Abstract: In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the whole blood circulation. We propose a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of poroelastic equations is coupled with a systemic 0D lumped model of the remainder of the circulation. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the rest of the circulatory system. We discuss well-posedness analysis for this multiscale model, as well as solution methods focused on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the interface conditions.