Uncertainty back-propagation in PLS model inversion for design space determination in pharmaceutical product development

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.

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Recently, the pharmaceutical industry has been facing several challenges associated to the use of outdated development and manufacturing technologies.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.

Evaluation of liquid-phase thermometry in impinging jet sprays using synchrotron x-ray scattering

Liquid thermometry during primary and secondary breakup of liquid sprays is challenging due to the presence of highly dynamic, optically complex flow features. This work evaluates the use of x-ray scattering from a focused, monochromatic beam of the Advanced Photon Source at Argonne National Laboratory for the measurement of liquid temperatures within the mixing zone of an impinging jet spray. The measured scattering profiles are converted to temperature through a previously developed two-component partial least squares (PLS) regression model. Transmitive mixing during jet merging is inferred through spatial mapping of temperatures within the impingement region. The technique exhibits uncertainties of ±2K in temperature and 2% in capturing the correct scattering profile, showing its potential utility for probing liquid temperature distributions in multiphase flows.