doi:10.1016/j.chroma.2006.09.073 
Copyright © 2006 Elsevier Inc. All rights reserved.
Prediction of measurement uncertainty in isotope dilution gas chromatography/mass spectrometry
Hiroshi Hasegawaa, 
, 
, Yoshihiko Shinoharaa, Takao Hashimotoa, Rieko Matsudab and Yuzuru Hayashib
aSchool of Pharmacy, Tokyo University of Pharmacy and Life Science, 1432-1 Horinouchi, Hachioji, Tokyo 192-0392, Japan
bNational Institute of Health Sciences, 1-18-1 Kami-Yoga, Setagaya, Tokyo 158-8501, Japan
Received 4 August 2006;
revised 22 September 2006;
accepted 25 September 2006.
Available online 11 October 2006.
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Abstract
An equation is theoretically derived which describes the relative standard deviation (RSD) of the amount ratios of analyte to its isotope-labeled variant in gas chromatography/mass spectrometry (GC/MS) using the stable isotope dilution method. The determination of methyltestosterone is taken as an example. The uncertainty equation proposed is justified by comparing the theoretical RSD values with the experimental RSD values obtained by replication over a wide range of analyte amount. The detection limit and quantitation limit are estimated from the continuous plot (precision profile) of the theoretical RSD against analyte amount.
Keywords: Uncertainty; GC/MS; Isotope dilution; FUMI theory
Fig. 1. Mutual contribution between analyte and IS in ID-GC/MS. At analyte m/z, the measured peak area, P, is observed as the sum of the net peak area, p, and the contribution peak, αq, where α denotes the contribution coefficient of IS to the analyte. Similarly, at IS m/z, the measured peak area, Q, is observed as the sum of the net peak area, q, and the contribution peak, βp, where β denotes the contribution coefficient of analyte to the IS.
Fig. 2. SIM tracing for MT at m/z 303.2 after injecting 1 μl aliquot of (A) the solution of [2H3]MT (102.0 nmol/ml) and (B) the mixed solution of MT (10 pmol/ml) and [2H3]MT (102.0 nmol/ml).
Fig. 3. Power spectra of baselines monitored at (A) m/z = 303.2 and (B) m/z = 306.2. One thousand twenty-four data points of the baseline data are Fourier-transformed. Zigzag line denotes the observed spectrum and smooth line the least-squares-fitted line of the model noise (white noise + Markov process). The fitted line (—) gives dP and dQ used in Eq. (9) (see Fig. 2).
Fig. 4. Precision profile for MT at α = 0.0032. (●) Experimental RSD (n = 6); (—) theoretical RSD (Eq. (9)). For Eq. (9), SD of peak areas: dP = 321, dQ = 302. The area measurements, P and Q, are the sum of the intensities over 81 data points around the peak center (−30 to 50) for both MT and [2H3]MT, respectively.
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