Modeling the Tablet Disintegration Process Using the Finite Difference Method

The purpose of the study is to present the finite difference method (FDM) and demonstrate its utility in modeling mass transport processes that are pharmaceutically relevant. In particular, diffusion processes are ideally suited for FDM because the governing equation, Fick's second law of diffusion, can be readily solved using FDM over a finite space and time. The method entails the mesh creation, space and time discretization, and solving Fick's second law at each node using finite difference-based numerical schemes. We applied FDM to study tablet disintegration, in which the tablet water uptake was simulated with an effective water diffusion coefficient; the tablet disintegration was controlled by a designated critical water content parameter, beyond which the node is treated as being disintegrated from the tablet. The resulting simulation agreed with the experimental tablet disintegration behaviors, under both disintegration-controlled and water uptake-controlled conditions. This study highlighted the unique advantage of FDM, capable of providing spatial-temporal information on water uptake and evolution of tablet size and shape during tablet disintegration, which was otherwise not available using other methods. The FDM method enabled more in-depth tablet disintegration studies. The model also has the potential to be calibrated and incorporated in tablet formulation DoE studies.