Mathematical Model of Gentamicin Sulfate Release from a Bioactive Textile Material as a Transdermal System Under In Vitro Conditions

Abstract

A mathematical model was developed to estimate the release of gentamicin sulfate from a bioactive textile material as a transdermal system for wound dressing. The gentamicin sulfate released from the antibiotic/chitosan hydrogel complexes was measured in vitro by the Franz diffusion cell technique. The diffusive transport of gentamicin sulfate through three connected compartments, that is, chitosan hydrogel, membrane, and solution, was considered by the formulation of a model based on Fick's second law. Initially, the total amount of gentamicin sulfate was placed within an already swollen chitosan hydrogel. The value of the diffusivity coefficient of the drug through the chitosan hydrogel was calculated for every initial amount of the active substance. For the initial concentration of gentamicin sulfate, which was lower than 2.81 x 10(4) mu g/mL, the diffusion coefficient was approximately constant. A higher amount of gentamicin sulfate in the hydrogel reduced its own transport as a consequence of an increase in the intensity of the interaction field between the molecules of gentamicin sulfate. The model provides the possibility of optimizing the process of drug release by ensuring a compromise between a higher value of the diffusivity coefficient and a desirable amount of gentamicin sulfate and a constant concentration within the solution over 48 h.