We present a computational model for the efficient simulation of vascularized tissues. A key aspect of such tissues is the interaction between the vessel and the surrounding material. The former expanding and contracting due to systemic circulation, and the latter reacting in the form of a counter-active (elastic) response. Our model is based on a geometrical multiscale 3D (elastic) -1D (fluid) coupled formulation, handling the effect of the vasculature on the elastic matrix with an immersed method. This allows us treat fluid inclusions at a lower dimensionality and thus to capture the interaction between the two phases of the material without requiring the discretization of the fluid-solid interface within the computational mesh. In order to study the effect of complex vessel networks, we explore the relationship between the coupled system and parameters that can be estimated at larger scale (macroscale). This goes in the direction of solving inverse problems in the context of tissue imaging. Available medical data usually have a limited resolution, typically at the scale of an effective - macro scale - tissue, and cannot resolve the microscale. We will present a brief mathematical background, as well as key aspects of the coupling and its applications.