A two-stage mechanistic reduced-order model of pharmaceutical tablet dissolution: Population balance modeling and tablet wetting functions

Abstract

We propose a two-stage reduced-order model (ROM) of pharmaceutical tablet dissolution that is comprised of (i) a mechanistic dissolution function of the active pharmaceutical ingredient (API) and (ii) a tablet wetting function. The former is derived from a population balance model, using a high-resolution finite volume algorithm for a given API crystal size distribution and dissolution rate coefficient. The latter is obtained from the mechanistic understanding of water penetration inside a porous tablet, and it estimates the rate at which the API is exposed to the buffer solution for a given formulation and the dimensions of the tablet, contact angle, and surface tension between the solid and liquid phases, liquid viscosity, and mean effective capillary radius of the pore solid structure. In turn, the two-stage model is mechanistic in nature and one-way coupled by means of convolution in time to capture the start time of the API dissolution process as water uptake, swelling, and disintegration take place. The two-stage model correlates dissolution profiles with critical process parameters (CPPs), critical material attributes (CMAs), and other crucial critical quality attributes (CQAs). We demonstrate the model’s versatility and effectiveness in predicting the dissolution profiles of diverse pharmaceutical formulations. Specifically, we formulate and fabricate acetaminophen and lomustine solid tablets using different API content and size distributions, characterize their dissolution behavior, and estimate capillary radius as a function of tablet porosity. The estimations generated by the proposed models consistently match the experimental data across all cases investigated in this study.