This paper is focused on pharmaceutical emulsions where hydrophobic drugs are encapsulated in the oil phase of an oil-in-water emulsion and delivered to patients via oral administration, parenteral delivery, ophthalmic medicine, and topical and transdermal creams. Important criteria for the formulation of pharmaceutical emulsions include biocompatibility, biodegradability and targeting of specific organs and tissues to improve drug effectiveness and reduce undesirable side effects. Consequently, the drug properties, emulsion characteristics, and administration route must be matched carefully for each application.

Pharmaceutical emulsions are manufactured by subjecting a coarse emulsion containing the hydrophobic drug to high pressure homogenization where the dispersion is forced through a small orifice under very high pressure. The homogenization process produces a distribution of emulsion drop sizes that depends on the chemical formulation, the initial coarse distribution, and the homogenizer operating conditions. The final properties of a pharmaceutical emulsion are a complex and often unknown function of many different variables. Clinical studies have shown that the drop size distribution has a significant impact on emulsion properties and the ultimate effectiveness of the drug delivery system. For example, the biodistribution of the encapsulated drug is strongly affected by drop size through complex physiological processes. In addition to exhibiting long-term stability and producing the desired drug-release kinetics, the emulsion should be essentially monodisperse with a desired drop size to target specific tissues and organs.

The population balance equation (PBE) modeling framework has been used to describe the evolution of the particle size distribution in a wide range of dispersed phase systems, including emulsions produced with high pressure homogenization. Successful application of the PBE modeling approach requires knowledge of functions for particle formation, aggregation, and breakup. Because functions that accurately predict experimental data are difficult to develop from fundamental principles, several inverse PBE techniques for extracting these functions from particle distribution data have been developed. We have previously applied these methods to a simulated batch emulsification vessel to examine the effect of transient drop size distribution measurement errors on the quality of the function approximation results (Raikar et al., 2006).

In this paper, we describe a nonlinear parameter estimation technique to determine the drop breakage functions for pharmaceutical emulsion prepared with high pressure homogenization under conditions that lead to negligible drop coalescence. A mechanistic function for the drop breakage rate is used to account for the effects of homogenization pressure, surface tension, and dispersed phase volume fraction, density, and viscosity. A standard empirical function is used to describe the distribution of daughter drops resulting from the binary breakage process. Drop size distribution measurements obtained after each pass of the homogenizer are used to estimate the unknown parameters of the breakage rate using nonlinear optimization based on a temporally discretized version of the PBE model. The impact of measurement errors on the reconstructed breakage functions is evaluated via simulation. Homogenization experiments with drop size distribution measurements obtained from dynamic light scattering are used to evaluate the estimation procedure. Extensibility of the identified PBE models to new emulsion formulations and homogenizer operating conditions is evaluated using both simulation and experiment.

References

N. Raikar, S. R. Bhatia, M. F. Malone and M. A. Henson, “Sensitivity Analysis of Inverse Population Balance Modeling for Turbulently Prepared Batch Emulsions,” Chemical Engineering Science, submitted (2006).