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Proceedings of the ASME 2013 International Mechanical Engineering Congress IMECE2013

November 15-21, 2013, San Diego, CA, USA

Paper Number: IMECE2013-62904

Predicting the treatment response of oral appliances for obstructive sleep apnea using computational fluid dynamics and fluid-structure interaction simulations

Moyin Zhao

School of Mechanical Engineering, University of New South Wales

Sydney, New South Wales, Australia

Tracie Barber School of Mechanical Engineering,

University of New South Wales Sydney, New South Wales, Australia

Peter Cistulli

Sleep & Circadian Group, Woolcock Institute of Medical Research,

Glebe, New South Wales, Australia

Kate Sutherland

Sleep & Circadian Group, Woolcock Institute of Medical Research,

Glebe, New South Wales, Australia

Gary Rosengarten

School of Aerospace, Mechanical and Manufacturing Engineering,

RMIT University, Victoria, Australia

ABSTRACT

In this study we used computational fluid dynamics (CFD) to analyze the therapeutic effect of an oral device (mandibular advancement splint – MAS, that protrudes the lower jaw during sleep) as a treatment for Obstructive Sleep Apnea (OSA). Anatomically-accurate upper airway (UA) computational models were reconstructed from magnetic resonance images (MRI) of 7 patients with and without a MAS device fitted. CFD simulations of UA airflow were performed at the maximum flow rate during inspiration. The CFD results indicated the lowest pressure often occurs close to the soft palate and the base of the tongue. The airway pressure gradient was estimated as the best indicator for treatment response since the change in the pressure drop forms a linear correlation with the change in patients’ Apnea-Hypopnea Index (AHI). This correlation has the potential to be developed into a model for predicting the outcome of the MAS treatment. However the rigid wall assumption of CFD models is the major uncertainty. To overcome this uncertainty we set up a full fluid-structure interaction model for a typical responder case with a compliant UA wall. The results demonstrated the different UA flow field associated with using MAS alleviated the airway collapse, which was successfully predicted for the untreated patient. We thus show for the first time that FSI is more accurate than CFD with

rigid walls for the study of OSA, and can predict treatment response. Comparison of the FSI and CFD results for the UA flow and pressure profiles showed variation between the models. The structural deflection in oropharynx effectively reformed the flow pattern, however, the maximum pressure drops of both results were close. This supports the competence of the CFD method in clinical applications, where maximum pressure drop data can be used to develop a treatment-predicting model.

Key words Sleep Apnea, Fluid Structure Interaction, CFD.

INTRODUCTION

Mandibular advancement splints (MAS) can be an effective treatment for Obstructive Sleep Apnea (OSA). They hold the lower jaw in a protruded position and help prevent the Upper Airway (UA) from occluding [1-3]. However not all patients respond to this form of treatment. Only 60-70% of patients have a clinical benefit from MAS. A complete treatment success (apnea-hypopnea index (AHI) < 5 after treatment) is only found for 35-40%, and reasons remain unclear [1].

Recently Computational Fluid Dynamics has been utilized to characterize the fluid flow in human airway models [4-7]. The patient-specific UA geometries are generated from medical imaging data like Computerized

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Tomography (CT) and magnetic resonance imaging (MRI) [4, 5, 7, 8]. The changes of UA flow parameters like pressure drop and flow resistance was found correlate to treatment outcomes [4, 5]. However, the airway flow field cannot represent the full mechanism of airway collapse since the walls were rigid.

The Fluid Solid Interaction (FSI) technique provides a possibility to reproduce the airway collapse by computational modeling [9]. A limited number of studies utilizing FSI for sleep apnea have been introduced into this field. One of the early studies modeled an idealized 2-D tongue model in 2007 [10], which was later developed into a 3-D tongue model in 2011 [11]. The original work also showed FSI modeling of soft palate movement within a realistic UA geometry [12]. A comparison of uvula displacement from pre- and post-operational cases using FSI simulations was able to indicate the effect of nasal surgery on OSA [9]. However, no previous studies fully demonstrated the difference between the UA flow profile within rigid and flexible entire UA boundaries.

In this paper, patient specific FSI models are developed based on previous CFD models [4]. An analysis of the flow field will be carried out on an entire compliant UA structure to simulate the process of UA collapse. The aim is to demonstrate the advantage of FSI simulations in OSA research in predicting the potential collapse location. This would assist clinicians to understand more about the mechanism of OSA. MATERIAL

Patients with OSA were recruited from a sleep disorders clinic for treatment with MAS. Treatment outcome was determined by a full cardiorespiratory polysomnography (PSG) study. The severity of OSA is defined by the Apnea and Hypopnea Index (AHI), derived from the total number of apnea and hypopneas per hour of sleep. One patient who was classified as a typical responder (post-treatment AHI<5/hr) to MAS was selected for this study (Table 1). The custom-made 2-piece MAS (Figure 1) used in this study was fabricated by SomnoDentMAS (SomnoMed Ltd, Crows Nest, Australia). Table 1: General characteristics of selected patient in this study. (WO-without MAS fitted, W-with MAS fitted)

Patient Age Gender BMI AHI (WO) AHI (W)

Responder 52 Male 29.41 41.5 2.1

Figure 1 Custom-made two-piece MAS. The device used in the study resembles the one pictured with the exception of a modification of the metal screw advancement mechanism which was replaced with an acrylic advancement mechanism to allow the device to be worn during MR imaging. The design features and efficacy of this appliance have been previously published [4].

MEDICAL IMAGING AND GEOMETRY GENERATION

The magnetic resonance imaging (MRI) of the upper airway was performed during wakefulness without and with MAS in place. 50 slices (512 x 512 matrix) are taken from the level above nasopharynx to the level below vocal cord with a thickness of 3mm. During scanning, the regular breathing and swallowing were permitted. The detail of scan protocol can refer to previous study [4]. UA surface models (Figure 2) were reconstructed with and without MAS fitted conditions in Amira5 (Visage Imaging, United States). The vertex-averaged smoothing algorithm was applied. The boundary vertices were recalculated according to the average position of their adjacent vertices, while the UA geometrical characteristics were preserved.

before treatment after treatment

Figure 2 The reconstruction of UA geometries of before and after MAS treatment. 3-D UA surface models were shown with 2-D Sagittal MRI

scans.

COMPUTATIONAL MODELS

UA surface models were developed into 3-D UA volumes for the fluid domains and 2 mm thick airway wall models for the solid domains. According to our previous work [4], refined unstructured hybrid volume

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mesh with 1.3 million and 1.6 million elements were generated respectively for the fluid regions in each condition. The UA solid wall was constructed with hexahedral elements (Figure 3). An additional grid convergence study was performed to determine the most efficient mesh for the structure. The result show 20,000 hexahedral computational grids were adequate for the UA structural pre-treatment. For the post-treatment model, a 27,000 hexahedral element mesh was sufficient for a grid independent solution.

(a) (b)

Figure 3 Computational grids for fluid (a) and solid (b) domains. The cross section views of each mesh are shown on the right.

SOLVER EQUATIONS

For fluid domain in the UA, the estimated range of Reynolds numbers (Re) indicated the flow was either laminar or transitional. The standard k-ω shear stress transport (k-ω SST) model was proven to be appropriate to simulate this complex flow [4]. The main governing equations of the fluid domain can be expressed as:

0i

i

u

x

(Eq. 1)

' 'j ji

i i j

i i i j i

u uuPu u u

x x x x x

(Eq. 2)

where u is the velocity, ρ is the fluid density, i and j represent the Cartesian cordinates. The fluid and solid domain are coupled through the stress tensor. general expression for the Cauchy stress tensor in an isotropic Newtonian fluid field is:

12 ( )

3

f

ij ij ij kk ijp (Eq. 3)

where ij is the rate of the strain tensor ij , and can

be given by:

1

2

jiij

j i

uu

x x

(Eq. 4)

In the structural field, the governing equation of linear elasity are:

2

2

i

s

ij

i

j

DF

x t

(Eq. 5)

where iF is the body forces, iD is the structural

displacement. The Cauchy stress tensor in the structural field is defined as:

(1 )(1 2 ) (1 )

s

ij kk ij ij

Ev E

v v v

(Eq. 6)

where E is the Young’s modulus, v is the Poisson’s

ratio, ij is the strain tensor (equation 4).

The coupling conditions of fluid and solid domain at the FSI boundary are the matching of the fluid velocity and structural displacement:

ii

Du

t

(Eq. 7)

and the force equilibrium across the FSI interface f s

ij ijn n (Eq. 8)

where n is the normal vector outward of the FSI interface. FLOW PROPERTIES AND BOUNDARY CONDITIONS

Identical boundary conditions were applied for

the fluid domain in CFD and FSI simulation. The time-

varied inlet boundary was defined at the nasopharynx.

The inlet flow profile was described as sinusoidal for a

time period of 1 second with a maximum flow rate of

166ml/s (10L / min) [5]. The outlet boundary was set of

the vocal cord. An average static pressure of 0 Pascal

(relative to 1 atm) was used at the outlet [4]. The

turbulence intensity was set as 10% [10]. The wall of

whole upper airway was assumed as no-slip and smooth.

For the solid domain in FSI model, the cross-sectional

surface at the soft palate and vocal cord was fixed for all

degrees of freedom. A FSI interface was defined at the

inner surface of UA wall model. The UA tissue was

defined as a homogeneous elastic material which had a

Young’s modulus of 7540 Pa and a Poisson’s ratio of

0.325 [13].

RESULTS

In order to analysis the flow profile in 3 dimensions across the UA, transverse cross-sectional planes were created every 5mm from inlet to discharge boundary. The FSI simulation of pre-treatment case ceased at 0.56s when collapse occurred on the oropharynx wall. The equivalent time in the cycle was used in the CFD. All Figures below present the pre-

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treatment result at the moment that flow rate reached 128 ml/s, which was at 0.56s. The post-treatment result was plotted at a flow rate of 166ml/s, which occurred at 1s. The collapse of the UA is demonstrated in the FSI simulations when the UA wall between anterior and posterior side touched at left side of oropharynx. The larynx showed a significant deflection. Very small deflections of the UA geometry were found in the post-treatment case.

Figure 4 and 5 show the velocity vectors on each plane obtained from the CFD and FSI simulations for the pre-treatment case. The FSI model has a slightly higher maximum flow velocity (9.99 m/s) at the velopharynx compared to CFD model (9.69 m/s). However, the compliant UA boundary results in a significant increase of average flow velocity in the oropharynx and larynx, by 12.9% and 13.8% respectively. The two models have a maximum difference in velocity (1.596 m/s) at the cross-section, 60mm from inlet, where UA collapse occurs. In the post-treatment cases, both the flow velocity and flow vector pattern are similar. A maximum velocity difference of 0.22m/s was found at the lower oropharynx.

CFD FSI

Figure 4 Velocity vector profile of pre-treatment (without MAS). Left side is CFD model and right side is FSI model.

CFD FSI Figure 5 Velocity vector profile of post-treatment (with MAS). Left side

is the CFD model and right side is FSI model.

The deformation of the UA boundary is largely

driven by the pressure force which is a result of the negative pressure in the UA lumen. The

Figure 6 and 7 show the pressure contours in each UA cross-section for the different cases. The FSI model of the pre-treatment case has a lower pressure profile from the lower velopharynx to the larynx. The pressure difference is small for the post-treatment models, with a slightly higher oropharygeal pressure predicted by the FSI model.

It has been pointed out in a previous study [4] that the maximum pressure drop closely correlated with the treatment response (changes in AHI). The maximum pressure drop is determined from the variation of minimum pressures across UA [4]. Figure 8 shows the minimum pressure values which were calculated from cross-section planes in all studied cases. Similar pressure drops (-65.5 for CFD, -63.2 for FSI) where found in velopharynx using the two methods. For the pre-treatment FSI model, the lower volume expansion in deformed oropharynx and larynx result a lower pressure level (average 9.3 Pa less than CFD) in these areas. These low UA pressure will further react on the UA structure by speeding up collapse progress. The self-contact of UA wall (60mm from inlet) results in a relatively low pressure region however it is only 11.66 Pa less than that found

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using CFD. Although the wall collapse resulted in a narrow gap or even a partially closed airway, the reduction of UA volume will be effective in reducing the pressure. This volume reduction is more likely to happen at the UA section with large space. Since there are negligible changes in the geometry and velocity features between post-treatment models (no airway collapse), their pressure profiles are reasonably close.

In this study, results show that the maximum pressure drop values are similar between CFD and FSI models for pre- and post-treatment cases. The treatment predicting model developed from above mentioned correlation will be still valid with UA model with compliant wall boundary condition. In further work the population of the case study will be increased. Additionally more anatomical and material information will be included in future FSI models, thus making the results more useful.

CFD FSI Figure 6 Pressure contours of pre-treatment (without MAS) case. Left

side is the CFD model and right side is FSI model.

CFD FSI

Figure 7 Pressure contours of post-treatment (with MAS) cases. Left side is the CFD model and right side is FSI model.

a. pre-treatment case

-70

-60

-50

-40

-30

-20

-10

0

0 20 40 60 80 100

FSI

CFD

Distance to inlet (mm)

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b. post-treatment case

Figure 8 pressure profiles of pre-treatment (a) and post-treatment (b) models. Graphs show the minimum pressure value of each cross-section plane (figure4&5).

CONCLUSION

This study compared the result of CFD and FSI simulations to model human upper airway flow related to sleep apnea. Specifically the effect of treatment using a mandibular advancement splint was investigated. The pre-treatment FSI model successfully simulated UA collapse which can complement the previous CFD study. The FSI simulations showed a reduced volume in oropharynx due to airway collapse and thus an increased flow velocity. This lowered down the level of static pressure which would further reinforce the UA collapsing. Interestingly the maximum pressure drop was preserved at the same level as CFD model. This supported the validity of the previous treatment predicting model [4]. The results show that reasonable accuracy can be found for a CFD model, without the need for the added complexity of the FSI analysis. However FSI analyses may be useful for accurately predicting the collapse site for clinical applications.

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-8

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-2

0

0 20 40 60 80 100

FSICFD

Distance to inlet (mm)

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