Predicting Pharmaceutical Particle Size Distributions Using Kernel Mean Embedding

In the pharmaceutical industry, the transition to continuous manufacturing of solid dosage forms is adopted by more and more companies. For these continuous processes, high-quality process models are needed. In pharmaceutical wet granulation, a unit operation in the ConsiGma TM -25 continuous powder-to-tablet system (GEA Pharma systems, Collette, Wommelgem, Belgium), the product under study presents itself as a collection of particles that differ in shape and size. The measurement of this collection results in a particle size distribution. However, the theoretical basis to describe the physical phenomena leading to changes in this particle size distribution is lacking. It is essential to understand how the particle size distribution changes as a function of the unit operation's process settings, as it has a profound effect on the behavior of the fluid bed dryer. Therefore, we suggest a data-driven modeling framework that links the machine settings of the wet granulation unit operation and the output distribution of granules. We do this without making any assumptions on the nature of the distributions under study. A simulation of the granule size distribution could act as a soft sensor when in-line measurements are challenging to perform. The method of this work is a two-step procedure: first, the measured distributions are transformed into a high-dimensional feature space, where the relation between the machine settings and the distributions can be learnt. Second, the inverse transformation is performed, allowing an interpretation of the results in the original measurement space. Further, a comparison is made with previous work, which employs a more mechanistic framework for describing the granules. A reliable prediction of the granule size is vital in the assurance of quality in the production line, and is needed in the assessment of upstream (feeding) and downstream (drying, milling, and tableting) issues. Now that a validated data-driven framework for predicting pharmaceutical particle size distributions is available, it can be applied in settings such as model-based experimental design and, due to its fast computation, there is potential in real-time model predictive control.