Mathematical modeling of surface-active and non-surface-active drug transport in emulsion systems

Mathematical models were developed for the prediction of surface-active and non- surface-active drug transport in triphasic (oil, water, and micellar) emulsion systems as a function of micellar concentration. These models were evaluated by comparing experimental and simulated data. Fick's first law of diffusion with association of the surface-active or complexation nature of the drug with the surfactant was used to derive a transport model for surface-active drugs. This transport model assumes that the oil/water (O/W) partitioning process was fast compared with membrane transport and therefore drug transport was limited by the membrane. Consecutive rate equations were used to model transport of non-surface-active drugs in emulsion systems assuming that the O/W interface acts as a barrier to drug transport. Phenobarbital (PB) and barbital (B) were selected as surface-active model drugs. Phenylazoaniline (PAA) and benzocaine (BZ) were selected as non- surface-active model drugs. Transport studies at pH 7.0 were conducted using side-by-side diffusion cells and bulk equilibrium reverse dialysis bag techniques. According to the surface-active drug model, an increase in micellar concentration is expected to decrease drug-transport rates. Using the Microsoft EXCEL program, the non-surface-active drug model was fitted to the experimental data for the cumulative amount of the model drug that disappeared from the donor chamber. The oil/continuous phase partitioning rates (k1) and the membrane transport rates (k2) were estimated. The predicted data were consistent with the experimental data for both the surface-active and non- surface-active models.