Bayesian Modeling and Computation for Analyte Quantification in Complex Mixtures Using Raman Spectroscopy

In this work, we propose a two-stage algorithm based on Bayesian modeling and computation aiming at quantifying analyte concentrations or quantities in complex mixtures with Raman spectroscopy. A hierarchical Bayesian model is built for spectral signal analysis, and reversible-jump Markov chain Monte Carlo (RJMCMC) computation is carried out for model selection and spectral variable estimation. Processing is done in two stages. In the first stage, the peak representations for a target analyte spectrum are learned. In the second, the peak variables learned from the first stage are used to estimate the concentration or quantity of the target analyte in a mixture. Numerical experiments validated its quantification performance over a wide range of simulation conditions and established its advantages for analyte quantification tasks under the small training sample size regime over conventional multivariate regression algorithms. We also used our algorithm to analyze experimental spontaneous Raman spectroscopy data collected for glucose concentration estimation in biopharmaceutical process monitoring applications. Our work shows that this algorithm can be a promising complementary tool alongside conventional multivariate regression algorithms in Raman spectroscopy-based mixture quantification studies, especially when collecting a large training dataset with high quality is challenging or resource-intensive.

💡 Research Summary

This paper presents a novel two-stage algorithm based on Bayesian modeling and computation for quantifying analyte concentrations in complex mixtures using Raman spectroscopy. The core innovation lies in its ability to perform accurate quantification with minimal training data, requiring only the pure spectrum of the target analyte as prior knowledge, unlike conventional multivariate regression methods which depend on large sets of mixture spectra with known concentrations.

The algorithm operates in two distinct stages. In the first stage, a hierarchical Bayesian model is constructed to decompose the pure analyte’s Raman spectrum. The spectrum is modeled as a sum of individual peaks (represented by pseudo-Voigt functions), a baseline (modeled with B-spline functions), and i.i.d. Gaussian noise. Since the number of peaks is unknown a priori, the model incorporates reversible-jump Markov chain Monte Carlo (RJMCMC) sampling for joint model selection (determining the number of peaks, k_P) and parameter estimation. The RJMCMC sampler estimates all relevant variables: peak parameters (location l, width w, shape weight ρ, amplitude β_P), baseline coefficients, noise variance (σ²), and the hyperparameter g from Zellner’s g-prior.

In the second stage, the peak representations (location, width, shape) learned from the first stage are fixed. For a new mixture spectrum, the RJMCMC sampler is run again, but this time only the amplitudes (β_P) of the target analyte’s peaks are estimated, with all other structural parameters held constant. These estimated amplitudes are proportional to the concentration of the target analyte in the mixture, enabling direct quantification.

The authors validate the algorithm through extensive numerical simulations. They test its performance across a wide range of conditions, including varying signal-to-noise ratios, degrees of peak overlap, and concentration levels. Comparative analysis with standard multivariate methods like Partial Least Squares Regression (PLSR) and Principal Component Regression (PCR) demonstrates a key advantage: the proposed Bayesian algorithm significantly outperforms these conventional methods in the small training sample size regime. This makes it particularly valuable for applications where collecting a large, high-quality calibration dataset is expensive, time-consuming, or impractical.

To demonstrate practical utility, the method is applied to a real-world experimental dataset from biopharmaceutical process monitoring. The task involves estimating glucose concentration from spontaneous Raman spectra collected during Chinese Hamster Ovary (CHO) cell cultures. The algorithm successfully tracks the glucose concentration trend throughout the process, effectively handling the complex, evolving background from the culture medium and cells. This application underscores the method’s robustness and potential for real-time monitoring in challenging environments.

In conclusion, this work introduces a powerful Bayesian framework as a complementary tool to traditional chemometric techniques for Raman spectroscopy. By leveraging prior knowledge of the pure analyte and using trans-dimensional MCMC for integrated peak/baseline analysis and model selection, it achieves reliable quantification with minimal training data. This approach is especially promising for applications in bioprocessing, material science, and any field where rapid, resource-efficient analysis of complex mixtures is required.