Relationship between cilia-induced and airflow-induced mucus clearance Sorin Mitran Applied Mathematics UNC Virtual Lung Project August 19, 2008

The Lung – Airway anatomy

The Lung - Bronchi physiology Tidal breathing ~4 s period 1 – 10 mm diameter Volume rate 200 ml/s Airflow speed m/s 10 < Reynolds < 1000 Cough 30 m/s average airflow speed m/s local maximum 4 x 10 3 < Reynolds < 4 x 10 4

PCL Newtonian (?) 7 micron layer Flow speed m/s Reynolds < Mucus Viscoelastic Continuum relaxation spectrum 1 < Weissenberg < 10 Reynolds < The Lung - Airway surface liquid

The Lung – Mucociliary transport

Methods – Physical models Fluids – structure interaction model Fluids o Air – compressible Navier-Stokes o Airway Surface Liquid o PCL – incompressible Navier-Stokes o Mucus – Oldroyd-B Structure o Linear elastic membrane o Linear elastic circumferential rings

Methods – Compressible Navier-Stokes (air)

Methods – Oldroyd-B (mucus)

Methods – Incompressible Navier-Stokes (PCL)

Methods – Linear elasticity (airway wall)

Methods – Numerical B EARCLAW code ( amath.unc.edu/bearclaw ) Finite volume Moving grid formulation Tracked interfaces, no mass through-flow o Wall – ASL o PCL – mucus o Mucus - air Explicit time marching (air, airway wall) Semi-implicit using projection (mucus, PCL) Adaptive mesh refinement o Shear wave in mucus time scale ~30 ms o Sound wave in air time scale ~30  s

Methods – Adaptive, moving mesh refinement

Results – Cough pulse formation

Results – High velocity cough jet in larger bronchus

Results – Mucus entrainment, tidal versus steady flow Re air = 40, We mucus = 0.1 0s 1s 2s 3s 4s

Rheology Results – Mucus entrainment, tidal, no cilia vs cilia Re air = 40, We mucus = 0.1 0s 1s 2s 3s 4s

Results – Mucus entrainment, cough Re air = 2000, We mucus = 0.1

Rheology Results – Mucus entrainment, cough, no cilia vs cilia Re air = 2000, We mucus = 0.1

Results – Mucus entrainment, cough Re air = 4000, We = 0.1, Re = Re air = 4000, We = 0.5, Re = Re air = 4000, We = 0.1, Re = Re air = 4000, We = 0.5, Re = t=2s

Conclusions Numerical model of flow, deformation processes in bronchi network Model captures effect of mucus friction, elasticity on momentum transfer from air ensuing mass transport Cilia motion dampens mucus layer ripples