The purpose of the present article is to provide a theoretical analysis heterogeneous model coupling ordinary differential equations (ODEs) and partial differential equations (PDEs), providing a local-in-time existence result for the solution. The heterogeneous problem will actually be split into subproblems. The solution of the original problem will be regarded as the solution of a suitable fixed point problem, based on the successive solution of the subproblems. Moreover, the authors study the role of matching conditions between the two submodels for the numerical simulation.