A Statistical Approach to Estimating Adsorption-Isotherm Parameters in Gradient-Elution Preparative Liquid Chromatography

TL;DR

This paper introduces a Bayesian statistical method with modified MCMC algorithms to efficiently estimate adsorption-isotherm parameters in chromatography, addressing issues of non-linearity and uncertainty in inverse problems.

Contribution

It presents a novel Bayesian sampling framework and modified MCMC algorithms for more effective adsorption-isotherm parameter estimation in chromatography.

Findings

Efficient parameter estimation demonstrated with synthetic data.

Successful application to real chromatography data.

Improved handling of uncertainties in inverse modeling.

Abstract

Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. However, due to the ill-posedness, the high non-linearity, and the uncertainty quantification of the corresponding physical model, the existing deterministic inversion methods are usually inefficient in real-world applications. To overcome these difficulties and study the uncertainties of the adsorption-isotherm parameters, in this work, based on the Bayesian sampling framework, we propose a statistical approach for estimating the adsorption isotherms in various chromatography systems. Two modified Markov chain Monte Carlo algorithms are developed for a numerical realization of our statistical approach. Numerical experiments with both synthetic and real data are conducted and described to show the efficiency of the proposed new method.