Modeling Drug Dissolution in 3-Dimensional Space.

Abstract

The purpose of the study is to present a mathematical model capable of describing drug particle dissolution in 3-dimensional (3D) space, and to provide experimental model verification. Through this study, we also aim to elaborate limitations of the classic, 1D-based Nernst-Brunner formalism in dissolution modeling. The 3D dissolution model was derived by treating the dissolution of a spherical particle as a diffusion-driven process, and by solving Fick's 2nd law of diffusion in spherical coordinates using numerical methods. The resulting model was experimentally verified through analyzing the dissolution behavior of single succinic acid particles in un-stirred water droplet under polarized light microscopy, in combination with image segmentation techniques. A set of working equations was developed to describe drug particle dissolution in 3D space. The predicted dissolution time and profile are in good agreement with the experimental results. The model clearly shows that the concentration gradient within the diffusion layer, in realistic 3D condition, must not be a constant value as implicated in the Nernst-Brunner formalism. The actual concentration profile is a hyperbola, and the concentration gradient at the surface of the particle can be significantly higher than the classic 1D-based dissolution model. The study demonstrates that the classic, 1D-based dissolution models may lead to significant under-estimation of drug dissolution rates. In contrast, modeling dissolution in 3D space yields more reliable results. This study merits further development of comprehensive 3D drug dissolution models, by considering polydispersed particle ensemble and imposing the changes of diffusion layer thickness during dissolution.