(39b) Model-Based Design of Experiments for Chromatography Method Development

Liquid chromatography is an integral purification process widely used in the pharmaceutical industry for both small molecules and biological macromolecules, separating high-value components of interest from impurities arising from upstream production. Most active pharmaceutical ingredients (APIs) in the drug discovery phase never reach clinical trials, and only a tiny fraction, approximately 1 in 8,000, ultimately gain FDA approval¹. This presents a significant challenge for pharmaceutical R&D departments, as they must deal with a large volume of separations for numerous molecules with distinct physicochemical properties and behavior. Consequently, the predictive capabilities of computational models have gained increasing interest for their ability to streamline chromatography method development, particularly in parameter estimation, scale-up, and optimization for preparative applications.

Parameter estimation in chromatography aims to identify either fluid-dynamic parameters or (adsorption) isotherm parameters that best represent the underlying physicochemical phenomena of a separation. Selecting the most appropriate isotherm model and accurately determining its parameters is crucial, since the isotherm model defines the adsorption-desorption behavior of the target molecule, which is the key aspect of the separation. Parameter estimation can be achieved through experimentation (e.g., Frontal Analysis) or via hybrid methods, which combine experimental data with modeling tools (e.g., Inverse Method). Although fully experimental methods can be resource-intensive, they generally achieve high parameter accuracy. Conversely, hybrid methods, though preferred due to reduced resource and time demands, have so far tended to be slightly less accurate. The Inverse Method (IM), a prominent example of the hybrid approach, involves fitting model parameters by matching simulations to experimental datasets. A more sophisticated approach is that of conventional Design of Experiments (DoE), or by relying solely on expert process knowledge. These practices, normally focused on a pre-chosen isotherm model, primarily consider statistical tests for goodness-of-fit, but neglect crucial aspects such as practical identifiability and parameter precision.

In our study, we present a rigorous methodology, which employs Model-Based Design of Experiments (MBDoE)^2,3 combined with statistical tests, to evaluate model structure suitability and parameter precision. The method focuses on selecting the most appropriate isotherm model from a set of candidate models, as well as determining its corresponding parameter values and analysing the statistical significance of those values. This MBDoE approach not only identifies the most appropriate isotherm model, but also yields a higher precision of the parameters with fewer experiments compared to conventional factorial DoE approaches; thus, experimental time and resources can be reduced. The approach also considers the precision of the parameter values and the associated model predictions.

In our case-studies, developed based on in-silico experiments, we have explored organic modifier-dependent isotherms applicable to both isocratic and gradient separations. The open-source platform CADET in Python was used for the simulations⁴. The parameter estimation employed the built-in gradient descent algorithm of CADET, while MBDoE was performed using a Bayesian optimization algorithm coupled with a Gaussian process as a surrogate objective function.

We will show how accurate isotherm model parameters can be obtained and how the accuracy of the model predictions can be estimated. The use of this methodology will significantly reduce the time and resources required for chromatography model development. The methodology can also identify how reliable the isotherm model is within the given experimental budget, thus providing a very useful tool for business decisions.

References

1. Bhutani, P., Joshi, G., Raja, N., Bachhav, N., Rajanna, P. K., Bhutani, H., Paul, A. T., & Kumar, R. (2021). Journal of Medicinal Chemistry, 64(5), 2339–2381.
2. Franceschini, G., & Macchietto, S. (2008). Chemical Engineering Science, 63(19), 4846–4872.
3. Waldron, C., Pankajakshan, A., Quaglio, M., Cao, E., Galvanin, F., & Gavriilidis, A. (2019). Industrial and Engineering Chemistry Research, 58(49), 22165–22177.
4. Leweke, S., & von Lieres, E. (2018). Computers & Chemical Engineering, 113, 274–294.