General Framework for Latent Variable Model Inversion for the Design and Manufacturing of New Products

Design space determination of pharmaceutical processes: Effects of control strategies and uncertainty

The identification of process Design Space (DS) is of high interest in highly regulated industrial sectors, such as pharmaceutical industry, where assurance of manufacturability and product quality is key for process development and decision-making. If the process can be controlled by a set of manipulated variables, the DS can be expanded in comparison to an open-loop scenario, where there are no controls in place. Determining the benefits of control strategies may be challenging, particularly when the available model is complex and computationally expensive - which is typically the case of pharmaceutical manufacturing. In this study, we exploit surrogate-based feasibility analysis to determine whether the process satisfies all process constraints by manipulating the process inputs and reduce the effect of uncertainty. The proposed approach is successfully tested on two simulated pharmaceutical case studies of increasing complexity, i.e., considering (i) a single pharmaceutical unit operation, and (ii) a pharmaceutical manufacturing line comprised of a sequence of connected unit operations. Results demonstrate that different control actions can be effectively exploited to operate the process in a wider range of inputs and mitigate uncertainty.

The inversion of multiresponse partial least squares models, a useful tool to improve analytical methods in the framework of analytical quality by design

Analytical Quality by Design (AQbD) is the adaptation of Quality by Design (QbD) when it is applied to the development of an analytical method. The main idea is to develop the analytical method in such a way that the desired quality of the Critical Quality Attributes (CQAs), stated via the analytical target profile (ATP), is maintained while allowing some variation in the Control Method Parameters (CMPs). The paper presents a general procedure for selecting factor levels in the CMPs to achieve the desired responses, characterized by the CQAs, when liquid chromatographic methods are to be used for the simultaneous determination of several analytes. In such a case, the CMPs are usually the composition of the ternary mobile phase, its flow rate, column temperature, etc., while typical CQAs refer to the quality of the chromatograms in terms of the resolution between each pair of consecutive peaks, initial and final chromatographic time, etc. The analytical target profile in turn defines the desired characteristics for the CQAs, the reason for the whole approach. The procedure consists of four steps. The first is to construct a D-optimal combined design (mixture-process design) to select the domain and levels of the CMPs. The second step is to fit a PLS2 model to predict the analytical responses expressed in the ATP (the good characteristics of the chromatogram) as a function of the CMPs. The third step is the inversion of the PLS2 model to obtain the conditions necessary to obtain the preset ATP in the corresponding CQAs. The inversion is performed computationally in order to estimate the Pareto front of these responses, namely, a set of experimental conditions to perform the chromatographic determination for which the desired critical quality attributes are met. The fourth final step is to obtain the Method Operable Design Region (MODR), that is, the region where the CMPs can vary while maintaining the quality of the CQAs. The procedure has been applied to some cases involving different analytes, all of which are regulated by the European Union due to their toxicity to human health, namely five bisphenols and ten polycyclic aromatic hydrocarbons.

A review on the modernization of pharmaceutical development and manufacturing - Trends, perspectives, and the role of mathematical modeling

Recently, the pharmaceutical industry has been facing several challenges associated to the use of outdated development and manufacturing technologies. The return on investment on research and development has been shrinking, and, at the same time, an alarming number of shortages and recalls for quality concerns has been registered. The pharmaceutical industry has been responding to these issues through a technological modernization of development and manufacturing, under the support of initiatives and activities such as quality-by-design (QbD), process analytical technology, and pharmaceutical emerging technology. In this review, we analyze this modernization trend, with emphasis on the role that mathematical modeling plays within it. We begin by outlining the main socio-economic trends of the pharmaceutical industry, and by highlighting the life-cycle stages of a pharmaceutical product in which technological modernization can help both achieve consistently high product quality and increase return on investment. Then, we review the historical evolution of the pharmaceutical regulatory framework, and we discuss the current state of implementation and future trends of QbD. The pharmaceutical emerging technology is reviewed afterwards, and a discussion on the evolution of QbD into the more effective quality-by-control (QbC) paradigm is presented. Further, we illustrate how mathematical modeling can support the implementation of QbD and QbC across all stages of the pharmaceutical life-cycle. In this respect, we review academic and industrial applications demonstrating the impact of mathematical modeling on three key activities within pharmaceutical development and manufacturing, namely design space description, process monitoring, and active process control. Finally, we discuss some future research opportunities on the use of mathematical modeling in industrial pharmaceutical environments.

Handling Variables, via Inversion of Partial Least Squares Models for Class-Modelling, to Bring Defective Items to Non-Defective Ones

In the context of binary class-modelling techniques, the paper presents the computation in the input space of linear boundaries of a class-model constructed with given values of sensitivity and specificity. This is done by inversion of a decision threshold, set with these values of sensitivity and specificity, in the probabilistic class-models computed by means of PLS-CM (Partial Least Squares for Class-Modelling). The characterization of the boundary hyperplanes, in the latent space (space spanned by the selected latent variables of the fitted PLS model) or in the input space, makes it possible to calculate directions that can be followed to move objects toward the class-model of interest. Different points computed along these directions will show how to modify the input variables (provided they can be manipulated) so that, eventually, a computed ‘object’ would be inside the class-model, in terms of the prediction with the PLS model. When the class of interest is that of “adequate” objects, as for example in some process control or product formulation, the proposed procedure helps in answering the question about how to modify the input variables so that a defective object would be inside the class-model of the adequate (non-defective) ones. This is the situation illustrated with some examples, taken from the literature when modelling the class of adequate objects.

A new approach based on inversion of a partial least squares model searching for a preset analytical target profile. Application to the determination of five bisphenols by liquid chromatography with diode array detector

The paper shows a procedure for selecting the control method parameters (factors) to obtain a preset 'analytical target profile' when a liquid chromatographic technique is going to be carried out for the simultaneous determination of five bisphenols (bisphenol-A, bisphenol-S, bisphenol-F, bisphenol-Z and bisphenol-AF), some of them regulated by the European Union. The procedure has three steps. The first consists of building a D-optimal combined design (mixture-process design) for the control method parameters, which are the composition of the ternary mobile phase and its flow rate. The second step is to fit a PLS2 model to predict six analytical responses (namely, the resolution between each pair of consecutive peaks, and the initial and final chromatographic time) as a function of the control method parameters. The third final step is the inversion of the PLS2 model to obtain the conditions needed for attaining a preset analytical target profile. The computational inversion of the PLS2 prediction model looking for the Pareto front of these six responses provides a set of experimental conditions to conduct the chromatographic determination, specifically 22% of water, mixed with 58% methanol and 20% of acetonitrile, keeping the flow rate at 0.66 mL min^-1. These conditions give a chromatogram with retention times of 2.180, 2.452, 2.764, 3.249 and 3.775 min for BPS, BPF, BPA, BPAF and BPZ, respectively, and excellent resolution among all the chromatographic peaks. Finally, the analytical method is validated under the selected experimental conditions, in terms of trueness and precision. In addition, the detection capability for the five bisphenols were: 596, 334, 424, 458 and 1156 μg L^-1, with probabilities of false positive and of false negative equal to 0.05.

Multivariate Six Sigma: A Case Study in Industry 4.0

The complex data characteristics collected in Industry 4.0 cannot be efficiently handled by classical Six Sigma statistical toolkit based mainly in least squares techniques. This may refrain people from using Six Sigma in these contexts. The incorporation of latent variables-based multivariate statistical techniques such as principal component analysis and partial least squares into the Six Sigma statistical toolkit can help to overcome this problem yielding the Multivariate Six Sigma: a powerful process improvement methodology for Industry 4.0. A multivariate Six Sigma case study based on the batch production of one of the star products at a chemical plant is presented.

General procedure to aid the development of continuous pharmaceutical processes using multivariate statistical modeling - an industrial case study

Streamlining the manufacturing process has been recognized as a key issue to reduce production costs and improve safety in pharmaceutical manufacturing. Although data available from earlier developmental stages are often sparse and unstructured, they can be very useful to improve the understanding about the process under development. In this paper, a general procedure is proposed for the application of latent variable statistical methods to support the development of new continuous processes in the presence of limited experimental data. The proposed procedure is tested on an industrial case study concerning the development of a continuous line for the manufacturing of paracetamol tablets. The main driving forces acting on the process are identified and ranked according to their importance in explaining the variability in the available data. This improves the understanding about the process by elucidating how different active pharmaceutical ingredient pretreatments, different formulation modes and different settings on the processing units affect the overall operation as well as the properties of the intermediate and final products. The results can be used as a starting point to perform a comprehensive and science-based quality risk assessment that help to define a robust control strategy, possibly enhanced with the integration of a design space for the continuous process at a later stage.