Mathematical models are recommended by the ICH Q8(2) guidelines on pharmaceutical development to generate enhanced process understanding and meet Quality-by-Design (QbD) guidelines. Mathematical models can be built using two fundamentally different paradigms: statistics or mechanistically (Table 1). We will discuss the differences between statistical and mechanistic models, and their use in improving your process development.
Understanding statistical models
Statistical approaches like big data, machine learning, and artificial intelligence use statistics to predict trends and patterns. All of these models learn from experience provided in the form of data. The more the experience, the better the model will be.
Typically, a lot of data is generated within a given parameter space. The model equations are derived by developing a probabilistic model that best describes the relationship between the dependent and independent variables. This model is then based on correlations in the data.
Statistical models are, however, bound to their calibration range and can only predict results within the data space they are calibrated from. In particular, they do not allow any major change in the process set-up. Since they are based on correlation and not causality, statistical models provide limited mechanistic process understanding.
How are mechanistic models set up?
Mechanistic models are based on the fundamental laws of natural sciences, including physical and biochemical principles. Less experimental data is needed to calibrate the model and determine unknown model parameters, such as adsorption coefficients, diffusivity, or material properties. An essential benefit of mechanistic versus statistical models is that the model parameters have an actual physical meaning, which facilitates the scientific interpretation of the results.
Since mechanistic models are based on natural laws they are valid far beyond the calibration space. In practice, this means that you can easily change process setup and parameters. Such as switching from a step elution to a gradient or vice versa, changing from batch to continuous processing, changing column dimensions, and much more. As they are based on natural principles, mechanistic models allow you to generate mechanistic process understanding and thus fufill QbD obligations, which is not the case with statistical models.
This opens a wide range of applications using the same mechanistic model without any further experimentation, including early-stage process development, process characterization and validation, and process monitoring and control. Even completely different scenarios can be simulated with no additional experimental effort, such as overloaded conditions, flow-through operations, or continuous chromatography. The model will evolve with the proceeding development lifecycle and account for holistic knowledge management, enabling a fast and lower cost replacement of lab experiments with computer simulation.