In this paper we construct a model to describe some
aspects of the
deformation of the central region of the human lung
considered as a
continuous
elastically deformable medium. To achieve this purpose, we study
the interaction
between the pipes composing the tree and the fluid that goes
through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key feature of our approach is the use
of a fixed point
theorem in order to find the optimal flow associated
to a deformed tree. We also give some numerical results with
interesting consequences on
human lung deformation during expiration, particularly
concerning the localization of the equal pressure point (EPP).