The present work seeks to elucidate the flow-structure dynamics of the upper airway so that improved clinical strategies for the alleviation of snoring and sleep apnoea can be developed and applied on an evidence basis. Analogue computational modelling, appropriately related to the anatomically correct system, is used. Hitherto, such modelling has been confined to flow in a rigidchannel to study flutter of the soft palate. Clinical evidence suggests that apneic events can involve combined motions and interactions of the soft palate and flexible walls of the pharynx. We model a flexible cantilevered plate (the soft-palate) mounted in a channel of square cross-section (the pharynx), the downstream side walls of which are flexible to capture deformation in airway collapse. Upstream of the flexible plate is a rigid plate (the hard palate) that spans the channel to permit airflow to be drawn from two inlets (oral and nasal). The commercial FSI software ADINA is used to construct the model and undertake the three-dimensional investigation. Results show that motions of the soft-palate have little effect on the deformation of the side walls. However, the amplitude and frequency of soft-palate vibrations are found to be strongly dependent upon side-wall stiffness and, hence, dynamics

Lucey, A. D.

Tetlow, G. A.

Wang, J.

University of Queensland eSpace

16th Australasian Fluid Mechanics Conference 
Crown Plaza, Gold Coast, Australia 
2-7 December 2007 
 
Flow-Structure Interaction in the Upper Airway: Motions of a  
Cantilevered Flexible Plate in Channel Flow with Flexible Walls 
 
J. Wang, G.A. Tetlow and A.D. Lucey 
Fluid Dynamics Research Group 
                Curtin University of Technology, Western Australia, 6845 AUSTRALIA 
             
Abstract 
The present work seeks to elucidate the flow-structure dynamics 
of the upper airway so that improved clinical strategies for the 
alleviation of snoring and sleep apnoea can be developed and 
applied on an evidence basis. Analogue computational modelling, 
appropriately related to the anatomically correct system, is used. 
Hitherto, such modelling has been confined to flow in a rigid-
channel to study flutter of the soft palate. Clinical evidence 
suggests that apneic events can involve combined motions and 
interactions of the soft palate and flexible walls of the pharynx. 
We model a flexible cantilevered plate (the soft-palate) mounted 
in a channel of square cross-section (the pharynx), the 
downstream side walls of which are flexible to capture 
deformation in airway collapse. Upstream of the flexible plate is 
a rigid plate (the hard palate) that spans the channel to permit 
airflow to be drawn from two inlets (oral and nasal). The 
commercial FSI software ADINA is used to construct the model 
and undertake the three-dimensional investigation. Results show 
that motions of the soft-palate have little effect on the 
deformation of the side walls. However, the amplitude and 
frequency of soft-palate vibrations are found to be strongly 
dependent upon side-wall stiffness and, hence, dynamics. 
 
Introduction  
The present work is motivated by the need to understand the 
complex fluid-structure interactions that occur in the upper 
airway. The coupled dynamics of airflow, soft-palate vibrations 
and motion of the airway walls (the pharynx) in humans underpin 
snoring and the more serious condition of sleep apnoea whereby 
the airway undergoes total closure. A complete understanding of 
the mechanical causes of these conditions is as yet unavailable. 
Endoscopic observations suggest that snoring noises originate 
from oscillations of the soft palate that separates oral and nasal 
inlets while airway collapse occurs in the oropharynx near the tip, 
or just downstream, of the soft palate. Clinical observations 
suggest that soft-palate motions are implicated in some 30% of 
apneic events.  Figure 1 identifies these anatomical landmarks on 
a reconstructed geometry of the upper airway that we obtained in 
[7] using catheter-based optical tomography in combination with 
CT-scans. 
 
The dynamics of a cantilevered flexible plate in channel flow as a 
model for the mechanics of snoring has received much attention; 
for example, see [1,2,4,6]. Such studies focus upon the stability 
characteristics of the flexible plate, showing that beyond a critical 
flow speed or Reynolds number, the plate succumbs to flutter 
instability.  However all such studies have been two-dimensional 
and assumed rigid channel walls. The study of flexible tubes 
through which a fluid is flowing has received vast attention for 
the rich dynamics that this system contains; for two excellent 
reviews of theoretical and experimental work, see [5] and [3]. 
 
In this paper we combine key features of the two distinct strands 
of study described above; the pharynx is a flexible tube in which 
is mounted a cantilevered flexible, the soft-palate. Each flexible 
component of the system has its own dynamics and these will be 
coupled through the fluid flow. Our goal herein is to take the first 
steps towards establishing an understanding of this complex 
flow-structure system. 
 
Nasal inlet 
Location of 
soft palate  
Oropharynx: 
Region of flexible 
wall with large 
deflections
Oral inlet
Figure 1. Anatomically measured upper airway model; from [7] 
 
Analogue Computational Modelling 
The analogue computational model is shown in Fig. 2. It is 
topologically mapped from the anatomically correct layout of 
Fig. 1 but is radically simpler to permit the extraction of only the 
core system dynamics. It comprises four rigid parts, one fluid 
block, a flexible plate (soft palate) and two flexible side walls.  
 
 
 
Figure 2. Analogue computational model; the arrows indicate 
inhalation through upper (nasal) and lower (oral) airways. 
Cantilevered 
attachment of 
flexible side 
walls
Cantilevered 
attachment of 
flexible soft 
palate 
Fluid outlet
342
The model permits airway closure only through the motion of the 
cantilevered flexible side walls that are allowed to slide freely 
(without leakage) past the upper and lower walls. The rigid upper 
wall represents the tongue that, although flexible, is stiff relative 
to the side walls of the oropharynx. The lower wall can be 
assumed rigid because the pharynx abuts the spine. The soft 
palate and two flexible side walls have identical dimensions (17 x 
15 x 0.5 mm) with material density 1000 kg/m3 and Poisson ratio 
0.33. The cross-section of the wholly rigid channel enclosing the 
upstream hard and soft palates has both width and height of 15 
mm. Within this section, the hard and soft palate are offset to 
give lower and upper channel heights of 9.7 mm and 4.8 mm 
respectively (with palate thicknesses being 0.5 mm). This 
asymmetry represents the different calibres of the oral and nasal 
airways that are separated by the palate. The lengths of the hard 
and soft palates are 9 mm and 17 mm respectively and the overall 
length of the system is 41 mm. All of these dimensions have been 
chosen to be broadly representative of an adult. There is a three-
sided fluid-structure interaction (FSI) boundary for the soft palate 
(upper and lower surfaces, and tip side surface) while there is just 
one interior FSI boundary for each side wall. Unsteady three-
dimensional laminar flow is assumed, modelled by the Navier-
Stokes and Continuity equations. The airflow is driven by a 
pressure loading, PΔ , applied across the length of the system. 
The external pressure is taken to be that of the inlet side. 
 
Numerical Investigation 
 
The commercial FSI software ADINA R&D, a fully coupled 
finite-element solver, is used for all of the investigations reported 
herein. Implicit schemes have been selected to predict the motion 
of all of the flexible surfaces and a transient analysis for the fluid 
dynamics. A series of numerical experiments is performed for a 
range of soft palate and side-wall material properties. A single 
applied pressure load of  Pa is used throughout and 
the properties of air are those at 20
28.0=ΔP
0 C.  The load is applied as a 
linear ramp function for the first 50 time steps of a numerical 
experiment to reach full load at 1 s. For the next 9 seconds, a 
further 150 time steps of size 0.06 s, at constant full load, are 
computed to predict the motion; thus, all time series run for 10 s. 
A high-resolution preliminary simulation was first carried using 
250,000 fluid tetrahedral elements and 30,000 solid brick 
elements.  Since displacements of soft-palate tip were found to be 
small, adaptive meshing was then not needed, and thus a simpler 
all-brick element model could be deployed. Moreover, we were 
able to reduce the level of discretisation down to 40,000 fluid 
plus 3,000 solid brick elements with just a 3% reduction to the 
accuracy of the maximum deflection of the soft palate. 
  
A typical result is shown schematically in Fig. 3. The soft palate 
is seen to deform upwards (y-displacement) and in the 
quantitative results that follow we track the position of Node A as 
being representative of soft-palate (maximum) deflection. This is 
reasonable since the deformation of the soft palate is 
overwhelmingly planar. Correspondingly, (z-displacement) 
deformation of the side-walls is represented by Node B, at mid-
channel height. In this case there is non-negligible variation in 
the vertical direction so choosing the mid-point records the 
maximum displacement. For this preliminary study, chosen to 
use a combination of pressure loading, channel dimensions and 
soft-palate properties that yields stable oscillatory behaviour, i.e. 
the mean flow speeds and Reynolds number are beneath those 
that would cause soft-palate flutter. 
 
Results 
 
First, we assess the effect of soft-palate motion on side-wall 
response. Next we reverse the investigation to quantify the effect 
of side-wall motion on soft-palate behaviour. Finally, we 
combine these results in a simple non-dimensional framework. 
Throughout we vary motion of the flexible components by 
changing their elastic moduli while keeping all other parameters, 
both geometric and material, unchanged. 
 
(a)
 
 
 
Figure 3. Illustrative simulation of the flow-structure interaction; 
(a) generation of a 10-second time series and centreline flow at 
final equilibrium, (b) pressure contours, (c) velocity magnitude. 
 
First, we assess the effect of soft-palate motion on side-wall 
response. Next we reverse the investigation to quantify the effect 
of side-wall motion on soft-palate behaviour. Finally, we 
combine these results in a simple non-dimensional framework. 
Throughout we vary motion of the flexible components by 
changing their elastic moduli while keeping all other parameters, 
both geometric and material, unchanged. 
 
The effect of soft-palate motion on side-wall response 
Figures 4 and 5 show time series for the palate-tip and side-walls 
for the two cases of side-wall elastic modulus (Ew) being 200 and 
2800 N/m2 respectively. For each case a range of soft-palate 
elastic modulus (EP) is used to vary the amplitude of its motion.  
 
It is seen throughout that the soft-palate deflects upwards into the 
narrower channel as shown through the independent methods of 
[6] while the side-walls move inwards to create a partial closure 
of the channel at its downstream end. Soft-palate oscillations are 
seen to be attenuated in these sub-critical conditions. The 
infinite-time result has the system arriving at a new static 
equilibrium position. The soft palate always comes to rest 
deflected into the upper, narrower, channel because there is 
greater flow-speed and mass flux through the lower, wider, 
Y
-D
is
pl
ac
em
en
t 
Node A
Tip Response 
Time ->
Z
-D
is
pl
ac
em
en
t 
Node B
Wall Response 
(b)Pressure 
(c)Velocity Magnitude
343
channel that has lower resistance; see Figs. 3b and 3c. At the 
soft-palate tip the upper and lower channel-flows combine. A 
separated shear layer exists that must deflect towards the top 
rigid wall like the flow over a backward facing step in the 
extreme case of infinite upper-channel resistance. The resulting 
curvature of the isobars in the lower channel relative to those in 
the upper channel then produces a net upwards force that deflects 
the soft-palate. As seen in Figs. 4 and 5, the lower the value of 
the soft-palate stiffness, the greater is its deflection. 
Tip Response
Ep=50 Pa
Ep=100 Pa
Ep=400 Pa
Ep=800 Pa
Ep=2800 Pa
-0.001
0.005
0.010
0.015
0.020
0.025
0.030
0 1 2 3 4 5 6 7 8 9 10
Time (s)
Y-
Di
sp
la
ce
me
nt
 (
cm
)
 
WALL Response
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 1 2 3 4 5 6 7 8 9 10
Time (s)
Z-
Di
sp
la
ce
me
nt
 (
cm
)
Ep=50 Pa
Ep=100 Pa
Ep=400 Pa 
Ep=800 Pa
Ep=2800 Pa
 
Figure 4. Time series of (a) soft-palate tip, and (b) side-wall mid-
point motion for a flexible side-wall with Ew =200 N/m2. 
 
Figures 4a and 5a clearly show that changing EP strongly 
influences the soft-palate deflection. However, corresponding 
changes in EW generate only a small change in side-wall 
deflection as evidenced by contrasting Figs. 4b and 5b. Equally 
evident in these latter figures is that the magnitude of the soft-
palate deflection has virtually no effect on the side-wall 
deformation. To further confirm the insensitivity of side-wall to 
soft-plate deflection we have artificially added uniform loads to 
the soft-palate, for just the first 0.5 s, that increase the amplitude 
of its oscillations. As already seen in Figs. 4a and 5a the soft-
palate deflection ultimately asymptotes to a static deformed state. 
Prior to this, very large amplitudes of oscillation are observed. 
and yet these motions have very little effect on the side-wall 
motion. In fact, an increase to the soft-palate amplitude by a 
factor of 28 results in only a maximum change of 2.8% in the 
amplitude of side-wall movement. This signals the insensitivity 
of side-wall motion to the dynamics of the soft plate. 
 
The effect of side-wall motion on soft-palate response 
The motion of the soft-palate tip has been recorded over a range 
of side-wall stiffness for a number of cases of soft-palate 
stiffness. Figures 6a and 6b respectively show the cases EP=200 
and 800N/m2. A broad contrast of the two figures (and noting the 
scales of the vertical axes) shows that soft-palate deformation 
decreases with increases to EP as already seen in Figs. 4a and 5a. 
Of greater interest in these figures is that both the transient 
oscillations of the soft palate and amplitude of the final static 
equilibrium achieved are strongly dependent upon EW and thus 
the deformation of the side walls. In most cases, the higher the 
deformation of the side walls – or extent of channel closure – 
then the more the soft-palate deforms. However, in Fig. 6a it is an 
intermediate value of EW that yields the highest transient 
amplitude of the soft-palate; this suggests some form of 
resonance between the motions of the different flexible surfaces. 
We also remark that for stiffer soft-palates the transient 
behaviour can feature incursions of the soft palate into the lower 
channel. 
(a)
 
Tip Response
Ep=50 Pa
Ep=100 Pa
Ep=400 Pa
Ep=800 Pa
Ep=2800 Pa
0.000
0.004
0.008
0.012
0.016
0.020
0 1 2 3 4 5 6 7 8 9 10
Time (s)
Y-
Di
sp
la
ce
me
nt
 (
cm
)
 
(a)
(b)
(b)Wall Response
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 1 2 3 4 5 6 7 8 9 10
Time (s)
Z-
Di
sp
la
ce
me
nt
 (
cm
)
Ep=50 Pa
Ep=100 Pa
Ep=400 Pa
Ep=800 Pa
Ep=2800 Pa
 
Figure 5. Time series of (a) soft-palate tip, and (b) side-wall mid-
point motion for a flexible side-wall with Ew =2800 N/m2. 
 
Characterisation of the coupled mechanics 
 
Since side-wall behaviour has been shown to be insensitive to 
soft-palate motions, its behaviour may be reasonably predicted by 
assuming a rigid soft palate. By contrast, soft-palate behaviour is 
strongly dependent upon both soft-palate and side-wall material 
properties. Three features of soft-palate response, drawn from 
Fig. 6 (and further results for other values of EP) are used to 
characterise this behaviour: (a) the final static-equilibrium tip 
deflection, (b) the peak amplitude [relative to the value of (a)] in 
the transient phase, and (c) the frequency of its oscillations in the 
transient phase. Displacements (a) and (b) are non-
dimensionalised based on in-vacuo plate mechanics for which the 
peak deflection due to a distributed load is (3 LPΔ 4/2EPh3) where 
L and h are the plate length and thickness respectively. We use 
PΔ  on the assumption that the transmural fluid loading is 
directly related to the applied streamwise pressure drop across the 
entire channel. For a time-scale to non-dimensionalise the 
frequency, we use k/(Ep)0.5 with k=1 for convenience. Figures 7a, 
7b and 7c then show the variation of the above three features for 
344
 different values of EP. While clear trends emerge, there is not 
total collapse of the data. This suggests that a more complex 
scheme is required that accounts for both solid and fluid 
parameters in the system. This is further suggested by a type of 
frequency lock-in when EW/EP=1 in Fig.7c and recalling that the 
only means of coupling is through the fluid medium. 
 
 
 
0 2 4 6 8 10 12 14
5
6
7
8
9
10
11
x 10-4
 
 
Tip Response
0.000
0.003
0.006
0.009
0.012
0.015
0 1 2 3 4 5 6 7 8 9 10
Time (s)
 Y
-D
is
pl
ac
em
en
t(
cm
)
Ew =150 Pa Ew =200 Pa
Ew =250 Pa Ew =300 Pa
Ew =400 Pa Ew =500 Pa
Ew =600 Pa Ew =800 Pa
Ew =1600 Pa Ew =2800 Pa
Rigid Wall
 
Tip Response
-0.002
0.001
0.003
0.005
0.007
0 1 2 3 4 5 6 7 8 9 10
Time (s)
Y-
Di
sp
la
ce
me
nt
 (
cm
)
Ew =150 Pa Ew =200 Pa
Ew =250 Pa Ew =300 Pa
Ew =400 Pa Ew =500 Pa
Ew =600 Pa Ew =800 Pa
Ew =1600 Pa Ew =2800 Pa
Rigid Wall
 
 
Figure 6. Effect of side-wall stiffness on tip motion for two 
different soft-palates: (a) EP=200, and (b) EP=800 N/m2 . 
 
Conclusions 
 
An analogue computational model of the upper airway, 
combining soft-palate and flexible side-walls coupled through 
airflow has been developed and used to explore the interaction 
between these three dynamical elements. It is shown that the 
side-wall response to the airflow is largely independent of 
motions of the upstream soft palate. Conversely, the motion and 
final equilibrium of the soft-palate is strongly dependent upon 
side-wall flexibility and, hence, deformation. This dependence 
has been mapped for the single geometric configuration adopted 
in this paper. Further work will seek to quantify the effect of 
transients on upper-airway stability in such cases as, one inlet 
channel closed (breathing through nose only) and the transition 
from inhalation to exhalation.  
 
References 
 
[1] Aurégan, Y. & Depollier, C.,Snoring: Linear stability 
analysis and in-vitro experiments. J. Sound Vib., 188, 1995, 
39-54. 
 
 
0 2 4 6 8 10 12 14
2
3
4
5
6
7
8
x 10-4
Ew / Ep
(a)
Ep=200 Pa Ep=350 Pa
Ep=500 Pa Ep=800 Pa
Ep=1600 Pa Ep=2800 Pa
(a)
(b)
 
0 0.5 1 1.5 2 2.5 3 3.5 4
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
 
Ew / Ep
(c)
(b)
(Ew / Ep)0.5 
Figure 7. Variation of non-dimensionalised soft-palate motion 
with side-wall stiffness: (a) final tip deflection, (b) peak 
amplitude of oscillation, and (c) frequency of oscillation. 
 
 [2] Balint, T.S. & Lucey A.D., Instability of a cantilevered 
flexible plate in viscous two-dimensional channel flow. J. 
Fluids Struct., 20, 2005,  893-912. 
 [3] Bertram, C.D.,Experimental Studies of Collapsible Tubes. In 
Flow Past Highly Compliant Boundaries and in Collapsible 
Tubes, eds. PW Carpenter & TJ Pedley, Kluver, 2003, 51-65 
[4] Guo, C.Q. & Paidoussis, M.P. Stability of Rectangular 
Plates with Free Side-Edges in Two-Dimensional Inviscid 
Channel Flow. J. Appl. Mech. 67, 2000, 171-176. 
[5] Heil, M. & Jensen, O.E. (2003) Flows in deformable tubes 
and channels. In Flow Past Highly Compliant Boundaries 
and in Collapsible Tubes, eds. PW Carpenter & TJ Pedley, 
Kluver, 2003, 15-49, Kluwer. 
[6] Tetlow, G.A., Lucey, A.D. & Balint, T.S. Instability of a 
cantilevered flexible plate in viscous channel flow driven by 
constant pressure drop. 2006, ASME Paper PVP2006-
ICPVT11-93943. 
[7] Wang, J., Tetlow. G.A., Lucey, A.D., Armstrong, J.J., Leigh, 
M.S., Paduch, A., Sampson, D.D, Walsh, J.H., Eastwood, 
P.R., Hillman, D.R., Harrison, S.,Dynamics of the human 
upper airway: On the development of a three-dimensional 
computational model. In IFMBE Proc. (CD) 14 (World 
Congress on Medical Physics and Biomechanical 
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Flow-Structure Interaction in the Upper Airway: Motions of a Cantilevered Flexible Plate in Channel Flow with Flexible Walls

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Flow-Structure Interaction in the Upper Airway: Motions of a Cantilevered Flexible Plate in Channel Flow with Flexible Walls

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