Partial Least Squares Based Decomposition of Five Spectrally Overlapping Factors

Abstract

The development of a multi-sensory fiber-optic based fluence rate probe (MSP) for light monitoring and dosimetry during photodynamic therapy (PDT) created the need for a robust multivariate signal analysis algorithm capable of quantifying the intensity of five component spectra, representing the sensors, which display a large degree of spectral overlap. Partial least squares (PLS) analysis, as an option for such an analysis algorithm, was evaluated through simulations in the presence of three types of noise, which experimentally may limit the accuracy of PLS quantification of component spectra contributions. Random, or white noise, background was varied over a range of 0–15% relative intensity. A non-random (Gaussian) background vector was simulated, as an experimentally relevant spectral interferent, over a range of 0–7% relative intensity. Spectral variation was modeled by a spectral shift of ±1–5 nm. Procedures for selecting preferred combinations of fluorophores, with minimum possible spectral overlap, were developed. To illustrate the importance of this selection process, PLS performance results were compared for two possible combinations of five fluorophores, as well as for the combination of three fluorophores currently in experimental use with MSPs. Experimentally anticipated worst-case quantifications were identified for all three types of simulated noise (5% random background, 0.5% Gaussian background, and ±2 nm spectral shift). The effects of single and combined types of noise were evaluated by independently varying each type of simulated noise over the experimentally relevant range. The mean percentage error in determining the fluorophore contributions and hence quantification of the fluence rate were compared with the required performance standard of better than 10% error for optical power meters in medical use. The PLS algorithm provided an accuracy of 7 ± 2% for five fluorophores and 3.3 ± 0.8% for three fluorophores, indicating that PLS is an appropriate choice for this application.