Mathematical modelling of drug delivery from pH-responsive nanocontainers.

Drug delivery systems represent a promising strategy to treat cancer and to overcome the side effects of chemotherapy. In particular, polymeric nanocontainers have attracted major interest because of their structural and morphological advantages and the variety of polymers that can be used, allowing the synthesis of materials capable of responding to the biochemical alterations of the tumour microenvironment. While experimental methodologies can provide much insight, the generation of experimental data across a wide parameter space is usually prohibitively time consuming and/or expensive. To better understand the influence of varying design parameters on the drug release profile and drug kinetics involved, appropriately-designed mathematical models are of great benefit. Here, we developed a novel mathematical model to describe drug transport within, and release from, a hollow nanocontainer consisting of a core and a pH-responsive polymeric shell. The two-layer mathematical model fully accounts for drug dissolution, diffusion and interaction with polymer. We generated experimental drug release profiles using daunorubicin and [Cu(TPMA)(Phenantroline)](ClO_4)_2 as model drugs, for which the nanocontainers exhibited excellent encapsulation ability. The in vitro drug release behaviour was studied under different conditions, where the system proved capable of responding to the selected pH stimuli by releasing a larger amount of drug in an acidic than in the physiological environments. By comparing the results of the mathematical model with our experimental data, we were able to identify the model parameter values that best-fit the data and demonstrate that the model is capable of describing the phenomena at hand. The proposed methodology can be used to describe and predict the release profiles for a variety of drug delivery systems.