microparticles in human nasal passage

microparticles in human nasal passage

Respiratory Physiology & Neurobiology 177 (2011) 9–18 Contents lists available at ScienceDirect Respiratory Physiology & Neurobiology journal homepa...

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Respiratory Physiology & Neurobiology 177 (2011) 9–18

Contents lists available at ScienceDirect

Respiratory Physiology & Neurobiology journal homepage: www.elsevier.com/locate/resphysiol

Numerical investigation of septal deviation effect on deposition of nano/microparticles in human nasal passage H. Moghadas a , O. Abouali a,∗ , A. Faramarzi b , G. Ahmadi c a b c

School of Mechanical Engineering, Shiraz University, Shiraz, Iran Department of Otolaryngology Head & Neck Surgery, Shiraz University of Medical Sciences, Shiraz, Iran Mechanical and Aeronautical Engineering Department, Clarkson University, Potsdam, NY, USA

a r t i c l e

i n f o

Article history: Accepted 22 February 2011 Keywords: Nasal airway Septal deviation CFD Nano-particle Micro-particle

a b s t r a c t Three dimensional computational models of both sides of human nasal passages were developed to investigate the effect of septal deviation on the flow patterns and deposition of micro/nano-particles in the realistic human nasal airways before and after septoplasty. A series of coronal CT scan images from a live 25-year old nonsmoking male with septal deviation in his right nasal passage was used to construct the model. For low to moderate activities, the steady airflows through the nasal passages were simulated. Eulerian and Lagrangian approaches were used, respectively, for nano- and micro-particles. The results show that the flow field and particle deposition strongly depend on the passage geometry especially for micro particles. In particular, the deposition rate in the passage with septal deviation was much higher compared with those in the normal (left) passage and the postoperative passage. Despite the similarity of total micro-particle deposition in the postoperative and the normal cavities, the regional deposition patterns were quite different in these passages. The deposition of nano-particles, however, showed similar trends in the postoperative right nasal passage and the normal left passage. The simulation results showed that in addition to the major alteration of the airflow pattern after the septoplasty operation, there are significant changes in the deposition pattern of nano- and micro-particles. Despite the anatomical differences between the available experimental configuration and the present computer model, the simulation results for the deposition efficiency of particles of different sizes are in qualitative agreement with the available data. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The nasal airways play an important role in the human respiratory system. They filter, heat and humidify the inspired air (Elad et al., 2008), and protect the lung by capturing particulate matter. Normal nasal airways are highly complex organs both geometrically and functionally (Doorly et al., 2008a; Chen et al., 2009). Abnormal airways could occur due to the presence of deviation and/or obstruction in the bony or cartilaginous septum of the nasal passage. Deviation in the nasal airways is a common disease that makes septoplasty one of the most frequently performed operations in the nasal airway. The present study is focused on the simulation of airflow and particle transport and deposition in an abnormal nasal passage with septal deviation. The current standard rhinometric measurements provide information on the total nasal airflow rate, pressure drop, and nasal cross-sectional area but cannot reveal changes in the patterns

∗ Corresponding author. Tel.: +98 711 613 3034; fax: +98 711 647 3511. E-mail address: [email protected] (O. Abouali). 1569-9048/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.resp.2011.02.011

of local airflow. Such general data is inadequate for quantifying the functional impact of nasal obstruction and the effectiveness of the subsequent surgical outcomes. For example, the long-term outcomes of septoplasty are still not quite satisfactory, and a large percent of the patients continue to complain about nasal obstruction following the operation. Recent advances in CFD (computational fluid dynamics) modeling permit the creation of computational models for individual patients. Furthermore, the computational modeling results can be obtained in several days rather than the several months that were previously required. Thus, CFD provides the opportunity to predict the details of nasal airflow and the corresponding transport of gaseous chemicals, aerosols, heat, and water vapor in the nasal cavity of an individual patient before and after operations. As a result, CFD can be used as a tool for virtual surgery to test various scenarios and for selecting the proper procedure for the optimal outcome of the operation before the surgery (Zhao and Dalton, 2007; Zachow et al., 2006; Ozlugedik et al., 2008). Understanding particle deposition in the human respiratory system is important in connection to odorant delivery rates (Zhao et al., 2004), therapeutic drug delivery (Inthavong et al., 2008a)

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and assessment of exposure to inhalation of aerosol pollutants. Emission from power plants, automobiles and other industrial sources are major sources of air pollution and cause related health problems. There is also increasing interest from pharmaceutical companies to extend the inhalation drug delivery process, which is typically mouth-based, to the nasal respiratory system (Kimbell et al., 2004; Gao et al., 2005). For all these applications, a better understanding of the parameters that control particle transport and deposition in the human respiratory system is necessary. Experimental studies of airflow through human nasal passages were performed by a number of investigators in recent years (Schreck et al., 1993; Hahn et al., 1993). Experimental results indicated that the airflow was laminar up to a breathing rate of 24 L/min (Hahn et al., 1993) or 15 L/min (Kelly et al., 2000). Kim and Chung (2003) showed that the geometric variations of the middle turbinate have a major effect on the airflow patterns in the nose. Doorly et al. (2008b) investigated the details of the mechanics of airflow in human nasal airways. In addition, a number of computational studies for simulating the airflow inside human nasal passages were reported in the literature (Keyhani et al., 1995; Subramaniam et al., 1998; Zhao et al., 2004; Weinhold and Mlynski, 2004; Zachow et al., 2006; Wen et al., 2008). Furthermore, many experimental and numerical studies on particle transport through human nasal passages were performed. Strong and Swift (1987), Cheng et al. (1988) and Swift et al. (1992) measured the capture of ultrafine particles in the human nasal passage. Cheng et al. (1993), Swift and Strong (1996), Cheng et al. (1996) and Cheng (2003) presented an empirical relation for deposition efficiency in the human nasal passage. Kelly et al. (2004a, 2004b) measured the particle deposition in a nasal airway replica model with different surface qualities. These included a SLA (Stereolithography) nasal replica model with greater surface roughness and a Viper nasal replica model (manufactured with a Viper Si2 machine) with a smooth surface. They suggested that the surface quality does not significantly affect the nasal deposition efficiency of nano-particles. However, the micro-particle deposition efficiency strongly depends on the surface roughness. Recently, computer simulations of particle transport and deposition in the nasal passages were reported by Zamankhan et al. (2006), Shi et al. (2007), Liu et al. (2007), Xi and Longest (2008) and Wang et al. (2009), among others. The effect of pathologic conditions, such as the presence of polyps, swelling, atrophy or resection of turbinates and enlarged adenoids in the nasal airflow, were studied using cadaver models by Tonndorf (1939), Proetz (1951), and Swift and Proctor (1977). Grützenmacher et al. (2006) inspected the presence of compensatory hypertrophy of turbinates. Chung and Kim (2008) applied DPIV (Digital Particle Image Velocimetry) procedure to study the consequence of turbinate modification on the airflow patterns in respiration. In addition, they studied the airflow patterns in both nasal cavities of a patient with an asymptomatic deviated nasal septum. Ozlugedik et al. (2008) inspected both the effects of septal deviation and concha bullosa on nasal airflow, as well as the aerodynamic changes induced by virtual septoplasty and partial lateral turbinectomy. Chen et al. (2009) carried out a CFD study to provide information on the aerodynamic consequences of nasal septal deviation on the turbulent airflow patterns and their related physiological functions. Although the normal nasal septum would be a straight midline structure between right and left nasal passages, most people have some degree of twist or irregularity of the nasal septum. In general, the deviated septum exists congenitally, but it may also be due to an accident. However, the number of symptomatic persons with deviated nasal septum is lower than that of asymptomatic patients. The nasal septum may cause nasal obstruction, epistaxis and drying out; thus the quality of the patient’s life can be seriously affected.

Fig. 1. Schematic of the lateral view of the right nasal cavity of a male patient. IT and MT refer to inferior and middle turbinates. IM and MM refer to inferior and middle meatuses.

To the authors’ knowledge, the effects of septal deviation on the micro- and nano-particle deposition in the nasal airways have not been reported in the literature. In the present study, several computer models of the nasal airway were developed for a human male subject who was referred to an otolaryngologist. The subject had nasal septal deviation with the main symptom of obstruction of the right side nasal passage. While the earlier studies typically were concerned with hypothetical configurations, in the present work, the CT (computed tomography) scans of the coronal sections of the patient’s nasal passages before and after an operation were used to generate a realistic airway configuration. The details of the airflow in the nasal passages pre and post septoplasty were then evaluated using a computational model. The simulated airflow field was then used, and the microand nano-particle transport and deposition in both pre and postoperative nasal passages were investigated. The simulation results show that the septum deviation strongly affects the airflow field in the airway. The septum deviation decreases the airflow in the partially blocked nasal passage, while it increases the overall particle deposition rate. Furthermore, the regional deposition patterns of both micro- and nano-particles were changed significantly after the operation. The simulation results for normal nose configuration are found to be in qualitative agreement with the available experimental data. 2. Computational model of the nasal airway The creation of an accurate 3-D (three dimensional) model of the complex geometry airway (Fig. 1) is the first step for the flow field simulation. In the current study, the coronal cross sections of both sides of the nasal cavities obtained by CT scan images of an adult male subject were used to construct a smooth airway passage for the pre and postoperative cases. The coronal cross sections were 2 mm apart and the resolution of the images was 512 × 512 pixels. The postoperative CT scan was taken three months after the septoplasty. The images before the septoplasty were acquired as a part of routine clinical procedure but for acquiring the images after the septoplasty, ethics approval was obtained. Fig. 2 show the pictures of the axial CT scans of cross sections of the nasal passage. It is seen that the major deviation was located in the main

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Fig. 2. Nasal coronal cross sections at various distances from the nostril produced by CATIA software. SD refers to the septal deviation. The darkened grey areas represent the airways.

airway region. Septal deviation started at about 30 mm from the nose tip, in the nasal valve region where the area of the airway begins to decrease. The asymmetry between the left and right cavities can be seen clearly from Fig. 2. At a distance of 46 mm from the nose tip, the deviation divided the right airway in two separated pathways. This separated segment continued to 50 mm away from the nose tip. Deviation decreased the cross section areas and the total volume of the passage, which led to several breathing problems for the patient. The two separated pathways reunited at a distance of 72 mm from the nose tip, but the shape of the reconnected pathway is different from the left nasal cavity. The deviation ended in the beginning of the nasopharynx region. It is seen that the two separated pathways of the airway in the right side were merged into a single airway after septoplasty, and the right cavity looks like a normal nose airway postoperatively. It should be pointed out that most of the people experience a nasal cycle, which is the alternating congestion and decongestion of the nasal airway. In addition, some parts of the nasal passages might be blocked by the mucus buildup. These can change the shape of the nasal cross sections during the different scan times. A specialist can remove the blockage due to the mucus buildup in the scanned pictures as it was done in our work. Therefore it should be emphasized that the flow pattern and the particle deposition in each numerical study correspond to the specific scan images of the nasal airway.

The coronal sections in the main airway have rather complex geometries, and their morphology changes sharply over short distances. In order to generate an accurate 3-D model from the 2-D coronal cross sections, knowledge of the anatomy of the nasal airway geometry is critical. Kimbell (2001) and Zamankhan et al. (2006) who used different methods for constructing the normal nasal passages noted the challenges of the reconstruction process. Here the 3-D geometry of human nasal airways was reconstructed in four steps. In the first step, CT-scan images from a male subject with septal deviation in the right cavity were taken. In the second step, CT-scan images with DICOM format were processed by MATLAB software and the boundary coordinates of the nasal cavities walls were identified. In the third step, the outcome of the image processing was imported into CATIA software and the nasal airway volume was created. The 3-D volume from CATIA was then exported to the mesh generation software GAMBIT to produce the 3-D computational domain. The generated unstructured computational grid includes approximately 800,000 tetrahedral elements for each passage. Several finer computational grids were also used to investigate the effect of grid refinements on the computational results. It was shown that the numerical results were grid independent for a computational grid with about 600,000 cells or more. The initial generated grid typically had high skewness because of the complexity of the nasal passages. Care was taken to decrease the skewness of the grid, which resulted in a better

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Fig. 3. Variations of passage cross sectional area versus axial distance from the nostril. BS and AS refer respectively to the before and after the septoplasty.

convergence for the numerical solutions and decreased the corresponding residual computations errors. For simulation of the airflow and particle transport and deposition, the FLUENT (6.3.12) software was employed. Fig. 3 shows the variation of the nasal cross sectional area with the distance from the nose tip. Before the operation, in the vestibule region, Z < 20 mm, both sides have roughly the same cross sectional area. In the region with Z > 25 mm, where the deviation starts in the right passage, the nasal cross sectional area is smaller than the left side. The maximum difference occurs in the main airway region at about 60–70 mm distance from the nose tip. For Z > 30 mm, the right side cross sectional area increases after the septoplasty due to removal of deviation. At the start of the main airway, the postoperative right side has a bigger cross section area compared with that of the left side; but at the end of the main airway, this trend becomes reversed. The left side volume was nearly 36.7% greater than the right side volume preoperatively, while this difference decreases to 15% after the surgery. Therefore, 16% of the obstruction is removed after the septoplasty. 3. Governing equations and boundary conditions There is still uncertainty on the critical Reynolds number of the flow rate for transition to turbulent flow in the nasal airway system. Hahn et al. (1993) reported that the flow is laminar for a flow rate of less than 12 L/min in a single nasal passage. Doorly et al. (2008b) reported some instability in the flow for this flow rate for an inspiratory jet entering the nasal cavity, but they observed a relatively undisturbed laminar flow within much of the cavity. Therefore, in general, the approximation of laminar flow for a flow rate less than 12 L/min seems reasonable especially for steady flows. In the present study, for low to moderate activities it is assumed that the airflow in the nasal cavity is laminar. The Reynolds numbers

in the nasal passages based on the average velocity and hydraulic diameter of the nostril are in the range of 100–450 for all cases studied. As noted before, for this range of Reynolds numbers that correspond to inspiration in a normal nasal cavity under rest condition, the flow regime is laminar. The airflow in the abnormal nasal cavity is also laminar, as the corresponding velocity magnitude is less than that for a normal cavity under the same pressure drop due to the passage partial blockage. Table 1 shows the Reynolds numbers in the normal nasal cavity and pre and postoperative passage with the blockage based on the average velocity and hydraulic diameter of the nostril. In addition, for dilute particle concentrations, a one-way coupling assumption was used. That is, the airflow transports the particle, but the effect of the particles on the flow is negligible. So the airflow field was first simulated, and then the trajectories of individual particles were calculated. The numerical solution was based on the finite volume formulation. The governing equations were integrated over each control volume to obtain a set of algebraic equations. These equations were solved by employing the SIMPLE algorithm for the pressure correction processes. The convective and diffusive terms were discretized, respectively, by the upwind and the central difference schemes. For the flow field simulation, the convergence criteria set the conditions that the non-dimensional residuals of equations reduce to <10−9 . The numerical simulation was performed on a PC with a 2.33 GHz, Core (TM) 2 Duo CPU and 2 GB RAM and took nearly 10 h of CPU time for each case. The governing equations for the airflow are continuity and conservation of momentum equations:

∇ · u = 0

(1)

1  · ∇u  = − ∇ P + ∇ 2 u  u 

(2)

 is the velocity vector, P is the fluid pressure,  In Eqs. (1) and (2), u is the fluid density, and  is the kinematical viscosity. The micro-particle transport and deposition calculations were performed by a Lagrangian approach: p 3CD Rep du  −u p) + g = (u dt 4p dp2 Cslip

(3)

 p is the particle velocity vector, dp is the particle diamIn Eq. (3), u eter, p is the particle density,  is the fluid viscosity, g is the p acceleration gravity, and Rep (Rep = |uj − uj |d/) is the particle Reynolds number. Here CD CD =

24 (1 + 0.15 Re0.687 ) p Rep

(4)

is the particle drag coefficient, and Cslip



Cslip = 1 +

2 1.257 + 0.4 exp dp



−1.1

dp 2

 (5)

is the Cunningham slip correction factor. In Eq. (5)  is the air mean free path. The nano-particle transport and deposition evaluations were performed using an Eulerian approach. The corresponding concen-

Table 1 Airflow volume flow rate and Reynolds numbers in various passages for different pressure drops. L, RA and RB refer, respectively, to the left side and right side after and before the septoplasty. P (Pa)

10 15 20

RB

RA

L

Re

Q (L/min)

Re

Q (L/min)

Re

Q (L/min)

97 130 161

4.0 5.4 6.7

184 240 290

7.5 9.8 11.8

159 204 242

7.9 10.2 12.1

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tration equation is given as,

∇ · (u C) = ∇ · [D∇ C]

(6)

In Eq. (6), C is the nano-particle concentration, and the particle mass diffusivity is given as, D=

kB TCslip 3dp

(7)

In Eq. (7), kB is the Boltzmann constant and T is the air absolute temperature. For the passage wall, a no slip flow boundary condition was used. At the nostril and at the outlet (the beginning of the nasopharynx region), pressure boundary conditions were imposed. A zero gage pressure was set at the nostril, and various negative gage pressures were imposed at the outlet. To estimate the micro-particle deposition, it was assumed that when the distance between the particle center and the surface was less than or equal to the particle radius the particle will attach to the surface and the possibility of the particle rebounding from the passage walls was ignored. The particles were injected uniformly at the nostril. To test the statistical independence, various numbers of the injected particles were tested. The simulation results showed that the particle deposition efficiency remains the same if the number of injected particles was larger than 420. The selected time step for particle trajectory analysis was typically one order of magnitude smaller than the corresponding particle relaxation time. The inlet velocity of the particles was set equal to average inlet air velocity at the nostril. 4. Results and discussion 4.1. Airflow simulation The airflow rates for various imposed pressure drops in the right cavity pre and postoperatively and the left cavity are compared in Table 1. For the same pressure drop, it is seen that the amount of air passing through the right nasal cavity before septoplasty is much smaller than that after the operation. Furthermore, the right postoperative passage has roughly the same volumetric airflow rate as the normal left cavity. Also for a given pressure drop, the nasal airflow in the abnormal right cavity before septoplasty is about 40–50% less that that in the normal left passage. After septoplasty, however, the differences reduce to less than 6%. Fig. 4 displays the velocity magnitude contours at several sections in right nasal passage pre and postoperatively for an airflow rate of Q = 7.5 L/min. In the preoperative right nasal cavity, the velocity magnitude is highest in the nasal valve and the main airway regions where the deviation resides. However, after the septoplasty, the peak velocity occurs in the nasal valve region, which is similar to normal nasal cavities as reported by several authors in the literature and noted in Section 1. Similarly, for the same pressure drop, the air speed is smaller in the preoperative right nasal cavity because of lower volume flow rate.

Fig. 4. Velocity magnitude contours for the right cavity before and after septoplasty for an airflow rate of 7.5 L/min.

correlating the nasal deposition efficiency of micro-particles. The S-shape variation of the deposition efficiency is clearly seen from this figure. The model predictions for the normal left nasal passage and postoperative right cavity, however, are somewhat lower than the experimental data, while the predicted deposition efficiency for the preoperative right passage is in the range of the experimental data. Differences between the present simulation results and the experimental data are perhaps due to the anatomical and geometrical differences of the nasal passages. As noted before, the present study is for a patient with one abnormal nasal passage while the experimental data were for normal nasal passages. Interestingly, the healthy left passage and the postoperative right cavity exhibit roughly identical trends. That suggests that the left nasal passage

4.2. Particle deposition 4.2.1. Micro-particles Mono-dispersed particles in the range of 1–50 ␮m were injected into the nasal airway, and their transport and deposition for different pressure drops in the range of 10–20 Pa were evaluated. Comparisons of the present model’s predictions for variation of deposition efficiency with the impaction parameter for different nasal passages for a pressure drop of 10 Pa with the earlier experimental data of Kelly et al. (2004a) are shown in Fig. 5. The impaction parameter is defined as IP = d2 Q, where d is the particle diameter and Q is the airflow rate, and has been used extensively for

Fig. 5. Axial velocity contours and particle concentration in different coronal sections of the pre and postoperative right nasal cavity for pressure drops of 10 and 40 Pa. Black dots identify particles that pass through the section.

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Fig. 6. Local deposition efficiencies for 5, 10 and 20 ␮m particles for pressure drops of 10 and 40 Pa in various nasal passages.

of the patient may have anatomically changed to compensate for the right blocked passage. Thus, the left passage may also have some differences with the nasal cavities of typical healthy people. In addition, the experimental models typically have wall roughness, while the present computer model has smooth walls, which could be another reason for the differences. As well, it should be pointed out that deposition efficiency reported by Kelly et al. (2004a) is for two nasal chambers but our results are for single nasal passage to emphasize the difference between the right nasal passage before and after the septoplasty. For the same pressure drop, Fig. 5 also shows that the preoperative right cavity has a markedly higher deposition fraction compared with the postoperative one. For example for IP = 26,733 ␮m2 cm3 /s, the deposition efficiency is 79% for the right preoperative cavity, 44% for the right postoperative passage, and 35% for the left nasal cavity. That is the difference of 35% between the right preoperative and the normal left cavity, and it decreases to 12% after the septoplasty. The reason for the significant increase in the deposition in the right abnormal nasal cavity is that the septum deviation blocks the airflow and turns the streamlines sharply, and thus increases the inertia impaction effect. 4.2.2. Regional deposition of micro-particles Local deposition of 5, 10 and 20 ␮m particles are plotted in Fig. 6 for pressure drops of 10 and 20 Pa in various nasal passages. It is seen that the deposition efficiency generally increases as particle size increases. For the 10 Pa pressure drop, most of the particle deposition in the right preoperative nasal cavity occurs in the main

airway region. This is because of the rapid change in the passage direction due to the septum’s deviation. In contrast, for the same pressure drop, higher particle depositions occur in the vestibule and nasal valve regions for the right postoperative and the normal left cavities. For these passages the airflow rates are higher due to the absence of blockage and the augmented inertial impaction which causes the particles to deposit in the earlier part of the nasal passage. For the pressure drop of 20 Pa, although the airflow rate increases but the local deposition shows the same trend with a higher deposition fraction. In fact, the local deposition patterns are quite different for pre and postoperative passages. This observation further shows the importance of the geometric feature of the nasal passages’ geometry on the micro-particle deposition. In the right postoperative and the left normal nasal cavities, for both pressure drops, most particles deposit in the vestibule region and a fraction of larger particles deposit in the nasal valve region. Particles of about 10 ␮m or smaller are able to pass through the nasal valve region, but most of them deposit in the main airway region. While not shown here, large fractions of particles smaller than a few microns pass through the nasal airway and penetrate into the tracheobronchial airways. The patterns of the particle deposition (not shown here) reveals that no 5 or 10 ␮m particles reach to the olfactory region in the preoperative right cavity and only a few 20 ␮m particles are deposited in this region. This indicates that therapeutic aerosol drug delivery to the olfactory region through nasal inhalation may be difficult for the preoperative right cavity due to the septal deviation. However, more particles are able to reach to the olfactory region in the

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Fig. 7. Deposition flux (non-dimensionalized with inlet concentration flux) contours of 2 nm, 5 nm and 10 nm particles in different passages for a breathing rate of 4 L/min.

postoperative right nasal cavity. Clearly, the septoplasty operation significantly changes the transport processes in the nasal valve and main airway regions. As noted before, for the postoperative nasal cavity, the majority of the air and particle flows are focused in the middle and the upper region of the passage. While for the preoperative conditions, the airflow and particles are distributed across the entire cross section of the passage.

4.2.3. Nano-particle deposition Dispersion and deposition of nano-particles in different nasal passages were studied using an Eulerian diffusion model approach. Brownian motion is the dominant mechanism for nano-particle deposition, and the simulation results show that the nano-particle deposition patterns are quite different from those of microparticles. For a breathing rate of 4 L/min in each passage, Fig. 7 shows the nano-particle deposition flux contours in different nasal cavities for 2 nm, 5 nm and 10 nm particles. Here the particle deposition fluxes are non-dimensionalized with flux at the inlet (−D(∂C/∂n)/Ui Ci , where Ui and Ci are the velocity and concentration at the inlet and n shows the normal direction to the passages walls). For a nasal passage and a constant breathing rate, it is seen that the nano-particle deposition increases as the particle size decreases. Furthermore, for a fixed size, the particle deposition decreases as the flow rate increases. While the nano-particle deposition patterns in various nasal passages are quite similar, Fig. 7 shows that the deposition efficiency is higher in the right nasal cavity with septal deviation preoperatively. For a breathing rate of 10 L/min, comparisons of the present and earlier simulation results with the experimental data of Kelly are shown in Fig. 8. While there are scatters in the experimental

data of Kelly et al. (2004b) for both the SLA and Viper models, the all simulation results capture the trend of the experimental data. It is also seen that the Lagrangian model of Zamankhan et al. (2006) agrees well with the experimental data for particles smaller than 20 nm; but for larger particles, their predicted deposition efficiencies are higher than the average of the experimental data. They suggested that the discrepancy is due to the inaccuracy of the linear interpolation scheme and the anatomical differences in

Fig. 8. Comparison of deposition efficiency versus nano-particles diameter with the earlier simulation results and experimental data. Letters S and V refer to the SLA and Viper nasal replica models in the work of Kelly et al. (2004b).

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Fig. 9. Local deposition efficiencies of 2 nm, 5 nm and 10 nm particles in various passages for a breathing rate of 12 L/min.

the nasal passages used. Xi and Longest (2008) constructed their numerical model using the same set of nasal images as used by Kelly et al. (2004b). They showed that the drift flux model with near-wall velocity corrections for particle transport could provide an effective approach for simulating the transport and deposition of nano-particles in human nasal airways. The present numerical results for nano-particle deposition are comparable with the lower bound of experimental data. While the nano-particle deposition rate shows a better agreement with the experimental data compared with the micro-particle results, they are underestimating the bulk of the data. Again the presence of experimental surface roughness could be the reason but to a lesser extent. Kelly et al. (2004b) also showed that the micro-particle deposition is significantly affected by wall roughness while nano-particle deposition is less sensitive to the surface conditions.

4.2.4. Regional deposition of nano-particle For breathing rates of 4 and 7.5 L/min, the local deposition of 2 nm, 5 nm and 10 nm particles in different nasal passages are compared in Fig. 9. This figure shows that the highest deposition rate occurs in the main airway region for all nasal passages. This is because of the larger area of the main airway region. The nasal valve region also generally captures more particles compared to the vestibule region. This trend of variation is quite different from that observed for micro-particles in Fig. 6. Fig. 9 also shows that as the nano-particle size or the breathing rate increase, the local deposition efficiency decreases. It is also seen that the local nano-particle

deposition pattern is quite similar before and after septoplasty; however, the total amount of particle deposition decreases after septoplasty. In general, the nano-particles have less variation in local deposition with changes in anatomy of nasal passage. That is, the Brownian motion of nano-particles leads to their rather uniform diffusion in the nasal passage, and the amount of capture will depend on the surface area of different regions.

Fig. 10. Comparison of total deposition efficiency of micro- and nano-particles in different passages for a breathing rate 7.5 L/min.

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4.2.5. Nano- and micro-particle deposition For a breathing rate of 7.5 L/min, Fig. 10 shows the total deposition efficiency of different pre and postoperative nasal cavities for the entire range of nano- and micro-particles. As expected the deposition efficiency follows a U-shape variation. As noted before, for nano-particles in the size range of d < 100 nm the dominant deposition mechanism is the Brownian diffusion and the deposition rate increases as particle size decreases. For micro-particles larger than a few ␮m, the dominate mechanism of deposition is the inertia impaction and the deposition rate increases with particle size. In the intermediate range of 100 nm < d < 1 ␮m, the strength of these deposition mechanisms diminishes and the deposition efficiency decreases sharply. In Fig. 10, for completeness, a linear interpolation was performed to find the deposition efficiency in the range of 100 nm to 1 ␮m.

higher breathing rates associated with heavier physical activities and exercises, the airflow in nasal passages could become turbulent. In this case, the influence of turbulence perturbation on particle dispersion and deposition needs to be included in the analysis. Also, abnormalities may exist in other nasal regions such as turbinates. It is expected that CFD could help the medical professional to select and optimize the surgical interventions for specific patients. In addition, the location, velocity, density and swirl of particle release from a nasal spray are quite important for effective therapeutic inhalation drug delivery. Again, CFD could provide considerable help in this regard. Finally, transport and deposition of non-spherical particles, such as fibers, are other challenges for future researchers (Fan and Ahmadi, 1995; Zhang et al., 2001; Shanley, 2008; Wang et al., 2008; Inthavong et al., 2008b). Addressing these challenging issues, however, are left for future studies.

5. Conclusions

References

In this study, computer simulation results for airflow and microand nano-particle deposition in the nasal cavities of a male patient with nasal deviation before and after a septoplasty operation were presented, and the changes in the airflow and particle deposition patterns were discussed. Based on the presented results, the following conclusions may be drawn: 1. The computer model predicted that the volumetric airflow rate in the patient’s abnormal nasal cavity with septal deviation is about 40–50% lower than that for the normal (left) nasal cavity. Thus, the blockage would cause breathing problems for the patient due to significant reduction of the airflow or increase in pressure drop during inspiration. Such symptoms were reported by the patient. 2. The simulations predicted that after removing the blockage, the airflow rate and pressure drop of the nasal cavity would be comparable with the normal right side passage. This prediction was consistent with the observation of the patient after the successful septoplasty operation that led to corrected function of the patient’s nasal airways. 3. The simulation results suggested that the abnormal shape of the passage due to septal deviation would lead to an increase in nano- and micro-particle deposition compared with the normal and postoperative passages. For example, the model suggests that after the septoplasty, the deposition of 15 ␮m particles would decrease by about 60% for a typical breathing rate. Similarly, the deposition of 2 nm particle would decrease by about 20%. 4. The postoperative and the normal nasal passages had different regional deposition patterns for microparticles, while their total deposition were roughly the same. Inertia impaction was the dominant mechanism for micro-particle deposition and a sharp variation in the flow direction increased the deposition rate. 5. The regional nano-particle deposition patterns for different pre and postoperative passages were quite similar. The dominant mechanism for nano-particle deposition was the Brownian diffusion, which led to a more uniform deposition pattern. The present study further shows that computational fluid dynamics (CFD) could provide a tool for predicting the airflow and particle deposition patterns in nasal passages that specific surgical interventions would produce. Such a tool is expected to help to refine surgical approaches for correcting nasal airway abnormalities and blockages. In the current study, for rest or low level physical activities, the laminar flow regime assumption was used for analyzing the airflow in the nasal cavities with and without septal deviation and associated nano- and micro-particle deposition patterns. For

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