Inversion of Latent Variable Regression Models to Support Product and Process Development

When designing a new product and its manufacturing process, there is the need to understand how the raw material properties and the process parameters interact and affect the product performances, in order to control them and optimize the manufacture. For these reasons, usually large amounts of experiments are carried out to independently excite all the driving forces acting on the system, in order to gain a deep understanding of the relations between inputs (raw materials, process parameters) and outputs (final product properties). Even if systematically designed, the number of experiments to be performed may become prohibitive, especially if a large number of candidate materials and permutations have to be considered, as for the formulation of a pharmaceutical product. If data on historically developed products were available, useful information could be drawn from these databases, to support the design and the optimization of new products and of their manufacturing processes, with the aim of accelerating the development cycle guiding the experimentation from the first steps.

Latent variable regression models (LVRMs) are tools specifically designed to analyze large datasets of highly correlated data reducing the vast information in them in a small number of variables (the latent variables) which indentify the underlying driving forces relating input data with system outputs. The driving forces identified from the available historical databases represented by the LVRM equations can then be used to support the design of new products: since the design activity aims at finding the best combination of inputs (raw material properties and process conditions) which ensure a desired product profile in output, the design objectives could be achieved through a LVRM inversion operation.

In this contribution we show how LVRM inversion [1,2] can be feasibly used to support pharmaceutical product and process development activities. Since the LVRM inversion can have several solutions depending on the rank of the historical datasets used to build the model, the inversion has to be posed as an optimization problem [3,4]. A framework is therefore proposed to manage the different constraints and objectives the design problem may have, in order to solve in each situation the most appropriate LVRM inversion problem.

The proposed procedure is tested on two different product design applications, related to a particle engineering problem for the design of a wet granulated product of desired properties and to the selection of the best formulation for a given API, in order to obtain blends suitable for direct compression. In both cases the LVRM inversion is shown to be very effective in estimating the best inputs to obtain the desired product in output, giving a systematic tool to guide experiments since the first stages of development for the establishment of the system design space.

References

[1] Jaeckle, C. M. and J. F. MacGregor (1998). Product design through multivariate statistical analysis of process data. AIChE J., 44, 1105-1118.

[2] Jaeckle, C. M. and J. F. MacGregor (2000). Industrial applications of product design through the inversion of latent variable models. Chemom. Intell. Lab. Sys., 50, 199-210.

[3] García-Muñoz, S., T. Kourti, J. F. MacGregor, F. Apruzzese and M. Champagne (2006). Optimization of batch operating policies. Part I. Handling multiple solutions. Ind. Eng. Chem. Res., 45, 7856-7866.

[4] García-Muñoz, S., J. F. MacGregor, D. Neogi, B. E. Letshaw and S. Mehta (2008). Optimization of batch operating policies. Part II. Incorporating process constraints and industrial applications. Ind. Eng. Chem. Res., 47, 4202-4208.