Skip to main content
Erschienen in: Journal of Engineering Mathematics 1/2018

20.09.2018

Modeling coating flow and surfactant dynamics inside the alveolar compartment

verfasst von: D. Kang, M. Chugunova, A. Nadim, A. J. Waring, F. J. Walther

Erschienen in: Journal of Engineering Mathematics | Ausgabe 1/2018

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We derive a new model for the coating flow inside the alveolar compartment, taking into account pulmonary surfactant production and recycling by Type 2 cells as well as its degradation. As the thickness of alveolar coating is much smaller than the average radius of the alveoli, we employ the classical lubrication approximation to describe the thin liquid film dynamics in the presence of pulmonary surfactant, which is a surface tension-reducing agent and thus prevents the lungs from collapse. In the lubrication limit, we derive a degenerate system of two coupled parabolic partial differential equations that describe the time evolution of the thickness of the coating film inside the alveoli together with that of the surfactant concentration at the interface. We present numerical simulations using parameter values consistent with experimental measurements. With Marangoni effects being significant, it is found that any initial non-uniformity in surfactant concentration leads to a very fast redistribution of surfactant and accompanying change in film thickness, followed by a much slower relaxation of the film thickness to equilibrium during which surfactant concentration remains relatively uniform.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Matthay MA, Folkesson HG, Clerici C (2002) Lung epithelial fluid transport and the resolution of pulmonary edema. Physiol Rev 82(3):569–600CrossRef Matthay MA, Folkesson HG, Clerici C (2002) Lung epithelial fluid transport and the resolution of pulmonary edema. Physiol Rev 82(3):569–600CrossRef
2.
Zurück zum Zitat Shier D, Butler J, Lewis R (2007) Human anatomy and physiology. McGraw-Hill, Boston Shier D, Butler J, Lewis R (2007) Human anatomy and physiology. McGraw-Hill, Boston
4.
Zurück zum Zitat West JB, Elliott AR, Guy HJ, Prisk GK (1997) Pulmonary function in space. JAMA 277(24):1957–1961CrossRef West JB, Elliott AR, Guy HJ, Prisk GK (1997) Pulmonary function in space. JAMA 277(24):1957–1961CrossRef
5.
Zurück zum Zitat Bryndina I, Vasilieva N (2014) Effects of simulated microgravity on surfactant and water balance of lung in animals with different resistance to stress. In: 40th COSPAR Scientific Assembly, 2–10 August 2014, Moscow, Russia, Abstract F4.4-17-14 Bryndina I, Vasilieva N (2014) Effects of simulated microgravity on surfactant and water balance of lung in animals with different resistance to stress. In: 40th COSPAR Scientific Assembly, 2–10 August 2014, Moscow, Russia, Abstract F4.4-17-14
6.
Zurück zum Zitat Williams MC, Cao Y, Hinds A, Rishi AK, Wetterwald A (1996) T1 alpha protein is developmentally regulated and expressed by alveolar type I cells, choroid plexus, and ciliary epithelia of adult rats. Am J Respir Cell Mol Biol 14(6):577–585CrossRef Williams MC, Cao Y, Hinds A, Rishi AK, Wetterwald A (1996) T1 alpha protein is developmentally regulated and expressed by alveolar type I cells, choroid plexus, and ciliary epithelia of adult rats. Am J Respir Cell Mol Biol 14(6):577–585CrossRef
7.
Zurück zum Zitat Verkman AS, Matthay MA, Song Y (2000) Aquaporin water channels and lung physiology. Am J Physiol Lung Cell Mol Physiol 278(5):L867–L879CrossRef Verkman AS, Matthay MA, Song Y (2000) Aquaporin water channels and lung physiology. Am J Physiol Lung Cell Mol Physiol 278(5):L867–L879CrossRef
8.
Zurück zum Zitat Crapo JD, Young SL, Fram EK, Pinkerton KE, Barry BE, Crapo RO (1983) Morphometric characteristics of cells in the alveolar region of mammalian lungs. Am Rev Respir Dis 128(2P2):S42–S46 Crapo JD, Young SL, Fram EK, Pinkerton KE, Barry BE, Crapo RO (1983) Morphometric characteristics of cells in the alveolar region of mammalian lungs. Am Rev Respir Dis 128(2P2):S42–S46
9.
Zurück zum Zitat Haies DM, Gil J, Weibel ER (1981) Morphometric study of rat lung cells. I. Numerical and dimensional characteristics of parenchymal cell population. Am Rev Respir Dis 123(5):533–541 Haies DM, Gil J, Weibel ER (1981) Morphometric study of rat lung cells. I. Numerical and dimensional characteristics of parenchymal cell population. Am Rev Respir Dis 123(5):533–541
10.
Zurück zum Zitat Carnielli VP, Zimmermann LJ, Hamvas A, Cogo PE (2009) Pulmonary surfactant kinetics of the newborn infant: novel insights from studies with stable isotopes. J Perinatol 29:S29–S37CrossRef Carnielli VP, Zimmermann LJ, Hamvas A, Cogo PE (2009) Pulmonary surfactant kinetics of the newborn infant: novel insights from studies with stable isotopes. J Perinatol 29:S29–S37CrossRef
11.
Zurück zum Zitat Notter RH, Gupta R, Schwan AL, Wang Z, Shkoor MG, Walther FJ (2016) Synthetic lung surfactants containing SP-B and SP-C peptides plus novel phospholipase-resistant lipids or glycerophospholipids. PeerJ 4:e2635CrossRef Notter RH, Gupta R, Schwan AL, Wang Z, Shkoor MG, Walther FJ (2016) Synthetic lung surfactants containing SP-B and SP-C peptides plus novel phospholipase-resistant lipids or glycerophospholipids. PeerJ 4:e2635CrossRef
12.
Zurück zum Zitat Fehrenbach H (2001) Alveolar epithelial type II cell: defender of the alveolus revisited. Respir Res 2(1):33CrossRef Fehrenbach H (2001) Alveolar epithelial type II cell: defender of the alveolus revisited. Respir Res 2(1):33CrossRef
13.
Zurück zum Zitat Castranova V, Rabovsky J, Tucker JH, Miles PR (1988) The alveolar type II epithelial cell: a multifunctional pneumocyte. Toxicol Appl Pharmacol 93(3):472–483CrossRef Castranova V, Rabovsky J, Tucker JH, Miles PR (1988) The alveolar type II epithelial cell: a multifunctional pneumocyte. Toxicol Appl Pharmacol 93(3):472–483CrossRef
14.
Zurück zum Zitat Warren NJ, Tawhai MH, Crampin EJ (2009) A mathematical model of calcium-induced fluid secretion in airway epithelium. J Theor Biol 259(4):837–849CrossRef Warren NJ, Tawhai MH, Crampin EJ (2009) A mathematical model of calcium-induced fluid secretion in airway epithelium. J Theor Biol 259(4):837–849CrossRef
15.
Zurück zum Zitat Walther FJ, Hernandez-Juviel JM, Waring AJ (2014) Aerosol delivery of synthetic lung surfactant. PeerJ 2:e403CrossRef Walther FJ, Hernandez-Juviel JM, Waring AJ (2014) Aerosol delivery of synthetic lung surfactant. PeerJ 2:e403CrossRef
16.
Zurück zum Zitat Halpern D, Jensen OE, Grotberg JB (1998) A theoretical study of surfactant and liquid delivery into the lung. J Appl Physiol 85:333–352CrossRef Halpern D, Jensen OE, Grotberg JB (1998) A theoretical study of surfactant and liquid delivery into the lung. J Appl Physiol 85:333–352CrossRef
17.
Zurück zum Zitat Halpern D, Fujioka H, Takayama S, Grotberg JB (2008) Liquid and surfactant delivery into pulmonary airways. Respir Physiol Neurobiol 163:222–231CrossRef Halpern D, Fujioka H, Takayama S, Grotberg JB (2008) Liquid and surfactant delivery into pulmonary airways. Respir Physiol Neurobiol 163:222–231CrossRef
20.
Zurück zum Zitat Jensen OE, Grotberg JB (1992) Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J Fluid Mech 240:259–288MathSciNetCrossRef Jensen OE, Grotberg JB (1992) Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J Fluid Mech 240:259–288MathSciNetCrossRef
21.
Zurück zum Zitat Gaver DP, Grotberg JB (1990) The dynamics of a localized surfactant on a thin film. J Fluid Mech 213:127–148CrossRef Gaver DP, Grotberg JB (1990) The dynamics of a localized surfactant on a thin film. J Fluid Mech 213:127–148CrossRef
22.
Zurück zum Zitat Chugunova M, King JR, Taranets R (2017) The interface dynamics of a surfactant drop on a thin viscous film. Eur J Appl Math 28(4):656–686MathSciNetCrossRef Chugunova M, King JR, Taranets R (2017) The interface dynamics of a surfactant drop on a thin viscous film. Eur J Appl Math 28(4):656–686MathSciNetCrossRef
23.
Zurück zum Zitat Chugunova M, Taranets R (2013) Nonnegative weak solutions for a degenerate system modelling the spreading of surfactant on thin films. Appl Math Res Express 1:102–126MATH Chugunova M, Taranets R (2013) Nonnegative weak solutions for a degenerate system modelling the spreading of surfactant on thin films. Appl Math Res Express 1:102–126MATH
24.
Zurück zum Zitat Venables JA (2000) Introduction to surface and thin film processes. Cambridge University Press, CambridgeCrossRef Venables JA (2000) Introduction to surface and thin film processes. Cambridge University Press, CambridgeCrossRef
25.
Zurück zum Zitat Escher J, Hillairet M, Laurençot P, Walker C (2011) Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant. Indiana Univ Math J 60:1975–2019MathSciNetCrossRef Escher J, Hillairet M, Laurençot P, Walker C (2011) Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant. Indiana Univ Math J 60:1975–2019MathSciNetCrossRef
26.
Zurück zum Zitat Escher J, Hillairet M, Laurençot P, Walker C (2012) Thin film equations with soluble surfactant and gravity: modeling and stability of steady states. Math Nachr 285(2–3):210–222MathSciNetCrossRef Escher J, Hillairet M, Laurençot P, Walker C (2012) Thin film equations with soluble surfactant and gravity: modeling and stability of steady states. Math Nachr 285(2–3):210–222MathSciNetCrossRef
27.
Zurück zum Zitat Garcke H, Wieland S (2006) Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. SIAM J Math Anal 37(6):2025–2048MathSciNetCrossRef Garcke H, Wieland S (2006) Surfactant spreading on thin viscous films: nonnegative solutions of a coupled degenerate system. SIAM J Math Anal 37(6):2025–2048MathSciNetCrossRef
28.
Zurück zum Zitat Borgas MS, Grotberg JB (1988) Monolayer flow on a thin film. J Fluid Mech 193:151–170CrossRef Borgas MS, Grotberg JB (1988) Monolayer flow on a thin film. J Fluid Mech 193:151–170CrossRef
29.
Zurück zum Zitat Lucassen J, Hansen RS (1967) Damping of waves on monolayer-covered surfaces. II. Influence of bulk-to-surface diffusional interchange on ripple characteristics. J Colloid Interface Sci 23:319–328CrossRef Lucassen J, Hansen RS (1967) Damping of waves on monolayer-covered surfaces. II. Influence of bulk-to-surface diffusional interchange on ripple characteristics. J Colloid Interface Sci 23:319–328CrossRef
30.
Zurück zum Zitat Kang D, Nadim A, Chugunova M (2016) Dynamics and equilibria of thin viscous coating films on a rotating sphere. J Fluid Mech 791:495–518MathSciNetCrossRef Kang D, Nadim A, Chugunova M (2016) Dynamics and equilibria of thin viscous coating films on a rotating sphere. J Fluid Mech 791:495–518MathSciNetCrossRef
31.
Zurück zum Zitat Kang D, Nadim A, Chugunova M (2017) Marangoni effects on a thin liquid film coating a sphere with axial or radial thermal gradients. Phys Fluids 29(7):072106CrossRef Kang D, Nadim A, Chugunova M (2017) Marangoni effects on a thin liquid film coating a sphere with axial or radial thermal gradients. Phys Fluids 29(7):072106CrossRef
32.
Zurück zum Zitat Rausch SMK, Haberthür D, Stampanoni M, Schittny JC, Wall WA (2011) Local strain distribution in real three-dimensional alveolar geometries. Ann Biomed Eng 39(11):2835–2843CrossRef Rausch SMK, Haberthür D, Stampanoni M, Schittny JC, Wall WA (2011) Local strain distribution in real three-dimensional alveolar geometries. Ann Biomed Eng 39(11):2835–2843CrossRef
33.
Zurück zum Zitat Nadim A (1996) A concise introduction to surface rheology with application to dilute emulsions of viscous drops. Chem Eng Commun 148–150:391–407CrossRef Nadim A (1996) A concise introduction to surface rheology with application to dilute emulsions of viscous drops. Chem Eng Commun 148–150:391–407CrossRef
34.
Zurück zum Zitat Carney DE, Bredenberg CE, Schiller HJ, Picone AL, McCann UG, Gatto LA, Bailey G, Fillinger M, Nieman GF (1999) The mechanism of lung volume change during mechanical ventilation. Am J Respir Crit Care Med 160(5):1697–1702CrossRef Carney DE, Bredenberg CE, Schiller HJ, Picone AL, McCann UG, Gatto LA, Bailey G, Fillinger M, Nieman GF (1999) The mechanism of lung volume change during mechanical ventilation. Am J Respir Crit Care Med 160(5):1697–1702CrossRef
35.
Zurück zum Zitat Edmonstone BD, Matar OK, Craster RV (2004) Flow of surfactant-laden thin films down an inclined plane. J Eng Math 50(2):141–156MathSciNetCrossRef Edmonstone BD, Matar OK, Craster RV (2004) Flow of surfactant-laden thin films down an inclined plane. J Eng Math 50(2):141–156MathSciNetCrossRef
36.
Zurück zum Zitat Parra E, Kinoshita K, Needham D (2016) Micropipette technique study of natural and synthetic lung surfactants at the air-water interface: presence of a SP-B analog peptide promotes membrane aggregation, formation of tightly stacked lamellae, and growth of myelin figures. Langmuir 32(41):10570–10581CrossRef Parra E, Kinoshita K, Needham D (2016) Micropipette technique study of natural and synthetic lung surfactants at the air-water interface: presence of a SP-B analog peptide promotes membrane aggregation, formation of tightly stacked lamellae, and growth of myelin figures. Langmuir 32(41):10570–10581CrossRef
37.
Zurück zum Zitat Podgórski A, Gradoń L (1993) An improved mathematical model of hydrodynamical self-cleansing of pulmonary alveoli. Ann Occup Hyg 37(4):347–366 Podgórski A, Gradoń L (1993) An improved mathematical model of hydrodynamical self-cleansing of pulmonary alveoli. Ann Occup Hyg 37(4):347–366
38.
39.
Zurück zum Zitat Wei HH, Fujioka H, Hirschl RB, Grotberg JB (2005) A model of flow and surfactant transport in an oscillatory alveolus partially filled with liquid. Phys Fluid 17(3):031510MathSciNetCrossRef Wei HH, Fujioka H, Hirschl RB, Grotberg JB (2005) A model of flow and surfactant transport in an oscillatory alveolus partially filled with liquid. Phys Fluid 17(3):031510MathSciNetCrossRef
40.
Zurück zum Zitat Nouraeyan N, Lambrinakos-Raymond A, Leone M, Sant’Anna G (2014) Surfactant administration in neonates: a review of delivery methods. Can J Respir Ther 50(3):91–95 Nouraeyan N, Lambrinakos-Raymond A, Leone M, Sant’Anna G (2014) Surfactant administration in neonates: a review of delivery methods. Can J Respir Ther 50(3):91–95
Metadaten
Titel
Modeling coating flow and surfactant dynamics inside the alveolar compartment
verfasst von
D. Kang
M. Chugunova
A. Nadim
A. J. Waring
F. J. Walther
Publikationsdatum
20.09.2018
Verlag
Springer Netherlands
Erschienen in
Journal of Engineering Mathematics / Ausgabe 1/2018
Print ISSN: 0022-0833
Elektronische ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-018-9972-8

Weitere Artikel der Ausgabe 1/2018

Journal of Engineering Mathematics 1/2018 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.