A homotopy for the reliable estimation of model parameters in chromatography processes

Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly nonlinear models, and limited prior knowledge of certain parameters, among others.

In this work we propose a homotopy-based globalization strategy that can be used in combination with iterative algorithms for the solution of parameter estimation problems. Our method is tailored to measurement data showing a single peak or multiple, possibly overlapping peaks, which often arises from bind-and-elute experiments. With our approach, convergence to a local optimum can be achieved even when initial guesses are far away from a solution. Moreover, we describe and discuss the calibration procedure for a real-world ion exchange chromatography process, here considering a complete chromatography system. This description may serve as a general blueprint for the estimation of model parameters in chromatography processes.