Mathematical solution for controlled drug release from a swelling hydrogel to the small intestine

Study on drug release from a moving boundary device has been quite popular among the researchers these days. Some research has been done pertaining to drug release in the small intestine. In this paper, we would like to develop a mathematical model for controlled drug release from a swelling hydrogel in the small intestine. For this project, we are considering drug release from a swelling hydrogel and a parameter of drug absorption in the small intestine. We start by solving the analytical solution for drug release from a swelling hydrogel. We derive the advection-diffusion equation to describe the drug transport. Landau transformation is applied onto the model to remove the convective term and the model is solved using the separation of variables method. We obtained a model of mass of drug release from a swelling hydrogel and the model is combined into a one-compartmental model of mass of drug in the small intestine. The model of mass of drugs in the small intestine is solved numerically using the forward finite difference method. The graph to simulate mass of drugs in the small intestine is presented in this paper.