In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper choice of coupling conditions between models. We also propose a way to include in the 1D model the effect of the external tissue surrounding the vessel and we discuss its importance whenever this effect is considered in the 3D model. Finally, we propose several numerical results in real human carotids, studying different configurations for the 1D model and highlighting the best one in view of the physical consistency. (c) 2012 Elsevier Inc. All rights reserved.