Effects of the deformation and size of the upper airway on the deposition of aerosols

Aerosol drug delivery in the human airway is significantly affected by the morphology and size of the airway. This work developed a CFD-DEM model to simulate and analyze air flow and powder dynamics in combined inhaler-airway systems with different degrees of airway deformation (non-deformed, 50%, and 75% deformed) and sizes (adult, 0.80, and 0.62 scaled). The airways were generated based on a regular airway constructed from the MRI images through finite element method (for deformed airways) or scaling-down (for smaller airways). The airways were connected to Turbuhaler ® through a connector. The results showed that under the same flow rate, the variation in the airway geometry and size had a minimum impact on the flow field and powder deposition in the device and the connector. However, deformation caused more particle deposition in the deformed region. Notably, the airway with 50% deformation had the most particles passing through the airway with the largest particle sizes due to its lower air velocity in the deformed area. Reducing airway size resulted in more powder deposition on the airway, particularly at the pharynx and mouth regions. This was because, with the same flow rate, the flow velocity in the smaller airway was higher, causing more particle – wall collisions in the mouth and pharynx regions. More importantly, the deposition efficiency in the 0.62-scaled airway was significantly higher than the other two airways, highlighting the importance of the different administration of aerosol drugs for young children.


Introduction
Dry powder inhalation (DPI) is a convenient and rapid way of delivering therapeutic drugs to the lungs to treat respiratory diseases such as asthma and chronic obstructive pulmonary disease (COPD) (Zhou et al., 2014;Chan, 2006).The effectiveness of DPI depends on powder formulation and characteristics, devices, and patient-related factors (Martin et al., 1997).Understanding their effects and interplay (Zhang et al., 2007) improves treatment.
The pharynx of the human upper airway is a flexible conduit made up of muscles that contract during respiration (Cheng et al., 2014).Previous studies have demonstrated the significant influence of upper airway deformation on flow field and powder deposition (Brouns et al., 2007;Bates et al., 2018;Zhao et al., 2020).Cheng et al. (Cheng et al., 2008;Cheng et al., 2011) studied the movement of epiglottis using the MRI (magnetic resonance imaging) technique.Their results showed that the upper airway deformation was marked by variability in airway deformation at the level of the soft palate and epiglottis which deformed laterally (soft palate) or in the anteroposterior direction (soft palate and epiglottis) and was likely related to craniofacial features, size of tongue and diameter of the upper airway.Their later study (Cheng et al., 2019) using a deformable silicone airway cast showed that throat deposition was lowest at 50 % lateral deformation and highest at 75 % lateral deformation of the upper airway at a flow rate of 60 L/min.They also observed a tendency for greater variation in throat deposition at lower flow rates among the airways with different degrees of deformation, which was consistent with the work by Zhao et al. (Zhao et al., 2020) who studied the effect of the deformation of soft palate using PIV (particle image velocimetry).
The airway dimension increases by 3 times from birth to adulthood, and the size variation also plays a significant role in powder deposition (Devadason et al., 1997;Newman et al., 2000).Golshahi et al. (Golshahi et al., 2012) conducted an in vitro study with the upper airways (based on the CT scan) from the ages of 6 to 14 years.Their results indicated that the lung deposition efficiency was higher for adults.They observed a similar effect using an Idealized Child Throat (ICT) model which was a smaller replica of the Alberta Idealized Throat (AIT) (Golshahi and Finlay, 2012).Delvadia et al. (Delvadia et al., 2012) studied the impact of airway dimension on drug deposition in a mouth-throat model and observed that lung deposition increased with age, comparable with the in vivo results of Newman et al. (Newman et al., 2000).
Computational fluid dynamics (CFD) modeling has been used to better understand the transport and deposition mechanisms of powders in the airway.Xi et al. (Xi et al., 2012) evaluated the age-related effects on the airflow and powder dynamics in the image-based nose throat models of four age groups from 10 days to 53 years old.The air velocities in the airways from age 10 days to 5 years were larger than those of adults while the deposition efficiency of ultra-fine particles (1-10 nm) tended to be independent of airway geometry and flow rates.Their subsequent research indicated that age effects affect pressure drop, and total and regional aerosol deposition (Jinxiang et al., 2014).Similar trends were also observed in other studies (Islam et al., 2021;Islam et al., 2021), which found significant differences in particle deposition and pressure drop between ages 50 to 70 years.Das et al. (Das et al., 2018) and Belka et al. (Belka et al., 2022) observed that the velocity in the airway of younger was larger than that of adults using a scaled-down adult airway model.Kolewe et al. (Kolewe et al., 2022) compared the upper airways of 6-year-olds and adults to an idealized model, finding that the idealized model more accurately predicted deposition characteristics.Williams et al. (Williams et al., 2022) investigated the effects of airway differences between adults and children with diseases, comparing them to healthy upper airways.They found that upper airway deposition was similar for smaller particles across all patients, while the local deposition hotspots differed in size, location, and intensity.
Considering the large variations in the morphology and dimensions of airways, it is important to understand their effects on powder deposition mechanisms through numerical modeling.This study aimed to understand how the variation of airways affects particle dispersion and deposition in the coupled inhaler-airway systems.A numerical model based on CFD, and the discrete element method (DEM) was developed to simulate fluid flow and aerosol powder to examine powder dynamics, particle size distribution, and local powder deposition in various airways and to compare the current results with previous research.

Device-airway geometry and meshing
In this work, A multi-dose dry powder inhaler Turbuhaler® (Astra-Zeneca) (Wetterlin, 1988;Milenkovic et al., 2013) was connected to an upper respiratory tract through an adaptor, as shown in Fig. 1a.The adapter utilized in the simulation is the same as that in the experiment by Cheng et al. (Cheng et al., 2019), serving as the connector between the inhaler and upper airway.The Turbuhaler device included an inhalation channel, a circulation chamber, and a helical mouthpiece (Zhu et al., 2022;Zhu et al., 2023), while the airway geometry was obtained by MRI images from a healthy human (Female, aged 45, BMI 22 kg/m 2 ), as used in a previous study (Cheng et al., 2019).Although this airway geometry cannot represent all adults, given its close relation to factors such as age, gender, health status, inhalation flow rates, and respiratory states (Delvadia et al., 2012;Williams et al., 2022;Vinchurkar et al., 2012;Xi et al., 2018;Bhardwaj et al., 2022), the key features like the mouth, pharynx, and larynx remain similar across different realistic upper airway models.

• Deformed airway generation
The airway was varied by changing its morphology and dimension.The previous studies (Cheng et al., 2008;Cheng et al., 2011) using MRI techniques showed three different patterns of upper airway deformation in humans, characterized by variability in airway deformation at the level of the soft palate and epiglottis.The upper airway at the level of the soft palate can deform laterally or in the anteroposterior direction.To mimic muscle motility degrees, two impactors were positioned at the sides of the pharynx, altering the airway's morphology by deforming the pharynx airway to 50 % and 75 % reductions in width, which has been demonstrated to significantly affect deposition behaviors (Cheng et al., 2019).Their studies also showed that anteroposterior collapse of the upper airway has less impact on throat deposition and lung dose, while lateral collapse has significant effects.Therefore, the following studies are focused on lateral compression.The deformed part of the airways was predicted through finite element method (FEM) simulation by applying lateral compression.
The FEM simulation was performed using ANSYS Mechanical 19.1.The deformed airways were generated based on a regular RUPAC (realistic upper airway cast) geometry as used in the previous experiment (Cheng et al., 2019) by adding an impactor at the soft palate.The airway and the impactor were then imported to ANSYS Meshing for mesh generation.In total 513,760 tetrahedral meshes were generated with an average size of 0.5 mm, as shown in Fig. 1.The static structural  model based on elastic deformation was adopted in the simulation.The material parameters are listed in Table 1.
The simulation setups are the same as the previous experiment by Cheng et al. (Cheng et al., 2019).Before the simulation, the impactor total displacement was defined based on the degree of deformation.In the FEA simulation, linear displacement was applied to the impactors, causing the lateral side of the airway wall to compress.The impactor stopped once it reached a predefined displacement, achieving varying degrees of deformation.In this work, the 50 % and 75 % deformations meant that the displacements of the impactor were 25 % and 37.5 % of the initial width of the soft palate, respectively.Fig. 2 shows the final deformed airways.The obtained magnitude of deformation was consistent with the experiment described by Cheng et al. (Cheng et al., 2019).The deformed airway casts were imported into Ansys SpaceClaim to extract the fluid domain for the CFD simulation, with the deformations at various degrees shown in Fig. 3b.

• Scaled airway generation
Previous studies showed that the upper airways of children with respect to that of adults ranged from 0.62 to 0.80 (Golshahi and Finlay, 2012;Das et al., 2018;Williams et al., 2022;Borojeni et al., 2015).The dimensions of the airway were thus varied by scaling down the regular airway (adult airway) by 0.62 (small airway corresponding to middle childhood) and 0.80 (medium airway corresponding to adolescence), as shown in Fig. 3c.It should be noted that the two scales were chosen based on the age recommendations provided in the inhaler introduction, indicating that the Turbuhaler (AstraZeneca) is suitable for use in adults and children aged 8 years and older.

• Mesh generation
The polyhedral meshes with 5 inflation layers and 1.2 growth rate were generated in ANSYS Fluent Meshing.The total number of meshes is 351 K, with mesh sizes for the inhaler inlet, inhaler chamber, inhaler double helix, and airway being 100 μm, 600 μm, 300 μm, and 800 μm, respectively.

CFD-DEM model
The CFD-DEM coupling was achieved through the User Defined Function (UDF) in ANSYS Fluent 19.1 and an in-house DEM model.
In the CFD model, the dynamics of a fluid are governed by Reynolds Averaged Navier-Stokes (RANS) equations, given by,

∂(ε) ∂t
where ρ, u, u′, P, τ and g are the density, mean and fluctuating velocities, pressure, viscous stress tensor and gravitational acceleration vector of the fluid, respectively.Void fraction, ε, is the ratio of the void volume in a CFD cell (cell volume minus particle volume) and the volume of the cell.A particle is regarded wholly inside a CFD cell if its center is in the cell.f pf is the total force per unit volume exerted on the fluid by all the particles at a given location and time.The k-ω SST (shear stress transport) Model was used in the work to solve the Reynolds stress tensor term ερu′u′ (Milenkovic et al., 2013).
In the DEM model, the particle movement is governed by Newton's second laws of motion, given by (Chu et al., 2016) where v i , ω i , I i and m i are, respectively, the translational velocity, angular velocity, moment of inertia and mass of particle i. R i is the radius vector pointing from the center of particle i to the contact point.
μ r is the rolling friction coefficient.ωi is the unit angular velocity of particle i. F n,ij , F t,ij and F v,ij are the normal contact, tangential contact and van der Waals forces between particles i and its neighboring particle j.Table 2 lists the details of those equations.where The DEM and CFD models were coupled through the exchange of the particle-fluid momentum.The total force per unit volume on the fluid by all the particles in a CFD cell is given by V cell , where N p and V cell are the number of particles in the cell and the volume of the cell.
In this work, the fully coupled CFD-DEM model was adopted to Turbuhaler and the adapter in which all the particle-wall-fluid interactions were explicitly calculated.As particles entered the airway, the particle phase became diluted and particle-particle interactions were minimal.Thus, the CFD-DEM model was simplified in the airway in which particle-particle interactions were ignored.In addition, a particle was assumed to be trapped once it contacts with the airway.The assumption is reasonable considering the human airway demonstrates strong adhesive properties towards dry aerosols and given that cohesive lubricants are often coated on the inner wall of the airway in in-vitro experiments (Zhang et al., 2007;Ahookhosh et al., 2020).Those treatments significantly reduced simulation time, allowing more particles to be simulated.

Simulation conditions
A simulation started with particles packed at the bottom of the inhaler under gravity.Air flow was then introduced and transported the particles to the chamber.These dispersed particles were then ejected from the mouthpiece and entered the adapter and the mouth region.The particles were then dispersed again due to the circulatory flow in the pharynx and gradually entered the larynx and trachea, and ultimately escaped from the airway's outlet.
Fig. 4 shows the particle size distribution (PSD) used in the simulations, which was based on the experimental measurements of the budesonide powder in Pulmicort Turbuhaler (Zhu et al., 2023).A parcel model was employed to further reduce simulation time, which used fewer larger parcel particles to represent real particles (Zhu et al., 2023;Di Renzo et al., 2021).The detailed principles and the scaling laws of the parcel method can be found in previous studies (Tausendschön et al., 2020;Nasato et al., 2015).In summary, the behavior of parcel particles should be equivalent to original particles based on the scaling rules to ensure consistent energy densities in the original and the parcel system (i.e. the translational velocity and total rotational kinetic energy are invariant) (Tausendschön et al., 2020;Nasato et al., 2015).A scaling factor α was defined as α = d parcel /d prim , where d parcel andd prim were the diameters of the parcel and the original particles, respectively.A parcel particle represents α 3 numbers of the primary particles.Scaling the forces acting on a particle was based on dimensionless overlap-based scaling.The normal and tangential contact forces were scale independent, while the normal damping force and the van der Waals forces were scaled by α and the drag force by α 3 in the parcel system.In the following discussion, the sizes of the original particles are used unless otherwise specified.
Table 3 lists the key parameters of the simulations.The flowrate was fixed at 60 L/min, which was close to the typical peak inspiratory flowrate of Turbuhaler (Newman et al., 2000;Ruzycki et al., 2014).The total mass of particles is 153 μg, within the typical dose range (100-400 μg) in Turbuhaler (Hoe et al., 2009;AstraZeneca, 2022).The timestep for the DEM simulations was set to 5 ns which was determined through sensitivity analysis based on the Rayleigh criterion.The CFD timestep was set to 0.2 µs to avoid particles jumping from one cell to another in one step causing numerical instability.

Table 2
Force models in the simulations.

Flow field and powder dispersion
Fig. 5 shows the flow field and particle dynamics in the inhalerairway (regular) system at different times.The flow field (Fig. 5a) is almost time-independent, showing higher velocity in the inhaler (particularly the double helix mouthpiece) and a much slower velocity region inside the adapter.As the air flow moves from the oral cavity to the pharynx, its velocity increases and reaches the maximum at the pharynx.
Fig. 5b-f show the dynamics of particles in the system.In Turbuhaler, the particles initially disperse rapidly but their velocities decrease upon entering the adapter.The dispersion behavior inside the inhaler is similar to a previous work (Zhu et al., 2023) using Turbuhaler with the same powder sizes and flow rates.As they enter the mouth-throat region, their velocities increase again causing some larger particles to deposit on the airway upon collisions.Significant powder deposition occurs in the pharynx region and only small sized powders tend to follow the air flow and pass through the larynx and trachea regions.Note that the dispersion process in Turbuhaler lasts less than 20 ms while the transportation process in the airway takes much longer (>250 ms).

Effect of airway deformation
This section shows the effect of airway deformation on air flow and powder deposition patterns.As the flow inside the inhaler and the adaptor shows no significant change, the discussion will focus on the airway region.
Fig. 6 shows the air velocity distribution with different degrees of airway deformation.The flow patterns before the deformation area (i.e.inhaler and mouth) remain consistent across different degrees of deformation (as shown in section A).However, the regions near the deformation area (i.e.pharynx and larynx) are profoundly influenced by the deformation.As shown in section B, the boundary between the small and large velocity regions in the pharynx becomes more obvious with increasing deformation.Both the low velocity and the circulation zone area increase with deformation, as shown in sections B and C. The effect of airway deformation, however, diminishes in other regions (e.g.trachea in section D).It is expected that the deformation has no impact on the flow within the bronchial airway.
Fig. 7 shows that the powder depositions before the deformation area are similar for different cases.Compared to the regular airway (Fig. 7a), the deposition in the larynx and trachea regions is less in the deformed airways, as shown in Fig. 7b and 7c.The decrease with increasing deformation is due to the smaller circulation zone and the expanding low-velocity zones at the pharynx in the deformed airways (see section B of Fig. 6).Consequently, more particles follow the high-velocity air flow, resulting in less particle deposition on the deformed side.
Fig. 8 provides a quantitative analysis of powder deposition.Fig. 8a shows that the deposition in the device is not affected by airway deformation, accounting for 16 % of the loaded dose for all the cases.The results are comparable to the previous study of 20 % deposition (Kugler et al., 2019).On the other hand, the deposition fraction of 51.8 % in the 50 % deformed airway is the lowest compared to deposition fractions of 56.8 % and 57.6 % in the regular and 75 % deformed airways, respectively.Interestingly, the trend is similar to the experimental observation from Cheng et al. (Cheng et al., 2019) who reported airway depositions of 59.4 %, 56.9 %, and 60.2 % using an Osmohaler-airway system for the regular, 50 % deformed, and 75 % deformed airways, respectively.A possible reason is that there is a lower velocity area in the 50 % deformed airway, as shown in Fig. 6, which leads to fewer particle-wall collisions compared to the other two airways.The similar findings in this work to the experiments (Cheng et al., 2019) indicate that, despite different inhalers being used in the experiments and simulations, the effect of deformation on powder deposition seems consistent.
Fig. 8b shows the local airway deposition patterns relative to the total deposition in the airways (excluding those in the device and adaptor).The deposition primarily concentrates on the pharynx (>75 %) followed by the mouth (15 % − 20 %).With increasing deformation, the deposition increases in the pharynx but decreases in the mouth region.The small depositions in the larynx and trachea become even less with airway deformation.
Fig. 9 shows the sizes of the particles leaving the airways (i.e.lung deposition) are significantly smaller (less than 3.5 μm) than those of the initial dose (shown in Fig. 6), indicating most of the larger particles are deposited in the inhaler and the airway.It is noted the particle sizes leaving the 50 % deformed airway are the largest among the three airways while those leaving the 75 % deformed airway are the smallest.This suggests that while mild airway deformation allows slightly more large particles to pass through in comparison to the regular airway, large airway deformation results in more small particles passing through the airway.

Effect of airway size
This section is to investigate how airway size affects airflow and powder deposition at the same flow rate of 60 LPM.
Fig. 10 shows the velocity distributions in the airways.While the velocity magnitude increases with decreasing airway size when the flow  rates are the same, the local velocity distributions at various locations are similar.In addition, more pronounced circulation flows are observed in the small airway, particularly in the trachea region (as shown in section D).
Fig. 11 shows the final powder deposition in the airways.While large particles are primarily deposited in the upper part of the airway (e.g.inhaler, mouth, and pharynx), small particles are concentrated in the pharynx and larynx.With decreasing airway size, a noticeable accumulation of large particles is deposited in the mouth region, and more small particles are deposited in the lower airway.This is because the high velocity in the small airway causes more particle-wall collisions and hence more particle deposition.
Fig. 12a presents overall powder deposition fraction in the device-airway system relative to the loaded dose.The depositions in the device and the adapter are similar for different sized airways, accounting for roughly 18 % and 3 % of the loaded dose, respectively.The depositions in the medium and regular airways are similar (~58 %) but the deposition in the small airway is much higher (70 %) due to the higher flow velocity.The simulation results of airway deposition are comparable with the previous experimental result (Devadason et al., 1997), which showed a decrease in airway depositions from the small airway to the regular airway.
Fig. 12b shows the local airway deposition with respect to the total deposition in the airway (excluding the deposition in the inhaler and adaptor).All the airways show that the deposition in the pharynx is dominant followed by the mouth.Compared to the regular airway, the deposition in the pharynx increases and decreases in the mouth in the medium airway due to higher velocity and enhanced circulation flow in the pharynx.However, the deposition in the mouth increases, and deposition in the pharynx decreases in the small airway compared to the other airways.This is attributed to the increased velocity in the mouth region in the small airway which enhances the chances of particle collisions with the mouth, resulting in more particle deposition and fewer particles deposited in the larynx and trachea.
Fig. 13 shows the size distributions of the particles leaving the airways (i.e.deposited into the lung).While the particle sizes coming out from the medium airway are similar to those from the regular airway, the particles from the small airway are significantly smaller with few particles larger than 2 μm.This indicates that particles are more difficult to reach the lung region for young children, potentially reducing the effectiveness of treatments.

Quantification of airway deposition with impaction parameter
Quantification of airway deposition is important for the control and optimization of DPI devices.Fig. 14 plots the deposition efficiency of all the cases in the current work as a function of the impaction parameter, which is the product of particle size and air flowrate square to describe the tendency of particle deposition by inertial impaction.Literature data (Cheng et al., 1999;Stahlhofen et al., 1989;DeHaan and Finlay, 2001) are also shown for comparison.The solid and dashed curves are the fitting curve and the standard deviation based on in vivo results summarized by Cheng et al. (Cheng et al., 1999).Other in vitro data include results from DeHaan and Finlay (DeHaan and Finlay, 2001) using a Turbuhaler-IMT system with a small adapter, and from Cheng et al. (Cheng et al., 2019) using an Osmohaler-RUPAC system with the  The figure shows that the current simulation and the previous in vitro deposition efficiencies are higher than those in vivo results, especially at larger impaction parameters.However, the simulation results exhibit a similar increasing trend to the in vivo trend line (solid line in Fig. 14), but with values that are consistently higher than those of the in vivo data.Additionally, the current results follow a similar trend to the experiments for different airway models except for the small airway, which exhibits much higher deposition efficiency than other airways, and the pronounced disparity in deposition efficiency between the small airways (young children) and the regular airways (adults).

Discussions
In this work, the effects of upper airway deformation on drug delivery and airway deposition extend previous in vitro experiments by Cheng et al. (Cheng et al., 2019), replicating the deformation of upper airway walls due muscle motility and soft palate deformation using mechanical actuators.The pattern of pharyngeal deformation is based on MRI work (Cheng et al., 2008).Although this approach is simplified compared to the realistic upper airway deformation during drug inhalation, it provides a method to evaluate the impact of airway deformation on drug delivery.However, previous in vitro studies fall short in capturing detailed information on drug delivery and deposition within the inhaler-airway systems, which are crucial for evaluating the efficiency of drug delivery and inhaler performance.
In the simulation, it is observed that deformation has minor effects on the flow field at the inhaler, mouth, larynx, and trachea, but significantly affects the pharynx.In a regular upper airway, there is a large circulation zone and high air velocity in the pharynx, leading to higher deposition.With 50 % deformation of the upper airways, the large circulation zone splits into two smaller zones, and air velocity decreases, resulting in reduced airway depositions.However, with 75 % deformation, the pharynx becomes longer and narrower, leading to the  disappearance of the circulation zone and an increase in air velocity.Consequently, more deposition is observed in the airway, making the deposition levels in the upper airway similar to those in the regular airway.Besides, due to the high velocity in the pharynx at 75 % deformation, larger particles are more likely to deposit in the upper airway, leading to smaller particle sizes in lung depositions.
This work also investigated the effects of the upper airway scale on drug delivery and airway deposition.Two upper airway scales, 0.8 and 0.62, are used to represent children over 5 years old (Golshahi and Finlay, 2012;Das et al., 2018;Williams et al., 2022;Borojeni et al., 2015).As the Turbuhaler (AstraZeneca) is recommended for use in individuals aged 8 years and older, smaller airway scales are excluded from our simulation.
The simulation indicates that air velocity increases as the scale decreases, and the circulation zone in the pharynx and trachea is enhanced with decreasing scale, particularly at a scale of 0.62.This results in increased airway deposition as the airway scale decreases.Furthermore, the high velocity in the smaller airways causes larger particles to be deposited in the airway, while smaller particles are more likely to reach the lung depositions.
The deposition efficiency for various deformations and scales is compared with previous in-vivo and in-vitro studies with different inhaler-airway systems in terms of impaction parameters.Except for the deposition efficiency in small airways, the simulation results demonstrate similar increasing trends with impaction parameters compared to the in vitro studies, although specific values differ among airway models.Moreover, compared with the deposition efficiency in simulations for regular airways, there is greater variability between the Turbuhaler-IMT systems and the Turbuhaler-regular airway systems and less variability between the Osmohaler-RUPAC systems and the Turbuhaler-regular airway systems.This indicates that the inhaler type has a minor effect on deposition efficiency in the adult upper airway.The deposition efficiency in small airways is significantly higher than in other airways, indicating that drug delivery for young children differs significantly from that for adults.This necessitates greater attention to inhaler design and drug formulation for young children.
It should be noted that the dynamics of upper airway deformation, which is the actual movement of the soft palate during inhalation of dry powders, are not considered in the present work.This study examined two degrees of deformation, 50 %, and 75 %, to evaluate the effects of soft palate deformation on powder dispersion, throat deposition, and lung dose.The primary aim of this work is to explore the feasibility of simulating airway deformation using CFD-DEM-FEM and to highlight the importance of upper airway deformation.The simulation of dynamic upper airway deformation and its impact on the deposition characteristics will be conducted in future studies.

Conclusions
The numerical study clearly demonstrated that aerosol delivery and deposition efficiency are significantly affected by airway deformation and airway size.The CFD-DEM simulations are consistent with the experimental findings of Cheng et al. (Cheng et al., 2019).The main findings are summarized as follows: • Airway deformation and size have a minimum impact on the air flow and powder deposition pattern in the device.• With increasing deformation, the circulation zone in the pharynx expands and the difference between low-velocity and high-velocity zones becomes more pronounced.The 50 % deformed airway has the highest powder deposition.Locally, deposition in the pharynx accounts for more than 75 % of the total airway deposition and the fraction increases with deformation.• Smaller airways have higher velocity and more pronounced circulation flow, causing larger powder deposition in the airway.The small airway has a significant increase in airway deposition compared to the regular and medium airways, suggesting a need for caution when assessing differences in deposition efficiency between adults and young children.• The simulated deposition efficiencies, characterized by the impaction parameter in the airways, are similar to those from in vitro studies, except in the small airways where significantly higher deposition efficiency is observed at the same impaction parameters.(Cheng et al., 1999;Stahlhofen et al., 1989) and in vitro (Cheng et al., 2019;DeHaan and Finlay, 2001)

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Model and mesh used in the FEM simulations.

Fig. 3 .
Fig. 3. Mesh and geometry for (a) Turbuhaler-RUPAC system, (b) deformed area with different degrees of deformations, and (c) airways of different scales.

Fig. 4 .
Fig. 4. Particle size distribution and the initial state as packed beds.

Fig. 5 .
Fig. 5. Flow field and particle dynamics at the flowrate of 60 L/min: (a) air flow velocity field; and (b)-(f) particle flows at 3 ms, 10 ms, 20 ms, 100 ms, and 250 ms, respectively.Particle sizes are scaled for clarity.

Fig. 8 .
Fig. 8. (a) Deposition fractions in different regions, and (b) local airway deposition fractions with respect to the total deposition in the airways.

Fig. 12 .
Fig. 12.Effect of airway size on powder deposition: (a) deposition fraction at different parts, and (b) local deposition fraction with respect to the total airway deposition.

Fig. 13 .
Fig. 13.Size distributions of the particles leaving the airways of different sizes.

Table 1
Parameters used in the FEA.

Table 3
Key parameters in the simulations. studies.
D.Gou et al.