Mathematical study of medicine diffusion from swelling chitosan film

Abstract

One of modern dosage forms is a medicine-saturated organic film: after putting this film onto a skin the medicine releases thus providing healing effect. Present article concerns films based on chitosan and containing amikacinum or cefazolinum. The most important characteristic of such film is rate of medicine release described by diffusion coefficient. To find it the film is placed in water and the average medicine concentration in the film is measured at different time moments. Two problems arise here. First, the film properties change because of its swelling. Second, diffusion is not the only process that takes place inside the film. To deal with these effects, authors suppose diffusion coefficient to be time-variable and complete the mathematical model with ODE describing detachment of medicine molecules from high-molecular matrix. All the equations in the model are solved analytically, so average medicine concentration in the film is known function of time. Thus, to solve stated inverse problem it is sufficient to find unknown scalar parameters of known functions using least-squares framework. Expressions arising in the solution are complicated so non-gradient methods are preferrable for optimization. Applying described procedure to experimental data leads to a good accuracy and the results may be explained from physicochemical point of view. In particular, the film swelling doesn’t influence release rate. In fact, the diffusion rate during first hours of experiment is large, and the main part of the medicine is released before swelling starts to play important role.