A Modeling of Biospray for the Upper Airways

Abstract

We here deal with a model of therapeutic sprays for the upper airways. We aim to model both inhaled and injected sprays. We propose a numerical solver for the kinetic equation which underlies our model, using a particle method. Eventually, we present two numerical tests for simple geometries of the airways. Résumé. Nous proposons dans ce travail une modélisation du comportement d'un brouillard de gouttelettesà but thérapeutique dans les voies respiratoires supérieures. Notre objectif est de mettre en place un modle pouvant représenterà la fois des sprays inhalés et des sprays injectés. Ce modèle est porté par uneéquation cinétique, pour laquelle nous présentons une résolution numérique par méthode particulaire. Enfin, nous donnons deux cas-tests pour des conduits respiratoiresà géométrie simple.

Two-species flocking particles immersed in a fluid

“…The collective behavior of the interaction particle systems such as flocking, aggregation, and synchronization has received a bulk of attention from various research fields arising in physics, biology, robotics, control theory and other disciplines [1,5,10,14,15,16,24,27,28,30]. The interaction between the flocking particles and fluids is first studied in [2].…”

Influence of the spray retroaction on the airflow

“…In the next section, we briefly describe our aerosol-air model originally presented in [4,6]. Then, in Sections 3 and 4, we study the influence of the aerosol on the air, in the case when the aerosol and air velocities do not have the same order of magnitude, i.e.…”

“…As in [3,4,6,11,12,16,19,20], we assume that the airways have a tree structure, that the airflow obeys the incompressible Navier-Stokes equations down to the sixteenth generation of the respiratory tract, and that the spray is described by a Vlasov equation. The action of the spray appears as a source term in the Navier-Stokes equations.…”

Large-time behavior for the Vlasov/compressible Navier-Stokes equations

“…In the last years, the interactions between particles and fluid have received a great deal of attentions due to a number of their applications such as biotechnology, medicine, aerosols, and sprays [4,8,28]. We refer to [24,26] for more physical backgrounds of the spray model.…”