Mathematical and Experimental Analysis of Microbicide Vaginal Gels

Abstract

HIV is a growing concern worldwide. With slow progress in the development of a vaccine, researchers have turned to alternate methods of preventing the spreading of HIV as a result of unprotected sexual intercourse. Developing a mechanism capable of protecting the vaginal or rectal epithelium from sexually transmitted pathogens can be an effective tool in the prevention of HIV infection. One such tool can come in the form of a microbicide gel, which provides a physical barrier and acts as a delivery vehicle for its active ingredient. In order for the microbicide to be an effective barrier and delivery vehicle, it must have the capability to coat the epithelium for a specific amount of time and sustain its structural integrity under the influence of gravity and other perturbation forces. In addition, to be used as a drug delivery vehicle the microbicide must serve the following functions: coat the surface completely without leaving any of the surface exposed, stay on the surface while influenced by external forces such as gravity and squeezing, and be able to contain potent concentrations of one or more active microbicidal ingredients. Many currently available vaginal spermicidal gels are applied using a syringe-like applicator. After vaginal application, several physical forces will perturb the gel: gravity, squeezing, surface tension and shearing. In this document I will outline the work that has been completed, for an original PhD dissertation, on the mathematical and experimental analysis of microbicide vaginal gels. This document contains an in-depth discussion of the methods taken to satisfy the following engineering goals: 1. An instrument/method for conducting gravity-induced flow experiments and obtaining spreading characteristics along with surface topography. 2. A numerical solution for a non-linear, second-order, partial differential equation that governs the evolution of the free surface of a spreading fluid. 3. A derivation and numerical solution for the 3-D power-law evolution equation. 4. A derivation and numerical solution for the 3-D Ellis evolution equation. All experimental and computational simulations presented in this study involve a finite bolus of fluid, with non-Newtonian viscous properties, spreading on an inclined plane under the influence of gravity. Using the two numerical models presented in this document, I conducted an in-depth parameter and parameter sensitivity analysis of the power-law model, and a parameter study of the Ellis model. Combining the experimental data with computational simulations allowed me to make the following conclusions: 1. Accounting for lateral slumping in the computational simulation will improve the theory's agreement with experiment. 2. Approximating the initial condition to disregard complex curvatures on the free surface, and only consider gross geometric parameters, will not compromise theoretical model's agreement with experiment. 3. The 3-D power-law model provides a sufficient approximation of Hydroxyethylcellulose (HEC) spreading under the influence of gravity, for gels at 2.4-3.0% HEC concentration. Furthermore, implementing a constitutive equation that accounts for the low-shear Newtonian plateau (Ellis constitutive eq.) does not improve the models agreement with experiment enough to justify its added complexity. In conclusion, the following work provides an original experiment and a computational simulation of non-Newtonian fluid spreading. It is my hope that this work can be used by researchers in the field of microbicide development and any other scenario where free surface flow of non-Newtonian fluids is applicable.