Aerosol deposition in the human upper airways

Application Challenge AC7-01 © copyright ERCOFTAC 2019

Best Practice Advice

Key Fluid Physics and Deposition Mechanisms

Airﬂow in the human upper airways transitions to turbulence due to geometric effects, such as the bent in the oropharyngeal region and the constriction at the glottis. The bent in the oropharynx causes substantial ﬁltering of inhaled aerosols due to inertial impaction on the airway walls. Filtering in the extrathoracic airways increases as the particle size and inhalation ﬂowrate increase.

As we move in the tracheobronchial airways, the Reynolds number is reduced because the air travels through a larger total cross-sectional area. As a result, airﬂow relaminarizes in the ﬁrst generations. At the ﬂowrate examined in the present AC, the main deposition mechanism in this region is inertial impaction, with signiﬁcant deposition at the bents and the bifurcations. At lower ﬂowrates, deposition can also be inﬂuenced by gravitational sedimentation because the residence times of the particles in the bronchial airways is longer.

Application Uncertainties

The differences between measurements and simulations can result from several uncertainties involved in the tests. A ﬁrst source of uncertainty are the in vitro inlet conditions, which might be different from the velocity and particle proﬁles assumed in the CFD simulations. In the experimental setup, various devices were placed upstream of the mouth inlet (see figure 5) and these devices are expected to alter the inlet ﬂow and particle conditions from what is prescribed in the simulations.

Another source of uncertainty between the experiment and the simulations is the size of the particles. Monodisperse particles have been assumed in the simulations whereas the aerosols generated in the experiments had a standard geometric deviation of size smaller than 1.24μm.

Computational Domain and Boundary Conditions

The geometry of the extrathoracic airways must be included because turbulence is generated in this region and alters transport and deposition of particles in the distal airways. In addition, signiﬁcant ﬁltering occurs in the mouth and throat, which affects the amount of inhaled aerosols that will eventually reach the desirable lung generations. In the present AC, in both LES and RANS tests the inlet at the mouth of the model was extruded in order to generate turbulent velocity conditions. This strategy was adopted due to the absence of a more realistic inlet velocity proﬁle.

Concerning the boundary conditions, the inlet velocity proﬁle and the particle distribution are important determinants of particle deposition and thus realistic inlet conditions should be used. At the outlets, it is important to apply correct pressures such that the ventilation of the airway tree is realistic. Otherwise, both the air and particle distribution in the trachea will not be predicted accurately.

In the LES simulations, the volumetric ﬂowrates at the 10 terminal outlets are prescribed based on the values measured in vitro (Table 3). These outlet conditions result in high asymmetry in the ventilation of the two lungs: the left lung receives 29% of the inhaled air whereas the right lung receives 71%.

In the RANS calculations, a simpliﬁed boundary condition setup was applied. Instead of applying prescribed ﬂowrates at the outlets of the system similarly to the experiments, a simpler strategy of applying the ﬂowrate at the inlet and zero pressure at the outlets was used. Using these boundary conditions, an overall good agreement with the experimental data was observed with small differences on the ventilation distribution after the third branching level. This approach may be used to obtain preliminary results, however, the correct application of the ﬂow ﬁeld for all the outlets is recommended in future works to better predict the ﬂow in the further downstream located sections of the system.

Discretisation and Grid Resolution

Since it is not possible to generate a structured hexahedral grid for the present geometry due to its complexity, a higher reﬁnement ratio should be applied to avoid numerical diffusion. In addition to that, layers of prismatic elements should be added near the wall boundaries for a better prediction of this region, not only with regard to flow properties itself, but the ﬂow conditions seen by the particles, i.e. mean velocity and turbulence properties. Despite the application of interpolated properties for the particle positions, a better agreement was observed when a reﬁnement was applied to the wall layers. Hence, a ﬁner grid in the vicinity of the wall is recommended for allowing more accurate particle tracking. Recommended values for the parameters involved in mesh generation (initial cell height, average expansion ratio, number of near-wall prism layers, average cell volume in the domain, number of computational cells etc.) can be found in Table 5.

Physical Modelling

Turbulence models

In the LES simulations, the dynamic version of the Smagorinsky-Lilly subgrid scale model (Lilly, 1992) is adopted in order to examine the unsteady ﬂow in the realistic airway geometries. Previous studies have shown that this model performs well in transitional ﬂows in the human airways (Radhakrishnan & Kassinos, 2009; Koullapis et al., 2016).

For the RANS simulations, the standard k-ω SST turbulence model is used due to its good prediction of such wall—bounded ﬂow (i.e. using a blending between wall and free-stream region) and low computational cost. Other turbulence models have not been considered but based on prior experince they are exprected to perform worse.

In order to better validate the numerical predictions of LES and RANS, a second application challenge will follow that will focus on airﬂow characteristics in the same geometry. Moreover, in this second AC, numerical predictions will be compared against PIV measurements.

Lagrangian particle tracking

Lagrangian particle tracking has been adopted in the present application. Although there is a number of forces acting on the particles (Drag, buoyancy, Basset (or history), pressure gradient force, lift due to shear and rotation and Brownian forces), only few of them are important when considering the transport of micron—sized particles in the human airways. This is mainly because the particle density is much greater than the density of the air (ρ_p / ρ_f ≥ 1000). Furthermore, in numerical simulations the particles are assumed spherical and, as a result, the important forces that need to be taken into account in lung deposition studies are drag, gravity and Brownian motion force. However, Lift force due to shear can also be important as particle size increases. This is evident in ﬁgure 21, that plots deposition fraction in the mouth—throat / trachea (segments 1&2) of the benchmark geometry for three particle sizes (1, 4.3 and 10μm) at a ﬂowrate of 60 L / min (LES results). In this case, the expression for the shear lift is obtained by Saﬂman (1965), Saﬂman (1968) and Mei (1992). It is observed that the Saﬂman lift force results in an increase in the deposition of 10μm particles by approximately 5%.

As described in the discrete phase modelling, the time step of the particle tracking calculation should automatically and independently be adapted along the trajectories by considering all relevant time scales, which are also changing throughout the ﬂow ﬁeld. This allows for numerically eﬂicient particle tracking. If such an approach is not possible, a veriﬁcation of the relevant time scales should be calculated by using averaged values in order to apply a correct time step for the simulations.

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