The pore geometry of pharmaceutical coatings: statistical modelling, characterization methods and transport prediction
This thesis contains new methods for bridging the gap between the pore geometry of porous materials and experimentally measured functional properties. The focus has been on diffusive transport in pharmaceutical coatings used in controlled drug delivery systems, but the methods are general and can be applied to other porous materials and functional properties. Relatively large datasets are needed to train realistic models connecting the pore geometry and diffusive transport properties of porous materials. 3-D statistical pore models based on microscopy images of the coating material were in this thesis used to generate large sets of pore structures, in which diffusive transport was computed numerically. Characterization measures capturing important features of the pore geometry were developed and used as predictors of diffusive transport rates in multiplicative regression models. The characterization measures have been implemented in a freely available software, MIST.
In Paper I, a Gaussian random field based pore model was developed and fitted to microscopy images of the coating material. Due to the large size of the data, the model was formulated using a Gaussian Markov random field approximation, which allows for efficient inference. A new method for solving linear equations with Kronecker matrices which reduced the complexity of the model fitting algorithm considerably was developed. The pore model was found to fit the microscopy images well. In Paper II, characterization measures that have been shown to provide good regression models for diffusive transport rates were developed further and implemented. Multiplicative regression models were fitted to pore structures from the model from Paper I, and the new methods were shown to give improved results. In Papers III and V characterization measures that capture a type of bottleneck effect which was observed in another set of microscopy images of the coating material (Papers III and IV), but which is not captured by existing methods, were invented. Pore structures with this type of bottleneck were generated using 3-D statistical pore models, and the new type of bottleneck was found to be an important determinant of diffusive transport rates when the regression models were fitted to simple pore structures (Paper V).