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The quantitative effect of an accessory ostium on ventilation of the maxillary sinus
Respiratory Physiology & Neurobiology 181 (2012) 62–73
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The quantitative effect of an accessory ostium on ventilation of the maxillary sinus Yang Na a , Kyunghun Kim a , Sung Kyun Kim a , Seung-Kyu Chung b,∗ a b
Department of Mechanical Engineering, Konkuk University, Seoul 143-701, Republic of Korea Department of Otorhinolaryngology-Head and Neck Surgery, Samsung Medical Center, Sungkyunkwan University, School of Medicine, Seoul, Republic of Korea
a r t i c l e
i n f o
Article history: Accepted 25 January 2012 Keywords: Maxillary sinus Accessory ostium Ventilation Computational fluid dynamics simulation Nitric oxide Peclet number
a b s t r a c t The airflow and gas exchange behaviors of the human maxillary sinus were quantified to better understand the effect of an accessory ostium (AO). An anatomically correct numerical domain was constructed using CT data from a male patient with mild nasal obstruction. For the purpose of comparison, a numerical model without an AO was also generated by artificially removing the AO from the original model using CAD software. A steady-flow field through the nasal cavity was simulated using ANSYS-FLUENT v13.0 with a target flow rate of 250 ml/s. The Volume of Fluid (VOF) method was used to investigate the concentration field of nitric oxide (NO) initially filled in the maxillary sinus. The simulation results showed that a transit flow through the maxillary sinus developed in the presence of an AO. As the flow entered the sinus through either a natural or accessory ostium from the middle meatus, the velocity was significantly reduced to a local maximum of approximately 0.034 m/s inside the sinus. This by-pass flow rate through the sinus of 2.186 × 10−1 to 3.591 × 10−1 ml/s was a small fraction of the total flow rate inhaled from the nostril, but it effectively changed the local flow topology and led to a larger reduction in NO concentration in the maxillary sinus. This more rapid reduction in NO concentration was due to enhanced ventilation activity afforded by convective transport of the transit stream through the flow path connecting the natural ostium and the AO. The inspiration and expiration phases were qualitatively similar in flow pattern except for the flow direction in the maxillary sinus, suggesting that the AO plays a similar physiological role during both inspiration and expiration in terms of ventilation. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The maxillary sinus, which is connected to the nasal cavity through a natural ostium, is susceptible to various infections. The resulting sinus disease, frequently accompanied by significant pain, is known to affect up to 15% of the population and thus is a major reason for medical consultation (Kaliner et al., 1997). Several earlier studies revealed that reduced sinus ventilation is associated with sinusitis (Proctor and Andersen, 1982; Hood et al., 2009; Rennie et al., 2011), but its role in the pathophysiological development of sinusitis is still not well understood. Although the detailed anatomy of the nasal cavity varies between individuals, the maxillary sinuses typically have a volume of 10–15 ml (Hood et al., 2009); therefore, they are the largest of the human paranasal sinuses. In addition to a natural ostium, which connects the maxillary sinus to the middle meatus, endoscopic in vivo examinations commonly reveal the presence of accessory
∗ Corresponding author. Tel.: +82 2 3410 3572; fax: +82 2 3410 3879. E-mail addresses: [email protected], [email protected] (S.-K. Chung). 1569-9048/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.resp.2012.01.013
ostia (AO) in the maxillary fontanelle. The prevalence of AO is controversial, but one study reported AO in 8–19.3% of patients with chronic rhinosinusitis and a lower rate of occurrence in healthy volunteers (Jog and McGarry, 2003; Mladina et al., 2009). An early study (Matthews and Burke, 1997) proposed that AO may cause sinusitis by allowing easier pathogen access, but a mechanistic relationship between sinusitis and AO was not suggested. Another common disease involving the AO is an antrochoanal polyp, which originates from the maxillary sinus mucosa. It frequently expands through the AO into the middle meatus and finally protrudes into the choana (Chung et al., 2002a,b; Frosini et al., 2009). Although the role of AO in the pathogenesis of antrochoanal polyps is unknown, detailed flow-field information may provide a better understanding of the development of antrochoanal polyps. The main difficulty in investigating the flow of maxillary sinuses with one or more ostia is that the sinuses are inaccessibile and geometrically complex. Due to the instrumental difficulty of in vivo measurements, most early studies were based on simplified geometry. For example, Rantanen (1974) reported that the pressures of the sinus and nasal cavity are highly correlated, suggesting limited net gas exchange between the maxillary sinus and nasal cavity.
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Fig. 1. Numerical geometry. (a) Case A with an accessory ostium, (b) Case B without an accessory ostium, (c) numerical configuration.
Fig. 2. (a–i) Sequence of selected CT images used for the construction of the present numerical domain (2 mm resolution for the current set of data). PO stands for a primary (natural) ostium and AO stands for an accessory ostium. Uncinate process is indicated by *.
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Fig. 3. Representative planes for presenting computational results. (a) Top view, (b) Plane 1 containing a natural ostium, (c) Plane 2 containing an accessory ostium, (d) Plane 3, (e) Plane 4, (f) Plane 5 in the nasal valve area.
More recent studies using simplified models have indicated that the presence of an AO can increase the ventilation rate of the maxillary cavity (Aust and Drettner, 1974; Lundberg et al., 1995; Hood et al., 2009; Rennie et al., 2011). A common finding among these studies is that the maxillary sinus had a significantly higher nitric oxide (NO) concentration than the nasal cavity. One study used a simplified physical model to investigate the effect of AO on the gas exchange behavior of the maxillary sinus (Hood et al., 2009); this study suggested that the presence of one or more AO could increase the sinus ventilation rate by several orders of magnitude. In their study using a mathematical model, Rennie et al. (2011)
also demonstrated that the presence of an AO increased the effective volume flow rate of ventilation of the maxillary sinus by up to 50 times. The results of these studies indicate that the presence of AO increases sinus gas exchange rate by increasing net flow to the sinus. Although the overall characteristics were believed to be reasonably captured in their physical models, more realistic investigations are required to overcome the limitations of simplified geometries for better relevance to human respiration. Studies have investigated sinus-flow alterations associated with sinonasal pathologies and the effect of surgical correction using computational analyses of accurate human nasal cavity geometry
Table 1 Variations of velocity and pressure with grid resolution for Case A with an accessory ostium.
1,190,000 mesh 2,350,000 mesh 4.160,000 mesh
Point 1 (in the middle of the right sinus)
Point 2 (in the middle of the left sinus)
Point 3 (inside the middle meatus)
Velocity (m/s)
Pressure (Pa)
Velocity (m/s)
Pressure (Pa)
Velocity (m/s)
Pressure (Pa)
2.442 × 10−3 2.025 × 10−3 1.925 × 10−3
−5.140 −5.222 −5.233
6.841 × 10−8 5.222 × 10−8 4.997 × 10−8
−4.280 −4.290 −4.292
1.549 1.538 1.537
−5.612 −5.616 −5.617
Table 2 Geometry and flow information in three representative planes inside the nasal cavity. Plane 3
Cross sectional area (m2 ) Hydraulic diameter (m) Mean velocity (m/s) Airflow rate (ml/s) Reynolds number
Plane 4
Plane 5
Right
Left
Right
Left
Right
Left
8.916 × 10−5 1.065 × 10−2 1.493 133.1 1089
11.43 × 10−5 1.206 × 10−2 1.022 116.9 844
8.741 × 10−5 1.055 × 10−2 1.523 133.1 1100
9.631 × 10−5 1.107 × 10−2 1.214 116.9 920
9.855 × 10−5 1.120 × 10−2 1.351 133.1 1036
9.396 × 10−5 1.094 × 10−2 1.244 116.9 932
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Fig. 4. Velocity distribution in two representative planes during inspiration. (a) Case A and (b) Case B.
based on CT or magnetic resonance imaging data (Lindemann et al., 2005; Xiong et al., 2008; Leong et al., 2010). The degree of sinus ventilation is likely to be modified by surgical interventions, such as middle meatal antrostomy (MMA), by changing the local
geometry for gas flow. This type of intervention is expected to enhance gas exchange, thus reducing the nitric oxide (NO) concentration, although it can possibly impair mucociliary transport. Although these computational studies provided useful flow field
Fig. 5. Velocity distribution in two representative planes during inspiration rescaled by using a value of v = 0.005 m/s as the upper limit. (a) Case A and (b) Case B.
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Fig. 6. Velocity distribution in two representative planes during expiration. (a) Case A and (b) Case B.
information in the maxillary sinus to demonstrate that aggressive sinus surgery can significantly change the intranasal flow behavior, they did not investigate the effect of AO. The main objective of the present work was to investigate the effect of AO on the ventilation characteristics of the maxillary sinus. Using human CT data, an anatomically correct numerical domain was constructed that accurately described the nasal cavity, including the middle meatus and ethmoid infundibulum surrounding the natural ostium of the maxillary sinus. For representation and visualization of the degree of ventilation of the maxillary cavity, volume fraction of NO was investigated. The Volume of Fluid (VOF) method was used to calculate the concentration of NO under steady normal breathing conditions with the assumption that the entire NO initially resided in the maxillary cavity. 2. Numerical methodology 2.1. Numerical domain based on a CT image To identify the physiological effect of the presence of an AO, two different models, one with an AO (Case A) and the other without an AO (Case B), were prepared (Fig. 1). A surface-rendered computational model of the nasal cavity, including the maxillary sinuses with the AO, was created using 0.35-mm thick CT data of an adult patient with a mild nasal obstruction of the right side during a common cold. A part of CT images acquired at the Samsung Medical Center in Korea as part of a routine clinical procedure is displayed in Fig. 2 to show the locations of both natural and accessory ostia. Permission for this study was obtained from the Institutional Review Board of the Samsung Medical Center. This patient had no mucosal pathology or polyps in the maxillary sinus or middle meatus except one small AO (approximately 1.6 mm × 1.6 mm in cross-section or equivalently 2.30 mm in diameter and 2.72 mm in length) in the posterior part of the maxillary fontanelle and a mild septal
deviation to the left side. The mean diameter of the natural ostium varied from 2.70 mm in the smallest section to 7.50 mm in the largest section. It was approximately 11.16 mm long. The distance between the natural ostium and AO was about 8 mm. The maxillary sinus volumes were 7.1 and 6.6 ml for the right and left sinuses, respectively, which are smaller than the value of 10–15 ml reported by Hood et al. (2009). To create a computational model representing a normal anatomical configuration without an AO, CAD software was used to artificially remove the AO from the Case A model, so that this model had only a natural ostium (Case B), as shown Fig. 1. To present the simulation results, mainly two skewed 2-D planes were selected, as shown in Fig. 3. Plane 1 represented the plane containing the natural ostium, whereas Plane 2 revealed the AO. Plane 3 to Plane 5 were selected in the nasal valve area for the evaluation of local flow rate and Reynolds number. The accuracy of the numerical result is related to the number of meshes and the mesh distribution. For both Case A and Case B, the grid-generating software GRIDGEN v15.14 was used to generate meshes with combined tetrahedral and prism elements. A prism layer placed near the surface was essential for reducing a truncation error as found in previous work with a similar geometry (Lee et al., 2010). The present numerical geometry with relatively small ostia contained several regions requiring careful resolution. Therefore, the computations were conducted using 3 different resolutions to validate the results, as summarized in Table 1. The velocity and pressure were compared at 3 representative locations: in the right sinus with an AO, in the left sinus, and in the nasal cavity. There was a reasonably small change in velocity and pressure with a change in grid resolution for a grid system of approximately 4,160,000 mesh elements. Therefore, additional computations with a higher resolution were not attempted in the present work. This grid resolution was higher than that of the previous work of Lee et al. (2010) in order to resolve flow variables in the presence of relatively small ostia.
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Fig. 7. Velocity distribution in two representative planes during expiration rescaled by using a value of v = 0.005 m/s as the upper limit. (a) Case A and (b) Case B.
Fig. 8. Comparison of streamline patterns during inspiration. Streamlines are colored by the magnitude of the velocity. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Fig. 9. Comparison of streamline patterns during expiration. Streamlines are colored by the magnitude of the velocity. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
In the present numerical domain, an air chamber was placed in front of the nostril, as shown in Fig. 1. This thermodynamically stagnant chamber allowed for the smooth induction of inhaled air through the nostril so that the streamlines of the air exhibited realistic curvatures. In addition to this kinematic advantage, the thermodynamic stagnation properties at the surface of the air chamber better represented inlet boundary conditions, although the size of the chamber was not large.
2.2. Fluid dynamic boundary conditions The respiration process was modeled by applying the pressure difference between the inlet and the outlet in order to mimic the natural respiration process, where airflow is controlled by pressure in the lungs. Since the air chamber outside the nostril is exposed to the atmosphere, a stagnation pressure at the inlet was assigned a constant value of atmospheric pressure during respiration. At the outlet, the exit pressure value was adjusted to obtain a breath rate of 250 ml/s. This flow rate corresponds to approximately half of the typical maximum value and thus effectively represented instances in the middle of inspiration or expiration. It was assumed that the general flow characteristics associated with the presence of AO were reasonably captured at these 2 instances, and thus, unsteady computations were not attempted. The inclusion of mucous wall movement did not significantly increase gas velocities in the ostium (Hood et al., 2009); therefore, for simplicity, the mucociliary effect was not considered here.
On the basis of the mean velocity and the hydraulic diameter near the nasal valve area, the estimated Reynolds number did not exceed 1200 for a target flow rate of 250 ml/s as summarized in Table 2. The flow at this maximum Reynolds number was not likely to be described properly with a turbulence model as noted in some recent studies (Croce et al., 2006; Hörschler et al., 2006). Thus, a laminar flow model was used throughout the computational domain. For simplicity, the effects of temperature and humidity variations along the airway surface were not taken into account. Therefore, all properties of inhaled air were evaluated at a constant temperature of 25 ◦ C throughout the simulation. 2.3. Trace of nitrogen monoxide To trace escaping NO from the maxillary sinus, the VOF method (Hurt and Nichols, 1981) incorporated in the ANSYS/Fluent package was used to track the interface between the air and the NO. The resulting volume fraction of NO was calculated to investigate the ventilation characteristics. To incorporate the VOF method, the momentum equation was rewritten to include the surface force:
du = −∇ p + ∇ · + Fb + Fs dt
(1)
, p and denote density, velocity vector, pressure and viswhere , u cous stress tensor, respectively. Also, Fb denotes body force, and Fs represents the surface force, including the effect of surface tension. Since the present configuration involved a continuous distortion of the free surface formed by NO and air, the VOF method with a continuum surface force (CSF) model was used. The density and
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Fig. 10. Pressure distribution in two representative planes during inspiration. (a) Case A and (b) Case B.
viscosity of the 2 gases are listed in Table 3. Using the volume fraction, C, of NO obtained via the VOF method described above, the density, , and viscosity, , of the mixture of 2 different gases were calculated as follow: = CNO + (1 − C)Air
(2)
= CNO + (1 − C)Air
(3)
3. Results 3.1. Velocity and pressure fields The additional flow path connected to the maxillary cavity through the AO did not globally change the velocity field except for a localized alteration of flow pattern near the ostia during inspiration, as shown in Figs. 4 and 5. The contours of Fig. 4 were prepared using the maximum velocity detected in the 2 representative planes; the contours of Fig. 5 were rescaled by using a significantly lower velocity value as the upper limit of the color map, so that the detailed flow field could be expressed near the ostia. This contour-level adjustment was necessary because the induced velocity in the maxillary sinus had a relatively lower magnitude. For reference, the Case A model had an AO in the right sinus, exhibited in Plane 2. The AO had a negligible effect on the global velocity field dynamics (Fig. 4), which is believed to be related to its small dimension compared to the other flow passages in the Table 3 Reference values for density and viscosity of air and NO gas.
Density (kg/m3 ) Viscosity (kg/m s)
Air
Nitric oxide
1.225 1.789 × 10−5
1.000 1.723 × 10−5
nasal cavity through which the inhaled air moves. However, even this small change in local topology resulted in a qualitatively different local flow pattern near the ostia. That is, the presence of an AO effectively provided the path for transit flow through the maxillary sinus. As a result, the air stream entered the maxillary sinus through the natural ostium from the middle meatus and then exited through the AO. Upon the reversal of the main flow during the phase change from inspiration to expiration, the overall behavior remained qualitatively the same, but the velocity magnitude was slightly reduced in the maxillary sinus, as shown in Figs. 6 and 7. The streamline patterns through the right sinus (Fig. 8) revealed the existence of by-pass flow in a wide region of the sinus of Case A. However, due to the conservation of mass, a steady-state nonzero net flow rate into the sinus is not possible when an AO does not exist, as in Case B. Therefore, the mechanical role of an AO is to produce a by-pass flow pattern through the natural ostium to the sinus, and then through the AO to the pharynx during inspiration. The mass flow rate for this by-pass flow was approximately 3.6 × 10−1 ml/s, or equivalently, 0.29% of half of the total flow rate inhaled through the nostril. The streamline distributions at expiration (Fig. 9) show that the direction of flow was reversed but, the overall flow pattern was similar to that of inspiration. However, the mass flow rate through the sinus was reduced by a factor of approximately 1.6, which is consistent with Figs. 5 and 7. This reduced flow rate is thought to be related to the increased local flow resistance resulting from the local geometric configuration of the AO. The interaction of the sinus and middle meatus can also be expressed in terms of pressure fields. The static pressure contours (Figs. 10 and 11) indicated that the presence of an AO produced little global change in pressure for both inspiration and expiration. Since the pressure inside the sinus was very close to that in the middle meatus, a sizable flow exchange rate was not expected. Due to the
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Fig. 11. Pressure distribution in two representative planes during expiration. (a) Case A and (b) Case B.
patient’s asymmetrical nasal cavity, the pressures of the right and left sinuses were different in both Case A and Case B. A meaningful pressure gradient is developed only in the main flow direction as shown in Figs. 12 and 13, and the pressure gradient between the nasal cavity and either natural or accessory ostia is negligible (Figs. 10 and 11). Thus, the fact that the new flow path connecting the two ostia accounted for only 0.29% of half of the total rate suggests that ventilation might be significantly restricted without a sizeable modification of the geometry, such as from large sinus interventions.
3.2. Volume fraction of nitric oxide Flow topology inside the sinus can be altered in the presence of an AO, although the magnitude of the induced velocity is limited (Figs. 8 and 9). The convective effect associated with the altered flow through the right sinus is likely to affect the local ventilation efficiency of the sinus. Many early reports showed that the concentration and the production rate of NO in the sinus are important in respiratory physiology (Aust and Drettner, 1974; Hood et al., 2009; Rennie et al., 2011). Therefore, the present work traced the
Fig. 12. Pressure profile along the nasal cavity during inspiration. (a) Plane 6, (b) Plane 7, (c) Plane 8 and (d) Plane 9.
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Fig. 13. Pressure profile along the nasal cavity during expiration. (a) Plane 6, (b) Plane 7, (c) Plane 8 and (d) Plane 9.
NO volume fraction in order to investigate the effect of an AO on ventilation behavior. To evaluate the variation of volume fraction in time, the NO volume fraction of the sinuses was initially set to 1. Any transport or production mechanism of NO into the domain
from the mucosa in the sinuses was neglected and thus, the NO concentration decreased in time during the steady simulation. From the respiration data of Lee et al. (2010), the time required for the flow rate to reach the maximum value of approximately 515 ml/s
Fig. 14. Variation of NO concentration with time at three instants, t = 0.11, t = 0.21 and t = 0.65 s during inspiration. The red color corresponds to the volume fraction of 1 and the blue color corresponds to the volume fraction of 0. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Fig. 15. Variation of NO concentration with time at three instants, t = 0.11, t = 0.21 and t = 0.65 s during expiration. The red color corresponds to the volume fraction of 1 and the blue color corresponds to the volume fraction of 0. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
was estimated to be Tmax = 0.65 s. Therefore, NO concentration distribution was presented at three representative time instants of t = Tmax /6, Tmax /3, Tmax (i.e. t = 0.11, 0.21 and 0.65 s) to show the declining behavior of concentration. Fig. 14 shows the contours of the volume fractions of NO during inspiration. In Case B, the relatively higher NO concentration in the right sinus was maintained during ventilation via diffusion driven by the concentration difference between the maxillary sinus and the nasal cavity. Therefore, the escape rate of NO from the maxillary sinus was relatively lower for this case. In contrast, in Case A, the AO created through-flow that enhanced convective transport, resulting in a larger area of NO dispersion in the nasal cavity. The Peclet number, based on the local velocity and hydraulic diameter of the AO, was approximately 1.2. The non-zero Peclet number indicates that the AO increased the relative contribution of the convective effect compared to the diffusion mechanism; however, because this Peclet number is low, the effect of convective transport is not dominant. The average volume fraction of NO in the right maxillary sinus in Case A dropped to 0.9437, 0.8973 and 0.7409 at t = 0.11, 0.21 and 0.65 s, respectively as summarized in Table 4. However, the rate of decrease of NO in Case B was much lower than in Case A. Thus, the Table 4 Average volume fraction of NO in the right maxillary sinus. Case A
t = 0.11 s t = 0.21 s t = 0.65 s
Case B
Inspiration
Expiration
Inspiration
Expiration
0.9437 0.8973 0.7409
0.9457 0.8991 0.7421
0.9799 0.9630 0.8913
0.9810 0.9637 0.8933
production of NO inside the sinus should be larger to sustain a certain level of NO concentration to make up for the loss through the ostia in Case A. During expiration, the degree of ventilation was similar to that during inspiration (Fig. 15), although the magnitude of transit flow rate was decreased by a factor of 1.6 in Case A. This study did not consider the effect of unsteady variation of the flow field, and thus the results should be interpreted with caution. Nevertheless, Figs. 14 and 15 suggest that the effect of an AO on sinus ventilation is similar in both phases of respiration in the mean sense. 4. Discussion The ventilation characteristics in the maxillary sinus in the presence of an AO were investigated using a computational fluid dynamics technique. An anatomically correct numerical model was constructed using the CT image of an adult male with a single AO. In order to identify the effect of the AO on the ventilation of maxillary sinus, two numerical models, one with an AO and the other without, were constructed and compared. In both models, the pressure boundary conditions were adjusted to produce a target air-flow rate of 250 ml/s during inspiration and expiration. The local ventilation behavior of the sinus was analyzed by tracing the NO and air concentration fields using a VOF method. Although the presence of a relatively small AO did not globally change velocity or pressure fields, there was a distinct alteration in local flow pattern inside the maxillary sinus. This local change in flow topology can be attributed to the transit stream through the flow path connecting the natural and accessory ostia. In the presence of the AO, approximately 0.29% of half of the flow rate
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inhaled through the nostril went through the sinus. The convective transport associated with this small by-pass flow reduced the NO volume fraction to about 74% in 0.65 s in the maxillary sinus. When the sinus and nasal cavity are connected only by the natural ostium, mass transfer can only occur via diffusion driven by a concentration gradient, because there is no net flow rate into or out of the sinus in a steady state. Therefore, in the presence of an AO, the reduced NO concentration in the sinus is attributed to enhanced ventilation by convective transport of the transit flow. The role of NO in the pathogenesis of sinusitis is not clearly understood, but it is generally accepted that high levels of NO production are protective. However, reports in the literature are not consistent. For example, one study reported significantly decreased levels of NO in the maxillary sinuses of patients with maxillary sinusitis and sepsis (Deja et al., 2003). Another study found that decreased NO levels were restored after treatment for sinusitis (Degano et al., 2005). On the other hand, one study reported significantly higher levels of NO metabolites in the maxillary sinuses of patients with chronic sinusitis, suggesting that elevated levels of NO and NO metabolites might damage healthy sinus epithelium (Naraghi et al., 2007). Thus, further studies on optimal NO concentrations are necessary. This study did not consider the effect of the size of the AO, but a larger ostium is expected to result in enhanced ventilation and increased convective transport. However, the effect of enlargement of the natural ostium is controversial (Kennedy et al., 1987; Setliff, 1996, 1997; Chiu and Kennedy, 2004); large antrostomy, used in early functional endoscopic sinus surgery, has been challenged by so-called small hole surgery. However, there is insufficient evidence in the literature that large antostomy aggravates maxillary sinusitis. To establish a pathophysiological role for the size of the ostia, further case studies must investigate the effect of NO concentration after sinus surgery in connection with pathogen introduction or foreign object removal from the sinus. Acknowledgement This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology 20100027525. References Aust, R., Drettner, B., 1974. Experimental studies of gas exchange through ostium of maxillary sinus. Uppsala J. Med. Sci. 79, 177–186. Chiu, A.G., Kennedy, D.W., 2004. Disadvantages of minimal techniques for surgical management of chronic rhinosinusitis. Curr. Opin. Otolaryngol. Head Neck Surg. 12 (1), 39–42. Chung, S.K., Chang, B.C., Dhong, H.J., 2002a. Surgical, radiologic and histologic findings of the antrochoanal polyp. Am. J. Rhinol. 16 (2), 71–76.
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Chung, S.K., Cho, D.Y., Dhong, H.J., 2002b. Computed tomogram findings of mucous recirculation between the natural and accessory ostia of the maxillary sinus. Am. J. Rhinol. 16 (5), 265–268. Croce, C., Fodil, R., Durand, M., Sbirlea-Apiou, G., Caillibotte, G., Papon, J.-R., Blondeau, J.-R., Coste, A., Isabey, D., Louis, B., 2006. In vitro experiments and numerical simulations of airflow in realistic nasal airway geometry. Ann. Biomed. Eng. 34 (6), 997–1007. Deja, M., Busch, T., Bachmann, S., Riskowsky, K., Campean, V., Wiedmann, B., Schwabe, M., Hell, B., Pfeilschifter, J., Falke, K., Lewandowski, K., 2003. Reduced nitric oxide in sinus epithelium of patients with radiological maxillary sinusitis and sepsis. Am. J. Repir. Crit. Care Med. 168 (3), 281–286. Degano, B.M., Genestal, M., Serrano, E., Rami, J., Arnal, J.F., 2005. Effect of treatment on maxillary sinus and nasal nitric oxide concentrations in patients with nosocomial maxillary sinusitis. Chest 128 (3), 1699–1705. Frosini, P., Picarella, G., Campora, E.D., 2009. Antrochoanal polyp: analysis of 200 cases. Acta Otorhinolaryngol. It. 29 (1), 21–26. Hood, C.M., Schroter, R.C., Doorly, D.J., Blenke, E.J.S.M., Tolley, N.S., 2009. Computational modeling of flow and gas exchange in models of the human maxillary sinus. J. Appl. Physiol. 107 (4), 1195–1203. Hörschler, I., Brücker, Ch., Schröder, W., Meinke, M., 2006. Investigation of the impact of the geometry on the nose flow. Eur. J. Mech. B: Fluids 25, 471–490. Hurt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225. Jog, M., McGarry, G.W., 2003. How frequent are accessory sinus ostia? J. Laryngol. Otol. 117 (4), 270–272. Kaliner, M.A., Osguthorpe, J.D., Fireman, P., Anon, J., Georgitis, J., Davis, M.L., Naclerio, R., Kennedy, D., 1997. Sinusitis: bench to bedside: current findings. Future directions. J. Allergy Clin. Immunol. 99, S829–S848. Kennedy, D.W., Zinreich, S.J., Shaalan, H., Kuhn, F., Naclerio, R., Loch, E., 1987. Endoscopic middle meatal antrostomy: theory, technique and patency. Laryngoscope 97 (8, Pt 3, Suppl. 43), 1–9. Lee, J.H., Na, Y., Kim, S.K., Chung, S.K., 2010. Unsteady flow characteristics through a human nasal airway. Respir. Physiol. Neurobiol. 172, 136–146. Leong, S.C., Chen, X.B., Lee, H.P., Wang, D.Y., 2010. A review of the implications of computational fluid dynamic studies on nasal airflow and physiology. Rhinology 48 (2), 139–145. Lindemann, J., Brambs, H.J., Keck, T., Wiesmiller, K.M., Rettinger, G., Pless, D., 2005. Numerical simulation of intranasal airflow after radical sinus surgery. Am. J. Otolaryngol. 26 (3), 175–180. Lundberg, J., Farkasszallasi, T., Weitzberg, E., Rinder, J., Lidholm, J., Anggard, A., Hokfelt, T., Lundberg, J.M., Alving, K., 1995. High nitric oxide production in human paranasal sinuses. Nat. Med. 1, 370–373. Matthews, B.L., Burke, A.J.C., 1997. Recirculation of mucus via accessory ostia causing chronic maxillary sinus disease. Otolaryngol. Head Neck Surg. 117, 422–423. Mladina, R., Vukovic, K., Poje, G., 2009. The two holes syndrome. Am. J. Rhinol. Allergy 23, 602–604. Naraghi, M., Deroee, A.F., Ebrahimkhani, M., Kiani, S., Dehpour, A., 2007. Nitric oxide: a new concept in chronic sinusitis pathogenesis. Am. J. Otolaryngol. 28 (5), 334–337. Proctor, D.F., Andersen, I., 1982. The Nose: Upper Airway Physiology and the Atmospheric Environment. Amsterdam, Elsevier Biomedical. Rantanen, T., 1974. Clinical function tests of the maxillary sinus ostium. Acta Otolaryngol. Suppl. 328, 1–38. Rennie, C.E., Hood, C.M., Blenke, E.J.S.M., Scroter, R.S., Doorly, D.J., Jones, H., Towey, D., Tolley, N.S., 2011. Physical and computational modeling of ventilation of the maxillary sinus. Otolaryngol. Head Neck Surg. 145, 165–170. Setliff III, R.C., 1996. Minimally invasive sinus surgery: the rationale and the technique. Otolaryngol. Clin. North Am. 29 (1), 115–124. Setliff III, R.C., 1997. The small-hole technique in endoscopic sinus surgery. Otolaryngol. Clin. North Am. 30 (3), 341–354. Xiong, G., Zhan, J., Zuo, K., Li, J., Rong, L., Xu, G., 2008. Numerical flow simulation in the post-endoscopic sinus surgery nasal cavity. Med. Biol. Eng. Comput. 46, 1161–1167.
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Respiratory Physiology & Neurobiology journal homepage: www.elsevier.com/locate/resphysiol
The quantitative effect of an accessory ostium on ventilation of the maxillary sinus Yang Na a , Kyunghun Kim a , Sung Kyun Kim a , Seung-Kyu Chung b,∗ a b
Department of Mechanical Engineering, Konkuk University, Seoul 143-701, Republic of Korea Department of Otorhinolaryngology-Head and Neck Surgery, Samsung Medical Center, Sungkyunkwan University, School of Medicine, Seoul, Republic of Korea
a r t i c l e
i n f o
Article history: Accepted 25 January 2012 Keywords: Maxillary sinus Accessory ostium Ventilation Computational fluid dynamics simulation Nitric oxide Peclet number
a b s t r a c t The airflow and gas exchange behaviors of the human maxillary sinus were quantified to better understand the effect of an accessory ostium (AO). An anatomically correct numerical domain was constructed using CT data from a male patient with mild nasal obstruction. For the purpose of comparison, a numerical model without an AO was also generated by artificially removing the AO from the original model using CAD software. A steady-flow field through the nasal cavity was simulated using ANSYS-FLUENT v13.0 with a target flow rate of 250 ml/s. The Volume of Fluid (VOF) method was used to investigate the concentration field of nitric oxide (NO) initially filled in the maxillary sinus. The simulation results showed that a transit flow through the maxillary sinus developed in the presence of an AO. As the flow entered the sinus through either a natural or accessory ostium from the middle meatus, the velocity was significantly reduced to a local maximum of approximately 0.034 m/s inside the sinus. This by-pass flow rate through the sinus of 2.186 × 10−1 to 3.591 × 10−1 ml/s was a small fraction of the total flow rate inhaled from the nostril, but it effectively changed the local flow topology and led to a larger reduction in NO concentration in the maxillary sinus. This more rapid reduction in NO concentration was due to enhanced ventilation activity afforded by convective transport of the transit stream through the flow path connecting the natural ostium and the AO. The inspiration and expiration phases were qualitatively similar in flow pattern except for the flow direction in the maxillary sinus, suggesting that the AO plays a similar physiological role during both inspiration and expiration in terms of ventilation. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The maxillary sinus, which is connected to the nasal cavity through a natural ostium, is susceptible to various infections. The resulting sinus disease, frequently accompanied by significant pain, is known to affect up to 15% of the population and thus is a major reason for medical consultation (Kaliner et al., 1997). Several earlier studies revealed that reduced sinus ventilation is associated with sinusitis (Proctor and Andersen, 1982; Hood et al., 2009; Rennie et al., 2011), but its role in the pathophysiological development of sinusitis is still not well understood. Although the detailed anatomy of the nasal cavity varies between individuals, the maxillary sinuses typically have a volume of 10–15 ml (Hood et al., 2009); therefore, they are the largest of the human paranasal sinuses. In addition to a natural ostium, which connects the maxillary sinus to the middle meatus, endoscopic in vivo examinations commonly reveal the presence of accessory
∗ Corresponding author. Tel.: +82 2 3410 3572; fax: +82 2 3410 3879. E-mail addresses: [email protected], [email protected] (S.-K. Chung). 1569-9048/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.resp.2012.01.013
ostia (AO) in the maxillary fontanelle. The prevalence of AO is controversial, but one study reported AO in 8–19.3% of patients with chronic rhinosinusitis and a lower rate of occurrence in healthy volunteers (Jog and McGarry, 2003; Mladina et al., 2009). An early study (Matthews and Burke, 1997) proposed that AO may cause sinusitis by allowing easier pathogen access, but a mechanistic relationship between sinusitis and AO was not suggested. Another common disease involving the AO is an antrochoanal polyp, which originates from the maxillary sinus mucosa. It frequently expands through the AO into the middle meatus and finally protrudes into the choana (Chung et al., 2002a,b; Frosini et al., 2009). Although the role of AO in the pathogenesis of antrochoanal polyps is unknown, detailed flow-field information may provide a better understanding of the development of antrochoanal polyps. The main difficulty in investigating the flow of maxillary sinuses with one or more ostia is that the sinuses are inaccessibile and geometrically complex. Due to the instrumental difficulty of in vivo measurements, most early studies were based on simplified geometry. For example, Rantanen (1974) reported that the pressures of the sinus and nasal cavity are highly correlated, suggesting limited net gas exchange between the maxillary sinus and nasal cavity.
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Fig. 1. Numerical geometry. (a) Case A with an accessory ostium, (b) Case B without an accessory ostium, (c) numerical configuration.
Fig. 2. (a–i) Sequence of selected CT images used for the construction of the present numerical domain (2 mm resolution for the current set of data). PO stands for a primary (natural) ostium and AO stands for an accessory ostium. Uncinate process is indicated by *.
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Fig. 3. Representative planes for presenting computational results. (a) Top view, (b) Plane 1 containing a natural ostium, (c) Plane 2 containing an accessory ostium, (d) Plane 3, (e) Plane 4, (f) Plane 5 in the nasal valve area.
More recent studies using simplified models have indicated that the presence of an AO can increase the ventilation rate of the maxillary cavity (Aust and Drettner, 1974; Lundberg et al., 1995; Hood et al., 2009; Rennie et al., 2011). A common finding among these studies is that the maxillary sinus had a significantly higher nitric oxide (NO) concentration than the nasal cavity. One study used a simplified physical model to investigate the effect of AO on the gas exchange behavior of the maxillary sinus (Hood et al., 2009); this study suggested that the presence of one or more AO could increase the sinus ventilation rate by several orders of magnitude. In their study using a mathematical model, Rennie et al. (2011)
also demonstrated that the presence of an AO increased the effective volume flow rate of ventilation of the maxillary sinus by up to 50 times. The results of these studies indicate that the presence of AO increases sinus gas exchange rate by increasing net flow to the sinus. Although the overall characteristics were believed to be reasonably captured in their physical models, more realistic investigations are required to overcome the limitations of simplified geometries for better relevance to human respiration. Studies have investigated sinus-flow alterations associated with sinonasal pathologies and the effect of surgical correction using computational analyses of accurate human nasal cavity geometry
Table 1 Variations of velocity and pressure with grid resolution for Case A with an accessory ostium.
1,190,000 mesh 2,350,000 mesh 4.160,000 mesh
Point 1 (in the middle of the right sinus)
Point 2 (in the middle of the left sinus)
Point 3 (inside the middle meatus)
Velocity (m/s)
Pressure (Pa)
Velocity (m/s)
Pressure (Pa)
Velocity (m/s)
Pressure (Pa)
2.442 × 10−3 2.025 × 10−3 1.925 × 10−3
−5.140 −5.222 −5.233
6.841 × 10−8 5.222 × 10−8 4.997 × 10−8
−4.280 −4.290 −4.292
1.549 1.538 1.537
−5.612 −5.616 −5.617
Table 2 Geometry and flow information in three representative planes inside the nasal cavity. Plane 3
Cross sectional area (m2 ) Hydraulic diameter (m) Mean velocity (m/s) Airflow rate (ml/s) Reynolds number
Plane 4
Plane 5
Right
Left
Right
Left
Right
Left
8.916 × 10−5 1.065 × 10−2 1.493 133.1 1089
11.43 × 10−5 1.206 × 10−2 1.022 116.9 844
8.741 × 10−5 1.055 × 10−2 1.523 133.1 1100
9.631 × 10−5 1.107 × 10−2 1.214 116.9 920
9.855 × 10−5 1.120 × 10−2 1.351 133.1 1036
9.396 × 10−5 1.094 × 10−2 1.244 116.9 932
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Fig. 4. Velocity distribution in two representative planes during inspiration. (a) Case A and (b) Case B.
based on CT or magnetic resonance imaging data (Lindemann et al., 2005; Xiong et al., 2008; Leong et al., 2010). The degree of sinus ventilation is likely to be modified by surgical interventions, such as middle meatal antrostomy (MMA), by changing the local
geometry for gas flow. This type of intervention is expected to enhance gas exchange, thus reducing the nitric oxide (NO) concentration, although it can possibly impair mucociliary transport. Although these computational studies provided useful flow field
Fig. 5. Velocity distribution in two representative planes during inspiration rescaled by using a value of v = 0.005 m/s as the upper limit. (a) Case A and (b) Case B.
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Fig. 6. Velocity distribution in two representative planes during expiration. (a) Case A and (b) Case B.
information in the maxillary sinus to demonstrate that aggressive sinus surgery can significantly change the intranasal flow behavior, they did not investigate the effect of AO. The main objective of the present work was to investigate the effect of AO on the ventilation characteristics of the maxillary sinus. Using human CT data, an anatomically correct numerical domain was constructed that accurately described the nasal cavity, including the middle meatus and ethmoid infundibulum surrounding the natural ostium of the maxillary sinus. For representation and visualization of the degree of ventilation of the maxillary cavity, volume fraction of NO was investigated. The Volume of Fluid (VOF) method was used to calculate the concentration of NO under steady normal breathing conditions with the assumption that the entire NO initially resided in the maxillary cavity. 2. Numerical methodology 2.1. Numerical domain based on a CT image To identify the physiological effect of the presence of an AO, two different models, one with an AO (Case A) and the other without an AO (Case B), were prepared (Fig. 1). A surface-rendered computational model of the nasal cavity, including the maxillary sinuses with the AO, was created using 0.35-mm thick CT data of an adult patient with a mild nasal obstruction of the right side during a common cold. A part of CT images acquired at the Samsung Medical Center in Korea as part of a routine clinical procedure is displayed in Fig. 2 to show the locations of both natural and accessory ostia. Permission for this study was obtained from the Institutional Review Board of the Samsung Medical Center. This patient had no mucosal pathology or polyps in the maxillary sinus or middle meatus except one small AO (approximately 1.6 mm × 1.6 mm in cross-section or equivalently 2.30 mm in diameter and 2.72 mm in length) in the posterior part of the maxillary fontanelle and a mild septal
deviation to the left side. The mean diameter of the natural ostium varied from 2.70 mm in the smallest section to 7.50 mm in the largest section. It was approximately 11.16 mm long. The distance between the natural ostium and AO was about 8 mm. The maxillary sinus volumes were 7.1 and 6.6 ml for the right and left sinuses, respectively, which are smaller than the value of 10–15 ml reported by Hood et al. (2009). To create a computational model representing a normal anatomical configuration without an AO, CAD software was used to artificially remove the AO from the Case A model, so that this model had only a natural ostium (Case B), as shown Fig. 1. To present the simulation results, mainly two skewed 2-D planes were selected, as shown in Fig. 3. Plane 1 represented the plane containing the natural ostium, whereas Plane 2 revealed the AO. Plane 3 to Plane 5 were selected in the nasal valve area for the evaluation of local flow rate and Reynolds number. The accuracy of the numerical result is related to the number of meshes and the mesh distribution. For both Case A and Case B, the grid-generating software GRIDGEN v15.14 was used to generate meshes with combined tetrahedral and prism elements. A prism layer placed near the surface was essential for reducing a truncation error as found in previous work with a similar geometry (Lee et al., 2010). The present numerical geometry with relatively small ostia contained several regions requiring careful resolution. Therefore, the computations were conducted using 3 different resolutions to validate the results, as summarized in Table 1. The velocity and pressure were compared at 3 representative locations: in the right sinus with an AO, in the left sinus, and in the nasal cavity. There was a reasonably small change in velocity and pressure with a change in grid resolution for a grid system of approximately 4,160,000 mesh elements. Therefore, additional computations with a higher resolution were not attempted in the present work. This grid resolution was higher than that of the previous work of Lee et al. (2010) in order to resolve flow variables in the presence of relatively small ostia.
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Fig. 7. Velocity distribution in two representative planes during expiration rescaled by using a value of v = 0.005 m/s as the upper limit. (a) Case A and (b) Case B.
Fig. 8. Comparison of streamline patterns during inspiration. Streamlines are colored by the magnitude of the velocity. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Fig. 9. Comparison of streamline patterns during expiration. Streamlines are colored by the magnitude of the velocity. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
In the present numerical domain, an air chamber was placed in front of the nostril, as shown in Fig. 1. This thermodynamically stagnant chamber allowed for the smooth induction of inhaled air through the nostril so that the streamlines of the air exhibited realistic curvatures. In addition to this kinematic advantage, the thermodynamic stagnation properties at the surface of the air chamber better represented inlet boundary conditions, although the size of the chamber was not large.
2.2. Fluid dynamic boundary conditions The respiration process was modeled by applying the pressure difference between the inlet and the outlet in order to mimic the natural respiration process, where airflow is controlled by pressure in the lungs. Since the air chamber outside the nostril is exposed to the atmosphere, a stagnation pressure at the inlet was assigned a constant value of atmospheric pressure during respiration. At the outlet, the exit pressure value was adjusted to obtain a breath rate of 250 ml/s. This flow rate corresponds to approximately half of the typical maximum value and thus effectively represented instances in the middle of inspiration or expiration. It was assumed that the general flow characteristics associated with the presence of AO were reasonably captured at these 2 instances, and thus, unsteady computations were not attempted. The inclusion of mucous wall movement did not significantly increase gas velocities in the ostium (Hood et al., 2009); therefore, for simplicity, the mucociliary effect was not considered here.
On the basis of the mean velocity and the hydraulic diameter near the nasal valve area, the estimated Reynolds number did not exceed 1200 for a target flow rate of 250 ml/s as summarized in Table 2. The flow at this maximum Reynolds number was not likely to be described properly with a turbulence model as noted in some recent studies (Croce et al., 2006; Hörschler et al., 2006). Thus, a laminar flow model was used throughout the computational domain. For simplicity, the effects of temperature and humidity variations along the airway surface were not taken into account. Therefore, all properties of inhaled air were evaluated at a constant temperature of 25 ◦ C throughout the simulation. 2.3. Trace of nitrogen monoxide To trace escaping NO from the maxillary sinus, the VOF method (Hurt and Nichols, 1981) incorporated in the ANSYS/Fluent package was used to track the interface between the air and the NO. The resulting volume fraction of NO was calculated to investigate the ventilation characteristics. To incorporate the VOF method, the momentum equation was rewritten to include the surface force:
du = −∇ p + ∇ · + Fb + Fs dt
(1)
, p and denote density, velocity vector, pressure and viswhere , u cous stress tensor, respectively. Also, Fb denotes body force, and Fs represents the surface force, including the effect of surface tension. Since the present configuration involved a continuous distortion of the free surface formed by NO and air, the VOF method with a continuum surface force (CSF) model was used. The density and
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Fig. 10. Pressure distribution in two representative planes during inspiration. (a) Case A and (b) Case B.
viscosity of the 2 gases are listed in Table 3. Using the volume fraction, C, of NO obtained via the VOF method described above, the density, , and viscosity, , of the mixture of 2 different gases were calculated as follow: = CNO + (1 − C)Air
(2)
= CNO + (1 − C)Air
(3)
3. Results 3.1. Velocity and pressure fields The additional flow path connected to the maxillary cavity through the AO did not globally change the velocity field except for a localized alteration of flow pattern near the ostia during inspiration, as shown in Figs. 4 and 5. The contours of Fig. 4 were prepared using the maximum velocity detected in the 2 representative planes; the contours of Fig. 5 were rescaled by using a significantly lower velocity value as the upper limit of the color map, so that the detailed flow field could be expressed near the ostia. This contour-level adjustment was necessary because the induced velocity in the maxillary sinus had a relatively lower magnitude. For reference, the Case A model had an AO in the right sinus, exhibited in Plane 2. The AO had a negligible effect on the global velocity field dynamics (Fig. 4), which is believed to be related to its small dimension compared to the other flow passages in the Table 3 Reference values for density and viscosity of air and NO gas.
Density (kg/m3 ) Viscosity (kg/m s)
Air
Nitric oxide
1.225 1.789 × 10−5
1.000 1.723 × 10−5
nasal cavity through which the inhaled air moves. However, even this small change in local topology resulted in a qualitatively different local flow pattern near the ostia. That is, the presence of an AO effectively provided the path for transit flow through the maxillary sinus. As a result, the air stream entered the maxillary sinus through the natural ostium from the middle meatus and then exited through the AO. Upon the reversal of the main flow during the phase change from inspiration to expiration, the overall behavior remained qualitatively the same, but the velocity magnitude was slightly reduced in the maxillary sinus, as shown in Figs. 6 and 7. The streamline patterns through the right sinus (Fig. 8) revealed the existence of by-pass flow in a wide region of the sinus of Case A. However, due to the conservation of mass, a steady-state nonzero net flow rate into the sinus is not possible when an AO does not exist, as in Case B. Therefore, the mechanical role of an AO is to produce a by-pass flow pattern through the natural ostium to the sinus, and then through the AO to the pharynx during inspiration. The mass flow rate for this by-pass flow was approximately 3.6 × 10−1 ml/s, or equivalently, 0.29% of half of the total flow rate inhaled through the nostril. The streamline distributions at expiration (Fig. 9) show that the direction of flow was reversed but, the overall flow pattern was similar to that of inspiration. However, the mass flow rate through the sinus was reduced by a factor of approximately 1.6, which is consistent with Figs. 5 and 7. This reduced flow rate is thought to be related to the increased local flow resistance resulting from the local geometric configuration of the AO. The interaction of the sinus and middle meatus can also be expressed in terms of pressure fields. The static pressure contours (Figs. 10 and 11) indicated that the presence of an AO produced little global change in pressure for both inspiration and expiration. Since the pressure inside the sinus was very close to that in the middle meatus, a sizable flow exchange rate was not expected. Due to the
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Fig. 11. Pressure distribution in two representative planes during expiration. (a) Case A and (b) Case B.
patient’s asymmetrical nasal cavity, the pressures of the right and left sinuses were different in both Case A and Case B. A meaningful pressure gradient is developed only in the main flow direction as shown in Figs. 12 and 13, and the pressure gradient between the nasal cavity and either natural or accessory ostia is negligible (Figs. 10 and 11). Thus, the fact that the new flow path connecting the two ostia accounted for only 0.29% of half of the total rate suggests that ventilation might be significantly restricted without a sizeable modification of the geometry, such as from large sinus interventions.
3.2. Volume fraction of nitric oxide Flow topology inside the sinus can be altered in the presence of an AO, although the magnitude of the induced velocity is limited (Figs. 8 and 9). The convective effect associated with the altered flow through the right sinus is likely to affect the local ventilation efficiency of the sinus. Many early reports showed that the concentration and the production rate of NO in the sinus are important in respiratory physiology (Aust and Drettner, 1974; Hood et al., 2009; Rennie et al., 2011). Therefore, the present work traced the
Fig. 12. Pressure profile along the nasal cavity during inspiration. (a) Plane 6, (b) Plane 7, (c) Plane 8 and (d) Plane 9.
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Fig. 13. Pressure profile along the nasal cavity during expiration. (a) Plane 6, (b) Plane 7, (c) Plane 8 and (d) Plane 9.
NO volume fraction in order to investigate the effect of an AO on ventilation behavior. To evaluate the variation of volume fraction in time, the NO volume fraction of the sinuses was initially set to 1. Any transport or production mechanism of NO into the domain
from the mucosa in the sinuses was neglected and thus, the NO concentration decreased in time during the steady simulation. From the respiration data of Lee et al. (2010), the time required for the flow rate to reach the maximum value of approximately 515 ml/s
Fig. 14. Variation of NO concentration with time at three instants, t = 0.11, t = 0.21 and t = 0.65 s during inspiration. The red color corresponds to the volume fraction of 1 and the blue color corresponds to the volume fraction of 0. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Fig. 15. Variation of NO concentration with time at three instants, t = 0.11, t = 0.21 and t = 0.65 s during expiration. The red color corresponds to the volume fraction of 1 and the blue color corresponds to the volume fraction of 0. (a) Case A and (b) Case B. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
was estimated to be Tmax = 0.65 s. Therefore, NO concentration distribution was presented at three representative time instants of t = Tmax /6, Tmax /3, Tmax (i.e. t = 0.11, 0.21 and 0.65 s) to show the declining behavior of concentration. Fig. 14 shows the contours of the volume fractions of NO during inspiration. In Case B, the relatively higher NO concentration in the right sinus was maintained during ventilation via diffusion driven by the concentration difference between the maxillary sinus and the nasal cavity. Therefore, the escape rate of NO from the maxillary sinus was relatively lower for this case. In contrast, in Case A, the AO created through-flow that enhanced convective transport, resulting in a larger area of NO dispersion in the nasal cavity. The Peclet number, based on the local velocity and hydraulic diameter of the AO, was approximately 1.2. The non-zero Peclet number indicates that the AO increased the relative contribution of the convective effect compared to the diffusion mechanism; however, because this Peclet number is low, the effect of convective transport is not dominant. The average volume fraction of NO in the right maxillary sinus in Case A dropped to 0.9437, 0.8973 and 0.7409 at t = 0.11, 0.21 and 0.65 s, respectively as summarized in Table 4. However, the rate of decrease of NO in Case B was much lower than in Case A. Thus, the Table 4 Average volume fraction of NO in the right maxillary sinus. Case A
t = 0.11 s t = 0.21 s t = 0.65 s
Case B
Inspiration
Expiration
Inspiration
Expiration
0.9437 0.8973 0.7409
0.9457 0.8991 0.7421
0.9799 0.9630 0.8913
0.9810 0.9637 0.8933
production of NO inside the sinus should be larger to sustain a certain level of NO concentration to make up for the loss through the ostia in Case A. During expiration, the degree of ventilation was similar to that during inspiration (Fig. 15), although the magnitude of transit flow rate was decreased by a factor of 1.6 in Case A. This study did not consider the effect of unsteady variation of the flow field, and thus the results should be interpreted with caution. Nevertheless, Figs. 14 and 15 suggest that the effect of an AO on sinus ventilation is similar in both phases of respiration in the mean sense. 4. Discussion The ventilation characteristics in the maxillary sinus in the presence of an AO were investigated using a computational fluid dynamics technique. An anatomically correct numerical model was constructed using the CT image of an adult male with a single AO. In order to identify the effect of the AO on the ventilation of maxillary sinus, two numerical models, one with an AO and the other without, were constructed and compared. In both models, the pressure boundary conditions were adjusted to produce a target air-flow rate of 250 ml/s during inspiration and expiration. The local ventilation behavior of the sinus was analyzed by tracing the NO and air concentration fields using a VOF method. Although the presence of a relatively small AO did not globally change velocity or pressure fields, there was a distinct alteration in local flow pattern inside the maxillary sinus. This local change in flow topology can be attributed to the transit stream through the flow path connecting the natural and accessory ostia. In the presence of the AO, approximately 0.29% of half of the flow rate
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inhaled through the nostril went through the sinus. The convective transport associated with this small by-pass flow reduced the NO volume fraction to about 74% in 0.65 s in the maxillary sinus. When the sinus and nasal cavity are connected only by the natural ostium, mass transfer can only occur via diffusion driven by a concentration gradient, because there is no net flow rate into or out of the sinus in a steady state. Therefore, in the presence of an AO, the reduced NO concentration in the sinus is attributed to enhanced ventilation by convective transport of the transit flow. The role of NO in the pathogenesis of sinusitis is not clearly understood, but it is generally accepted that high levels of NO production are protective. However, reports in the literature are not consistent. For example, one study reported significantly decreased levels of NO in the maxillary sinuses of patients with maxillary sinusitis and sepsis (Deja et al., 2003). Another study found that decreased NO levels were restored after treatment for sinusitis (Degano et al., 2005). On the other hand, one study reported significantly higher levels of NO metabolites in the maxillary sinuses of patients with chronic sinusitis, suggesting that elevated levels of NO and NO metabolites might damage healthy sinus epithelium (Naraghi et al., 2007). Thus, further studies on optimal NO concentrations are necessary. This study did not consider the effect of the size of the AO, but a larger ostium is expected to result in enhanced ventilation and increased convective transport. However, the effect of enlargement of the natural ostium is controversial (Kennedy et al., 1987; Setliff, 1996, 1997; Chiu and Kennedy, 2004); large antrostomy, used in early functional endoscopic sinus surgery, has been challenged by so-called small hole surgery. However, there is insufficient evidence in the literature that large antostomy aggravates maxillary sinusitis. To establish a pathophysiological role for the size of the ostia, further case studies must investigate the effect of NO concentration after sinus surgery in connection with pathogen introduction or foreign object removal from the sinus. Acknowledgement This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology 20100027525. References Aust, R., Drettner, B., 1974. Experimental studies of gas exchange through ostium of maxillary sinus. Uppsala J. Med. Sci. 79, 177–186. Chiu, A.G., Kennedy, D.W., 2004. Disadvantages of minimal techniques for surgical management of chronic rhinosinusitis. Curr. Opin. Otolaryngol. Head Neck Surg. 12 (1), 39–42. Chung, S.K., Chang, B.C., Dhong, H.J., 2002a. Surgical, radiologic and histologic findings of the antrochoanal polyp. Am. J. Rhinol. 16 (2), 71–76.
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