Section: New Results

Lung and respiration modeling

Participants : Laurent Boudin, Muriel Boulakia, Céline Grandmont, Jessica Oakes, Ayman Moussa, Irène Vignon-Clementel.

• In [20] , we consider the non-reactive fully elastic Boltzmann equation for mixtures. We deduce that, under the standard diffusive scaling, its limit for vanishing Mach and Knudsen numbers is the Maxwell-Stefan model for a multicomponent gaseous mixture.

• In [49] , we first deal with the modelling and the discretization of an aerosol evolving in the air, in the respiration framework, within a domain which can be fixed or moving. We also investigate basic numerical properties of the numerical code which was developped, and also focus on the influence of the aerosol on the airflow.

• In [38] , the aim of the study was to determine susceptibility differences between healthy and emphysematous rats exposed to airborne particles. To do this, we performed animal exposure experimenters and measured particle deposition concentrations with Magnetic Resonance Imaging. We showed that overall deposition was significantly higher in the elastase-treated rats compared to the healthy ones, suggesting enhanced susceptibility to airborne particles in diseased lungs. Current work aims at integrating such experimental data into modeling [39] and compare numerical simulations with experiments. To extend particle modeling to expiration, a 1D particle transport model is under development [44] .

  While it is known that the retention of fine particles is less in microgravity (uG) compared to normal gravity (1G) levels, it was unknown the spatial relationship of deposited particles. In [26] , rats were exposed to 1 micron diameter particles on the NASA uG airplane and compared to rats exposed in 1G. We found that the ratio of deposited particles in the central airways compared to the peripheral ones, was significantly less in the uG than in 1G, indicating enhanced deposition in the periphery. This data suggests that toxicology effects of exposure to Moon dust may not be insignificant.

• In [51] , we establish stability estimates for the unique continuation property of the nonstationary Stokes problem. These estimates hold without prescribing boundary conditions and are of logarithmic type. They are obtained thanks to Carleman estimates for parabolic and elliptic equations. Then, these estimates are applied to an inverse problem where we want to identify a Robin coefficient defined on some part of the boundary from measurements available on another part of the boundary.