-time curves for both components. The solid lines correspond to band 1 (masses 25 and 26) and the broken lines correspond to band 2 (masses 39 and 41). Figure 3 shows the result of the ion band method when 1% random noise was added to the observations. Table 2 summarizes estimation errors (using peak maximum) observed during simulation. The first line for each component gives an estimated error which is purely due to change in concentration inside the band; the second line gives the r.m.s. error with 1% noise. TCM GC-MS DATA
The ion band method has been used to analyze actual GC-MS data collected from the TCM. The compounds used in the test were the p-xylene and ethylbenzene isomers. (This work was reported in ref. 5.) The common base peak of the isomers is at mass 91; however, both compounds have masses 105 and 106 which can be used as an ion band. The relative abundances at
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
123
Total Ion Current 300,
Time in set
Fig.
1.
Ion Band Dcconvolution
: no noise
-
200-
E 8 .E
150-
.I
loo-
! u
using Band 1
50 -
o-
-50 ’ 0
2
4
6
8
10 Scan number
Fig. 2.
12
14
16
18
2c
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
124
Ion Band Deconvolution : 40 db noise
250 -
200E B 5 .s 3 z8
150 -
loo-
g u 50 -
O-501
I
0
2
4
6
8
10
12
14
16
18
20
Scan number Fig. 3.
these masses as determined by the TCM are 16% and 27% for p-xylene and 3% and 31% for ethylbenzene. The first experiment used concentrations of 2.27 ppm for p-xylene and 2.5 1 ppm for ethylbenzene. Shown in Fig. 4 is the reconstructed total ion chromatogram (RTIC) for the coeluting isomers. The PWHH of the peak is approximately 12 s, which is about 3 s wider than that measured for a single peak of either component. The reconstructed ion chromatograms (RIC) for masses 105 and 106 for the same sample are shown in Fig. 5. The data were analyzed by the ion band method and the result of the deconvolution is illustrated in Fig. 6. The resulting errors in concentration determinations are 7% for p-xylene and 14% for ethylbenzene respectively. TABLE
2
Ion band prediction
errors (%)
Compound
Band 1 (K=2)
Band 2 (K=3)
Average of both bands
Propadiene (With noise) Methyl acetylene (With noise)
6.1 21.3 1.02 7.1
5.95 11.1 0.67 3.2
0.1 13.6 0.8 3.8
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
125
RECONSTRUCTED TOTAL ION CHROMATOGRAM 50, 45 40Sample Mix: 35 -
Ethylbenzene + p-Xylcne (2.51 ppm) (2.27 ppm)
30 2520 15 10 50 125
130
135
140
145
150
155
SCAN NO. Fig. 4.
RECONSTRUCTED ION CHROMATOGRAMS
Sample Mix: Ethylbenzene + p-Xylene (2.51 ppm) (2.27 ppm)
SCAN NO. Fig. 5.
18D
126
A. Lokshin/lnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127 COMPONENT RBSOLUTION BY ION BAND METHOD
p-XYLENE
: ETHYLBBNZENE 1.5 :
: :
/
l-
Actual Concentrations: Ethylbenzene - 2.51 ppm
1
-0.5 12.5
130
135
140
145
150
155
160
SCAN NUMBER
Fig. 6.
The method was also applied to a sample of lower concentration, that is 0.40 ppm for ethylbenzene and 0.36 ppm for p-xylene. The results are shown in Fig. 7. For this concentration level the measurement errors are 15% for ethylbenzene and 3% for p-xylene. These results are in good agreement with the conclusions of computer simulation. CONCLUSION
The ion band monitoring method developed in this paper allows one to resolve multicomponent GC (or LC) peaks in cases where no unique ions can be found. This is achieved by monitoring a band of neighboring masses and then resolving a system of linear equations. The choice of maximum band size, K, depends on the scan rate and the SNR degradation that can be tolerated. The exact expression is given by the eqns. 13. The discussion shows that the SIM method of GC-MS and the LS method of mass spectroscopy can be regarded as particular realizations of the ion band monitoring method proposed here, with the band size parameter, K, assuming limit values of 1 and A4 respectively. If a GC curve has a known shape then the restrictions on K can be relaxed owing to the smoothing from the fitting of the sampled curve {cj(t,)}. Equations 14 reflect this relaxation. The ion band method can be used even when the coeluting components have unique ions, when it will provide additional points on the concentration-time curve. This will improve the
A. Lokshinllnt. J. Mass Spectrom. Ion Processes 120 (1992) 117-127
127
COMPONENTRESOLUTIONBY ION BAND METHOD 0.4 )
:
-0.1 -
:
:, 3’ ’ ;,;’
Actual Concentrations:
Ethylbenzene (.4 ppm) + p-Xylene (136ppm) -0.2 132
134
136
138
140
142
144
146
148
150
SCAN NO. Fig. 7.
overall system accuracy and will give additional’assurance ions are not contaminated by an unexpected compound.
that the selected
ACKNOWLEDGMENT
I thank Dr. Laarni Davidson for providing GC-MS experimental data, Dr. Laarni Davidson and Dr. Robert Hertel for stimulating discussions, and all my colleagues from Perkin-Elmer AS0 who read and commented on this paper. REFERENCES T. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958. J.R. Chapman, Computerized Mass Spectrometry, The Institute of Physics, Bristol, UK, 1980, pp. 365-375. G.H. Weiss and J. Rice, Optimal parameters for the measurement of the half-width of a Gaussian peak, Sep. Sci. Technol., 17 (1982) 1101-l 115. R. Delley, The peak width of nearly Gaussian peaks, Chromatographia, 18 (1984) 374-382. M. Rotheram, L. Davidson, A. Lokshin and P. Chang, Space Station Freedom trace contaminant monitor, Int. Conf. Life Support and Biospherics, Huntsville, AL, February 18-20, 1992.