0
Research Papers

Contributions of Kinetic Energy and Viscous Dissipation to Airway Resistance in Pulmonary Inspiratory and Expiratory Airflows in Successive Symmetric Airway Models With Various Bifurcation Angles

[+] Author and Article Information
Sanghun Choi

Department of Mechanical Engineering,
Kyungpook National University,
Daegu 41566, South Korea
e-mail: s-choi@knu.ac.kr

Jiwoong Choi

IIHR-Hydroscience & Engineering,
Iowa City, IA 52242;
Department of Mechanical and
Industrial Engineering,
The University of Iowa,
Iowa City, IA 52242
e-mail: jiwoong-choi@uiowa.edu

Ching-Long Lin

IIHR-Hydroscience & Engineering,
Iowa City, IA 52242;
Department of Mechanical and
Industrial Engineering,
3131 Seamans Center for the Engineering
Arts and Sciences Iowa City,
The University of Iowa,
Iowa City, IA 52242
e-mail: ching-long-lin@uiowa.edu

1Corresponding author.

Manuscript received April 27, 2017; final manuscript received September 26, 2017; published online November 9, 2017. Assoc. Editor: Alison Marsden.

J Biomech Eng 140(1), 011010 (Nov 09, 2017) (13 pages) Paper No: BIO-17-1180; doi: 10.1115/1.4038163 History: Received April 27, 2017; Revised September 26, 2017

The aim of this study was to investigate and quantify contributions of kinetic energy and viscous dissipation to airway resistance during inspiration and expiration at various flow rates in airway models of different bifurcation angles. We employed symmetric airway models up to the 20th generation with the following five different bifurcation angles at a tracheal flow rate of 20 L/min: 15 deg, 25 deg, 35 deg, 45 deg, and 55 deg. Thus, a total of ten computational fluid dynamics (CFD) simulations for both inspiration and expiration were conducted. Furthermore, we performed additional four simulations with tracheal flow rate values of 10 and 40 L/min for a bifurcation angle of 35 deg to study the effect of flow rate on inspiration and expiration. Using an energy balance equation, we quantified contributions of the pressure drop associated with kinetic energy and viscous dissipation. Kinetic energy was found to be a key variable that explained the differences in airway resistance on inspiration and expiration. The total pressure drop and airway resistance were larger during expiration than inspiration, whereas wall shear stress and viscous dissipation were larger during inspiration than expiration. The dimensional analysis demonstrated that the coefficients of kinetic energy and viscous dissipation were strongly correlated with generation number. In addition, the viscous dissipation coefficient was significantly correlated with bifurcation angle and tracheal flow rate. We performed multiple linear regressions to determine the coefficients of kinetic energy and viscous dissipation, which could be utilized to better estimate the pressure drop in broader ranges of successive bifurcation structures.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

West, J. B. , 2008, Respiratory Physiology: The Essentials, Lippincott Williams & Wilkins, Baltimore, MD.
Sorkness, R. L. , Bleecker, E. R. , Busse, W. W. , Calhoun, W. J. , Castro, M. , Chung, K. F. , Curran-Everett, D. , Erzurum, S. C. , Gaston, B. M. , Israel, E. , Jarjour, N. N. , Moore, W. C. , Peters, S. P. , Teague, W. G. , and Wenzel, S. E. , and for the National Heart Lung and Blood Institute's Severe Asthma Research Program, 2008, “ Lung Function in Adults With Stable but Severe Asthma: Air Trapping and Incomplete Reversal of Obstruction With Bronchodilation,” J. Appl. Physiol., 104(2), pp. 394–403. [CrossRef] [PubMed]
Make, B. J. , and Martinez, F. J. , 2008, “ Assessment of Patients With Chronic Obstructive Pulmonary Disease,” Proc. Am. Thorac. Soc., 5(9), pp. 884–890. [CrossRef] [PubMed]
Choi, S. , Hoffman, E. A. , Wenzel, S. E. , Castro, M. , Fain, S. B. , Jarjour, N. N. , Schiebler, M. L. , Chen, K. , and Lin, C. L. , 2015, “ Quantitative Assessment of Multiscale Structural and Functional Alterations in Asthmatic Populations,” J. Appl. Physiol., 118(10), pp. 1286–1298. [CrossRef] [PubMed]
Montaudon, M. , Lederlin, M. , Reich, S. , Begueret, H. , Tunon-de-Lara, J. M. , Marthan, R. , Berger, P. , and Laurent, F. , 2009, “ Bronchial Measurements in Patients With Asthma: Comparison of Quantitative Thin-Section CT Findings With Those in Healthy Subjects and Correlation With Pathologic Findings,” Radiology, 253(3), pp. 844–853. [CrossRef] [PubMed]
Choi, S. , Hoffman, E. A. , Wenzel, S. E. , Castro, M. , and Lin, C.-L. , 2014, “ Improved CT-Based Estimate of Pulmonary Gas Trapping Accounting for Scanner and Lung Volume Variations in a Multi-Center Study,” J. Appl. Physiol., 117(6), pp. 593–603. [CrossRef] [PubMed]
Busacker, A. , Newell , J. D., Jr. , Keefe, T. , Hoffman, E. A. , Granroth, J. C. , Castro, M. , Fain, S. , and Wenzel, S. , 2009, “ A Multivariate Analysis of Risk Factors for the Air-Trapping Asthmatic Phenotype as Measured by Quantitative CT Analysis,” Chest, 135(1), pp. 48–56. [CrossRef] [PubMed]
Pedley, T. J. , Schroter, R. C. , and Sudlow, M. F. , 1970, “ Energy Losses and Pressure Drop in Models of Human Airways,” Respir Physiol., 9(3), pp. 371–386. [CrossRef] [PubMed]
Pedley, T. J. , Schroter, R. C. , and Sudlow, M. F. , 1970, “ The Prediction of Pressure Drop and Variation of Resistance Within the Human Bronchial Airways,” Respir. Physiol., 9(3), pp. 387–405. [CrossRef] [PubMed]
Pedley, T. J. , Schroter, R. C. , and Sudlow, M. F. , 1971, “ Flow and Pressure Drop in Systems of Repeatedly Branching Tubes,” J. Fluid Mech., 46(2), pp. 365–383. [CrossRef]
Pedley, T. J. , Sudlow, M. F. , and Milic-Emili, J. , 1972, “ A Non-Linear Theory of the Distribution of Pulmonary Ventilation,” Respir. Physiol., 15(1), pp. 1–38. [CrossRef] [PubMed]
Pedley, T. J. , 1977, “ Pulmonary Fluid Dynamics,” Annu. Rev. Fluid Mech., 9(1), pp. 229–274. [CrossRef]
White, F. M. , 2011, Fluid Mechanics, McGraw-Hill, New York.
Hyatt, R. E. , and Wilcox, R. E. , 1963, “ The Pressure-Flow Relationships of the Intrathoracic Airway in Man,” J. Clin. Invest., 42, pp. 29–39. [CrossRef] [PubMed]
Ismail, M. , Comerford, A. , and Wall, W. A. , 2013, “ Coupled and Reduced Dimensional Modeling of Respiratory Mechanics During Spontaneous Breathing,” Int. J. Numer. Methods Biomed. Eng., 29(11), pp. 1285–1305. [CrossRef]
Kim, M. , Bordas, R. , Vos, W. , Hartley, R. A. , Brightling, C. E. , Kay, D. , Grau, V. , and Burrowes, K. S. , 2015, “ Dynamic Flow Characteristics in Normal and Asthmatic Lungs,” Int. J. Numer. Methods Biomed. Eng., 31(12), p. e02730.
Comer, J. K. , Kleinstreuer, C. , and Zhang, Z. , 2001, “ Flow Structures and Particle Deposition Patterns in Double Bifurcation Airway Models,” J. Fluid Mech., 435, pp. 25–54.
Lin, C.-L. , Tawhai, M. H. , McLennan, G. , and 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(2–3), pp. 295–309. [CrossRef] [PubMed]
Choi, J. , Tawhai, M. H. , Hoffman, E. A. , and Lin, C.-L. , 2009, “ On Intra-and Intersubject Variabilities of Airflow in the Human Lungs,” Phys. Fluids, 21(10), p. 101901. [CrossRef]
Choi, J. , Xia, G. , Tawhai, M. , Hoffman, E. A. , and Lin, C.-L. , 2010, “ Numerical Study of High-Frequency Oscillatory Air Flow and Convective Mixing in a CT-Based Human Airway Model,” Ann. Biomed. Eng., 38(12), pp. 3550–3571. [CrossRef] [PubMed]
Choi, J. , 2011, “Multiscale Numerical Analysis of Airflow in CT-Based Subject Specific Breathing Human Lungs,” Ph.D. dissertation, University of Iowa, Iowa City, IA. http://ir.uiowa.edu/etd/2685/
van Ertbruggen, C. , Hirsch, C. , and Paiva, M. , 2005, “ Anatomically Based Three-Dimensional Model of Airways to Simulate Flow and Particle Transport Using Computational Fluid Dynamics,” J. Appl. Physiol., 98(3), pp. 970–980. [CrossRef] [PubMed]
Katz, I. M. , Martin, A. R. , Muller, P. A. , Terzibachi, K. , Feng, C. H. , Caillibotte, G. , Sandeau, J. , and Texereau, J. , 2011, “ The Ventilation Distribution of Helium-Oxygen Mixtures and the Role of Inertial Losses in the Presence of Heterogeneous Airway Obstructions,” J. Biomech., 44(6), pp. 1137–1143. [CrossRef] [PubMed]
Borojeni, A. A. , Noga, M. L. , Martin, A. R. , and Finlay, W. H. , 2015, “ Validation of Airway Resistance Models for Predicting Pressure Loss Through Anatomically Realistic Conducting Airway Replicas of Adults and Children,” J. Biomech., 48(10), pp. 1988–1996. [CrossRef] [PubMed]
Kang, M. Y. , Hwang, J. , and Lee, J. W. , 2011, “ Effect of Geometric Variations on Pressure Loss for a Model Bifurcation of the Human Lung Airway,” J. Biomech., 44(6), pp. 1196–1199. [CrossRef] [PubMed]
Weibel, E. R. , 1963, Morphometry of the Human Lung, Springer-Verlag, Berlin. [CrossRef]
Miyawaki, S. , Hoffman, E. A. , and Lin, C.-L. , 2017, “ Numerical Simulations of Aerosol Delivery to the Human Lung With an Idealized Laryngeal Model, Image-Based Airway Model, and Automatic Meshing Algorithm,” Comput Fluids, 148, pp. 1–9. [CrossRef] [PubMed]
Geuzaine, C. , and Remacle, J. F. , 2009, “ Gmsh: A 3-D Finite Element Mesh Generator With Built-In Pre‐ and Post-Processing Facilities,” Int. J. Numer. Methods Eng., 79(11), pp. 1309–1331. [CrossRef]
Miyawaki, S. , Choi, S. , Hoffman, E. A. , and Lin, C.-L. , 2016, “ A 4DCT Imaging-Based Breathing Lung Model With Relative Hysteresis,” J. Comput. Phys., 326, pp. 76–90. [CrossRef] [PubMed]
Lin, C. L. , Lee, H. , Lee, T. , and Weber, L. J. , 2005, “ A Level Set Characteristic Galerkin Finite Element Method for Free Surface Flows,” Int. J. Numer. Methods Fluids, 49(5), pp. 521–547. [CrossRef]
Vreman, A. W. , 2004, “ An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications,” Phys. Fluids, 16(10), pp. 3670–3681. [CrossRef]
Jarrin, N. , Benhamadouche, S. , Laurence, D. , and Prosser, R. , 2006, “ A Synthetic-Eddy-Method for Generating Inflow Conditions for Large-Eddy Simulations,” Int. J. Heat Fluid Flow, 27(4), pp. 585–593. [CrossRef]
Weinberger, S. E. , Cockrill, B. A. , and Mandel, J. , 2008, Principles of Pulmonary Medicine, 5th eds., Elsevier Health Sciences, Philadelphia, PA. [PubMed] [PubMed]
Jahani, N. , Choi, S. , Choi, J. , Iyer, K. , Hoffman, E. A. , and Lin, C. L. , 2015, “ Assessment of Regional Ventilation and Deformation Using 4D-CT Imaging for Healthy Human Lungs During Tidal Breathing,” J. Appl. Physiol., 119(10), pp. 1064–1074. [CrossRef] [PubMed]
Pare, P. D. , Wiggs, B. R. , James, A. , Hogg, J. C. , and Bosken, C. , 1991, “ The Comparative Mechanics and Morphology of Airways in Asthma and in Chronic Obstructive Pulmonary Disease,” Am. J. Respir. Crit. Care Med., 143(5 Pt. 1), pp. 1189–1193.
Wongviriyawong, C. , Harris, R. S. , Greenblatt, E. , Winkler, T. , and Venegas, J. G. , 2013, “ Peripheral Resistance: A Link Between Global Airflow Obstruction and Regional Ventilation Distribution,” J. Appl. Physiol., 114(4), pp. 504–514. [CrossRef] [PubMed]
Jalal, S. , Nemes, A. , Van de Moortele, T. , Schmitter, S. , and Coletti, F. , 2016, “ Three-Dimensional Inspiratory Flow in a Double Bifurcation Airway Model,” Exp. Fluids, 57(9), p. 148. [CrossRef]
Banko, A. J. , Coletti, F. , Schiavazzi, D. , Elkins, C. J. , and Eaton, J. K. , 2015, “ Three-Dimensional Inspiratory Flow in the Upper and Central Human Airways,” Exp. Fluids, 56(6), p. 117. [CrossRef]
White, F. M. , and Corfield, I. , 2006, Viscous Fluid Flow, McGraw-Hill, New York.
Wu, D. , Tawhai, M. H. , Hoffman, E. A. , and Lin, C.-L. , 2014, “ A Numerical Study of Heat and Water Vapor Transfer in MDCT-Based Human Airway Models,” Ann. Biomed. Eng., 42(10), pp. 2117–2131. [CrossRef] [PubMed]
Wongviriyawong, C. , Harris, R. S. , Zheng, H. , Kone, M. , Winkler, T. , and Venegas, J. G. , 2012, “ Functional Effect of Longitudinal Heterogeneity in Constricted Airways Before and After Lung Expansion,” J. Appl. Physiol., 112(1), pp. 237–245. [CrossRef] [PubMed]
Choi, S. , Hoffman, E. A. , Wenzel, S. E. , Tawhai, M. H. , Yin, Y. , Castro, M. , and Lin, C.-L. , 2013, “ Registration-Based Assessment of Regional Lung Function Via Volumetric CT Images of Normal Subjects Vs. Severe Asthmatics,” J. Appl. Physiol., 115(5), pp. 730–742. [CrossRef] [PubMed]
Yin, Y. , Choi, J. , Hoffman, E. A. , Tawhai, M. H. , and Lin, C. L. , 2013, “ A Multiscale MDCT Image-Based Breathing Lung Model With Time-Varying Regional Ventilation,” J. Comput. Phys., 244, pp. 168–192.
Yin, Y. , Choi, J. , Hoffman, E. A. , Tawhai, M. H. , and Lin, C. L. , 2010, “ Simulation of Pulmonary Air Flow With a Subject-Specific Boundary Condition,” J. Biomech., 43(11), pp. 2159–2163. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematics of (a) symmetric airway geometries with five different bifurcation angles (15 deg, 25 deg, 35 deg, 45 deg, and 55 deg), (b) two major branch paths, (c) bifurcation angle between the current branch and its parent branch, and (d) the control surface and volume defined for quantitative analysis of the pressure drop

Grahic Jump Location
Fig. 2

Pressure drop averaged over two major paths (Fig. 1(b)) with the bifurcation angle 35 deg. Left [(a), (c), (e)] and right [(b), (d), (f)] columns show inspiration and expiration cases, respectively. Top [(a), (b)], middle [(c), (d)], and bottom [(e), (f)] rows show results when low (10 L/min), moderate (20 L/min) and high (40 L/min) flow rates were applied, respectively.

Grahic Jump Location
Fig. 3

Contour on a sliced plane and isosurface at 0.25 of turbulence kinetic energy: (a) on inspiration and (b) on expiration at the high flow rate (Qtrachea = 40 L/min)

Grahic Jump Location
Fig. 4

(a) Average wall shear stress and (b) airway resistance averaged for five different bifurcation angles for inspiration and expiration at the moderate flow rate (Qtrachea = 20 L/min). (c) Average wall shear stress and (d) airway resistance for inspiration at three different flow rates with the bifurcation angle 35 deg. (e) Average wall shear stress and (f) airway resistance for expiration at three different flow rates with the bifurcation angle 35 deg.

Grahic Jump Location
Fig. 5

Comparison of the pressure drop due to viscous dissipation ΔPVis and the pressure drop due to the Poiseuille flow assumption (ΔPPoiseuille) at three different flow rates with the same bifurcation angle of 35 deg: (a) inspiration and (b) expiration

Grahic Jump Location
Fig. 6

Kinetic energy coefficient (K) according to generation number of (a) moderate inspiration (Qtrachea = 20 L/min) with five different bifurcation angles, (b) moderate expiration (Qtrachea = 20 L/min) with five different bifurcation angles, (c) inspiration with three different flow rates at the bifurcation angle 35 deg, and (d) expiration with three different flow rates at the bifurcation angle 35 deg

Grahic Jump Location
Fig. 7

Color-coded velocity vectors [(a) and (b)] and kinetic energy distribution [(c) and (d)] on the distal control surface between inspiration [(a) and (c)] and expiration [(b) and (d)]. The first fluctuating eigenmode (POD-derived coherent vortical structure) identified by the isosurface of λ2 = −0.02, and velocity vector tangent on the distal control surface between inspiration (e) and expiration (f).

Grahic Jump Location
Fig. 8

Viscous dissipation coefficient (γ) according to generation number of (a) inspiration with five different bifurcation angles, (b) expiration with five different bifurcation angles, (c) inspiration with three different flow rates, and (d) expiration with three different flow rates

Grahic Jump Location
Fig. 9

Average wall shear stress projected on surface meshes [(a) and (b)] and grid-resolved viscous dissipation on a perpendicular plane inside the volume meshes [(c) and (d)]. Left figures [(a) and (c)] are for inspiration and right figures are for expiration [(b) and (d)] at the moderate flow rate with a bifurcation angle 35 deg.

Grahic Jump Location
Fig. 10

Model comparisons using constant and variable coefficients of kinetic energy (K) and viscous dissipation (γ and η) for inspiration [(a) and (c)] and expiration cases [(b) and (d)]. (a) and (c) Use the constant and variable coefficients of kinetic energy (K), while (c) and (d) use the constant and variable coefficients of viscous dissipation (γ and η). All data points between the zeroth and tenth generations were employed in this analysis.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In