Polydisperse Microparticle Transport and Deposition to the Terminal Bronchioles in a Heterogeneous Vasculature Tree

The atmospheric particles from different sources, and the therapeutic particles from various drug delivery devices, exhibit a complex size distribution, and the particles are mostly polydisperse. The limited available in vitro, and the wide range of in silico models have improved understanding of the relationship between monodisperse particle deposition and therapeutic aerosol transport. However, comprehensive polydisperse transport and deposition (TD) data for the terminal airways is still unavailable. Therefore, to benefit future drug therapeutics, the present numerical model illustrates detailed polydisperse particle TD in the terminal bronchioles for the first time. Euler-Lagrange approach and Rosin-Rammler diameter distribution is used for polydisperse particles. The numerical results show higher deposition efficiency (DE) in the right lung. Specifically, the larger the particle diameter (dp > 5 μm), the higher the DE at the bifurcation area of the upper airways is, whereas for the smaller particle (dp < 5 μm), the DE is higher at the bifurcation wall. The overall deposition pattern shows a different deposition hot spot for different diameter particle. These comprehensive lobe-specific polydisperse particle deposition studies will increase understanding of actual inhalation for particle TD, which could potentially increase the efficiency of pharmaceutical aerosol delivery at the targeted position of the terminal airways.

Extensive in vivo and in silico studies have been performed on monodisperse particle TD for both the extrathoracic and intrathoracic regions of the lung [11][12][13][14][15][16][17][18][19] . The monodisperse particle TD study has improved understanding of airway deposition patterns for the upper airways. Relatively few studies have been conducted on polydisperse particle TD in the lung airways. The ambient and occupational settings of aerosol particulate matter are polydisperse 20 , and polydisperse particles have been associated with adverse respiratory health effects 21 . A series of data on monodisperse aerosol particle TD 22 has been used to predict polydisperse particle TD in the human lung.
Lognormal size distribution is used for the theoretical study of regional and total deposition. Discrete monodisperse fraction base size distribution shows greater error for regional deposition, especially for particle sizes smaller than 2 µm 23 . A series of monodisperse and polydisperse aerosol particle depositions in a packed bed shows higher total deposition for polydisperse particles than monodisperse particles 20 . The total 1-μm aerosol deposition in the packed bed without a charged neutralizer (an instrument which is used to neutralize the charge of the electronically charged aerosol particle) is 51% for polydisperse particles and 44% for monodisperse particles. An opposite deposition percentage is observed for a charged neutralizer system. The theoretical artificial neural network (ANN) prediction of polydisperse aerosol deposition in a human lung shows a more accurate deposition pattern (<0.025% error) for all regions of the lung 24 . An In Vivo study of radioactive polydisperse particle deposition in a child's respiratory tract shows the extra thoracic deposition pattern 25 ; a 72% ± 17% polydisperse aerosol (1 μm-9 μm) deposition was observed in the extrathoracic region.
A recent CFD study by 26 for a ring less trachea model and a Zygote5 model showed a maximum 68.35% polydisperse particle deposition in the mouth piece and the entire lung model. Particles were injected from the Novolizer dry power inhaler device and spray entered the mouth in a conical fashion. The Zygote5 model considered first seven generations, and a ring structure was used in the trachea. No CFD or experimental study has been conducted which considers the entire branching pattern for polydisperse particle TD for a whole or large-scale lung model. To more accurately assess the polydisperse aerosol TD and respiratory health risk, it is important to investigate the various lobe specific studies.
The present study is the first approach to investigate polydisperse particle TD in the first 17 generations of an asymmetric lung model by considering a likely entire branching pattern. This study calculated the total air flow rate distribution at the five different lobes of a 17-generation model. A detail polydisperse particle TD was performed in the different lobes of the terminal airways and the deposition hot spot at the right and left lung, and different lobes was investigated.

Numerical Methods
Governing equations and boundary conditions. The present 17-generation anatomical model is proposed by Schmidt, et al. 27 and is an extension of the CFD study of Gemci, et al. 28 and Islam, et al. 6 . Details of the anatomical model can be found in a previous computational study conducted by Islam, et al. 6 . An advanced meshing technique was used to generate the unstructured tetrahedral mesh for the complex anatomical model. A fine boundary inflation layer with dense hexahedral mesh was generated near the wall and the final geometry contained approximately 34 million computational cells. Details about the meshing can be found in the Supplementary Section. A complete validation has been performed for the monodisperse particle TD, which can be found in the previous study by Islam, et al. 6 . The Large Eddy Simulation (LES) model was used to calculate the air flow in this study. Large eddies are calculated directly; on the contrary, the rest of the smaller eddies are calculated by using a Smagorinsky-Lilly subgrid-scale (SGS) model. The detail of the governing equations and boundary conditions can be found in the Supplementary Sections. 6,29 is used at the inlet surface. All the particles are injected through the inlet surface; a total 14,800 particles are injected. To check the convergence of the local particle deposition, a different number of particles are injected into the 17-generation model and found the local particle deposition fraction is no more than 1%. In order to minimize the discretization initialization time for the large-scale 17-generation model, a total 14,800 particles are injected for the final simulation. The flow rate is scaled by the face area and particles are injected through the face area. The detail particle properties and governing equations can be found in the Supplementary Section. Figure 1 shows the polydisperse particle initial distribution at the inlet surface. Figure 1(a) shows the initial position of the different diameter particles; the initial distribution is coloured by a different diameter. The minimum diameter 10 −6 m, maximum diameters 10 −5 m, and mean diameter 5×10 −6 m is used in the Rosin-Rammler distribution method. Figure 1(b) shows the diameter distribution percentage plot. The diameter distribution plot shows a small percentage variation for different diameter particles; however, the initial position of the different diameter particle and the distribution percentage is random.

Results and Discussion
Air Flow Simulation. The present study accounts for airflow, polydisperse microparticle TD in a large-scale 17-generation conduit model, and calculates flow rate distribution percentage in the five different lobes. The velocity contour at different selected planes of the upper airways are presented and which can be found in the Supplementary Section. Table 1 shows the total flow rate distribution at the different lobes of the 17-generation model for different flow rates. The overall flow rate percentage shows that flow distribution is higher in the right lung than in the left. Total flow rate distribution also shows higher flow percentage at the right lower lobe than in all other lobes, and the lower flow distribution at the right middle lobe, compared to other lobes. The highly asymmetric anatomical bifurcating branches significantly influence flow rate distribution at the different lobes. The benchmark experimental data of Cohen, et al. 30 and Horsfield, et al. 31 also show a similar trend of flow rate distribution at the different lobes, which satisfactorily supports the findings of the present study. Particle Transport and Deposition. The current study performs a comprehensive polydisperse particle TD by considering different deposition parameters. A wide range of micro-size particles (1 ≤ d μm ≤ 10) are considered for better prediction of polydisperse particle deposition at the terminal airways. Polydisperse particle initial diameter distribution and total deposition comparison for different flow rates is shown in Fig. 2. The primary y-axis shows the DE of the deposited particles and the secondary y-axis shows the initial diameter distribution of the polydisperse particles. The overall DE of the polydisperse particle for different flow rates shows an increasing trend, except at the 9 lpm flow rate. For the 9 lpm flow rate, the DE shows a fluctuating trend, and about 34% of injected 1-μm particles are deposited, while 42% of injected 10-μm particles are deposited. The DE for 25 lpm and 60 lpm flow rates shows an increasing trend, irrespective of particle diameter. For a 60 lpm flow rate, 46.3% of 1-μm-sized particles are deposited and 93.1% of 10-μm sized particles are Figure 1. Polydisperse particle distribution, (a) schematic diagram of particle initial distribution at inlet and legend shows microparticle (μm) diameter, and (b) particle initial distribution curve based on diameter. with the calculated R 2 value is 0.8753. The calculated third order polynomial analytical equation can be used for the validation purpose as it fits nicely with the present results. The analytical equations can also be used to predict the overall deposition pattern for a large scale model. Figure 3 displays the polydisperse particle deposition pattern for a 17-generation whole lung model by examining the entire possible branching pattern. A wide range of micro-diameter particles (1 μm ≤ dp ≤ 10 μm) is considered in the present study, in which diameter is shown in different sizes and colours. Figure 3(a,c) show polydisperse particle deposition scenario for 9 lpm and 60 lpm flow rates respectively. Figure 3(b) shows enlarged deposition in the right upper lobe and part of the right middle lobe. Figure 3(d) shows the deposition pattern in the bifurcation area of the upper airway. The overall deposition pattern shows higher deposition concentration in the first few generations. At the 9 lpm flow rate, a lesser number of larger diameter particle (d p > 5 μm) are deposited in the bifurcation area of the first and second generation compared to 60 lpm flow rate. Figure 3(b) shows a significant number of particles deposited in the bifurcation wall at the 9 lpm flow rate. For the 60 lpm flow rate, on the contrary, a significant amount of larger diameter (d p > 7 μm) particles are deposited in the bifurcation angle of the first and the second generation than in the 9 lpm flow rate. Figure 3(d) illustrates that fewer particles are deposited in the tracheal wall and the bifurcation wall at the 60 lpm flow rate. The enlarged deposition example also shows that smaller diameter particles are deposited mainly in the bifurcation wall, not at the carinal angle. Figure 3(a,d) show a noticeable amount of smaller diameter particles (d p < 5 μm) deposited at the terminal airways for both flow rates. Moreover, a significant number of smaller diameter particles (d p < 5 μm) are deposited at the terminal airways of the 17-generation model in the 25 lpm flow rate; the deposition figure can be found in the Supplementary Section. The reason for this type of deposition is microparticle inertia, and the inertial impaction is the dominant mechanism. With increased particle diameter, the momentum relaxation time τ m = ρ p d p 2 C s /18μ significantly increases and inertia becomes the vital component for the deposition 32 . Because of the higher inertia, larger diameter particles are deposited at the carinal angle area. A detailed discussion of the mechanism can be found in the authors' previous work 6 . Inertial parameter (IP) can be defined as; where ρ is the density, d p is the particle diameter and Q is the flow rate. According to eqn. 4, inertial parameter value is increased regardless of flow rate and particle diameter. The inertial parameter value is significantly higher with a higher flow rate and larger diameter particles, which ultimately indicates that inertial impaction is dominant for larger diameter particles and high flow rates. To investigate the polydisperse particle deposition hot spot, deposited particle concentration curve has been calculated. The density curve and the detail discussion can be found in the Supplementary Section.
For better understanding of the polydisperse particle deposition, DE in the right lung and left lung has been investigated and third order analytical polynomial equations are derived from the DE curve. The detail discussion and the developed equations can be found in the Supplementary Section. Figure 4 shows the lobar DE of a polydisperse particle for different flow rates. The DE for various diameter particles in the five different lobes is calculated. Figure 4(a) shows the lobar DE for a 9 lpm flow rate; different colours represent various lobes. The overall deposition DE shows higher deposition at the right upper lobes and lower deposition at the left upper lobes. The overall DE trend at the different lobes is fluctuating, which could reveal the size-specific deposition pattern at different lobes. Figure 4(a) shows that larger diameter particles are deposited mainly at the right upper lobes. Figure 4(a) also shows that the deposition concentration of 4 μm ≤ d p ≤ 6 μm diameter particles are higher at the right lower lobes. However, for a 9 lpm flow rate, particles ranging from 6 μm ≤ d p ≤ 8 μm diameter are deposited mainly at the left lower lobes. The DE curve also illustrates that for lower flow rates, 6 μm and 7 μm diameter particle deposition concentrations are higher at the right middle lobe. Figure 4(b) shows the lobar deposition pattern for different diameter particles in five different lobes at 25 lpm flow rates. The overall deposition pattern shows higher DE at the right upper lobe and lower DE at the left upper lobe. Figure 4(c) shows that the DE at the right lower lobe is higher, and lower at the left upper lobe. Figure 4(c) shows that the DE at the left upper lobe decreases with increased particle diameter; the main reasons for this are gravitational force and the anatomical structure of the left upper lobe. Because of gravity and the higher inertia of the microparticle, fewer micro-diameter particles enter into the left upper lobe. The lobar deposition density comparison for different diameter particles reveals different deposition hot spots for various lobes, as shown in Fig. 5. At the right upper lobes, upper generations are the deposition hot spots and 10-μm diameter particle deposition concentration is higher than in particles of different diameters. On the contrary, the deposition density of the 7 μm ≤ d p ≤ 9 μm diameter particle is higher at the upper generation of the right middle lobe. Figure 5(d) shows different deposition hot spots at the left upper lobe for particles of different diameters. Table 2 shows deposition hot spot for different diameter particle at 9lpm flow rate. The lobe-specific deposition concentration comparison for polydisperse particles significantly increases understanding of the pharmaceutical particle deposition pattern at the terminal airways, which could advance respiratory health risk assessments.

Conclusions
A comprehensive air flow particle TD study has been performed in this study. The present large-scale respiratory model illustrates detail polydisperse particle TD for different flow rates using the Rosin-Rammler diameter distribution technique for polydisperse particle injection. The following conclusions can be drawn from the resulting study: • Total flow rate distribution at the right lung is 1.3 times higher than that in the left lung and the total flow rate distribution at the lower lobes is higher than in the upper lobes. Specifically, minimum flow rate percentage is at the right middle lobe. • Larger particle (d p > 5 μm) deposition concentration is higher at the bifurcation area (carinal angle) of the first couple of generations, whereas smaller diameter particle (d p < 5 μm) deposition concentration is higher at the bifurcation wall of the anatomical model. • DE efficiency of the polydisperse particle is higher in the right lung than in the left lung, regardless of the flow rates. The present CFD study is the first comprehensive approach to demonstrate the polydisperse particle TD in different lobes of a large scale vasculature tree. The advanced CFD model performed inclusive lobar deposition and found different deposition hot spot for various deposition parameters. The present model developed new analytical equations for the deposition in the right lung, left lung and different lobes, which would potentially provide overall deposition understanding for a large scale model. The detail flow rate distribution calculation at different lobes will contribute to knowledge of air flow transport for a whole lung airway. Numerical predictions offer proven approximation of therapeutic aerosol particle deposition in the terminal airways of different lobes, generated from nebulizers, dry power inhalers and metered dose inhalers. The complete lobe-specific polydisperse particle TD study, together with clinical observations, will increase knowledge of site-specific drug delivery into the lower airways and the alveolar region of the lung. Detailed numerical prediction for lobar deposition will aid the pharmaceutical industry in the design of more efficient lobe-specific drug delivery and potentially advance the entire drug delivery sector. A more advanced, patient-specific case study will follow.