Comparison of Polymeric Drug Delivery Models

Abstract

Although there have been significant advances in the fields of theoretical condensed matter and computational physics, when confronted with the complexity and diversity of nanoparticles available in conventional laboratories a number of modeling challenges remain. These challenges are generally shared among application domains, but the impacts of the limitations and approximations we make to overcome them (or circumvent them) can be more significant one area than another. In the case of nanoparticles for drug delivery applications some immediate challenges include the incompatibility of length-scales, our ability to model weak interactions and solvation, the complexity of the thermochemical environment surrounding the nanoparticles, and the role of polydispersivity in determining properties and performance. Some of these challenges can be met with existing technologies, others with emerging technologies including the data-driven sciences; some others require new methods to be developed. In this thesis we will briefly review some simple methods and techniques that can be applied to these (and other) challenges, and demonstrate some results using nanoparticle polymeric based drug delivery platforms as an exemplar. A mathematical model is developed for the simultaneous treatment of polymeric nanoparticles and drug release with autocatalytic effects and nonconstant effective diffusivity of the drug. A mechanistic reaction-diffusion model with pore evolution coupled to hydrolysis and related to the effective diffusivity through hindered diffusion theory is proposed. Experimental background motivating the attention to the size-dependent effects of autocatalysis on drug release and a brief review of related mathematical models are presented. The model equations are derived, solved numerically with a computational [MATLAB] code developed for this work and described in detail, and compared to the analytical solutions to the model in limiting cases. The model performance for the case of drug release from microspheres of different sizes is presented to highlight the capability of the model for predicting size-dependent, autocatalytic effects on the polymer and the release of drug. Lastly, we examined which release model of the nanoparticles gave the best fit to the experimental results. The released profile was fitted to several release models (the Higuchi, zero-order, Hixson Crowell, first order, and KorsmeyerPeppas) and the best fit determined based on coefficient of determination (ð€œ´ð€¬¶) value.