Section: New Results

Lung and respiration modeling

Participants : Laurent Boudin, Muriel Boulakia, Céline Grandmont, Nicolas Pozin, Irene Vignon-Clementel.

In [46], we proved the existence of global weak solutions to the incompressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain with absorption boundary conditions for the kinetic part. This model arises from the study of respiratory aerosol in the human airways. The proof is based on a regularization and approximation strategy designed for our time-dependent framework.

In [52] we develop a lung-ventilation model. The parenchyma is described as an elastic homogenized media, irrigated by the tracheo-bronchial tree, a nonlinear resistive pipe network. Both are strongly coupled, and an efficient algorithm that takes advantage of the tree dyadic structure is proposed. This framework is used with different types of boundary conditions, including a nonlinear Robin model of the surrounding lung structures, to exhibit global and local coupling effects, for various ventilations. The model is also compared to a more classical exit-compartment (0D) approach.

In [34], we present a new framework that is designed to simulate ventilation and particle fate throughout the respiration cycle, both difficult to dynamically image. The flow and the particle transport and deposition models in the main bronchi are coupled to 1D models that account for the distal lobar lung structures. This enables modeling of inspiration as well as expiration. This leads to differentiated particle deposition over time, and between lobes and generations. Strong agreement to previously collected regional rat experimental data is shown, as the 1D models account for lobe-dependent morphology.