Model-driven optimal experimental design for calibrating cardiac electrophysiology models

Background and Objective: Models of the cardiomyocyte action potential have contributed immensely to the understanding of heart function, pathophysiology, and the origin of heart rhythm disturbances. However, action potential models are highly nonlinear, making them difficult to parameterise and limiting to describing ‘average cell’ dynamics, when cell-specific models would be ideal to uncover inter-cell variability but are too experimentally challenging to be achieved. Here, we focus on automatically designing experimental protocols that allow us to better identify cell-specific maximum conductance values for each major current type.Methods and Results: We developed an approach that applies optimal experimental designs to patch-clamp experiments, including both voltage-clamp and current-clamp experiments. We assessed the models calibrated to these new optimal designs by comparing them to the models calibrated to some of the commonly used designs in the literature. We showed that optimal designs are not only overall shorter in duration but also able to perform better than many of the existing experiment designs in terms of identifying model parameters and hence model predictive power.Conclusions: For cardiac cellular electrophysiology, this approach will allow researchers to define their hypothesis of the dynamics of the system and automatically design experimental protocols that will result in theoretically optimal designs

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

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

Sensitivitätsanalyse und robustes Prozessdesign pharmazeutischer Herstellungsprozesse

The existence of parameter uncertainties(PU) limits model-based process design techniques. It also hinders the modernization of pharmaceutical manufacturing processes, which is necessitated for intensified market competition and Quality by Design (QbD) principles. Thus, in this thesis, proper approaches are proposed for efficient and effective sensitivity analysis and robust design of pharmaceutical processes. Moreover, the point estimate method (PEM) and polynomial chaos expansion (PCE) are further implemented for uncertainty propagation and quantification (UQ) in the proposed approaches. Global sensitivity analysis (GSA) provides quantitative measures on the influence of PU on process outputs over the entire parameter domain. Two GSA techniques are presented in detail and computed with the PCE. The results from case studies show that GSA is able to quantify the heterogeneity of the information in PU and model structure and parameter dependencies affects significantly the final GSA result as well as output variation. Frameworks for robust process design are introduced to alleviate the adverse effect of PU on process performance. The first robust design framework is developed based on the PEM. The proposed approach has high computational efficiency and is able to take parameter dependencies into account. Then, a novel approach, in which the Gaussian mixture distribution (GMD) concept is combined with PEM, is proposed to handle non-Gaussian distribution. The resulting GMD-PEM concept provides a better trade-off between process efficiency and probability of constraint violations than other approaches. The second robust design framework is based on the iterative back-off strategy and PCE. It provides designs with the desired robustness, while the associated computational expense is independent from the optimization problem. The decoupling of optimization and UQ provides the possibility of implementing robust process design to more complex pharmaceutical manufacturing processes with large number of PU. In this thesis, the case studies include unit operations for (bio)chemical synthesis, separation (crystallization) and formulation (freeze-drying), which cover the complete production chain of pharmaceutical manufacturing. Results from the case studies reveal the significant impact of PU on process design. Also they show the efficiency and effectiveness of the proposed frameworks regarding process performance and robustness in the context of QbD.Die pharmazeutische Industrie muss sowohl den gestiegenen Wettbewerbsdruck standhalten als auch die von Regulierungsbehörden geforderte QbD-Initiative (Quality by Design) umsetzen. Modellgestützte Verfahren können einen signifikanten Beitrag leisten, aber Parameterunsicherheiten (PU) erschweren jedoch eine zuverlässige modellgestützte Prozessauslegung. Das Ziel dieser Arbeit ist daher die Erforschung von effizienten Approaches zur Sensitivitätsanalyse und robusten Prozessdesign der pharmazeutische Industrie. Methoden, Point Estimate Method (PEM) und Polynomial Chaos Expansion (PCE), wurde implementiert, um effizient Unsicherheitenquantifizierung (UQ) zu erlauben. Der globalen Sensitivitätsanalyse (GSA) ist eine systematische Quantifizierung von Parameterschwankungen auf die Simulationsergebnisse. Zwei GSA Techniken werden im Detail vorgestellt und an Beispielen demonstriert. Die Ergebnisse zeigen sowohl den Mehrwert der GSA im Kontext des robusten Prozessdesigns als auch die Relevanz zur korrekten Berücksichtigung von Parameterkorrelationen bei der GSA. Um den schädlichen Einfluss von PU auf die modellgestützte Prozessauslegung zusätzlich zu minimieren, wurden weitere Konzepte aus der robusten Optimierung untersucht. Zunächst wurde das erste Konzept basierend auf der PEM entwickelt. Das erste Konzept zeigt einen deutlich reduzierte Rechenaufwand und kann auch die Parameterkorrelationen entsprechend in der robusten Prozessauslegung berücksichtigen. In einem zweiten Schritt wurde ein neuer Ansatz, der die Gauß-Mischverteilung mit der PEM kombiniert, hierzu für nicht normalverteilte PU erfolgreich implementiert. Weiterhin wurde eine iterative Back-off-Strategie erforscht, die auch die PU entsprechend berücksichtigt aber leichte Rechenaufwand zeigt. Durch die Entkoppelung von UQ und Optimierung können wesentlich komplexere pharmazeutische Herstellungsprozesse mit einer hohen Anzahl an PU implementiert werden. Die in dieser Arbeit untersuchten verfahrenstechnische Grundoperationen decken somit einen Großteil der gesamten Produktionskette der pharmazeutischen Herstellung ab. Die Ergebnisse der untersuchten Beispiele zeigen deutlich den Einfluss von PU auf das modellgestützte Prozessdesign auf. Mithilfe der vorgeschlagenen Approaches können die PU effektiv und effizient bei einer optimalen Balance von Rechenaufwand und der geforderten Zuverlässigkeit ganz im QbD-Sinne berücksichtigt werden