Mathematically modelling the stability of solid dispersions in storage

Many drugs currently on the market or in development are poorly water-soluble. This presents a serious challenge to the pharmaceutical industry because orally delivered drugs that are poorly soluble tend to pass through the gastrointestinal tract before they can fully dissolve, leading to poor drug bioavailability. One strategy to improve drug solubility is to use a solid dispersion. A solid dispersion typically consists of a hydrophobic drug embedded in a hydrophilic polymer matrix. When the dispersion dissolves in the stomach, drug-polymer interactions maintain the drug at supersaturated levels, thereby accelerating drug dissolution. Unfortunately, despite extensive research, the dissolution behaviour of solid dispersions is only partially understood. This makes the design of successful solid dispersions a somewhat hit and miss affair. Clearly, the construction of reliable mathematical models that capture the key interactions between the drug, polymer and solvent molecules in a dissolving solid dispersion would greatly assist with their rational design. In this presentation, we develop mathematical models describing the storage and dissolution of solid dispersions. The models consist of coupled systems of nonlinear partial differential equations. We then analyze in detail a particular problem describing a solid dispersion in storage. The drug-polymer interaction in the dispersion is modelled using Flory-Huggins theory , and we use the model to identify regimes in the model parameter space that lead to stable, metastable and unstable storage behaviour (phase separation).We illustrate the various phenomena arising using numerical simulations.