(493b) Model-Based Design of Experiments for Identification of Organic Modifier Dependent Isotherms in RPLC

High Performance Liquid Chromatography (HPLC) is one of the most important purification processes in the pharmaceutical industries for the separation of both small synthetic and large biological molecules. The increasing costs and demand for sustainable solutions in chromatography has led researchers to shift toward modeling and the use of simulation tools to design and intensify the process. First-principle models have been developed and used in chromatography for almost three decades. These models are characterized by system-specific parameters, typically either fluid-dynamic coefficients or (adsorption) isotherm parameters. The parameter values are traditionally acquired through intensive experimentation, which is costly both in terms of resources and in terms of time.

Frontal Analysis¹ is one of the most common techniques for estimating isotherm parameters. However, the outdated and resource-intensive nature of the method has urged researchers to resort to alternatives such as the Inverse Method² (IM), which relies on curve-fitting. With the IM, parameters are fitted to proposed isotherm models by matching simulated chromatograms to experimental data. But experimental data are not always sufficiently informative, and thus experimental conditions that are based on process intuition and conventional Design of Experiments (DoE) can in fact impede the parameter estimation and increase the experimental effort. In Process Systems Engineering, Model-Based Design of Experiments (MBDoE) methodologies³ have been proposed and used extensively in the identification of kinetic models for microreactor systems⁴. In this work, we propose leveraging such MBDoE methodologies to identify suitable isotherm models and their parameters for Reversed Phase HPLC.

The proposed methodology relies on a step-by-step procedure involving: a) a preliminary screening of potential isotherm models, including an investigation of the goodness-of-fit of the model; b) a practical identifiability test, to assess whether the parameters can be uniquely estimated for the proposed models under a given experimental budget; c) model discrimination, to select the most suitable model structure; and d) further refinement of the parameter precision, tested based on Monte Carlo simulations, to quantify the impact of the parametric uncertainty.

The methodology is demonstrated based on a case-study of a known system described by in-silico experiments. The in-silico experiments were conducted with the bi-Langmuir isotherm as the “true” isotherm model. In the investigation, candidate models, including this and other Langmuir-type isotherms, were proposed as suitable models. The isotherms were always coupled with the same transport-phenomena model, the Equilibrium Dispersion Model (EDM). The EDM is a good choice owing to the large range of its applications and its low computational cost. We assumed a constant dispersion coefficient to focus solely on the identification of the isotherm model and of its parameters. For the Reversed Phase Liquid Chromatography (RPLC) case study, the saturation capacity of the adsorbent and the retention factor were assumed to depend on the organic modifier⁴. The simulations were conducted in CADET, an open-source platform for modeling and simulation in Python⁵. Optimisation was conducted with a CADET built-in gradient descent algorithm, while for the MBDoE we employed a Bayesian optimisation algorithm.

We will demonstrate how accurate isotherm model parameters can be obtained and how the accuracy of the model parameters can be quantified. We will also demonstrate how one can transition from a supervised implementation of the methodology to a fully automated one. Automation will allow the user to work with multiple chromatography systems at the same time, thus enabling faster and less resource-intensive chromatography method development. This methodology will significantly reduce the time and resources required for chromatography model development. It can also identify how reliable the isotherm model is within the given experimental budget, thus providing a useful tool for business decisions.

References

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