Bano, Gabriele (2019) *Pharmaceutical development and manufacturing in a Quality by Design perspective: methodologies for design space description.* [Ph.D. thesis]

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## Abstract (italian or english)

In the last decade, the pharmaceutical industry has been experiencing a period of drastic change in the way new products and processes are being conceived, due to the introduction of the Quality by design (QbD) initiative put forth by the pharmaceutical regulatory agencies (such as the Food and Drug Adminstration (FDA) and the European Medicines Agency (EMA)).

One of the most important aspects introduced in the QbD framework is that of design space (DS) of a pharmaceutical product, defined as “the multidimensional combination and interaction of input variables (e.g. material attributes) and process parameters that have been demonstrated to provide assurance of quality”. The identification of the DS represents a key advantage for pharmaceutical companies, since once the DS has been approved by the regulatory agency, movements within the DS do not constitute a manufacturing change and therefore do not require any further regulatory post-approval. This translates into an enhanced flexibility during process operation, with significant advantages in terms of productivity and process economics.

Mathematical modeling, both first-principles and data-driven, has proven to be a valuable tool to assist a DS identification exercise. The development of advanced mathematical techniques for the determination and maintenance of a design space, as well as the quantification of the uncertainty associated with its identification, is a research area that has gained increasing attention during the last years.

The objective of this Dissertation is to develop novel methodologies to assist the (i) determination of the design space of a new pharmaceutical product, (ii) quantify the assurance of quality for a new pharmaceutical product as advocated by the regulatory agencies, (iii) adapt and maintain a design space during plant operation, and (iv) design optimal experiments for the calibration of first-principles mathematical models to be used for design space identification.

With respect to the issue of design space determination, a methodology is proposed that combines surrogate-based feasibility analysis and latent-variable modeling for the identification of the design space of a new pharmaceutical product. Projection onto latent structures (PLS) is exploited to obtain a latent representation of the space identified by the model inputs (i.e. raw material properties and process parameters) and surrogate-based feasibility is then used to reconstruct the boundary of the DS on this latent representation, with significant reduction of the overall computational burden. The final result is a compact representation of the DS that can be easily expressed in terms of the original physically-relevant input variables (process parameters and raw material properties) and can then be easily interpreted by industrial practitioners.

As regards the quantification of “assurance” of quality, two novel methodologies are proposed to account for the two most common sources of model uncertainty (structural and parametric) in the model-based identification of the DS of a new pharmaceutical product.

The first methodology is specifically suited for the quantification of assurance of quality when a PLS model is to be used for DS identification. Two frequentist analytical models are proposed to back-propagate the uncertainty from the quality attributes of the final product to the space identified by the set of raw material properties and process parameters of the manufacturing process. It is shown how these models can be used to identify a subset of input combinations (i.e., raw material properties and process parameters) within which the DS is expected to lie with a given degree of confidence. It is also shown how this reduced space of input combinations (called experiment space) can be used to tailor an experimental campaign for the final assessment of the DS, with a significant reduction of the experimental effort required with respect to a non-tailored experimental campaign. The validity of the proposed methodology is tested on granulation and roll compaction processes, involving both simulated and experimental data.

The second methodology proposes a joint Bayesian/latent-variable approach, and the assurance of quality is quantified in terms of the probability that the final product will meet its specifications. In this context, the DS is defined in a probabilistic framework as the set of input combinations that guarantee that the probability that the product will meet its quality specifications is greater than a predefined threshold value. Bayesian multivariate linear regression is coupled with latent-variable modeling in order to obtain a computationally friendly implementation of this probabilistic DS. Specifically, PLS is exploited to reduce the computational burden for the discretization of the input domain and to give a compact representation of the DS. On the other hand, Bayesian multivariate linear regression is used to compute the probability that the product will meet the desired quality for each of the discretization points of the input domain. The ability of the methodology to give a scientifically-driven representation of the probabilistic DS is proved with three case studies involving literature experimental data of pharmaceutical unit operations.

With respect to the issue of the maintenance of a design space, a methodology is proposed to adapt in real time a model-based representation of a design space during plant operation in the presence of process-model mismatch.

Based on the availability of a first-principles model (FPM) or semi-empirical model for the manufacturing process, together with measurements from plant sensors, the methodology jointly exploits (i) a dynamic state estimator and (ii) feasibility analysis to perform a risk-based online maintenance of the DS. The state estimator is deployed to obtain an up-to-date FPM by adjusting in real-time a small subset of the model parameters. Feasibility analysis and surrogate-based feasibility analysis are used to update the DS in real-time by exploiting the up-to-date FPM returned by the state estimator. The effectiveness of the methodology is shown with two simulated case studies, namely the roll compaction of microcrystalline cellulose and the penicillin fermentation in a pilot scale bioreactor.

As regards the design of optimal experiments for the calibration of mathematical models for DS identification, a model-based design of experiments (MBDoE) approach is presented for an industrial freeze-drying process. A preliminary analysis is performed to choose the most suitable process model between different model alternatives and to test the structural consistency of the chosen model. A new experiment is then designed based on this model using MBDoE techniques, in order to increase the precision of the estimates of the most influential model parameters. The results of the MBDoE activity are then tested both in silico and on the real equipment.

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