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Numerical study of flow fields in an airway closure model

Published online by Cambridge University Press:  08 April 2011

C.-F. TAI ,
S. BIAN ,
D. HALPERN ,
Y. ZHENG ,
M. FILOCHE  and
J. B. GROTBERG
C.-F. TAI*
Affiliation:
Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
S. BIAN
Affiliation:
Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
D. HALPERN
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
Y. ZHENG
Affiliation:
Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
M. FILOCHE
Affiliation:
Physique de la Matière Condensée, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
J. B. GROTBERG
Affiliation:
Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: petertai@umich.edu
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Abstract

The liquid lining in small human airways can become unstable and form liquid plugs that close off the airways. Direct numerical simulations are carried out on an airway model to study this airway instability and the flow-induced stresses on the airway walls. The equations governing the fluid motion and the interfacial boundary conditions are solved using the finite-volume method coupled with the sharp interface method for the free surface. The dynamics of the closure process is simulated for a viscous Newtonian film with constant surface tension and a passive core gas phase. In addition, a special case is examined that considers the core dynamics so that comparisons can be made with the experiments of Bian et al. (J. Fluid Mech., vol. 647, 2010, p. 391). The computed flow fields and stress distributions are consistent with the experimental findings. Within the short time span of the closure process, there are large fluctuations in the wall shear stress. Furthermore, dramatic velocity changes in the film during closure indicate a steep normal stress gradient on the airway wall. The computational results show that the wall shear stress, normal stress and their gradients during closure can be high enough to injure airway epithelial cells.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 483 - 502
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Baker, C. S., Evans, T. W., Randle, B. J. & Haslam, P. L. 1999 Damage to surfactant-specific protein in acute respiratory distress syndrome. Lancet 353, 1232–1237.CrossRefGoogle ScholarPubMed
Bian, S., Tai, C.-F., Halpern, D., Zheng, Y. & Grotberg, J. B. 2010 Experimental study of flow fields in an airway closure model. J. Fluid Mech. 647, 391–402.CrossRefGoogle Scholar
Bilek, A. M., Dee, K. C. & Gaver, D. P. 2003 Mechanisms of surface-tension-induced epithelial cell damage in a model of pulmonary airway reopening. J. Appl. Physiol. 94, 770–783.CrossRefGoogle Scholar
Campana, D. M., Di Paolo, J. & Saita, F. A. 2004 A 2-D model of Rayleigh instability in capillary tubes – surfactant effects. Intl J. Multiphase Flow 30, 431–454.Google Scholar
Campana, D. M. & Saita, F. A. 2006 Numerical analysis of the Rayleigh instability in capillary tubes: The influence of surfactant solubility. Phys. Fluids 18, 022104.CrossRefGoogle Scholar
Cassidy, K. J., Halpern, D., Ressler, B. G. & Grotberg, J. B. 1999 Surfactant effects in model airway closure experiments. J. Appl. Physiol. 87, 415–427.Google Scholar
Chen, Y. J. & Steen, P. H. 1997 Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge. J. Fluid Mech. 341, 245–267.Google Scholar
Crystal, R. G. 1997 The Lung: Scientific Foundations. Lippincott.Google Scholar
Dargaville, P. A., South, M. & McDougall, P. N. 1996 Surfactant abnormalities in infants with severe viral bronchiolitis. Arch. Dis. Child. 75, 133–136.Google Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–929.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71, 036601.CrossRefGoogle Scholar
Ferziger, J. H. & Peric, M. 1996 Computational Methods for Fluid Dynamics. Springer.CrossRefGoogle Scholar
Fujioka, H. & Grotberg, J. B. 2004 Steady propagation of a liquid plug in a two-dimensional channel. J. Biomech. Engng - Trans. ASME 126, 567–577.CrossRefGoogle Scholar
Fujioka, H. & Grotberg, J. B. 2005 The steady propagation of a surfactant-laden liquid plug in a two-dimensional channel. Phys. Fluids 17, 082102.Google Scholar
Fujioka, H., Takayama, S. & Grotberg, J. B. 2008 Unsteady propagation of a liquid plug in a liquid-lined straight tube. Phys. Fluids 20, 062104.CrossRefGoogle Scholar
Ghadiali, S. N. & Gaver, D. P. 2008 Biomechanics of liquid–epithelium interactions in pulmonary airways. Respir. Physiol. Neurobiol. 163, 232–243.CrossRefGoogle ScholarPubMed
Greaves, I. A., Hildebrandt, J. & Hoppin, J. F. G. 1986 Handbook of Physiology. The Respiratory System: Mechanics of Breathing. American Physiology Society.Google Scholar
Griese, M., Essl, R., Schmidt, R., Rietschel, E., Ratjen, F., Ballmann, M. & Paul, K. 2004 Pulmonary surfactant, lung function, and endobronchial inflammation in cystic fibrosis. Am. J. Respir. Crit. Care Med. 170, 1000–1005.CrossRefGoogle ScholarPubMed
Guerin, C., LeMasson, S., DeVarax, R., MilicEmili, J. & Fournier, G. 1997 Small airway closure and positive end-expiratory pressure in mechanically ventilated patients with chronic obstructive pulmonary disease. Am. J. Respir. Crit. Care Med. 155, 1949–1956.CrossRefGoogle ScholarPubMed
Gunther, A., Siebert, C., Schmidt, R., Ziegler, S., Grimminger, F., Yabut, M., Temmesfeld, B., Walmrath, D., Morr, H. & Seeger, W. 1996 Surfactant alterations in severe pneumonia, acute respiratory distress syndrome, and cardiogenic lung edema. Am. J. Respir. Crit. Care Med. 153, 176–184.Google Scholar
Halpern, D., Fujioka, H. & Grotberg, J. B. 2010 The effect of viscoelasticity on the stability of a pulmonary airway liquid layer. Phys. Fluids 22, 011901.CrossRefGoogle ScholarPubMed
Halpern, D. & Grotberg, J. B. 1992 Fluid-elastic instabilities of liquid-lined flexible tubes. J. Fluid Mech. 244, 615–632.Google Scholar
Halpern, D. & Grotberg, J. B. 1993 Surfactant effects on fluid-elastic instabilities of liquid-lined flexible tubes: a model of airway closure. J. Biomech. Engng - Trans. ASME 115, 271–277.Google Scholar
Halpern, D. & Grotberg, J. B. 2003 Nonlinear saturation of the Rayleigh instability due to oscillatory flow in a liquid-lined tube. J. Fluid Mech. 492, 251–270.Google Scholar
Hammond, P. S. 1983 Nonlinear adjustment of a thin annular film of viscous-fluid surrounding a thread of another within a circular cylindrical pipe. J. Fluid Mech. 137, 363–384.CrossRefGoogle Scholar
Heil, M. 1999 Airway closure: Occluding liquid bridges in strongly buckled elastic tubes. J. Biomech. Engng - Trans. ASME 121, 487–493.CrossRefGoogle ScholarPubMed
Heil, M., Hazel, A. L. & Smith, J. A. 2008 The mechanics of airway closure. Respir. Physiol. Neurobiol. 163, 214–221.CrossRefGoogle ScholarPubMed
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225.CrossRefGoogle Scholar
Huh, D., Fujioka, H., Tung, Y. C., Futai, N., Paine, R., Grotberg, J. B. & Takayama, S. 2007 Acoustically detectable cellular-level lung injury induced by fluid mechanical stresses in microfluidic airway systems. Proc. Natl Acad. Sci. USA 104, 18886–18891.CrossRefGoogle ScholarPubMed
Johnson, M., Kamm, R. D., Ho, L. W., Shapiro, A. & Pedley, T. J. 1991 The nonlinear growth of surface-tension-driven instabilities of a thin annular film. J. Fluid Mech. 233, 141–156.CrossRefGoogle Scholar
Kay, S. S., Bilek, A. M., Dee, K. C. & Gaver, D. P. 2004 Pressure gradient, not exposure duration, determines the extent of epithelial cell damage in a model of pulmonary airway reopening. J. Appl. Physiol. 97, 269–276.CrossRefGoogle ScholarPubMed
Keller, J. B. & Miksis, M. J. 1983 Surface-tension-driven flows. SIAM J. Appl. Math. 43, 268–277.Google Scholar
Macklem, P. T., Proctor, D. F. & Hogg, J. C. 1970 Stability of peripheral airways. Respir. Physiol. 8, 191–203.CrossRefGoogle ScholarPubMed
Muscedere, J. G., Mullen, J. B. M., Gan, K. & Slutsky, A. S. 1994 Tidal ventilation at low airway pressures can augment lung injury. Am. J. Respir. Crit. Care Med. 149, 1327–1334.CrossRefGoogle ScholarPubMed
Osher, S. J. & Fedkiw, R. P. 2003 Level Set Methods and Dynamic Implicit Surfaces. Springer.Google Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25, 220–252.CrossRefGoogle Scholar
Piirila, P. & Sovijarvi, A. R. A. 1995 Crackles: recording, analysis and clinical significance. Eur. Respir. J. 8, 2139–2148.Google Scholar
Rasanen, J. & Gavriely, N. 2005 Response of acoustic transmission to positive airway pressure therapy in experimental lung injury. Intensive Care Med. 31, 1434–1441.Google Scholar
Ryskin, G. & Leal, L. G. 1984 Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech. 148, 19–35.CrossRefGoogle Scholar
Shyy, W. 1994 Computational Modeling for Fluid Flow and Interfacial Transport. Elsevier.Google Scholar
Tai, C.-F. & Shyy, W. 2005 Multigrid computations and conservation law treatment of a sharp interface method. Numer. Heat Trans. B 48, 405–424.CrossRefGoogle Scholar
Taskar, V., John, J., Evander, E., Robertson, B. & Jonson, B. 1997 Surfactant dysfunction makes lungs vulnerable to repetitive collapse and reexpansion. Am. J. Respir. Crit. Care Med. 155, 313–320.Google Scholar
tAAAAVeen, J., Beekman, A. J., Bel, E. H. & Sterk, P. J. 2000 Recurrent exacerbations in severe asthma are associated with enhanced airway closure during stable episodes. Am. J. Respir. Crit. Care Med. 161, 1902–1906.Google Scholar
White, J. P. & Heil, M. 2005 Three-dimensional instabilities of liquid-lined elastic tubes: A thin-film fluid–structure interaction model. Phys. Fluids 17, 031506.CrossRefGoogle Scholar
Ye, T., Shyy, W., Tai, C.-F. & Chung, J. 2004 Assessment of sharp- and continuous-interface methods for drop in static equilibrium. Comput. Fluids 33, 917–926.CrossRefGoogle Scholar
Zheng, Y., Fujioka, H., Bian, S., Torisawa, Y., Huh, D., Takayama, S. & Grotberg, J. B. 2009 Liquid plug propagation in flexible microchannels – a small airway model. Phys. Fluids 21, 071903.CrossRefGoogle ScholarPubMed