Soluble surfactant and airway surface liquid transport are examined using a mathematical model of Marangoni flows which accounts for airway branching and for cyclic airway stretching. Both radial and longitudinal wall strains are considered. The model allows for variation of the amplitude and frequency of the motion, as may occur under a variety of ventilatory situations occurring during surfactant replacement therapy. The soluble surfactant dynamics of the thin fluid film are modeled by linear sorption. The delivery of surfactants into the lung is handled by setting the proximal boundary condition to a higher concentration compared to the distal boundary condition. Starting with a steady-state, nonuniform, surfactant distribution, we find that transport of surfactant into the lung is enhanced for increasing strain amplitudes. However, for fixed amplitude, increasing frequency has a smaller effect. At small strain amplitudes, increasing frequency enhances transport, but at large strain amplitudes, increasing cycling frequency has the opposite effect.
Issue Section:
Fluids/Heat/Transport
1.
Corbet
, A.
, Bucciarelli
, R.
, Goldman
, S.
, Mammel
, M.
, Wold
, D.
, and Long
, W.
, 1991
, “Decreased mortality rate among small premature infants treated at birth with a single dose of synthetic surfactant: a multicenter controlled trial
,” J. Pediatr. (St. Louis)
, 118
(2
), pp. 277
–284
.2.
Kendig
, J. W.
, Notter
, R. H.
, Cox
, C.
et al., 1991
, “A comparison of surfactant as immediate prophylaxis and as rescue therapy in newborns of less than 30 weeks gestation
,” N. Engl. J. Med.
, 324
, pp. 865
–871
.3.
Long
, W.
, Corbet
, A.
, Cotton
, R.
, Courtney
, S.
, McGuiness
, G.
, Walter
, D.
, Watts
, J.
, Smyth
, J.
, Bard
, H.
, and Chernick
, V.
, 1991
, “A controlled trial of synthetic surfactant in infants weighing 1250 g or more with respiratory distress syndrome. The American Exosurf Neonatal Study Group I, and the Canadian Exosurf Neonatal Study Group
,” N. Engl. J. Med.
, 325
(24
), pp. 1696
–703
.4.
Jobe
, A. H.
, 1993
, “Pulmonary surfactant therapy
,” N. Engl. J. Med.
, 328
(12
), pp. 861
–868
.5.
Fuhrman
, B. P.
, Paczan
, P. R.
, and DeFrancisis
, M.
, 1991
, “Perfluorocarbon-associated gas exchange
,” Crit. Care Med.
, 19
(5
), pp. 712
–22
.6.
Wolfson
, M. R.
, Greenspan
, J. S.
, Deoras
, K. S.
, Rubenstein
, S. D.
, and Shaffer
, T. H.
, 1992
, “Comparison of gas and liquid ventilation: clinical, physiological, and histological correlates
,” J. Appl. Physiol.
, 72
(3
), pp. 1024
–31
.7.
Leach
, C. L.
, Fuhrman
, B. P.
, Morin
, F. C.
, and Rath
, M. G.
, 1993
, “Perfluorocarbon-associated gas exchange (partial liquid ventilation) in respiratory distress syndrome: a prospective, randomized, controlled study
,” Crit. Care Med.
, 21
(9
), pp. 1270
–8
.8.
Tutuncu
, A. S.
, Akpir
, K.
, Mulder
, P.
, Erdmann
, W.
, and Lachmann
, B.
, 1993
, “Intratracheal perfluorocarbon administration as an aid in the ventilatory management of respiratory distress syndrome
,” Anesthesiology
, 79
(5
), pp. 1083
–93
.9.
Hirschl
, R. B.
, Parent
, A.
, Tooley
, R.
, McCracken
, M.
, Johnson
, K.
, Shaffer
, T. H.
, Wolfson
, M. R.
, and Bartlett
, R. H.
, 1995
, “Liquid ventilation improves pulmonary function, gas exchange, and lung injury in a model of respiratory failure
,” Ann. Surg.
, 221
(1
), pp. 79
–88
.10.
Espinosa
, F. F.
, and Kamm
, R. D.
, 1998
, “Meniscus formation during tracheal instillation of surfactant
,” J. Appl. Physiol.
, 85
(1
), pp. 266
–72
.11.
Halpern
, D.
, Jensen
, O. E.
, and Grotberg
, J. B.
, 1998
, “A theoretical study of surfactant and liquid delivery into the lung
,” J. Appl. Physiol.
, 85
(1
), pp. 333
–352
.12.
Espinosa
, F. F.
, and Kamm
, R. D.
, 1999
, “Bolus dispersal through the lungs in surfactant replacement therapy
,” J. Appl. Physiol.
, 86
(1
), pp. 391
–410
.13.
Grotberg
, J. B.
, Halpern
, D.
, and Jensen
, O. E.
, 1995
, “Interaction of exogenous and endogenous surfactant: spreading-rate effects
,” J. Appl. Physiol.
, 78
, pp. 750
–756
.14.
Gaver
, D. P.
, and Grotberg
, J. B.
, 1990
, “The dynamics of a localized surfactant on a thin film
,” J. Fluid Mech.
, 213
, pp. 127
–148
.15.
Troian
, S. M.
, Herbolzheimer
, E.
, and Safran
, S. A. P. R. L.
, 1990
, “Model for the fingering instability of spreading surfactant drops
,” Phys. Rev. Lett.
, 65
, pp. 333
–336
.16.
Jensen
, O. E.
, and Grotberg
, J. B.
, 1992
, “Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture
,” J. Fluid Mech.
, 240
, pp. 259
–288
.17.
Espinosa
, F. F.
, Shapiro
, A. H.
, Fredberg
, J. J.
, and Kamm
, R. D.
, 1993
, “Spreading of exogenous surfactant in an airway
,” J. Appl. Physiol.
, 75
, pp. 2028
–2039
.18.
Siegfried
, W.
, 1993
, “Perspectives in gene therapy with recombinant adenoviruses
,” Exp. Clin. Endocrinol.
, 101
(1
), pp. 7
–11
.19.
Grotberg, J. B., 1994, Pulmonary flow and transport phenomena, In: Ann. Rev. Fluid Mech., J. L. Lumley, M. Van Dyke, and H. L. Reed, eds, Annual Reviews, Inc., Palo Alto, pp. 529–571.
20.
Jensen
, O. E.
, Halpern
, D.
, and Grotberg
, J. B.
, 1994
, “Transport of a passive solute by surfactant-driven flows
,” Chem. Eng. Sci.
, 49
(8
), pp. 1107
–1117
.21.
Bull, J. L., D. Halpern, and J. B. Grotberg, 1999, The effect of time-periodic airway stretch on surfactant and liquid transport in the lung, in Interfaces for the Twenty-First Century, Monterey, CA.
22.
Bull
, J. L.
, Nelson
, L. K.
, Walsh
, J. T.
, Glucksberg
, M. R.
, Schurch
, S.
, and Grotberg
, J. B.
, 1999
, “Surfactant-spreading and surface-compression disturbance on a thin viscous film
,” J. Biomech. Eng.
, 121
(1
), pp. 89
–98
.23.
Bull
, J. L.
, and Grotberg
, J. B.
, 2003
, “Surfactant spreading on thin viscous films: film thickness evolution and periodic wall stretch
,” Exp. Fluids
, 34
(1
), pp. 1
–15
.24.
Jensen
, O. E.
, 1998
, “The stress singularity in surfactant-driven thin-film flows. Part 2. Inertial effects
,” J. Fluid Mech.
, 372
, pp. 301
–322
.25.
Weh
, L.
, and Linde
, H.
, 1973
, “Kraterfrmige Oberflchenstraungen in Anstrichfilmen, verursacht durch Silikonlzustze
,” Plaste Kautsch.
, 20
, pp. 849
–860
.26.
Keshgi
, H. S.
, and Scriven
, L. E.
, 1991
, “Dewetting, nucleation and growth of dry regions
,” Chem. Eng. Sci.
, 46
, pp. 519
–26
.27.
Gaver
, D. P.
, and Grotberg
, J. B.
, 1992
, “Droplet spreading on a thin viscous film
,” J. Fluid Mech.
, 235
, pp. 399
–414
.28.
Halpern
, D.
, and Grotberg
, J. B.
, 1992
, “Dynamics and transport of a localized soluble surfactant on a thin film
,” J. Fluid Mech.
, 237
, pp. 1
–11
.29.
Jensen
, O. E.
, and Grotberg
, J. B.
, 1993
, “The spreading of heat or soluble surfactant along a thin liquid film
,” Phys. Fluids A
, 5
(1
), pp. 58
–68
.30.
Yih
, C.-S.
, 1969
, “Three-dimensional motion of a liquid film induced by surface-tension variation or gravity
,” Phys. Fluids
, 12
(10
), pp. 1982
–1987
.31.
Davis
, S. H.
, Liu
, A.-K.
, and Sealy
, G. R.
, 1974
, “Motion driven by surface-tension gradients in a tube lining
,” J. Fluid Mech.
, 62
, pp. 737
–751
.32.
Espinosa
, F. F.
, and Kamm
, R. D.
, 1997
, “Thin layer flows due to surface tension gradients over a membrane undergoing non-uniform, periodic strain
,” Ann. Biomed. Eng.
, 25
(6
), pp. 913
–925
.33.
Weibel, E. R. and D. M. Gomez, 1962, “Architecture of the human lung,” Science Wash. D.C. 137, pp. 577–585.
34.
Sleigh, M. A., 1991, Mucus Propulsion, In: The Lung: Scientific Foundations, R. G. Crystal and J. B. West, eds, Raven, New York, pp. 189–196.
35.
Otis
, Jr., D. R.
, Ingenito
, E. P.
, Kamm
, R. D.
, and Johnson
, M.
, 1994
, “Dynamic surface tension of surfactant TA: experiments and theory
,” J. Appl. Physiol.
, 77
(6
), pp. 2681
–8
.36.
Krueger
, M. A.
, and Gaver
, D. P.
, 2000
, “A theoretical model of pulmonary surfactant multilayer collapse under oscillating area conditions
,” J. Colloid Interface Sci.
, 229
, pp. 353
–364
.37.
Horn
, L. W.
, and Davis
, S. H.
, 1975
, “Apparent surface tension hysteresis of a dynamical system
,” J. Colloid Interface Sci.
, 51
, pp. 459
–475
.38.
Bastacky
, J.
, Lee
, C. Y.
, Goerke
, J.
, Koushafar
, H.
, Yager
, D.
, Kenaga
, L.
, Speed
, T. P.
, Chen
, Y.
, and Clements
, J. A.
, 1995
, “Alveolar lining layer is thin and continuous: low-temperature scanning electron microscopy of rat lung
,” J. Appl. Physiol.
, 79
(5
), pp. 1615
–28
.39.
Widdicombe
, J.
, 1997
, “Airway and alveolar permeability and surface liquid thickness: Theory
,” J. Appl. Physiol.
, 82
(1
), pp. 3
–12
.40.
Craster
, R. V.
, and Matar
, O. K.
, 2000
, “Surfactant transport on mucus films
,” J. Fluid Mech.
, 425
, pp. 235
–258
.41.
Ingenito
, E. P.
, Mark
, L.
, Morris
, J.
, Espinosa
, F. F.
, Kamm
, R. D.
, and Johnson
, M.
, 1999
, “Biophysical characterization and modeling of lung surfactant components
,” J. Appl. Physiol.
, 86
(5
), pp. 1702
–1714
.42.
Schurch
, S.
, Bachofen
, H.
, Goerke
, J.
, and Possmayer
, F.
, 1989
, “A captive bubble method reproduces the in situ behavior of lung surfactant monolayers
,” J. Appl. Physiol.
, 67
, pp. 2389
–2396
.43.
Ferziger, J. H. and M. Peric, 2002, Computational methods for fluid dynamics, Berlin, Springer.
44.
Slutsky, A. S., 1991, Mechanical Ventilation, In: The Lung: Scientific Foundations, R. G. Crystal and J. B. West, eds, Raven, New York, pp. 2163–2174.
45.
Dreyfuss
, D.
, and Saumon
, G.
, 1998
, “Ventilator-induced lung injury-Lessons from experimental studies
,” Crit. Care Med.
, 157
(1
), pp. 294
–323
.46.
Tremblay
, L. N.
, and Slutsky
, A. S.
, 1998
, “Ventilator-induced injury: From barotrauma to biotrauma
,” Proc. Assoc. Am. Physicians
, 110
(6
), pp. 482
–488
.47.
Tremblay, L. N., A. S. Slutsky, D. Dreyfuss, and G. Saumon, 1998, Ventilator-induced lung injury: mechanisms and clinical correlates, In: Physiological basis of ventilatory support, J. J. Marini and A. S. Slutsky, eds, Marcel Dekker, New York, pp. 395–451.
48.
Halpern
, D.
, and Grotberg
, J. B.
, 1993
, “Surfactant effects on fluid-elastic instabilities of liquid-lined flexible tubes: a model of airway closure
,” J. Biomech. Eng.
, 115
(3
), pp. 271
–277
.49.
Jensen
, O. E.
, 1997
, “The thin liquid lining of a weakly curved cylindrical tube
,” J. Fluid Mech.
, 331
, pp. 373
–403
.50.
Rosenzweig
, J.
, and Jensen
, O. E.
, 2002
, “Capillary-elastic instabilities of liquid-lined lung airways
,” J. Biomech. Eng.
, 124
(6
), pp. 650
–655
.51.
Cassidy
, K. J.
, Gavriely
, N.
, and Grotberg
, J. B.
, 2001
, “Liquid plug flow in straight and bifurcating tubes
,” J. Biomech. Eng.
, 123
(6
), pp. 580
–589
.52.
Crystal, R. G. and J. B. West, 1991, The lung: scientific foundations, ed, R. G. Crystal et al., Vol. 1, New York, NY, Raven Press, 2224 see p. 199.
53.
Serafini
, S.
, and Michaelson
, E.
, 1977
, “Length and distribution of cilia in human and canine airways
,” Bull. Eur. Physiopathol Respir.
, 13, pp.
551
–559
.54.
Davis, S. S., 1973, Rheological examination of sputum and saliva and the effect of drugs, In: Rheology of Biological Systems, H. L. Gabelnick and M. Litt, eds, Charles C. Thomas, Springfield, pp. 157–194.
55.
Sleigh
, M. A.
, Blake
, J. R.
, and Liron
, N.
, 1988
, “The propulsion of mucus by cilia
,” J. Endocrinol.
, 137
, pp. 726
–741
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