Computers in Biology and Medicine 61 (2015) 8–18
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Numerical simulation of airflow and micro-particle deposition in human nasal airway pre- and post-virtual sphenoidotomy surgery Hojat Bahmanzadeh a, Omid Abouali a,n, Mohammad Faramarzi b, Goodarz Ahmadi c a
School of Mechanical Engineering, Shiraz University, Shiraz, Iran Department of Otolaryngology Head & Neck Surgery, Shiraz University of Medical Sciences, Shiraz, Iran c Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, USA b
art ic l e i nf o
a b s t r a c t
Article history: Received 3 October 2014 Accepted 14 March 2015
In the present study, the effects of endoscopic sphenoidotomy surgery on the flow patterns and deposition of micro-particles in the human nasal airway and sphenoid sinus were investigated. A realistic model of a human nasal passage including nasal cavity and paranasal sinuses was constructed using a series of CT scan images of a healthy subject. Then, a virtual sphenoidotomy by endoscopic sinus surgery was performed in the left nasal passage and sphenoid sinus. Transient airflow patterns pre- and post-surgery during a full breathing cycle (inhalation and exhalation) were simulated numerically under cyclic flow condition. The Lagrangian approach was used for evaluating the transport and deposition of inhaled micro-particles. An unsteady particle tracking was performed for the inhalation phase of the breathing cycle for the case that particles were continuously entering into the nasal airway. The total deposition pattern and sphenoid deposition fraction of micro-particles were evaluated and compared for pre- and post-surgery cases. The presented results show that sphenoidotomy increased the airflow into the sphenoid sinus, which led to increased deposition of micro-particles in this region. Particles up to 25 μm were able to penetrate into the sphenoid in the post-operation case, and the highest deposition in the sphenoid for the resting breathing rate occurred for 10 μm particles at about 1.5%. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Nasal airway Sphenoid sinus Sphenoidotomy CFD Micro-particle Unsteady flow
1. Introduction Rhinosinusitis is one of the most common diseases that cause suffering for many patients. In order to treat those patients who do not respond to pharmaceutical medications, Endoscopic Sinus Surgery (ESS) is prescribed. Sphenoidotomy is used to relieve the infections, polyps, or tumors in the sphenoid sinus. The sphenoid sinus is one of the deepest and largest sinuses in the nasal passage. Sphenoidotomy is performed without resection of the turbinate and by creating an opening into the anterior wall of the sphenoid sinus or enlarging the natural ostium of the sphenoid sinus. If the surgeon approaches the sphenoid sinus through removal of ethmoid sinuses, then the procedure is called transethmoidal sphenoidotomy [1]. This procedure requires dissection of the uncinate process in order to visualize the natural ostium of the maxillary sinus. After identification of the anterior ethmoid area, its cells are dissected. Then posterior ethmoid sinuses are identified and dissected. Finally, the sphenoid is opened inferiorly and medially, and the ostium is enlarged laterally. Sphenoidotomy causes some alteration in the nasal airway structure. This
n
Corresponding author. Tel.: þ 98 711 613 3034; fax: þ 98 711 647 3511. E-mail address:
[email protected] (O. Abouali).
http://dx.doi.org/10.1016/j.compbiomed.2015.03.015 0010-4825/& 2015 Elsevier Ltd. All rights reserved.
leads to changes in airflow and deposition patterns of the inhaled particles in the nasal airway. Before an actual surgery, a virtual surgery can be helpful for specialists and surgeons to assess the potential changes in both the nasal airflow and deposition of the aerosol particles. In addition, the virtual surgery would allow for testing various alternatives and for optimal surgical planning [2]. Recently, due to the rapid growth in computer technology, researchers have been able to prepare accurate 3-D computational models from CT scan images. Moreover, these nasal models can be virtually modified to reflect the predicted results of the proposed surgical techniques [3]. In contrast to experimental approaches, Computational Fluid Dynamics (CFD) techniques provide a powerful research tool to investigate the airflow in the human nasal airway [4–9], as well as transport and deposition of aerosol particles [10–15]. Even more complex transport processes such as elongated fiber deposition and stochastic effects of turbulence on particle motion can be studied numerically [16–19]. There have been several CFD studies of nasal airway models with surgical modifications. Lindemann et al. [20] simulated the airflow in the nasal cavity after a virtual radical sinus surgery during inhalation. They showed that aggressive turbinectomy leads to disturbed intranasal air conditioning caused by reduction of the surface area. Chen et al. [21] and Na et al. [22] investigated the effect of surgical turbinate resection on airflow characteristics. Surgical correction of septal deviation has
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been one of the common procedures in otolaryngology. Ozlugedik et al. [23] and Garcia et al. [24] carried out CFD studies on airflow in a nasal cavity model with septal deviation. Moghadas et al. investigated the impact of septal deviation on the deposition of nano/ micro-particles in a human nasal passage using a computational modeling approach. Their results suggested that there would be marked changes in the deposition pattern of particles after septoplasty, surgery to straighten the nasal septum [25]. A number of numerical investigations of sinus-flow changes with surgical modifications have been reported in the literature [20,26,27]. Hood et al. studied the gas exchange in the maxillary sinus and scrutinized the effects of ostium size and the accessory ostium on the sinus ventilation rate [28]. Rennie et al. investigated sinus ventilation experimentally and numerically for single- and double-ostium sinuses [29]. Abouali et al. [2] constructed realistic 3-D computational models of the human nasal passage for pre- and post-virtual uncinectomy and Middle Meatal Antrostomy (MMA). They showed that after maxillary sinus endoscopic surgery, the maxillary sinus ventilation changes dramatically and the deposition of inhaled nano/micro-particles in the sinus increases. In earlier studies of the human sinus-nasal flow, steady air and particle flow conditions have been assumed to simplify the computational modeling effort and cost. The significance of the transient nature of respiratory flows has already been pointed out by Shi et al. [12], Lee et al. [30], Zhu et al. [31,32] and Chung et al. [33], among others. The motion and deposition of inhaled particles during cyclic breathing, however, have been rarely studied. The exceptions are the studies of Zhang et al. [34] in a triple bifurcation lung airway model, the Takano et al. [35] analysis of the human larynx region, and the Inthavong et al. [36] simulations of microparticle deposition in a tracheobronchial airway model. It is worth mentioning that only Häußermann et al. [37] experimentally investigated micro-particle deposition in the nasal airway using human breathing patterns. An unsteady model of nano-particle transport was also performed by Zhang and Kleinstreuer [38] and Shi et al. [12]. The presented literature survey shows that the numerical investigation of micro-particle transport and deposition in a nasal airway under unsteady condition (cyclic inhalation and exhalation) has not been reported in the literature. In addition, computational modeling of the ethmoidotomy and sphenoidotomy effects on the nasal airflow and deposition of inhaled pollutants and particles is missing. In the present study, a realistic human airway model was constructed, and a virtual sphenoidotomy operation was performed on the left nasal passage and sphenoid sinus. In order to capture the time-dependent characteristics of transport
Vestibule Main airway & Ethmoid cells Sphenoid sinus
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processes and the features of transient airflow structures, the full breathing cycles were simulated numerically under cyclic flow condition and the particle deposition pattern was investigated in the inhalation phase.
2. Computational model of the nasal airway To create a three-dimensional model of the nasal cavity including paranasal sinuses for the pre- and post-operative cases, coronal cross sections for the left side of the nasal cavity and sinuses obtained by computed tomography (CT) scan images of a healthy adult male were used in this study. The scans consisted of coronal cross sections spaced 0.625 mm apart with a spatial resolution of 512 512 pixels from the tip of the nostrils to the beginning of the nasopharynx. The images were acquired as a part of the routine clinical procedure. The boundary between the airway mucosa and air in the nasal cavity and paranasal sinuses was determined in each CT scan's slice under the supervision of a specialist. To reconstruct the 3-D model consisting of the nasal cavity and sinuses, the boundaries were connected to each other to create a smooth surface, and form the volume using commercial software. Finally, the model was exported as STL (Stereolithography) file format into ANSYS-ICEM software for meshing. Details of the modeling process of the human nose may also be found in the works of Zubair et al. [39,40]. Fig. 1 shows different views of the constructed model including the description of different parts. To produce the post-surgery model, the uncinectomy, ethmoidotomy and sphenoidotomy were performed virtually by the otolaryngologist through resecting the uncinate process and removing ethmoid cells and a part of the anterior wall of the sphenoid sinus on the coronal cross sections. Fig. 2 shows the lateral view of the computational model with locations of several cross sections corresponding to an area that has undergone surgery. Comparison between cross sections preand post-operation is also shown. Fig. 3 compares the variations of the cross-sectional areas of the nasal passage with the distance from the nostril for pre- and postoperation cases. It is seen that after surgery the nasal cross-section area has been enlarged compared with that before the surgery. The enlargement of the nasal passage was initiated from the uncinate process near the maxillary ostium at a distance of 52 mm from the nostril and continued to the sphenoid sinus region at a distance of 88 mm from the nostril. Fig. 4 shows the shape of the sphenoid for pre- and post-operative cases. It is seen that a portion of the anterior wall of the sphenoid around the sinus ostium has been removed.
Ethmoid cells
Maxillary sinus Frontal sinus
Nasal value area
prismatic layers
tetrahedral cells
Fig. 1. (a) Schematic of the constructed nasal model and (b) one coronal cross section of generated hybrid mesh.
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Pre-operation
Post-operation
Fig. 2. Comparison of coronal cross sections of pre- and post-operation models.
Fig. 3. Variation of the cross-section areas of nasal passage pre- and post-operation versus axial distance from the nostril.
The computational grid was generated by the grid-generating software ICEM-CFDTMANSYS (Canonsburg, PA). Because of the complexity of the nasal geometry, an unstructured computational grid, with a hybrid mesh consisting of four-prismatic boundary layers along the walls with an inner core of tetrahedral elements, was used. The maximum computational cell element size was 0.53 mm and the worst cell element had equiangle skewness of about 0.8. The total number of the tetrahedral and prism elements
in the computational grid was approximately 2,400,000 and 2,800,000, respectively, for pre and post-operative cases. Thickness of the first prism layer and the total thickness of four layers growing exponentially were, respectively, 0.05 mm and 0.27 mm. In Fig. 1(b) a cross section of the hybrid mesh is shown. The prism layer placed at the nasal airway walls was necessary for accurate prediction of the near-wall particle trajectories and the deposition flux and viscous effect. A grid sensitivity examination was carried out, and the grid cell size was selected so that the simulation results were independent of the number of grid elements. The meshes were then imported into Fluent14.0 (ANSYS, Canonsburg, PA, USA) to simulate the airflow, and the associated particle transport and deposition. All calculations were performed in a PC with a 3.4 GHz, Core (TM) i7 CPU, and 8 GB RAM. Typical run times for cyclic and steady inhalation conditions were, respectively, about 192 and 2 h.
3. Governing equations and boundary condition Due to the significant geometry variations in the nasal airways, the critical flow rate and/or the critical Reynolds number for transitions from laminar to turbulent regime cannot be specified with certainty. Hahn et al. reported that the flow is laminar in a single nasal passage
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Fig. 4. Comparison of the shape of sphenoid for (a) pre- and (b) post-operation cases.
for a flow rate less than 12 L/min [41]. More recent studies of realistic nasal airways indicated that the laminar flow is maintained for flow rates less than 10 L/min in a single nasal passage [42,43]. Doorly et al. noted instability in the airflow for a breathing rate of 12 L/min in a half-nasal model, but they reported relatively undisturbed laminar flows within much of the cavity [44]. In this study, simulations for a nasal airway model were presented under unsteady flow condition with the maximum breathing rates of 5, 7.5 and 10 L/min. Therefore, it is assumed that the flow is in the laminar regime. The Reynolds numbers, based on the inlet average velocity and hydraulic diameter of the nostril, are 599, 899, and 1196, respectively, for maximum inspiratory flow rates of 5, 7.5, and 10 L/min. A one-way coupling assumption for the gas–solid flow was used since the volume fraction of particles is very low. This means that the airflow transports the particles, but the effects of particle motion on the flow, which are negligibly small, are neglected. The governing equations for the airflow are continuity and balance of momentum. For unsteady and incompressible laminar flows these are ! ∇U u ¼ 0
ð1Þ
! ∂u 1 ! ! ! ð2Þ þ ð u U∇Þ u ¼ ∇P þ υ∇2 u ρ ∂t ! In Eqs. (1) and (2), u is the velocity vector, t is the time, P is the fluid pressure, ρ is the constant fluid density, and υ is the kinematic viscosity. The governing equations were integrated over each control volume to acquire a set of algebraic equations. These equations were resolved using the SIMPLE algorithm. The convective and diffusive terms were discretized, respectively, by the upwind and the central difference schemes. The particle transport and deposition calculations were evaluated by the Lagrangian trajectory analysis approach. Under the one-way coupling assumption, the airflow field was first simulated, and then the trajectories of particles were determined by solving the particle equation of motion. Trajectories of particles can be tracked by integrating a force balance equation consisting of drag, inertia and gravity force acting on the particle. Accordingly !p 3μC D Rep ! !p du ¼ u u þg 2 dt 4ρ d
ð3Þ
p p
!p In Eq. (3), u is the particle velocity vector, dp is the particle diameter, ρp is the particle density, μ is the fluid viscosity, g is the
Fig. 5. Sinusoidal time variation of the breathing pattern. Minus sign indicates that the airflow exits the outlet of the model.
! !p acceleration gravity, and Rep (Rep ¼ ρ u u d=μ) is the particle Reynolds number. The drag coefficient C D is given by [45] CD ¼
24 ð1 þ 0:15 Rep 0:687 Þ Rep Cslip
Here, C slip is the Cunningham slip correction factor given as dp 2λ 1:257 þ 0:4exp 1:1 C slip ¼ 1 þ dp 2λ
ð4Þ
ð5Þ
where λ is the air mean free path. To simulate a more realistic full-respiration cycle, including inhalation and exhalation breathing conditions, a time-dependent computational model with time-varying boundary condition was used. Specifically, the flow rate at the outlet of the computational domain which ends at the beginning of the nasopharynx was prescribed as a sinusoidal function of time as shown in Fig. 5. That is, in the first half-period of the breathing cycle, the airflow from nostril to nasopharynx simulates the inhalation phase; in the second half-period, the flow is reversed and moves from the nasopharynx toward the nostril and simulates the exhalation phase. Three different sinusoidal flow rates, with peak values of 5, 7.5 and 10 L/min were used in these simulations. Two breathing cycles were evaluated, and the data for the second cycle were used for the analysis to reduce the effect of initial conditions. The duration of each breathing cycle was 4 s in which the first 2 s were considered for the inhalation phase and the last 2 s were for the exhalation phase. It should be emphasized that the real time variation of the inhalation/exhalation flow rate is not quite
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sinusoidal. For example, Lee et al. reported the time variation of the human nasal airway flow rate for the average breathing rate of 35 L/min [30]. Unfortunately, the time variation of the flow pattern for lower breathing rates is not available in the literature, and earlier studies typically used a sinusoidal form similar to the one used in the present work [31,32]. The airway walls were considered to be rigid and the no-slip (zero velocity) condition was assumed. Zero gauge pressure was set at the nostril. Time steps of 0.1 s, 0.05 s and 0.02 s in the numerical integration were used to test the solution independence of the time steps. Approximately the same results for time steps less than 0.05 s were observed; therefore, 0.05 s was selected as the flow time step in the present study. In the earlier computational studies for steady inhalation conditions, the injection of particles was typically performed only once. Here in order to simulate the continuous entering of particles into the nasal airway in the inhalation phase, 2000 micro-particles were injected uniformly into the nostrils at each time step of 0.1 s. Thus, in the inhalation period, a total of 38,000 (2000 19) particles were injected into the nasal cavity. To select the appropriate injection time step, a sensitivity study was performed. The time step was decreased up to a point for which the deposition results were independent of the time step. The number of injected particles was also selected in such a way to ensure the independence of the simulation results from the number of injected particles within an error of about 0.5%. The stepby-step injection of particles provides a more realistic representation of particle inhalation at the nostril for evaluating the transient particle deposition during the breathing cycle. It should be emphasized that this type of injection corresponds to the inhalation of pollutants and suspended particles in the surrounding atmosphere, which are inhaled during the entire inhalation phase. Therapeutic drug particles are typically introduced during specific periods within the inhalation phase; hence, extending the results of the present study for inhalation drug delivery should be taken with caution. Initial particle velocities were assumed to be equal to the average fluid velocity at the nostril at each time. The microparticles that passed through the nasopharynx were assumed to deposit in the lower region of respiratory system and not to return to the upper airways during the exhalation. The particle rebounding from the surfaces was neglected, and the particle was assumed to deposit when the distance between the particle center and the adjacent surface was less than or equal to the particle radius.
Pre-operation
Deposition fraction (DF) was also specified as the ratio of the number of trapped particles to the number of particles entering the nostril during inhalation. Micro-particles with aerodynamic diameters in the range of 1–30 μm were simulated to examine a wide range of nasal deposition efficiencies. While particles greater than 20 μm are typically not inhalable by the human nose, the simulations were performed up to 30 μm for completeness.
4. Results and discussion 4.1. Airflow simulation Fig. 6 shows the airflow streamlines at peak of inhalation for a peak breathing rate of 7.5 L/min for pre- and post-surgery nasal
Fig. 7. Flow rate entering the sphenoid sinus during inhalation: (a) pre-operation and (b) post-operation.
Post-operation
Fig. 6. Streamlines at peak inhalation for a breathing intensity with peak value of 7.5 L/min.
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Fig. 8. Fraction of the airflow through the sphenoid during inhalation: (a) preoperation and (b) post-operation.
passages. For the pre-surgery case, it is observed that the bulk of the airflow passes along the middle and lower regions of the nasal cavity, while a small amount of flow reaches the ethmoid and sphenoid sinuses. This figure also shows that none of the streamlines enter the sphenoid sinus for the pre-surgery nasal passage. For the post-sphenoidotomy case, the airflow field in the sphenoid sinus alters markedly as a portion of the airflow streamlines, which passes through the nasal airway, enters the sphenoid. Fig. 7 compares the time variations of sinus ventilation flow rates for breathing with peaks of 5, 7.5 and 10 L/min for the pre- and postoperative nasal passages. It is seen that the airflow rate entering the sphenoid sinus increases markedly with the breathing intensity in the inhalation period. The high flow rate entering the sinus during inhalation occurs because the airflow direction is in line with the sinus ostium in this period. Comparison of the pre- and post-surgery cases shows that the sphenoid sinus ventilation after the operation increases. For example, for the peak inhalation rate of 10 L/min for the preoperative case, the peak flow rate reaching the sphenoid sinus is about 1.5 mL/min, which can be ignored. In the post-operative state the flow rate reaches to about 1500 mL/min, which shows significant increase. The total volume flow entering the sphenoid sinus during inhalation of a breathing cycle is evaluated and is compared with the total breathing rate in Fig. 8. This figure shows the ratio of the volume of air entering the sinus compared to the total volume for pre- and post-operative cases during the inhalation period. It is observed that about 16–18% of inhaled air reaches the sinus after surgery, indicating high ventilation in the sphenoid. For example, for the breathing intensity with a peak of 7.5 L/min, about 17% of the inhaled airflow reaches the sphenoid sinus. In addition, it is seen that in the preoperative case, a negligible fraction of airflow enters the sphenoid during the inhalation phase of the breathing cycle. Using a steady inhalation analysis, Abouali et al. [1] reported that after an uncinectomy and MMA operation on the
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maxillary sinus, approximately 25% of the inhaled airflow enters into the sinus for the breathing under resting condition. From the physiological point of view, many earlier studies suggested that nitric oxide (NO) in exhaled air is produced mainly in the paranasal sinuses [46,47]. In the paranasal sinuses, nitric oxide adjusts the mucocilliary clearance function [48] and is highly beneficial for sinus host defense in that it contributes to keeping the sinuses sterile and devoid of bacteria and viruses under normal conditions. In contrast, as a result of a reduction in NO level in the sinuses, the subject might be prone to sinus infections [49]. Thus, excessive air ventilation of the sphenoid sinus after surgery may reduce the concentration of nitric oxide and cause adverse physiological effects on the sinus function. Fig. 9 displays the velocity magnitude contours at different coronal sections for peak inhalation (t¼1 s) with a maximum flow rate of 7.5 L/min in the left nasal passage pre- and post-surgery. In general, velocity magnitude in the superior, middle and inferior meatus as well as close to the wall of the nasal septum is higher than in other parts of the nasal passage for all breathing conditions due to smaller cross-section areas. The dark blue regions correspond to the low velocity regions in the normal sinuses, such as the frontal for which very little flow enters. Comparison of pre- and post-operative situations at peak inhalation (t¼1 s) shows that the velocity magnitude in the middle and inferior regions for the post-operation case decreases slightly, but the magnitude of velocity in the sphenoid and dissected ethmoid cells area increases dramatically. The changes in the ethmoid and sphenoid regions were due to the airflow penetration through the opened ethmoid and sphenoid, which, in turn, enhances the volume fraction of airflow in upper portions of the nasal passage after surgery. In addition, the average velocity in the sphenoid inlet increases from 0.015 m/s for the pre-operative case to 0.3 m/s for the post-operative case. It can be seen that in the inhalation phase, ventilation of the sphenoid sinus occurs at a high velocity near the wall, which may have an adverse effect on the distribution of mucosa on the sinus walls. This figure also shows that the airflow from the upper part of the enlarged ostium enters the sinus and exits from below toward nasopharynx. During inhalation, a high velocity is observed in the nasal valve which is similar to the prior reports in the literature [50]. High velocities are also found in the inferior meatus close to the nasopharynx due to the narrow airflow passage in these regions. The corresponding velocity magnitudes for pre and post-operation cases are, respectively, about 2.5 and 2.6 m/s. During inhalation, the static pressure progressively reduces in the direction of the airflow stream. Fig. 10 compares the variation of the absolute value of the pressure drop between nostril and nasopharynx during the inhalation phase of the breathing cycle for pre- and postoperation conditions for breathing with a peak of 7.5 L/min. Comparison of pressure drop for pre- and post-sphenoidotomy in Fig. 10 indicates that during inhalation, the pressure difference between the nose entrance and nasopharynx decreases after surgery, which is due to the enlargement of airflow passage in certain areas due to surgery (especially in the ethmoid region). Nasal resistance is defined as the ratio of pressure drop to the volume flow rate, which is also a criterion for breathing comfort. The variation of nasal resistance during inhalation is shown in Fig. 11. After a sphenoidotomy, the nasal resistance and pressure drop decrease significantly. For example, the nasal resistance before surgery is 47 Pa s/L, and after surgery it reduces to 36 Pa s/L at the maximum inhalation rate of 7.5 L/min. Hence, after surgery less effort is needed for breathing the same flow rate. 4.2. Particle deposition Experimental data for particle deposition in the nasal cavity under cyclic breathing at rest conditions are rather limited. Therefore, for
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Pre-operation
Post-operation
C B A
A
C
B
Pre-operation
A
B
C
Post-operation Fig. 9. Velocity magnitude contours for various cross sections at peak inhalation for a breathing intensity with peak value of 7.5 L/min. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
100 90
present work, 5 L/min present work, 7.5 L/min present work, 10 L/min
deposition fraction (%)
80
Fig. 10. Pressure drop during inhalation for pre and post-operation cases for a cyclic breathing with a peak of 7.5 L/min.
70 60 50 40
kelly et al. (viper), 10 L/min [49] kelly et al. (viper), 15 L/min [49] kelly et al. (viper), 20 L/min [49] kelly et al. (SLA), 10 L/min [49]
kelly et al. (SLA), 15 L/min [49] kelly et al. (SLA)-20 L/min [49] Schroeter et al. (Model A) [50]
30 20
Schroeter et al. (Model B) [50] Schroeter et al. (Model C) [50]
10 0 100
1000
10000 2
2
100000
1000000
3
d Q (µm cm /s)
Fig. 12. Comparison of deposition fraction versus impaction parameter with the simulation results and experimental data.
Fig. 11. Nasal resistance variation with time during inhalation for pre- and postoperation cases for a breathing cycle with a peak of 7.5 L/min.
computational model validation, the deposition rate of micro-particles in pre-operation nasal models for constant inhalation rates of 5, 7.5 and 10 L/min are compared with the available experimental data of Kelly et al. [51] and computer simulation of Schroeter et al. [52] in Fig. 12. Viper and SLA terms in this figure are related to the same nasal replicas which are produced by two different manufacturing methods that led to different surface roughness. In Fig. 12, the horizontal axis is the impact parameter, d2Q, which is shown in logarithmic scale. Here,
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Qpeak=10 L/min
Qpeak=5 L/min Pre-operation
15
Post-operation
Pre-operation
Post-operation
1 µm
1 µm
1 µm
1 µm
10 µm
10 µm
10 µm
10 µm
20 µm
20 µm
20 µm
20 µm
Fig. 13. Micro-particle deposition patterns on the nasal passage and sphenoid sinus walls at the end of inhalation phase. Two left and two right columns are for two different breathing intensities with a peak of 5 and 10 L/min, respectively.
Q is the airflow rate entering one nostril and d is the particle diameter. According to Fig. 12, the deposition curves corresponding to three different breathing rates used in the present study roughly coincide to a single curve in terms of impaction parameter, and they are in reasonable agreement with the simulation results of Model C of Schroeter et al. [52]. This figure shows, however, that there are some differences between the present simulation results and both the experimental data of Kelly et al. [51] and simulations of Schroeter et al. [52], Models A and B. In particular, the simulations under predict the data of Kelly et al. [51] for the impaction parameter by more than 10,000 μm2 cm3/s. Schroeter et al. [52] reconstructed nasal CFD models with different degrees of surface smoothness using the same MRI data used by Kelly in construction of their nasal replicas. Model A is without any surface smoothing; Model B and Model C are, respectively, with slight and more smoothing. The particle depositions predicted by the present model are quite close to the simulation results for Model C (smoothest) of Schroeter et al. [52]. Their simulation results for Models A and B are closer to the experimental data of Kelly et al. [51], which indicate that the particle deposition in the nasal passage increases with an increase in the surface roughness. In fact, when surface roughness is relatively high, flow near the surface fluctuates more, which leads to an increase in the deposition of particles traveling in the vicinity of airway walls. When the surface roughness is high, the deposition by interception mechanism becomes more effective. The increase of particle deposition with surface roughness in duct flows was observed experimentally by Montgomery and Corn [53] and in the computer simulations of Fan and Ahmadi [54] and Li and Ahmadi [55]. Therefore, it is conjectured that the difference between the present simulation results and the experimental data of
Kelly et al. [51] is due to the roughness in the nasal cavity replica in the experimental work. The local deposition of micro-particles under cyclic breathing in the nasal passage and sinuses for pre- and post-operation cases are analyzed, and the results are described in this section. Monodispersed 1, 10 and 20 μm particles are injected continuously at the nostril during the inhalation period with initial velocity equal to the mean airflow velocity at the inlet, and their trajectories are tracked during one inhalation phase. For two different breathing cycles with peak flow rates of 5 and 10 L/min, the corresponding deposition patterns at the end of the inhalation period are shown in Fig. 13. Comparison of deposition patterns of 1, 10 and 20 μm particles shows that deposition of micro-particles increases with the increase of either particle diameter or breathing intensity. This observation is as expected since the inertial effect is the dominant mechanism for particle deposition in the nasal cavity for the studied size range. Fig. 13 also shows that the effect of breathing intensity on the particle deposition is more pronounced for large 20 μm particles compared with small 1 μm particles. Large particles with diameters of 10 and 20 μm have large inertia, and their trajectories deviate from flow streamlines when the airflow has sharp turns. As a result, a large number of inertial particles deposit on the nasal surfaces. Fig. 13 also shows that before the operation no particle enters the sphenoid sinus because the sinus is a poorly ventilated organ. After a sphenoidotomy, however, for both breathing intensities, a number of particles with different diameters (1, 10 and 20 μm) enter into the sphenoid sinus, and some particles deposit on the sinus wall because of the enhanced ventilation. In summary, this type of surgery,
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Fig. 14. Deposition fractions in sphenoid sinus post-operatively at the end of inhalation phase for different breathing cycles with peak value of 5, 7.5 and 10 L/min.
including the enlarging of the sinus inlet, opening of ethmoid cells and removing part of the uncinate process, significantly increases the micro-particle transport into the sphenoid sinus. In the sphenoid sinus, the pattern and amount of particle deposition vary with particle diameter and breathing intensity. The amount of deposition, however, is more sensitive to the particle diameter than to the airflow rate. In addition, almost all deposited particles in the sphenoid sinus settle on the lower half of the sinus cavity. This is because, as seen in Fig. 6, the air circulation in this region is stronger, and gravitational sedimentation also moves the particles downward. For the post-operation case, variation of computed deposition fractions of micro-particles in the size range of 1–30 μm at the end of the inhalation phase for different breathing intensities with peaks of 5, 7.5 and 10 L/min are shown in Fig. 14. Sphenoidotomy causes noticeable increase in particle deposition in the sphenoid sinus, and this increase varies with particle size and breathing rates. Fig. 14 shows that the deposition in the sinus increases with particle size and reaches a maximum for 10 μm diameter; deposition then decreases for larger particles. That is, the highest deposition fraction of 1.5% in the sphenoid occurs for 10 μm particles. This is because most of the larger particles deposit in the anterior parts of the nasal cavity, and only a small fraction reaches the sinus. Abouali et al. [2] reported a similar trend of variation with particle size for the deposition fraction in the maxillary sinus. After an endoscopic sphenoidotomy, infection of the sinus may not be removed completely or it might even relapse; therefore a topical aerosol therapy option may be required after surgery. Simulation results suggest that aerosolized drug delivery to the sphenoid sinus after ESS is best accomplished by droplets with a diameter of 10 μm. Larger droplets are filtered by the anterior regions and are unable to reach the sphenoid sinus. Smaller particles follow the inhaled flow to the lower airway regions without being trapped on the sinus walls. The simulation results for the case before surgery suggest that, since the sphenoid sinus is a poorly ventilated cavity, topical aerosolized drug delivery to the sinus by the common aerosol therapy methods has limited effect. One unwanted complication of endoscopic sphenoidotomy may be exposure of the sinus to inhaled bioaerosols and allergens, which may predispose the patients to infectious diseases and allergic reactions. Bacteria, fungal spores and viruses are the most common bioaerosols in the size range of 0.02–30 μm [56], which are found everywhere in the ambient air all the time. Although a sphenoidotomy may resolve sinusitis inflammation by extracting infections through an enlarged drainage route, it would also allow exposure to a significant amount of bioaerosols that can easily penetrate into the sphenoid sinus. These bioaerosols can grow and proliferate in the mucus-lined sinus and contribute to more severe infections and inflammation in the sinus. Therefore, it is recommended that the patients avoid exposure to bioaerosols or allergens to the extent possible.
A limitation of the simulations shown in Fig. 12 is that the airflow is steady and particle tracking was performed only for the steady inhalation condition. As mentioned before, in the present work an unsteady particle tracking is performed for the inhalation phase, and particles are released continuously at the nostril at each time step. For the unsteady simulations, the required computational resources are extensive. To keep the computational effort manageable, airflow and particle transport simulations are performed for one of the nasal passages and the nasal cavity is truncated before the nasopharynx region. This truncation introduces some approximations for the inlet boundary conditions during the exhalation phase. Therefore, the results for the exhalation phase are rough approximations and are not presented. In addition, the present study showed that most of the micro-particle deposition occurs during the inhalation phase. Therefore, neglecting the deposition during the exhalation phase does not alter the total deposition results to a noticeable extent. Simulating the exhalation condition that includes the return of the exhaled particles and studying their effect on the deposition fraction are left for a future study. Such an expanded study would require inclusion of the effect of the entire lower respiratory system on airflow and particle transport, as well as the need to use the full nasal model. In a recent work [57], the authors studied the facial effect on the distribution and focusing of the inhaled particles at the nostril under a steady inhalation condition. Extension of the present unsteady simulation to include the facial effect and effect of the surrounding environment are left for a future study.
5. Conclusions In the present study, a numerical simulation of cyclic breathing for a model of the human nasal airway and paranasal sinuses before and after endoscopic sphenoidotomy (transantral-ethmoidectomy) was used, and the time variation of airflow during the inhalation and exhalation phases and micro-particle deposition during the inhalation were analyzed. The main conclusions of this study are the followings: 1. The simulations show that a very small amount of airflow enters the normal sphenoid sinus during inhalation. A sphenoidotomy operation along with associated modifications noticeably changes the airflow pattern in the ethmoid area and inside the sphenoid sinus, and as a result a part of the main airflow through the nasal passage enters the sphenoid during inhalation. In addition, a sphenoidotomy significantly decreases the nasal resistance to airflow and therefore the pressure drop across the nose decreases. 2. Increased airflow into the sinus after an endoscopic sphenoidotomy causes deposition of micro-particles in the sphenoid sinus. Almost all the deposited particles settle on the lower half of the sinus cavity. Before the operation almost no particles could enter this sinus. 3. Particles up to 25 μm are able to penetrate into the sphenoid in the post-operation case. Furthermore, for the resting breathing rate, the highest deposition fraction of 1.5% in the sphenoid occurs for the 10 μm particles. 4. The significant increase in the deposition of inhaled particles in the sphenoid after the sphenoidotomy (transantral-ethmoidectomy) has important consequences for optimizing not only inhalation drug delivery to the sphenoid sinus but also the adverse effect of inhaled bioaerosols and allergens entering the sinus. 5. Virtual sinus surgery can simulate various surgical modification scenarios and predict their outcomes. Virtual sinus surgery will assist surgeons to understand the consequences of their
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surgical interventions on the sinus ventilation and the change in inhaled aerosol deposition and to evaluate drug delivery to the sinus. It should be emphasized that this study was focused on the effects of virtual surgery and some details of the unsteady flow particle deposition in the nasal airway was not discussed. The important features of the unsteady flow effects on flow in the upper respiratory tract and the associated particle transport and deposition will be discussed in a forthcoming paper.
Conflict of interest statement All the authors declare that there is no potential conflict of interest including any financial, personal or other relationships with other people or organizations within that could inappropriately influence (bias) this work.
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