## Abstract

We investigated the axial dispersive effect of the upper airway structure (comprising mouth cavity, oropharynx, and trachea) on a traversing aerosol bolus. This was done by means of aerosol bolus experiments on a hollow cast of a realistic upper airway model (UAM) and three-dimensional computational fluid dynamics (CFD) simulations in the same UAM geometry. The experiments showed that 50-ml boluses injected into the UAM dispersed to boluses with a half-width ranging from 80 to 90 ml at the UAM exit, across both flow rates (250, 500 ml/s) and both flow directions (inspiration, expiration). These experimental results imply that the net half-width induced by the UAM typically was 69 ml. Comparison of experimental bolus traces with a one-dimensional Gaussian-derived analytical solution resulted in an axial dispersion coefficient of 200–250 cm^{2}/s, depending on whether the bolus peak and its half-width or the bolus tail needed to be fully accounted for. CFD simulations agreed well with experimental results for inspiratory boluses and were compatible with an axial dispersion of 200 cm^{2}/s. However, for expiratory boluses the CFD simulations showed a very tight bolus peak followed by an elongated tail, in sharp contrast to the expiratory bolus experiments. This indicates that CFD methods that are widely used to predict the fate of aerosols in the human upper airway, where flow is transitional, need to be critically assessed, possibly via aerosol bolus simulations. We conclude that, with all its geometric complexity, the upper airway introduces a relatively mild dispersion on a traversing aerosol bolus for normal breathing flow rates in inspiratory and expiratory flow directions.

- mouth cavity
- glottis
- aerosol dispersion

the upper airway geometry, with its glottic narrowing embedded in a tortuous oropharyngeal pathway, affects aerosol deposition and dispersion on its way to the lungs. Previous experimental and numerical studies have mainly concentrated on aerosol deposition, using realistic upper airway models with varying degrees of geometric simplification (14, 16). Aerosol transport is generally considered under steady-flow conditions, except for a recent work by Grgic et al. (10), in which small volumes of aerosols (aerosol boluses) delivered in different stages of the inspiratory phase were used to study the effect of flow accelerations on aerosol deposition in the upper airway. Besides the deposition of an aerosol bolus, its degree of volumetric dispersion also offers a sensitive tool to characterize aerosol transport. Indeed, aerosol boluses delivered to different lung depths are being used to quantify all aerosol mixing processes, except for Brownian diffusion, that are collectively referred to as “convective mixing” (8). Several sources of convective mixing have been identified (6, 18), such as turbulent mixing, cardiogenic mixing, and asymmetry between inspiratory and expiratory flow patterns (e.g., secondary flows, ventilation heterogeneity). These effects are operational to different extents at different lung depths. They can be quantified experimentally via their effect on aerosol boluses (typically confined to an initial volume of 50–100 ml) inhaled to various lung depths and recovered at the mouth.

The degree to which aerosol boluses disperse in extra- and intrathoracic airways has been the subject of several studies (9, 12, 18, 20, 22, 23). It has been suggested that convective mixing of boluses inhaled to penetration volumes between ∼100 ml (past the carina) and ∼200 ml (end of anatomic dead space) can be accounted for by empirical formulas for dispersion in a network of branching conductive airways, such as those proposed by Scherer et al. (19), Ultman (22), or van der Kooij et al. (24). Rosenthal et al. (18) speculated that the larynx may elicit a degree of bolus dispersion comparable to that in the conductive airways and concluded their study with a call for a dedicated study of bolus dispersion in the larynx. Simone et al. (21) studied the transport of He and SF_{6} boluses through a larynx cast inserted in a straight tube. They pointed out that the laryngeal jet would tend to increase dispersion and that the turbulence propagated from the high shear boundary of the jet would tend to decrease dispersion. Ultman et al. (23) showed in five normal subjects that effective axial dispersion undergone by He and SF_{6} boluses in the first 80 ml of the upper airway ranged from 290 to 390 cm^{2}/s. This is in contrast with the effective axial dispersion of 2,400 cm^{2}/s attributed to the oropharynx to match simulated and experimental values of aerosol bolus dispersion for very shallow boluses (7); the same study obtained excellent agreement between simulated and experimental bolus dispersion as a function of volumetric depth in conductive and alveolated airways. In recent years, sophisticated three-dimensional (3D) computational fluid dynamics (CFD) simulation studies in realistic upper airway geometries (e.g., Ref. 15) have provided detailed predictions of flow patterns, including laryngeal jets, vortices, and turbulent intensities. However, the accuracy of these CFD simulations remains difficult to validate, and a relatively easy way to do so would be to predict the dispersive effect on an aerosol bolus. This simulated bolus then represents a relevant physiological measure that can be obtained experimentally for comparison.

Whether it is for the study of convective mixing or for medication targeting, an aerosol bolus inhaled to any given lung depth must transit the upper airway, and it is crucial to quantitatively predict its dispersive effect. Such a quantitative description of the dispersive effect of the upper airway is currently lacking in the literature. We therefore aimed to quantify bolus dispersion by carrying out aerosol bolus experiments on a physical cast of a realistic upper airway model (UAM) (3) and by performing corresponding CFD simulations in exactly the same 3D geometry. We tested the hypotheses that bolus dispersion may be different in inspiratory and expiratory flow directions and that bolus dispersion in either flow direction may deviate from that dictated by a simple Gaussian from which a one-dimensional (1D) axial dispersion coefficient is derived. Irrespective of the exact experimental bolus shape, it represents a physiological measure that can be used to test the accuracy of CFD simulation methods currently employed to study aerosol transport in the upper airway.

## MATERIALS AND METHODS

#### Experimental methods.

The 3D geometry of the UAM was retrieved from previous work (3) and cast into a silicone hollow model assembled in two halves (one half is depicted in Fig. 1). Briefly, the UAM geometry had been previously derived from a smoothened representative upper airway geometry obtained with multislice computerized tomography (CT) imaging on five healthy never-smoking male subjects (average age 38 yr; range 26–52 yr). Importantly, CT imaging had been initiated above the nasal cavity and synchronized with inhalation in order to obtain a representative glottic area during slow inhalation. Glottic area was 125 mm^{2} in this UAM, total UAM volume was 90.6 cm^{3}, and the average UAM cross section amounted to 2.78 cm^{2}.

For a selected case of inspiration at 500 ml/s, we employed a particle image velocimetry (PIV) fluid flow measurement system that was in use for a parallel study (13), where the methods are extensively described. Briefly, during inspiration a hollow (negative) version of the UAM geometry was created in a block of transparent silicone. For visualization of fluid flow through this model, a water-glycerin mixture was used with a viscosity of 5.88 × 10^{6} m^{2}/s. The PIV measurements were performed in a central sagittal plane at a volumetric flow rate of 11.2 l/min, corresponding to a Reynolds number of ∼2,600 (based on inlet diameter). A New Wave MinilaseII Nd-Yag laser (532-nm wavelength, 100 mJ/pulse) was synchronized with a pulse separation. The pulse separation was chosen in such a way that the reflection of the tracer particles (10-μm hollow glass spheres) shifted 5 pixels between an image pair. The laser beams were combined and formed into a sheet with cylindrical optics. This pulsed sheet was passed through the model, parallel to the flow, and the light scattered from the particles was recorded with a PCO sensicam QE 5-Hz camera. Approximately 4,000 image pairs were recorded. The images were analyzed with PIVview 2C software (PIVTEC).

The aerosol generating system consisted of an ACORN II nebulizer (Marquest Medical Products, Englewood, CO) from which a diluted suspension of 1-μm polystyrene latex particles (Duke Scientific, Palo Alto, CA) was aerosolized and passed via a silica gel drying tunnel into a the 50-ml tube between *valves 1* and *2*. The aerosol continuously entered the 50-ml tube via one sliding valve (*valve 2*) and was evacuated through a filter via another sliding valve (*valve 1*) so as to obtain a steady concentration of aerosol in the 50-ml tube. In preparation for the 50-ml aerosol delivery to the UAM, *valves 1* and *2* were then switched to obtain an open passage between the air from behind the flowmeter and the syringe. By having the syringe aspire a volume of 2 liters, the 50-ml aerosol was pulled through the UAM and the photometer (PARI, Starnberg, Germany); the syringe was operated manually with visual feedback from the flowmeter. Throughout the experiment, the photometer continuously recorded the particle concentration as a function of aspired volume (obtained by integration of the flow); data acquisition was at 100 Hz.

Aerosol bolus tests were performed with the UAM in the inspiratory position (as depicted in Fig. 1) and alternating target flows between 250 ml/s and 500 ml/s in a series of 12 tests in total. At these two flows, Reynolds numbers were ∼1,300 and ∼2,600, respectively. A similar test sequence was performed with the UAM in the expiratory position, i.e., by connecting the tracheal end to *valve 1* and the UAM mouthpiece end to the photometer. In both inspiratory and expiratory UAM configurations, the aerosol was made to enter the UAM via a 90° bend beyond *valve 1*. The use of a 90° bend has been shown to render the incoming aerosol profile flatter than when delivered in a straight line (25), enabling a better comparison with a CFD-simulated uniform injection of particles at the model inlet. Also, based on our previous experience with a similar setup in which boluses could be monitored during both inspiration and expiration by placing the photometer between *valve 1* and an actively breathing subject (26, 27), the bolus was seen to remain well contained within a 50-ml volume on entering the subject. Preliminary tests on the present setup confirmed that this was also the case for a bolus entering the UAM.

Bolus dispersion was quantified in terms of its half-width, i.e., the volumetric width between concentrations at half-peak height, and of its standard deviation, i.e., the second moment of the volume-dependent bolus concentration curve (2). Half-widths and standard deviations were indicated by HW_{in} and SD_{in} for inspiration and by HW_{ex} and SD_{ex} for expiration; all are obtained by a simple formula (18) for each flow direction. For instance, SD_{in} is computed as: (1) with the UAM in the inspiratory configuration (i.e., bolus injected at the mouth and recovered at the end of the trachea), and SD_{ex} is computed as: (2) with the UAM in the expiratory configuration (i.e., bolus injected at the end of the trachea and recovered at the mouth). The same type of formulas are used to obtain HW_{in} and HW_{ex}.

#### Computational methods: CFD simulations.

With the existing UAM 3D geometric boundaries of Fig. 1, a preliminary grid resolution study was conducted. Comparison of flow fields obtained with unstructured hexahedral meshes of either 800,000 or 2,170,000 cells (Hexpress, Numeca, Brussels, Belgium) had indicated that the velocity magnitude in a cross section downstream of the larynx varied by <2% between the two meshes considered. Therefore, the UAM with the hexahedral mesh containing 800,000 cells was used here. All flow field computations were performed with a commercial CFD software package (Fluent 6.3, ANSYS, Canonsburg, PA). An incompressible Reynolds-averaged Navier-Stokes (RANS) solver was employed to simulate the fluid flow, and a two-equation shear stress transport k-ω model was used to model the turbulence. The k-ω model has been proposed previously to be the most adequate turbulence model for simulating transitional flows in the upper airways (16, 28). For the spatial discretization, a second-order upwind scheme and a third-order MUSCL scheme were used for the momentum and the k-ω equation, respectively. The SIMPLE algorithm was used for pressure-velocity coupling. A typical simulation of the flow field to obtain a convergence level of three orders of magnitude took ∼11–12 h on a 2.4-MHz dual-core processor (AMD Opteron, Sunnyvale, CA).

For the particle phase, we used an eddy interaction model (EIM) in which the fluctuating part of the instantaneous velocity is modeled assuming isotropic turbulence and assigned to an eddy with known lifetime and length scale. One-micrometer particles were injected homogeneously at the UAM inlet cross section so as to obtain a uniform particle number per surface area distribution over the entire cross section. A preliminary particle number study injecting 10,000, 15,000, or 30,000 particles had indicated that the half-widths of particle concentration profiles obtained at the geometry outlet differed by 0.7% between 10,000 and 30,000 particles and by 0.6% between 15,000 and 30,000 particles. For the present simulations, 15,000 particles were considered and an automated particle tracking scheme was employed, which is a combination of a high-order trapezoidal scheme and a low-order implicit scheme; ∼5 h was required to track 15,000 particles.

#### Theoretical axial dispersion coefficient.

In an attempt to find a 1D dispersion coefficient *D* to characterize the axial dispersion undergone by an aerosol bolus in the UAM, the particle profile recovered at the model outlet was compared with the analytical solution of the 1D diffusion equation corresponding to an aerosol profile initially confined between axial locations *x* = −*h* and *x* = +*h* (4): (3) where C is particle number concentration as a function of space and time, *x* is axial pathway length, *D* is the axial dispersion coefficient, and *u*_{o} is an average velocity defined as the ratio of flow rate (250 or 500 ml/s) over an average cross section (2.78 cm^{2}). With a homogeneous injection of the 15,000 particles at the UAM inlet surface, the injected aerosol bolus in the CFD simulations effectively occupied an initial volume of 0.125 cm^{3}, corresponding to an initial aerosol bolus slab thickness of 0.045 cm (= 2*h*) at the initial bolus position (*x* = 0). When considering such a bolus passing a fixed location, for instance at *x* = 32.6 cm (i.e., UAM length), the transformation of the time-dependent concentration trace into a volume-dependent trace via flow rate shows a half-width that increases as a function of *D* up to ∼2,500 cm^{2}/s and then levels off (Fig. 2*A*). By contrast, when considering the spatial dispersion of typical concentration curves obtained with *Eq. 3* at a fixed point in time (*t* = 0.05 s here), and varying *D*, a steady increase of spatial dispersion with *D* is observed (Fig. 2*B*). In this case the flow rate does not interfere with half-width, since it merely translates the entire diffusing bolus along the *x*-direction at a faster pace.

#### Statistical analysis.

With Statistica5.1 (StatSoft, Tulsa, OK) two-way ANOVA (with flow direction and magnitude of flow as factors) was performed, with a Bonferroni post hoc comparison and a significance level accepted at *P* = 0.05.

## RESULTS

#### Experimental results.

Actual flows corresponding to bolus tests with the UAM in the inspiratory and expiratory configurations and with a target flow of 250 ml/s were 260 ± 12(SD) and 262 ± 14(SD) ml/s, respectively. For the UAM tests with a target flow of 500 ml/s, actual inspiratory and expiratory flows were 497 ± 28(SD) and 490 ± 38(SD) ml/s, respectively. Six typical photometer traces corresponding to a bolus test with the UAM in the inspiratory configuration are presented in Fig. 3*A*. In Fig. 3*B*, the representative traces of Fig. 3*A* are normalized to peak height and compared with the corresponding analytical solution of *Eq. 3* for *D* = 200 cm^{2}/s and *D* = 250 cm^{2}/s. While neither option perfectly captures the entire bolus curve, particularly in its tail portion, the analytical solution corresponding to *D* = 200 cm^{2}/s best matches the initial part of the bolus, including its half-width, while the *D* = 250 cm^{2}/s solution somewhat better captures the bolus tail. This is particularly true for *D* = 250 cm^{2}/s at a flow of 250 ml/s (Fig. 3*B*, *right*), yet at the expense of an overestimated bolus half-width.

Figure 4 summarizes the average (±SE) values of the experimental bolus dispersion indexes. Overall, there were small decreases in HW_{in}, HW_{ex}, SD_{in}, and SD_{ex} with increasing flow rate (*P* = 0.02 for flow effect in ANOVA), but none of the post hoc pairwise comparisons reached significance. There were no statistically significant differences between HW_{in} and HW_{ex} or between SD_{in} and SD_{ex}.

#### CFD simulation results.

Figure 5 shows a typical CFD-simulated flow field obtained for a 500 ml/s inhalation and the corresponding PIV measurements carried out by our group (unpublished observation). The experimental data, which were only available for inspiration, were retrieved from a dedicated fluid mechanics study conducted in parallel (13). Apparent from Fig. 5 is the similarity of the laryngeal jet between CFD simulation and PIV measurements.

CFD-simulated inspiratory and expiratory aerosol deposition in the UAM were 3% and 4%, respectively, for 250 ml/s and 8% and 9%, respectively, for 500 ml/s. Figure 6 shows the CFD-simulated particle concentration traces at the model outlet, which were normalized to their respective bolus peaks, for 250 ml/s and 500 ml/s. The bolus half-widths corresponding to the CFD-simulated particle concentration curves were much smaller for expiration than for inspiration at both 250 ml/s (HW_{in} = 69 ml; HW_{ex} = 20 ml) and 500 ml/s (HW_{in} = 49 ml; HW_{ex} = 20 ml). Also superimposed on the inspiratory traces of Fig. 6*A* are the corresponding analytical solutions from *Eq. 3* with *D* = 200 cm^{2}/s for 250 ml/s and 500 ml/s. In Fig. 6*B*, the analytical solution with *D* = 25 cm^{2}/s is displayed, merely to illustrate the degree of underestimation of axial bolus dispersion for the expiratory UAM configuration. The marked difference in half-width between the CFD-generated boluses in Fig. 6, *A* and *B*, is in contrast to the very similar half-widths obtained in bolus experiments with the UAM in inspiratory and expiratory configurations (Fig. 4).

## DISCUSSION

With respect to the primary aim of this study, we have found that the dispersion of an experimental aerosol bolus transiting a realistic model of the upper airway including the trachea can be reasonably approximated by a Gaussian fit (*Eq. 3*). The remaining discrepancy was in the bolus tail, where the experimental bolus showed a slightly greater skew than the Gaussian fit, especially at breathing flows exceeding quiet breathing (>250 ml/s). Depending on the physiological application, and whether it is required to better capture the bolus peak and half-width or its tail, an effective axial dispersion of 200–250 cm^{2}/s adequately characterizes the dispersion process in this segment of the airway tree. Inspiratory and expiratory boluses showed roughly the same bolus dispersion, and bolus dispersion only slightly decreased by increasing flow from 250 to 500 ml/s. The CFD numerical simulations reproduced experimental results for inspiration but not for expiration, warranting further scrutiny on the part of the numerical methods (turbulence models and parameters) used to describe transitional flows in structures such as the UAM used here.

Our experiments show that the upper airway geometry leads to a 80- to 90-ml-wide bolus at the model outlet, for a 50-ml bolus at the model inlet under quiet breathing conditions (250–500 ml/s) and in either inspiratory or expiratory flow direction. When correcting an average 85-ml bolus at the UAM outlet for the nonzero initial aerosol bolus according to *Eqs. 1* and *2*, the net dispersion half-width HW_{in} or HW_{ex} amounts to 69 ml [= ]. For medical aerosols, this implies that a typical aerosol from a pressurized metered dose inhaler, which is typically fired into a 250-ml holding chamber before inhalation, will undergo a net dispersion in the upper airway (including the trachea) such that its volumetric dispersion beyond that point becomes no more than 260 ml [i.e., to obtain 69-ml net dispersion]. With respect to the target lung volume for aerosol medication, this degree of volumetric dispersion induced by the upper airway is negligible from a clinical standpoint.

From a physiological standpoint, the degree of dispersion induced by the upper airway concerns its contribution to the overall convective mixing process at different lung penetration volumes (V_{p}) proximal to the gas exchanging zone. Only some laboratories have actually measured the half-width of exhaled aerosol boluses after inhalation to very shallow V_{p} (<100 ml) (2, 23). For instance, in 79 normal subjects, Brand et al. (2) measured an average half-width (corrected for the 20-ml inhaled bolus width) of 70 ml and 120 ml for aerosol boluses inhaled to a V_{p} of 20 ml and 50 ml, respectively (respiratory flow was 250 ml/s). Assuming, on the basis of our experiments, that net UAM dispersion in each flow direction amounts to 69 ml, the combined UAM dispersion of a 20-ml bolus during inspiratory and expiratory phases can be predicted according to *Eqs. 1* and *2* as follows. At the end of inspiration a 20-ml bolus gets dispersed over 71.5 ml [ to obtain 69-ml net dispersion], and at the end of expiration this 71.5-ml bolus gets dispersed over 99 ml [ to obtain 69-ml net dispersion]. Finally, when correcting this 99-ml bolus half-width at the end of expiration for the initial 20-ml inspiratory bolus, the predicted cumulative half-width for the inspiratory and expiratory cycle amounts to 97 ml, falling in the 70- to 120-ml half-width range obtained by Brand et al. (2) for V_{p} ranging between 20 and 70 ml in human subjects.

In five normal subjects, Ultman et al. (23) previously obtained an average SD value of 55 ml for SF_{6} gas boluses inhaled to a penetration volume corresponding to the UAM volume (91 ml). When cumulating SD values from our UAM experiments in either flow direction according to *Eqs. 1* and *2*, the corresponding SD value we obtain is 59 ml. This excellent agreement can provide an answer to the open suggestion put forward by Ultman (22) that the dispersion obtained from a full inspiratory and expiratory cycle, on basis of experiments that study inspiratory and expiratory dispersive effects separately, may represent an overestimation of the real cumulative dispersion. The comparison of our cumulative UAM data to this relatively limited set of experimental data on human subjects does suggest that in the upper airway segment dispersion effects occurring during inspiratory and expiratory phases are approximately additive.

The present in vitro study shows that the impact of the upper airway on aerosol dispersion is relatively small. A previous in vitro study by Simone et al. (21) was concerned with the impact of the larynx on mixing in various segments of a three-generation branching model. These authors studied the SD of 5-ml SF_{6} gas boluses in a broad range of Reynolds numbers, and they normalized the SD^{2} values they measured in various model segments by the corresponding segment volume squared in order to obtain a dimensionless number for comparison with other studies. Considering Reynolds number between 1,000 and 2,000, their (SD/volume)^{2} ratio for the upper airway segment, including a somewhat simplified larynx, amounted to 0.14 [= (20 ml)^{2}/(53 ml)^{2}]; our corresponding value is 0.22 [= (43 ml)^{2}/(91 ml)^{2}]. Like Simone et al. (21), we also found a decreasing dispersion with increasing flow, but the magnitude of flow-dependent changes seen here is much smaller than the 20% SD decrease found by Simone et al. (21) between Reynolds number 1,000 and 2,000. We can only speculate that this is due to geometric differences, in particular, the fact that the larynx cast in Simone et al. (21) was embedded in a straight tube directly leading to the tracheobronchial model. With the upper airway structure studied here, a transiting aerosol is subjected to complex changes in both cross section and angle, all of which may have an effect on the flow dependence of bolus dispersion. The present study suggests that a realistic upper airway indeed induces poorly flow-dependent bolus dispersion in the 250–500 ml/s flow range.

Another interesting finding by Simone et al. (21) in their in vitro branching plus larynx model was that the largest degree of dispersion originated at the first bifurcation. Taken together with our finding of a relatively limited dispersion induced by a more realistic model of the upper airway and trachea, this could explain the broad range of half-widths (70–150 ml) obtained in human subjects for shallow volumetric depths (V_{p} < 100 ml) across different studies. Indeed, the exact V_{p}, i.e., the volume of air following the inhaled aerosol in any experimental setup, may be subjected to some variability regarding the exact upper airway structures that have been crossed by the aerosol bolus under study. Therefore, the outcome half-width value in each experimental setup possibly depends on whether a shallow bolus has actually passed the carina and whether a markedly asymmetric recombination of boluses at the first bifurcation took place or not. Rosenthal et al. (18) speculated that there may be a faster increase of dispersion with V_{p} in the upper airway structure than in the conductive airways. The present study suggests that at least the upper airway including the trachea has a relatively limited dispersive effect.

The CFD simulations only partly confirmed the experimental observations, in that HW_{in} with the UAM in the inspiratory configuration averaged 59 ml for flow rates of 250 and 500 ml/s but expiratory HW_{ex} was just 20 ml in this flow range (vs. 69 ml in experiments). Like the UAM experiments, the corresponding CFD simulations also produced slightly tighter boluses at higher flows. However, the CFD simulations also predicted a markedly different shape for expiratory and inspiratory boluses, which was not observed experimentally. In particular, the CFD-simulated expiratory bolus peak was almost impossible to associate with a proper Gaussian-derived solution (*Eq. 3*; Fig. 6*B*), given the sharp initial peak and the long tail.

The above discrepancy between CFD simulations and experiments points to a problem with the CFD methodology using RANS with a k-ω turbulence model. RANS k-ω simulations have been widely used in recent CFD studies of gas and aerosol transport in the upper airway by us (4, 14) and others (16, 28), and they generally tend to overestimate aerosol deposition. A recent comparison of experimental PIV and simulated flow patterns of the carrier gas (13) indicated that large eddy simulation (LES) better captures the experimental patterns of turbulent kinetic energy than RANS k-ω. Given that turbulence is crucial to both aerosol deposition and dispersion in the upper airway, it may be worthwhile pursuing the LES approach in the future, despite its being far more time-consuming than RANS. Given that CFD tools are currently finding such a widespread use in the prediction of the fate of aerosols in the lungs, and that the transitional laminar-turbulent flow regime in the upper airway poses a particular challenge, it is recommended that the bolus dispersion be used as a sensitive tool to validate emerging CFD approaches such as LES. Indeed, it has been observed previously (7) that total deposition is a relatively crude measure of aerosol behavior. However, bolus dispersion may be a more adequate tool to validate CFD simulations of aerosol transport in the human lung, and in particular in the upper airway.

#### Limitations.

In all its simplicity, the aerosol bolus dispersion experiment does present some pitfalls and limitations. First, the equipment used for bolus experiments monitors aerosol concentrations that are averaged over part or the entirety of the tube cross section, thereby neglecting any nonuniformity that may potentially develop within a given cross section. Second, any attempt at a simple quantification of aerosol dispersion usually relies on a 1D Gaussian approach (*Eq. 3*) to extract one axial dispersion coefficient, which is ideally suited for describing concentrations of a dispersing gas by molecular diffusion. Since convective mixing of aerosol in the UAM may be more complex, it is not surprising that a Gaussian does not fully mimic the bolus shape. Indeed, the experimental bolus tail cannot be fully captured by *Eq. 3*, and depending on the exact choice of fitting criteria (either fitting the entire bolus curve or fitting its half-width), the corresponding dispersion coefficient will slightly vary. We should bear in mind that physiological bolus dispersion studies either consider bolus half-width (i.e., ignoring the bolus tail altogether) or exclude all bolus concentrations below 15% of the bolus peak value when computing bolus SD or bolus skewness (i.e., effectively ignoring part of the bolus tail) (2). Hence, comparison between physiological bolus experiments will not suffer much from the degree of discrepancy with the Gaussian characterization that we observe here in the bolus tail. Third, there is a limitation of using bolus traces at the model outlet (Fig. 2*A*) to estimate spatial dispersion actually undergone by a bolus inside the model (Fig. 2*B*). For instance, a time (or volume)-dependent concentration trace at the outlet of a 32.6-cm tube in a perfect 1D case of axial dispersion given by *Eq. 3* shows a leveling off of bolus half-width somewhere between *D* = 2,500 and *D* = 5,000 cm^{2}/s (Fig. 2*A*), which in addition partly depends on the flow rate. However, for *D* values below 1,000 cm^{2}/s, there is a monotonic increase of half-width with *D* and a relatively limited dependence on flow rate. Given that the physiologically relevant *D* values indicated by the present study are well below 1,000 cm^{2}/s, bolus half-width can indeed be considered a suitable parameter to quantitatively study aerosol transport in the upper airway under normal breathing conditions.

On basis of experiments (21) or simulations (15), several authors have duly argued that aerosol transport in the upper airway can have an impact on airways downstream from it. Conversely, the presence of a bifurcation at the tracheal end may affect bolus dispersion inside the trachea. This is a limitation of studying any partial model of the respiratory system, as is the case here. Yet it must be recognized that realistic 3D experiments and simulations in the entire lung are simply not feasible, and in some cases they are also not necessary. For instance, to test the effect on aerosol bolus dispersion or deposition of glottic area, it would suffice to consider only this segment and compare numerical with bolus experiments in exactly the same 3D geometry under exactly the same flow conditions, as was done here. Also, CFD studies of aerosol transport in the alveolar space (e.g., Ref. 11) do not need more than a reasonable estimate of axial dispersion of a bolus transiting the extra- and intrathoracic airways compartments for comparison with bolus experiments performed by human subjects. For the conductive airways compartment a satisfactory empirical formula of axial dispersion already existed in the literature (19, 22, 24), and for the oropharynx an axial dispersion value of 2,400 cm^{2}/s was adopted (7). The present experiments provide a direct measure of axial dispersion in the upper airway compartment, comprising oropharynx and trachea, which ranges from 200 to 250 cm^{2}/s. Some variations on this range may exist, depending on, for instance, intersubject glottic aperture or intrasubject glottic area variations during respiration (1). However, we suspect these to have a minor effect on bolus dispersion, for two reasons. First, there is a small intersubject variability of bolus dispersion of shallow boluses and an absence of correlation of any bolus parameter with sex (2). Second, in a numerical study in a laryngeal channel with pseudo-time-varying glottis between 112 mm^{2} (peak inspiration) and 66 mm^{2} (peak inspiration), Renotte et al. (17) found minor differences in velocity profiles between inspiration and expiration.

#### Summary.

We have found experimentally that a realistic geometry of the upper airway between the mouth and the end of the trachea induces a relatively mild dispersion on a traversing aerosol bolus. CFD simulations reproduced these results for inspiration, but not for expiration, indicating that the turbulence models should be scrutinized to capture all aspects of aerosol transport in the upper airway. For those studies of aerosol bolus behavior in airways peripheral to the trachea requiring an estimate of bolus dispersion while trespassing the upper airway, an axial dispersion coefficient of 200–250 cm^{2}/s can be adopted under normal breathing conditions.

## GRANTS

This study was funded by the Fund for Scientific Research-Flanders and Vrije Universiteit Brussel (VUB) research council in the framework of a horizontal research activity (HOA).

## Footnotes

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- Copyright © 2008 the American Physiological Society