An asymptotic model for drug dissolution in a standardized flow-through apparatus

Asymptotic methods are employed to analyse, interpret and improve on an often-used model for the dissolution of drug particles in a standardized flow-through dissolution cell, United States Pharmacopeia Apparatus 4 (USP4). The model is based on a simplified description for the mass and momentum conservation for an individual spherical drug particle that is free to move and dissolves in a solvent that is pumped vertically upwards into a cylindrical cell. Mathematically, the model consists of a nonlinear ordinary differential equation for the particle radius which is intricately coupled to an integrodifferential equation containing the Basset integral history term for the particle velocity; both equations evolve over time. We nondimensionalize the equations and derive novel asymptotic solutions for the two cases normally of practical interest: when the pumping is uniform in time and when it is pulsatile. Subsequent comparison with numerical results is found to show excellent agreement; moreover, whereas the asymptotic solutions are obtained instantaneously, the numerical solutions require many hours of calculation, as a consequence of the cumulative computational burden of the history term. The suitability of the often-cited Ranz-Marshall correlation for the mass transfer associated with particle dissolution is also investigated. Lastly, the relevance of the model as regards experimental dissolution data obtained from a USP4 cell is discussed.