Calibration graphs in isotope dilution mass spectrometry

Isotope-based quantitation is routinely employed in chemical measurements. Whereas most analysts seek for methods with linear theoretical response functions, a unique feature that distinguishes isotope dilution from many other analytical methods is the inherent possibility for a nonlinear theoretical response curve. Most implementations of isotope dilution calibration today either eliminate the nonlinearity by employing internal standards with markedly different molecular weight or they employ empirical polynomial fits. Here we show that the exact curvature of any isotope dilution curve can be obtained from three-parameter rational function, y = f(q) = (a₀ + a₁q)/(1 + a₂q), known as the Padé[1,1] approximant. The use of this function allows eliminating an unnecessary source of error in isotope dilution analysis when faced with nonlinear calibration curves. In addition, fitting with Padé model can be done using linear least squares.