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Respiration Simulation of Human Upper Airway for Analysis of Obstructive Sleep Apnea Syndrome Renhan Huang and Qiguo Rong* College of Engineering, Peking University, Beijing 100871, P.R. China [email protected], [email protected]

Abstract. Obstructive sleep apnea syndrome (OSAS) is a disease that the pharyngeal portion collapses repeatedly during sleep and finally results in the cessation of breathing. So far the potential pathogenesis factors that may cause OSAS are discussed from two main aspects: anatomic abnormalities of the upper airway and the weak or absence of nerve control mechanism. In this study, a three-dimensional finite element model which possesses high geometrical similarity with the real anatomical structure is built. By making use of the pressure in upper airway measured in normal expiration and apnea episode, the fluid field in upper airway and the displacement of the soft tissue around the airway are calculated using fluid-structure coupled algorithm, and then the result between normal respiration and apnea episode are compared. According to the result, the region where the maximum negative pressure and the largest displacement occur will be the most domains the airway collapses and breath apnea appears. Keywords: OSAS, upper airway, fluid-structure interaction, FEM.

1 Introduction Obstructive Sleep Apnea Syndrome (OSAS) is a common sleep-related breathing disordered characterized by repetitive pharyngeal collapse, cessation and reopen of the airflow in the oral and nasal cavity (Figure 1). It is reported to affect approximately 4% of the United States population[1]. Severity of OSAS is measured by the apnea-hypopnea index (AHI), where apnea is defined as cessation of airflow for at least 10 seconds. For mild OSAS patient, the AHI is 5-15, as for severe patient, the AHI can be more than 30. The most representative symptoms are snoring and excessive daytime somnolence, which will decrease quality of the life and increase the risk of cardiovascular and cerebrovascular disease [2-4]. Although the pathology of the OSAS is complicated, fundamentally it can be concluded into two main aspects: anatomic abnormalities of the upper airway and the weak or absence of nerve control mechanism. The narrow and obstruction of the upper airway, which may be caused by kinds of anatomic abnormalities, will greatly affect the fluid filed in upper airway and lead to collapse of some parts of upper airway. In order to obtain enough airflow during inspiration, more negative pressure is *

Corresponding author.

K. Li et al. (Eds.): LSMS/ICSEE 2010, LNBI 6330, pp. 588 – 596, 2010. © Springer-Verlag Berlin Heidelberg 2010

Respiration Simulation of Human Upper Airway

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needed at the region where the upper airway area is narrow. As soon as the negative pressure descends below the pressure of peripheral tissue, the collapse will occur. Furthermore, required by the needs of speech, swallowing, respiration and other physiological function, a complex control system with more than twenty various muscles playing a role in upper airway. These groups of muscles interact in a complex fashion, constriction or dilatability according to breath state, to maintain the ventilation. If this nerve control mechanism becomes weak or even absence, the upper airway may collapse under a small negative pressure in lumen.

Fig. 1. Obstructive sleep apnea

Based on the analysis of OSAS from physiological and pathological view, it can be known that the whole process from airflow enters the upper airway from nasal cavity at the beginning of breath to the collapse of the pharyngeal portion, is a problem that possesses material and geometrical nonlinearity, fluid and structure interaction and lift self-adapting from mechanical view. The motion state of upper airway in breath apnea can be studied by mechanical model [5-6]. Each potential reason can be treated as a control factor of the mechanical model. By changing these control factor, it is studied that how the relevant potential reason affects OSAS. The biomechanical study of OSAS aims at providing theoretical principle and technical support for the prevention and treatment. As a result, some mechanical models have been developed and some useful results have been achieved.[7-16] Based on CT medical images of ten volunteers, the 3D FE model of the upper airway was reconstructed by using the method of surface rendering, and the airflow of the whole cavity is simulated numerically and analyzed by the FE method(Yinxi Liu et al )[17]. A pharyngeal airway model characterized by a maximum narrowing at the site of retropalatal pharynx was reconstructed from cross-sectional magnetic resonance of a patient with obstructive sleep apnea, and two flow –modeling strategies: steady Reynolds-Averaged Navier-Stokes(RANS) methodology and Large Eddy Simulation were employed to analysis the fluid field in

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upper airway(Mihai Mihaescu et al)[18]. A computational fluid dynamics model was constructed using raw data from three-dimensional computed tomogram images of an OSAS patient, and then the low Reynolds number κ − ε model was adopted to reproduce the important transition from laminar to turbulent flow in the pharyngeal airway (Soo-Jin Jeong et al) [19]. Computational fluid dynamic analysis was used to model the effect of airway geometry on internal pressure in the upper airway of three children with obstructive sleep syndrome and three controls. Model geometry was reconstructed from magnetic resonance images obtained during quiet tidal breathing, meshed with an unstructured grid, and solved at normative peak resting flow, the unsteady Reynolds-averaged Navier-Stokes equations were solved with steady flow boundary conditions in inspiration and expiration, using a two-equation low-Reynolds number turbulence model(Chun Xu et al)[20]. Up to now, all the models that involved OSAS study are simplified more or less in geometric configuration, especially the bone tissue and soft tissue around the upper airway are excluded in the model. In fact the bone tissue such as skull, neck and hyoid may restrict the deformation of the airway because of their high young’s modulus, and the soft tissue around the upper airway may act on it by active contraction. As a result, the skull, neck and hyoid and other anatomical characteristic such as maxillary antrum, sphenoid sinus and frontal sinus must be taken into account in order to obtain a result close to physiological condition. It is necessary of using fluid-structure interaction algorithm because the pressure originated from airflow acts on the wall of upper airway, resulting in the structural deformation which can change the pressure distribution in reverse. In this paper, a finite element model including airway, skull, neck, hyoid and soft tissue around the upper airway is presented, besides a preliminary fluid structure interaction simulation result from an respiration during a second is explained.

2 Method Computer modeling was conducted using CT data obtained from a 26-year-old male person. Three-dimensional CT scanning was performed on a GE MEDICAL SYSTEMS/LightSpeed VCT scanning station with the 1.25 mm thickness. Scanning was conducted while the person was awake in the supine position. The scanned images were transferred to Materialise’s Interactive Medical Image Control System 10.0. MIMICS is an interactive tool for the visualization and segmentation of CT images as well as MRI images and 3D rendering of objects. The regions of interest were isolated and reconstructed into 3D models one by one according to gray level threshold segmentation. Different tissue has different density so that each tissue has a special gray level threshold in the CT images. The very dense parts are corresponding to high threshold while the soft tissue with a low threshold value. As a sequence using both an upper and a lower threshold can separate an interested part. The thresholds used to obtain airway, skull, neck, hyoid and soft tissue are demonstrated in Table 1. Then each part of the model was imported into Geomagic Studio 10 (A reverse engineering software maked by US Raindrop Company) to be edited by manual and was exported with NURBS (Non-Uniform Rational B-Splines). After that all of them were transferred to Ansys 11.0 to be assembled as a whole model, which can be meshed


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Table 1. Gray thresholds for Different Tissues

Lower threshold Higher threshold

Cavum -1024 -420

Bone 226 3071

Soft tissue -700 225

using an unstructured grid. The 4-node tetrahedral element possessing well fitting function was selected because of the complexity of the model. Specially 4-node shell element type was used to mesh the outside surface of the airway, which was not only can be treated as the parameter transfer interface between fluid domain and structure domain required by the algorithm but also can be applied initial stress for the further study in the future. Finally the meshed model was shifted to Adina (Automatic Dynamic Incremental Nonlinear Analysis) 8.6.0 to accomplish the fluid-structure coupled simulation. Figure 2 and Figure 3 demonstrate the finite element model used to calculation, where different tissue is rendered with distinct color. The finite element model information is listed in Table 2. The ADINA system has a structural analysis capability as well as a fluid analysis capability. The anailability of both capabilities within the same code provides the base for developing sophisticated fluid-structure interaction tools. For fluid-structure interaction problems, the fluid model must be based on an arbitrary-Lagrangian-Eulerian coordinate system since the fluid-structure interface is deformable. The fundamental conditions applied to the fluid-structure interfaces are kinematic condition or displacement compatibility

d f = ds And the dynamic condition or traction equilibrium

n ⋅ Tf = n ⋅ Ts Where df and ds are, respectively, the fluid and solid displacement and Tf and Ts are, respectively, the fluid and solid stresses. The fluid and solid parts are coupled as follows: the fluid nodal positions on the fluid-structure interfaces are determined by the kinematic conditions. The displacements of the other fluid nodes are determined automatically by the program to preserve the initial mesh quality. The governing equations of fluid flow in their ALE formulations are then solved. In steady-state analyses, the mesh velocities are always set to zero even the fluid nodal displacements are updated. Accordingly the fluid velocities on the fluid-structure interfaces are zero. According to the dynamic conditions, on the other hand, the fluid traction is integrated into fluid force along fluid-structure interfaces and exerted onto the structure node.

F (t ) = ∫ h d T f ⋅ ds Where hd is the virtual quantity of the solid displacement[21].

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Fig. 2. Finite element model Table 2. FEM Model Information

Element Type Node Element

Airway Skull Neck Hyoid Soft tissue 3-D Fluid 3-D Solid 3-D Solid 3-D Solid 3-D Solid 15927 35271 36548 1924 465843 66498 31153 31223 1735 369933

Interface Shell 9461 18926

Table 3. Material Property for FEM Model[22] Young's Modulus(Pa)

Poisson Ratio

Density(g/mm3)

Bone (Skull Neck Hyoid)

1.37×1010

0.3

1.85×10-3

Soft Tissue

1.0×104

0.45

1.06×10-3

Shell Part One

1.37×1010

0.3

1.85×10-3

Shell Part Two

1.0×104

0.45

1.06×10-3

Shell Part Three

2.02×106

0.3

1.25×10-3

Actually, the mechanical characteristic of biological tissue is nonlinear. As a preliminary research, however, linear constitutive relation is used for the purpose of optimizing time consumption. Owing to the fact that water forms most of the soft tissue component; it can be taken as quasi-incompressible. Human upper airway is a complex lumen which can be partitioned into various individual segments having distinct anatomical properties and physiological functions. These individual segments act as singularities whose contributions cannot be ignored in the understanding of the overall upper airway behavior. So the surface of the airway is divided into three parts as exhibition in Figure 4. The part (The verdant part in Fig 4) embodied in the nasal cavity hardly has deformation when respiration because it is very close to the hard tissue, so a high Young’s Modulus value is assigned to it. Based on anatomy, there are a series of cartilage rings around the wall of airway from hyoid downward to the branchus, so this part (The purple part in Fig 4) reflects a cartilage mechanical property. The rest part of the surface (The yellow part in Fig 4) is treated as the same


Fig. 3. Norma Sagittalis of the FEA Model

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Fig. 4. Segments of Upper Airway Wall

material property as soft tissue. There are three material models was used. Particularly the detailed value is demonstrated in Table 3. During the sleep in the supine position, the back side of the head contacting to the bed is fixed, as a sequence the skull and the neck are hardly moved when breathing. Their tiny displacements are almost make no difference for the deformation of the upper airway, therefore all freedom degree of the bone tissue are fixed except for the hyoid which is imbedded in muscle and connects to neither the skull nor the neck. As for the fluid model used for the upper airway, viscous incompressible laminar flow model is chosen. In fact due to the complexity of the geometric configuration of the upper airway plus the highly instability of airflow when collapse occur, a turbulence model may be more possible to obtained the real outcome. The first step of this project, however, focuses in the fluid-structure interaction effect so the turbulence phenomenon is neglected and left as the next work. The parameter used for the airflow is as follows: 1.297×10-6g/mm3, 1.81×10-5Pa for density and viscosity coefficient, respectively. At the nostril where is the airflow inlet, a zero pressure is applied while at the hypopharynx a variable a time varying pressure function is exerted as the outlet boundary condition. The pressure function was measured with titration at normal breath situation. The gravity of the soft tissue around the anterior upper airway isn't taken into account because the configuration of the airway has been the station after the gravity effect in spine position. A segment of load lasting 1.2 second in expiration is picked for calculation. The time step is designed quite small at the beginning, for the purpose of obtaining a reasonable initial condition for the iteration in the transient analyses.

3 Results and Discussion Figure 5 shows the displacement contour of soft tissue. According to the distribution, the maximum displacement appears at the anterior of the soft tissue around the neck. This is reasonable because this domain is far from the fixed bone tissue and near the outlet where normal pressure traction was directly applied. The fact that the displacement

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magnitude at the time of 0.05 second is quite large compared to the situation at the time of 1.2 second is also rational as the pressure in the upper airway varies from the maximum to the nearly zero during the expiration process. Figure 6 demonstrates the pressure contour of the upper airway. According to the distribution, the pressure near the nostril is close to atmosphere. The maximum pressure at each time step is almost agree with the variation of the pressure function. It is worth to draw attention to the nasal cavity where the pressure changes intensively. The complicated configuration of the nasal cavity increases the airway resistance and as a sequence a large pressure gradient.

Fig. 5. Displacement distribution in soft tissue at the 0.05s and 1.20s in expiration

Fig. 6. Pressure distribution in upper airway at the 0.05s, 0.4s, 0.8s and 1.20s in expiration

As to the currently model by now, there are four aspects that could be improved. First, only 1.2 second in expiration phase is simulation. Usually a integrated respiration period last 4 seconds and the apnea only occurs in the inspiration phase. So the simulation must comprise of several respiration period so as to make it significant for the obstructive sleep apnea syndrome. Second, although the model in this paper has the quality that reflects more details than the others that are more or less simplified, but the muscles and fat should be added to the model in the subsequence work in


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order to get more meaningful results. Third, the material characteristic that used in those models is linear elastic model, which can’t really reflect the mechanical property of soft tissue. The mechanical characteristic of soft tissue around the upper airway, including muscle and fat, is nonlinearity. As a result, nonlinearity constitutive relation must be used in order to achieve a precise simulation. In addition, the deformation of the collapse part of airway should be described in large deformation theory. However it’s a pity that it is still unused in actual calculation. The deformation of the collapsed position compared to the diameter of upper airway has been beyond the small deformation hypothesis, so the large deformation theory should be used. The last but not the least, there is hardly study work that regards nerve control mechanism in respiration. It is well known that each physiological activity is accurately controlled by nervous system and respiration is no exception. How to embody this selfregulating feedback control mechanism in the model calculation is worth studying.

4 Conclusion In this study, a finite element model including airway, skull, neck, hyoid and soft tissue around the upper airway is developed, besides a preliminary fluid structure interaction simulation result from a expiration during a second is explained. Although it is the first step of the whole project plan, its result verifies that the biomechanical method is workable and useful. The further research is in progress.

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