We propose a fully coupled model for the description of fluid dynamics of blood, plasma filtration, and mass transport by a coronary drug eluting stent. We deduce an analytical solution for a reduced model for drug dissolution and establish suitable boundary conditions accounting for the smaller scale of the coating of the stent with respect to the release medium. This approach allows for a reduction of the computational cost of the simulations on realistic three-dimensional stent geometries. Numerical experiments to show the effectiveness of the method applied to the approximation of the multiscale model are also presented.