International audienceIn this article we develop a lung-ventilation model. The parenchyma is described as an elastic homogenized media. It is irrigated by a space-filling dyadic resistive pipe network, which represents the tracheo-bronchial tree. In this model the tree and the parenchyma are strongly coupled. The tree induces an extra viscous term in the system constitutive relation, which leads, in the finite element framework, to a full matrix. We consider an efficient algorithm that takes advantage of the tree dyadic structure to enable a fast matrix-vector product computation. This framework can be used to model both free and mechanically induced respiration, in health and disease. Patient-specific lung geometries acquired from CT scans are considered. Realistic Dirichlet boundary conditions can be deduced from surface registration on CT images. The model is compared to a more classical exit-compartment approach. Results illustrate the coupling between the tree and the parenchyma, at global and regional levels, and how conditions for the purely 0D model can be inferred. Different types of boundary conditions are tested, including a nonlinear Robin model of the surrounding lung structures
