INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Int. J. Numer. Meth. Biomed. Engng. 2012; 28:528–546 Published online 20 January 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cnm.1486

Fluid–structure interaction modeling of upper airways before and after nasal surgery for obstructive sleep apnea Ying Wang 1 , Jie Wang 3 , Yingxi Liu 1,2 , Shen Yu 1 , Xiuzhen Sun 1,2, * ,† , Shouju Li 1 , Shuang Shen 1 and Wei Zhao 1 1 State

Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning, 116024, People’s Republic of China 2 Department of Otorhinolaryngology, the Second Affiliated Hospital of Dalian Medical University, Dalian, Liaoning, 116027, People’s Republic of China 3 Department of Otolaryngology, Bei Jing Tongren Hospital, Capital Medical University, Beijing, 100730, People’s Republic of China

SUMMARY Nasal obstruction frequently has been associated with obstructive sleep apnea (OSA). Although correction of an obstructed nasal airway is considered an important component in OSA treatment, the effect of nasal surgery on OSA remains controversial. Variation in airway anatomy between before and after nasal surgery may cause significant differences in airflow patterns within the upper airway. In this paper, anatomically accurate models of the interaction between upper airway and soft palate were developed from prenasal and post-nasal surgery multidetector computed tomography data of a patient with OSA and nasal obstruction. Computational modeling for inspiration and expiration was performed by using fluid–structure interaction method. The airflow characteristics such as velocity, turbulence intensity and pressure drop, and displacement distribution of soft palate are selected for comparison. Airway resistances significantly decrease after the nasal surgery, especially in the velopharynx region because of an enlarged pharyngeal cavity and a reduced upstream resistance. Meanwhile, the decreased aerodynamic force would result in a smaller displacement of soft palates, which would lead to slight impact of the soft palate motion on the airflow characteristics. The present results suggest that airflow distribution in the whole upper airway and soft palate motions have improved following nasal surgery. Copyright © 2012 John Wiley & Sons, Ltd. Received 26 November 2010; Revised 7 May 2011; Accepted 2 November 2011 KEY WORDS:

obstructive sleep apnea; nasal surgery; aerodynamic force; fluid–structure interaction

1. INTRODUCTION The upper airway related problems recently have been common medical issues and concerns affecting a significant portion of the human population all over the world. One of the major human airway diseases is obstructive sleep apnea (OSA), which is a common disorder that results from the combination of a structurally small upper airway and a loss of muscle tone during sleep. Young et al. [1] reported that approximately 1 in 5 adults had at least mild OSA and 1 in 15 adults had moderate or severe OSA. The complex etiology of OSA has resulted in an array of treatment options. Upper airway surgery is an important treatment option for patients with OSA, particularly for those who have failed or cannot tolerate positive airway pressure therapy. Surgical

*Correspondence to: Xiuzhen Sun, Department of Otorhinolaryngology, the Second Affiliated Hospital of Dalian Medical University, Dalian, Liaoning, 116027, People’s Republic of China. † E-mail: [email protected] Copyright © 2012 John Wiley & Sons, Ltd.

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interventions aim to reduce anatomical upper airway obstruction in the nose, oropharynx, and hypopharynx [2]. The observation that nasal obstruction may affect breathing during sleep has been well known [3]. Both daytime nasal obstruction and nocturnal nasal congestion have been shown as risk factors for sleep-disordered breathing [4, 5]. Although the treatment of nasal obstruction plays an important role in sleep apnea surgery [6], controversial data from observational studies exist regarding the effect of nasal surgery on OSA [3, 7–9]. In general, polysomnography in a sleep laboratory is used to assess objectively the efficacy of surgical intervention for OSA. The procedure is, however, expensive, intrusiveness, time consuming and, in some centers, the waiting times are unacceptable. Therefore, the effect of an improved nasal airway on OSA after nasal surgery has been inconsistent and often lack adequate objective outcome measurements [3, 9, 10]. It is well known that structural/anatomical factors play an important role in the pathogenesis of OSA [11], and the primary outcome of surgical intervention is a change in airway anatomy. Variations in airway anatomy between before and after surgical interventions may result in differences in airflow patterns within the upper airway. Knowledge of airflow in the human upper airway is essential to understand many aspects of the physiology and pathology of the respiratory tract [12, 13]. Therefore, the accurate knowledge of airflow behaviors in upper airways before and after nasal surgery may be an important step in evaluating the results of nasal surgical intervention for OSA. A myriad of experimental investigations provided valuable descriptions of airflow patterns in the upper airway [12,14–23], but focused mainly on healthy nasal cavity alone or were carried out using idealized airway model. The detailed quantitative information about airflow in realistic anatomical upper airway models concerning abnormal nasal or/and pharyngeal airways is limited. Recently, CFD and fluid–structure interaction (FSI) methods have been used to investigate the airflow patterns in human airways with or without airway diseases [13, 24–34], and airway deformation and collapse [35–38]. Computational modeling by these methods has enabled prediction and evaluation of the effect of surgical interventions on the aerodynamic characteristic, including the study of septoplasty [39], turbinate surgery [40, 41], functional endoscopic surgery [42], adenotonsillectomy [43], maxillomandibular advancement surgery [44] and so on. Huang et al. [45, 46] generated various anatomic perturbations in the structure to assess the impact of anatomic manipulations (uvulopalatopharyngoplasty, palatal stiffening, and tongue stiffening) on pharyngeal mechanics and the closing pressure. They suggested that computational modeling was feasible and could be used to generate hypotheses for subsequent clinical trials regarding anatomic manipulations for treatment of OSA. However, prediction or assessment of the aerodynamic characteristics within the upper airway in a patient with OSA who has undergone nasal surgery has not been reported. The airway anatomy and the movement of the soft palate and/or walls of the pharynx likely play an important role in the genesis and the development of OSA [34, 38, 47]. FSI modeling, which can capture biological flow features, motions, and deformations of soft tissues, has received growing interest because of the potential impact of the models in the medical field [38, 48]. Most published works on modeling the FSI of the upper airway, combined with the type of simplified models [35–38, 45, 46, 49, 50], provided an essential platform for understanding the phenomenology that would guide interpretation of numerical results from a highly complex full FSI model of the upper airway [34]. However, a simplified geometry neglects the influence of complicated threedimensional (3D) airway anatomic structure on the flow. Computational modeling of the flow field based on anatomically correct upper airway geometry is needed to fully understand the influence of morphology on OSA, and further investigate diagnosis and treatment related problems on this disease. In this paper, anatomically accurate patient-specific models of the upper airway are reconstructed from prenasal and post-nasal surgery multidetector computed tomography (MDCT) data of a patient with OSA and nasal obstruction. FSI modeling will be used to assess the impact of anatomical variations after the nasal surgery on the aerodynamics airflow patterns in upper airways and soft palate movements in both inspiration and expiration. In addition, pathological and physiological changes are generally correlated with changes in tissue stiffness as well. Therefore, the impact of stiffness variation of the soft palate on airflow patterns is considered. Copyright © 2012 John Wiley & Sons, Ltd.

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2. MATERIALS AND METHODS 2.1. Computed tomogram image acquisition The imaging used in this study was conducted at the Department of Otolaryngology, Beijing Tongren Hospital. The data were derived from MDCT scans (Brilliance 64, Philips Medical Systems, Cleveland, OH, USA) of a patient at baseline (i.e., before surgery) and three months after nasal surgery, who had nasal obstruction and snored for 12 years. The anatomic cause of nasal airway obstruction (septal deviation, bilateral inferior turbinate hypertrophy, and bilateral middle meatus stenosis) was documented based on CT scan and nasal endoscopic examination. He was diagnosed with OSA based on an overnight polysomnography (Alice 4 System; Healthdyne Technologies, Marietta, GA, USA). The apnea–hypopnea index (AHI) was 6.7/h. The minimum oxygen saturation was 71.0%. The patient underwent nasal surgical procedures, which included endoscopic septoplasty, inferior turbinate outfracture and enlarged ostium of the maxillary sinus. After the nasal surgery, an improvement in snoring and quality of life was described by the patient and his wife. 2.2. Model reconstruction and grid independence The preoperative and postoperative CT images appeared at the interval of 0.5 mm along the axial direction. As shown in Figure 1(a), the present FSI models, which consist of the upper airway models (nasal cavity, nasopharynx, oropharynx, laryngopharynx and oral cavity) and soft palate models, were reconstructed into 3D images using the medical imaging software MIMICS 10.01 (Materialise Inc., Leuven, Belgium). On the basis of the anatomy of the soft palate

Figure 1. (a) Three-dimensional FSI model of preoperative upper airway and soft palate based on the CT data; (b) anatomical illustration of the soft palate [51]; and (c) a finite element model of the soft palate containing four pairs of palatal muscles. Copyright © 2012 John Wiley & Sons, Ltd.

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(Figure 1(b) [51]), the artificially bilateral palatal muscles (tensor veli palatini, levator veli palatini, palatopharyngeus, palatoglossus) were built (Figure 1(c)). The FSI models were then discretized by a mesh of unstructured tetrahedral elements within commercial finite-element software (ANSYS, Ansys Inc., Canonsburg, PA, USA). A grid convergence analysis was performed on both fluid and solid field by repeating the solution with four different meshes (Grid 1, Grid 2, Grid 3, and Grid4) to establish grid independence solutions. For reliable comparisons of the results obtained from preoperative and postoperative models, the same domain was meshed by the similar size elements. To reduce the computational resources needed for the grid sensitivity study, data concerning the grid sensitivity study were presented only for inspiration. The effects of the grid convergence on velocity field, pressure field and displacement variables were assessed in both preoperative and postoperative models. Changes in total pressure drop through the upper airway and average velocity near the nasal valve region were used as convergence criteria for the fluid domain, and change in average displacement in the vicinity of free edges of the soft palate (uvula) was used as convergence criteria for the solid domain. An acceptable level of grid-independence was achieved when changes in those criteria (relative errors, er D j.valuecoarse  valuefine /=valuefine j) were less than 1%. As shown in Figure 2, changes of the total pressure drop, average velocity, and displacement between Grid 3 and Grid 4 were 0.91%, 0.06%, and 0.15% for preoperative model, 0.88%, 0.07%, and 0.84% for postoperative model. It was suggested that changes in those criteria become practically negligible if Grid3 is used. Accordingly, all the data presented in the current work were from a simulation with Grid3. The mesh for the preoperative subject contained 238,000 nodes and 965,000 cells across the fluid domain, 17,900 nodes and 84,000 cells across the solid domain, whereas the postoperative subject had 251,000 nodes and 1,062,000 cells across the fluid domain, 16,200 nodes and 71,000 cells across the solid domain.

Figure 2. Effects of computational cell size on calculated results at the inspiratory flow rate of 628 mL/s. Variations of pressure drop through upper airway and average velocity near the nasal valve region for (a) preoperative airway and (c) postoperative airway. Variations of average displacement in the vicinity of uvula for (b) preoperative soft palate and (d) postoperative soft palate. Copyright © 2012 John Wiley & Sons, Ltd.

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2.3. Numerical simulation Numerical simulation of 3D FSI between the upper airway and the soft palate in both inspiration and expiration was performed using ANSYS. An ambient static pressure condition was set at the nostril (the flow outlet). No-slip boundary conditions for velocity were set at airway walls. A velocity boundary condition was established at the laryngopharynx (the flow inlet). The tidal volume of normal adults is about 400600 ml [52] and an upper limit value of 600 mL was used in this study. On the basis of the tidal volume and the respiratory cycle (similar sinusoidal variation based on medical observation, see Ref. [41]), the peak flow rate (Q/ 628 mL/s was established. In the present work, steady inspiratory and expiratory flow rates of 628 mL/s were considered. At the inlet, turbulence intensity was set to be 10%, and the turbulence length scale was set to be 1 mm. The corresponding range of Reynolds numbers ranged from 449 to 5537. The flow in both preoperative and postoperative upper airways was mostly in the transitional flow region, which prevails in the Reynolds number range of 2300 < Re < 8000. However, 3D flow features such as flow separation and recirculation might trigger a transition to turbulence at lower Reynolds numbers [47]. Thus, it was reasonable and necessary to implement a turbulent flow model for the simulation of accurate flow characteristics in the fluid region. Although computationally expensive LES should be the preferred tool to capture relevant airway-related flow feature [33, 53], k  ! results with affordable computational effort were closer to LES results [53]. Mylavarapu et al. [20] used five different turbulence models to predict accurately the flow characteristics associated with the upper airway and compared with the experimental data. Their data show that the standard k ! turbulence model is a better predictor for the experimental measurements. Accordingly, k  ! turbulence was adopted in the present work to predict airflow characteristics in the upper airways. The soft palate is firmly attached to the posterior edge of the bony palate (hard palate) [54]. The hard palate is the tough, leathery, nonmovable part. Therefore, the anterior edge of the soft palate was assumed to be immobile .ui D 0/. As shown in Figure 1(b), the soft palate contains five muscles: (1) tensor veli palatine (TVP); (2) levator veli palatine (LVP); (3) palatoglossus; (4) palatopharyngeus; and (5) musculus uvulae. The soft palate is the very flexible, posterior one-third of the palate from which the uvulae hangs. Bilaterally, it is joined to the tongue and pharynx by the palatoglossal and palatopharyngeal folds and is strengthened by the palatine aponeurosis, formed by the TVP muscle and LVP muscle. As shown in Figure 1(b), TVP originates from the scaphoid fossa of the sphenoid and membranous portion of the eustachian tube. LVP arises from the under surface of the apex of the petrous part of the temporal bone and from the medial lamina of the cartilage of the auditory tube. The palatopharyngeus muscle, which originates from the posterior hard palate and the palatine aponeurosis, passes behind the tonsil forming the posterior tonsillar pillar and inserts into the posterior border of the thyroid cartilage [55]. The palatoglossus arises from palatine aponeurosis at the posterior part of the hard palate and is insertered into the side and dorsum of the tongue, which originates at the bone structure. Accordingly, the bottom of the bilateral palatal muscles was also assumed to be immobile. Most soft tissues exhibit a nonlinear, inelastic, heterogeneous, nearly incompressible, and anisotropic characteristic, and these vary from point to point, from time to time and from individual to individual. However, it may be sufficient to model their behavior within the context of an elasticity or viscoelasticity theory under particular conditions of interest [56]. Soft tissues exhibit both solid-like and fluid-like behaviors. That is, they often exhibit characteristic behaviors of viscoelasticity. Although the viscoelastic properties of soft tissues have been determined directly by in vivo or in vitro experiments [57–61], these values demonstrated great variation in viscoelastic parameters for different human and animal soft tissues. Therefore, viscoelastic parameters used in the finite element analysis studies of the soft tissues have even greater uncertainty [60]. Additionally, nonlinear material model parameters and test data are not available for the airway itself and the surrounding soft tissues [62]. Therefore, in most of the numerical studies on the biomechanical characteristics of the airway for OSA, soft biological tissues of the airway itself and the surrounding soft tissues were often modeled as a linear elastic continuum [36, 38, 45, 62–64]. Chouly et al. [38] investigated the mechanical behavior of the tongue based on the theory of linear elasticity in small deformations. Their numerical prediction was successfully validated using in vitro experimental Copyright © 2012 John Wiley & Sons, Ltd.

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measurements. Although biologic tissues are not fully described by a linear elastic material, small deformations combined with linear elasticity should be sufficient as a first approximation under particular conditions of interest [38, 62], and the models they presented could play an important role in understanding the pathophysiology of pharyngeal collapse when some experimental data on the realistic properties of biological tissues are used. The adopted material properties in this current work are shown in Table I on the basis of previous literatures [45, 64]. During breathing, the flow in the upper airway will affect in various extents movement of the soft palates, while soft palate movements in turn influence the airflow field. Numerical simulations of the interaction between airflow domain and structure domain (soft palate) were performed using sequential coupling method. The combined effects of flow and soft palate motion were obtained by solving the two sets of governing equations separately and exchanging information via the FSI interface (Figure 1(a)). Pseudotime-integration was performed for steady state flows with the backward Euler scheme. The solutions were generated using the implicit backward Euler time integration scheme for the flow equations and the Newmark scheme for the structural equation. Implicit methods that are frequently unconditionally stable and thus have no restrictions on the time step may provide an efficient alternative. The uniform time step used for both preoperative and postoperative simulation was 0.01 s. The end time was 0.5 s. A stagger loop was used to ensure that the coupling has converged at the end of each time step. At each time step, the maximum number of iterations for a stagger loop was 5. The FSI iteration loop was repeated until convergence was reached for each time period. Figure 3 contains the time histories for pressure and velocity of a point .P / on the section e (or e0) surface, and Y -displacement of a point (P 0) on the vicinity of the uvula in both

Table I. Material properties of the human soft palate and palatal muscles model used in the simulations. Material Soft palate Bilateral palatal muscles

Young’s modulus E (MPa)

Poisson’s ratio ./

0.025 0.98

0.42 0.45

Figure 3. Time histories for pressure, velocity, and displacement in both preoperative and postoperative operative models at the inspiratory flow rate of 628 mL/s. Pressure (a) and velocity (b) of a point .P / on the section e surface in the preoperative model. Y -displacement of a point .P 0 / on the vicinity of uvula in the preoperative model (c). Pressure (d) and velocity (e) of a point (P / on the section e 0 surface in the postoperative model. Y -displacement (f) of a point .P 0 / on the vicinity of uvula in the postoperative model. Copyright © 2012 John Wiley & Sons, Ltd.

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preoperative and postoperative models for the inspiration. For both models, the FSI results at the last time step (t D 0.5 s) are depicted and discussed in the following text. Assuming that the viscous Newtonian fluid is incompressible and homogeneous, the governing equations ae given by the continuity equation and the Navier–Stokes equations as follows: @vi D0 @xi

(1)

@p @2 vi @vi @vi D C C fi C vj @t @xj @xi @xj @xj

(2)





The constitutive model for airflow in the upper airway is described by the following equation:   @vj @vi ijf D pıij C  C @xj @xi

(3)

where  is the fluid density,  is the dynamic viscosity coefficient, vi is the velocity vector, xi is the position vector, p is the fluid pressure, and ijf is the stress tensor in fluid systems. Concerning the structure, the constitutive behavior is given by the Hooke’s law (linear elasticity). The following equations govern the structure deformation: 3



X @ij @ 2 ui D C fi @t 2 @xj

(4)

j D1

E E ij D "kk ıij C "ij .1 C /.1  2/ .1 C /

1 where "ij D 2



@ui @uj C @xj @xi

 (5)

Here, ui is the solid displacement in a given direction, ij is the stress tensor, "ij is the strain matrix, E is the Young’s modulus, and  is Poisson’s ratio. The fluid field and structural field share a common interface. At this FSI interface, , coupling conditions vi D

dui and ijs  n D ijf  n dt

(6)

hold with the interface fluid velocity v , the interface structural displacement u , the stress tensor of both fluid ijf and structure ijs and the normal vector of the interface n. 3. RESULTS 3.1. Geometry comparisons Computed tomography images in Figure 4 show the difference in airway shape between preoperative and postoperative upper airway at the same coronal and axial cross-sections. These sections are used for further flow distribution analysis. The information available from CT data, such as crosssectional area (CSA) and surface area-to-volume ratio (SAVR), can reflect differences in airway geometry. The CSA versus the axial distance from the nostril to the hypopharynx between preoperative and postoperative upper airway are compared (Figure 5). The CSA of the nasal cavity after the surgery is much larger than that of the preoperative model from the anterior portions of middle turbinate (AMT) to the choana. Although slight variations in each side of the postoperative nasal cavity geometry exist, a general trend in the CSA can be observed (Figure 5(a)). Moreover, the CSA profile from the nasopharynx to the hypopharynx of the postoperative model is similar to the preoperative model. Yet, a larger CSA is observed from velopharynx to epiglottis (Figure 5(b)). Besides, SAVR defined as the ratio of the nasal airway surface area to volume for the region extending from the nostril to the end of the septum, is a useful measurement to determine whether a nasal cavity is narrow or wide. The narrower the cavity is, the larger is the SAVR, and vice versa [26]. As shown in Copyright © 2012 John Wiley & Sons, Ltd.

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Figure 4. (a) Preoperative CT images of representative coronal and axial sections whose positions are marked in Figure 1(a) (a–f sections). (b) Postoperative CT images at the same cross sections (a0 –f0 sections).

Figure 5. The comparison of cross-sectional areas versus the axial distance from the preoperative and postoperative geometries. (a) The cross-sectional area of each side of the nasal cavity from the nostril to the choana; (b) the cross-sectional area of the airway from the choana to the hypopharynx (NV, nasal valve; AIT, anterior portions of inferior turbinate; AMT, anterior portions of middle turbinate; VP, velopharynx; EP, epiglottis).

Table II, before nasal surgery the nose has a SAVR of 1.01 mm1 , which reduces to 0.68 mm1 after surgery. Also, the SAVR of the right cavity is the same as that of the left cavity in the postoperative subject. 3.2. Airflow characteristics On the basis of prenasal and post-nasal surgery CT data, 3D FSI simulations of the airflow and soft palate motion at inspiratory and expiratory flow rate of 628 mL/s are performed. Airflow characteristics, such as velocity, turbulence intensity, and pressure can be obtained at any point in the models. A full picture of the flow features is best realized when streamline analysis is combined with velocity contours plots. A streamline provides a qualitative visualization of the flow field. For preoperative and postoperative simulations, a series of streamlines are generated (Figure 6). A comparison of the streamlines indicates that most of the streamlines are smoothly varying curves and no distinct recirculation regions are observed in both preoperative and postoperative models. Some exceptions are evident in the regions of the nasal vestibule, nasopharynx, velopharynx and the epiglottis. Figures 6(a) and (c) show that most of the flow pass through the middle and lower regions of the nasal passages in the preoperative upper airway. After the nasal surgery, the streamlines in the nasal cavity are concentrated in the middle region (Figures 6(b) and (d)). From the streamlines pattern, we can confirm that preoperative and postoperative upper airways have increased circulation in regions Copyright © 2012 John Wiley & Sons, Ltd.

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Table II. Nasal passage dimensions for both presubject and post-subject anatomies. Subject Preoperation

Postoperation

Region

SA (mm2 )

Volume (ml)

SAVR (mm1 )

Right cavity Left cavity Both cavity Right cavity Left cavity Both cavity

8990 8640 17,630 7090 6820 13,910

9.2 8.3 17.5 10.5 10.1 20.6

0.98 1.04 1.01 0.68 0.68 0.68

SA, surface area; SAVR, surface-area-to-volume ratio of the nose from the nostrils to the posterior end of the septum.

Figure 6. Flow streamlines for the flow rate of 628 mL/s in preoperative and postoperative models. (a) Preoperation, inspiration; (b) postoperation, inspiration; (c) preoperation, expiration; (d) postoperation, expiration. The streamlines are colored to describe the relative speed of flow with red for fast and blue for slow.

of the velopharynx and the epiglottis. The contours of velocity magnitude on the exact same coronal and axial sections between the preoperative and postoperative models are compared (Figure 7). Velocity values presented have been nondimensionalized by the corresponding maximum velocity of the upper airway, vMax . As shown in Figure 6, vMax is found to differ among the four cases. In the preoperative upper airway, the dimensionless velocity profiles for both inspiration and expiration are similar but not identical. One distinct difference is located in the nasopharyngeal region (Figures 7(a) and (c)). A low velocity is observed in the nasal cavity. In the velopharyngeal region, the flow accelerates to its maximum velocity in both inspiration and expiration. In the postoperative upper airway, a high velocity flow advances along the base of the nasal cavity in the nasal valve region. Velocity profiles show a considerable decrease in the pharynx, especially the velopharynx compared with preoperative model (Figures 7(b) and  (d)).  2 The variation of the turbulence intensity I D kavg =vin between the preoperative and postoperative upper airways for inspiration and expiration, averaged over the local cross-sectional area, is shown in Figure 8. In both preoperative and postoperative operative models, the turbulence intensity becomes strong near the nasal valve in inspiration and expiration. Relatively weak turbulence is observed in the nasal main passage. Slight difference between the inspiration (decreasing the turbulence intensity) and expiration (increasing the turbulence intensity) is observed in the domain from the posterior end of the middle turbinate to the nasopharynx ( 5.5 to 7 cm). When the air enters the nasopharynx, the turbulence intensity decreases and then becomes strong at the dorsal nasopharynx because of bending in the upper airways. In the pharyngeal region for both models, turbulence intensity is particularly strong on the velopharyngeal and epiglottis regions for inspiration. However, significant turbulence intensity is mainly in the velopharyngeal region for expiration, Copyright © 2012 John Wiley & Sons, Ltd.

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Figure 7. Contours of dimensionless velocity magnitude .v=vMax / in six cross-sectional planes for the flow rate of 628 mL/s in preoperative and postoperative models. (a) Preoperation, inspiration; (b) postoperation, inspiration; (c) preoperation, expiration; (d) postoperation, expiration.

and the turbulence fluctuations are comparatively weak in the epiglottis. In contrast, the turbulence intensity for expiration is higher than that for inspiration at the same cross-sections in the regions of the nasopharyx and velopharynx. The maximum turbulence intensity .IMax / is located near the velopharyngeal region in the preoperative upper airway. After the surgery, the most intense region of turbulence locates at the nasal valve region. Quantitative comparisons of flow allocation percentages for each region in nasal passages are shown in Table III to further investigate the distribution of airflow in the nose before and after nasal surgery. These percentages are calculated as quotient of the flow rate through each of these regions and the total flow rate for the corresponding side of the nasal passage. The dissimilarity of the regional flow allocation between the right and left sides is found in the preoperative nasal cavity. More flow pass through MP and IM in the right cavity. In the left cavity, the flow mainly passes through the MP and MM. After the surgery, there are relatively symmetric allocations in the two sides of the nasal cavity. The flow analysis shows that about 85% of the flow passes through the MP and MM on each side. The numerical computations are mostly concerned with the pressure distribution in the airway to evaluate the role of airway shape in flow resistance and airway collapse [16]. Figure 9 shows the pressure drops in the upper airway along the streamline paths for the preoperative and postoperative subjects. In the preoperative model, the pressure changes rapidly when the flow cross the AMT in the right nasal cavity for both inspiration and expiration. However, in the left nasal cavity, the pressure gradient is relatively uniform. After the surgery, the variation in pressure drop in the right side is essentially the same as that in the left side. The major pressure drops occur in the nasal valve region. A similar trend in pressure drop in pharyngeal regions is found in the two models. Yet, the pressure drop in the postoperative pharynx is much lower than that in the preoperative subjects, especially in the velopharyngeal region (Figure 9 (b)). The pressure drop in the velopharynx region decreases to 21% and 33% for inspiration and expiration, respectively. 3.3. Soft palate motions Figure 10 shows the initial position and displacement distribution of the soft palate for both inspiration and expiration. Comparison of results reveals that the displacement distributions of preoperative Copyright © 2012 John Wiley & Sons, Ltd.

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Figure 8. Comparison of area-averaged turbulence intensity at different axial locations between the preoperative and postoperative models for inspiratory and expiratory flow rate of 628 mL/s. Table III. Flow allocation percentages at various regions in nasal passages. Inspiration Subject

Expiration

IM (%)

MM (%)

MP (%)

OR (%)

IM (%)

MM (%)

MP (%)

OR (%)

Preoperation

R L

26.1 20.0

14.4 29.8

42.4 37.7

17.1 12.5

26.9 20.7

13.9 21.5

46.0 45.0

13.2 12.8

Postoperation

R L

6.5 8.3

42.6 43.8

43.1 41.6

7.8 6.3

7.5 9.4

40.8 42.1

45.6 42.6

6.1 5.9

IM, inferior meatus; MM middle meatus; MP, medial passage; OR, olfactory region.

and postoperative soft plates are similar. The displacements in expiration are higher than that in inspiration. The maximum displacement magnitude .uMax / occurs in the vicinity of the free edges (uvula). Eight nodes spaced apart along the centerline of the soft palate (red lines as shown in Figure 11(a)) are selected. As shown in Figure 11, the soft palate motions induced by the air flow are mainly along the Y -axis and secondarily along the Z-axis and the displacement in X -axis is very small. In inspiration, two soft palates mainly move anteriorly (–Y / and inferiorly (–Z), while the major movement is posteriorly .CY / and superiorly .CZ/ in expiration. However, displacements of the soft palate have decreased remarkably after the surgery (reduce by 82.6% for inspiration and 49.9% for expiration). Copyright © 2012 John Wiley & Sons, Ltd.

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Figure 9. Comparison of pressure drops at different axial locations for the inspiratory and expiratory flow rate of 628 ml/s between the preoperative and postoperative models. (a) Two sides of the nasal cavity and (b) pharynx.

Figure 10. Initial position (grids) and displacement distribution of soft palate after computation for the inspiratory and expiratory flow rate of 628 mL/s. (a) Preoperation, inspiration; (b) postoperation, inspiration; (c) preoperation, expiration; (d) postoperation, expiration.

3.4. Effects of stiffness of the soft palate on FSI simulations Generally, pathological and physiological changes are correlated with changes in tissue stiffness as well. For example, in patients with OSA, the muscles are so relaxed that the soft palate tissue collapses and blocks the airway. Therefore, an overly relaxed soft palate is one airway factor that has been proposed as the causative agent of OSA. It is possible that in some patients, more rigidity of the soft palate is required to prevent collapse and airway obstruction. Theoretically, this could be Copyright © 2012 John Wiley & Sons, Ltd.

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Figure 11. The displacements of eight nodes in soft palates for the inspiratory and expiratory flow rate of 628 mL/s. (a)X-axis displacement .ux /; (b) Y -axis displacement .uy /; and (c) Z-axis displacement .u´ /.

Table IV. Comparisons of FSI results among different Young’s modulus values of the preoperative and postoperative models for the inspiratory and expiratory flow rate of 628 mL/s. E (MPa)

P Total (Pa)

vMax (m/s)

uMax (103 m)

IMax

Pre

Post

Pre

Post

Pre

Post

Pre

Post

Inspiration

0.025 0.1 1

440.17 449.55 457.81

230.18 232.47 233.26

16.788 17.383 17.762

12.352 12.352 12.352

2.35 2.36 2.36

1.26 1.28 1.28

0.592 0.219 0.072

0.103 0.041 0.016

Expiration

0.025 0.1 1

507.30 451.99 418.57

230.67 221.45 218.59

21.256 19.957 18.686

13.605 13.592 13.588

2.58 2.49 2.45

1.47 1.42 1.41

1.625 0.674 0.124

0.814 0.232 0.053

P   Total , the pressure drop across the upper airway. Inspiration: PTotal D PNostril  PMin . Expiration: PTotal D PMax  PNostril . vMax , the maximum magnitude of airflow velocity in the upper airway. IMax , the maximum turbulence intensity in the upper airway .IMax D kMax =vi2n /. uMax , the maximum magnitude of the displacement of the soft palate.

achieved by increasing the stiffness of the palate. The Young’s modulus of a material is the property used to characterize stiffness. Table IV compares FSI results among different Young’s modulus values of the soft palate in the preoperative and postoperative models at the same flow rate of 628 mL/s. The displacements of the soft palate reduce with the increase of the Young’s modulus values in both inspiration and expiration. Meanwhile, airflow characteristics of the upper airways are affected by changes in the stiffness of the soft palate at the same boundary conditions. In the preoperative upper airway, the comparatively inconspicuous increases in pTotal , vMax , and IMax by Copyright © 2012 John Wiley & Sons, Ltd.

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stiffening the soft palate are observed in inspiration. In contrast, a significant impact of the stiffness of the soft palate on the airflow characteristics is found in expiration. An increase in the stiffness of the soft palate results in a smaller fluid dynamic parameter. In the postoperative upper airway, flow characteristics remained relatively invariant for each Young’s modulus value of the soft palate for both inspiration and expiration.

4. DISCUSSION Preoperative and postoperative FSI results indicate that there are significant changes in the internal aerodynamics patterns and soft palate movements. Comparison of streamline can give a general sense of changes in airflow pattern. Quantitative determinations of flow allocation indicate a bilaterally asymmetric allocation in the preoperative nasal cavity. After the nasal surgery, two approximately equivalent air passages result in relatively symmetric allocations in two sides of the nasal cavity. The velopharynx of a patient with OSA is the flow-limiting structure during sleep [13]. From the preoperative results, the maximum airflow velocity and pressure drop located in the vicinity of the velopharynx because of the smallest flow area, where the turbulence fluctuations in this region are very strong for both inspiration and expiration. The pressure drop prediction of the preoperative model is consistent with experimental measurements by Mylavarapu et al. [20], who measured pressure distributions in a 3D anatomically accurate airway model of the OSA patient and found that the largest pressure drop was located near the site of the minimum crosssectional area (i.e., velopharynx). In the postoperative upper airway, the maximum values for the velocity and pressure drop are located near the nasal valve, and significant turbulence occurs in this region. Similar results were obtained in nasal cavity models by Xi and Longest [30], and they found that turbulence occurred mainly in the nasal vestibule-valve region and the dorsal nasopharynx for inspiration. However, turbulent fluctuation in the upper airway for expiration has never been demonstrated before. The pressure distribution in the airway can be used to evaluate the role of airway shape in flow resistance. Airway flow resistance is extremely important for diagnostics, the control of therapy progress after surgical operations, and the assessment of the efficacy of applied treatments. It is defined as R D p=Q, where p is pressure drop across the airway passage and Q is airflow rate. The nasal cavity is a parallel-connected fluid passage. The total nasal resistance is calculated with the equation RN D RRight  RLeft =.RRight C RLeft / that uses the individual resistances in the right and left nasal passages. For comparison with the preoperative airway resistance, the upper airway resistance .RUA / computed in the postoperative model is much lower for the same inspiratory and expiratory flow rate of 628 mL/s. Although values of nasal resistance .RN / are high before the surgery, low percentages of the RUA (31.8% for inspiration and 29.7% for expiration) are found. The enlarged MM and MP in the postoperative nasal cavity help the airflow to go more smoothly from the nasal valve to the choana, and thus decreased values of RN is found after the surgery. However, their percentages of RUA increased to 40.6% for inspiration and 44.3% for expiration. In normal adults, approximately half of the respiratory airway resistance is provided by the nasal airway [65]. The nasal valve is the flow-limiting segment of the nasal cavity because of its narrow cross-sectional area [66]. The valve is responsible for more than half of RN [67]. This is expected because the nasal valve is the region of minimum CSA in the left and right nasal passages after the nasal surgery. In the preoperative nasal cavity, the right nasal passage is narrowest at the vicinity of the AMT; the flowlimiting segment of the nasal cavity is in this region. It is observed that an improved nasal airway is associated with a reduction in mouth breathing during sleep, which relieves the mucosal hyperaemia and oedema [10]. The soft palate volume is 9.702 cm3 in the preoperative model, and it reduces to 7.208 cm3 after the nasal surgery. This variation suggests a relief of the soft palate oedema after surgery. Because the configuration of the pharyngeal lumen is determined by the size and shape of the soft tissue structures adjacent to it (such as the faucial and lingual tonsils, tongue, and soft palate) and their spatial orientation in relation to each other [68], decrease in soft palate volume is likely to help increase the size of the pharyngeal airway. Meanwhile, reduced nasal resistance, the Bernoulli effect, and reduced dynamic compliance of the pharynx are dynamic factors that can also Copyright © 2012 John Wiley & Sons, Ltd.

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prevent pharyngeal narrowing [69]. Therefore, both an enlarged pharynx and a reduced upstream resistance after the nasal surgery might contribute to a great reduction in pharyngeal resistance. The soft palate is soft, flexible, and lies at the upper end of the pharyngeal airway where it acts as a flap or valve [70]. During breathing, the soft palate mainly moves in an anterior–posterior direction (Y -axis) in the airway caused by the aerodynamic force (pressure force and shear force) acting on the interface. With reductions of the aerodynamic force after the nasal surgery, the range of soft palate motion is significantly smaller than that in the preoperative model for both inspiration and expiration. Despite the fact that inspiration causes a complete occlusion of the upper airway with a consequent cessation of airflow and hypoxia in patients with OSA [71], 20% of patients show occlusion in the nasopharynx with the soft palate during exhalation [72]. The present results show that the soft palate moves posteriorly and superiorly during expiration in both preoperative and postoperative models. Excessive displacement of the soft palate in the preoperative model may lead to potentially increased risk to the nasopharyngeal obstruction during expiration. Therefore, the risk of the nasopharyngeal obstruction during expiration may be reduced with decreased range of the soft palate motion after the nasal surgery. Besides, snoring, which is a cardinal feature of the OSA, is characterized by oscillations of the soft palate and their adjacent tissues during sleep [73, 74]. Reduced motions of soft palates may also be beneficial to snoring reduction after the nasal surgery. Variations of the range of soft palate motion apparently have effects on the air space between the soft palate to the posterior pharyngeal wall, which has been associated as an important structural and physiological contributor to OSA [75]. Variable posterior pharyngeal airspace will result in the changes of aerodynamic characteristics. However, it is noticed that influences of soft palate motion on airflow characteristics are different in different models at the same flow rate especially in expiration. With increases of the stiffness, a comparatively significant influence of decreased range of soft palate motion on the aerodynamic characteristics is observed only in the preoperative model. In the postoperative model, displacements of the soft palate for different Young’s modulus values are very small. The smaller motion has minimal impact on the flow pattern within the upper airway for both inspiration and expiration. These comparisons may suggest that influences of soft palate motion on airflow characteristics are dependent on the airway anatomy itself. After the surgery, the improvement of airflow distribution, which is induced by changes in airway anatomy, decreases the aerodynamic force. This variation can lead to smaller soft palate motions, and the smaller motions in turn reduce the influence on the airflow distribution. One limitation of this study is the rigid wall assumption. Compared with nasal structures, the pharyngeal airway is not sufficiently supported by bony or cartilaginous structures [76]. Therefore, the rigid pharyngeal wall assumption is not consistent with the physical reality of the situation. The flexibility of airway walls will be investigated in a future study. Another limitation is that biologic tissues are not fully described by a linear elastic material with isotropic material properties. In the current study, as pointed out in Section 1, the main objective is to compare the aerodynamics airflow patterns in upper airways and soft palate movements between preoperative and postoperative models. Considering the uncertainty of nonlinear viscoelastic parameters and the difficulty of FSI simulation, linear elastic assumption of material properties, which is consistent with other recent approaches [36, 38, 45, 62, 64], is used in structural simulation for preoperative and postoperative models. We believed that the same assumption and consistent material parameters applied in both models could reduce the influence of linear elastic assumption on first comparison study. Nevertheless, the pathophysiology of OSA is estimated more accurately if the actual material properties are used. Accordingly, experimental investigations should be performed to determine actual material properties of soft tissues, which will be applied in our future numerical studies. Additionally, considering differences in airway anatomy among human individuals, it is impossible to derive conclusions that will be valid for each and every case. Regardless of these limitations, we believe the present results can provide physiological insights on the airway structure in OSA and have clinical relevance. Comparative FSI numerical simulations based on patient-specific models could be used to explore the exact role of nasal surgery in OSA treatments. In addition, snoring, as a marker of the coexistence of OSA, is mainly characterized by oscillations of the soft palate as the air passes through. We believe 3D anatomically accurate FSI models can be applied to investigate the mechanics of snoring and effects of abnormal structure on snoring levels. Copyright © 2012 John Wiley & Sons, Ltd.

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5. CONCLUSION The FSI modeling in the present work gives insight into interactions between the airflow distribution and soft palate movement, and suggests the significant influence of the airway anatomical variation induced by nasal surgery on the airflow characteristics and soft palate motions during breathing. Beneficial changes in airflow patterns of the upper airway are observed after the nasal surgery. Qualitative and quantitative analysis can provide some useful information for evaluating the outcome of nasal surgery for OSA. Computational modeling by FSI method may be a viable approach for doctors to consider the influence of various factors in OSA to develop the optimal treatment plan.

NOMENCLATURE er Re Q vi I k p xi ui E v  p  pTotal u R RN RRight RLeft RUA

relative error Reynolds number flow rate (mL/s) velocity vector (m/s) turbulence intensity turbulence kinetic energy (m2 /s2 / pressure (Pa) position vector (m) displacement vector (m) Young’s modulus (MPa) magnitude of airflow velocity in the upper airway (m/s) pressure drop (Pa) pressure drop across the upper airway (Pa) magnitude of the displacement of the soft palate (m) flow resistance (Pa s/mL) resistance of nasal cavity (Pa s/mL) resistance of the right nasal passage (Pa s/mL) resistance of the left nasal passage (Pa s/mL) resistance of upper airway (Pa s/mL)

Greek symbols    ij "ij

fluid density (kg/m3 / dynamic viscosity coefficient (N  s/m2 / Poisson’s ratio stress tensor (Pa) strain matrix (Pa)

Subscripts Max Min In avg

maximum minimum inlet area-average values

ACKNOWLEDGEMENTS

The authors wish to thank the doctors of the Department of Otolaryngology at the Beijing Tongren Hospital, and Department of Otorhinalaryngology at the Second Affiliated Hospital of Dalian Medical University for their assistances on the design and technical assistance of this study. The research was supported by the National Natural Science Foundation of China (No. 10872043, 10902022, 11032008). Copyright © 2012 John Wiley & Sons, Ltd.

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