Abstract
A thresholded Gaussian random field model is developed for the microstructure of porous materials. Defining the random field as a solution to stochastic partial differential equation allows for flexible modelling of nonstationarities in the material and facilitates computationally efficient methods for simulation and model fitting. A Markov Chain Monte Carlo algorithm is developed and used to fit the model to three-dimensional confocal laser scanning microscopy images. The methods are applied to study a porous ethylcellulose/hydroxypropylcellulose polymer blend that is used as a coating to control drug release from pharmaceutical tablets. The aim is to investigate how mass transport through the material depends on the microstructure. We derive a number of goodness-of-fit measures based on numerically calculated diffusion through the material. These are used in combination with measures that characterize the geometry of the pore structure to assess model fit. The model is found to fit stationary parts of the material well. Lay description We develop a stochastic model for the pore structure of a polymer material which is used as coatings to control drug release from pharmaceutical tablets. The pore geometries of the coatings determine how quickly the drug is released. For instance, the drug transport through a coating with many bottlenecks will be slower compared to the transport through a coating with a lower number of bottlenecks. The model will in future work be used to analyze how the rate of transport of the drug through the coating depends on the distribution of bottlenecks and other characteristics of the pore geometry. In this article we present the model. Each stochastic simulation from the model gives a different pore structure, but with similar pore geometries. This randomness in the model captures that each coating is different. We develop an efficient mathematical algorithm to fit the model to microscopy images of the material. The algorithm uses the information in the microscopy images to find the parameters of the model that make the pore geometry of the microscopy images as similar as possible to the pore geometries of stochastic simulations from the model. To determine how similar the geometries are we use measures that summarize different properties of the pore geometries. We also derive a new measure which compares the results of numerically calculated transport through the pore structures. These measures show that the stochastic simulations from the model are similar to the microscopy images, and we conclude that the model fits the data well.