title: Pulmonary fluid flow challenges for experimental and mathematical modeling.
abstract: Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make.
authors.affiliation: *Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA; The Marsico Lung Institute, Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; Department of Mathematics, Department of Biomedical Engineering, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; NASA Bioscience and Engineering Institute, The University of Michigan, Ann Arbor, MI 48109, USA levy@hmc.edu.
authors.forename: Rachel
authors.initials: R
authors.lastname: Levy
authors.affiliation: *Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA; The Marsico Lung Institute, Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; Department of Mathematics, Department of Biomedical Engineering, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; NASA Bioscience and Engineering Institute, The University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: David B
authors.initials: DB
authors.lastname: Hill
authors.affiliation: *Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA; The Marsico Lung Institute, Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; Department of Mathematics, Department of Biomedical Engineering, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; NASA Bioscience and Engineering Institute, The University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: M Gregory
authors.initials: MG
authors.lastname: Forest
authors.affiliation: *Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA; The Marsico Lung Institute, Department of Physics and Astronomy, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; Department of Mathematics, Department of Biomedical Engineering, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA; NASA Bioscience and Engineering Institute, The University of Michigan, Ann Arbor, MI 48109, USA.
authors.forename: James B
authors.initials: JB
authors.lastname: Grotberg
mesh_terms: D015633:Extravascular Lung Water / Q000737:chemistry*; D006801:Humans; D057446:Hydrodynamics; D008168:Lung / Q000502:physiology*; D008954:Models, Biological; D012212:Rheology / Q000379:methods*
references.citation: J Rheol (N Y N Y). 2013;57:1247
references.pmid: 24526800
references.citation: Eur J Respir Dis Suppl. 1987;153:159-64
references.pmid: 3480812
references.citation: Science. 1962 Aug 24;137(3530):577-85
references.pmid: 14005590
references.citation: J Exp Biol. 1972 Apr;56(2):459-67
references.pmid: 5022843
references.citation: Biochem J. 1991 Jun 15;276 ( Pt 3):677-82
references.pmid: 2064606
references.citation: J Biomech Eng. 1989 Nov;111(4):288-97
references.pmid: 2486367
references.citation: Respir Physiol. 1969 Dec;8(1):58-65
references.pmid: 5366416
references.citation: Annu Rev Biomed Eng. 2001;3:421-57
references.pmid: 11447070
references.citation: Adv Drug Deliv Rev. 2009 Feb 27;61(2):86-100
references.pmid: 19166889
references.citation: Biorheology. 1983;20(2):239-49
references.pmid: 6871438
references.citation: PLoS One. 2014 Feb 18;9(2):e87681
references.pmid: 24558372
references.citation: J Appl Physiol. 1974 Sep;37(3):447-51
references.pmid: 4415628
references.citation: Biochem J. 2002 Feb 1;361(Pt 3):537-46
references.pmid: 11802783
references.citation: Phys Fluids (1994). 2010 Jan;22(1):11901
references.pmid: 20157445
references.citation: J Pediatr. 1998 Oct;133(4):509-12
references.pmid: 9787688
references.citation: Phys Fluids (1994). 2009 Jul;21(7):71903
references.pmid: 19704915
references.citation: J Biomech Eng. 2006 Oct;128(5):707-16
references.pmid: 16995757
references.citation: J Clin Invest. 1998 Sep 15;102(6):1125-31
references.pmid: 9739046
references.citation: Macromolecules. 1993;26(4):852-5
references.pmid: 11537900
references.citation: Proc Natl Acad Sci U S A. 2006 Nov 28;103(48):18131-6
references.pmid: 17116883
references.citation: Am J Respir Cell Mol Biol. 2006 May;34(5):527-36
references.pmid: 16415249
references.citation: Respir Physiol Neurobiol. 2008 Nov 30;163(1-3):178-88
references.pmid: 18439882
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066305
references.pmid: 23368036
references.citation: J Immunol. 2005 Jul 15;175(2):1090-9
references.pmid: 16002710
references.citation: J Appl Physiol (1985). 1999 Jul;87(1):415-27
references.pmid: 10409603
references.citation: Phys Fluids (1994). 2008 Jun;20(6):62104
references.pmid: 19547724
references.citation: Rep Prog Phys. 2016 Jul;79(7):074601
references.pmid: 27245584
references.citation: N Engl J Med. 2010 Dec 2;363(23):2233-47
references.pmid: 21121836
references.citation: J Appl Physiol (1985). 1994 Nov;77(5):2333-40
references.pmid: 7868452
references.citation: Am J Respir Crit Care Med. 2001 May;163(6):1470-5
references.pmid: 11371420
references.citation: J Biomech Eng. 1993 Aug;115(3):271-7
references.pmid: 8231142
references.citation: J Appl Physiol (1985). 1997 Jan;82(1):3-12
references.pmid: 9029192
references.citation: J Appl Physiol (1985). 1994 Jun;76(6):2627-35
references.pmid: 7928893
references.citation: Lab Chip. 2011 Feb 21;11(4):609-19
references.pmid: 21152526
references.citation: J Theor Biol. 1986 Aug 21;121(4):381-402
references.pmid: 3796001
references.citation: Biophys J. 2010 Jan 6;98(1):57-66
references.pmid: 20085719
references.citation: J Biomech. 1975 Jul;8(3-4):179-90
references.pmid: 1150686
references.citation: J Appl Physiol. 1972 Dec;33(6):711-4
references.pmid: 4643846
references.citation: Br J Dis Chest. 1970 Oct;64(4):185-91
references.pmid: 5499982
references.citation: Am J Respir Cell Mol Biol. 1999 Apr;20(4):605-11
references.pmid: 10100991
references.citation: Biorheology. 1981;18(3-6):659-66
references.pmid: 7326401
references.citation: Am Rev Respir Dis. 1988 Mar;137(3):726-41
references.pmid: 3278666
references.citation: Respir Physiol Neurobiol. 2008 Nov 30;163(1-3):222-31
references.pmid: 18585985
references.citation: Comput Struct. 2007;85(11-14):763-774
references.pmid: 19169426
references.citation: Am J Respir Crit Care Med. 1997 Jan;155(1):313-20
references.pmid: 9001330
references.citation: Respir Physiol. 1985 Sep;61(3):277-88
references.pmid: 4059687
references.citation: Proc Am Thorac Soc. 2007 Aug 1;4(4):399-405
references.pmid: 17652507
references.citation: AMA J Dis Child. 1959 May;97(5, Part 1):517-23
references.pmid: 13649082
references.citation: J Biomech Eng. 2005 Oct;127(5):798-806
references.pmid: 16248309
references.citation: N Engl J Med. 2004 Jun 24;350(26):2645-53
references.pmid: 15215480
references.citation: J Biomech Eng. 2004 Oct;126(5):567-77
references.pmid: 15648809
references.citation: Biochem J. 1987 Aug 1;245(3):757-62
references.pmid: 3663189
references.citation: Respir Physiol. 1989 Feb;75(2):141-56
references.pmid: 2711049
references.citation: Eur Respir J. 2004 Jan;23(1):146-58
references.pmid: 14738247
references.citation: J Biomech Eng. 1999 Oct;121(5):487-93
references.pmid: 10529915
references.citation: AJR Am J Roentgenol. 1984 May;142(5):903-6
references.pmid: 6609569
references.citation: J Appl Physiol (1985). 2003 Feb;94(2):770-83
references.pmid: 12433851
references.citation: Am J Physiol Lung Cell Mol Physiol. 2009 Jan;296(1):L92-L100
references.pmid: 18931053
references.citation: Respir Physiol Neurobiol. 2008 Nov 30;163(1-3):232-43
references.pmid: 18511356
references.citation: Am J Med. 2003 Jul;115(1):68-9
references.pmid: 12867239
references.citation: Biol Rev Camb Philos Soc. 1974 Feb;49(1):85-125
references.pmid: 4206625
references.citation: J Biomech Eng. 2001 Dec;123(6):580-9
references.pmid: 11783729
references.citation: J Appl Physiol (1985). 1991 Aug;71(2):742-8
references.pmid: 1938748
references.citation: Biophys J. 1992 Oct;63(4):1045-58
references.pmid: 19431847
references.citation: Am J Physiol Lung Cell Mol Physiol. 2009 Nov;297(5):L881-91
references.pmid: 19700641
references.citation: Biomed Microdevices. 2011 Aug;13(4):731-42
references.pmid: 21487664
references.citation: N Engl J Med. 2006 Jan 19;354(3):241-50
references.pmid: 16421365
references.citation: J Appl Physiol (1985). 1989 Dec;67(6):2389-96
references.pmid: 2606846
references.citation: J Appl Physiol (1985). 1999 Jan;86(1):391-410
references.pmid: 9887154
references.citation: Science. 2012 Aug 24;337(6097):937-41
references.pmid: 22923574
references.citation: Proc Natl Acad Sci U S A. 2007 Nov 27;104(48):18886-91
references.pmid: 18006663
references.citation: J Appl Physiol (1985). 1989 Jun;66(6):2511-5
references.pmid: 2745313
references.citation: Phys Fluids (1994). 2011 Feb;23(2):21301
references.pmid: 21403768
references.citation: Pulm Pharmacol Ther. 2006;19(2):96-100
references.pmid: 15970448
references.citation: J Appl Physiol (1985). 2007 Nov;103(5):1796-807
references.pmid: 17673567
references.citation: J Biol Chem. 2003 Dec 12;278(50):50393-401
references.pmid: 13679362
references.citation: Respir Physiol. 1970 Jan;8(2):191-203
references.pmid: 5413420
references.citation: J Appl Physiol (1985). 2002 Mar;92(3):949-56
references.pmid: 11842025
references.citation: Respir Physiol. 1978 Jan;32(1):91-104
references.pmid: 625614
references.citation: Bull Math Biol. 2007 Jan;69(1):289-327
references.pmid: 16804652
references.citation: Am J Respir Crit Care Med. 1998 Dec;158(6):1900-6
references.pmid: 9847284
references.citation: Chest. 1993 Feb;103(2):488-95
references.pmid: 8432142
references.citation: Clin Otolaryngol Allied Sci. 1998 Oct;23(5):403-13
references.pmid: 9800075
references.citation: J Appl Physiol (1985). 1997 Jan;82(1):233-9
references.pmid: 9029221
references.citation: J Lab Clin Med. 1978 Mar;91(3):423-31
references.pmid: 304876