Calculation of the confidence range in order to obtain a linear calibration graph in stable isotope dilution mass spectrometry: application to reference methods and pharmacological studies

Abstract

Isotope dilution mass spectrometry is a technique that has been shown t o be capable of producing the accuracy and precision required of a reference method. The use of a labelled standard, selected ion monitoring and isotope ratio measurements has been applied t o the determination of many compounds. In pharmacology, drug metabolism can be studied using 'inverse dilution'. The calibration graph is obtained by plotting peak-area ratio against the ratio of the amount of unlabelled compound to that of labelled compound. The graph is of hyperbolic form, part of which can be linearized. To define the limits of this linear confidence range, calculation procedures are described. The equations given are clearly useful in determining the limits within which the operator can control the relative error. These equations are defined for isotope dilution whatever the ratio of the amount of unlabelled t o labelled compound. Examples are discussed.

Evaluation of minimal 13C-labelling for stable isotope dilution in organic analysis

“…For molecules containing more than 60 carbon atoms the use of 4 or more carbon-13 atoms would be recommended. Thus, we can conclude that for small organic molecules up to 20 carbon atoms, currently found in environmental analysis, the choice of single or multiple 13 C-labelling will not have a drastic influence on the overall uncertainty of the procedure. For larger molecules, multiple labelling would be advisable for lower propagated uncertainties.…”

“…Then, the value increases as the number of carbon atoms in the molecule, m, grows. The lower error propagation values are always found when 4 carbon-13 atoms are used for labelling and it could be expected that lower values still will be found for larger 13 C-labelling. However, for small organic molecules, where m < 20, there is almost no difference in the error magnification factors when 1, 2 or 4 carbon-13 atoms are used for labelling.…”

“…For the 13 According to all the previous results, it was decided to use a fragmentation pattern of a ¼ 0.980 for the C 6 H 6 O + ion and b ¼ 0.020 for the C 6 H 5 O + ion in the calculations of the 'estimated' isotope patterns for all compounds. The standard uncertainties of the fragmentation factors were calculated to be 0.002 for both a and b.…”

“…10,11 In these situations, a minimal labelling (e.g. a single 13 C label in the molecule) might be useful as no isotopic effects or changes in retention time are expected. The problem with this choice is that, due to the spectral overlap, the minimal labelling provides non-linear isotope dilution calibration graphs and this has been traditionally avoided in organic IDMS.…”

“…Previous works have been devoted to the linearization of the calibration curves by applying complex mathematical linearizing methods. 12,13 Also, Thienpont et al 14 proposed the use of labelled compounds with a mass increment of only 1-2 units using single point-calibration methods. For this purpose, the contribution of the unlabelled analyte at the m/z value monitored for the labelled analogue (and vice versa) must be determined previously.…”