The impact of actuator nozzle and surroundings condition on drug delivery using pressurized-metered dose inhalers

The most commonly used method to deliver aerosolized drugs to the lung is with pressurized metered-dose inhalers (pMDIs). The spray actuator is a critical component of pMDI, since it controls the atomization process by forming aerosol plumes and determining droplet size distribution. Through computational fluid dynamics (CFD) simulations, this study investigated the effect of two different nozzle types (single conventional and twin nozzles) on drug deposition in the mouth-throat (MT) region. We also studied the behavior of aerosol plumes in both an open-air environment and the MT geometry. Our study revealed that spray aerosol generated in an unconfined, open-air environment with no airflow behaves distinctly from spray introduced into the MT geometry in the presence of airflow. In addition, the actuator structure significantly impacts the device's efficacy. In the real MT model, we found that the twin nozzle increases drug deposition in the MT region, and its higher aerosol velocity negatively affects its efficiency.


3D
Three Particle velocity (m/s) U(x) Plume velocity (m/s) U 0 Initial velocity of plume (m/s) V Volume of computational cell (m 3 ) w(x) Plume width (m) w 0 Plume width at location where velocity is U 0 (m)

Introduction
Respiratory diseases such as asthma and chronic obstructive pulmonary disease (COPD) are among the most common causes of severe illness and death worldwide (Ahookhosh et al. 2021;Kunda et al. 2017;Williams et al. 2022).Direct delivery of inhaled drugs to the lung for treating these pulmonary diseases provides the quickest responses (Kaviratna et al. 2019;Narayanan et al. 2022).With aerosolized drugs, delivering sufficient doses of medication to the destination area is key to minimizing systemic side effects and achieving maximum efficiency (Ahookhosh et al. 2019;Kaviratna et al. 2019).
Pressurized metered-dose inhalers (pMDIs) are the most widely used devices to deliver aerosolized drugs to the respiratory tract (Biswas et al. 2017;Kunda et al. 2017;Ogrodnik et al. 2016;Sarkar et al. 2017).PMDIs are popular because they are: compact, portable, and low-cost (Ahookhosh et al. 2021;Duke et al. 2021a).However, even with these excellent features of pMDIs, only 5-30% of the medication reaches the treatment area of the lung; in other words, the delivered drugs tend to deposit in the mouth-throat (MT) region before reaching the target region (McKiernan 2019).An accurate understanding of the initial plume formation and expansion would help to improve the efficiency of the device; however, physical and behavioural characterization of the pMDI is complex, due to the entirely transient, turbulent, three-dimensional, and multi-phase nature of the spray (Duke et al. 2019;Ogrodnik et al. 2016).A key component of a pMDI is the spray actuator nozzle, which controls the atomization process (forms aerosol plumes and determines droplet size distribution) (Kleinstreuer et al. 2007).The lung deposition of an aerosol delivered by a pMDI may depend on the fine particle fraction (FPF), and the amount of released FPF relies on the design of the formulation and structure of the actuator (Biswas et al. 2017).
Over the past decades, several studies have investigated the optimization of critical parameters of the performance of pMDIs.In 2007, Kleinstreuer et al. simulated a human upper airway replica and used different propellants and exit-nozzle diameters to investigate the drug droplet mass fraction that passes through the trachea.They found that the smaller, 0.25 mm nozzle diameter generated finer particles and showed better performance than the 0.5 mm nozzle.However, the presence of a spacer complicated any conclusions about a relationship between FPF and orifice size and formulation of the canister.Sadeghi et al. (2023) investigated how the location of an inhaler's nozzle in the mouth affects the amount of medication deposited.They found significantly greater amounts of drugs were deposited when the nozzle was positioned placed 10 mm closer to the throat inside the mouth.Their study involved a simulation of the spray from a soft mist inhaler's (SMI) nozzle within the mouth.Further, the comprehensive studies conducted by Ahookhosh et al. (2020) and Kadota et al. (2022) utilized CFD to examine the effect of the airflow characteristics on behavior of particles within a realistic respiratory airway model.They highlighted that the airflow within the respiratory system varies between patients and can influence the deposition rate of inhaled particles.Similarly, by considering particle-particle interaction, Spasov et al. (2022) demonstrate a substantial difference in deposition when comparing a steady plug flow to a time-dependent swirling flow.Smyth et al. (2006) demonstrated that the actuator orifice length and sump depth influenced spray patterns and particle size distribution.Chen et al. (2017a, b) found that different nozzle designs and actuator materials can affect the plume configuration generated by pMDIs.However, their study showed no correlations between aerosol performance, plume angles, nozzle design with aerosol deposition.Dastoorian et al. (2022) studied the effect of plume angle on drug deposition and found that smaller cone angles produced larger particles, but larger cone angles increased mouth deposition.Duke et al. (2021b) discovered that pMDI actuators with twin-hole orifices with smaller diameter holes (0.22 mm) could produce up to 75% more FPF compared to the conventional single-hole orifices.They also found that larger length-to-diameter ratios are beneficial for pMDI nozzles.Their plume configuration analysis occurred in an open environment without considering the flow rate for these different actuator geometries.Studies have demonstrated that aerosol behaviours are different in an open space versus a confined area, as the latter limits plume expansion.Plume properties also change when inhalation flow is used, compared to noflow conditions (Moraga-Espinoza et al. 2018).Talaat et al. (2022) recently suggested that a study on plume behaviour should be done under close to real conditions during drug delivery, but this is currently not experimentally feasible.
CFD simulation has become increasingly important for demonstrating plume behaviours, and for transport and deposition of inhaled particles in in silico models of the respiratory system, which are challenging to obtain by in vivo and in vitro studies (Bhardwaj et al. 2022;Kadota et al. 2022;Wu et al. 2022).Our study employed CFD modelling to integrate realistic conditions while exploring the impact of nozzle geometry on plume configuration.We modelled the conventional (single nozzle) and specific (twin nozzle with a longer orifice length) nozzle geometries and compared hydrodynamic parameters in the real geometry of the MT,

CFD model development
The 3D model geometry drawing and mesh generation for the MT airway and actuator shapes of pMDI were carried out in the ANSYS (Analysis of Systems) Workbench (ANSYS, Inc).2021), (2019); the spray was modelled as an injection of droplets composed of the drug (i.e., ipratropium bromide), the propellant (hydrofluoroalkane (HFA) 134a), and the co-solvent (ethanol).The properties of these components are provided in Table 1.

Mesh generation
Our geometries, including a cylinder representing the open-air environment, two nozzle geometries, and the real MT model, were discretized using tetrahedral elements in ANSYS® Workbench.The prism elements with eight layers of thickness and a transition ratio of 0.272 were generated in the region near the airway wall to capture the high gradients near the walls (Feng et al. 2021;Talaat et al. 2022).
The geometries and mesh were imported into ANSYS Fluent 2020R2 (ANSYS® release 2020 R2 v20.2, Inc).The tetrahedral and prism elements were then converted to a polyhedral and poly-prism mesh, respectively, as shown in Fig. 1.Published studies (Feng et al. 2021) have shown better convergency, greater accuracy due to more cell connectivity, and lower computation cost, so we used the polyhedronbased mesh in our present work.
Mesh independence tests were performed for both openair and MT models, and each setup was simulated until the end of spray injection.Table 2 demonstrates the number of meshes for each model.The open-air model's geometry was divided into six coaxial cylinders with different lengths to generate the multiple mesh sizes (Fig. 1a).This allowed the mesh size to increase from the inner cylinder toward the outer and avoided the unnecessary cost of computation due to high mesh numbers.
Figure 2 shows the mean velocity profile at the end of the injection timepoint, t = 0.1 s, for different mesh sizes.Figure 2a presents the mean axial velocity of the plume along the centerline, from the nozzle exit to 100 mm away for the open-air model.This figure shows that the axial velocity is independent of mesh size near the nozzle exit.However, from a distance of almost 50 mm, we notice a difference between Case 2 and Case 3, due to changing mesh size in this area.Percent root mean squared error (RMSE%) was utilized to quantify the differences among the profiles: RMSE%= × 100 (Khan et al. 2020), where u i and u j are aerosol velocities of Cases with different mesh numbers.RMSE% of Case 1 and Case 2, Case 2 and Case 3,  and Case 3 and Case 4 were 10.48%, 7.59%, and 4.73%, respectively.Since the difference between Case 3 and Case 4 was below 5%, we proceeded with our simulations with Case 3 with 1,868,138 meshes.The MT model was segmented into three regions, the mouth, pharynx, and trachea, as shown in Fig. 2(b).The mean axial velocities through the radial direction of three cross-sections, one in each of the mouth (MM´), pharynx (PP´), and trachea (TT´) regions, were compared in Fig. 2b (i-iii).In the mouth region, the RMSE% of Case A and Case B was 48.28%, and Case B and Case C was 7.45%.In the pharynx area, they were 70.02% and 9.43%; in the trachea region, 8.1% and 5.88%, respectively.Due to the difference between Case B and Case C in all regions less than 10%, Case B, with 2,629,917 meshes, was chosen.

Continuous phase
Drug delivery in the airway is a multi-phase flow phenomenon.The complexity of the MT geometry creates a transition from a laminar to turbulent flow (Ahookhosh et al. 2021;Chen et al. 2017b, a).We utilized the large eddy simulation (LES) model for our simulations.LES modelling of airflow in the MT geometry is comparable to in vitro studies and can accurately predict the transition from laminar to turbulent flow (Cui and Gutheil 2011;Huang et al. 2021).

2022):
where u i is time-averaged velocity, P is time-averaged pres- sure, ρ is mixture density, μ is mixture dynamic viscosity, F i is body force from external forces, and s is dynamic viscosity at sub-grid scales.Dynamic kinetic energy ( k sgs ) was used to model the sub- grid scale stresses, which are defined as: where Δ f is filter size computed from Δ f = V 1∕3 , C k and C are constants (Kim and Menon 1997).
We adopted the inhalation flow rate of 30 L/min (the normal maximum inspiratory flow rate for an adult at rest) to simulate breathing conditions (Biswas et al. 2017;Gurumurthy and Kleinstreuer 2021;Longest and Hindle 2009;Wu et al. 2022;Zhang et al. 2006).The inlet and outlet were set to inlet velocity and outlet-pressure conditions, respectively, and the nozzle and MT wall were set to the no-slip boundary condition.The time step size for this simulation was set at 0.2 ms.

Discrete phase
The spray emitted from a pMDI is a high-speed, transient, turbulent, and multi-component flow which consists of propellant, ethanol, and drug.The Lagrangian discrete phase model (DPM) was employed to inject a multi-component solution into the pMDI flow field.Mass fractions of propellant, ethanol, and drug were 85%, 14.79%, and 0.21%, respectively (Duke et al. 2019).Due to dilute particle flow, a two-way coupling between the fluid and particles, that neglects particle-particle interaction, was considered (Ahookhosh et al. 2021;Rahman et al. 2021).The Rosin-Rammler method (in size ranges from 1 µm to 20 µm) was employed to describe the particle distribution.The set injection properties of a solid-cone injection for both nozzles are provided in Table 3.The trajectory of inhaled particles is derived from the Lagrangian approach, based on Newton's second law.The force balance equation for particles is given by: where u p , ρ p , d p , and m p are the velocity, density, diameter, and mass of particles, respectively and u f is the velocity of the fluid (Ahookhosh et al. 2021;Narayanan et al. 2022).The C D is the drag coefficient for spherical particles (Morsi and Alexander 1972): The particle's Reynolds number is given by: where a i are constants obtained over different ranges of Reynolds numbers (Morsi and Alexander 1972).
In the present work, a "trap" boundary condition was employed on the wall of the airway and an "escape" for the outlet.The SIMPLEC (semi-implicit method for pressure linked equations-consistent) pressure-velocity coupling algorithm was used for solving the models, and the leastsquares cell-based, the second-order, and the second-order upwind scheme were applied to calculate the cell gradients, pressure, and momentum, respectively.In addition, bounded central differencing was employed for the discretization of momentum.The average simulation times for the open-air and MT models' simulations were approximately 24 h and 50 h, respectively.For these simulations, we employed the Niagara cluster with 40 Intel CascadeLake cores at 2.5 GHz, 80 cores processor, and 20 GiB/202 GB RAM per node.

CFD model validation
Figure 3 shows the velocity of the generated plume at different distances from the nozzles.Our CFD results agreed reasonably well with the data obtained by Versteeg et al. (2017) and Buchmann et al. (2014), who used a high-speed imaging technique.However, in the latter study, they could not measure velocity near the exit nozzle due to the limitation of their experimental setup.Therefore, their results are (5) m P du p dt = 18 available from a 25 mm distance from the nozzle, as seen in Fig. 3a.
There is a difference between our results and the results from Duke et al. (2021), although the trend is the same.Duke et al. (2021) estimated spray velocity near the nozzle using an image cross-correlation technique for the initial velocity of the plume ( U 0 ) and by assuming axisymmetric spray, utilized a simple mathematical model to calculate the velocity at different distances from the nozzle: , where w 0 is the plume width at the location where its velocity is U 0 and w(x) is plume width where veloc- ity is U(x) .The differences between Duke et al. (2021)'s results and others confirm that their proposed correlation is unable to sufficiently predict plume velocity.The twin nozzle was a novel idea proposed by Duke et al. (2021).Figure 3b compares our results and those of for the plume velocity for the twin nozzle.The experimental data was limited to a distance of 40 mm from the nozzle; hence the reported results were constrained within this range.Although the CFD data exhibits a similar trend, there are quantitative discrepancies between the datasets.It is worth mentioning that the proposed correlation by Duke et al. (2021)'s, which is demonstrated for a single nozzle in Fig. 3a, lacks accuracy in predicting the velocity profile.
Based on this, it can be concluded that our spray model is sufficiently valid.
After validating our spray model in an open-air environment, the next step was to validate our CFD model for aerosol deposition in the MT geometry.Figure 4 shows the MT deposition efficiency versus the impaction parameter (the product of the square of the aerodynamic diameter and the volumetric flow rate).This figure shows that our CFD results agree with other literature results from in vivo testing (Stahlhofen et al. 1989) and in vitro experiments (Cheng et al. 2015;Zhou et al. 2011).Stahlhofen et al. (1989)  proposed a semi-empirical model of the available in vivo data of aerosol deposition in the airway as a function of the impaction parameter.The solid line and dashed lines (corresponding to the standard deviation of the in vivo data) in Fig. 4 are relevant to their model.According to our data, particles with a size of less than 5 microns are more likely to pass through the MT, while larger particles tend to have a higher deposition rate.Considering the variety of MT geometries and breathing patterns used in in vivo studies, our CFD model underestimated the average in vivo data for the small particles' deposition efficiency.However, the trend of our results is similar to that reported using the in vitro

Plume behaviour
The plume injected by pMDIs and the size of the generated particles depend on the formulation of the canister, the actuator structure, and the surrounding environment (Chen et al. 2017b, a;McKiernan 2019).The effect of the two latter parameters on the plume is shown in Figs. 5 and 7. Effects of the surrounding conditions are discussed in Sect.3.3.
Figure 5 shows the plume generated from conventional (Fig. 5a) and twin nozzles (Fig. 5b) in the open-air region.Fig. 5b shows the two separated plumes of the twin nozzle expand after they exit the nozzles within the bowl.Then, the two plumes collapse before entirely leaving the actuator structure, and one continuous plume appears, like the conventional one.Our result is aligned with that of Duke et al. (2021).The spray collapse phenomenon causes a decrease in plume width and an increase in tip penetration (Chang et al. 2023;Nishida et al. 2009).Given that the diameter of the twin nozzle is smaller than the conventional one, as presented in Fig. 5a, the smaller diameter and plume collapse can affect the penetration of the plume, compared with the conventional one.As can be seen in Fig. 5b, the width of the twin nozzle plume (after the collapse) started declining, in contrast with the conventional one that enhanced steadily (Fig. 5a) and thus, it has less width of plume than the conventional one.Figure 6a presents the mean particle diameter in different cross-sections of the plume, calculated for both nozzles.The twin nozzle injected finer particles than the conventional one, in agreement with Duke et al. (2021).Since the difference between the penetration rates of these two nozzles (Fig. 6b) was not remarkable (13%), fine particles were likely produced by two jets mixing at high speed at a short distance from the plume's exit in the twin model.Producing finer particles may reduce deposition in the upper airway and, as a result, increase the efficiency of pMDI.
Figure 7 illustrates the plume velocities obtained in the middle of the injection time (0.05 s), spanning from the nozzle exit to a distance of 40 mm from the centerline.The velocities were calculated for both the open-air (unconfined) and MT (confined) models, considering both the conventional and twin nozzle configurations.We observed a notable difference in the results between the open-air and MT scenarios, with a 22% difference for the conventional nozzle and a more substantial 58% difference for the twin nozzle.The confined and intricate geometry of the MT model, coupled with a flow rate of 30 L/min into the mouth, contributes to a steeper decrease in plume velocity compared to the open-air model and the no-flow condition.The twin nozzle configuration exhibits a significantly greater reduction in velocity intensity than the conventional nozzle.This remarkable decrease can be attributed to the collision of the two jet streams at an early stage.The collision introduces additional turbulence, which amplifies the decline in velocity intensity.The findings represented in Fig. 7 emphasize the importance of studying drug delivery from inhalers under realistic breathing flow conditions, considering the complex airway geometry.It highlights the necessity of incorporating airway geometry simulations to evaluate inhaler device performance accurately.

Flow pattern in MT model
Figure 8 illustrates the velocity contours at mid-plane in the extrathoracic (ET) region (in the MT model) for the conventional nozzle (model A) and twin nozzle (model B) at 0.05 s after injection.We can see vorticities near the palate because of the expansion of geometry and flow separation; this expansion within the mouth alters the airflow dynamics, causing disturbances and changes in its direction and intensity (Inthavong et al. 2011;Shang et al. 2019).The velocity contour illustrates the flow behaves differently in the MT models.The vortices in models A and B vary in location and intensity, which could be attributed to differences in injection velocities.In contrast to model A, the pharynx region of model B exhibits a greater flow velocity and a more distinct mixing zone, resulting in the emergence of vorticity in this area.One plausible explanation for this phenomenon could be the high-velocity plume's forceful impact with the wall at the end of the throat, influencing the flow dynamics.The observed vorticity zones a vital role in the particle deposition pattern (Gunatilaka et al. 2020;Shet et al. 2017).In addition, we noticed that the dominance of the main flow in the trachea area for model B, under the influence of pharynx region's flow, displaced the vorticity adjacent to the posterior wall, which can increase the probability of deposition in these areas.
Particle trajectories shown in Fig. 9 indicate that the aerosol severely impinges on the throat wall because of the high inertia of aerosols.Model B, with its higher velocity (Fig. 9b), caused the aerosol flow to spread widely, rotate, and nearly reach the anterior side of the throat wall.On the contrary, the injected plume of model A, as shown in Fig. 9a, remained in the posterior part of the throat wall after collision.The flow dispersion obtained in model B affected the amount and location of drug deposition.
Due to the bends and geometric complexity of the MT, a secondary flow was generated along with the primary flow.The secondary flow pattern through throat cross sections is shown in Fig. 10 in different positions: pharynx (P1 and P2), larynx (P3), and trachea (P4 and P5), and compared with the flow field injected by two nozzles (models A and B).In the pharynx area (P1 and P2), the aerosol flow, which was injected at high velocity, impinged the throat wall at the posterior position.
The high velocity is evident in the contour velocity plot in this MT region.On the other hand, when the flow enters the end of the pharynx region (P2), the main flow field is pushed into the center of the throat as the force of gravity overcomes the centrifugal force at the end of the bend; this effect is particularly noticeable in model B; higher inertia of its flow resulted in a more significant flow displacement towards the throat's central region.
The secondary streamlines in the larynx region (P3) indicate two vorticities on the left side for both models.However, we can see more dominant recirculation flows in model B, which probably contribute to the higher spray rate of around 10 m/s in model B, contrasted with the 6 m/s spray rate in model A, in the pharynx region.This heightened turbulence intensity in model B contributed to the substantial mixing effect we saw.
After the flow entered the trachea region (P4 and P5), the laryngeal jet dominated, and the velocity magnitude increased significantly, which caused most of the recirculation flows to disappear in both models.However, due to the expansion of the trachea after plane P4 and centrifugal force (Cui and Gutheil 2011;Zhang et al. 2002), the recirculation region re-developed, and the central flow occurred in the anterior portion of the trachea.In model B, the development of the recirculation zone was more irregular, and there were no vorticities.In contrast, two weak symmetrical vortices in the circulation region at the posterior side of P5 were noticed in model A. These results indicate that spray momentum significantly influences the flow field through the MT.This flow pattern can change a medication particles' transport and deposition patterns in the respiratory system (Longest et al. 2009).

Regional deposition
Figure 11 displays particle dispersion based on the particle size in the ET region for both models.Inhaled particles can be deposited in the respiratory system through various mechanisms, inertial impaction, gravitational sedimentation, and Brownian motion.Brownian motion primarily affects smaller submicron particles, while inertial impaction is more influential for larger micron particles in the upper airway (Chen et al. 2018;Kadota et al. 2017;Sosnowski 2018Sosnowski , 2021)).As injected particles had the same density and shape and airflow was constant, only the size of the particle and inertia were the factors that can affect the deposition mechanism in the ET region (Sosnowski 2018).The figure demonstrates that particles larger than 4µm are predominantly found in this particular area, indicating that the mechanism of inertial impaction primarily influences their deposition.For model A, using a conventional nozzle, more particles were deposited on the posterior wall of the throat, pharynx region, and upper side of the trachea, as reported by Xi et al. (2016), while in model B, deposition was observed on the anterior side as well as in the same locations as in model A. These results are supported in Fig. 9b, which verifies the dispersion of particles in the specified region for model B. This figure indicates that the particles move around after colliding with the posterior wall, ultimately covering a significant portion of the anterior area.Consequently, the scattering of particles in the anterior area contributes to their deposition in that region.
Figure 12 shows the particle deposition fractions in all MT regions (mouth, pharynx, trachea, and lung).It compares the effect of aerosol bursts and momentum on drug deposition.About 55% of the particles injected from the conventional pMDI nozzle deposited in the MT, and the remaining particles passed through the trachea, in agreement with in vitro results (Biswas et al. 2017;Kaviratna et al. 2019;Lim et al. 2021) and CFD modelling studies (Kleinstreuer et al. 2007;Walenga and Longest 2016) with similar MT geometries.Less than 2% and 3% deposited in the mouth and trachea region, respectively.Switching to a twin nozzle with a smaller diameter and a higher speed of plume increased the MT deposition by around 97%; less than 3% of the particles reached the deeper lung region.About 74% and 22% of drugs were deposited in the pharynx and trachea regions, respectively.
Our results contrast Duke et al. ( 2021) 's experimental work, which found that a twin nozzle improved the function of pMDI.They utilized the USP-IP, which is a more simplified MT airway geometry than the one used in the present simulations.Previous studies illustrated that airway geometry significantly influences the transport and deposition of aerosol particles in the MT area (Islam et al. 2021;Kadota et al. 2022;Kaviratna et al. 2019;Longest et al. 2009Longest et al. , 2012)).
From the particle trajectory shown in Fig. 9b, higher drug deposition in the pharynx and trachea regions was expected for model B. However, we found that, despite generating finer particle sizes, the higher turbulence intensity of aerosol injected by the twin nozzles plus the collision of two jets, resulted in decreased amounts of aerosolized drug reaching the lung (our treatment target) compared to the conventional nozzle.

Conclusions
We conducted a CFD study, injecting two different spray models using two different nozzles (conventional and twin nozzles) into open-air and MT geometries.The LES-DPM model was utilized to predict accurate flow fields and investigate the effect of surrounding conditions on a pMDIgenerated plume's behaviour.In addition, the effects of the nozzle's shape, diameter, and length on the transport and deposition of drugs were studied.Finally, we validated our CFD models with experimental results.We noticed that the two separated aerosol sprays from the twin nozzle collapsed at a short distance after exiting the orifices, and one continuous plume entered the space with a higher speed, shorter width, and finer diameter of particles compared to the plume generated by the conventional one.In addition, we found that the aerosol spray developed in an open-air environment (representing an unconfined region) and with no breathing flow parameter behaved considerably differently from the case in which the spray was injected into the MT geometry in the presence of airflow.Thus, it is essential to investigate the plume behaviour in the MT geometry.We note that conducting such experiments is currently not technically possible, which is why we rely on CFD.
As a vital part of the pMDI, the actuator structure can remarkably change the inhaler's efficiency.Our data showed that, in the real MT airway, which influences the flow field distribution, the twin nozzle enhanced the drug deposition in the MT region.So, according to the present study, not only does the higher velocity of aerosol generated by a twin nozzle not improve the function of pMDI in terms of drug delivery, but it also worsens its efficiency.
In this study, only the actuator part of the inhaler was simulated; however, considering all details of pMDI geometry and respiratory tract (such as branches of the bronchial airway) in future studies should provide a more precise flow field structure.It is the distal respiratory areas which are ideal targets for drug deposition.Assessing the efficiency of inhalers would be more informative when following particles that have entered the lower lung region.Furthermore, we still need to explore the interaction between particles in the DPM model, and this parameter can affect the transport pattern of injected particles.

Fig. 1
Fig. 1 Schematics and mesh of a open-air model, b MT model, and c conventional nozzle and twin nozzle of pMDI

Fig. 2
Fig. 2 Mean axial velocity (m/s) of the plume a along the centerline from the nozzle in the open-air model, without airflow for four mesh cases according to Table 2, and b through the radial distance (mm)

Fig. 3
Fig. 3 Comparison of plume mean axial velocity (m/s) in the open-air model, without airflow, at a different distance (mm) of nozzle exists of pMDI of the present study and in vitro results for a conventional nozzle, and b twin nozzle

Fig. 4 Fig. 5
Fig.4Comparison of deposition efficiencies (-) in MT model, with 30 L/min of airflow between the present study and and in-vivo and in vivo results as a function of impaction parameters (µm 2 L/min) for the conventional nozzle 0

Fig. 6
Fig. 6 Comparison of a mean particle diameter (µm), and b particle penetration rate (mm) of particles injected from nozzles at the different crosssections of the plume in the open-air model without airflow

Fig. 7
Fig.7 Comparison of axial velocity (m/s) of the plume at the centerline of the nozzles in the open-air model, without airflow, and within MT model, with 30 L/min of airflow, for a conventional nozzle, and b twin nozzle

Fig. 8
Fig. 8 Comparison of velocity magnitude (m/s) contour at mid-plane at 0.05 s a model A, and b model B

Fig. 9
Fig. 9 Comparison of flow velocity (m/s) streamlines at mid-plane at 0.05 s a model A, and b model B

Fig. 10
Fig. 10 Velocity magnitude (m/s) contour and streamlines at cross-sections of MT model, model A (left side), and model B (right side) at 0.1 s

Fig. 11
Fig. 11 Particle dispersion diameter (µm) in the entire MT region a model A, and b model B

Table 2
Number of mesh in open-air and MT models

Table 3
Properties of injection model for two nozzles