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

2. The Lung – Airway anatomy

3. The Lung - Bronchi physiology Tidal breathing ~4 s period 1 – 10 mm diameter Volume rate 200 ml/s Airflow speed 0.1 - 0.5 m/s 10 < Reynolds < 1000 Cough 30 m/s average airflow speed 100-200 m/s local maximum 4 x 10 3 < Reynolds < 4 x 10 4

4. PCL Newtonian (?) 7 micron layer Flow speed 10 -5 m/s Reynolds < 10 -4 Mucus Viscoelastic Continuum relaxation spectrum 1 < Weissenberg < 10 Reynolds < 10 -3 The Lung - Airway surface liquid

5. The Lung – Mucociliary transport

6. 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

7. Methods – Compressible Navier-Stokes (air)

8. Methods – Oldroyd-B (mucus)

9. Methods – Incompressible Navier-Stokes (PCL)

10. Methods – Linear elasticity (airway wall)

11. 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

12. Methods – Adaptive, moving mesh refinement

15. Results – Cough pulse formation

16. Results – High velocity cough jet in larger bronchus

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

18. Rheology 200818 Results – Mucus entrainment, tidal, no cilia vs cilia Re air = 40, We mucus = 0.1 0s 1s 2s 3s 4s

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

20. Rheology 200820 Results – Mucus entrainment, cough, no cilia vs cilia Re air = 2000, We mucus = 0.1

21. Results – Mucus entrainment, cough Re air = 4000, We = 0.1, Re = 10 -3 Re air = 4000, We = 0.5, Re = 10 -3 Re air = 4000, We = 0.1, Re = 10 -4 Re air = 4000, We = 0.5, Re = 10 -4 t=2s

22. 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