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

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.