Estimation of design space for an extrusion–spheronization process using response surface methodology and artificial neural network modelling

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The application of the Quality by Design principles is one of the key issues of the recent pharmaceutical developments. In the past decade a lot of knowledge was collected about the practical realization of the concept, but there are still a lot of unanswered questions.

The key requirement of the concept is the mathematical description of the effect of the critical factors and their interactions on the critical quality attributes (CQAs) of the product. The process design space (PDS) is usually determined by the use of design of experiment (DoE) based response surface methodologies (RSM), but inaccuracies in the applied polynomial models often resulted in the over/underestimation of the real trends and changes making the calculations uncertain, especially in the edge regions of the PDS. The completion of RSM with artificial neural network (ANN) based models is therefore a commonly used method to reduce the uncertainties. Nevertheless, since the different researches are focusing on the use of a given DoE, there is lack of comparative studies on different experimental layouts. Therefore, the aim of present study was to investigate the effect of the different DoE layouts (2 level full factorial, Central Composite, Box–Behnken, 3 level fractional and 3 level full factorial design) on the model predictability and to compare model sensitivities according to the organization of the experimental data set.

It was revealed that the size of the design space could differ more than 40% calculated with different polynomial models, which was associated with a considerable shift in its position when higher level layouts were applied. The shift was more considerable when the calculation was based on RSM. The model predictability was also better with ANN based models. Nevertheless, both modelling methods exhibit considerable sensitivity to the organization of the experimental data set, and the use of design layouts is recommended, where the extreme values factors are more represented.

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