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Aerosol deposition in mucus-lined ciliated airways
Part of:
JFM Notebooks
Published online by Cambridge University Press: 02 October 2025
Abstract
We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall – an outcome that is harmful in case of allergens and pathogens, but beneficial in case of aerosolised drugs. We adopt the weighted-residual integral boundary-layer model of Dietze and Ruyer-Quil (J. Fluid Mech. 762, 2015, 68–109, to describe the dynamics of the mucus–air interface, as well as the flow in both phases. The transport of mucus induced by wall-attached cilia is also considered, via a coarse-grained boundary condition at the base of the mucus. We show that the capillary-driven Rayleigh–Plateau instability plays an important role in particle deposition by drawing the mucus into large annular humps and leaving substantial areas of the wall exposed to particles. We find, counter-intuitively, that these mucus-depleted zones enlarge on increasing the mucus volume fraction. Our simulations are eased by the fact that the effects of cilia and air turn out to be rather simple: the long-term interface profile is slowly translated by cilia and is unaffected by the laminar airflow. The streamlines of the airflow, though, are strongly modified by the non-uniform mucus film, and this has important implications for aerosol entrapment. Particles spanning a range of sizes (0.1–50 microns) are modelled using the Maxey–Riley equation, augmented with Brownian forces. We find a non-monotonic dependence of deposition on size. Small particles diffuse across streamlines due to Brownian motion, while large particles are thrown off streamlines by inertial forces – particularly when air flows past mucus humps. Intermediate-sized particles are tracer-like and deposit the least. Remarkably, increasing the mucus volume need not increase entrapment: the effect depends on particle size, because more mucus produces not only deeper humps that intercept inertial particles, but also larger depleted zones that enable diffusive particles to deposit on the wall.
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References
Aghaei, Y., Sajadi, B. & Ahmadi, G. 2023 The effect of the mucus layer and the inhaled air conditions on the droplets fate in the human nasal cavity: a numerical study. J. Aerosol Sci. 171, 106163.10.1016/j.jaerosci.2023.106163CrossRefGoogle Scholar
Altshuler, B., Palmes, E.D., Yarmus, L. & Nelson, N. 1959 Intrapulmonary mixing of gases studied with aerosols. J. Appl. Physiol. 14 (3), 321–327.10.1152/jappl.1959.14.3.321CrossRefGoogle ScholarPubMed
Bagheri, F., Mitra, D., Perlekar, P. & Brandt, L. 2012 Statistics of polymer extensions in turbulent channel flow. Phys. Rev. E
86, 056314.10.1103/PhysRevE.86.056314CrossRefGoogle ScholarPubMed
Beelen, R. et al. 2014 Effects of long-term exposure to air pollution on natural-cause mortality: an analysis of 22 European cohorts within the multicentre escape project. Lancet 383 (9919), 785–795.10.1016/S0140-6736(13)62158-3CrossRefGoogle ScholarPubMed
Blake, J. 1975 On the movement of mucus in the lung. J. Biomech. 8 (3–4), 179–190.10.1016/0021-9290(75)90023-8CrossRefGoogle ScholarPubMed
Blake, J. 2001 Fluid mechanics of ciliary propulsion. In Computational Modeling in Biological Fluid Dynamics, (ed. Fauci, L.J. & Gueron, S.), pp. 1–51. Springer New York.Google Scholar
Bottier, M., Blanchon, S., Pelle, G., Bequignon, E., Isabey, D., Coste, A., Escudier, E., Grotberg, J.B., Papon, J.F. & Filoche, M. 2017
a A new index for characterizing micro-bead motion in a flow induced by ciliary beating: part i, experimental analysis. PLOS Comput. Biol. 13 (7), 1–19.Google Scholar
Bottier, M., Peña Fernández, M., Pelle, G., Isabey, D., Louis, B., Grotberg, J.B. & Filoche, M. 2017
b A new index for characterizing micro-bead motion in a flow induced by ciliary beating: part ii, modeling. PLOS Comput. Biol. 13 (7), 1–21.Google Scholar
Button, B., Cai, L.H., Ehre, C., Kesimer, M., Hill, D.B., Sheehan, J.K., Boucher, R.C. & Rubinstein, M. 2012 A periciliary brush promotes the lung health by separating the mucus layer from airway epithelia. Science 337 (6097), 937–941.10.1126/science.1223012CrossRefGoogle ScholarPubMed
Chakrabarti, B., urthauer, F., S, & Shelley, M.J. 2022 A multiscale biophysical model gives quantized metachronal waves in a lattice of beating cilia. Proc. Natl Acad. Sci. 119 (4), e2113539119.10.1073/pnas.2113539119CrossRefGoogle Scholar
Chakrabarti, B. & Saintillan, D. 2019 Hydrodynamic synchronization of spontaneously beating filaments. Phys. Rev. Lett. 123, 208101.10.1103/PhysRevLett.123.208101CrossRefGoogle ScholarPubMed
Chatelin, R. & Poncet, P. 2016 A parametric study of mucociliary transport by numerical simulations of 3D non-homogeneous mucus. J. Biomech. 49 (9), 1772–1780.10.1016/j.jbiomech.2016.04.009CrossRefGoogle ScholarPubMed
Choudhury, A., Filoche, M., Ribe, N.M., Grenier, N. & Dietze, G.F. 2023 On the role of viscoelasticity in mucociliary clearance: a hydrodynamic continuum approach. J. Fluid Mech. 971, A33.10.1017/jfm.2023.682CrossRefGoogle Scholar
Dietze, G.F. 2024 Liquid plugs in narrow tubes: application to airway occlusion. J. Fluid Mech. 998, A50.10.1017/jfm.2024.607CrossRefGoogle Scholar
Dietze, G.F., Lavalle, G. & Ruyer-Quil, C. 2020 Falling liquid films in narrow tubes: occlusion scenarios. J. Fluid Mech. 894, A17.10.1017/jfm.2020.267CrossRefGoogle Scholar
Dietze, G.F. & Ruyer-Quil, C. 2013 Wavy liquid films in interaction with a confined laminar gas flow. J. Fluid Mech. 722, 348–393.10.1017/jfm.2013.98CrossRefGoogle Scholar
Dietze, G.F. & Ruyer-Quil, C. 2015 Films in narrow tubes. J. Fluid Mech. 762, 68–109.10.1017/jfm.2014.648CrossRefGoogle Scholar
epa.gov 2024 Final updates to the air quality index (aqi) for particulate matter. Available at https://www.epa.gov/system/files/documents/2024-02/pm-naaqs-air-quality-index-fact-sheet.pdf.Google Scholar
Erken, O., Fazla, B., Muradoglu, M., Izbassarov, D., Romanò, F. & Grotberg, J.B. 2023 Effects of elastoviscoplastic properties of mucus on airway closure in healthy and pathological conditions. Phys. Rev. Fluids 8, 053102.10.1103/PhysRevFluids.8.053102CrossRefGoogle Scholar
Erken, O., Romanò, F., Grotberg, J.B. & Muradoglu, M. 2022 Capillary instability of a two-layer annular film: an airway closure model. J. Fluid Mech. 934, A7.10.1017/jfm.2021.1126CrossRefGoogle Scholar
Everett, D.H. & Haynes, J.M. 1972 Model studies of capillary condensation. i. Cylindrical pore model with zero contact angle. J. Colloid Interface Sci. 38 (1), 125–137.10.1016/0021-9797(72)90228-7CrossRefGoogle Scholar
Farnoud, A., Tofighian, H., Baumann, I., Garcia, G.J.M., Schmid, O., Gutheil, E. & Rashidi, M.M. 2020 Large eddy simulations of airflow and particle deposition in pulsating bi-directional nasal drug delivery. Phys. Fluids 32 (10), 101905.10.1063/5.0024264CrossRefGoogle Scholar
Fu, P., Guo, X., Cheung, F.M.H. & Yung, K.K.L. 2019 The association between PM2.5 exposure and neurological disorders: a systematic review and meta-analysis. Sci. Total Environ. 655, 1240–1248.10.1016/j.scitotenv.2018.11.218CrossRefGoogle Scholar
Fulford, G.R. & Blake, J.R. 1986 Muco-ciliary transport in the lung. J. Theor. Biol. 121 (4), 381–402.10.1016/S0022-5193(86)80098-4CrossRefGoogle ScholarPubMed
Gardiner, C. 2009 Stochastic Methods: A Handbook for the Natural and Social Sciences. Springer.Google Scholar
Gauvreau, G.M., El-Gammal, A.I. & O’Byrne, P.M. 2015 Allergen-induced airway responses. Eur. Respir. J. 46 (3), 819–831.10.1183/13993003.00536-2015CrossRefGoogle ScholarPubMed
Ghatak, A., Khanna, R. & Sharma, A. 1999 Dynamics and morphology of holes in dewetting of thin films. J. Colloid Interface Sci. 212 (2), 483–494.10.1006/jcis.1998.6052CrossRefGoogle ScholarPubMed
Ghorui, S., Kundu, D., Chakravarty, A. & Panchagnula, M.V. 2024 The impact of asymmetric branching on particle deposition in conducting airways. Intl J. Multiphase Flow 179, 104935.10.1016/j.ijmultiphaseflow.2024.104935CrossRefGoogle Scholar
Gilpin, W., Bull, M.S. & Prakash, M. 2020 The multiscale physics of cilia and flagella. Nat. Rev. Phys. 2, 74–88.10.1038/s42254-019-0129-0CrossRefGoogle Scholar
Grabowski, W.W. & Wang, L.-P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293.10.1146/annurev-fluid-011212-140750CrossRefGoogle Scholar
Gsell, S., Loiseau, E., D’Ortona, U., Viallat, A. & Favier, J. 2020 Hydrodynamic model of directional ciliary-beat organization in human airways. Sci. Rep. 10, 8405.10.1038/s41598-020-64695-wCrossRefGoogle ScholarPubMed
Guha, A. 2008 Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311–341.10.1146/annurev.fluid.40.111406.102220CrossRefGoogle Scholar
Guo, H., Fauci, L., Shelley, M. & Kanso, E. 2018 Bistability in the synchronization of actuated microfilaments. J. Fluid Mech. 836, 304–323.10.1017/jfm.2017.816CrossRefGoogle Scholar
Halpern, D., Bull, J.L. & Grotberg, J.B. 2004 The effect of airway wall motion on surfactant delivery. J. Biomech. Engng 126 (4), 410–419.10.1115/1.1784475CrossRefGoogle ScholarPubMed
Halpern, D., Fujioka, H. & Grotberg, J.B. 2010 The effect of viscoelasticity on the stability of a pulmonary airway liquid layer. Phys. Fluids 22 (1), 011901.10.1063/1.3294573CrossRefGoogle ScholarPubMed
Halpern, D. & Grotberg, J.B. 1992 Fluid-elastic instabilities of liquid-lined flexible tubes. J. Fluid Mech. 244, 615–632.10.1017/S0022112092003227CrossRefGoogle Scholar
Hays, S.R. & Fahy, J.V. 2003 The role of mucus in fatal asthma. Am. J. Med. 115 (1), 68–69.10.1016/S0002-9343(03)00260-2CrossRefGoogle ScholarPubMed
Hazel, A.L., Heil, M., Waters, S.L. & Oliver, J.M. 2012 On the liquid lining in fluid-conveying curved tubes. J. Fluid Mech. 705, 213–233.10.1017/jfm.2011.346CrossRefGoogle Scholar
Hazra, S. & Picardo, J.R. 2025
a Deriving thin-film averaged equations using computer algebra. J. Engng Math. 154 (1), 5.10.1007/s10665-025-10478-zCrossRefGoogle Scholar
Hazra, S. & Picardo, J.R. 2025
b Probabilistic plugging of airways by sliding mucus films. Phys. Rev. Fluids. 10 (9), 094002.10.1103/zqkx-56gnCrossRefGoogle Scholar
Hegedűs, C.J., Balásházy, I. & Farkas, Á 2004 Detailed mathematical description of the geometry of airway bifurcations. Respir. Physiol. Neurobiol. 141 (1), 99–114.10.1016/j.resp.2004.03.004CrossRefGoogle ScholarPubMed
Heil, M., Hazel, A.L. & Smith, J.A. 2008 The mechanics of airway closure. Respir. Physiol. Neurobiol. 163 (1-3), 214–221.10.1016/j.resp.2008.05.013CrossRefGoogle ScholarPubMed
Heyder, J., Gebhart, J., Rudolf, G., Schiller, C.F. & Stahlhofen, W. 1986 Deposition of particles in the human respiratory tract in the size range 0.005–15
${\unicode{x03BC}}$
m. J. Aerosol Sci. 17 (5), 811–825.10.1016/0021-8502(86)90035-2CrossRefGoogle Scholar
${\unicode{x03BC}}$
m. J. Aerosol Sci. 17 (5), 811–825.10.1016/0021-8502(86)90035-2CrossRefGoogle ScholarHill, D.B. et al. 2014 A biophysical basis for mucus solids concentration as a candidate biomarker for airways disease. PloS One 9 (2), e87681.10.1371/journal.pone.0087681CrossRefGoogle ScholarPubMed
Hindmarsh, A.C. & Petzold, L.R. 1995 Algorithms and software for ordinary differential equations and differential-algebraic equations, part ii: higher-order methods and software packages. Comput. Phys. 9 (2), 148–155.10.1063/1.168540CrossRefGoogle Scholar
Ireland, P.J., Vaithianathan, T., Sukheswalla, P.S., Ray, B. & Collins, L.R. 2013 Highly parallel particle-laden flow solver for turbulence research. Comput. Fluids 76, 170–177.10.1016/j.compfluid.2013.01.020CrossRefGoogle Scholar
Jensen, O.E. 1997 The thin liquid lining of a weakly curved cylindrical tube. J. Fluid Mech. 331, 373–403.10.1017/S0022112096004120CrossRefGoogle Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M.G. 2012 Falling Liquid Films. Springer.10.1007/978-1-84882-367-9CrossRefGoogle Scholar
Keeler, J.A., Patki, A., Woodard, C.R. & Frank-Ito, D.O. 2016 A computational study of nasal spray deposition pattern in four ethnic groups. J. Aerosol. Med. Pulmonary Drug Deliv. 29 (2), 153–166.10.1089/jamp.2014.1205CrossRefGoogle ScholarPubMed
Kim, C.S., Abraham, W.M., Chapman, G.A. & Sackner, M.A. 1985 Influence of two-phase gas–liquid interaction on aerosol deposition in airways. Am. Rev. Respir. Dis. 131 (4), 618–623.10.1164/arrd.1985.131.4.618CrossRefGoogle ScholarPubMed
Kim, C.S. & Eldridge, M.A. 1985 Aerosol deposition in the airway model with excessive mucus secretions. J. Appl. Physiol. 59 (6), 1766–1772.10.1152/jappl.1985.59.6.1766CrossRefGoogle ScholarPubMed
Kleinstreuer, C. & Zhang, Z. 2010 Airflow and particle transport in the human respiratory system. Annu. Rev. Fluid Mech. 42, 301–334.10.1146/annurev-fluid-121108-145453CrossRefGoogle Scholar
Knowles, M.R. & Boucher, R.C. 2002 Mucus clearance as a primary innate defense mechanism for mammalian airways. J. Clin. Invest. 109 (5), 571–577.10.1172/JCI0215217CrossRefGoogle ScholarPubMed
Kumar, P., Jutur, P., Roy, A. & Panchagnula, M. 2024 Evidence of chaotic mixing in the alveolar region of the lung. arXiv:2403.13917.Google Scholar
Lansley, A.B. 1993 Mucociliary clearance and drug delivery via the respiratory tract. Adv. Drug Deliv. Rev. 11 (3), 299–327.10.1016/0169-409X(93)90014-UCrossRefGoogle Scholar
Lauga, E. 2020 Locomotion and Transport in Complex Fluids. Cambridge University Press.10.1017/9781316796047.019CrossRefGoogle Scholar
Levy, R., Hill, D.B., Forest, M.G. & Grotberg, J.B. 2014 Pulmonary fluid flow challenges for experimental and mathematical modeling. Integr. Compar. Biol. 54, 985–1000.10.1093/icb/icu107CrossRefGoogle ScholarPubMed
Li, A. & Ahmadi, G. 1995 Computer simulation of particle deposition in the upper tracheobronchial tree. Aerosol Sci. Tech. 23 (2), 201–223.10.1080/02786829508965304CrossRefGoogle Scholar
Lin, C.L., Tawhai, M.H., McLennan, G. & Hoffman, E.A. 2007 Characteristics of the turbulent laryngeal jet and its effect on airflow in the human intra-thoracic airways. Respir. Physiol. Neurobiol. 157 (2), 295–309.10.1016/j.resp.2007.02.006CrossRefGoogle ScholarPubMed
Lister, J.R., Rallison, J.M., King, A.A., Cummings, L.J. & Jensen, O.E. 2006 Capillary drainage of an annular film: the dynamics of collars and lobes. J. Fluid Mech. 552, 311–343.10.1017/S0022112006008822CrossRefGoogle Scholar
Liu, C., Xue, C., Sun, J. & Hu, G. 2016 A generalized formula for inertial lift on a sphere in microchannels. Lab on a Chip 16, 884–892.10.1039/C5LC01522GCrossRefGoogle ScholarPubMed
Manolidis, M., Isabey, D., Louis, B., Grotberg, J.B. & Filoche, M. 2016 A macroscopic model for simulating the mucociliary clearance in a bronchial bifurcation: the role of surface tension. J. Biomech. Engng 138 (12), 121005.10.1115/1.4034507CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.10.1017/S0022112087000193CrossRefGoogle Scholar
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.10.1063/1.864230CrossRefGoogle Scholar
Meurer, A. et al. 2017 SymPy: symbolic computing in Python. PeerJ Comput. Sci. 3, e103.10.7717/peerj-cs.103CrossRefGoogle Scholar
Mitran, S.M. 2007 Metachronal wave formation in a model of pulmonary cilia. Comput. Struct. 85 (11–14), 763–774.10.1016/j.compstruc.2007.01.015CrossRefGoogle Scholar
Mittal, R., Ni, R. & Seo, J.H. 2020 The flow physics of Covid-19. J. Fluid Mech. 894.10.1017/jfm.2020.330CrossRefGoogle Scholar
Morawska, L., Buonanno, G., Mikszewski, A. & Stabile, L. 2022 The physics of respiratory particle generation, fate in the air, and inhalation. Nat. Rev. Phys. 4 (11), 723–734.10.1038/s42254-022-00506-7CrossRefGoogle ScholarPubMed
Oldenburg, A.L., Chhetri, R.K., Hill, D.B. & Button, B. 2012 Monitoring airway mucus flow and ciliary activity with optical coherence tomography. Biomed. Opt. Express 3 (9), 1978–1992.10.1364/BOE.3.001978CrossRefGoogle Scholar
Oron, A., Davis, S.H. & Bankoff, S.G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931.10.1103/RevModPhys.69.931CrossRefGoogle Scholar
Öttinger, H.C. 1996 Stochastic Processes in Polymeric Fluids. Springer.10.1007/978-3-642-58290-5CrossRefGoogle Scholar
Pedley, T.J. 1977 Pulmonary fluid dynamics. Annu. Rev. Fluid Mech. 9 (1), 229–274.10.1146/annurev.fl.09.010177.001305CrossRefGoogle Scholar
Pednekar, D.D., Liguori, M.A., Marques, C.N.H., Zhang, T., Zhang, N., Zhou, Z., Amoako, K. & Gu, H. 2022 From static to dynamic: a review on the role of mucus heterogeneity in particle and microbial transport. ACS Biomater. Sci. Engng 8 (7), 2825–2848.10.1021/acsbiomaterials.2c00182CrossRefGoogle ScholarPubMed
Picardo, J.R. & Narayanan, R. 2017 Interfacial pattern selection in defiance of linear growth. J. Fluid Mech. 829, 345–363.10.1017/jfm.2017.545CrossRefGoogle Scholar
Quek, Y.L.R., Lim, K.M. & Chiam, K.H. 2018 Three-dimensional computational model of multiphase flow driven by a bed of active cilia. Comput. Fluids 170, 222–235.10.1016/j.compfluid.2018.05.001CrossRefGoogle Scholar
Rahimi-Gorji, M., Pourmehran, O., Gorji-Bandpy, M. & Gorji, T.B. 2015 CFD simulation of airflow behavior and particle transport and deposition in different breathing conditions through the realistic model of human airways. J. Mol. Liquids 209, 121–133.10.1016/j.molliq.2015.05.031CrossRefGoogle Scholar
Randell, S.H. & Boucher, R.C. 2006 Effective mucus clearance is essential for respiratory health. Am. J. Respir. Cell Mol. Biol. 35 (1), 20–28.10.1165/rcmb.2006-0082SFCrossRefGoogle ScholarPubMed
Ravichandran, S., Deepu, P. & Govindarajan, R. 2017 Clustering of heavy particles in vortical flows: a selective review. Sādhanā 42 (4), 597–605.10.1007/s12046-017-0621-0CrossRefGoogle Scholar
Ravichandran, S., Picardo, J.R., Ray, S.S. & Govindarajan, R. 2020 Fluid Dynamics in Clouds. Springer, 1–23.Google Scholar
Rayleigh, L. 1892 On the instability of cylindrical fluid surfaces. Phil. Mag. 34 (207), 177–180.10.1080/14786449208620304CrossRefGoogle Scholar
Rogers, D.F. 2004 Airway mucus hypersecretion in asthma: an undervalued pathology? Curr. Opin. Pharmacol. 4 (3), 241–250.10.1016/j.coph.2004.01.011CrossRefGoogle ScholarPubMed
Romanò, F., Fujioka, H., Muradoglu, M. & Grotberg, J.B. 2019 Liquid plug formation in an airway closure model. Phys. Rev. Fluids 4, 093103.10.1103/PhysRevFluids.4.093103CrossRefGoogle Scholar
Romanò, F., Muradoglu, M., Fujioka, H. & Grotberg, J.B. 2021 The effect of viscoelasticity in an airway closure model. J. Fluid Mech. 913, A31.10.1017/jfm.2020.1162CrossRefGoogle Scholar
Romanò, F., Muradoglu, M. & Grotberg, J.B. 2022 Effect of surfactant in an airway closure model. Phys. Rev. Fluids 7 (9), 093103.10.1103/PhysRevFluids.7.093103CrossRefGoogle Scholar
Ruyer-Quil, C., Bresch, D., Gisclon, M., Richard, G.L., Kessar, M. & Cellier, N. 2023 Sliding and merging of strongly sheared droplets. J. Fluid Mech. 972, A40.10.1017/jfm.2023.726CrossRefGoogle Scholar
Sedaghat, M.H., Shahmardan, M.M., Norouzi, M., Jayathilake, P.G. & Nazari, M. 2016 Numerical simulation of muco-ciliary clearance: immersed boundary-lattice Boltzmann method. Comput. Fluids 131, 91–101.10.1016/j.compfluid.2016.03.015CrossRefGoogle Scholar
Singh, R.K., Picardo, J.R. & Ray, S.S. 2022 Sedimenting elastic filaments in turbulent flows. Phys. Rev. Fluids 7, 084502.10.1103/PhysRevFluids.7.084502CrossRefGoogle Scholar
Sleigh, M.A., Blake, J.R. & Liron, N. 1988 The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 137 (3), 726–741.10.1164/ajrccm/137.3.726CrossRefGoogle ScholarPubMed
Smith, D.J. 2018 Biological fluid mechanics under the microscope: a tribute to John Blake. ANZIAM J. 59 (4), 416–442.Google Scholar
Smith, D.J., Gaffney, E.A. & Blake, J.R. 2007
a Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid. Bull. Math. Biol. 69, 1477–1510.10.1007/s11538-006-9172-yCrossRefGoogle Scholar
Smith, D.J., Gaffney, E.A. & Blake, J.R. 2007
b A model of tracer transport in airway surface liquid. Bull. Math. Biol. 69 (3), 817–836.10.1007/s11538-006-9163-zCrossRefGoogle Scholar
Smith, D.J., Gaffney, E.A. & Blake, J.R. 2007
c A viscoelastic traction layer model of muco-ciliary transport. Bull. Math. Biol. 69 (1), 289–327.10.1007/s11538-006-9177-6CrossRefGoogle ScholarPubMed
Smith, D.J., Gaffney, E.A. & Blake, J.R. 2008 Modelling mucociliary clearance. Respir. Physiol. Neurobiol. 163 (1-3), 178–188.10.1016/j.resp.2008.03.006CrossRefGoogle ScholarPubMed
Smith, D.J., Gaffney, E.A. & Blake, J.R. 2009 Mathematical modelling of cilia-driven transport of biological fluids. Proc. R. Soc. Lond. A. 465 (2108), 2417–2439.Google Scholar
Spungin, B. & Silberberg, A. 1984 Stimulation of mucus secretion, ciliary activity, and transport in frog palate epithelium. Am. J. Physiol. Cell Physiol. 247 (5), C299–C308.10.1152/ajpcell.1984.247.5.C299CrossRefGoogle ScholarPubMed
Tsuda, A., Filipovic, N., Haberthür, D., Dickie, R., Matsui, Y., Stampanoni, M. & Schittny, J.C. 2008 Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography. J. Appl. Physiol. 105 (3), 964–976.10.1152/japplphysiol.90546.2008CrossRefGoogle ScholarPubMed
Tsuda, A., Henry, F.S. & Butler, J.P. 2013 Particle transport and deposition: basic physics of particle kinetics. Compar. Physiol. 3 (4), 1437.10.1002/j.2040-4603.2013.tb00526.xCrossRefGoogle ScholarPubMed
Tsuda, A., Laine-Pearson, F.E. & Hydon, P.E. 2011 Why chaotic mixing of particles is inevitable in the deep lung. J. Theor. Biol. 286, 57–66.10.1016/j.jtbi.2011.06.038CrossRefGoogle ScholarPubMed
Tsuda, A., Rogers, R.A., Hydon, P.E. & Butler, J.P. 2002 Chaotic mixing deep in the lung. Proc. Natl Acad. Sci. 99 (15), 10173–10178.10.1073/pnas.102318299CrossRefGoogle ScholarPubMed
Vanaki, S.M., Holmes, D., Saha, S.C., Chen, J., Brown, R.J. & Jayathilake, P.G. 2020 Muco-ciliary clearance: a review of modelling techniques. J. Biomech. 99, 109578.10.1016/j.jbiomech.2019.109578CrossRefGoogle Scholar
Vasquez, P.A., Jin, Y., Palmer, E., Hill, D. & Forest, M.G. 2016 Modeling and simulation of mucus flow in human bronchial epithelial cell cultures–part i: idealized axisymmetric swirling flow. PLoS Comput. Biol. 12 (8), e1004872.10.1371/journal.pcbi.1004872CrossRefGoogle Scholar
Virtanen, P. et al. 2020 SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272.10.1038/s41592-019-0686-2CrossRefGoogle ScholarPubMed
Wang, S.M., Inthavong, K., Wen, J., Tu, J.Y. & Xue, C.L. 2009 Comparison of micron- and nanoparticle deposition patterns in a realistic human nasal cavity. Respir. Physiol. Neurobiol. 166 (3), 142–151.10.1016/j.resp.2009.02.014CrossRefGoogle Scholar
Weibel, E.R., Cournand, A.F. & Richards, D.W. 1963 Morphometry of the Human Lung. vol. 1. Springer.10.1007/978-3-642-87553-3CrossRefGoogle Scholar
Weichenthal, S. 2012 Selected physiological effects of ultrafine particles in acute cardiovascular morbidity. Environ. Res. 115, 26–36.10.1016/j.envres.2012.03.001CrossRefGoogle ScholarPubMed
Williams, D.M. & Rubin, B.K. 2018 Clinical pharmacology of bronchodilator medications. Respir. Care 63 (6), 641–654.10.4187/respcare.06051CrossRefGoogle ScholarPubMed
Zhang, Z., Kleinstreuer, C. & Kim, C.S. 2002 Micro-particle transport and deposition in a human oral airway model. J. Aerosol Sci. 33 (12), 1635–1652.10.1016/S0021-8502(02)00122-2CrossRefGoogle Scholar
Hazra and Picardo supplementary movie 1
Animation of the motion of small diffusive particles ($Pe = 2 x 10^4, St = 9 x 10^{-7}$), in an airway with a mucus film of initial thickness 0.115 times the airway radius.
File
9.8 MB
Hazra and Picardo supplementary movie 2
Animation of the motion of intermediate tracer-like particles ($Pe = 9 x 10^5, St = 2 x 10^{-3}$), in an airway with a mucus film of initial thickness 0.115 times the airway radius.
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8.3 MB
Hazra and Picardo supplementary movie 3
Animation of the motion of larger, heavy, inertial particles ($Pe = 9 x 10^6, St = 2 x 10^{-1}$), in an airway with a mucus film of initial thickness 0.115 times the airway radius.
File
8.6 MB
Hazra and Picardo supplementary material 4
Hazra and Picardo supplementary material 4
File
3.6 MB