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.

References

References
1.
West
,
J. B.
,
2008
,
Respiratory Physiology: The Essentials
,
Lippincott Williams & Wilkins
,
Baltimore, MD
.
2.
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
.
3.
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
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
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
.
9.
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
.
10.
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
.
11.
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
.
12.
Pedley
,
T. J.
,
1977
, “
Pulmonary Fluid Dynamics
,”
Annu. Rev. Fluid Mech.
,
9
(
1
), pp.
229
274
.
13.
White
,
F. M.
,
2011
,
Fluid Mechanics
,
McGraw-Hill
,
New York
.
14.
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
.
15.
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
.
16.
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.
17.
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.
18.
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
.
19.
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
.
20.
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
.
21.
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/
22.
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
.
23.
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
.
24.
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
.
25.
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
.
26.
Weibel
,
E. R.
,
1963
,
Morphometry of the Human Lung
,
Springer-Verlag
,
Berlin
.
27.
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
.
28.
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
.
29.
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
.
30.
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
.
31.
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
.
32.
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
.
33.
Weinberger
,
S. E.
,
Cockrill
,
B. A.
, and
Mandel
,
J.
,
2008
,
Principles of Pulmonary Medicine
, 5th eds.,
Elsevier Health Sciences
, Philadelphia, PA.
34.
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
.
35.
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
.
36.
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
.
37.
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
.
38.
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
.
39.
White
,
F. M.
, and
Corfield
,
I.
,
2006
,
Viscous Fluid Flow
,
McGraw-Hill
,
New York
.
40.
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
.
41.
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
.
42.
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
.
43.
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.
44.
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
.
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