Forced expiration maneuver is the gold standard in Pulmonary Function Test (PFT). During this maneuver, the patient has first to breath at rest, perform a deep inspiration at Total Lung Capacity (TLC), then exhale all the air contained in his lung as fast as possible. The flow rate and the lung volume are recorded in time, and the curve plotting flow rate vs. the volume is called "Flow-volume loop at forced expiration". Using the spirometry performed during such a forced maneuver, one can for instance measure the Forced Expiration Volume after 1 second (FEV1). The reduction of this volume with respect to the Force Vital Capacity (FVC) - hence the reduction of the ratio FEV1/FVC - constitutes the clinical criterion of an obstruction of the intrathoracic airways. Despite being robust and clinically relevant, this definition of airway obstruction through a single scalar value is too crude. Full and detailed study of the entire flow-volume loop enables a finer analysis of the lung mechanics. Airway obstruction can be directly assessed, qualitatively and quantitatively in these curves. Performing such an analysis would allow the physician to achieve a first and rapid diagnosis of the lung airway system.

However, even if flow-volume loops contain inherently more information than the simple FEV1/FVC data, these "black box" analyses are a strong schematization of the lung complexity, as they aggregate into one curve a very large number of local mechanical and physiological characteristics of the lung. The studies carried out in our group have led to the elaboration of the first mathematical and numerical model able to simulate the forced expiration maneuver in the entire tracheobronchial tree (PhD thesis of Magali Florens). This model simulates the time dependent air flow in the lung described as a network of compliant airways (through "tube laws"). It gives access the whole map of fluxes in any point of the bronchial tree. These studies have been funded through the ANR project ANR ANR10-BLAN-1119 ("SAMOVAR"), in collaboration with ER10 of University UPMC (Pitié-Salpêtrière) and team 13 of IMRB (Henri Mondor), also member of DHU A-TVB.

**A few significant publications::**

- B. Mauroy, M. Filoche, J.S. Andrade Jr., B. Sapoval, “Interplay between geometry and flow distribution in an airway tree”, Phys. Rev. Lett. 90, 14 (2003).
- M. Florens, B. Sapoval, M. Filoche, “The optimal branching asymmetry of a bidirectional distribution tree”, Comput. Phys. Commun. 182:1932-1936 (2011).
- M. Filoche and M. Florens, “The stationary flow in a heterogeneous compliant vessel network”, J. Phys.: Conf. Ser. 319:012008 (2011).
- C.-F. Tai, S. Bian, D. Halpern, Y. Zheng, M. Filoche, J.B. Grotberg, “Numerical study of flow fields in an airway closure model”, J. Fluid Mech. 677:483–502 (2011).