Quantitating VOCs in Serum Using Automated Headspace-SPME/Cryo-Focusing/Isotope Dilution/Capillary GC/MS

In January 2007, the author’s lab received a frozen shipment of calibration standards and quality control (QC) samples to perform method validation for quantitating traces of volatile organic compounds (VOCs) in serum. Samples were supplied in 2-mL flamed-sealed glass ampoules containing 1.2 mL of calf serum previously spiked with 11 toxic VOCs (10 distinct chromatographically separated VOC peaks plus m- and p-xylene, which coelute). The validation batch consisted of 20 replicate sets of calibration standards and 20 replicate sets of QCs. Each QC set included a QC-Low (QC-L; each VOC analyte is expected to be ~250 ppb) and a QC-High (QC-H; each VOC analyte is expected to be ~8000 ppb).

The samples arrived during a weekend when no staff was available to place them in the freezer, and thawed by the time staff returned to the office. This violated the sampling protocol of the method. After the samples were replaced, the laboratory conducted a comparative study (during the initial validation) to assess the effect of the thawed QC samples against their equivalent (the reissued batch that remained frozen throughout the shipping and receiving cycle). The quantitated results for both batches of QCs were compared by calculating a mean, standard deviation and variance over N replicate QC samples for each of the chromatographically separated VOCs.

This article reports the results of applying a t statistical comparison of two means over replicate QC samples at each of two different QC concentration levels (ppb; each VOC, except for coeluted m- and p-xylene) for each of 10 chromatographically separated VOCs.

Experimental

Instrumentation

A 6890/5973N inert GC-MSD (Agilent Technologies, Santa Clara, Calif.) incorporating a split/splitless inlet with electronic pressure control (EPC) and a single quadrupole mass selective detector were used to generate the data. The GC/MS was interfaced to a computer installed with ChemStation software (Agilent Technologies) for chromatographic control, data acquisition and storage. An MPS2 multipurpose autosampler (Gerstel GmbH & Co. KG, Mulheim an der Ruhr, Germany) was mounted above the GC/MS. Software control was via Maestro (Gerstel) integrated into ChemStation software. The robotic rail and arm perform liquid delivery, static headspace sampling and solid-phase microextraction (SPME). A CTS2 cryotrap, incubator with pulsed agitation, Peltier-cooled sample tray and 505 Controller (all from Gerstel GmbH & Co. KG) were installed as well.

 Figure 2 – SPME fiber assembly attached to the MPS2 SPME holder (courtesy of Gerstel).

This method uses only the lower rail injection unit with the Gerstel SPME Kit for the following operations: moving headspace (HS) vials from the Peltier tray to the incubator, penetrating the HS vial septum with the SPME fiber assembly during incubation, extruding and retracting the SPME fiber for analyte extraction, withdrawing the SPME assembly, inserting the SPME assembly needle into the split/splitless inlet and extruding the SPME fiber into the injector glass liner for analyte volatilization. The SPME fiber remains in the inlet throughout the chromatographic run. Figure 1 shows how the SPME fiber connects to the metal rod and assembly; Figure 2 shows the SPME fiber assembly and Gerstel SPME fiber holder that attaches to the MPS2.

 Figure 1 – Schematic of SPME fiber assembly (courtesy of MilliporeSigma, Billerica, Mass.).

Ten of the 11 VOCs were chromatographically separated on a DB-VRX (Agilent Technologies) wall-coated open-tubular (WCOT) column. Analytes separated on the WCOT column were quantitated using the ChemStation RTE integrator. The stationary phase of the column (40 m × 0.18 mm × 1.0 μm film thickness) was designed specifically for the resolution of volatile, halogenated and aromatic hydrocarbons. A new WCOT column must be conditioned for optimal chromatographic performance. Table 1 lists MPS2 and GC/MS operating conditions and parameters required to conduct the instrumental method: automated headspace solid-phase microextraction with cryo-focusing isotope dilution gas chromatography-mass spectrometry (HS-SPME-C-ID-GC/MS).

Table 1 – MPS2 and GC/MS operating conditions used to calibrate and quantitate selected VOCs extracted from serum samples via HS-SPME

The VOC panel was spiked into a serum matrix at seven concentration levels for the calibrators and two QC levels (Table 2). Since m- and p-xylene coelute, the concentration of these two VOCs is twice that of the other nine VOCs. Fixed-volume aliquots of all samples (calibrators, QCs) were added to 10-mL HS vials and were isotopically diluted with internal standards, which are analogs of the analytes labeled with 13C or 2H (Table 3). (It is essential to use isotope dilution in GC/MS to achieve good precision and accuracy.1) Following isotopic dilution, the HS vials were loaded onto the Peltier-cooled sample tray, and each was sampled with the robotic sampling head using a carboxen/polydimethylsiloxane (CAR/PDMS)-coated fiber of 75-μm film thickness (SPME Fiber Assembly, MilliporeSigma).

Table 2 – Calibration levels used to quantitate the 14 or 15 sets of QC samples studied in this study (all 14 or 15 replicate QC-L and all 14 replicate QC-H samples used were quantitated against a calibration that met the r2 = 0.9900 criteria)
Table 3 – Retention times, m/z ratios for quantitative and confirmatory ions with corresponding isotopically labeled internal standards needed to quantify 10 chromatographically separated VOCs including one coeluted pair, m- and p-xylene

The SPME fiber was inserted into the headspace above the serum and was exposed to each sample for 8 minutes. After the VOC analytes were extracted from the HS, thermally desorbed within the 300 °C inlet, cryofocused at –110 °C, and heated ballistically, they were chromatographed on the DB-VRX WCOT column and transported via carrier gas into the MSD. The MSD is a single quadrupole mass spectrometer that includes an ion source (electron impact ionization), mass analyzer (quadrupole) and detector (high-energy dynode and electron multiplier) all under high vacuum. It was operated in scan mode from a mass-to-charge ratio (m/z) of 35 to 250 to allow for identification of unknowns in the sample.2

Methods

One ChemStation method was used to quantify the VOCs and two Maestro sample prep methods were used. One sample prep method was used to condition a new SPME fiber and the other to operate the MPS2 and run samples. The SPME fiber holder must be adjusted to accommodate the height of the 10-mL HS vial cap to prevent the bottom of the retracted coated fiber from breaking when the septum piercing needle penetrates the septum cap.

Table 3 lists each VOC, its GC retention time, its target or quantitative m/z ion and one or two qualifier m/z ions. Fourteen QC-L and 14 QC-H samples that thawed after receipt at the lab (Batch 1 [B1]) and 15 QC-L and 15 QC-H samples that did not thaw upon receipt (Batch 2 [B2]) comprise the two sets of data whose means for each of 10 VOCs will be compared statistically. Twenty sets of B1 and 20 sets of B2 were provided and analyzed by HS-SPME-C-ID-GC/MS. Each set consisted of seven calibrator vials, one QC-L vial and one QC-H vial. The sets were run according to the following sequence. First set: B1 calibrator vials, B1 QC vials, blank sample vial, B2 calibrator vials, B2 QC vials. After this run was completed, all 19 subsequent sets were prepared and run using this sequence.

To prepare the sample, the top of a glass ampoule was broken, and an aliquot of calf serum (previously spiked by the provider with the VOC panel) was transferred to a 10-mL headspace vial and was subsequently spiked with the VOC panel of internal standards. Of the 20 sets, 14 sets of B1 and 15 sets of B2 met the calibration curve criteria (r2= 0.9900) to calculate a mean, standard deviation and variance. These sets comprised the replicate quantitated results used in the calculations.

Results

Theoretical background for HS-SPME

SPME was used to sample the headspace and preconcentrate the chemical species in the HS above a serum specimen that was continuously agitated and held at a constant temperature of 35 °C. These fixed experimental conditions establish a constant partition coefficient KVOCfs(SPME) for a specific VOC, where f refers to the CAR/PDMS-coated SPME fiber and s is the sample. KVOCfs(SPME) is defined as being equal to the ratio of the concentration of a given VOC in the fiber, Cf, to that in the sample, CS, once equilibrium is reached and assuming a negligible contribution from the HS sample interface. For HS-SPME, Pawliszyn compared extraction-time profiles for a stirred versus unstirred aqueous phase and showed that sample agitation shortens the time it takes to reach a plateau.3 The equation that defines KVOC fs(SPME) can be algebraically manipulated to yield the fundamental relationship for quantitative analysis.4,5 as follows:

Where:

no = maximum amount of VOC analyte that is partitioned into the SPME polymer coating (in moles) after sufficient incubation time and under exhaustive extraction conditions
Vf = volume of polymer coating on the SPME fiber
VS = volume of sample (such as water, serum or whole blood)
Co = original concentration of VOC analyte in the sample
Cf and CS = concentration of the VOC analyte in the fiber and sample, respectively, once equilibrium is reached.

Solving Eq. (1) for no yields

Upon examining Eq. (2), three simplifying assumptions are evident: 1) If KVOC fs(SPME) >> VS, as might be true for small sample volumes, then Eq. (2) simplifies to no = VSCo and demonstrates that the maximum amount of VOC analyte partitioned into the SPME fiber is directly proportional to the original VOC concentration, Co, of that VOC in the sample. 2) If, however, a large sample volume is used, KVOC fs(SPME)Vf << VS, then Eq. (2) simplifies to no = KVOC fs(SPME)·Vf · Co and demonstrates that the maximum amount of VOC analyte partitioned into the SPME fiber is also directly proportional to the original concentration, Co, of that VOC in the sample. 3) It is not necessary to exhaustively extract VOCs from the HS to achieve quantification. It has been shown that when an aqueous solution is effectively agitated, a steady-state diffusion model can be used.6 This model leads to a linear concentration gradient both in the bulk sample and in the PDMS-coated fiber using Fick’s first law:

As the sampling time t becomes very large, Eq. (3) reduces to Eq. (2). Hence, Eq. (3) can be rewritten in terms of n as a function of sampling time t according to:

Where a is a constant composed of various mass transfer coefficients, Kfs(SPME), Vf and Vs.

The author revised this model to include nonsteady-state considerations.7

All three assumptions lead to the conclusion that the amount of analyte partitioned into the SPME fiber, n, can be related to the initial concentration of analyte, Co, in the sample. The number of moles of VOCs partitioned into the SPME fiber depends only on the original concentration of VOCs in the sample, Co, provided that the sampling time, t, the rates of diffusion and the phase ratio all remain constant from sample to sample. The number of sorption sites on the SPME fiber is finite. As the concentration of VOCs increases, competition for sorption sites on the SPME fiber coating limits the number of sorption sites between analyte and internal standard.2

Figure 3 shows a total ion chromatogram for one QC-L sample drawn from B2. This chromatogram is minimally informative since 13C isotopically labeled VOCs coelute with their 12C analogs, while 2H isotopically labeled VOCs differ only slightly in retention time from their 1H analogs.

 Figure 3 – Typical GC/MS total ion chromatogram for one QC-L sample from B2. Column: DB-VRX, 40 m × 0.18 mm × 1.0 μm film thickness; 110 °C (hold for 1.50 min) then to 130 °C at 2.0 °C/min; then to 235 °C at 40 °C/min.

Importance of the t distribution

The importance of using the student’s t distribution when considering a small number of replicate measurements as is appropriate here was discussed earlier.8 As established by the central limit theorem, for a normal distribution of x values, where N is large, 95% of the time values will be found in the confidence interval for the population mean μx according to

Where sx is the standard deviation in the mean 𝑥̄ of N replicate samples.

For small N (<20), it can be shown that the variable

is not distributed normally but as a student’s t distribution:

Thus, we find the dependence of the value of t on the number of degrees of freedom, ν, where ν = N-1. Integrals of student’s t distribution are tabulated in an inverse form with t as a function of ∫𝑡∞ 𝑃(𝑡)𝑑𝑡 (one-sided) or 2∫𝑡∞ 𝑃(𝑡)𝑑𝑡 (two-sided) and ν. As ν increases, the t distribution begins to approximate the normal distribution.8 The number of degrees of freedom df will be used instead of ν in the mathematical equations shown below.

Comparison of two means using t statistics

 Figure 4 – Flow chart showing experimental design and results.

Analytical chemists have four mathematical options to consider when t statistics are to be used to decide whether or not two experimental means differ9: A) comparing two independent averages with known variances, B) comparing two independent averages with unknown and equal variances, C) comparing two independent averages with unknown and unequal variances and D) comparing two dependent averages (paired data). This article considers only B and C. It is assumed that both batches are independent of one another. Since the lot of VOC samples prepared and sent by the supervisory agency was the initial lot at the onset of the validation for VOCs, the variance in each mean is assumed to be unknown.

QC samples from both batches were quantitated against the B2 calibration, and then QC samples from both batches were quantitated against their respective calibrations (i.e., B1 QCs against the B1 calibration and B2 QCs against the B2 calibration) to determine if it matters whether the QCs are quantitated against their respective calibration or against only the B2 (good) calibration. Figure 4 summarizes the tabular results below.

Applying t statistics for option B to compare B1 and B2 means; both batches quantitated against the B2 calibration

When implementing option B (above), the two variances must satisfy the null hypothesis, i.e., there is no difference. An F test is conducted to assess whether the two variances satisfy the null hypothesis.9-11 Eq. (6) assumes that the larger variance is placed in the numerator and the smaller variance is placed as the denominator.

Where 𝑠𝐴2 is the larger estimated variance with 𝑛𝐴 – 1 degrees of freedom and 𝑠𝐵2 is the smaller estimated variance with 𝑛𝐵 – 1 degrees of freedom.

If the null hypothesis is confirmed, the equations below are used to find tcalc, according to Refs. 9 and 10.

Where
𝑥̄1 is the mean of 𝑛1 replicate quantitated analytical results in ppb for a specific VOC such as benzene from B1
𝑥̄2 is the mean of 𝑛2 replicate quantitated analytical results in ppb for a specific VOC such as benzene from B2
𝑠𝑝 is the pooled standard deviation
df is the number of degrees of freedom.

Table 4 shows the Excel spreadsheet created to apply the option B equations for chloroform (CHCl3). Identical spreadsheets (not shown) were created for the nine other VOCs. Coeluting peaks m- and p-xylene were quantitated as one chromatographically resolved peak. B1 data (ratio of m/z 83 CHCl3 abundance to m/z 86 13CHCl3 abundance) was quantitated against the B2 calibration for chloroform to yield the quantitated results in ppb CHCl3. B2 CHCl3 calibration met the r2 ≥ 0.9900 criteria discussed above. Each of the remaining nine ppb VOCs was calculated against its respective B2 calibration, and these VOCs also met the criteria, 𝑟2 ≥ 0.9900. As shown in Table 4, the standard deviation and variance were first calculated for the N-1 degrees of freedom shown for both QC-L and QC-H. Using Eq. (6), the Fcalc value is shown for both QC levels and compared to the tabulated F value. Note that Fcalc = 2.84 (rounded off for CHCl3 from that shown in Table 4) for the QC-L comparison of variances. This value exceeds the tabulated F value for a two-tailed chi distribution with α = 0.05 denoted by F0.05/2,13,14 = 2.51. The null hypothesis, i.e., no difference exists when comparing the squared variances for CHCl3 between B1 and B2, is refuted for the QC-Ls. The same conclusion is reached for CHCl3 when comparing B1 and B2 variances for the QC-Hs, since Fcalc= 2.82 vs F0.05/2,14,13 = 2.55. Note that the value of Fcalc for the QC-Hs is very close to that for the QC-Ls despite significant differences in concentration (~8000 ppb CHCl3 vs ~250 ppb CHCl3). Although the t test is now irrelevant, tcalc was found using Eqs. 7–9 and was compared to tabulated values for t for purposes of completeness.

Table 4 – Example spreadsheet listing replicate quantitated results in ppb and results of calculating 𝑥̄, s, s2, Fcalc and tcalc from applying option B statistics for CHCl3*

Table 5 summarizes the findings when two independent means with unknown and equal variances (option B from above) are compared based on applying t statistics for all VOCs of interest. Three significant figures are reported for the tabulated and calculated F values, and four significant figures are reported for the tabulated and calculated t values as shown in Table 5 and all subsequent summary tables (Tables 7, 9 and 11). Except for CHCl3, all other VOCs for the QC-L samples confirmed the null hypothesis with respect to variances: Fcalc < F0.05/2,13,14. Of all the VOCs for the QC-H samples, only three VOCs confirmed the null hypothesis with respect to variances: Fcalc < F0.05/2,14,13. Despite some of the VOCs exhibiting unequal variances based on results from applying the F test, their respective tcalc values were calculated and are shown in Table 5. The null hypothesis with respect to means was confirmed for all VOCs except for 1,2-dichloroethane in the QC-L samples. Chloroform, 1,2-dichlorethane, benzene and carbon tetrachloride failed the t test for QC-H, while the remaining VOCs passed. Failed F test values are shown in red and failed t test values in green. The assumption that the variances between the good and bad batch were unknown and unequal leads to a similar evaluation using option C.

Table 5 – Results of comparing the means (good vs bad batch) for all 10 VOCs (m- and p-xylene coelute) using option B statistics with results quantitated against B2 calibration*

Applying t statistics for option C to compare B1 and B2 means; both batches quantitated against the B2 calibration

If the F test finds that the variances between B1 and 2 are unknown and unequal (option C), the appropriate t statistics can be applied using the equation for tcalc and for the number of degrees of freedom df as shown below.9

Where
𝑥̄1 is the mean of 𝑛1 replicate quantitated analytical results in ppb for a specific VOC such as benzene from B1
𝑥̄2 is the mean of 𝑛2 replicate quantitated analytical results in ppb for a specific VOC such as benzene from B2
s1 is the standard deviation for the B1 QC results for a specific VOC such as benzene
s2 is the standard deviation for the B2 QC results for a specific VOC such as benzene
df is the number of degrees of freedom associated with the tabulated t.

Note that df will always be between the smaller of (n1 – 1) and (n2 – 1) and the sum of (n1 + n2 – 2). The absolute difference between the two means is generally used when applying Eq. (10).9

Table 6 illustrates how a spreadsheet was created to implement the t statistics for option C using Eqs. (10) and (11) for CHCl3 in a manner similar to what was shown in Table 4 for option B. Since the variances are assumed to be unequal, this spreadsheet does not consider the F test. For the QC-L comparison of means for CHCl3, tcalc < t(0.05/2,22), confirming a null hypothesis. For the QC-H comparison of means for CHCl3, tcalc < t(0.05/2,24), again confirming a null hypothesis.

Table 6 – Example spreadsheet listing replicate quantitated results in ppb and results of calculating 𝑥̄, s, s2 and tcalc from applying option C statistics for CHCl3*

Table 7 shows a comparison of means for B1 and 2 for all VOCs using Eqs. (10) and (11). All VOCs at both QC levels showed that tcalc < t(0.05/2,df) with one exception. The QC results for 1,2-dichloroethane refuted the null hypothesis with respect to its means between B1 and 2 in the QC-L but not in the QC-H. Comparison of means at QC levels in B1 and 2, quantitated against the B2 calibration, proved that, for most of the VOCs studied, it is more appropriate to assume unknown and unequal variances. Consider a comparison of means using options B and C with both batches quantitated against (instead of the B2 calibration) their respective calibrations.

Table 7 – Results of comparing the means (good vs bad batch) for all 10 VOCs (m- and p-xylene coelute) using option C statistics with results quantitated against B2 calibration*

Applying t statistics for option B to compare B1 and B2 means; both batches quantitated against their respective calibration

Table 8 illustrates how a spreadsheet was created to apply option B t statistics when B1 QC results were quantitated against the B1 calibration for CHCl3. Each B1 calibration met the r2 = 0.9900 criteria as discussed above. As before, B2 QCs were quantitated against the B2 calibration. For QC-L CHCl3, the null hypothesis was confirmed for both the F and t tests, and for QC-H CHCl3, the null hypothesis was confirmed for the F test but not the t test. Table 9 shows the results for comparing means between both batches for all VOCs assuming option B comparison of means, t statistics. For QC-L, the null hypothesis was confirmed for the F and t tests. However, for QC-H, only styrene and o-xylene (the last two eluted VOCs) have confirmation of a null hypothesis in both tests. The first four VOCs passed the F test and failed the t test, while the next four VOCs (in GC elution order) failed the F test yet passed the t test.

Table 8 – Example spreadsheet listing replicate quantitated results in ppb and results of calculating 𝑥̄, s, s2, Fcalc and tcalc from applying option B statistics for CHCl3*
Table 9 – Results of comparing the means (good vs bad batch) for all 10 VOCs (m- and p-xylene coelute) using option B statistics with results quantitated against their respective calibration*

Applying t statistics for option C to compare B1 and B 2 means; both batches quantitated against their respective calibration

Table 10 illustrates how a spreadsheet was created to apply option C comparison of means, t statistics when B1 QC results were quantitated against the B1 calibration for CHCl3. Each B1 calibration met the r2 = 0.9900 criterion discussed above. As before, B2 QCs were quantitated against the B2 calibration. Again, only the t test is relevant and, in the case of CHCl3, both QC levels confirmed the null hypothesis. Table 11 shows the results for comparing means between both batches for all VOCs assuming the option C comparison of means, t statistics. For the QC-L, the first six VOCs confirmed the null hypothesis, while the last four VOCs refuted it. For the QC-H, only CCl4 refuted the null hypothesis.

Table 10 – Example spreadsheet listing replicate quantitated results in ppb and results of calculating 𝑥̄, s, s2 and tcalc from applying option C statistics for CHCl3*
Table 11 – Summary of results comparing the means (good vs bad batch) for all 10 VOCs (m- and p-xylene coelute) using option C statistics with results quantitated against their respective calibration*

Discussion

Upon comparing Tables 5 and 9, in which option B statistics are compared and the results quantitated against the B2 calibration versus their respective calibration, it is clear that, although the F and t tests frequently refuted the null hypotheses across the 10 VOCs, more failures are seen in the QC-H than in the QC-L. Eight of 10 VOCs (Table 5) refuted the null hypothesis F test for QC-H when calibrated against the B2 calibration. Four of 10 VOCs (Table 9) for the QC-H failed the F test when calibrated against their respective calibrations. However, most VOCs in the QC-L passed the F test irrespective of whether B1 or 2 was used to calibrate.

An overall significant decline in failures is noted can be seen when Tables 7 and 11 are compared to Tables 5 and 9. Only 1,2-dichloroethane in the QC-L (Table 7) failed to confirm the null hypothesis with respect to a comparison of means (failed the t test) when quantitated against the B2 calibration. No VOCs failed the t test (Table 7) for the QC-H when quantitated against the B2 calibration. The last four eluting VOCs (Table 11) refuted the null hypothesis for the QC-L with respect to a comparison of means (failed the t test) when quantitated against their respective calibration. Only carbon tetrachloride out of 10 VOCs (Table 11) failed the t test for the QC-H when quantitated against their respective calibration.

Conclusion

Option C with results quantitated against the B2 calibration exhibited the least number of refuted null hypothesis over the 10 chromatographically separated VOCs. This conclusion was reached using the applied mathematics of t statistics, while illustrating significant differences in analytical chemistry outcomes.

References

  1. Loconto, P. Use of weighted least squares and confidence band calibration statistics to find reliable instrument detection limits for trace organic chemical analysis. Am. Lab. 2015, 47(7), 34–9.
  2. Chemical Terrorism Laboratory Network. VOC Analysis by SPME/GC/MS, Centers for Disease Control and Prevention, and subsequent training guides, notes and discussions.
  3. Pawliszyn, J. Solid Phase Microextraction: Theory and Practice, Wiley-VCH: New York, N.Y., 1997, pp 74–86.
  4. Loconto, P. Trace Environmental Quantitative Analysis. Principles, Techniques, and Applications, 2nd ed., CRC Press: Boca Raton, Fla., 2006, pp 255–68.
  5. Snow, N. and Slack, G. In: Grob, R. and Barry, E., Eds. Modern Practice of Gas Chromatography, 4th ed. Wiley-Interscience: Hoboken, N.J., 2004, pp 574–84.
  6. Ai, J. Solid phase micro-extraction for quantitative analysis in non-equilibrium situations, Anal. Chemi. 1997, 69(6), 1230–6.
  7. Ai, J., Solid-phase micro-extraction in headspace analysis. Dynamics in non-steady state mass transfer. Anal. Chem. 1998, 70(22), 4822–6.
  8. Perrin, C. Mathematics for Chemists. Wiley-Interscience: New York, N.Y., 1970, pp 154–7.
  9. Anderson, R. Practical Statistics for Analytical Chemists, Van Nostrand Reinhold: New York, N.Y., 1987, pp 72–8.
  10. Mode, E. Elements of Probability and Statistics,. Prentice-Hall: Englewood Cliffs, N.J., 1966, p 205.
  11. Einax, J.; Zwansiger, H. et al. Chemometrics in Environmental Analysis. VCH: Weinheim, Germany, 1997, pp 35–40.

Paul R. Loconto, Ph.D.,is a consultant in analytical chemistry and chemical education, 4300 Manitou Dr., Okemos, Mich. 48864, U.S.A.; tel.: 517-347-4195; e-mail: [email protected]. David Isenga made a significant contribution to the computational aspects of this paper. The efforts of the technical support teams from Gerstel Inc. and Agilent Technologies, Inc. are greatly appreciated. This work was supported by the Michigan Public Health Institute, Okemos; Michigan Department of Community Health, Bureau of Laboratories, Lansing; Department of Health and Human Services, Centers for Disease Control and Prevention and Public Health Emergency Preparedness.

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