Uncertainty Evaluation of the Analysis of 11-Nor-9-carboxy- 9 -tetrahydrocannabinol in Human Urine by GC/MS

k v r 52 r 6 480~487 (2008) Yakhak Hoeji Vol. 52, No. 6 GC/MS w d y sƒ ½ # Á Á Á Á *Á½ *Á, *w x t (Received October 6, 2008; Revised December 2, 2008) Uncertainty Evaluation of the Analysis of 11-Nor-9-carboxy- 9 -tetrahydrocannabinol in Human Urine by GC/MS Jin Young Kim #, Jae Chul Jeong, SungIll Suh, Yong Jun Suh, Jeong Jik Lee*, Jong Sang Kim* and Moon Kyo In Drug Analysis Laboratory, Supreme Prosecutors' Office, 706, Banporo, Seocho-gu, Seoul 137-730, Korea *Department of Quality Management, Korea Institute of Construction Materials, Seoul 137-073, Korea Abstract We described an estimation of measurement uncertainty in quantitative analysis of 11-nor-9-carboxy- 9 -tetrahydrocannabinol (THCCOOH), the major metabolite of 9 -tetrahydrocannabinol, in urine sample by solid-phase extraction (SPE) and GC/MS detection. The analytical results were compared and the different contributions to the uncertainty were evaluated. Inter-day and inter-person validation were performed using statistical analysis of several indicative factors. Measurement uncertainty associated with target analyte in real forensic samples was estimated using quality control (QC) data. Traceability of measurement was established through traceable standards, calibrated volumetric glassware and volume measuring device. The major factors of contribution to combined standard uncertainty, were calibration linearity, inter-day repeatability and inter-person reproducibility, while those associated with preparation of analytical standards and sampling volume were not so important considering the degree of contribution. Relative combined standard uncertainties associated with the described method was 12.05% for THCCOOH. Keywords uncertainty of measurement, urinanalysis, GC/MS, 11-nor-9-carboxy-delta 9-tetrahydrocannabinol (Cannabis sativa L.) dk ˆ (methamphetamine) pp l q p n k p. 1) p l p(high), d (happy smoke), rpp pl, p. ml (hemp)pv k n (marijuana). l m v p ee (hashishi)p. n l 1960 t t p k r 1970 rp l 1975 p m. 2000 l s p ' k l ' s p m } o l. l 420s p p p sq, p l 60l sp p (cannabinoid) p. # l p rql (r ) 02-535-4173 (Žd) 02-535-4175 (E-mail) paxus@spo.go.kr p t 9 -tetrahydrocannabinol(thc)p qn p p tn p, ~ rp ~ 11-nor-9- carboxy- 9 -tetrahydrocannabinol(thccooh) (Fig. 1). 2-4) q THCCOOH l l l Ž r t v n p. 5) p rp t THCCOOH l 4~8e 4t r v pp p k r p. 6,7) l ~ p l lp ll Žr rp l e n tn. v v rp e l l p r rp v. p ee l r(method validation) r er e m v (QC) e p r (precision)m r (accuracy) p e ˆ l. p p p n p e r, e q, nkrs e l p m, q l m pq p m 480

t ~ p r 481 Fig. 1 Chemical structures of delta-9-tetrahydrocannabinol and its metabolite(11-nor-9-carboxy-tetrahydrocannabinol). e p p on v m. l r (uncertainty of measurement) 8) p r p n kl p l p e r rp q rp p. l l ll pp o rl r m. n t ~ rl l m p t p np p }k l, e(measurand)p r, np r p t (standard uncertainty), t (combined standard uncertainty) q (expanded uncertainty) m. p l r e k 95%p e l r p sq o m. 9) np l r e m npp m p eˆ n m. x t v THCCOOHp 1ml n p o (vial)l 0.1 mg/ml, t v THCCOOH-d 3 p 1ml n p o l 10 µg/ml rs r p Cerilliant l p m. rl n n ekp p J. T. Baker l p m. o ~ ekp N,O-bis(trimethylsilyl)trifluoroacetamide/1% trimethylchlorosilane(bstfa/1% TMCS) Alltech p m. ~ l n v Oasis MCX(60 mg, 3 ml) Waters l p m. tnkp p t vp methanoll l rp 10, 1, 0.1 µg/ml e sr mp, n r v -20 o Cl m.»» tnkp sr o p Brand p n d (10 ml)m p Eppendorf p (1000 µl)p n mp, e l n e p kp r o p Eppendorf p (1000 µl)p n m. r} rp q q p ƒ p Rapid Trace SPE workstationp n l ~ (solid-phase extraction, SPE)p m. l n q Agilent Technologies 6890 Gas Chromatograph(GC)l 5973 Mass Selective Detector l GC/MS n m. p DB-5MS(25m 0.25mm I.D., 0.25 µm film thickness, J&W Scientific, USA) n m. m }p 200 o Cl 1 oveˆ, 30 o C/minp 290 o C v m m, l d 35 o C/min p 300 o C v m de 2 ove. tp m op m 250 o Cm 280 o C r m. n ~ p o p 0.7 ml/minp r m, tp p e(splitless mode)p purge-on timep 0.75 p r m. e Agilent Technologies 7683 q tp q (autosampler) n l q l tp m. 2008 6o 7o v k 2 o k q ~p r p l npqp p l n e n m. k p n v kp p p } l s e n m. l n s e n p n r v -20 o Cl m. e p ' t e '(SPO-DRUG-QA-04, 2006) l r l ee m. 5) e 3mlp 1mlj 3 l e (16 100 mm) l p, 1 µg/ml p t v 45 µl ~ m. 10 M KOH nk 200 µl pn l ml 30, k p ~ l ph 4 sr m. ~ n v o ˆm 1mlm v 1ml 2ml/minp tl. vl e 2ml/minp t, v 2mlm 4ml tl } m. e p vp r vl n p ethyl acetate 3 ml 2ml/minp tl p THCCOOH p m. n kp pr k (30 kpa) m (45 o C) v l v eˆ, q l o ~ ek BSTFA/1% TMCS 50 µl l 70 o Cl 15 o ~ pp e. e mp p t 1µl GC/MSl tp l m (Fig. 2). r o tl sq l o Vol. 52, No. 6, 2008

482 vmërq~ë dpë ntëprvë s Ëp t ~p 5 ng/ml, e m p p }, r kp l r Š m. p (inter-day) r p e q 4p l r mp, e q (inter-person) r p e q l r m. y d Fig. 2 Preparation procedures of urine sample for the analysis of THCCOOH. r mp, 3 v p THCCOOH tnk(10, 1, 0.1 µg/ml)p s e l ~ l (calibration curve)p q m. l l THCCOOHp r o 2.0~40 ng/ml r l tnkp ~ l 4 p p r(calibration point)l e rs m. l l THCCOOH-d 3 p ˆml l 1µg/ml rs tnk 45 µl l p p e m p p } l m. s r} e t 1µl GC/MSl tp l mp, p q m. t (QC) s e 3mll THCCOOH tnkp ~ l l THCCOOHp rp e p (urine sampling), rr p r} GC/MS q pn rp. l THCCOOHp rl n e rl, rl n tnkp, p pn l p r p, rp r p ˆ l p e ql p rp 5 v n p. l THCCOOH p npp ep p p r m. C i =x i Ëf vol' Ëf std Ëf cal' Ëf variation Ëf person (1) C i : l r THCCOOHp xi : y i -b/m, q l r f vol' : } p p f std : tnkp p f cal' : p v l p p Fig. 3 Uncertainty factors associated with measurement results. J. Pharm. Soc. Korea

t ~ p r 483 f variation : QC e p r p f person : e q r p THCCOOHp e (1)l np p Fig. 3l e l e mp, p n p. f vol' p t THCCOOHp kp e l n p. f cal' p pn l r p rl n p, f std tnkp m l n p. f variation p er lqp p p np( vp m, rp )l p n p, f person e q l r np( redš, q )l p n p. f variation f person v (QC) e l r m l ˆ l. 10,11) l s p e l oo t vp ~ t p n p f r t r} l p mr, n p v, e e k e qp sq e p r p r m. 12) š GUM(Guide to the Expression of Uncertainty in Measurement)p r 8) np (p p e )p r, p np Ž k, p p n t, er e l r p p n l m ˆ 4 p. v r l npp n t, t l t. t l e tl pq(coverage factor, k) l q, ˆ. 13) v d y sƒ p r l e r rl (pipette)p (u pipet' ) npp l p. q~p r r q n m. r r 95%p e l (k=2) 0.006 mlmp, p t (u pipet' ) 0.003 mlpl. r 1ml l p t (u r pipet' ) 0.003pl. 1ml p n l e 3mlp r 1mlj 3 r p t m. 1mlj 3 rl p t (u r vol' ) e(2)l rn, 0.001732 mlpp k p l. u r vol' = u r pipet' ------------- = 0.003 ------------ n 3 (n : 1, 2,..., i) e r rp o qo (ν eff ) np t p qo e(3)p Welch-Satterthwaite equationl rn l p ( )m. ν eff = u 4 c ----------- 4 u i ---- ν i (ν eff : the effective degrees of freedom, u c : the combined standard uncertainty, u i : the individual standard uncertainties, ν i : the degrees of freedom) t y sƒ tnkp nl tnk(stock standard solution, S)p rs l n. tnk sr rp tnkp, n n d (volumetric flask) p npp. tnkp 10 1 tnk(1st working standard solution, W1)p rs rp p o l r tnkp t m. n t vp pv p l t (u purity(s) ) t (u r purity(s) ) l Table Il r m. t vp l rn t v kp l B p pn l m, t t l m. tnk l n n d l p n n d q~p, m l p. d q~p r r 95%p e l (k=2) 0.008 ml t (u cert' ) 0.004 ml pp k pl. m l p t Ž} Table I Uncertainty of purity of THCCOOH Analyte Concentration range (mg/ml) Standard uncertainty (u purity(s) ) (2) (3) Relative standard uncertainty (u r purity(s) ) THCCOOH 0.0968±0.0008 0.000462 0.004771 Vol. 52, No. 6, 2008

484 vmërq~ë dpë ntëprvë s Ëp Table II Relative standard uncertainties of diluted standard solutions (working solutions) and standard preparation Analyte Conc' (mg/ml) u r purity(s) u r flask u r pipet' u r std(w1) u r std(w2) u r std(w3) u r std THCCOOH 0.1000 0.00477149 0.00040007-0.00478823 - - - 0.0100-0.00040007 0.003 0.00478823 0.00566456 - - 0.0010-0.00040007 0.003-0.00566456 0.00642240-0.0001-0.00040007 0.003 - - 0.00642240 - - - - - 0.00478823 0.00566456 0.00642240 0.009811 0.00025 ml/ o Cp e e m s p 20±5 o Cp t (u temp' ) 0.000722 mlpp k pl. rž l n d pn rl p t (u flask ) 0.004 mlpl, o qo (ν eff ) l. t (u r flask ) e(4)l rn l 0.0004p p m. tnk sr rp t e(9)p rn l 0.009811plp p p Table IIl ˆ l. u r flask = u vol' -------- V 1 (4) (u flask = ( u cert' ) 2 +u ( temp' ) 2, V 1 =10 ml) 1 tnk(w1)p sr rl l m p pq t vp m n d l p v pq e(5)l rn l t (u r std(w1) ) m, p Table IIl r m. u r std W1 ( ) = ( u r purity( S) ) 2 +u ( r flask ) 2 2 tnk(w2)p 1 tnkp e 10 l r s. W2 rse m 1 tnkp, l n n d pq, qll p pq v e(6)l rn l 2 tnkp t (u r std(w2) ) m. p p e(7)l rn l 3 tnk (W3)l t l Table IIl m. (5) u r std( W2 ( ) 2 +u ( r flask ) 2 +u ( r std( W1) ) 2 ) = u r pipet' (6) u r std( W3 ( ) 2 +u ( r flask ) 2 +u ( r std( W2) ) 2 ) = u r pipet' tnk l n l p n r r 95%p e l (k=2) 0.006 mlp t (u pipet' ) 0.003 ml p k p. t (u r pipet' ) e(8)l rn l 0.003 pp k pl, o qo (ν eff ) m. (7) u r pipet' = u pipet' ----------- V 2 (8) (V 2 =1 ml) tnk rsm ržp l Fig. 4 Representative SIM (selected ion monitoring) chromatogram obtained from spiked urine sample containing 15 ng/ml of THCCOOH. J. Pharm. Soc. Korea

t ~ p r 485 u r std = ( u r std( W1) ) 2 +u ( r std( W2) ) 2 +u ( r std( W3) ) 2 QC w y sƒ redšp, vp m (matrix effect), rp q p l pl Š lk p rl t l p QC e n l QC e p r (precision) redšp r pql (u precision ) r p. 14) e l 5.0 ng/ml p QC e ˆ l m. p e q p (inter-day) r rp o 4p l r mp p e q pl rp rp p lv redš q p n QC e l r m m. Fig. 4 ~ t vp QC e p Š p. po 15) r ep e(10) p, inter-day inter-person l t e(11)m p r lv. e(11) THCCOOHl p Table III Standard uncertainty of inter-day repeatability No. THCCOOH (5.0 ng/ml) 1st day 2nd day 3rd day 4th day 1 4.720 4.846 4.467 4.495 2 5.023 4.736 4.487 4.693 3 4.972 4.736 4.508 4.696 4 4.924 4.741 4.509 4.883 Mean 4.920 4.765 4.493 4.692 Variance 0.018 0.003 0.0004 0.025 Standard uncertainty (u variation ) Relative standard uncertainty (u r variation ) 0.165032 0.033 Table IV Standard uncertainty of inter-person reproducibility No. THCCOOH (5.0 ng/ml) 1st person 2nd person 3rd person 1 4.720 4.609 4.714 2 5.023 4.870 4.527 3 4.972 4.991 4.390 4 4.924 4.863 4.604 5 4.959 4.922 4.435 Mean 4.920 4.851 4.534 Variance 0.014 0.021 0.017 Standard uncertainty (u person ) Relative standard uncertainty (u r person ) 0.197161 0.039 (9) QC e p r p e q r pl t 0.165032m 0.197161plp, p QC e p r p e q r pl t (u r variation, u r person ) 0.033 0.039pl (Table III, IV). y=µ+a i +ε ij (10) (µ: expected value of random variable x, A i : error between the groups, ε ij : measurement error) u precision =s A = M between-m within ------------------------------------ (11) n 0 (M between : sum of squares between groups, M within : sum of squares within groups, n 0 : number of measurements) w y sƒ p v p r p tn npp. p rp r r(1 e)l p p r p ee l r (R 2 ) p f p. p p o r ep p p ˆ p. y i =(mëx i )+b (12) (y i : ratio of the analyte area to internal standard area, x i : analyte concentration, m: slope, b: intercept of the calibration curve) p 4 (2, 10, 20, 40 ng/ml)p tnkp 2 l q m (Table V). p p q rp rr s p l r p m. THCCOOHp p r 0.9995, n 0.0631, y-r 0.009p p ˆ l. er nqp e THCCOOH p l rn l 2 l lp 11.53 ng/mlpl. r p q l p pp el p p. 16) u cal' = s y ---- m 1 --+ 1 p n x-x --+ ( -------------- )2 S xx (13) (x i =(y i -b/m), p: number of measurements to determine x i, n: number of measurements for the calibration, d i =y i -(mëx i )-b, d = d i /n, s y =( ( d i -d) 2 )/(n-2), x = x i /n, S xx = ( x i -x )2 ) Table Vp p e(13)l rn l llv l t (u r cal' ) 0.024853plp Table VIl ˆ l. Vol. 52, No. 6, 2008

486 vmërq~ë dpë ntëprvë s Ëp Table V Calculations for least-squares analysis 2 No. x i y i x i Ëy i x i d i d i 2 d i - d (d i - d ) 2 s xx 1 02 0.124 000.249 0004.0-0.01091 0.00012-0.010257 0.000105 256 2 02 0.136 000.273 0004.0-0.00120 0.00000-0.001857 0.000003 256 3 10 0.655 006.548 0100.0-0.01480 0.00022-0.015462 0.000239 064 4 10 0.643 006.428 0100.0-0.00281 0.00001-0.003467 0.000012 064 5 20 1.279 025.571 0400.0-0.00754 0.00006-0.008195 0.000067 004 6 20 1.253 025.052 0400.0-0.01841 0.00034-0.017754 0.000315 004 7 40 2.499 099.951 1600.0-0.03422 0.00117-0.033564 0.001127 484 8 40 2.565 102.597 1600.0-0.03193 0.00102-0.032593 0.001062 484 Sum 144 9.153 266.67 4208.0-0.0029344-0.0029309 1616 ( )2 x i = y i-b --------, d i =mx i -b, d i = d i ----------, S xx = x i -x m n Table VI Detailed estimation of uncertainty contributions in the results of THCCOOH analysis in human urine samples Uncertainty factors Relative standard uncertainty THCCOOH Effective degrees of freedom, ν eff Coverage factor, k Degree of contribution (%) Sample volume (u r vol' ) 0.002 8. - 000.2 Standard solution (u r std ) 0.010 8. - 005.3 Run control (precision, u r variation ) 0.033 15.0-023.3 Inter-person (precision, u r person ) 0.039 14.0-037.6 Calibration curve (u r cal' ) 0.025 06.0-033.7 Relative combined standard uncertainty (u r (C)) 0.058 35.8 2.1 100.0 Relative expanded uncertainty (U r (E)) 0.120 - - - Uncertainty was quantified for a single measurement of drug user urine sample. Coverage factor, k, was obtained from the Student's t-distribution corresponding to the calculated effective degrees of freedom of relative combined standard uncertainty using a confidence level of 95.45%. y y q o l p np l t Table VIl r m. pqp p qo o qo, k 95% e tl p pq k r mp, p t llv t (u r (C)) 0.058pl. p p pn l ll v q (U r (E)) pp ep pn l m. U r (E)=kËu r (C) (14) e(14)p q (U r (E)) 0.12p lp, p Table VIl m. l THCCOOHp r p 95% e l l (11.53±1.39) ng/ml(k=2.1, e t k 95%)pl. Table VIl GC/MS pn t ~ p r srp s Ër m. e s l e p k np p l p. l l t THCCOOH r l l npp p l r p sq o e p f p vp r rp ˆ q m. r v l ˆ p l m. nk r p p n p p e r, p l n p r, p t rp k p. ržp l t t, pq(k) l s q m. er lqp l THCCOOHp r p 11.53pl, q 0.12m. r p k 95%p e l pq k=2.1p l (11.53±1.39) ng/ml(k=2.1, e t k 95%)plp, THCCOOHp l 12.05%m. l l Š npp 5 v e p, tnkp rs, p rp, e q rp q GC/MS p v pl. r rp l 5 v np t e q rp q, p J. Pharm. Soc. Korea

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