Mathematical models: mechanistic vs. statistical
Given the recent Quality-by-Design guidelines by international regulatory agencies as released in ICH(R2) Q8, mathematical models are recommended to generate an enhanced process understanding. Mathematical models can be built using two fundamentally different paradigms: with statistics or mechanistically.
Statistical approaches like big data, machine learning and artificial intelligence utilize 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. To enable better interpretability using heat maps, the parameter space is often restricted to 2D. 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 are actually a black box and do not provide any mechanistic process understanding.
Mechanistic models are based on the fundamental laws of natural sciences. Physical and biochemical principles constitute the model equations. Few 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 vs. statistical models is that the model parameters have an actual physical meaning, which facilitates the scientific interpretation of the results.
Since natural laws are generally valid, mechanistic models are as well – even far beyond the calibration space. In practice, this means that you can easily change process parameters and the actual set-up: Switching from a step elution to a gradient or vice versa; changing from batch to continuous processing; changing column dimensions; and much more. This opens a wide range of model applications using one and the same mechanistic model: From early-stage process development, process characterization and validation to process monitoring and control. The model will thereby evolve with the proceeding development lifecycle and account for holistic knowledge management.
As they are based on natural principles, mechanistic models allow you to generate mechanistic process understanding and thus fulfil Quality-by-Design obligations – which is also not the case with statistical models.
Both mechanistic and statistical models have their pros and cons. Mechanistic models are ideal to build digital twins of downstream chromatography processes. Why? Watch our video on digital downstream process twins, to see what impact the difference between statistical and mechanistic models have on building a digital twin.