Mathematical modeling and parametrical analysis of the temperature dependency of control drug release from biodegradable nanoparticles

In this study we describe a mathematical analysis that considers the temperature effects of the controlled drug release process from biodegradable poly-d,l-lactide-co-glycolide (PLGA) nanoparticles. Temperature effects are incorporated and applied to two drug release models. The first one consists of a two-stage release process that considers only simultaneous contributions of initial burst and nanoparticle degradation–relaxation (BR model). The second one is a three release stage model that considers, additionally, a simultaneous drug diffusion (BRD model) step. In these models, the temperature dependency of the release parameters, initial burst constant, k(b), the rate of degradation–relaxation constant, k(r), time to achieve 50% of release, t(max), and effective diffusion coefficient constant (D(e)), are determined using mathematical expressions analogous to the Arrhenius equation. The temperature dependent models are used to analyze the release of previously encapsulated Rhodamine 6G dye as a model drug in polyethylene glycol modified PLGA nanoparticles. The experimental data used to develop the mathematical model was obtained from release studies carried out in phosphate buffer pH 7.4 at 37 °C, 47 °C, and 57 °C. Multiphasic release behaviors with an overall increase rate associated with the incubation temperature were observed. The study incorporates a parametrical analysis that can evaluate diverse temperature variation effects of the controlled release parameters for the two models.