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Estimation of the measurement uncertainty of methamphetamine and amphetamine in hair analysis
Forensic Science International 185 (2009) 59–66
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Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Estimation of the measurement uncertainty of methamphetamine and amphetamine in hair analysis Sooyeun Lee *, Yonghoon Park, Wonkyung Yang, Eunyoung Han, Sanggil Choe, Miae Lim, Heesun Chung National Institute of Scientific Investigation, 331-1 Sinwol-7-dong, Yangcheon-gu, Seoul 158-707 Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Article history: Received 27 January 2008 Received in revised form 15 December 2008 Accepted 18 December 2008
The measurement uncertainties (MUs) were estimated for the determination of methamphetamine (MA) and its main metabolite, amphetamine (AP) at the low concentrations (around the cut-off value of MA) in human hair according to the recommendations of the EURACHEM/CITAC Guide and ‘‘Guide to the expression of uncertainty in measurement (GUM)’’. MA and AP were extracted by agitating hair with 1% HCl in methanol, followed by derivatization and quantification using GC–MS. The major components contributing to their uncertainties were the amount of MA or AP in the test sample, the weight of the test sample and the method precision, based on the equation to calculate the mesurand from intermediate values. Consequently, the concentrations of MA and AP in the hair sample with their expanded uncertainties were 0.66 0.05 and 1.01 0.06 ng/mg, respectively, which were acceptable to support the successful application of the analytical method. The method precision and the weight of the hair sample gave the largest contribution to the overall combined uncertainties of MA and AP, for each. ß 2009 Elsevier Ireland Ltd. All rights reserved.
Keywords: Measurement uncertainty Hair analysis Methamphetamine Amphetamine Method precision
1. Introduction Quality assurance is a major concern in the area of forensic toxicology because the analytical results have a great effect on administrative and legal consequences. In recent years, many analytical chemistry laboratories have employed a quality management system, compliant to international quality standards such as ISO/IEC 17025. For forensic laboratories, the Crime Laboratory Accreditation Programs of the American Society of Crime Laboratory Directors/Laboratory Accreditation Board (ASCLD/LAB) have been well known as accreditation programs and the ASCLD/LAB-International Program was newly established in 2003 based on the ISO/IEC 17025 standards and the ASCLD/LABInternational Supplemental Requirements [1]. These programs require applicants and/or accredited laboratories to demonstrate the reliability of analytical data objectively in various ways: proper validation of analytical methods, regular participation in proficiency tests, etc. The estimation of the measurement uncertainty (MU) is another accreditation requirement of ISO/IEC 17025. According to the EURACHEM/CITAC Guide [2], the MU is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of values that could reasonably be
* Corresponding author. Tel.: +82 2 2600 4937; fax: +82 2 2600 4939. E-mail address: [email protected] (S. Lee). 0379-0738/$ – see front matter ß 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.forsciint.2008.12.012
attributed to the measurand and expressed the number after . Nowadays, it is recommended that the quantitative findings should be presented with their MU to evaluate the reliability of the results [3,4]. The application of drug analysis in hair has significantly increased in both forensic and clinical toxicology: illegal drug use, postmortem cases, drug-facilitated crimes, workplace drug testing, doping control, drug treatment or management programs, clinical diagnosis, gestational drug exposure, therapeutic drug monitoring (TDM), etc. [5,6]. In Korea, hair analysis is critical because it is accepted by law enforcement agencies as one of important corroborative facts for drug abuse. The hair analysis provides information not only on chronic drug use but also on drug use period according to the rate of hair growth [5], which has a key effect on legal decision. Usually, the result of hair testing is reported as positive and negative, for which several criteria were proposed for obtaining a positive result: evaluation of possible passive contamination, identification of metabolites, use of metabolites-to-parent drug ratios, use of assay values of decontamination washes and use of threshold values (cut-off values) [7,8]. In case other criteria are satisfactory, the determination of positive or negative depends significantly on the quantification results, so the cut-off value can be a key criterion. However, it can be difficult to determine if a quantified value is positive or negative when the value is very close to the cut-off value. In the human sports testing field, the decision limit, which is the threshold plus the MU, is adopted to establish a doping offence [9,10]. Even though the MU
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S. Lee et al. / Forensic Science International 185 (2009) 59–66
Fig. 1. Hair analysis procedure.
could be applied in a different way to the identification of a prohibited substance to supply legal evidence, it is necessary to establish the MU at the cut-off value as one of supplementary criteria in forensic analysis. Methamphetamine (MA) has received the most attention as a drug of abuse in Korea. It undergoes some N-demethylation to amphetamine (AP), its major active metabolite [11]. As stated in our standard operating procedure (SOP), a MA concentration of greater than the cut-off value (0.5 ng/mg) [7] and an AP greater than lower limit of detection (LLOD) along with appropriate compound ion ratios are required to prove an individual’s MA use. Therefore, this research aims to estimate the MU of MA and AP at the low concentrations (around the cut-off value of MA) in human hair. 2. Experimental 2.1. Chemicals Methanol, ethyl acetate and hydrochloric acid (HCl) were analytical grade. MA hydrochloride and AM sulfate were obtained from Lipomed AG (Switzerland) for the preparation of a spiked hair sample. The solutions of MA, AP, MA-d5 and AP-d5 (1 mg/ml, 99% for each) from Cerilliant (TX, USA) were used to prepare the stock and working standard solutions. Dimethylsulfoxide (DMSO) and Trifluoroacetic anhydride (TFAA) were purchased from Sigma–Aldrich (MO, USA). 2.2. Preparation of a hair sample The preparation of a hair sample was carried out using a slight modification of a method described elsewhere [13]. Briefly, each ca. 60 mg of MA hydrochloride and AM sulfate were dissolved in a small volume of distilled water in a 1000 ml glass beaker. Then, 250 ml of 0.02 M HCl in DMSO and 250 ml distilled water were added in succession in the beaker in an ice bath. Drug-free hair (ca. 10 g) was soaked in the solution for 24 h. The hair was removed, rinsed in a sufficient volume of methanol several times and air-dried. 2.3. Preparation of stock and working standard solution Each 1 mg/ml of MA and AP was diluted in a 10 ml volumetric flask (Flask 10) with 1% HCl in methanol (Stock solution, 99 mg/ml). The working standard solution
was prepared by two steps: pipetting (Pipette 1) 1 ml of the stock solution into a 100 ml volumetric flask (Flask 100) and diluting with 1% HCl in methanol (Intermediate standard solution) followed by pipetting (Pipette 1) 1 ml of the intermediate standard solution into a 10 ml volumetric flask (Flask 10) and diluting with 1% HCl in methanol (Working standard solution). A 10–100 ml autopipette (Autopipette A) and a 200–1000 ml autopipette (Autopipette B) were used to make five sets of calibrators (2.5, 5, 10, 25, 50, 75 and 100 ng). 2.4. Hair analysis The experimental procedure (Fig. 1) given here was fully validated [12]. Shortly, triplicate hair samples were accurately weighed (ca. 10 mg), cut into very small pieces of less than 1 mm and agitated with 3 ml of 1% HCl in methanol for 20 h at 38 8C. MA-d5 and AP-d5 were added as internal standards. The hair extract was evaporated to dryness at 45 8C under N2 gas and then the residue was derivatized with 100 ml of TFAA/ethyl acetate (1:1) at 65 8C for 15 min. The excess derivatizing reagent was removed and the residue was reconstituted in ethanol for GC–MS analysis (Agilent 6890/5973 GC-MS system). The GC was equipped with a 30-mlong, 0.25-mm-i.d., 0.25-mm-film-thickness HP-5MS capillary column. The inlet temperature was 260 8C and the helium flow rate was 1.0 ml/min. The oven was programmed to operate at an initial temperature of 100 8C for 1 min, to increase the temperature to 270 8C at a heating rate of 20 8C/min and to hold at 270 8C for 10 min. The MS was operated in selected ion monitoring (SIM) mode. The TFAA derivatized ions for MA, AP, MA-d5 and AP-d5 were as follows: MA, m/z 154, 118, 110, 91; AP, m/z 140, 118, 91; MA-d5, 158, 122; AP-d5, 144, 122. 2.5. Evaluation of method precision Method precision was examined by analyzing hair samples spiked with low (8 ng), medium (40 ng) and high (80 ng) concentrations of MA and AP, respectively, using the same method described in the previous hair analysis section. The six aliquots of each sample were analyzed on the first day, followed by triplicates for the four consecutive days. 2.6. MU estimation The estimation of the MU was performed in compliance with the EURACHEM/ CITAC Guide [2] and ‘‘Guide to the expression of uncertainty in measurement (GUM)’’ [14]. In brief, there are six steps involved in developing the MU: Specification of the measurand; Identifying uncertainty sources; Quantifying uncertainty; Calculating the combined uncertainty; Calculating the degrees of freedom; Calculating the expanded uncertainty. Therefore, this study followed the process to derive an expanded uncertainty. Firstly, the mesurand was clearly
S. Lee et al. / Forensic Science International 185 (2009) 59–66
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expressed as a mathematical equation based on the experimental method. Secondly, the possible sources of uncertainty were listed according to the equation and an initial cause and effect diagram was proposed. Thirdly, considering the relationship among parameters which have an effect on the sources, an expanded cause and effect diagram was given. Then, the uncertainties of individual components were evaluated and quantified using analytical data. In order to adjust different units of measurement, the individual standard uncertainties (SU) were changed into the relative standard uncertainties (RSU) equivalent. Next, each RSU was combined by the root-sum-of-squares (RSS) method to give the combined standard uncertainty (CSR). After that, the degree of freedom of the CSR was calculated and an appropriate coverage factor was determined. Finally, an expanded uncertainty was given using the coverage factor.
3. Results Fig. 2. Initial cause and effect diagram.
3.1. Specification of the measurand According to the EURACHEM/CITAC Guide [2], it is necessary to define what is being measured and express quantitatively the relationship among the measurands in the first step. The concentration of MA or AP in the test sample (CMA or AP) was calculated by a simple mathematical model:
of the method precision (fprecision) as follows: C MA
or AP
¼
c0 f precision ðng=mgÞ W
(3)
3.2. Identifying uncertainty sources C MA
or AP
c0 ðng=mgÞ ¼ W
(1)
where c0 is the amount of MA or AP in the test sample and W is the weight of the test sample. Because c0 was derived from a calibration curve, CMA or AP was also given by C MA
or AP
¼
A 0 B0 1 ðng=mgÞ W B1
(2)
where A0 is the peak area ratio of MA or AP to IS (MA-d5 or AP-d5) and B0 and B1 is the intercept and the slope of the calibration curve, respectively. Furthermore, since the method precision should be considered as a major source of the MU in any quantification method [9], the equation was expanded using the correction factor
The relevant uncertainty sources are shown in the cause and effect diagrams (Figs. 2 and 3). From Eq. (1), CMA or AP was associated with c0 and W, which were the major bones in the initial cause and effect diagram (Fig. 2). c0 was calculated from a calibration curve and W was subjected to two main sources of uncertainty: variation of a balance and repeatability of measurement. This initial cause and effect diagram was expanded with the added correction factor, method precision. Moreover, the working standard solution was considered as another uncertainty source of c0 because hair samples spiked with standard solutions were used instead of a certified reference material. Also, the repeatability of measurement and the variation of solvent volume due to temperature change overlap with the uncertainty of the method precision, where those factors are already covered
Fig. 3. Expanded cause and effect diagram.
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[9]. Therefore, the effect of the repeatability of weighing hair was not included and those of the repeatability and the temperature change in using a 10 ml volumetric flask and 1 ml pipette to prepare the working standard solution were not considered. However, the repeatability and the temperature effect of the volumetric apparatus for the preparation of both the stock solution and the intermediate standard solution were regarded as contributors to the estimation of the MU since the solutions were made beforehand. Finally, the expanded cause and effect diagram was given as Fig. 3. 3.3. Quantifying uncertainty 3.3.1. c0 In order to create the RSU of c0 (ur(c0)), the two uncertainty components, one from the preparation of the working standard solution and the other from the calibration curve, were combined as follows: for MA, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðCalÞ ur ðc0 Þ ¼ u2r ðStdÞ þ u2r ðCalÞ ¼ u2r ðStdÞ þ c0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0:0011 ¼ 0:0131 ¼ 0:01312 þ 6:5799
and for AP, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:0022 2 ur ðc0 Þ ¼ 0:01312 þ ¼ 0:0131 10:0763 where ur(Std) is the RSU of the working standard solution, ur(Cal) is that of the calibration curve and u(Cal) is the SU of the calibration curve. Since the working standard solutions of MA and AP were prepared using chemicals with same purity and identical apparatus, the uncertainties ur(Std) were equal. For the calculation of ur(Std), following uncertainties were considered: uncertainty in the preparation of the stock solution, ur(Stock); uncertainty in the use of Autopipette A to make the calibrators, u(AutopipetteA); uncertainty in the use of Autopipette B to make the calibrators, u(AutopipetteB); uncertainty in the use of Pipette 1 to make the intermediate standard solution, u(Pipette1); uncertainty in the use of Pipette 1 to make the working standard solution, u0 (Pipette1); uncertainty in the use of Flask 10 to make the working standard solution, u(Flask10); uncertainty in the use of Flask 100 to make the intermediate standard solution, u(Flask100). The detailed calculation of ur(Std) was summarized in Table 1. According to the manufacturer’s certificate of analysis, it was assumed that the purity of each solution of MA and AP was 100 1%, which was converted to 1.0 0.01 mg/ml. A rectangular
Table 1 A summary of the calculation of ur(Std) for MA and AP. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 2 2 uðAuto pi petteAÞ 2 uðAuto pi petteBÞ 2 uðPi pette1Þ 2 u ðPi pette1Þ 2 uðFlask10Þ uðFlask100Þ u2r ðStockÞ þ 3 þ4 þ þ þ þ Vol:ðAuto pi petteAÞ Vol:ðAuto pi petteBÞ Vol:ðPi pette1Þ Vol:ðPi pette1Þ Vol:ðFlask10Þ Vol:ðFlask100Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:0001 2 0:0005 2 0:0095 2 0:0035 2 0:0144 2 0:3751 2 þ4 þ þ þ þ ¼ 0:0131 ¼ 0:00702 þ 3 0:1 1 1 1 10 100
ur ðStdÞ ¼
Uncertainty in the preparation of the stock solution: ur(Stock) rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi uðPurityÞ 0:006 2 ¼ þ uðFlask10Þ þ 0:0391 ¼ 0:0070 ur ðStockÞ ¼ 0:99 10 Purity Volume pffiffi ¼ 0:006 mg=ml uðPurityÞ ¼ 0:01 3
uðFlask10Þ ¼
ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 ðTol10Þ þ u2 ðTem p10Þ þ u2 ðRe peat10Þ ¼ 0:01442 þ 0:03632 þ 0:00162 ¼ 0:0391 ml
pffiffi ¼ 0:0144 ml uðTol10Þ ¼ 0:025 3 pffiffi ¼ 0:0363 ml; ð10 5 1:259 103 Þ ¼ 0:0630 ml uðTem p10Þ ¼ 0:0630 3 pffiffiffiffi ¼ 0:0016 ml uðRe peat10Þ ¼ 0:0049 10
Uncertainty in the use of Autopipette A to make the calibrators: u(AutopipetteA) ¼ 0:0001 ml uðAuto pi petteAÞ ¼ 0:0002 2 Uncertainty in the use of Autopipette B to make the calibrators: u(AutopipetteB) uðAuto pi petteBÞ ¼ 0:001 2 ¼ 0:0005 ml Uncertainty in the use of Pipette 1 to make the intermediate standard solution: u(Pipette1) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðPi pette1Þ ¼ u2 ðTol1Þ þ u2 ðTem p1Þ þ u2 ðRe peat1Þ ¼ 0:00352 þ 0:00362 þ 0:00812 ¼ 0:0095 ml pffiffi ¼ 0:0035 ml uðTol1Þ ¼ 0:006 3 pffiffi ¼ 0:0036 ml; ð1 5 1:259 103 Þ ¼ 0:0063 ml uðTem p1Þ ¼ 0:0063 3 pffiffiffiffi ¼ 0:0081 ml uðRe peat1Þ ¼ 0:0255 10
Uncertainty in the use of Pipette 1 to make the working standard solution: u0 (Pipette1) pffiffi ¼ 0:0035 ml u0 ðPi pette1Þ ¼ uðTol1Þ ¼ 0:006 3
Uncertainty in the use of Flask 10 to make the working standard solution: u(Flask10) pffiffi ¼ 0:0144 ml uðFlask10Þ ¼ uðTol10Þ ¼ 0:025 3
Uncertainty in the use of Flask 100 to make the intermediate standard solution: u(Flask100) ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 ðTol100Þ þ u2 ðTem p100Þ þ u2 ðRe peat100Þ ¼ 0:09242 þ 0:36342 þ 0:00662 ¼ 0:3751 ml
uðFlask100Þ ¼
pffiffi ¼ 0:0924 ml uðTol100Þ ¼ 0:16 3 pffiffi ¼ 0:3634 ml; ð100 5 1:259 103 Þ ¼ 0:6295 ml uðTem p100Þ ¼ 0:6295 3 pffiffiffiffi ¼ 0:0066 ml uðRe peat100Þ ¼ 0:0208 10
S. Lee et al. / Forensic Science International 185 (2009) 59–66
distribution is used when a certificate or other specification gives limits without specifying a level of confidence [2]. Therefore, the uncertainty of purity (u(Purity)) was calculated by the semi-range of 0.01 divided by the function for the rectangular distribution (Table 1). Moreover, the uncertainty of tolerance of the glassware was estimated using results obtained from manufacturer’s certificates and the function of the rectangular distribution. Since the glassware had been calibrated at 20 8C but the temperature of our laboratory is adjusted at 20 5 8C, the effect of temperature on the volume of methanol was also considered using the coefficient of expansion of methanol, 1.259 103. The uncertainty of repeatability of the glassware was calculated using the standard deviation from ten measurements (Table 1). The uncertainties of Autopipette A and B in their certificates of calibration were 0.0002 and 0.001 ml, respectively, with a 95% degree of confidence. Therefore, the uncertainties were standardized to a 68% degree of confidence (Table 1). The calibration curve was given by Aj = ciB1 + B0 where Aj is the jth measurement of the peak area ratio of the ith calibration standard, ci is the amount of the ith calibration standard and B1 and B0 are the slope and the intercept of the calibration curve, respectively. The seven calibration standards were measured five times each (Fig. 4), providing the results of mean values of the different calibration standards, slopes and intercepts for MA and AP in Table 2. The B1 and B0 of MA are 0.0195 and 0.0720 with a correlation coefficient r of 0.9987 and those of AP are 0.0197 and 0.0001 with r of 0.9991, for each. The triplicate hair samples were analyzed, leading to c0 of 6.5977 and 10.0763 ng for MA and AP,
63
Table 2 Calibration results. Amount (ng)
MA
2.5 5 10 25 50 75 100
0.1151 0.1718 0.2814 0.5620 1.0220 1.5439 2.0287
AP 0.0564 0.1009 0.2117 0.4642 0.9747 1.5069 1.9678
B1 B0 r
0.0195 0.0720 0.9987
0.0197 0.0001 0.9991
B1, slope; B0, intercept; r, correlation coefficient.
respectively. Therefore, the uncertainty u(Cal) of MA was given by as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S 1 1 ðc0 cÞ2 uðCalÞ ¼ þ þ B1 p n Sxx sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:0000562 1 1 ð6:5799 38:21Þ2 þ þ ¼ ¼ 0:0011 ng 0:0195 3 35 8658:93 with the residual standard deviation S given by Pn 2 j¼1 ½A j ðB0 þ B1 c j Þ ¼ 0:0000316 S¼ n2 and Sxx ¼
n X ðc j cÞ2 ¼ 8658:93 j¼1
where B1 is the slope, p is the number of measurements to determine c0, n is the number of measurements for the calibration, c0 is the amount of MA in the test sample, c is the mean value of the different calibration standards (n number of measurements), i is the index for the number of calibration standards and j is the index for the number of measurements to obtain the calibration curve. The uncertainty u(Cal) of AP was calculated as the same manner, resulting in 0.0022 ng. 3.3.2. W The uncertainty of weighing the hair sample (u(W)) was equivalent to that of the variation of a balance. Thus, for the estimation of u(W), the uncertainties of tolerance (u(Tol)) and resolution (u(Resol)) of the balance were combined as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðWÞ ¼ u2 ðTolÞ þ u2 ðResolÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð2:050 104 Þ þ ð2:887 105 Þ ¼ 2:070 104 g ¼ 0:2070 mg uðTolÞ ¼
0:00041 ¼ 2:050 104 g 2
uðResolÞ ¼
0:0001=2 pffiffiffi ¼ 2:887 105 g 3
Using the value obtained, the RSU of weighing was ur (W) = 0.2070/10 = 0.0207.
Fig. 4. Calibration curves of MA and AP (r, correlation coefficient).
3.3.3. Method precision The uncertainties of the method precision for MA and AP were calculated using the pooled standard deviation (sp) given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPN 2 u sp i¼1 vi si and u ¼ pffiffiffiffiffi sp ¼ t P N m v i¼1 i
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S. Lee et al. / Forensic Science International 185 (2009) 59–66
Table 3 Results of the evaluation of method precision. Spiked amount (ng) (A) MA 8
40
80
CSU (B) AP 8
40
80
CSU
3.4. Calculating the overall combined uncertainty
Day
Mean
Standard deviation
Degrees of freedom
SU (ng)
RSU
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
6.69 7.97 8.62 8.20 7.15 36.04 42.08 45.16 41.53 44.93 76.43 85.40 87.09 80.18 85.45
0.30 0.69 0.45 0.26 0.21 0.46 0.31 0.95 0.65 2.05 0.92 1.23 1.54 0.50 0.46
5 2 2 2 2 5 2 2 2 2 5 2 2 2 2
0.1772
0.0221
–
–
–
–
The concentration of MA or AP in the test sample (CMA or AP) was calculated using the equation (1) as follows: 6:5799 1:0 ¼ 0:66 ng=mg C MA ¼ 10 C AP ¼
0.4346
0.0109
0.4464
0.0056
10:0763 1:0 ¼ 1:01 ng=mg 10
The RSUs of three components, c0, W and method precision, were combined and the CSUs of MA and AP were given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C MA u2r ðc0 Þ þ u2r ðWÞ þ u2r ð f precision Þ uc ðC MA Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:66 0:01312 þ0:02072 þ0:02532 ¼ 0:0232 ng=mg qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C AP u2r ðc0 Þ þ u2r ðWÞ þ u2r ð f precision Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1:01 0:01312 þ0:02072 þ0:01912 ¼ 0:0313 ng=mg
uc ðC AP Þ ¼
0.6477
0.0253
3.5. Calculating the degrees of freedom 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
6.88 7.88 8.22 8.39 7.66 36.82 42.48 43.26 42.47 43.36 77.11 84.95 86.60 81.01 85.16
–
–
0.29 0.33 0.36 0.20 0.31 0.82 0.44 0.92 0.42 0.04 1.24 1.13 0.29 0.24 1.01
5 2 2 2 2 5 2 2 2 2 5 2 2 2 2
–
–
0.1333
0.0167
0.2996
0.0075
The degrees of freedom for MA and AP were approximated by the Welch-Satterthwaite formula: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u4 ðyÞ veff ¼ PN c 4 i¼1 ui ðyÞ=vi
0.4403
0.0055
where veff is the effective degree of freedom, uc(y) is the combined standard uncertainty, ui(y) is the individual standard uncertainty, and vi is the degree of freedom of ui(y). A summary of the calculation of the degrees of freedom for MA and AP is shown in Table 4. The degrees of freedom veff of MA and AP were 74.4 and 144.9, for each.
0.5490
0.0191
3.6. Calculating the expanded uncertainty
SU: standard uncertainty; RSU: relative standard uncertainty; CSR: combined standard uncertainty.
where vi is the degree of freedom of the ith sample, si is the standard deviation of the ith sample and m is the number of independent measurements. The results of the evaluation of the method precision for MA and AP with their SU, RSU and CSU are shown in Table 3. The uncertainties ur(fPrecision) of MA and AP were 0.0253 and 0.0191, respectively.
The degrees of freedom of MA and MA were large enough to consider the coverage factor (k) as 2 at the 95% significance level. Thus, the expanded uncertainties of CMA and CAP were given by UðC MA Þ ¼ 2 0:0232 0:05 ng=mg UðC AP Þ ¼ 2 0:0313 0:06 ng=mg Therefore, the concentrations of MA and AP in the hair sample with their expanded uncertainties were 0.66 0.05 and 1.01 0.07 ng/mg, respectively.
Table 4 A summary of the calculation of the degrees of freedom for MA and AP.
A. MA Uncertainty factor vi veff B. AP Uncertainty factor vi
c0 1.158×109 Working standard Calibration curve solution 33 ∞
c0 4.392×108 Working standard Calibration curve solution 33 ∞
W
Method precision
∞
19.8137
W
Method precision
∞
20.6578
74.4
144.9 veff c0, the amount of MA or AP in the test sample; W, the weight of the test sample; vi, the degrees of freedom of the individual standard uncertainty; veff, the effective degrees of freedom.
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4. Discussion and conclusion The estimation of the MU has become an issue in the quality control of clinical, doing and forensic laboratories because it has an effect on a clinical diagnosis and a judicial decision as well as the interpretation of analytical results. Even though the assessment of the MU was originated from the area of clinical chemistry, its importance has been lately realized in forensic analytical chemistry, where uncertainty not only has to be calculated with precision, but it also has to be both small and reliable enough to support effective decision making [10]. Moreover, the documentation of the MU is essential to acquire an accreditation. Our laboratory has been especially concerned about the reliability of analytical findings for the determination of MA and AP in hair because we need to prepare for the recent social changes such as the internationalization of MA-related crimes as well as the introduction of a new judicial system in Korea. Until now, many studies on the estimation of the MU in analytical procedures have been conducted [4,9,15–17]. In those studies, the different components contributing to the MU were considered depending on the analytical method. In doping control for horses, the preparation of the calibrators and the test sample, the method precision and recovery were the four main sources for the testosterone quantification and the largest uncertainty was originated from the method precision [9]. Gullberg reported that biological/sampling, analytical and traceability components were involved to calculate the MU in forensic breath-alcohol analysis [15], among which the biological/sampling component contributed most to the overall combined uncertainty. In the study of the simultaneous determination of V(V) and Mo(VI) at trace levels in a synthetic water sample after precolumn chelation and extraction with N-benzoyl-N-phenylhydroxylamine, the followings were contributed to the overall uncertainty: the operational or working uncertainty from the preparation of the stock, intermediate and the calibration solutions, the inherent uncertainty from liquid– liquid extraction, chromatographic separation and chemical calibration and the uncertainty from method bias [4]. The overall relative uncertainty in the determination of lead in blood was obtained by combining the uncertainties of the precision studies, the analysis of certified reference materials (CRMs) and recovery tests [16]. According to another study published recently, jasmonic acid in Lemna minor L. was determined by liquid chromatography with fluorescence detection with its MU. The authors of this study elucidated that sampling, sample processing and chromatographic determination were considered as sources of the MU and the method recovery and sample homogeneity were the main contributors to uncertainty [17]. The method recovery was regarded as a effective factor in previous studies [9,16,17]. In hair analysis, it is very difficult to determine the extraction recovery because hair is a solid matrix. Thus, determining if the recovery contributes to uncertainty depends on extraction efficiency. The method employed in the present paper was fully validated and showed good recoveries for MA and AP [12]. However, this recovery was determined using spiked hair samples as usual. Therefore, the extraction efficacy was compared with another extraction method, the ultrasonicationbased method, which was also fully validated, using spiked and authentic hair samples as well as NIST SRM 2379 certified reference material. As a result, both of the methods were acceptable to analyze MA and AP in hair [12]. Therefore, it was considered that the recovery did not have a significant effect on the MU in the current method. The homogeneity of hair samples could affect the MU in actual cases because the amounts of MA and AP in authentic hair can vary drastically between individuals, between hairs of an individual or even along hair shaft, depending on drug use patterns. Never-
Fig. 5. Contribution of the different sources to the overall combined uncertainties.
theless, the homogeneity was not considered in the current study because the fortified sample was used. Further study on this is definitely required in authentic hair samples. In our study, we estimated the MU of MA and AP in hair analysis combining the uncertainties from the amount of MA or AP in the test sample, the weight of the test sample and the method precision based on the equation to calculate the mesurand from intermediate values. As a result, the RSUs of each parameter for MA and AP were as follows: For MA, ur(c0) = 0.0131, ur(W) = 0.0207, ur(fprecision) = 0.0253; for AP, ur(c0) = 0.0131, ur(W) = 0.0207, ur(fprecision) = 0.0191. The influence of the method precision on the overall combined uncertainty was most significant while that of the calibration curve was negligible in MA. However, the weight of the hair sample had a great effect on the overall combined uncertainty in AP (Fig. 5). According to recent publications, the MU varied depending on a measured concentration [15,18]. The higher breath alcohol concentration showed the higher standard uncertainty [15]. However, the relative uncertainty of benzodiazepines decreased as the concentration increased [18]. From this point of view, Leung et al. estimated the MU at the threshold level of testosterone in horse urine and suggested that the MU should be established at the various concentrations [9]. Therefore, we also determined the MU of MA and its main metabolite, AP, around the cut-off value of MA. Consequently, this study showed a procedure and results to estimate the MU of MA and AP around the cut-off value of MA, which has been accepted in hair analysis by our laboratory. The concentrations of MA and AP in the hair sample with their expanded uncertainties were 0.66 0.05 and 1.01 0.06 ng/mg, respectively. The method precision and the weight of the hair sample gave the largest contribution to the overall combined uncertainties of MA and AP, for each. The expanded uncertainties of both MA and AP were acceptable, which supported the successful application of the analytical method. Acknowledgments The authors thank Mr. Sungjoo Jeon and Youngsun Oh at the Korea Testing and Research Institute for Chemical Industry (KTR) in Korea for their support.
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References [1] http://www.ascld-lab.org/dual/aslabdualaboutascldlab.html. [2] Quantifying uncertainty in analytical measurement, EURACHEM/CITAC Guide, second ed., 2000. [3] H.H. Maurer, Demands on scientific studies in clinical toxicology, Forensic Sci. Int. 165 (2007) 194–198. [4] G. Bagura, M. Sa´nchez-Vin˜asa, D. Ga´zqueza, M. Ortegab, R. Romeroa, Estimation of the uncertainty associated with the standard addition methodology when a matrix effect is detected, Talanta 66 (2005) 1168–1174. [5] P. Kintz, Value of hair analysis in postmortem toxicology, Forensic Sci. Int. 142 (2004) 127–134. [6] F. Musshoff, B. Madea, New trends in hair analysis and scientific demands on validation and technical notes, Forensic Sci. Int. 165 (2007) 204–215. [7] R. Wennig, Potential problems with the interpretation of hair analysis results, Forensic Sci. Int. 107 (2000) 5–12. [8] P. Kintz, P. Mangin, What constitutes a positive result in hair analysis: proposal for the establishment of cut-off values, Forensic Sci. Int. 70 (1995) 3–11. [9] G.N. Leung, E.N. Ho, W.H. Kwok, D.K. Leung, F.P. Tang, T.S. Wan, A.S. Wong, C.H. Wong, J.K. Wong, N.H. Yu, A bottom-up approach in estimating the measurement uncertainty and other important considerations for quantitative analyses in drug testing for horses, J. Chromatogr. A. 1163 (2007) 237–246. [10] E. Spirito, F. Botre, The role of measurement uncertainty in doping analysis, Int. J. Risk Assess. Manage. 5 (2005) 374–386.
[11] R.C. Baselt, Disposition of Toxic Drugs and Chemicals in Man, Chemical Toxicology Institute, Foster City, CA, 2000, p. 527. [12] S. Lee, Y. Park, W. Yang, E. Han, S. Choe, S. In, M. Lim, H. Chung, Development of a reference material using methamphetamine abuser’s hair samples for the determination of methamphetamine and amphetamine in hair, J. Chromatogr. B 865 (2008) 33–39. [13] M.J. Welch, L.T. Sniegoski, S. Tai, Two new standard reference materials for the determination of drugs of abuse in human hair, Anal. Bioanal. Chem. 376 (2003) 1205–1211. [14] Guide to the expression of uncertainty in measurement, International organization for standardization, 1995. [15] R. Gullberg, Estimating the measurement uncertainty in forensic breath-alcohol analysis, Accred. Qual. Assur. 11 (2006) 562–568. [16] M. Patriarca, M. Castelli, F. Corsetti, A. Menditto, Estimate of uncertainty of measurement from a single-laboratory validation study: application to the determination of lead in blood, Clin. Chem. 50 (2004) 1396–1405. [17] J. Kristl, B. Krajncˇicˇ, D. Brodnjak-Voncˇina, M. Veber, Evaluation of measurement uncertainty in the determination of jasmonic acid in Lemna minor L. by liquid chromatography with fluorescence detection, Accred. Qual. Assur. 12 (2007) 303– 310. [18] E.F. Dussy, C. Hamberg, T.A. Briellmann, Quantification of benzodiazepines in whole blood and serum, Int. J. Legal Med. 120 (2006) 323–330.
Contents lists available at ScienceDirect
Forensic Science International journal homepage: www.elsevier.com/locate/forsciint
Estimation of the measurement uncertainty of methamphetamine and amphetamine in hair analysis Sooyeun Lee *, Yonghoon Park, Wonkyung Yang, Eunyoung Han, Sanggil Choe, Miae Lim, Heesun Chung National Institute of Scientific Investigation, 331-1 Sinwol-7-dong, Yangcheon-gu, Seoul 158-707 Republic of Korea
A R T I C L E I N F O
A B S T R A C T
Article history: Received 27 January 2008 Received in revised form 15 December 2008 Accepted 18 December 2008
The measurement uncertainties (MUs) were estimated for the determination of methamphetamine (MA) and its main metabolite, amphetamine (AP) at the low concentrations (around the cut-off value of MA) in human hair according to the recommendations of the EURACHEM/CITAC Guide and ‘‘Guide to the expression of uncertainty in measurement (GUM)’’. MA and AP were extracted by agitating hair with 1% HCl in methanol, followed by derivatization and quantification using GC–MS. The major components contributing to their uncertainties were the amount of MA or AP in the test sample, the weight of the test sample and the method precision, based on the equation to calculate the mesurand from intermediate values. Consequently, the concentrations of MA and AP in the hair sample with their expanded uncertainties were 0.66 0.05 and 1.01 0.06 ng/mg, respectively, which were acceptable to support the successful application of the analytical method. The method precision and the weight of the hair sample gave the largest contribution to the overall combined uncertainties of MA and AP, for each. ß 2009 Elsevier Ireland Ltd. All rights reserved.
Keywords: Measurement uncertainty Hair analysis Methamphetamine Amphetamine Method precision
1. Introduction Quality assurance is a major concern in the area of forensic toxicology because the analytical results have a great effect on administrative and legal consequences. In recent years, many analytical chemistry laboratories have employed a quality management system, compliant to international quality standards such as ISO/IEC 17025. For forensic laboratories, the Crime Laboratory Accreditation Programs of the American Society of Crime Laboratory Directors/Laboratory Accreditation Board (ASCLD/LAB) have been well known as accreditation programs and the ASCLD/LAB-International Program was newly established in 2003 based on the ISO/IEC 17025 standards and the ASCLD/LABInternational Supplemental Requirements [1]. These programs require applicants and/or accredited laboratories to demonstrate the reliability of analytical data objectively in various ways: proper validation of analytical methods, regular participation in proficiency tests, etc. The estimation of the measurement uncertainty (MU) is another accreditation requirement of ISO/IEC 17025. According to the EURACHEM/CITAC Guide [2], the MU is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of values that could reasonably be
* Corresponding author. Tel.: +82 2 2600 4937; fax: +82 2 2600 4939. E-mail address: [email protected] (S. Lee). 0379-0738/$ – see front matter ß 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.forsciint.2008.12.012
attributed to the measurand and expressed the number after . Nowadays, it is recommended that the quantitative findings should be presented with their MU to evaluate the reliability of the results [3,4]. The application of drug analysis in hair has significantly increased in both forensic and clinical toxicology: illegal drug use, postmortem cases, drug-facilitated crimes, workplace drug testing, doping control, drug treatment or management programs, clinical diagnosis, gestational drug exposure, therapeutic drug monitoring (TDM), etc. [5,6]. In Korea, hair analysis is critical because it is accepted by law enforcement agencies as one of important corroborative facts for drug abuse. The hair analysis provides information not only on chronic drug use but also on drug use period according to the rate of hair growth [5], which has a key effect on legal decision. Usually, the result of hair testing is reported as positive and negative, for which several criteria were proposed for obtaining a positive result: evaluation of possible passive contamination, identification of metabolites, use of metabolites-to-parent drug ratios, use of assay values of decontamination washes and use of threshold values (cut-off values) [7,8]. In case other criteria are satisfactory, the determination of positive or negative depends significantly on the quantification results, so the cut-off value can be a key criterion. However, it can be difficult to determine if a quantified value is positive or negative when the value is very close to the cut-off value. In the human sports testing field, the decision limit, which is the threshold plus the MU, is adopted to establish a doping offence [9,10]. Even though the MU
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Fig. 1. Hair analysis procedure.
could be applied in a different way to the identification of a prohibited substance to supply legal evidence, it is necessary to establish the MU at the cut-off value as one of supplementary criteria in forensic analysis. Methamphetamine (MA) has received the most attention as a drug of abuse in Korea. It undergoes some N-demethylation to amphetamine (AP), its major active metabolite [11]. As stated in our standard operating procedure (SOP), a MA concentration of greater than the cut-off value (0.5 ng/mg) [7] and an AP greater than lower limit of detection (LLOD) along with appropriate compound ion ratios are required to prove an individual’s MA use. Therefore, this research aims to estimate the MU of MA and AP at the low concentrations (around the cut-off value of MA) in human hair. 2. Experimental 2.1. Chemicals Methanol, ethyl acetate and hydrochloric acid (HCl) were analytical grade. MA hydrochloride and AM sulfate were obtained from Lipomed AG (Switzerland) for the preparation of a spiked hair sample. The solutions of MA, AP, MA-d5 and AP-d5 (1 mg/ml, 99% for each) from Cerilliant (TX, USA) were used to prepare the stock and working standard solutions. Dimethylsulfoxide (DMSO) and Trifluoroacetic anhydride (TFAA) were purchased from Sigma–Aldrich (MO, USA). 2.2. Preparation of a hair sample The preparation of a hair sample was carried out using a slight modification of a method described elsewhere [13]. Briefly, each ca. 60 mg of MA hydrochloride and AM sulfate were dissolved in a small volume of distilled water in a 1000 ml glass beaker. Then, 250 ml of 0.02 M HCl in DMSO and 250 ml distilled water were added in succession in the beaker in an ice bath. Drug-free hair (ca. 10 g) was soaked in the solution for 24 h. The hair was removed, rinsed in a sufficient volume of methanol several times and air-dried. 2.3. Preparation of stock and working standard solution Each 1 mg/ml of MA and AP was diluted in a 10 ml volumetric flask (Flask 10) with 1% HCl in methanol (Stock solution, 99 mg/ml). The working standard solution
was prepared by two steps: pipetting (Pipette 1) 1 ml of the stock solution into a 100 ml volumetric flask (Flask 100) and diluting with 1% HCl in methanol (Intermediate standard solution) followed by pipetting (Pipette 1) 1 ml of the intermediate standard solution into a 10 ml volumetric flask (Flask 10) and diluting with 1% HCl in methanol (Working standard solution). A 10–100 ml autopipette (Autopipette A) and a 200–1000 ml autopipette (Autopipette B) were used to make five sets of calibrators (2.5, 5, 10, 25, 50, 75 and 100 ng). 2.4. Hair analysis The experimental procedure (Fig. 1) given here was fully validated [12]. Shortly, triplicate hair samples were accurately weighed (ca. 10 mg), cut into very small pieces of less than 1 mm and agitated with 3 ml of 1% HCl in methanol for 20 h at 38 8C. MA-d5 and AP-d5 were added as internal standards. The hair extract was evaporated to dryness at 45 8C under N2 gas and then the residue was derivatized with 100 ml of TFAA/ethyl acetate (1:1) at 65 8C for 15 min. The excess derivatizing reagent was removed and the residue was reconstituted in ethanol for GC–MS analysis (Agilent 6890/5973 GC-MS system). The GC was equipped with a 30-mlong, 0.25-mm-i.d., 0.25-mm-film-thickness HP-5MS capillary column. The inlet temperature was 260 8C and the helium flow rate was 1.0 ml/min. The oven was programmed to operate at an initial temperature of 100 8C for 1 min, to increase the temperature to 270 8C at a heating rate of 20 8C/min and to hold at 270 8C for 10 min. The MS was operated in selected ion monitoring (SIM) mode. The TFAA derivatized ions for MA, AP, MA-d5 and AP-d5 were as follows: MA, m/z 154, 118, 110, 91; AP, m/z 140, 118, 91; MA-d5, 158, 122; AP-d5, 144, 122. 2.5. Evaluation of method precision Method precision was examined by analyzing hair samples spiked with low (8 ng), medium (40 ng) and high (80 ng) concentrations of MA and AP, respectively, using the same method described in the previous hair analysis section. The six aliquots of each sample were analyzed on the first day, followed by triplicates for the four consecutive days. 2.6. MU estimation The estimation of the MU was performed in compliance with the EURACHEM/ CITAC Guide [2] and ‘‘Guide to the expression of uncertainty in measurement (GUM)’’ [14]. In brief, there are six steps involved in developing the MU: Specification of the measurand; Identifying uncertainty sources; Quantifying uncertainty; Calculating the combined uncertainty; Calculating the degrees of freedom; Calculating the expanded uncertainty. Therefore, this study followed the process to derive an expanded uncertainty. Firstly, the mesurand was clearly
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expressed as a mathematical equation based on the experimental method. Secondly, the possible sources of uncertainty were listed according to the equation and an initial cause and effect diagram was proposed. Thirdly, considering the relationship among parameters which have an effect on the sources, an expanded cause and effect diagram was given. Then, the uncertainties of individual components were evaluated and quantified using analytical data. In order to adjust different units of measurement, the individual standard uncertainties (SU) were changed into the relative standard uncertainties (RSU) equivalent. Next, each RSU was combined by the root-sum-of-squares (RSS) method to give the combined standard uncertainty (CSR). After that, the degree of freedom of the CSR was calculated and an appropriate coverage factor was determined. Finally, an expanded uncertainty was given using the coverage factor.
3. Results Fig. 2. Initial cause and effect diagram.
3.1. Specification of the measurand According to the EURACHEM/CITAC Guide [2], it is necessary to define what is being measured and express quantitatively the relationship among the measurands in the first step. The concentration of MA or AP in the test sample (CMA or AP) was calculated by a simple mathematical model:
of the method precision (fprecision) as follows: C MA
or AP
¼
c0 f precision ðng=mgÞ W
(3)
3.2. Identifying uncertainty sources C MA
or AP
c0 ðng=mgÞ ¼ W
(1)
where c0 is the amount of MA or AP in the test sample and W is the weight of the test sample. Because c0 was derived from a calibration curve, CMA or AP was also given by C MA
or AP
¼
A 0 B0 1 ðng=mgÞ W B1
(2)
where A0 is the peak area ratio of MA or AP to IS (MA-d5 or AP-d5) and B0 and B1 is the intercept and the slope of the calibration curve, respectively. Furthermore, since the method precision should be considered as a major source of the MU in any quantification method [9], the equation was expanded using the correction factor
The relevant uncertainty sources are shown in the cause and effect diagrams (Figs. 2 and 3). From Eq. (1), CMA or AP was associated with c0 and W, which were the major bones in the initial cause and effect diagram (Fig. 2). c0 was calculated from a calibration curve and W was subjected to two main sources of uncertainty: variation of a balance and repeatability of measurement. This initial cause and effect diagram was expanded with the added correction factor, method precision. Moreover, the working standard solution was considered as another uncertainty source of c0 because hair samples spiked with standard solutions were used instead of a certified reference material. Also, the repeatability of measurement and the variation of solvent volume due to temperature change overlap with the uncertainty of the method precision, where those factors are already covered
Fig. 3. Expanded cause and effect diagram.
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[9]. Therefore, the effect of the repeatability of weighing hair was not included and those of the repeatability and the temperature change in using a 10 ml volumetric flask and 1 ml pipette to prepare the working standard solution were not considered. However, the repeatability and the temperature effect of the volumetric apparatus for the preparation of both the stock solution and the intermediate standard solution were regarded as contributors to the estimation of the MU since the solutions were made beforehand. Finally, the expanded cause and effect diagram was given as Fig. 3. 3.3. Quantifying uncertainty 3.3.1. c0 In order to create the RSU of c0 (ur(c0)), the two uncertainty components, one from the preparation of the working standard solution and the other from the calibration curve, were combined as follows: for MA, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðCalÞ ur ðc0 Þ ¼ u2r ðStdÞ þ u2r ðCalÞ ¼ u2r ðStdÞ þ c0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0:0011 ¼ 0:0131 ¼ 0:01312 þ 6:5799
and for AP, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:0022 2 ur ðc0 Þ ¼ 0:01312 þ ¼ 0:0131 10:0763 where ur(Std) is the RSU of the working standard solution, ur(Cal) is that of the calibration curve and u(Cal) is the SU of the calibration curve. Since the working standard solutions of MA and AP were prepared using chemicals with same purity and identical apparatus, the uncertainties ur(Std) were equal. For the calculation of ur(Std), following uncertainties were considered: uncertainty in the preparation of the stock solution, ur(Stock); uncertainty in the use of Autopipette A to make the calibrators, u(AutopipetteA); uncertainty in the use of Autopipette B to make the calibrators, u(AutopipetteB); uncertainty in the use of Pipette 1 to make the intermediate standard solution, u(Pipette1); uncertainty in the use of Pipette 1 to make the working standard solution, u0 (Pipette1); uncertainty in the use of Flask 10 to make the working standard solution, u(Flask10); uncertainty in the use of Flask 100 to make the intermediate standard solution, u(Flask100). The detailed calculation of ur(Std) was summarized in Table 1. According to the manufacturer’s certificate of analysis, it was assumed that the purity of each solution of MA and AP was 100 1%, which was converted to 1.0 0.01 mg/ml. A rectangular
Table 1 A summary of the calculation of ur(Std) for MA and AP. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 2 2 uðAuto pi petteAÞ 2 uðAuto pi petteBÞ 2 uðPi pette1Þ 2 u ðPi pette1Þ 2 uðFlask10Þ uðFlask100Þ u2r ðStockÞ þ 3 þ4 þ þ þ þ Vol:ðAuto pi petteAÞ Vol:ðAuto pi petteBÞ Vol:ðPi pette1Þ Vol:ðPi pette1Þ Vol:ðFlask10Þ Vol:ðFlask100Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:0001 2 0:0005 2 0:0095 2 0:0035 2 0:0144 2 0:3751 2 þ4 þ þ þ þ ¼ 0:0131 ¼ 0:00702 þ 3 0:1 1 1 1 10 100
ur ðStdÞ ¼
Uncertainty in the preparation of the stock solution: ur(Stock) rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi uðPurityÞ 0:006 2 ¼ þ uðFlask10Þ þ 0:0391 ¼ 0:0070 ur ðStockÞ ¼ 0:99 10 Purity Volume pffiffi ¼ 0:006 mg=ml uðPurityÞ ¼ 0:01 3
uðFlask10Þ ¼
ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 ðTol10Þ þ u2 ðTem p10Þ þ u2 ðRe peat10Þ ¼ 0:01442 þ 0:03632 þ 0:00162 ¼ 0:0391 ml
pffiffi ¼ 0:0144 ml uðTol10Þ ¼ 0:025 3 pffiffi ¼ 0:0363 ml; ð10 5 1:259 103 Þ ¼ 0:0630 ml uðTem p10Þ ¼ 0:0630 3 pffiffiffiffi ¼ 0:0016 ml uðRe peat10Þ ¼ 0:0049 10
Uncertainty in the use of Autopipette A to make the calibrators: u(AutopipetteA) ¼ 0:0001 ml uðAuto pi petteAÞ ¼ 0:0002 2 Uncertainty in the use of Autopipette B to make the calibrators: u(AutopipetteB) uðAuto pi petteBÞ ¼ 0:001 2 ¼ 0:0005 ml Uncertainty in the use of Pipette 1 to make the intermediate standard solution: u(Pipette1) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðPi pette1Þ ¼ u2 ðTol1Þ þ u2 ðTem p1Þ þ u2 ðRe peat1Þ ¼ 0:00352 þ 0:00362 þ 0:00812 ¼ 0:0095 ml pffiffi ¼ 0:0035 ml uðTol1Þ ¼ 0:006 3 pffiffi ¼ 0:0036 ml; ð1 5 1:259 103 Þ ¼ 0:0063 ml uðTem p1Þ ¼ 0:0063 3 pffiffiffiffi ¼ 0:0081 ml uðRe peat1Þ ¼ 0:0255 10
Uncertainty in the use of Pipette 1 to make the working standard solution: u0 (Pipette1) pffiffi ¼ 0:0035 ml u0 ðPi pette1Þ ¼ uðTol1Þ ¼ 0:006 3
Uncertainty in the use of Flask 10 to make the working standard solution: u(Flask10) pffiffi ¼ 0:0144 ml uðFlask10Þ ¼ uðTol10Þ ¼ 0:025 3
Uncertainty in the use of Flask 100 to make the intermediate standard solution: u(Flask100) ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 ðTol100Þ þ u2 ðTem p100Þ þ u2 ðRe peat100Þ ¼ 0:09242 þ 0:36342 þ 0:00662 ¼ 0:3751 ml
uðFlask100Þ ¼
pffiffi ¼ 0:0924 ml uðTol100Þ ¼ 0:16 3 pffiffi ¼ 0:3634 ml; ð100 5 1:259 103 Þ ¼ 0:6295 ml uðTem p100Þ ¼ 0:6295 3 pffiffiffiffi ¼ 0:0066 ml uðRe peat100Þ ¼ 0:0208 10
S. Lee et al. / Forensic Science International 185 (2009) 59–66
distribution is used when a certificate or other specification gives limits without specifying a level of confidence [2]. Therefore, the uncertainty of purity (u(Purity)) was calculated by the semi-range of 0.01 divided by the function for the rectangular distribution (Table 1). Moreover, the uncertainty of tolerance of the glassware was estimated using results obtained from manufacturer’s certificates and the function of the rectangular distribution. Since the glassware had been calibrated at 20 8C but the temperature of our laboratory is adjusted at 20 5 8C, the effect of temperature on the volume of methanol was also considered using the coefficient of expansion of methanol, 1.259 103. The uncertainty of repeatability of the glassware was calculated using the standard deviation from ten measurements (Table 1). The uncertainties of Autopipette A and B in their certificates of calibration were 0.0002 and 0.001 ml, respectively, with a 95% degree of confidence. Therefore, the uncertainties were standardized to a 68% degree of confidence (Table 1). The calibration curve was given by Aj = ciB1 + B0 where Aj is the jth measurement of the peak area ratio of the ith calibration standard, ci is the amount of the ith calibration standard and B1 and B0 are the slope and the intercept of the calibration curve, respectively. The seven calibration standards were measured five times each (Fig. 4), providing the results of mean values of the different calibration standards, slopes and intercepts for MA and AP in Table 2. The B1 and B0 of MA are 0.0195 and 0.0720 with a correlation coefficient r of 0.9987 and those of AP are 0.0197 and 0.0001 with r of 0.9991, for each. The triplicate hair samples were analyzed, leading to c0 of 6.5977 and 10.0763 ng for MA and AP,
63
Table 2 Calibration results. Amount (ng)
MA
2.5 5 10 25 50 75 100
0.1151 0.1718 0.2814 0.5620 1.0220 1.5439 2.0287
AP 0.0564 0.1009 0.2117 0.4642 0.9747 1.5069 1.9678
B1 B0 r
0.0195 0.0720 0.9987
0.0197 0.0001 0.9991
B1, slope; B0, intercept; r, correlation coefficient.
respectively. Therefore, the uncertainty u(Cal) of MA was given by as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S 1 1 ðc0 cÞ2 uðCalÞ ¼ þ þ B1 p n Sxx sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:0000562 1 1 ð6:5799 38:21Þ2 þ þ ¼ ¼ 0:0011 ng 0:0195 3 35 8658:93 with the residual standard deviation S given by Pn 2 j¼1 ½A j ðB0 þ B1 c j Þ ¼ 0:0000316 S¼ n2 and Sxx ¼
n X ðc j cÞ2 ¼ 8658:93 j¼1
where B1 is the slope, p is the number of measurements to determine c0, n is the number of measurements for the calibration, c0 is the amount of MA in the test sample, c is the mean value of the different calibration standards (n number of measurements), i is the index for the number of calibration standards and j is the index for the number of measurements to obtain the calibration curve. The uncertainty u(Cal) of AP was calculated as the same manner, resulting in 0.0022 ng. 3.3.2. W The uncertainty of weighing the hair sample (u(W)) was equivalent to that of the variation of a balance. Thus, for the estimation of u(W), the uncertainties of tolerance (u(Tol)) and resolution (u(Resol)) of the balance were combined as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðWÞ ¼ u2 ðTolÞ þ u2 ðResolÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð2:050 104 Þ þ ð2:887 105 Þ ¼ 2:070 104 g ¼ 0:2070 mg uðTolÞ ¼
0:00041 ¼ 2:050 104 g 2
uðResolÞ ¼
0:0001=2 pffiffiffi ¼ 2:887 105 g 3
Using the value obtained, the RSU of weighing was ur (W) = 0.2070/10 = 0.0207.
Fig. 4. Calibration curves of MA and AP (r, correlation coefficient).
3.3.3. Method precision The uncertainties of the method precision for MA and AP were calculated using the pooled standard deviation (sp) given by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPN 2 u sp i¼1 vi si and u ¼ pffiffiffiffiffi sp ¼ t P N m v i¼1 i
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S. Lee et al. / Forensic Science International 185 (2009) 59–66
Table 3 Results of the evaluation of method precision. Spiked amount (ng) (A) MA 8
40
80
CSU (B) AP 8
40
80
CSU
3.4. Calculating the overall combined uncertainty
Day
Mean
Standard deviation
Degrees of freedom
SU (ng)
RSU
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
6.69 7.97 8.62 8.20 7.15 36.04 42.08 45.16 41.53 44.93 76.43 85.40 87.09 80.18 85.45
0.30 0.69 0.45 0.26 0.21 0.46 0.31 0.95 0.65 2.05 0.92 1.23 1.54 0.50 0.46
5 2 2 2 2 5 2 2 2 2 5 2 2 2 2
0.1772
0.0221
–
–
–
–
The concentration of MA or AP in the test sample (CMA or AP) was calculated using the equation (1) as follows: 6:5799 1:0 ¼ 0:66 ng=mg C MA ¼ 10 C AP ¼
0.4346
0.0109
0.4464
0.0056
10:0763 1:0 ¼ 1:01 ng=mg 10
The RSUs of three components, c0, W and method precision, were combined and the CSUs of MA and AP were given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C MA u2r ðc0 Þ þ u2r ðWÞ þ u2r ð f precision Þ uc ðC MA Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:66 0:01312 þ0:02072 þ0:02532 ¼ 0:0232 ng=mg qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C AP u2r ðc0 Þ þ u2r ðWÞ þ u2r ð f precision Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1:01 0:01312 þ0:02072 þ0:01912 ¼ 0:0313 ng=mg
uc ðC AP Þ ¼
0.6477
0.0253
3.5. Calculating the degrees of freedom 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
6.88 7.88 8.22 8.39 7.66 36.82 42.48 43.26 42.47 43.36 77.11 84.95 86.60 81.01 85.16
–
–
0.29 0.33 0.36 0.20 0.31 0.82 0.44 0.92 0.42 0.04 1.24 1.13 0.29 0.24 1.01
5 2 2 2 2 5 2 2 2 2 5 2 2 2 2
–
–
0.1333
0.0167
0.2996
0.0075
The degrees of freedom for MA and AP were approximated by the Welch-Satterthwaite formula: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u4 ðyÞ veff ¼ PN c 4 i¼1 ui ðyÞ=vi
0.4403
0.0055
where veff is the effective degree of freedom, uc(y) is the combined standard uncertainty, ui(y) is the individual standard uncertainty, and vi is the degree of freedom of ui(y). A summary of the calculation of the degrees of freedom for MA and AP is shown in Table 4. The degrees of freedom veff of MA and AP were 74.4 and 144.9, for each.
0.5490
0.0191
3.6. Calculating the expanded uncertainty
SU: standard uncertainty; RSU: relative standard uncertainty; CSR: combined standard uncertainty.
where vi is the degree of freedom of the ith sample, si is the standard deviation of the ith sample and m is the number of independent measurements. The results of the evaluation of the method precision for MA and AP with their SU, RSU and CSU are shown in Table 3. The uncertainties ur(fPrecision) of MA and AP were 0.0253 and 0.0191, respectively.
The degrees of freedom of MA and MA were large enough to consider the coverage factor (k) as 2 at the 95% significance level. Thus, the expanded uncertainties of CMA and CAP were given by UðC MA Þ ¼ 2 0:0232 0:05 ng=mg UðC AP Þ ¼ 2 0:0313 0:06 ng=mg Therefore, the concentrations of MA and AP in the hair sample with their expanded uncertainties were 0.66 0.05 and 1.01 0.07 ng/mg, respectively.
Table 4 A summary of the calculation of the degrees of freedom for MA and AP.
A. MA Uncertainty factor vi veff B. AP Uncertainty factor vi
c0 1.158×109 Working standard Calibration curve solution 33 ∞
c0 4.392×108 Working standard Calibration curve solution 33 ∞
W
Method precision
∞
19.8137
W
Method precision
∞
20.6578
74.4
144.9 veff c0, the amount of MA or AP in the test sample; W, the weight of the test sample; vi, the degrees of freedom of the individual standard uncertainty; veff, the effective degrees of freedom.
S. Lee et al. / Forensic Science International 185 (2009) 59–66
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4. Discussion and conclusion The estimation of the MU has become an issue in the quality control of clinical, doing and forensic laboratories because it has an effect on a clinical diagnosis and a judicial decision as well as the interpretation of analytical results. Even though the assessment of the MU was originated from the area of clinical chemistry, its importance has been lately realized in forensic analytical chemistry, where uncertainty not only has to be calculated with precision, but it also has to be both small and reliable enough to support effective decision making [10]. Moreover, the documentation of the MU is essential to acquire an accreditation. Our laboratory has been especially concerned about the reliability of analytical findings for the determination of MA and AP in hair because we need to prepare for the recent social changes such as the internationalization of MA-related crimes as well as the introduction of a new judicial system in Korea. Until now, many studies on the estimation of the MU in analytical procedures have been conducted [4,9,15–17]. In those studies, the different components contributing to the MU were considered depending on the analytical method. In doping control for horses, the preparation of the calibrators and the test sample, the method precision and recovery were the four main sources for the testosterone quantification and the largest uncertainty was originated from the method precision [9]. Gullberg reported that biological/sampling, analytical and traceability components were involved to calculate the MU in forensic breath-alcohol analysis [15], among which the biological/sampling component contributed most to the overall combined uncertainty. In the study of the simultaneous determination of V(V) and Mo(VI) at trace levels in a synthetic water sample after precolumn chelation and extraction with N-benzoyl-N-phenylhydroxylamine, the followings were contributed to the overall uncertainty: the operational or working uncertainty from the preparation of the stock, intermediate and the calibration solutions, the inherent uncertainty from liquid– liquid extraction, chromatographic separation and chemical calibration and the uncertainty from method bias [4]. The overall relative uncertainty in the determination of lead in blood was obtained by combining the uncertainties of the precision studies, the analysis of certified reference materials (CRMs) and recovery tests [16]. According to another study published recently, jasmonic acid in Lemna minor L. was determined by liquid chromatography with fluorescence detection with its MU. The authors of this study elucidated that sampling, sample processing and chromatographic determination were considered as sources of the MU and the method recovery and sample homogeneity were the main contributors to uncertainty [17]. The method recovery was regarded as a effective factor in previous studies [9,16,17]. In hair analysis, it is very difficult to determine the extraction recovery because hair is a solid matrix. Thus, determining if the recovery contributes to uncertainty depends on extraction efficiency. The method employed in the present paper was fully validated and showed good recoveries for MA and AP [12]. However, this recovery was determined using spiked hair samples as usual. Therefore, the extraction efficacy was compared with another extraction method, the ultrasonicationbased method, which was also fully validated, using spiked and authentic hair samples as well as NIST SRM 2379 certified reference material. As a result, both of the methods were acceptable to analyze MA and AP in hair [12]. Therefore, it was considered that the recovery did not have a significant effect on the MU in the current method. The homogeneity of hair samples could affect the MU in actual cases because the amounts of MA and AP in authentic hair can vary drastically between individuals, between hairs of an individual or even along hair shaft, depending on drug use patterns. Never-
Fig. 5. Contribution of the different sources to the overall combined uncertainties.
theless, the homogeneity was not considered in the current study because the fortified sample was used. Further study on this is definitely required in authentic hair samples. In our study, we estimated the MU of MA and AP in hair analysis combining the uncertainties from the amount of MA or AP in the test sample, the weight of the test sample and the method precision based on the equation to calculate the mesurand from intermediate values. As a result, the RSUs of each parameter for MA and AP were as follows: For MA, ur(c0) = 0.0131, ur(W) = 0.0207, ur(fprecision) = 0.0253; for AP, ur(c0) = 0.0131, ur(W) = 0.0207, ur(fprecision) = 0.0191. The influence of the method precision on the overall combined uncertainty was most significant while that of the calibration curve was negligible in MA. However, the weight of the hair sample had a great effect on the overall combined uncertainty in AP (Fig. 5). According to recent publications, the MU varied depending on a measured concentration [15,18]. The higher breath alcohol concentration showed the higher standard uncertainty [15]. However, the relative uncertainty of benzodiazepines decreased as the concentration increased [18]. From this point of view, Leung et al. estimated the MU at the threshold level of testosterone in horse urine and suggested that the MU should be established at the various concentrations [9]. Therefore, we also determined the MU of MA and its main metabolite, AP, around the cut-off value of MA. Consequently, this study showed a procedure and results to estimate the MU of MA and AP around the cut-off value of MA, which has been accepted in hair analysis by our laboratory. The concentrations of MA and AP in the hair sample with their expanded uncertainties were 0.66 0.05 and 1.01 0.06 ng/mg, respectively. The method precision and the weight of the hair sample gave the largest contribution to the overall combined uncertainties of MA and AP, for each. The expanded uncertainties of both MA and AP were acceptable, which supported the successful application of the analytical method. Acknowledgments The authors thank Mr. Sungjoo Jeon and Youngsun Oh at the Korea Testing and Research Institute for Chemical Industry (KTR) in Korea for their support.
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