In order to assess the impact of the laryngopharyngeal anatomy on airflow and particle deposition in the nasal airways, four computational models with varying geometric details have been considered. We started from a highly realistic nasal-laryngeal airway model that was recently developed based on MRI images of a 53-yearold male (weight 73 kg and height 173 cm) [24]. The MRI tracings were first segmented in MIMICS (Materialise, Ann Arbor, MI) according to the contrast between osseous structures and intranasal air to convert the raw image data into a set of cross-sectional contours that define the airway of interest. Based on these contours, an internal nasal surface geometry was constructed in Gambit (Ansys, Inc.) as shown in Figure 1. This same MRI image set has also been used in a number of nasal particle deposition experiments [7,25-27], and therefore a direct comparison between simulated and experimental results is possible.

Bedsides the anatomically accurate nasal passages, three other key features characterize this image-based model, namely, a hanging uvula, a flat-plated pharynx, and a triangular-shaped glottal aperture. Movement of the uvula alters the airway morphology that connects the nasoand oropharynx. In this study, the uvula rests on the back of the throat and partially obstructs the inferior nasopharynx, resulting in two flow passages. This might be attributed to the supine position of the patient during image acquisition. Posterior to the uvula, the pharynx is featured by narrow and flat air channels, which converge into the wedge-shaped glottis in the larynx. In order to approximate the in vivo airway morphology that was captured in the images, anatomical details such as the epiglottis and the two pharyngeal sinuses on either side of the larynx were also retained, as shown in Figure 1(a). In light of the glottis, several studies have reported a triangular-shaped cross-section based on bronchoscope images in living subjects [28,29]. The triangular cross section is formed by the vocal folds with one point of the triangle resting on the ventral surface and two points on the dorsal surface, as shown in the plane E-E’ in the right panel of Figure 1(a). In contrast to this, in vitro studies with larynx replica casts have reported a more elliptical shape [1]. In this study, the triangular shape of the glottis observed in the CT data has also been retained.

As a first simplification, the hanging uvula was removed in Model 1, resulting in an un-obstructed nanopharynx in Model 2 (Figure 1(b)). This model represents the condition when a subject takes the upright position and the soft palate bends downward due to its own weight. Further simplifications have been made to generate Model 3. This model consists of a much simpler, elliptical pharynx. The oropharynx, epiglottis, and the two laryngeal sinuses (Figure 1(c)), has been eliminated as most previous studies did [7-9,30]. Rodenstein et al. [31] reported that pharynx had a transverse to anterior-posterior

ratio of 2.5 for healthy subjects. Thus, for Model 3, we assume that the pharynx is approximately an elliptical pipe with the major axis 2.5 times as large as the minor axis. The fourth geometry model (i.e., Model 4) excludes the triangular-shaped larynx and is composed of an elliptical pipe downstream of the nasal cavity (Figure 1(d)).

During exhalation, airflow enters the upper trachea, travels through the larynx, pharynx, and nasal turbinates, and exits the nostrils. By retaining the laryngeal-pharyngeal region, more physiologically realistic inlet flow conditions are provided to the nasal cavity. As a result, the flow field and particle deposition characteristics in the nasal cavity considered in this study will better represent in vivo conditions compared with some previous studies that had excluded the larynx and pharynx. Therefore, inclusion of the laryngeal-pharyngeal region allows for the results of this computational study to be directly compared with previous in vivo nasal deposition data. In order to characterize deposition distributions, the nosethroat airway were divided into different sub-regions that include the vestibule, valve region (VR), turbinate region (TR), olfactory region (OR), nasopharynx (NP), pharynx, and larynx (Figure 1(a)). In order to quantify the airflow distributions within the nasal passages, a coronal slice in the turbinate region was further divided into superior, middle, inferior meatus (abbreviated as SM, MM, and IM, respectively) and the medial passage (MP), which will be discussed in later sections.

Steady exhalation was assumed for all simulations with uniform velocity profiles and particle distributions at the tracheal inlet (Figure 1(a)). Initial particle velocities were assumed to match the local fluid velocity. Atmospheric pressure conditions were assumed at the two nostrils (outlets). The airway surface was assumed smooth and rigid with no-slip (u_wall = 0) and perfect absorption conditions. In the body, the extrathoracic airway is lined with a thin layer of mucus, which captures particles at initial contact and clears them to the throat or nasal vestibule by mucocilliary movement within a time period of 10 to 15 minutes. Mass diffusion and metabolism of deposited particles may occur within the mucus layer and may change the zero-concentration conditions at the wall. However, due to the slow speed of the mucocilliary movement compared with the intranasal airflow and relatively low deposition rates, the no-slip and perfect absorption conditions are reasonable approximations in this study.

The flow conditions considered in this study are assumed to be isothermal and incompressible. The mean inlet Reynolds number at the trachea varies from 368 to 3302. The maximum Reynolds number based on the hydraulic diameter of the glottal aperture is approximately 8037. Therefore, laminar, transitional, and fully turbulent conditions in the nasal-laryngeal model are expected. To resolve these multiple flow regimes, the low Reynolds number (LRN) k - w model was selected based on its ability to accurately predict pressure drop, velocity profiles, and shear stress for transitional and turbulent flows. Moreover, the LRN k - ω model was shown to provide an accurate solution for laminar flow as the turbulent viscosity approaches zero [32].

The transport and deposition of the submicrometer particles are simulated with a well-tested discrete Lagrangian tracking model, which is enhanced with userdefined functions (UDFs) accounting for the finite particle inertial effects that might be significant for submitcrometer particle depositions. The aerosols evaluated in this study had a tracheal Stokes number (St_k =) with a range of 1.68 ´ 10⁻⁸ to 1.0 ´ 10⁻³ and were assumed to be dilute and to not influence the continuous-phase, i.e., one-way coupled particle motion. In our previous studies, the UDF-enhanced Lagrangian model with near-wall interpolation algorithm [33,34] has been shown to provide close agreement with experimental deposition data in upper respiratory airways for both submicrometer [34] and micrometer particles [35]. More details of the Largrangian tracking model can be found in [34].

To solve the governing mass and momentum conservation equations in each of the cases considered, the CFD package ANSYS Fluent was employed. User-supplied Fortran and C programs were implemented for the calculation of initial particle profiles, particle deposition factors, grid convergence, and deposition enhancement factors. For this study, a specific set of user-defined functions were applied that considered the Brownian force, anisotropic turbulence effect, and near-wall velocity interpolation. All transport equations were discretized to be at least second order accurate in space. A segregated implicit solver was applied to evaluate the resulting linear system of equations. This solver uses the Gauss-Seidel method in conjunction with an algebraic multigrid approach to improve the calculation performance on tetrahedral meshes. Convergence of the flow field solution was assumed when the global mass residual was reduced from its original value by five orders of magnitude and the residual-reduction-rates for both mass and momentum were sufficiently small.

The computational meshes of the four nasal-laryngeal airway models were generated with ANSYS IECM CFD (Ansys, Inc). Due to the high complexity of the model geometries, unstructured tetrahedral meshes were generated with high-resolution prismatic cells in the near-wall region (Figure 1(a)). A grid sensitivity analysis was conducted by testing the effects of different mesh densities with approximately 620,800, 1,140,400, 1,975,600 and 3,212,000 control volumes while keeping the nearwall cell height constant at 0.05 mm. Since the changes in both total and sub-regional depositions were less than 1% when increasing mesh size from 1,975,600 to 3,212,000, the final grid for reporting flow field and deposition conditions consisted of approximately 1,975,600 cells with a thin five-layer pentahedral grid in the nearwall region and a first near-wall cell height of 0.05 mm.

For discrete Lagrangian tracking, the number of seeded particles required to produce count-independent depositions was considered. Particle count sensitivity testing was performed by incrementally releasing groups of 10,000 particles. The number of groups was increased until the deposition rate change was less than 1%. Due to the low deposition rates, more particles were required for fine aerosols to generate count-independent results compared with ultrafine aerosols. The final number of particles tracked for 1 - 40 nm and 100 - 1000 nm aerosols were 150,000 and 600,000, respectively.

Dimensions of the four models considered are shown in Figure 2 in terms of perimeter, cross-sectional area and hydraulic diameter as a function of distance downstream of the nasopharynx as denoted in Figure 1(a) (middle panel). As expected, Model 1 exhibits the highest variability in reported geometric parameters. The minimum hydraulic diameter at a distance of 7 mm corresponds to the airway obstruction associated with the hanging uvula. It is interesting to note that Model 1 has substantially smaller effective flow area (i.e., d_h) in the oropharynx region than Model 2. A further examination of the axial cross-sections of Model 1 in this region reveals highly irregular contours as exhibited in Slice A-A’ and B-B’ in

Figure 1(a). This shape irregularity, accompanied by a much reduced effective flow area, is expected to induce significant jet effect and turbulence generation, and therefore significant energy dissipation in this region.

There is less variation in the geometric parameters of Models 3 and 4. In the laryngeal-pharyngeal region, both models (i.e., 3 and 4) have smaller flow area (d_h) than Models 1 and 2. The dip in cross-sectional area at a distance of 47 mm corresponds to the epiglottis that spreads above the glottal aperture at an angle of approximately 30˚ to the posterior wall of the pharynx (Fig ure 1(a), Slice C-C’). The larynx is located at a distance of 78 mm or so downstream of the nasopharynx.

The influence of the pharyngo-laryngeal geometries on exhalation breathing resistance is illustrated in Figure 3. Figure 3(a) shows the pressure distribution in the airway

as a function of the axial distance from the tracheal inlet at an exhalation flow rate of 30 L/min for the four models considered. For Model 1, the maximum pressure drop is observed in the pharynx/nasopharynx region which is about 170 Pa in magnitude and is about 76% of the expiratory pressure drop between the upper trachea and nostrils. This abrupt pressure drop results from the airway obstruction as the hanging uvula partially blocks the pharyngeal passage. As discussed, Model 1 was based on images of a subject in a supine position during image acquisition. It is expected that changing from upright to supine position has the potential of causing pharyngeal obstruction as the uvula yields due to its own weight and that the degree of obstruction varies depending on the elasticity properties of the subject’s soft palate and uvula. Considering that this pressure drop is about three times that of the laryngeal region, which is the maximum of the other three models (Models 2, 3, 4), it is possible that the patient of Model 1 has an over-flexible uvula and hence a high degree of airway obstruction. Respiratory tissues in the pharyngeal region are quite collapsible. Severe pressure drop could possibly trigger or expedite the collapse of airway walls and induce the symptoms of hyponea (i.e., reduced airflow capacity) or apnea (i.e., complete airway obstruction). Meanwhile, flow instability may cause vibration of the pliable pendant uvula, resulting in snoring of the supine subject. It is therefore interesting to postulate that an over-flexible uvula may be one major reason for sleep disorders such as sleep apnea, whose constriction of the pharyngeal airway and the resultant elevated pressure drop induces further pharyngeal airway collapse.

For Models 2 and 3, which corresponds to the upright position, the glottis and nasal cavity each constitutes a breathing resistance of about 50 Pa. However, there is less pressure recovery in the pharynx of Model 2 comparing to that of Model 3. Considering the fourth model, which totally excludes the anatomical details of glottis and pharynx, there is negligible pressure drop within the larynx-pharynx region, and almost all the pressure drop comes from the convoluted nasal passages.

Figure 3(b) shows the logrithmatic diagram of the pressure drop vs. exhalation flow rate in comparison to in vitro [26] and in vivo measurements [36]. Overall, the predicted pressure drop agrees well with that of a comparable physiological condition. For example, the in vitro nasal replica in Kelly et al. [26] retains the nasal cavity only and is equivalent with Model 4 in this study. As expected, the pressure drops of the above two cases also match well. Similar observations were also found in the comparison between post-exercise in vivo data [36] and Model 2, or the comparison between pre-exercise in vivo data [36] and Model 1. Therefore, the numerical predictions appear to adequately capture the nasal breathing resistances.