|Eleanor Lin |
B.S., Aeronautics and Astronautics,
B.S., B.S., Mathematics
Massachusetts Institue of Technology, Class of 2008
M.S., Institute of Computation and Mathematical Engineering,
Stanford University, 2010
Email: eleanorl @ stanford . edu
Our lungs, with surface area roughly of a tennis court, are a vast entry port into our body. In every cubic meter of ambient air, there are about 35 million particles with diameter greater than 2.5 microns. These include smoke, dust, pollen, bacteria and viruses. One can also intentional breath in particles for drug delivery purposes. We would like to understand where these particles deposit, and how these particles depend on the particle size distribution as well as variabilities in lung geometry.
To do this, we have built a "virtual inhaler". We take MRI scans of lungs and construct an unstructured computational mesh. The lungs are a tree of bifurcating tubes, starting at the trachea and ending in the alveoli. We cut the geometry at some generation of the tree and create outlets. Then we compute the flow field on this mesh by solving the incompressible Navier-Stokes Equations. A velocity profile is specified at the inlet, non-stick boundary condition is applied at the walls, and pressure boundary condition is applied at the outlets. A time-dependent velocity profile can be applied at the inlet to simulate breathing.
Lagrangian particles are then introduced to the flow, and each of their positions are tracked as they are carried through the lungs by the flow field. Brownian motion is important for particles of this size, especially near the walls where the velocities are lower and diffusion dominates. The walls of the lungs are covered with a thick layer of mucus, and the depth and viscosity of the mucus makes it such that any particle which makes contact with it will be stuck. Therefore, we model the walls as perfect sinks.
Fig 1: These are plots of our simulation for a 5-generation human lung geometry. The plot on the left shows the pressure distribution, and the plot on the right shows the final deposition pattern.