A 1D fluid model is implemented for the purpose of fluid-structure interaction (FSI) simulations in complex and completely collapsible geometries, particularly targeting the case of obstructive sleep apnea (OSA). The fluid mechanics are solved separately from any solid mechanics, making possible the use of a highly complex and/or black-box solver for the solid mechanics. The fluid model is temporally discretized with a second-order scheme and spatially discretized with an asymmetrical fourth-order scheme that is robust in highly uneven geometries. A completely collapsing and reopening geometry is handled smoothly using a modified area function. The numerical implementation is tested with two driven-geometry cases: (1) an inviscid analytical solution and (2) a completely closing geometry with viscous flow. Three-dimensional fluid simulations in static geometries are performed to examine the assumptions of the 1D model, and with a well-defined pressure-recovery constant the 1D model agrees well with 3D models. The model is very fast computationally, is robust, and is recommended for OSA simulations where the bulk flow pressure is primarily of interest.

References

References
1.
Young
,
T.
,
Skatrud
,
J.
, and
Peppard
,
P.
,
2004
, “
Risk Factors for Obstructive Sleep Apnea in Adults
,”
JAMA
,
291
(
16
), pp.
2013
2016
.10.1001/jama.291.16.2013
2.
Hudgel
,
D.
,
1992
, “
Mechanisms of Obstructive Sleep-Apnea
,”
Chest
,
101
(
2
), pp.
541
549
.10.1378/chest.101.2.541
3.
Malhotra
,
A.
, and
White
,
D. P.
,
2002
, “
Obstructive Sleep Apnoea
,”
Lancet
,
360
(
9328
), pp.
237
245
.10.1016/S0140-6736(02)09464-3
4.
Bertram
,
C. D.
,
2008
, “
Flow-Induced Oscillation of Collapsed Tubes and Airway Structures
,”
Resp. Physiol. Neurobiol.
,
163
(
1–3
), pp.
256
265
.10.1016/j.resp.2008.04.011
5.
Isono
,
S.
,
Remmers
,
J.
,
Tanaka
,
A.
,
Sho
,
Y.
,
Sato
,
J.
, and
Nishino
,
T.
,
1997
, “
Anatomy of Pharynx in Patients With Obstructive Sleep Apnea and in Normal Subjects
,”
J. Appl. Physiol.
,
82
(
4
), pp.
1319
1326
.
6.
Chouly
,
F.
,
Van Hirtum
,
A.
,
Lagree
,
P. Y.
,
Pelorson
,
X.
, and
Payan
,
Y.
,
2008
, “
Numerical and Experimental Study of Expiratory Flow in the Case of Major Upper Airway Obstructions With Fluid-Structure Interaction
,”
J. Fluid. Struct.
,
24
(
2
), pp.
250
269
.10.1016/j.jfluidstructs.2007.08.004
7.
Tobin
,
M.
,
Chadha
,
T.
,
Jenouri
,
G.
,
Birch
,
S.
,
Gazeroglu
,
H.
, and
Sackner
,
M.
,
1983
, “
Breathing Patterns. 1. Normal Subjects
,”
Chest
,
84
(
2
), pp.
202
205
.10.1378/chest.84.2.202
8.
Evans
,
J. A.
, and
Whitelaw
,
W. A.
,
2009
, “
The Assessment of Maximal Respiratory Mouth Pressures in Adults
,”
Respir. Care
,
54
(
10
), pp.
1348
1359
.
9.
Berg
,
S.
,
Cole
,
P.
,
Hoffstein
,
V.
, and
Haight
,
J.
,
2001
, “
Upper Airway Pressures in Snorers and Nonsnorers During Wakefulness and Sleep
,”
J. Otolaryngology
,
30
(
2
), pp.
69
74
.10.2310/7070.2001.20801
10.
Schwartz
,
A.
,
Smith
,
P.
,
Wise
,
R.
,
Gold
,
A.
, and
Permutt
,
S.
,
1988
, “
Induction of Upper Airway Occlusion in Sleeping Individuals With Subatmospheric Nasal Pressure
,”
J. Appl. Physiol.
,
64
(
2
), pp.
535
542
.
11.
Yu
,
C.-C.
,
Hsiao
,
H.-D.
,
Lee
,
L.-C.
,
Yao
,
C.-M.
,
Chen
,
N.-H.
,
Wang
,
C.-J.
, and
Chen
,
Y.-R.
,
2009
, “
Computational Fluid Dynamic Study on Obstructive Sleep Apnea Syndrome Treated With Maxillomandibular Advancement
,”
J. Craniofac. Surg.
,
20
(
2
), pp.
426
430
.10.1097/SCS.0b013e31819b9671
12.
Issa
,
F.
, and
Sullivan
,
C.
,
1984
, “
Upper Airway Closing Pressures in Obstructive Sleep-Apnea
,”
J. Appl. Physiol.
,
57
(
2
), pp.
520
527
.
13.
Heil
,
M.
, and
Jensen
,
O. E.
,
2003
, “
Flows in Deformable Tubes and Channels—Theoretical Models and Biological Applications
.”,
Flow Past Highly Compliant Boundaries and in Collapsible Tubes
(ed.
P. W.
Carpenter
&
T. J.
Pedley
).
Kluwer Academic
,
Dordrecht
.
14.
Grotberg
,
J.
, and
Jensen
,
O.
,
2004
, “
Biofluid Mechanics in Flexible Tubes
,”
Ann. Rev. Fluid Mech.
,
36
, pp.
121
147
.10.1146/annurev.fluid.36.050802.121918
15.
Shome
,
B.
,
Wang
,
L.
,
Santare
,
M.
,
Prasad
,
A.
,
Szeri
,
A.
, and
Roberts
,
D.
,
1998
, “
Modeling of Airflow in the Pharynx With Application to Sleep Apnea
,”
ASME J. Biomech. Eng.
,
120
(
3
), pp.
416
422
.10.1115/1.2798009
16.
Allen
,
G. M.
,
Shortall
,
B. P.
,
Gemci
,
T.
,
Corcoran
,
T. E.
, and
Chigier
,
N. A.
,
2004
, “
Computational Simulations of Airflow in an In Vitro Model of the Pediatric Upper Airways
,”
ASME J. Biomech. Eng.
,
126
(
5
), pp.
604
613
.10.1115/1.1800554
17.
Nithiarasu
,
P.
,
Hassan
,
O.
,
Morgan
,
K.
,
Weatherill
,
N. P.
,
Fielder
,
C.
,
Whittet
,
H.
,
Ebden
,
P.
, and
Lewis
,
K. R.
,
2008
, “
Steady Flow Through a Realistic Human Upper Airway Geometry
,”
Int. J. Num. Meth. Fluid
,
57
(
5
), pp.
631
651
.10.1002/fld.1805
18.
Backer
,
J. D.
,
Vanderveken
,
O.
,
Vos
,
W.
,
Devolder
,
A.
,
Verhulst
,
S.
,
Verbraecken
,
J.
,
Parizel
,
P.
,
Braem
,
M.
,
de Heyning
,
P. V.
, and
Backer
,
W. D.
,
2007
, “
Functional Imaging Using Computational Fluid Dynamics to Predict Treatment Success of Mandibular Advancement Devices in Sleep-Disordered Breathing
,”
J. Biomech.
,
40
(
16
), pp.
3708
3714
.10.1016/j.jbiomech.2007.06.022
19.
Vos
,
W.
,
Backer
,
J. D.
,
Devolder
,
A.
,
Vanderveken
,
O.
,
Verhulst
,
S.
,
Salgado
,
R.
,
Germonpre
,
P.
,
Partoens
,
B.
,
Wuyts
,
F.
,
Parizel
,
P.
, and
Backer
,
W. D.
,
2007
, “
Correlation Between Severity of Sleep Apnea and Upper Airway Morphology Based on Advanced Anatomical and Functional Imaging
,”
J. Biomech.
,
40
(
10
), pp.
2207
2213
.10.1016/j.jbiomech.2006.10.024
20.
Lucey
,
A. D.
,
King
,
A. J. C.
,
Tetlow
,
G. A.
,
Wang
,
J.
,
Armstrong
,
J. J.
,
Leigh
,
M. S.
,
Paduch
,
A.
,
Walsh
,
J. H.
,
Sampson
,
D. D.
,
Eastwood
,
P. R.
, and
Hillman
,
D. R.
,
2010
, “
Measurement, Reconstruction, and Flow-Field Computation of the Human Pharynx With Application to Sleep Apnea
,”
IEEE Trans. Biomed. Eng.
,
57
(
10, Part 1
), pp.
2535
2548
.10.1109/TBME.2010.2052808
21.
Heenan
,
A.
,
Matida
,
E.
,
Pollard
,
A.
, and
Finlay
,
W.
,
2003
, “
Experimental Measurements and Computational Modeling of the Flow Field in an Idealized Human Oropharynx
,”
Experiment. Fluid.
,
35
(
1
), pp.
70
84
.10.1007/s00348-003-0636-7
22.
Johnstone
,
A.
,
Uddin
,
M.
,
Pollard
,
A.
,
Heenan
,
A.
, and
Finlay
,
W.
,
2004
, “
The Flow Inside an Idealised Form of the Human Extra-Thoracic Airway
,”
Experiment. Fluid.
,
37
(
5
), pp.
673
689
.10.1007/s00348-004-0857-4
23.
Ball
,
C. G.
,
Uddin
,
M.
, and
Pollard
,
A.
,
2008
, “
High Resolution Turbulence Modelling of Airflow in an Idealised Human Extra-Thoracic Airway
,”
Comput. Fluid.
,
37
(
8
), pp.
943
964
.10.1016/j.compfluid.2007.07.021
24.
Ball
,
C. G.
,
Uddin
,
M.
, and
Pollard
,
A.
,
2008
, “
Mean Flow Structures Inside the Human Upper Airway
,”
Flow Turb. Combust.
,
81
(
1–2
), pp.
155
188
.10.1007/s10494-007-9113-3
25.
Mihaescu
,
M.
,
Murugappan
,
S.
,
Kalra
,
M.
,
Khosla
,
S.
, and
Gutmark
,
E.
,
2008
, “
Large Eddy Simulation and Reynolds-Averaged Navier–Stokes Modeling of Flow in a Realistic Pharyngeal Airway Model: An Investigation of Obstructive Sleep Apnea
,”
J. Biomech.
,
41
(
10
), pp.
2279
2288
.10.1016/j.jbiomech.2008.04.013
26.
Mylavarapu
,
G.
,
Murugappan
,
S.
,
Mihaescu
,
M.
,
Kalra
,
M.
,
Khosla
,
S.
, and
Gutmark
,
E.
,
2009
, “
Validation of Computational Fluid Dynamics Methodology Used for Human Upper Airway Flow Simulations
,”
J. Biomech.
,
42
(
10
), pp.
1553
1559
.10.1016/j.jbiomech.2009.03.035
27.
Xu
,
C.
,
Sin
,
S.
,
McDonough
,
J. M.
,
Udupa
,
J. K.
,
Guez
,
A.
,
Arens
,
R.
, and
Wootton
,
D. M.
,
2006
, “
Computational Fluid Dynamics Modeling of the Upper Airway of Children With Obstructive Sleep Apnea Syndrome in Steady Flow
,”
J. Biomech.
,
39
(
11
), pp.
2043
2054
.10.1016/j.jbiomech.2005.06.021
28.
Huang
,
Y.
,
White
,
D. P.
, and
Malhotra
,
A.
,
2007
, “
Use of Computational Modeling to Predict Responses to Upper Airway Surgery in Obstructive Sleep Apnea
,”
Laryngoscope
,
117
(
4
), pp.
648
653
.10.1097/MLG.0b013e318030ca55
29.
Wang
,
Y.
,
Wang
,
J.
,
Liu
,
Y.
,
Yu
,
S.
,
Sun
,
X.
,
Li
,
S.
,
Shen
,
S.
, and
Zhao
,
W.
,
2012
, “
Fluid-Structure Interaction Modeling of Upper Airways Before and After Nasal Surgery for Obstructive Sleep Apnea
,”
Int. J. Num. Meth. Biomed. Eng.
,
28
(
5
), pp.
528
546
.10.1002/cnm.1486
30.
Huang
,
Y.
,
Malhotra
,
A.
, and
White
,
D.
,
2005
, “
Computational Simulation of Human Upper Airway Collapse Using a Pressure-/State-Dependent Model of Genioglossal Muscle Contraction Under Laminar Flow Conditions
,”
J. Appl. Physiol.
,
99
(
3
), pp.
1138
1148
.10.1152/japplphysiol.00668.2004
31.
Huang
,
Y.
,
White
,
D.
, and
Malhotra
,
A.
,
2005
, “
The Impact of Anatomic Manipulations on Pharyngeal Collapse—Results From a Computational Model of the Normal Human Upper Airway
,”
Chest
,
128
(
3
), pp.
1324
1330
.10.1378/chest.128.3.1324
32.
Chouly
,
F.
,
Van Hirtum
,
A.
,
Lagree
,
P.-Y.
,
Pelorson
,
X.
, and
Payan
,
Y.
,
2009
, “
Modelling the Human Pharyngeal Airway: Validation of Numerical Simulations Using In Vitro Experiments
,”
Med. Biol. Eng. Comput.
,
47
(
1
), pp.
49
58
.10.1007/s11517-008-0412-1
33.
Heil
,
M.
,
2004
, “
An Efficient Solver for the Fully Coupled Solution of Large-Displacement Fluid-Structure Interaction Problems
,”
Comput. Meth. Appl. Mech. Eng.
,
193
(
1–2
), pp.
1
23
.10.1016/j.cma.2003.09.006
34.
Heil
,
M.
,
Hazel
,
A. L.
, and
Boyle
,
J.
,
2008
, “
Solvers for Large-Displacement Fluid-Structure Interaction Problems: Segregated Versus Monolithic Approaches
,”
Comput. Mech.
,
43
(
1
), pp.
91
101
.10.1007/s00466-008-0270-6
35.
Degroote
,
J.
,
Bruggeman
,
P.
,
Haelterman
,
R.
, and
Vierendeels
,
J.
,
2008
, “
Stability of a Coupling Technique for Partitioned Solvers in FSI Applications
,”
Comput. Struct.
,
86
(
23–24
), pp.
2224
2234
.10.1016/j.compstruc.2008.05.005
36.
Causin
,
P.
,
Gerbeau
,
J.
, and
Nobile
,
F.
,
2005
, “
Added-Mass Effect in the Design of Partitioned Algorithms for Fluid-Structure Problems
,”
Comput. Meth. Appl. Mech. Eng.
,
194
(
42–44
), pp.
4506
4527
.10.1016/j.cma.2004.12.005
37.
Cancelli
,
C.
, and
Pedley
,
T. J.
,
1985
, “
A Separated-Flow Model for Collapsible-Tube Oscillations
,”
J. Fluid Mech.
,
157
, pp.
375
404
.10.1017/S0022112085002427
38.
Shapiro
,
A. H.
,
1977
, “
Steady Flow in Collapsible Tubes
,”
ASME J. Biomech. Eng.
,
99
(
3
), pp.
126
147
.10.1115/1.3426281
39.
Pedley
,
T.
, and
Luo
,
X.
,
1998
, “
Modelling Flow and Oscillations in Collapsible Tubes
,”
Theoret. Computat. Fluid Dyn.
,
10
(
1–4
), pp.
277
294
.10.1007/s001620050064
40.
Jensen
,
O.
, and
Pedley
,
T.
,
1989
, “
The Existence of Steady Flow in a Collapsed Tube
,”
J. Fluid Mech.
,
206
, pp.
339
374
.10.1017/S0022112089002326
41.
Jensen
,
O.
,
1990
, “
Instabilities of Flow in a Collapsed Tube
,”
J. Fluid Mech.
,
220
, pp.
623
659
.10.1017/S0022112090003408
42.
Jensen
,
O.
,
1992
, “
Chaotic Oscillations in a Simple Collapsible-Tube Model
,”
ASME J. Biomech. Eng.
,
114
(
1
), pp.
55
59
.10.1115/1.2895450
43.
Aittokallio
,
T.
,
Gyllenberg
,
M.
, and
Polo
,
O.
,
2001
, “
A Model of a Snorer's Upper Airway
,”
Math. Biosci.
,
170
(
1
), pp.
79
90
.10.1016/S0025-5564(00)00062-6
44.
White
,
F. M.
,
1999
,
Fluid Mechanics
,
McGraw-Hill
,
Boston, MA
.
45.
Roache
,
P. J.
,
1997
, “
Quantification of Uncertainty in Computational Fluid Dynamics
,”
Ann. Rev. Fluid Mech.
,
29
, pp.
123
160
.10.1146/annurev.fluid.29.1.123
46.
Smith
,
B.
,
2004
, “
Pressure Recovery in a Radiused Sudden Expansion
,”
Experiments In Fluids
,
36
(
6
), pp.
901
907
.10.1007/s00348-003-0773-z
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