Statistical comparison of Fourier transform infrared spectra

Spectroscopic assessment of whether a biological sample has changed as a result of processing or degradation is generally carried out by qualitative comparison of spectra, without statistical analysis, resulting in a subjective evaluation of sample stability. Here, we present a formalism for quantitative statistical comparison of signal-averaged Fourier transform infrared spectra, commonly used to assess molecular properties of biological samples. Expressions are derived permitting the comparison of 1. single beam spectra; 2. transmittance spectra obtained by calculating the ratio of single beam spectra of a sample and background; and 3. absorbance spectra derived from transmittance spectra. An application of these results to the degradation of cartilage is presented. Two absorbance spectra of a cartilage sample taken in succession are found to be statistically identical with respect to the ratio of the amplitude of the amide I band to the amplitude of the amide II band. However, a spectrum of the same sample acquired after a 24-h degradation period, while similar to the spectrum of the fresh sample, is found to have an altered ratio of these spectral band amplitudes, consistent with degradation of the cartilage matrix.