Abstract

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

Highlights

  • Mathematical models have been proven to be an indispensable tool in chemical engineering research and design

  • Optimal tuning of those model parameters according to the experimental data is an essential step in the process of model development where model parameters are iteratively adapted until simulation results fit the given measurement data best [12,14]

  • In our work, we have successfully demonstrated the benefit of robustification and global sensitivity analysis (GSA) concepts for model-based optimal experimental design (MB-OED) to gain the most informative data and to improve parameter estimates, respectively

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Summary

Introduction

Mathematical models have been proven to be an indispensable tool in chemical engineering research and design. The aim of MB-OED is to redesign the experimental setup ensuring high sensitivities of all parameters over the course of the experimental run To this end, a dynamic optimization problem has to be solved, which typically includes the following generic steps; see . The resulting optimal design variables determine the setup of the experimental run, which is expected to produce new informative measurement data These data, in turn, represent operating conditions at which, in general, the model parameters show an increased sensitivity leading to more precise parameter estimates. Reliable sensitivity measures are mandatory for MB-OED to provide the most informative data possible This aspect is relevant for syntheses of active pharmaceutical ingredients, where typically the number of novel drugs and the number of experimental runs are limited. This last point, as mentioned previously, is of critical relevance when analyzing novel but exceedingly rare drug candidates

Design
Sensitivity Measures
Local Parameter Sensitivities
Robustification
Global Parameter Sensitivities
Implementation Aspects
Optimal Design Measures
Local Design Measures
Global Design Measures
Case Studies
A Fed-Batch Bioreactor
Conclusions
Full Text
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