Strategies for 13C enrichment calculation in Fourier-transform infrared CO2 spectra containing spectral overlapping and nonlinear abundance-amount relations utilizing response surface fits

The metabolism can be explored via 13C labeling of biological active substances and subsequent quantification of 13C enrichment in the exhaled carbon dioxide in breath. The resulting tracer enrichment values can be determined by Fourier-transform Infrared Spectroscopy (FTIR), since different CO2 isotopologues result in distinct absorption lines in the spectrum.The corresponding determination poses two challenges: first, FTIR absorbance can contain a nonlinear relationship between analyte amount and spectral signal and second, the spectral peaks for the different isotopologues overlap. The overlap precludes a separate calibration to asses the isotopologue concentration values and with it a determination of enrichments from concentration values. We propose here, first, a data reduction step like Principal Component Analysis (PCA) to convert the spectral information into one score pertaining to the 13CO2 enrichment. In a second step, a calibration function between score and enrichment values was established. The enrichment score can be derived by normalizing a subset of the spectrum by some measure for the 12CO2 sample content. Alternatively, the overlapping spectra were decomposed into two isotopologue spectra and the intensity of the separated spectra was used to form an enrichment score. For spectral separation, either Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) was used or a novel decomposition strategy developed for this paper called Rotation and Angle-Bending Bayesian induced Transformation - Multivariate Curve Resolution (RABBIT – MCR) that operates in a Principal Component Analysis (PCA) subspace and is derived from MCR. We compared 13C enrichment estimates from FTIR CO2 spectra using different normalization variants with the two spectral separation models. In conclusion, the two spectral separation variants performed nearly equal, but better than any normalization variant.