Search Advanced

Mathematical Biosciences and Engineering

2015, Volume 12, Issue 5: 1107-1126. doi: 10.3934/mbe.2015.12.1107
Previous Article Next Article

Cilium height difference between strokes is more effective in driving fluid transport in mucociliary clearance: A numerical study

  • 1.
    Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556
  • 2.
    Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303
  • Mucociliary clearance is the first line of defense in our airway. The purpose of this study is to identify and study key factors in the cilia motion that influence the transport ability of the mucociliary system. Using a rod-propel-fluid model, we examine the effects of cilia density, beating frequency, metachronal wavelength, and the extending height of the beating cilia. We first verify that asymmetry in the cilia motion is key to developing transport in the mucus flow. Next, two types of asymmetries between the effective and recovery strokes of the cilia motion are considered, the cilium beating velocity difference and the cilium height difference. We show that the cilium height difference is more efficient in driving the transport, and the more bend the cilium during the recovery stroke is, the more effective the transport would be. It is found that the transport capacity of the mucociliary system increases with cilia density and cilia beating frequency, but saturates above by a threshold value in both density and frequency. The metachronal wave that results from the phase lag among cilia does not contribute much to the mucus transport, which is consistent with the experimental observation of Sleigh (1989). We also test the effect of mucus viscosity, whose value is found to be inversely proportional to the transport ability. While multiple parts have to interplay and coordinate to allow for most effective mucociliary clearance, our findings from a simple model move us closer to understanding the effects of the cilia motion on the efficiency of this clearance system.

    Citation: Ling Xu, Yi Jiang. Cilium height difference between strokes is more effective in driving fluid transport in mucociliary clearance: A numerical study[J]. Mathematical Biosciences and Engineering, 2015, 12(5): 1107-1126. doi: 10.3934/mbe.2015.12.1107

    Related Papers:

    [1] Nerion Zekaj, Shawn D. Ryan, Andrew Resnick . Fluid-structure interaction modelling of neighboring tubes with primary cilium analysis. Mathematical Biosciences and Engineering, 2023, 20(2): 3677-3699. doi: 10.3934/mbe.2023172
    [2] Zhangli Peng, Andrew Resnick, Y.-N. Young . Primary cilium: a paradigm for integrating mathematical modeling with experiments and numerical simulations in mechanobiology. Mathematical Biosciences and Engineering, 2021, 18(2): 1215-1237. doi: 10.3934/mbe.2021066
    [3] Alex Viguerie, Sangita Swapnasrita, Alessandro Veneziani, Aurélie Carlier . A multi-domain shear-stress dependent diffusive model of cell transport-aided dialysis: analysis and simulation. Mathematical Biosciences and Engineering, 2021, 18(6): 8188-8200. doi: 10.3934/mbe.2021406
    [4] Benchawan Wiwatanapataphee, Yong Hong Wu, Thanongchai Siriapisith, Buraskorn Nuntadilok . Effect of branchings on blood flow in the system of human coronary arteries. Mathematical Biosciences and Engineering, 2012, 9(1): 199-214. doi: 10.3934/mbe.2012.9.199
    [5] Youcef Mammeri, Damien Sellier . A surface model of nonlinear, non-steady-state phloem transport. Mathematical Biosciences and Engineering, 2017, 14(4): 1055-1069. doi: 10.3934/mbe.2017055
    [6] Guohui Zhang, Jinghe Sun, Xing Liu, Guodong Wang, Yangyang Yang . Solving flexible job shop scheduling problems with transportation time based on improved genetic algorithm. Mathematical Biosciences and Engineering, 2019, 16(3): 1334-1347. doi: 10.3934/mbe.2019065
    [7] Panagiotes A. Voltairas, Antonios Charalambopoulos, Dimitrios I. Fotiadis, Lambros K. Michalis . A quasi-lumped model for the peripheral distortion of the arterial pulse. Mathematical Biosciences and Engineering, 2012, 9(1): 175-198. doi: 10.3934/mbe.2012.9.175
    [8] B. Wiwatanapataphee, D. Poltem, Yong Hong Wu, Y. Lenbury . Simulation of Pulsatile Flow of Blood in Stenosed Coronary Artery Bypass with Graft. Mathematical Biosciences and Engineering, 2006, 3(2): 371-383. doi: 10.3934/mbe.2006.3.371
    [9] Kun Zhang, Hanping Hou, Zhiqiang Dong, Ziheng Liu . Research on integrated inventory transportation optimization of inbound logistics via a VMI-TPL model of an existing enterprise. Mathematical Biosciences and Engineering, 2023, 20(9): 16212-16235. doi: 10.3934/mbe.2023724
    [10] Sandesh Athni Hiremath, Christina Surulescu, Somayeh Jamali, Samantha Ames, Joachim W. Deitmer, Holger M. Becker . Modeling of pH regulation in tumor cells: Direct interaction between proton-coupled lactate transporters and cancer-associated carbonicanhydrase. Mathematical Biosciences and Engineering, 2019, 16(1): 320-337. doi: 10.3934/mbe.2019016
  • Mucociliary clearance is the first line of defense in our airway. The purpose of this study is to identify and study key factors in the cilia motion that influence the transport ability of the mucociliary system. Using a rod-propel-fluid model, we examine the effects of cilia density, beating frequency, metachronal wavelength, and the extending height of the beating cilia. We first verify that asymmetry in the cilia motion is key to developing transport in the mucus flow. Next, two types of asymmetries between the effective and recovery strokes of the cilia motion are considered, the cilium beating velocity difference and the cilium height difference. We show that the cilium height difference is more efficient in driving the transport, and the more bend the cilium during the recovery stroke is, the more effective the transport would be. It is found that the transport capacity of the mucociliary system increases with cilia density and cilia beating frequency, but saturates above by a threshold value in both density and frequency. The metachronal wave that results from the phase lag among cilia does not contribute much to the mucus transport, which is consistent with the experimental observation of Sleigh (1989). We also test the effect of mucus viscosity, whose value is found to be inversely proportional to the transport ability. While multiple parts have to interplay and coordinate to allow for most effective mucociliary clearance, our findings from a simple model move us closer to understanding the effects of the cilia motion on the efficiency of this clearance system.


    [1] Eur J Respir Dis Suppl., 128 (1983), 280-286.
    [2] Nature, 282 (1979), 717-720.
    [3] Bull Math Biophys., 29 (1967), 419-428.
    [4] Proc. Gamb. Phil. Soc., 70 (1971), 303-310.
    [5] J. Fluid Mech., 55 (1972), 1-23.
    [6] Science, 337 (2012), 937-941.
    [7] Respir Physiol Neurobiol., 163 (2008), 202-207.
    [8] J. Comput Phys., 168 (2001), 464-499.
    [9] Thorax, 55 (2000), 314-317.
    [10] J Allergy Clin Immunol., 112 (2003), 518-524.
    [11] Br Med Bull., 34 (1978), 25-27.
    [12] SIAM J. Sci. Comput., 23 (2001), 1204-1225.
    [13] Phys. Fluids, 17 (2005), 031504, 21pp.
    [14] Ann N Y Acad Sci., 1101 (2007), 494-505.
    [15] N. ENGL. J. MED., 354 (2006), 241-250.
    [16] PNAS, 110 (2013), 4470-4475.
    [17] J. Physiol., 388 (1987), 1-8.
    [18] J. Comput Phys., 77 (1988), 85-108.
    [19] Bull Math Biol., 67 (2005), 137-168.
    [20] J Appl Physiol Respir Environ Exerc Physiol., 48 (1980), 965-971.
    [21] Am Rev Respir Dis., 116 (1977), 281-286.
    [22] Cell Motil Cytoskeleton, 39 (1998), 9-20.
    [23] J. Comput Phys., 59 (1985), 308-323.
    [24] J Clin Invest., 109 (2002), 571-577.
    [25] J. Comput Phys., 160 (2000), 705-719.
    [26] PloS One, 4 (2009), e8157.
    [27] {SIAM}, 2007.
    [28] Toxicol Pathol, 35 (2007), 116-129.
    [29] Am Rev Respir Dis., 130 (1984), 497-498.
    [30] Cell Motility, 2 (1982), 35-39.
    [31] J Clin Invest., 102 (1998), 1125-1131.
    [32] CRC Press, 2001.
    [33] Comput Struct., 85 (2007), 763-774.
    [34] Am J Respir Crit Care Med, 169 (2004), 459-467.
    [35] J. Comput Phys., 25 (1977), 220-252.
    [36] AIP Conf. Proc., 28 (1976), p49.
    [37] PNAS, 74 (1977), 2045-2049.
    [38] J Cell Sci., 47 (1981), 331-347.
    [39] J Cell Biol., 26 (1965), 805-834.
    [40] Biol Cell, 103 (2011), 159-169.
    [41] Am J Physiol Lung Cell Mol Phyiol., 304 (2013), L170-L183.
    [42] Eur J Respir Dis. Suppl., 128 (1983), 287-292.
    [43] Comp Biochem Physiol A Comp Physiol., 94 (1989), 359-364.
    [44] Proc. R. Soc. Lond. A, 209(1951), 447-461.
    [45] J. Fluid Mech., 31 (1968), 305-308.
    [46] Ciliary and Flagellar Membranes, (Ed: Bloodgood RA) (1990), 363-388. Springer US.
    [47] Bull Math Biol., 70 (2008), 1192-1215.

  • This article has been cited by:

    1. Paul Macklin, Shannon Mumenthaler, John Lowengrub, 2013, Chapter 150, 978-3-642-36481-5, 349, 10.1007/8415_2012_150
    2. MunJu Kim, Damon Reed, Katarzyna A. Rejniak, The formation of tight tumor clusters affects the efficacy of cell cycle inhibitors: A hybrid model study, 2014, 352, 00225193, 31, 10.1016/j.jtbi.2014.02.027
    3. Patrícia Santos-Oliveira, António Correia, Tiago Rodrigues, Teresa M Ribeiro-Rodrigues, Paulo Matafome, Juan Carlos Rodríguez-Manzaneque, Raquel Seiça, Henrique Girão, Rui D. M. Travasso, Hans Van Oosterwyck, The Force at the Tip - Modelling Tension and Proliferation in Sprouting Angiogenesis, 2015, 11, 1553-7358, e1004436, 10.1371/journal.pcbi.1004436
    4. Gianluca Ascolani, Timothy M. Skerry, Damien Lacroix, Enrico Dall’Ara, Aban Shuaib, Revealing hidden information in osteoblast’s mechanotransduction through analysis of time patterns of critical events, 2020, 21, 1471-2105, 10.1186/s12859-020-3394-0
    5. Nick Štorgel, Matej Krajnc, Polona Mrak, Jasna Štrus, Primož Ziherl, Quantitative Morphology of Epithelial Folds, 2016, 110, 00063495, 269, 10.1016/j.bpj.2015.11.024
    6. Zuzanna Szymańska, Maciej Cytowski, Elaine Mitchell, Cicely K. Macnamara, Mark A. J. Chaplain, Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling, 2018, 80, 0092-8240, 1366, 10.1007/s11538-017-0292-3
    7. Paul Macklin, Hermann B. Frieboes, Jessica L. Sparks, Ahmadreza Ghaffarizadeh, Samuel H. Friedman, Edwin F. Juarez, Edmond Jonckheere, Shannon M. Mumenthaler, 2016, Chapter 12, 978-3-319-42021-9, 225, 10.1007/978-3-319-42023-3_12
    8. Stefan Hoehme, Adrian Friebel, Seddik Hammad, Dirk Drasdo, Jan G. Hengstler, 2017, Chapter 22, 978-1-4939-6504-5, 319, 10.1007/978-1-4939-6506-9_22
    9. P. Van Liedekerke, A. Buttenschön, D. Drasdo, 2018, 9780128117187, 245, 10.1016/B978-0-12-811718-7.00014-9
    10. Yafei Wang, Erik Brodin, Kenichiro Nishii, Hermann B. Frieboes, Shannon M. Mumenthaler, Jessica L. Sparks, Paul Macklin, Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach, 2021, 11, 2045-2322, 10.1038/s41598-020-78780-7
    11. Waseem Asghar, Rami El Assal, Hadi Shafiee, Sharon Pitteri, Ramasamy Paulmurugan, Utkan Demirci, Engineering cancer microenvironments for in vitro 3-D tumor models, 2015, 18, 13697021, 539, 10.1016/j.mattod.2015.05.002
    12. P. Van Liedekerke, M. M. Palm, N. Jagiella, D. Drasdo, Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results, 2015, 2, 2196-4378, 401, 10.1007/s40571-015-0082-3
    13. Annelies Lejon, Bert Mortier, Giovanni Samaey, Variance-Reduced Simulation of Multiscale Tumor Growth Modeling, 2017, 15, 1540-3459, 388, 10.1137/15M1043224
    14. H. L. Rocha, R. C. Almeida, E. A. B. F. Lima, A. C. M. Resende, J. T. Oden, T. E. Yankeelov, A hybrid three-scale model of tumor growth, 2018, 28, 0218-2025, 61, 10.1142/S0218202518500021
    15. Mark A. J. Chaplain, 2020, Chapter 7, 978-3-030-32856-6, 149, 10.1007/978-3-030-32857-3_7
    16. Chin F. Ng, Hermann B. Frieboes, Model of vascular desmoplastic multispecies tumor growth, 2017, 430, 00225193, 245, 10.1016/j.jtbi.2017.05.013
    17. Mohammad Soheilypour, Mohammad R. K. Mofrad, Agent‐Based Modeling in Molecular Systems Biology, 2018, 40, 0265-9247, 1800020, 10.1002/bies.201800020
    18. Andrés A. Barrea, Matias E. Hernández, Rubén Spies, Optimal chemotherapy schedules from tumor entropy, 2017, 36, 0101-8205, 991, 10.1007/s40314-015-0275-7
    19. Kelvin K.L. Wong, Three-dimensional discrete element method for the prediction of protoplasmic seepage through membrane in a biological cell, 2017, 65, 00219290, 115, 10.1016/j.jbiomech.2017.10.023
    20. Angela M. Jarrett, Ernesto A.B.F. Lima, David A. Hormuth, Matthew T. McKenna, Xinzeng Feng, David A. Ekrut, Anna Claudia M. Resende, Amy Brock, Thomas E. Yankeelov, Mathematical models of tumor cell proliferation: A review of the literature, 2018, 18, 1473-7140, 1271, 10.1080/14737140.2018.1527689
    21. Lee-Ling Sharon Ong, Justin Dauwels, H. Harry Asada, 2013, 2D data-driven stalk cell prediction model based on tip-stalk cell interaction in angiogenesis, 978-1-4577-0216-7, 4537, 10.1109/EMBC.2013.6610556
    22. J. Tinsley Oden, Ernesto A. B. F. Lima, Regina C. Almeida, Yusheng Feng, Marissa Nichole Rylander, David Fuentes, Danial Faghihi, Mohammad M. Rahman, Matthew DeWitt, Manasa Gadde, J. Cliff Zhou, Toward Predictive Multiscale Modeling of Vascular Tumor Growth, 2016, 23, 1134-3060, 735, 10.1007/s11831-015-9156-x
    23. Bing Wang, Fu Tan, Jia Zhu, Daijun Wei, A new structure entropy of complex networks based on nonextensive statistical mechanics and similarity of nodes, 2021, 18, 1551-0018, 3718, 10.3934/mbe.2021187
    24. A. Carrasco-Mantis, T. Alarcón, J.A. Sanz-Herrera, An in silico study on the influence of extracellular matrix mechanics on vasculogenesis, 2023, 231, 01692607, 107369, 10.1016/j.cmpb.2023.107369
    25. Cicely K. Macnamara, Biomechanical modelling of cancer: Agent‐based force‐based models of solid tumours within the context of the tumour microenvironment, 2021, 1, 2689-9655, 10.1002/cso2.1018
    26. Ernesto A. B. F. Lima, Danial Faghihi, Russell Philley, Jianchen Yang, John Virostko, Caleb M. Phillips, Thomas E. Yankeelov, Stacey Finley, Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth, 2021, 17, 1553-7358, e1008845, 10.1371/journal.pcbi.1008845
    27. Adrianne L. Jenner, Munisha Smalley, David Goldman, William F. Goins, Charles S. Cobbs, Ralph B. Puchalski, E. Antonio Chiocca, Sean Lawler, Paul Macklin, Aaron Goldman, Morgan Craig, Agent-based computational modeling of glioblastoma predicts that stromal density is central to oncolytic virus efficacy, 2022, 25, 25890042, 104395, 10.1016/j.isci.2022.104395
    28. Nina Verstraete, Malvina Marku, Marcin Domagala, Hélène Arduin, Julie Bordenave, Jean-Jacques Fournié, Loïc Ysebaert, Mary Poupot, Vera Pancaldi, An agent-based model of monocyte differentiation into tumour-associated macrophages in chronic lymphocytic leukemia, 2023, 26, 25890042, 106897, 10.1016/j.isci.2023.106897
    29. Heber L. Rocha, Boris Aguilar, Michael Getz, Ilya Shmulevich, Paul Macklin, A multiscale model of immune surveillance in micrometastases gives insights on cancer patient digital twins, 2024, 10, 2056-7189, 10.1038/s41540-024-00472-z
  • Reader Comments
  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2432) PDF downloads(446) Cited by(6)

Preview PDF
Download XML
Export Citation
Article outline
Abstract
References

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog