Modeling Controlled Release Drug Delivery through Core-Shell Microparticles Using Finite Differences for Spatially Dependent Diffusivity

Eye illnesses affect millions of people each year. In order to reduce the number of injections and increase the efficiency of the treatment of eye illnesses, it is important to determine the appropriate and correct dosage of drugs. The focus of our research involves studying controlled release drug delivery from core-shell microparticles with two layers of drug releasing materials. We use data from our collaborators who conduct the experiments and have determined the material properties of the materials and the drugs and conducted the drug release studies. For predicting drug release from the core-shell microparticles, we consider diffusion (the dominant transport mode in the biomaterials of interest for eye applications) through a symmetric sphere with variable diffusion coefficients (each of the materials has a distinct uniform diffusion coefficient for that layer of the core-shell concentric spheres). We use the method of lines where the spatial derivatives in the partial differential equation for drug diffusion from the sphere are approximated with finite difference formulas that account for variable diffusivity, yielding a spatially discretized systems of ordinary differential equations (ODEs) in time that are solved using one of MATLAB’s built-in ODE solvers. We numerically integrate the solution concentration profiles to predict the cumulative release profiles. We used parameter estimation (nonlinear least squares optimization) to determine the diffusion coefficients of specific drugs in the materials of interests and the corresponding burst release amount from experimental data of cumulative release from microspheres composed of only one material. With these properties, we are able to determine the cumulative release of drug in a predictable and repeatable manner from microparticles with different layer configurations consisting of chitosan and polycaprolactone for BSA and bevacizumab release.