Population Balance Model for Simulation of the Supersaturation–Precipitation Behavior of Drugs in Supersaturable Solid Forms

Abstract

We developed a simulation method to describe in vitro drug concentration−time profiles under supersaturated conditions. In a nonsink dissolution test of carbamazepine polymorphic form III (CBZIII), a model supersaturable solid, the concentration of carbamazepine reached a supersaturated state against its dihydrate form (CBZDH). After a certain period, de-supersaturation due to the precipitation of CBZDH was observed. In the simulation of this typical dissolution−precipitation profile, the precipitation process of CBZDH was simulated by a population balance model in which the rates of primary/secondary nucleation and growth of CBZDH were considered. Six rate constants in the precipitation model were determined from de-supersaturation profiles in unseeded isothermal crystallization experiments of CBZDH. The dissolution process of CBZIII was modeled on the basis of its dissolution profile under a sink condition. The simulated concentration versus time curves satisfactorily reproduced the characteristics of dissolution, supersaturation, and precipitation behavior of the model drug. The presented method will enable rational design of formulations and accurate prediction of the oral absorbability of drugs in supersaturable solid forms.