The Motion and Deposition of Small Particles in the Human Lung Acinus, Part B: Weibel’s Model of Bifurcating Airways

Authors

  • Yakir Vanunu Israel Institute of Technology
  • Shimon Haber Israel Institute of Technology

DOI:

https://doi.org/10.14738/bjhmr.103.14765

Abstract

Weibel’s model A for the human lung is applied in which the lung comprises a binary bifurcating tree of 23 generations of airways. It assumes that each airway bifurcates into two airways their sizes defined by the generation number. The goal of this analysis is to predict deposition efficiencies of various size particles which reach the human acinus vis-a-vis generation number, a result that can be used in designing inhaled therapeutical particles or preventing dangerous substances like Covid 19 of reaching the blood stream. The simulations account for particle convection, the effects of gravity and Brownian motion. Applying ANSYS Fluent, a commercial program which includes a two-phase model for finite volumes, it is found that particle diameters within the range (0.4 ¸ 1.0 mm) and densities as low as 500 kg/m3 reach deep into the human lung acinus and are likely to reach the blood stream. Particles of higher densities and diameters outside the foregoing range deposit at lower branches of the acinar tree, the smaller particles due to dominant diffusion and the bigger due to gravity.

References

ANSYS Inc., (2013) ANSYS Fluent User's Guide, Southpointe, 275 Technology Drive, Canonsburg, PA 15317, U.S.A, Release 15.0.

ANSYS Inc., (2017). ANSYS Fluent Tutorial Guide, Southpointe, 2600 ANSYS Drive, Canonsburg, PA 15317, U.S.A, Release 18.0.

Bachofen H and Weibel ER. (1977). Structural alterations of lung parenchyma in the aging human lung: a morphometric study. J Appl Physiol 43(6): 1189–1197.

Cardoso WV and Lü J. (2006). Regulation of early lung morphogenesis: questions, facts and controversies. Development 133: 1611-1624

Geiser M and Kreyling WG. (2010). Deposition and biokinetics of inhaled nanoparticles. Part Fibre Toxicol 14: 7-12.

Elder A, Gelein R, Finkelstein JN, Cox C and Oberdörster G. (2000). Pulmonary inflammatory response to inhaled ultrafine particles is modified by age, ozone exposure, and bacterial toxin. Inhal Toxicol 3: 227-246.

Ensor DS. (2011). Aerosol Science and Technology: History and Reviews. 27709 - 2194.

Gehr P, Heyder J and Rittinghausen S. (1992). The lung as a passive filter in inhalation of environmental particles. Exp Lung Res 18(2): 151-62.

Gehr P, Bachofen M and Weibel ER. (1978). The normal human lung: ultrastructure and morphometric estimation of diffusion capacity. Respir Physiol 32(2): 121-140.

Goldberg IS, Lam KY, Bernstein B and Hutchens JO. (1977). Solutions to the Fokker- Planck equations governing simultaneous diffusion and gravitational settling of aerosol particles from a stationary gas in a horizontal circular tube. J Aerosol Sci 9(3): 209-218.

Goldberg IS. (1980). Deposition of aerosol particles due to simultaneous diffusion and gravitational sedimentation within a spherical chamber – solutions to the fokker- planck equations, J Aerosol Sci 12(1): 11-14.

Goldberg IS. (1980). A correction to the small-time approximation of diffusive deposition from a uniform initial concentration of particles in a circular tube with adsorbing walls", J Aerosol Sci 12(1): 15-17.

Haber S, Butler JP, Brenner H, Emanuel I and Tsuda A. (2000). Flow field in self-similar expansion on a pulmonary alveolus during rhythmical breathing. J Fluid Mech 405: 243- 268.

Haber S, Yitzhak D and Tsuda A. (2003). Gravitational deposition in a rhythmically expanding and contracting alveolus. J Appl. Physiol 95: 657-671, 2003.

Haber S, Itzhak D and Tsuda A. (2010). The effect of alveoli rhythmical expansion on trajectories and deposition sites of aerosols in the acinar region. Part II: Spherical particles in a gravity-free environment. J Aerosol Medicine and Pulmonary Drug Delivery 10: 1089.

Hinds WC. (1999). Aerosol Technology – properties, behavior and measurement of airborne particles. Department of environmental health sciences, Center for occupational and environmental health, UCLA School of Public Health, Los Angeles, California.

Horsfield K and Cummings G. (1968). Morphology of the Bronchial tree in man. J Appl Physiol 24: 373-383.

Hofemeier P and Sznitman J. (2015), Revisiting pulmonary acinar particle transport: convection, sedimentation, diffusion, and their interplay. J Appl Physiol 118: 1375– 1385.

Hofemeier P, Koshiyama K, Wada S, Sznitman J. (2017). One (sub-) acinus for all: Fate of inhaled aerosols in heterogeneous pulmonary acinar structures, Euro J Pharma Sci 560: 8531, Japan.

Hsia CCW, Hyde DM, Ochs M and Weibel ER. (2010). An official research policy statement of the American Thoracic Society/European Respiratory Society: standards for quantitative assessment of lung structure. American Journal of Respiratory and Critical Care Medicine 181(4): 394–418.

Kawanami O, Basset F, Ferrans VJ, Soler P, Crystal RG. (1981). Pulmonary Langerhans’ cells in patients with Fibrotic Lung Disorders. Lab Invest 44(3): 227-237.

Koullapis PG, Stylianou FS, Sznitman J, Olsson B, Kassinos SC. (2020). Towards whole- lung simulations of aerosol deposition: A model of the deep lung. J Aerosol Sci 144: 105541.

Kreyling WG, Semmler-Behnke M and Möller W. (2006). Ultrafine particle-lung interactions: does size matter? J Aerosol Med 19(1): 74-83. 255

Lutchen KR and Gillis H. (1997). Relationship between heterogeneous changes in airway morphometry and lung resistance and elastance. J Appl Physiol 83(4): 1192– 1201.

Miura T, (2015) Models of lung branching morphogenesis, JB Review – Mathematical Modeling of Cell Behaviors during Morphogenesis. J of Biochemistry, 157(3):121–127.

Möller W, Felten K, Sommerer K, Scheuch G, Meyer G and Meyer P. (2008). Deposition, retention, and translocation of ultrafine particles from the central airways and lung periphery. Am J Respir Crit Care Med 177(8): 867-876.

Nowak N, Kakade PP and Annaprazada AV. (2003). Computational fluid dynamics simulation of airflow and aerosol deposition in human lungs. Ann Biomed Eng 31: 374- 390.

Oberdörster G, Oberdörster E and Oberdörster J. (2005). Nanotoxicology: an emerging discipline evolving from studies of ultrafine particles. Environ Health Perspect 113(7): 823- 839.

Phalen RF, Yeh HC, Schum GM and Raabe OG. (1978). Application of an idealized model to morphometry of the mammalian tracheobronchial tree. Anat Rec 190: 167- 176.

Sofialidis D, (2013) Using the Discrete Phase Model (DPM) in ANSYS Fluent, PRACE Autumn School –Industry Oriented HPC Simulations, University of Ljubljana, Faculty of Mechanical Engineering.

Tawhai MH and Hunter PJ. (2001). Multibreath washout analysis: Modeling influence of conducting airway asymmetry. Resp Physiol 127: 249-258.

Tawhai MH, Pullan AJ and Hunter PJ. (2000). Generation of an anatomically based three-dimensional model of the conducting airways. Ann Biomed Eng 28: 793-802.

Tschanz SA, Burri PH and Weibel ER. (2011). A simple tool for stereological assessment of digital images: the STEPanizer. J Microscopy 243(1): 47–59.

Tsuda A, Henry FS, James P. Butler JP. (2008) Gas and aerosol mixing in the acinus, Respiratory Physiology & Neurobiology, ELSEVIER journal, Molecular and Integrative Physiological Sciences, Harvard School of Public Health.

Tsuda A, Henry FS, Butler JP. (2013). Particle Transport and Deposition: Basic Physics of Particle Kinetics. Comprehensive Physiology 3: 1437‐1471.

Vanunu Y and Haber S. (2023). The motion and deposition of small particles in the human lung acinus. Part A: Micron size, infinitely long airway. Submitted to J Appl Physiol.

Varnera VD, Nelson CM. (2016). Computational models of airway branching morphogenesis, Seminars in Cell & Developmental Biology, ELSEVIER journal, Department of Chemical & Biological Engineering and Department of Molecular Biology, Princeton University.

Vockeroth DW, Haverkamp HC, O’Brien KJ, Nieman GF and Perchiazzi G. (2008). Alveolar dynamics during mechanical ventilation in an acute lung injury model. Ann of Biomedical Engng, 36(4): 584–595.

Weibel ER. (1963). Morphometry of the Human Lung. New England Journal of Medicine, 269(21) 1136–1141.

Weibel ER. (1984). The pathway for oxygen, structure and function in the mammalian respiratory system. Cambridge MA, Harvard University Press.

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Published

2023-06-03

How to Cite

Vanunu, Y., & Haber, S. (2023). The Motion and Deposition of Small Particles in the Human Lung Acinus, Part B: Weibel’s Model of Bifurcating Airways. British Journal of Healthcare and Medical Research, 10(3), 223–256. https://doi.org/10.14738/bjhmr.103.14765