Incertidumbre Por Curva 1
Incertidumbre Por Curva 1
Incertidumbre Por Curva 1
An approach was proposed for the estimation of measurement un- Multiple-point calibration is the most popular method used
certainty for analytical methods based on one-point calibration. The in quantitative analysis. Because of the need of knowing the
proposed approach is similar to the popular multiple-point calibra- MU for any quantitative data, approaches for estimating the MU
# The Author [2012]. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
general anesthetic with analgesic and hallucinogenic proper- with 100 mL K/NK standard working solution to prepare the
ties. It was originally used in veterinary medicine; however, its 100 ng/mL K/NK standard calibration solution.
ability to produce intensely vivid psychedelic effects causes its
frequent abuse. In Taiwan, it is at the top of the list for quan-
tities seized by the law enforcement for the past six consecu- Preparation of 100 ng/mL K/NK urine samples
tive years. The procedures of the estimation of MU and the The urine samples of 100 ng/mL K/NK were prepared by
results of the estimation are reported and discussed. spiking 100 mL K/NK standard working solution ( prepared
from a different batch of Cerilliant standard) into 1-mL drug-
free urines that were collected from drug-free individuals.
Experimental
Materials
Different batches of ketamine (K), ketamine-d4 (K-d4), norketa- Extraction procedure of urine
mine (NK) and norketamine-d4 (NK-d4) standards were pur- One milliliter of K/NK standard calibration solution and urine
chased from Cerilliant Corporation (Round Rock, TX) for the sample were added to 100 mL internal standard (IS, K-d4 and
preparation of calibration solution and spiked urine samples. NK-d4, 1 mg/mL) and 1 mL phosphate buffer ( pH 6.0) before
516 Ma et al.
GC–MS analysis where Cx is the concentration of K or NK in a urine sample; Y
GC –MS analysis was performed on an Agilent 6890 GC–5973 is the ratio of the peak area of K or NK in the sample (AS) to
MSD system. A HP-5MS column was used for gas chromato- deuterated internal standard (AIS) [(Eq. (2)]; and b is the slope
graphic separation. The oven temperature was initially set at of the one-point calibration curve [Eq. (3)]:
1508C for 1 min, ramped to 2808C at a ramping rate of 308C/
min and held at 2808C for 5 min. The injector and transfer line AS
Y ¼ ð2Þ
temperatures were set at 170 and 2808C, respectively. A con- AIS
stant flow mode was used, and the helium carrier gas was set
AStd
at a flow rate of 0.8 mL/min. An aliquot of 1 mL was injected
A
using the splitless mode. For MS analysis, selected ion monitor- b ¼ IS ð3Þ
ing (SIM) was chosen to monitor the following ions (m/z): K CStd
(180, 182, 209), K-d4 (184, 213), NK (166, 168, 195), NK-d4
A single calibration solution (CStd) with concentration equal to
(170, 199) (the quantification ions are in bold).
the threshold value of 100 ng/mL was analyzed to establish the
slope, b; AStd is the peak area of CStd.
Methods and Results
Estimation of the Measurement Uncertainty in Quantitative Determination of Ketamine and Norketamine in Urine Using a One-Point Calibration Method 517
and measurement conditions and variations observations. matrix effect and temporal effect (GC –MS stability). To ac-
The laboratory was not responsible for sampling and only one count for the matrix effect, spiked urine samples of 100 ng/mL
GC –MS was used; therefore, these two sources of uncertainty K and NK were prepared using five different drug-free urines.
were not included. To account for the temporal effect, spiked urine samples
Other potential uncertainty sources such as the finite reso- were analyzed at equal time intervals. The experiment was
lution of balance, pipettes and flasks have been included in the carried out in the following sequence (40 urine samples
precision study of volumetric apparatuses. Approximation in per batch):
the method such as the purity of reference material has been
CCCCCS1S2S3S4S5S6S7S8P1S9S10S11S12S13S14S15S16P2S17S18S19S20
included in the uncertainty of calibration solution. The trace-
S21S22S23S24P3S25 S26S27S28S29S30S31S32P4S33S34S35S36S37S38S39S40P5
ability of reference material and equipment (balance, pipettes
and volumetric flasks) has been included in the supplier’s cer- C symbolizes the calibrator, Sn:1 – 40 represents the regular test
tificate or reports of external calibration. urine samples and Pn:1 – 5 represents the five spiked urine
samples. Regular injections of QC samples and washing sol-
vents were not shown in the preceding sequence. Data across
Concentration of the calibrator
six weeks were pooled to provide a more representative rela-
518 Ma et al.
Table II
Summary of the Calculations for Relative Uncertainty of CStd, ur(CStd)
2: ur ½pipetteð1mLÞ A
0:00011
uðtol:Þ ¼ ¼ 0:000056ðmLÞ
2
4: ur ½pipetteð100mLÞ
0:000095
uðtol:Þ ¼ ¼ 0:000048ðmLÞ
2
uðprecisionÞ ¼ 0:000335ðmLÞ
V a50%MeOH DT 0:1 7:183 104 5
uðtemp:Þ ¼ pffiffiffi ¼ pffiffiffi ¼ 0:00021ðmLÞ
3 3
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
uðpipetteð100mLÞÞ 0:0000482 þ 0:0003352 þ 0:000212
ur ðpipetteð100mLÞÞ ¼ ¼ ¼ 0:004
0:1mL 0:1
5: ur ½pipetteð1mLÞ B
0:00011
uðtol:Þ ¼ ¼ 0:000056ðmLÞ
2
uðprecisionÞ ¼ 0:0018ðmLÞ
6: ur ðCStd Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K : ur ðCStd Þ ¼ ur ðCref Þ2 þ 3 ður ðpipetteð1mLÞ AÞ2 þ ur ðflaskð10mLÞÞ2 Þ þ ur ðpipetteð100mLÞÞ2 þ ur ðpipetteð1mLÞ BÞ2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ 0:0032 þ 3 ð0:00282 þ 0:00272 Þ þ 0:0042 þ 0:00192
¼ 0:0086
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
NK : ur ðCStd Þ ¼ ur ðCref Þ2 þ 3 ður ðpipetteð1mLÞ AÞ2 þ ur ðflaskð10mLÞÞ2 Þ þ ur ðpipetteð100mLÞÞ2 þ ur ðpipetteð1mLÞ BÞ2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ 0:0162 þ 3 ð0:00282 þ 0:00272 Þ þ 0:0042 þ 0:00192
¼ 0:018
Estimation of the Measurement Uncertainty in Quantitative Determination of Ketamine and Norketamine in Urine Using a One-Point Calibration Method 519
Eq. (5) provided the standard uncertainty for an unknown Table IV
sample having a predicted concentration of Y/b. S is the esti- ur(AS/AIS) for K and NK
mated standard deviation of one-point calibration. Sx 2 is the sum
K NK
of squares of all the concentrations used to establish the curve.
One calibration point should produce a curve with a slope. As a Week RSD (%) Week RSD (%)
result, 30 slopes were obtained over six weeks. The slopes 1 3.5 1 2.8
obtained during the six-week period were 0.0118 to 0.0149 for 2 3.6 2 1.3
3 3.5 3 3.1
K and 0.0117 to 0.0144 for NK. For a more conservative estima- 4 2.1 4 1.3
tion, the largest u(Calibration) was chosen for calculation. 5 2.0 5 3.3
6 1.0 6 1.8
Among the 30 AS/AIS and 30 b, 1.22/0.0118 and 1.22/0.0117
provided the largest u(Calibration) for K and NK, respectively: ur(AS/AIS) 2.8 ur(AS/AIS) 2.4
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:033 1:22 2
uðCalibrationÞK ¼ 1þ =1002 These values were compared with ttable, for 24 degrees of
0:0118 0:0118
freedom at 95% confidence. Because the ttable value (2.06) is
520 Ma et al.
the effective degrees of freedom and the level of confidence. the equation of uncertainty, which is derived for a calibration
The Welch-Satterthwaite formula was used to approximate the curve without an intercept (17) was then used to calculate the
effective degrees of freedom of uc(y): uncertainty due to calibration.
The expanded uncertainties for K and NK are 10 and 8 ng/mL,
uc4 ðyÞ respectively. If a sample is found with a concentration of K at
neff ¼ ð6Þ
P
N ui4 ðyÞ 110 ng/mL (NK, 108 ng/mL), then there is 95% probability
i¼1 ni
that the true concentration is above the threshold. Therefore, a
positive decision can be made if the measured value is over
The effective degrees of freedom were calculated for K and NK 110 and 108 ng/mL, for K and NK, respectively.
as 52 and 62, respectively. Because of the high degree of Table V shows that the uncertainties due to calibration and
freedom, the coverage factor k was assumed to be 2 with 95% sample signals were the major sources of MU. Because the un-
confidence. The expanded uncertainties, U, for K and NK were certainties are propagated in the form of variance (ur(x)2), the
therefore 2 times the combined uncertainties for each: uncertainty of the calibrator’s concentration (the preparation
of standard solutions) made a minor contribution to MU.
U ðCK Þ ¼ 2 5 ¼ 10 ng =mL
Estimation of the Measurement Uncertainty in Quantitative Determination of Ketamine and Norketamine in Urine Using a One-Point Calibration Method 521
9. Tessini, C., Mardones, C., Rivas, L., von Baer, D. (2009) Measurement 14. Clinical and Laboratory Standards Institute. (2010). Gas chromatog-
uncertainty of shikimic acid in red wines produced in Chile. raphy/mass spectrometry confirmation of drugs; Approved
Accreditation and Quality Assurance, 14, 381–387. Guideline—Second edition, C43-A2, Wayne, PA.
10. Kristl, J., Krajnčič, B., Brodnjak-Vončina, D., Veber, M. (2007) 15. Kim, B., Hwang, E., So, H.Y., Son, E.K., Kim, Y. (2010) Development
Evaluation of measurement uncertainty in the determination of jas- of a model system of uncertainty evaluations for multiple measure-
monic acid in Lemna minor L. by liquid chromatography with fluor- ments by isotope dilution mass spectrometry: Determination of
escence detection. Accreditation and Quality Assurance, 12, folic acid in infant formula. Bulletin of the Korean Chemistry
303–310. Society, 31, 3139–3144.
11. Ambrus, A. (2004) Reliability of measurements of pesticide residues 16. Leito, S., Mölder, K., Künnapas, A., Herodes, K., Leito, I. (2006)
in food. Accreditation and Quality Assurance, 9, 288– 304. Uncertainty in liquid chromatographic analysis of pharmaceutical
12. Peters, F.T., Maurer, H.H. (2007) Systematic comparison of bias product: Influence of various uncertainty sources. Journal of
and precision data obtained with multiple-point and one-point Chromatography A, 1121, 55 –63.
calibration in six validated multianalyte assays for quantification 17. Caulcutt, R., Boddy, R. Statistics for analytical chemists, Chapter 7.
of drugs in human plasma. Analytical Chemistry, 79, 4967 – Chapman and Hall, London, (1983).
4976. 18. Ott, J.B., Boerio-Goates, J. Chemical thermodynamics: Advanced
13. Bjørk, M.K., Nielsen, M.K.K., Markussen, L.Ø., Klinke, H.B., Linnet, Applications. Academic Press, London, (2000), pp. 271– 291.
K. (2010) Determination of 19 drugs of abuse and metabolites in 19. Zarei, H.A., Jalili, F., Assadi, S. (2007) Temperature dependence of
522 Ma et al.