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the Effect of Cross-Contribution to the
Intensity of Ions Designating the Analyte and
the Internal Standard in Quantitative GC-MS
Chiung Dan Chang,b
and Ray H. Liua
aDepartment of Medical Technology, Fooyin University, Kaohsiung, Taiwan bDepartment of Laboratory, Yang Ming Hospital, Chiayi, Taiwan
cDepartment of Laboratory, Ben Tang Cheng Ching Hospital, Taichung, Taiwan
dDepartment of Pathology, Chang Bing Show Chwan Memorial Hospital, Changhua, Taiwan eDepartment of Criminal Investigation, Central Police University, Taoyuan, Taiwan
fDepartment of Forensic Sciences, Central Police University, Taoyuan, Taiwan
In gas chromatography-mass spectrometry methods of analysis adopting the analyte’s isotopic analog as the internal standard (IS), the cross-contribution (CC) phenomenon—contribution of IS to the intensities of the ions designating the analyte, and vice versa—has been demonstrated to affect the quantitation data. A novel approach based on the deviations of the empirically observed concentrations of a set of standards was developed to assess the accuracy of the empirically derived CC data. This approach demonstrated that normalization of ion intensities derived from the analyte and the IS generates reliable CC data. It further demonstrated that an ion-pair (designating the analyte and the IS) with !5% or higher CC will result in a very limited linear calibration range. (J Am Soc Mass Spectrom 2008, 19, 598–608) © 2008 American Society for Mass Spectrometry
In 1984, guidelines were established for the U.S. Federal Workplace Drug Testing Program, mandat-ing (1) specific “cutoff” concentrations as positive/ negative criteria, and (2) certain concentration-related quality control and method validation requirements. Accurate quantitation of drugs/metabolites in biologi-cal specimens has since, in addition to being a scientific pursuit, evolved into a legal issue.
Selected ion monitoring (SIM) has long been estab-lished as the most effective approach for data collection where gas chromatography-mass spectrometry (GC-MS) is used for the quantitation of various categories of analytes. Among various calibration approaches ap-plied to SIM GC-MS protocols, internal standard (IS) method using isotopically-labeled analog (ILA) of the analyte as the IS has been well studied [2–7] and now widely adopted in forensic, clinical, and environmental laboratories. With ILA as the IS, one area of concern is the ion intensity cross-contribution (CC) between the analyte and the IS.
Cross-contribution is defined as the contribution of the IS to the intensities of the ions designating the
analyte and vice versa. Since the measured ion intensi-ties are used for the quantitation of the analyte, adopt-ing an ion-pair with significant CC to designate the analyte and the IS will generate inaccurate analyte concentrations. For example, when the contribution of the IS to the intensity of the ion designating the analyte is more significant, the observed apparent analyte con-centration will be higher than its true value. This error will become more significant as the analyte’s concentra-tion is lowered. On the other hand, the observed apparent analyte concentration will be lower than its true value when the analyte’s contribution to the inten-sity of the ion designating the IS is more significant. Similarly, this error will become more significant as the analyte’s concentration is increased.
Theoretical considerations  and approaches in-volving high-resolution ion monitoring  and com-puter programming for deconvoluting mass spectral peak abundance[6, 7]have been reported. The need to address this phenomenon in “real world data” was also highlighted by the inclusion of a section entitled, “Cor-rections for Contamination and Isotope Spillover,” in a 2006 book by Duncan et al. . In their book, the authors illustrated a nonlinear relationship (Figure 8.4) between the monitored response and the analyte con-centration, and further demonstrated (Figure 8.3) that a
Address reprint requests to Professor Ray H. Liu, Department of Medical Technology, Fooyin University, 151 Ching-Hsueh Road, Ta-Liao Hsiang, Kaohsiung Hsien 831-02, Taiwan. E-mail:email@example.com
Published online January 31, 2008 © 2008 American Society for Mass Spectrometry. Published by Elsevier Inc. Received October 3, 2007
1044-0305/08/$32.00 Revised November 28, 2007
linear relationship can be expected by removing the portion of the intensity of the ions designating the analyte that was cross-contributed by (spillover from) the IS (and vice verse).
Our interest in this area includes empirical measure-ments of the CC data [9–11], characterization of the effect of CC on the calibration curve,and the gener-ation of favorable ion-pairs for designating the analyte and the IS, mainly through various chemical derivati-zation (CD) routes.
The CC phenomenon has long been recognized and, as mentioned above, many correction approaches have been reported. However, to the best of our knowledge, assessing the accuracy (trueness) of the empirically determined CC data, which could have been affected by systematic and random errors, has not been addressed. This study develops a novel approach to evaluate empirically-derived CC values, advancing current knowledge in this important analytical parameter.
Standards and Reagents
The following analytes and deuterated ISs (in 1 or 0.1 mg/mL methanol solution) were purchased from Cer-illiant Corp., Austin, TX: 3,4-methylenedioxyamphet-amine (MDA), hydromorphone (HM), MDA-d5, and
hydromorphone-d6 (HM-d6). Derivatization reagents,
N-methyl-N-(t-butyldimethylsilyl)trifluoroacetamide (with 1% t-butyldimethyl-chlorosilane) and N,O-bis-(trimethylsilyl)trifluoroacetamide with (1% t-trimethylchlorosilane), were purchased from Pierce Chemical Co., Rockford, IL. All other common chemi-cals and solvents were of HPLC grade.
Sample Preparation and Derivatization Procedure
For full-scan and SIM data collection, the analytes (MDA and HM) and the ISs (MDA-d5 and HM-d6)
solutions were prepared individually. For example, for the run including only MDA, 5 !L of the MDA standard (1 mg/mL in methanol) was transferred into a 16 " 100-mm glass tube. For the run including only MDA-d5,
50 !L of the MDA-d5 standard (0.1 mg/mL methanol
solution) was used. Thus, an equal amount of the MDA and MDA-d5 was used in these two parallel
The procedures described below were then followed to form the t-butyldimethylsilyl (t-BDMS) or the tri-methylsilyl (TMS) derivatives of the analytes and the ISs. The 16 " 100-mm glass tube containing the analyte or the IS as prepared in the last paragraph was evapo-rated to dryness under a stream of nitrogen at 50 °C. To the dried residue was added 50 !L acetonitrile and 50 !L of the selected derivatization reagent; the tube was capped, mixed, and incubated for 20 min at 90 °C in a heating block . The mixture was cooled for GC-MS
analysis. The structures of the derivatized analytes and ISs are shown inFigure 1along with their mass spectra.
Instrumentation, Analytical Parameters, and Data
GC-MS analysis was performed on an Agilent 6890 GC interfaced to an Agilent 5975 MSD (Agilent, Palo Alto, CA). A 12-m HP-ULTRA-1 crosslinked 100% methyl siloxane capillary column (0.20-mm i.d., 0.33-!m film thickness) from Agilent (Wilmington, DE) was used for this study. Helium carrier gas flow rate was 1.0 mL/ min. The injector and GC-MS interface temperatures were maintained at 250 °C and 280 °C, respectively. For MDA experiment, the GC oven temperature was initi-ated at 75 °C (held for 0.5 min), raised to 200 °C at 20°C/min (held for 1 min), then to 275 °C at 40°C/min (held for 1 min); for HM, the GC oven temperature was initiated at 160 °C (held for 1 min), raised to 250 °C at 20 °C/min (held for 3 min), then to 290 °C at 10 °C/min (held for 2 min). These oven temperature programming parameters are obviously more than what are needed for this study; however, they are routinely used in this laboratory for the analyses of respective categories of compounds and have been adopted here to facilitate the identification of specific derivatization products.
Typically, a full-scan mass spectrum of the derivat-ized analyte or IS was obtained by injecting the CD product into the GC-MS system. The scan-range was typically set from m/z 50 to the molecular weight of the anticipated product with the maximal number of CD groups, rounded to the next “50” or “100.” A separate run was repeated for the isotopic analog of the analyte. Information derived from these ion chromatograms (retention time and mass spectrometric data) were used to characterize the analyte or the IS. Full-scan mass spectrometric data were stored as digital files that were then converted into mass spectra of a more desirable format for systematic presentation as shown inFigure 1. This conversion was carried out using DeltaGraph software (DeltaPoint, Seattle, WA) on an Apple iMac G5 computer (Cupertino, CA).
Full-scan mass spectrometric data obtained from these runs were reviewed to select ions (Figures 2and3) that may be suitable for designating the analyte and its IS in routine GC-MS protocols. These CD products (the analyte of interest and its isotopic analogs) were in-jected (separately) into the GC-MS again under SIM mode, and the ions selected from the full-scan mass spectrometric data were monitored. General criteria adopted for SIM ion selection included: (1) full-scan intensity data indicated less than 10% CC; and (2) the ion’s relative intensity in the full-scan mass spectrum was "10%. Ions with lower intensity would have been included if there were less than three pairs of ions that met the above criteria. Mass spectrometric data derived from these SIM runs were then used to evaluate the CC data. Details of the methodology have been described in
our earlier publications[9, 10]and briefly illustrated in the next section using the data derived from the MDA/ MDA-d5 system as the example.
Normalization of SIM Data Derived from the
Analyte and the IS and the Calculation
of CC Data
Full-scan mass spectra of t-BDMS derivatized MDA and MDA-d5 (Figure 1) indicate the following ion-pairs
meet the selection criteria described in the last para-graph: m/z 100/104, 158/162, 236/241, 278/283 (Figure 2). They were further examined by the SIM protocol. Shown in Table 1 is one set of the observed raw ion intensity data (in % relative intensity for full-scan; in
integrated peak area for SIM). Also included in this table are the normalized SIM data (for MDA-d5) and
the CC data calculated based on the raw and the normalized data. Example calculations for the nor-malization process and the derivation of CC data are shown below.
For the SIM run including only MDA, the intensity of the base-peak ion for MDA (m/z 158) was 20,146,666. On the other hand, the intensity for the corresponding ion (m/z 162) for MDA-d5, in the run including only
MDA-d5, was 40,018,206. Thus, all SIM ion intensity data
derived from the run including only MDA-d5 were
adjusted by a factor of 20,147,110/40,018,206 (or 0.5034) and shown in the last column inTable 1. For example, the normalized intensity for the ion m/z 100 collected
Figure 1. Full-scan mass spectra and molecular information of (A) MDA/MDA-d5 (as t-BDMS
derivatives) and (B) hydromorphone/hydromorphone-d6(as TMS derivatives). (All spectra were
during the run including only MDA-d5is now 76,615 "
0.5034 (or 38,568).
Two sets of CC data were then calculated, both using the raw data generated from the run including only MDA, but using the raw or the normalized data generated from the run including only MDA-d5. For example, for the
ion-pair m/z 100/104, the run including only MDA gener-ated an intensity value of 1291,998, while the run includ-ing only MDA-d5generated an intensity value of 76,615;
thus, MDA-d5would have contributed 76,615/1291,998 #
5.93% to the intensity measured for m/z 100, if an equal amount of MDA and MDA-d5were present. (It should be
pointed out that the CC hereby defined differs from what has been adopted by Barbalas and Garland . Specifi-cally, we define the CC of the IS to the analyte as the intensity ratio of this ion generated by the IS to that generated by the analyte, when equal amounts of the IS and the analyte are present. For their purpose, Barbalas and Garland defined a “coefficient”, which is the intensity ratio of the ion designating the analyte to that designating the IS, when only the IS is present.)
The second set of CC data were calculated using the normalized ion intensity for MDA-d5. Since the
normal-ized intensity for the ion m/z 100 collected during the run including only MDA-d5 is 38,568, the percent CC
calculated based on the normalized data is 38,568/ 1291,998 # 2.99%. Both sets of CC data (5.93% and 2.99%) are shown inTable 1.
Results and Discussion
In a 1989 studyon the quantitation of benzoylecgo-nine (a cocaine metabolite), it was noted that the CC phenomenon between the ion-pair (ions designating the analyte and the IS) systematically affected the resulting quantification data. Accordingly, a procedure was devel-oped in a later studyto determinate the CC of ion-pairs that may potentially be used to designate the analyte and the selected IS. With these data available, it was then possible to select the ion-pair with no (or minimal) CC for the quantitation purpose. However, whether the method developed indeed produced accurate CC values has al-ways been an area of concern. Thus, a follow-up study
was conducted to develop three additional methods (improved direct measurement, internal standard, and standard addition), and they were compared against the method (direct measurement) developed earlier. This later study  concluded that “all methods produce practically the same order, among ions derived from each isotopic analog, in their extents in contributing to the intensities of respective ions designated for a specific counter isotopic analog. Thus, all methods can be used to select the best ion-pair within a selected analyte/[IS] for the intended quantitative analysis protocol” . How-ever, the accuracy (trueness) of the empirically deter-mined CC data still could not be assessed. With this in mind, the approach described below is proposed to
deter-Figure 2. Fragments of major ions derived from MDA (as t-BDMS derivatives).
mine whether a set of empirically determined CC is indeed accurate.
Assessing the Accuracy of the Empirically
Determined Cross-Contribution Values
A four-step process was developed to assess whether a set of empirically derived CC data for a specific ion-pair designating an analyte/IS system are correct. Steps of this approach are first outlined below, while details of each step have either been described in the Experimen-tal section or will be further illustrated later: (1) the CC of an selected ion-pair were determined using the raw ion intensity data , followed by the calculation of another set of CC data using normalized ion intensity data; (2) a series of standard solutions were prepared and then analyzed to obtain a set of experimentally observed concentrations; (3) the two sets of CC data (derived from raw and normalized ion intensity data) were alternately used to derive two sets of theoretically calculated concentrations for this set of standards; and finally, (4) these three sets of concentrations were eval-uated to determine if either set of the theoretically calculated concentrations is the same (allowing experi-mental errors) as the set of the experiexperi-mentally observed concentrations.
The concentrations of individual standards in each set deviated from their respective true values, but with different implications. Deviations of the experimentally observed concentrations were caused by the true CC imbedded in the adopted ion-pair designating the ana-lyte and the IS, while deviations, if any, of the theoret-ically calculated concentrations were caused by incor-porating incorrect empirically determined CC values (two sets) into the calculation. Thus, if the set of CC data under examination are accurate, these deviations result-ing from the theoretically calculated data, usresult-ing this set of CC, should coincide well with the experimentally observed (permitting random experimental errors). On the other hand, significant differences between these
two sets of deviations indicate existence of significant random and/or systematic errors in deriving this set of CC data under examination.
For this study, the MDA/MDA-d5 system was
se-lected as the exemple analyte/IS system and t-BDMS the derivatization group. Data derived from this system will be fully presented to illustrate the details of the approach, while only the concluding data for the HM/ HM-d6system (with TMS as the derivatization group)
will be presented to support the validity of the ap-proach hereby reported.
Ion-Pair Selection and Ion Intensity Measurement
Shown in Figure 2 are the fragments of major ions observed in the mass spectrum derived from MDA. The first four ions retain the structural framework in where most (or all) labeling deuterium atoms are positioned; they can potentially be used to designate the analyte and the IS. The last ion, [M $ 158]% (or m/z 135) for
MDA and [M $ 162]%(or m/z 136) for MDA-d 5, differ
only by one atomic unit and, thus, is not suitable for designating the analyte and the IS. Ion m/z 73 comes from the derivatization group (TMS, t-BDMS). It is not characteristic of the analyte of interest and cannot be used to designate the analyte and the IS.
Cross contribution data shown in Table 1 indicate that the most favorable ion-pair for designating MDA/ MDA-d5 is m/z 158/162. Both ions in this pair exhibit
high intensities and low CC; thus, they were selected as the control in this study to illustrate the generation of high-quality quantitation data. Ions m/z 100/104 have reasonable intensities, but also with significant CC. Adopting this ion-pair for quantitation will result in noticeable error. Since the main objective of this study is to examine the interference consequence of CC in the quantitation process, ion-pair m/z 100/104 (with signif-icant CC) was selected to fully illustrate the deviation phenomenon and the assessment process as outlined in the first paragraph of the last subsection. The other two
Table 1. MDA and MDA-d5ion intensity data collected under full-scan (in %) and SIM (peak area) modea
Raw data from the MDA run Raw data from the MDA-d5run Normalized data for MDA-d5
(m/z) Full-scan(rel. int.) (%CC by MDA-dSIM ion intensity5)
(rel. int.) SIM ion intensity(% CC by MDA) SIM ion intensity(% CC by MDA)
Ions designating MDA
100 6.6% 1,291,998 (5.93%; 2.99%)b 0.4% 76,615 38,568
158 100% 20,146,666 (0.10%; 0.05%) 0.1% 19,859 9,997
236 4.0% 857,201 (1.024%; 0.52%) 0.0% 8,777 4,418
278 2.1% 472,570 (0.25%; 0.13%) 0.0% 1,179 594
Ions designating MDA-d5
104 0.2% 88,342 5.8% 2,247,498 (3.93%) 1,131,390 (7.81%)
162 0.3% 109,115 100% 40,018,206 (0.27%) 20,147,165 (0.54%)
241 0.0% 158 4.4% 1,938,632 (0.01%) 975,907 (0.02%)
283 0.0% 248 2.0% 913,091 (0.03%) 459,650 (0.05%)
aAll data shown in this table were obtained from a single experiment. Reproducibility data are shown inTable 2.
bData shown inside parentheses are CC data (in %). When two CC data are given, the first and the second data were derived, respectively, from raw
ion-pairs, m/z 236/241 and 278/283, will not be dis-cussed further.
Ion intensities derived from MDA and MDA-d5may
not be compatible for the following reasons: (1) due to experimental errors, the quantities of MDA and MDA-d5 may not be exactly the same; (2) the
derivati-zation reaction for MDA and MDA-d5, performed in
separate tubes, may not be completed to the same extent; and (3) the separate injections and data collec-tions for MDA and MDA-d5in the GC-MS process may
also involve variations. For these reasons, the CC data calculated based on the raw intensity data produced in two separate runs for MDA and MDA-d5may include
bias. Thus, alternatively, intensity data of MDA-d5ions
were converted into “normalized” values with the assumption that the base-peak ions (m/z 158 and 162 in this case) of the MDA and MDA-d5 would have the
same intensities (the normalized intensity data are shown in the last column inTable 1).
The normalization process was intended to correct experimental errors. Systematic factors, such as isotopic effect on the ion fragmentation process that might have been caused by the deuterium atoms in MDA-d5, have
not been addressed. If the isotopic effect is a significant factor, the CC of MDA toward the intensities of ions designating MDA-d5(and vice versa) would have been
under- or over-estimated depending on whether the isotope effect would reduce or enhance the intensities of the corresponding ion fragments derived from MDA-d5. Thus, assessing the CC data derived from the
normalization process can also reveal whether isotope effect is a significant factor in the system under exam-ination.
Multiple Measurements for Precision Study
The reproducibility of the calculated CC data were examined at two levels. First, each of the run including only MDA and the run including only MDA-d5 was
injected into the GC-MS system six times. The resulting ion intensity data were used for the calculation of the CC data as described in the Experimental section. At the second level, a new set of MDA and MDA-d5 was
prepared individually in a different day and again each
injected six times. Mean, standard deviation, and coef-ficient of variation (CV%) for the CC data derived from the raw ion intensity data are shown in Table 2. The corresponding means of CC data derived from the nor-malized ion intensity data are also included in the table. Corresponding data derived from days 1 and 3 were averaged and entered into the last two columns of the table. All CC data shown in Tables 1 and 2 were rounded to the second digit after the decimal point. Cross contribution at this level (one hundredth of 1%) will not contribute to observable difference in practical applications.
The precisions of the resulting CC data were as-sessed by the observed standard deviation and CV% of these measurements. As shown inTable 2, the CV% for CC in the parts per hundred range were between 11% and 23%, while the CV% for the CC data in the parts per thousand range were between 15% and 36%. These precision data are not poor ones, considering the fact that each CC value was derived from a highly abundant ion in one run and a very low abundant ion in another run. This is especially true for the CC in the parts per thousand range and, in this case, it should not be a matter of concern for the following reasons: (1) the intensities of the CC ions are negligibly, making their precise measurement impossible; and, perhaps more importantly, (2) with such low CC, quantitation data resulting from the adoption of these ion-pairs would not really be affected. This latter statement is further supported by the exemplar data shown in the next section.
Selection of Ion-Pairs and Calibration Method
Shown inTable 3are two sets of data (for ion-pairs m/z 100/104 and 158/162) derived from a series of standard solutions prepared in drug-free urine with the concen-trations of MDA ranging from 30 to 4000 ng/mL. As mentioned earlier, ion-pair m/z 158/162 exhibits mini-mal CC; thus, adopting this ion-pair for quantitation can generate high-quality data. Data are shown in the lower section ofTable 3to serve as a control, indicating deviations resulting from the ion-pair m/z 100/104 are indeed caused by the significant CC imbedded in the
Table 2. Precision of cross contribution data derived from within- and between-day measurements
Day 1 Day 3 Days 1 and 3
Raw data Normalized Raw data Normalized Raw data Normalized
Ion Meana SD CV% Mean Meana SD CV% Mean Mean Mean
Ions designating MDA
100 5.85 0.82 14 3.02 5.98 1.40 23 2.96 5.92 2.99
158 0.11 0.02 19 0.06 0.17 0.06 36 0.08 0.14 0.07
Ions designating MDA-d5
104 4.22 0.46 11 8.09 4.16 0.87 21 8.08 4.19 8.09
162 0.27 0.04 15 0.51 0.30 0.08 27 0.59 0.28 0.55
measurement of ion intensities. For the purpose of this study, significant deviations resulting from the adopta-tion of ion-pair m/z 100/104 as the quantitaadopta-tion ion-pair can better illustrate the novel approach proposed for assessing the empirically determined CC data.
It should be noted that most analytical protocols would select the most favorable ion-pair to designate the analyte and the IS and adopt a multiple-point approach instead of the one-point calibration approach. One-point calibration is a two-point linear model using one calibrator and assuming that the response is “0” when the analyte’s concentration is at 0 ng/mL. This approach provides accurate quantitation data when the analyte’s concentration in the test sample is at the vicinity of the concentration of the selected one-point calibrator. With only two data points available, one-point calibration must adopt the linear model with a
very limited linear range, especially when the CC of the selected ion-pair is significant. On the other hand, with multiple-point calibration, linear and other models, such as polynomial or hyperbolic, can be used to fit the observed data, thus compensating for CC effect that are highly significant at the lower and higher ends. This would results in a much wider calibration range.
Effect of CC on Calibration Curve
The ion intensity ratios shown in the second column of
Table 3 are the empirically observed values for the ion-pairs designating MDA and MDA-d5. The
concen-trations shown in the third column are the empirically observed concentrations of these standards based on the ratios shown in the second column, using the 500
Table 3. Effect of cross contribution on empirically determined and theoretically calculated concentrations of a series of standard solutions
Theoretically calculated with CC derived from
Empirically observed Raw ion intensity data Normalized ion intensity data Theoretical conc. Ion int. ratio Observed conc. (% deviation) Ion int. ratio Calculated conc. (% deviation) Ion int. ratio Calculated conc. (% deviation) m/z 100/104a 30 0.1425 42.8 (42.5) 0.0947 79.7 (165.8) 0.0978 42.9 (42.9) 50 0.1944 58.3 (16.6) 0.1183 99.6 (99.2) 0.1427 62.5 (25.1) 80 0.3085 92.5 (15.7) 0.1536 129.4 (61.7) 0.2094 91.7 (14.7) 100 0.3978 119.3 (19.3) 0.1770 149.1 (49.1) 0.2534 111.1 (11.1) 200 0.6713 201.4 (0.68) 0.2937 247.4 (23.7) 0.4689 205.5 (2.8) 300 1.083 324 (8.3) 0.4093 344.7 (14.9) 0.6770 296.7 ($1.1) 500 1.667b 500 (Calibrator) 0.6370 536.5 (7.3) 1.0719 469.7 ($6.1) 800 2.525 757.3 ($5.3) 0.9703 817.3 (2.2) 1.617 708.5 ($11.4) 1,000 3.149 944.5 ($5.5) 1.187 1,000 (0.012) 1.952 855.2 ($14.5) 1,300 3.336 1,000 ($23) 1.5052 1,268 (-2.5) 2.416 1059 ($18.5) 1,700 4.037 1,211 ($28.8) 1.915 1,613 ($5.09) 2.975 1304 ($23.3) 2,000 4.510 1,353 ($32.4) 2.213 1,864 ($6.8) 3.355 1470 ($26.5) 3,000 5.786 1.736 ($42.1) 3.151 2,654 ($11.5) 4.425 1939 ($35.4) 4,000 6.726 2,017 ($49.6) 4.0101 3,378 ($15.6) 5.268 2309 ($42.3) m/z 158/162c 30 0.0832 25.5 ($15) 0.0326 31.3 (4.5) 0.0607 30.3 (1.1) 50 0.1370 42.0 ($16) 0.0534 51.3 (2.7) 0.1006 50.3 (0.64) 80 0.2354 72.2 ($9.8) 0.0845 81.3 (1.7) 0.1606 80.3 (0.35) 100 0.3107 95.3 ($4.7) 0.1053 101.3 (1.3) 0.2005 100.2 (0.24) 200 0.5920 181.5 ($9.3) 0.2092 201.2 (0.61) 0.3998 199.9 ($0.045) 300 0.9828 301.3 (0.43) 0.3129 301.1 (0.36) 0.5987 299.4 ($0.21) 500 1.631b 500 (Calibrator) 0.5203 500.6 (0.12) 0.9952 497.6 ($0.48) 800 2.723 834.8 (4.3) 0.8310 799.5 ($0.064) 1.587 793.4 ($0.83) 1000 3.645 1,118 (11.8) 1.038 998.4 ($0.16) 1.979 989.5 ($1.1) 1300 3.969 1,217 ($6.4) 1.348 1296 ($0.27) 2.564 1282 ($1.4) 1700 5.196 1,593 ($6.3) 1.760 1693 ($0.41) 3.338 1669 ($1.8) 2000 6.169 1,891 ($5.4) 2.068 1990 ($0.51) 3.915 1957 ($2.1) 3000 9.593 2,941 ($1.9) 3.093 2975 ($0.82) 5.809 2905 ($3.2) 4000 12.59 3,860 ($3.5) 4.111 3955 ($1.1) 7.664 3832 ($4.2)
aThese data were taken from the MDA/MDA-d
5system using the raw ion intensity data to calculate the CC data: the contribution of MDA-d5to the
intensities of ions designating MDA are 5.92% for m/z 100 and 0.14% for m/z 158; the contribution of MDA to the intensities of ions designating MDA-d5are 4.19% for m/z 104 and 0.28% for m/z 162.
bAverage of triplicates.
cNormalized ion intensity data were used to calculate the CC data: the contribution of MDA-d
5to the intensities of ions designating MDA are 2.99%
for m/z 100 and 0.068% for m/z 158; the contribution of MDA to the intensities of ions designating MDA-d5are 8.09% for m/z 104 and 0.55% for m/z
ng/mL standard as the calibration standard. The per-centage figures shown inside parentheses in the third column are percentage deviations of the empirically observed concentrations from the true (or prepared) concentrations.
To best illustrate the effect of CC on quantitation result, one-point calibration approach was used to derive the observed concentration resulting from each ion intensity ratio. Calibration curve approach would have averaged out the positive/negative deviations exhibited by standards at the lower and higher ends of the curve, thus reducing the deviations that serve as the basis of this study. With one-point calibration, the observed concentration of a standard/specimen can deviate from its true value significantly when the CC of the adopted ion-pair is significant. Thus, for the stan-dard with 4000 ng/mL analyte, 2017 ng/mL was ob-served adopting m/z 100/104 as the quantitation ion-pair. The corresponding concentration was 3860 ng/mL when ion-pair m/z 158/162 was adopted as the quanti-tation ion-pair.
As we have reported earlier, the CC phenome-non will cause the intensity ratio values shown in the second column to deviate from a linear relationship when plotted against their respective concentrations. This nonlinear relationship and need for correction has also been emphasized by Duncan et al.as discussed in the Introduction section. Our objective for this part of the study is to evaluate the accuracy of the two sets of CC data that were derived from direct measurement without and with a normalization process. For this purpose, each set of the CC data was used to derive a set of ion intensity ratios for this series of standard solutions. The calculated intensity ratios were then used to derive the concentrations of this series of standards. With two sets of CC data, we have calculated two sets of intensity/concentration figures. These two sets of calculated ratio/concentration data are shown in the fourth/fifth and the sixth/seventh columns inTable 3. Theoretically calculated data were derived with the following stipulations: (1) as justified in the second paragraph of this subsection, quantitation is based on one-point calibration, of which the concentrations of the analyte and the IS in the calibrator were both 500 ng/mL; (2) the intensities of the ions, designating the analyte and the IS, increase and decrease linearly with their concentrations; and (3) the CC values (i.e., ana-lyte’s contribution to the intensity of the ion designating the IS and the IS’s contribution to the ion designating the analyte) as empirically determined, were applied. Stipulation “2” is true as shown by the data resulting from the m/z 158/162 ion-pair. The most important aspect of this study is that if the empirically derived CCs were inaccurate, stipulation “3” would embed a systematic error in the calculated concentrations. This error would allow for assessing the trueness of the CC values as discussed in the next section.
With these stipulations in mind, a sample calculation (with m/z 100 for the analyte and m/z 104 for the IS) is
shown below. At 500 ng/mL, the average intensity ratio for m/z 100 (I100) to 104 (I104) derived from the raw data
for the 12 measurements (six for day 1 and six for day 2) shown inTable 2 was I100/I104#0.5936/1.
When the analyte’s concentration is 4000 ng/mL and the IS’s concentration remains at 500 ng/mL, the I100/
I104 ratio without CC would have been [0.5936 "
(4000/500)]/1, or 4.749/1 [instead of (4000/500)/1, or 8/1]. However, taking the 5.92% and 4.19% directly-measured CC data into account, the resulting ion inten-sity ratio would have been
I100/I104# (4.749 % 0.0592)/(1 % 4.749 " 0.0419) #
4.0101. With this calculated ion intensity ratio, the resulting concentration of the analyte, X, can be calcu-lated as follows:
0.5936/500 # 4.0101/X; X # 4.0101 " 500/0.5936 # 3378 ng/mL.
Thus, the calculated concentration of the analyte is (3378–4000)/4000, or $15.6%, lower than the expected value, 4000 ng/mL. The theoretically calculated concen-trations for the standards at other concenconcen-trations (and their deviations from the respectively expected values) were similarly calculated and placed in the fourth and fifth columns ofTable 3.
Shown in the sixth and seventh columns ofTable 3
are the same as the data shown in the fourth and the fifth columns, except that the ion intensity data, for ions
m/z 100 and 104, and thereby derived normalized CC data, were used for calculation. Basically, the calcula-tion is the same as shown above, with the excepcalcula-tion that I100/I104#1291998/1131499 # 1.1418, while the CCs for
the IS to the analyte and the analyte to the IS are 2.99% and 8.09%, respectively.
Graphic Presentation on the Evaluation of CC
Data Based on the Consistency of the Empirically
Observed and Theoretically Calculated
Shown in the second and the fourth columns ofTable 3
are the empirically and the theoretically calculated concentration (using the CC data derived from raw ion intensity data). Deviations of these concentrations from the expected values (for standards at different concen-tration levels) were plotted inFigure 4(A). Clearly, the calculated concentrations (Figure 4(A)-(b) are not con-sistent with what have been actually observed, and their deviations from the expected values are even more significant than that derived from the empirically ob-served concentrations (Figure 4(A)-(a). This is a clear indication that the CC values derived from the raw ion intensity data and used as the basis for theoretical calculations to derive the concentrations shown in col-umn 4 were inaccurate.
Could this deviation be caused by experimental errors, such as using different quantities of MDA and MDA-d5 or difference in the completion of the
possibilities were ruled out because the curve (Figure 4(A)-(c) generated by the deviation data shown in the seventh column ofTable 3exhibits excellent agreement with the curve derived from the empirically observed concentration data. Thus, CC data derived from the normalization process, but not from raw intensity data, can fully describe the observed MDA concentrations that were calculated based on experimentally observed ion intensity ratios. It is thus concluded that the ion intensity normalization process produce more accurate CC data.
To validate what have been stated above, another set of standards were prepared and experiments were performed. The resulting plots are shown in Figure 4(B).Figure 4(A) and (B) exhibit excellent agreement.
To further prove the normalized intensity data can be reliably used for the calculation of CC values in
other analyte/IS systems, the TMS-derivatized HM/ HM-d6 system (see Figure 1B for full-scan mass
spectra and molecular information), with an ion-pair exhibiting significant CC, was randomly selected as another example. Studies parallel to that adopted for the MDA/MDA-d5 system were performed.
Adopt-ing m/z 234/240 (Figure 3) as the quantitation ion-pair designating HM/HM-d6, the CC of the IS to the
analyte and the analyte to the IS, which were calcu-lated based on the raw ion intensity data, were 1.14 and 9.83, respectively. The corresponding CC data using the normalized data were 2.70 and 4.15, respec-tively. The resulting curves are shown inFigure 5. It is interesting to note that curve (b) starts higher than curves (a) and (c) in Figure 4A and B, while the reverse is true inFigure 5, reflect that the normaliza-tion processes in the MDA/MDA-d5 and the HM/
Figure 4. Comparison of errors derived from observed concentrations and those calculated with corrections of CC data derived from two methods, the MDA/MDA-d5system (m/z 100/104). (A) and
(B): results of the first and the second set of study; (a) deviation of empirically observed from the expected concentrations; (b) deviation of the theoretically calculated concentrations, using CC data (5.92% and 4.19% for the MDA/MDA-d5system), derived from raw intensity data, from the expected
concentrations; and (c) deviation of theoretically calculated concentrations, using CCs data (2.99% and 8.09% for the MDA/MDA-d5system), derived from normalized intensity data, from the expected
HM-d6 systems adjusted the relative analyte/IS ion
intensity in opposite directions.
It is noted that curves (a) and (c) inFigure 5do not coincide as well as the corresponding curves inFigure 4. We believe this does not invalidate the application of the normalization approach to the HM/HM-d6system;
instead, it is a reflection of more significant experimen-tal errors incurred in the HM/HM-d6 study. Further
study will be conducted in the future to include other analyte/IS systems and CC data derived from other methods.
In conclusion, the ion intensity normalization pro-cess has been proven effective for generating accurate CC data, at least for the MDA/MDA-d5 system, and
perhaps more importantly, the CC evaluation approach developed in this study is proven effective. This result further indicates that potential H/D isotope effect in the ion fragmentation process does not play an important role in the generation of ions adopted in our study. This is not surprising as the ion-pairs adopted for quantita-tion purpose were generated without the breaking of C–H/C–D bonds in the corresponding analyte/IS mo-lecular framework.
Effects of CC on Achievable Linear Range
In theory, if the intensity of the ion designating the analyte includes contribution by the IS, the percentage of the intensity of this ion derived from the IS becomes increasingly significant as the analyte’s concentration is lowered. Consequently, the achievable limit of quanti-tation would be at a higher level when the contribution of the IS to the intensity of the ion designating the analyte becomes larger. Similarly, if the analyte makes a significant contribution to the intensity of the ion
des-ignating the IS; then, as the analyte’s concentration becomes higher, the observed concentration will be-come increasingly lower than the true value.
Shown inTable 3are data related to the effect of CC on achievable linear range. Two sets of ion-pairs (one with significant CC, one with negligible CC) from the MDA/MDA-d5 system were adopted for illustration.
For the m/z 100/104 ion-pair (upper section of the table), based on the raw ion intensity data, the CC of the IS to the analyte and the analyte to the IS were 5.92% and 4.19%, respectively. With these levels of CC, the accept-able concentration range (with less than 20% deviations from the expected values) derived from the empirically observed data (columns 1 and 2 inTable 3) is limited to 200–1000 ng/mL, using 500 ng/mL as the one-point calibration standard.
The lower section ofTable 3 provides the parallel quantification data adopting an ion-pair (m/z 158/ 162) with much lower CC. Based on raw ion intensity data, the CC of the IS to the analyte and the analyte to the IS were 0.14% and 0.28%, respectively. With these levels of CC data, the deviations of the empirically observed concentrations within the entire range stud-ied (30 – 4000 ng/mL) were all lower than 20% (col-umn 2 inTable 3).
In conclusion, this study has developed a novel approach to assess the accuracy of the CC data between the ions designating the analyte and the deuterated IS, and concluded that the normalized ion intensity data can be reliably used for the calculation of the CC values, at least for the systems studied. Empirically and theo-retically calculated data both indicate that an ion-pair with !5% (or higher) CC will result in a very limited linear calibration range.
Figure 5. A parallel set of data derived from the study on the HM/HM-d6system (m/z 234/240); (a)
deviation of empirically observed from the expected concentrations; (b) deviation of the theoretically calculated concentrations, using CC data (1.14% and 9.83% for the hydromorphone/hydromor-phone-d6 system), derived from raw intensity data, from the expected concentrations; and (c)
deviation of theoretically calculated concentrations, using CCs data (2.70% and 4.15% for the hydromorphone/hydromorphone-d6 system), derived from normalized intensity data, from the
The authors gratefully acknowledge financial support from (Taiwanese) National Bureau of Controlled Drugs (DOH-96-NNB-1004) and National Science Council (NSC 95-2745-M-242-003-URD), and technical support provided by Ms. Meng-Yen Wu.
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