Response-surface fits and calibration transfer for the correction of the oxygen effect in the quantification of carbon dioxide via FTIR spectroscopy.

During routine Fourier-Transform Infrared Spectroscopy (FTIR) based quantification of carbon dioxide in breath, it is necessary to account for a non-linear signal response to the analyte concentration and disturbance factors arising from the gas background matrix. These factors as well as day-to-day fluctuation should be corrected via calibration. We present a novel strategy to combine the information of previous calibrations with a minimal number of actual calibration measurements to obtain a precise calibration. After decomposition of the FTIR spectra via principal component analysis (PCA) into scores (corresponding to intensity) and loadings (corresponding to spectral curves), an empirical response surface fit equation between scores, analyte concentration and disturbance factors is established. The fit equation can be characterized via the coefficients determined by calibration. Out of a pool of coefficients gained from several calibrations, a multivariate inter-day distribution is generated. By requiring the coefficient set of the actual calibration to be a sample of the multivariate inter-day distribution, the number of necessary routine calibration samples is reduced to two. The corresponding coefficients are determined using the Lagrange Multipliers approach and the inter-day variability of coefficients is estimated using Bayesian statistics and Hierarchical models. The best calibration parameters in terms of calibration equation, wavelength region, preprocessing options and choice of routine calibration samples were determined; optimized for minimal number of calibration samples.