Mathematical modelling of drug transport in emulsion systems.

Two mathematical models for the prediction of drug transport in triphasic (oil, water and micellar) emulsion systems as a function of micellar concentration have been developed and these models were evaluated by comparing experimental and simulated data. Fick's first law was used to derive a transport model for hydrophilic drugs, assuming 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 hydrophobic drugs in emulsion systems assuming that the o/w interface acts as a barrier to drug transport. Benzoic acid and phenol were selected as hydrophilic model drugs. Phenylazoaniline and benzocaine were selected as hydrophobic model drugs. Transport studies at pH 3.0 and 7.0 were conducted using side-by-side diffusion cells. According to the hydrophilic model, an increase in micellar concentration is expected to decrease drug transport rates. The effective permeability coefficients (Peff) of drugs were calculated using an equation relating Peff and the total apparent volume of drug distribution (determined experimentally using drug/membrane permeability and partition coefficient values). The hydrophobic model was fitted to the experimental data for the cumulative amount of model drug in the receiver cells using a weighted least-squares estimation program (PCNONLIN). The oil/continuous phase partitioning rates (k1) and the membrane transport rates (k2) were estimated. The goodness of fit was assessed from the correlation coefficients of plots of predicted versus experimental data. The predicted data were consistent with the experimental data for both the hydrophilic and hydrophobic models.