CFD Modelling of Air Flow and Fine Powder Deposition in the Respiratory Tract

CFD modelling of air flow and fine powder deposition in the respiratory tract

Yun Hwan Kim

A thesis in fulfilment of the requirements for the degree of Master of Philosophy

School of Materials Science and Engineering Faculty of Science

April 2017

THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet

Surname or Family name: Kim

First name: Yun Hwan Other name/s:

Abbreviation for degree as given in the University calendar: M.Phil.

School: School of Materials Science and Engineering Faculty: Science

Title:

CFD modelling of air flow and fine powder deposition in the respiratory tract

Abstract

This project was to investigate and observe characteristics of micro particles suspended in the ambient air or pharmaceutical aerosols with respect to the mechanisms of deposition in human airways under different inspiratory conditions. Such determination includes pattern observations of inspiratory flow-field of the air, particle trajectory during inspiratory conditions and particle deposition. Computational fluid dynamic (CFD) was employed to simulate above problems, aiming to observe flow-field of the inspiratory air and characteristic of flow turbulence in the respiratory tract as well as particle behaviour in the respiratory tract regarding to the particle deposition. In order to do so, three different airway models were employed for the simulations: two realistic airway models introduced by Kitaoka and Weibel airways model. The motion of micro-sized particles between 1~20 µm were simulated under the steady state two inlet- inspiratory conditions – inhalation condition (60 L/min) and breathing condition (18 L/min); to evaluate deposition efficiency. Inertial impaction was dominantly caused high density deposition of particles in upper tracheobronchial region, particularly in regions where daughter airways bifurcate. Results also showed that the velocity in the first bifurcation of airway was higher than the inlet velocity. Back pressures were been observed in lower generations, and high pressures were been observed at every bifurcation regions. The increase of velocity was observed where the fluid directions rapidly changed. Turbulence kinetic energy was the least in main bronchus of respiratory tract and fluctuated from generation to generation. In Kitaoka’s generation 0-7 model, deposition fractions of 2 µm, 6 µm and 10 µm particles were 6.6%, 60.7% and 91.5% respectively under inhalation condition whereas deposition fractions of such particles were 2.9%, 9.0% and 44.9% under breathing condition. In Kitaoka’s generation 0-11 model, deposition fractions of 2 µm, 6 µm and 10 µm particles were 30.9%, 80.1% and 99.8% respectively under inhalation condition whereas deposition fractions of such particles were 16.2%, 24.4% and 62.6% under breathing condition. Furthermore in Weibel’s generation 3-6 model, deposition fractions of 2 µm, 6 µm and 10 µm particles were 9.7%, 38.3% and 97.4% respectively under inhalation condition whereas deposition fractions of such particles were 3.2%, 15.6% and 56.2% under breathing condition.

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ORIGINALITY STATEMENT

‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’

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ACKNOWLEDGEMENT

First of all, I would like to greatly thank my LORD Jesus Christ, for giving me the opportunity allowing me to undertake the great piece of research under the great supervisor, Professor Runyu Yang, for the purposes of fulfilling His great plan in my life.

Also, I was so blessed to have tremendous support from my parents and friends. I would not be standing at where I am without your endless understanding and encouragements.

“The fear of the LORD is the beginning of the knowledge, and the heart of the discerning acquires knowledge, for the ears of the wise seek it out.”

– King Solomon’s Proverbs –

ABSTRACT

This project had the objective to investigate and observe characteristics of micro particles suspended in the ambient air or pharmaceutical aerosols with respect to the mechanisms of deposition in human airways under different inspiratory conditions. Such determination includes pattern observations of inspiratory flow-field of the air, particle trajectory during inspiratory conditions and particle deposition. All those results are relevant to diversified fields as its applicable scope is not limited to the pharmaceutical aerosol devices development but also to the environmental study and combustion development.

Computational fluid dynamic (CFD) was employed to simulate above problems, aiming to observe flow-field of the inspiratory air and characteristic of flow turbulence in the respiratory tract as well as particles behaviour in the respiratory tract regarding to the particle deposition. In order to do so, three different airway models were employed for the simulations: two realistic airway models introduced by Kitaoka and one idealised airway model based on the morphological study of Weibel that was widely utilized for both numerical and experimental studies of particle deposition in human airways. Two realistic airway models of Kitaoka correspond to generation 0-7 and 0-11 respectively, whereas the idealised airway model corresponds to generation 3-6. Those three airway models are a portion of upper tracheobronchial region which the boundary of realistic airway models both start from trachea whereas idealised airway model starts from bronchiolus. Generation 0-7 and 0-11 model corresponds from trachea to 7th airway bifurcations and from trachea to 11th airway bifurcations in tracheobronchial region respectively, and generation 3-6 model corresponds to an airway portion from 3rd airway bifurcation to 6th airway bifurcation.

The motion of micro-sized particles between 1~20 µm were simulated under two inlet- inspiratory conditions – induced inhalation condition (60 L/min) and normal breathing condition (18 L/min) to evaluate deposition efficiency. The flow-field and fluid momentum generated in realistic airway models under both conditions have shown direct influence to the motion of the inhaled particles. Inertial impaction was dominantly caused high density deposition of particles in upper tracheobronchial region particularly in regions where daughter airways bifurcate. Results also have shown that iii

the velocity in the first bifurcation of airway was higher than the inlet velocity. Back pressures were been observed in lower generations, and high pressures were been observed at every bifurcation regions. Fluid velocity gradually decreased toward the outlets and the increase of velocity was observed where the fluid directions rapidly changed. Turbulence kinetic energy was shown to be the least in main bronchus of respiratory tract and fluctuated from generation to generation.

Furthermore, the aerodynamic sizes of particles were also highly related to the variation of deposition efficiency, as greater size particles caused higher rate of particle deposition. In generation 0-7 realistic airways model, deposition fractions of 2 µm, 6 µm and 10 µm particles were 6.6%, 60.7% and 91.5% respectively under inhalation condition, whereas deposition fractions of such particles were 2.9%, 9.0% and 44.9% under breathing condition. In generation 0-11 realistic airways model, deposition fractions of 2 µm, 6 µm and 10 µm particles were 30.9%, 80.1% and 99.8% respectively under inhalation condition, whereas deposition fractions of such particles were 16.2%, 24.4% and 62.6% under breathing condition. Furthermore in generation 3- 6 idealised airways model, deposition fractions of 2 µm, 6 µm and 10 µm particles were 9.7%, 38.3% and 97.4% respectively under inhalation condition, whereas deposition fractions of such particles were 3.2%, 15.6% and 56.2% under breathing condition. This indicates that the micro-sized particles most likely undergo inertial impaction in upper tracheobronchial region when they are inhaled, by depositing on the wall of bifurcation region and the bottom wall of downward airways. Higher particle deposition rates are likely occurred during induced inhalation condition, whereas particles are comparatively less deposited during breathing condition. Gentle inspiratory condition with lower flowrate may lead to have lower particle deposition rate in airways when particle inhaler is in use.

Results comparisons between idealised airway model and realistic airway models have shown the similar patterns including flow-field, particle trajectory and particle deposition. However, idealised airway model provides better observation of local concentration of deposition whereas realistic airway models provide better observation of global status of deposition concentration in upper tracheobronchial region. If geometrical reliability is considered, realistic airway model suggests better solutions in comparison to the idealised airway model.

NOMENCLATURE

퐴 Cross-Sectional Area of the particle

퐶푐 Cunningham Slip Factor

퐶푑 Drag Coefficient

퐷 Cross-Sectional Diameter of the Airway

푑 Cross-Sectional Diameter of the Particle

퐹푑푟푎푔 Drag Force

퐹푒푙푒푐푡푟푖푐 Electric Force

퐹푒푙푒푐푡푟표−푠푡푎푡푖푐 Electro-Static Force

푓 Frequency of the Inspiration

푔 Gravitational Constant

푚 Mass of the Particle

푁퐺푒푛푒푟푎푡푖표푛 Number of bronchial tree branches at generation

푁 Total number of input particles

푛 Number of particles entered into the targeted region

푞, 푞1 표푟 푞2 Electric Charge

푟 Distance between two charges

푈0 Fluid Velocity

푉푟푒푙 Particle Velocity relative to the Fluid

푉푝 Particle Velocity

푉푓 Fluid Velocity

퐹푟 Froude Number

푅푒 Reynolds Number

푆푡 Strouhal Number

푠푡푘 Stokes Number

훼 Womersley Number

휌 or 휌푎푖푟 Air Density

휌푝푎푟푡푖푐푙푒 Particle Density

휇 Dynamic Viscosity of the air

휏 Inhalation/Inspiration Duration

푣 Kinematic Viscosity of the air

휀0 The permittivity of free space constant

휏푟푒푙 Particle relaxation time

휆 Mean free path of molecules in the air

휂푑푒푝표푠푖푡푖표푛 Deposition Efficiency

ABBREVIATION

CFD Computational Fluid Dynamic

COPD Chronic Obstructive Pulmonary Disease

DDPM Dense Dispersed Phase Model

DEM Discrete Element Method

DNS Direct Numerical Simulation

DPI Dry Powder Inhaler, Dry Powder Inhalation

DPM Discrete Phase Model

FTLE Finite-time Lyapunov Exponent

ICRP International Commission on Radiological Protection

KG7 Kitaoka realistic airway model in generation 0–7

KG11 Kitaoka realistic airway model in generation 0–11

LES Large Eddy Simulation

LRN Low Reynolds Number

MDI Metered Dose Inhaler

NS Navier-Stokes

PIFR Peak Inspiratory Flowrate

RANS Reynolds Averaged Navier-Stokes

SMI Soft Mist Inhaler

TUI Text User Interface

UDF User Defined Function

WHO World Health Organisation

WM Weibel idealised airway model in generation 3–6

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TABLE OF CONTENTS

ORIGINALITY STATEMENT ...... i

ACKNOWLEDGEMENT ...... ii

ABSTRACT ...... iii

NOMENCLATURE ...... v

ABBREVIATION ...... vii

TABLE OF CONTENTS ...... viii

LIST OF FIGURES ...... xi

LIST OF TABLES ...... xvi

1. INTRODUCTION ...... 2

2. LITERATURE REVIEW...... 5

2.1 Theoretical characterisation of flow and particle deposition in respiratory tract.... 5

2.1.1 The structure of respiratory tract ...... 5

2.1.2 Conceptual respiratory tract models...... 7

2.1.3 Flow Dynamics in the Respiratory System ...... 8

2.2 Particle Deposition in the Respiratory System...... 14

2.2.1 Particle Dynamics in the Respiratory System ...... 14

2.2.2 Stokes Number & Froude Number ...... 17

2.2.3 Deposition Efficiency...... 19

2.3 CFD Modelling ...... 20

2.3.1 Governing Equations ...... 21

2.3.2 Simulation of extra-thoracic region ...... 23

2.3.3 Simulation of tracheobronchial region ...... 29

2.4 Summary ...... 39

3. CFD MODEL DEVELOPMENT OF THE RESPIRATORY TRACT SIMULATION ...... 41

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3.1 Introduction ...... 41

3.2 Numerical Model ...... 42

3.2.1 Respiratory tract geometry and discretisation ...... 42

3.2.2 CFD models ...... 45

3.2.3 Simulation Conditions ...... 48

3.3 Results and discussion ...... 49

3.3.1 Grid independence test ...... 49

3.3.2 Model validation ...... 50

3.3.3 Fluid Flow field ...... 53

3.3.4 Particle trajectory and deposition ...... 62

3.4 Conclusion ...... 68

4. COMPARISON OF THE RESPIRATORY TRACT MODELS ...... 70

4.1 Introduction ...... 70

4.2 Flow in Weibel idealised airway model ...... 71

4.2.1 Geometry creation and simulation conditions...... 71

4.2.2 Model validation ...... 73

4.2.3 Flow fields ...... 75

4.3 Comparison of flow in different models ...... 79

4.3.1 Geometry and mesh...... 79

4.3.2 Simulation conditions ...... 81

4.3.3 Comparison of flow fields ...... 82

4.3.4 Comparison of particle trajectory and deposition ...... 87

4.3.5 Deposition Efficiency...... 96

4.4 Conclusion ...... 98

5. SUMMARY AND FUTURE WORK ...... 99

REFERENCES ...... 102

Appendix A ...... 108

Appendix B ...... 110

LIST OF FIGURES

Figure 2-1: Generation creation in respiratory system (Kleinstreuer, et al., 2008) ...... 6 Figure 2-2: Bifurcation growth comparison between Finlay and Weibel's conceptual lung model ...... 8 Figure 2-3: Fluid velocity comparison between Finlay and Weibel airway model during inhalation and breathing conditions ...... 9 Figure 2-4: Comparison of dimensionless number variation against generation in the Finlay and Weibel's lung models – (a) Reynolds number; (b) Strouhal number; and (c) Womersley number ...... 13 Figure 2-5: Schematic diagram of Particle motion in fluid flow (Finlay, 2001) ...... 15 Figure 2-6: Comparison of dimensionless numbers variation against generation in Finlay and Weibel's lung model – (a) Stokes number (b) Froude number ...... 19 Figure 2-7: Streamline at Pharynx Plane, 1D from G Plane and whole airway in (a) 125 L/min case (b) 254 L/min case (Sung & Ryou, 2012) ...... 23 Figure 2-8: Enhanced condensational growth delivery of an initially 900 nm aerosol with a humidity stream temperature of 39 °C in terms of (a) trajectories and (b) deposition locations contoured according to droplet size (Longest and Holbrook, 2012)...... 24 Figure 2-9: Schematic of geometry utilized by Rahiminejad et al. (2016) to simulate respiratory airflow and pressure field during sneezing condition. Note that alphabet a ~h represent for cross section of 2D contour visualizations...... 25 Figure 2-10: This shows a 2D velocity magnitude contours at particular positions presented in Figure 2-30 during normal sneezing condition for the flowrate of 470 L/min (Rahiminejada, et al., 2016)...... 26 Figure 2-11: The male mannequin including realistic extra-thoracic region airway model was developed by Naseri et al. (2014) – (a) schematic of the computational domain (b) model of the mannequin with the attached upper airway (c) the developed 3D model of the upper airways ...... 27 Figure 2-12: Deposition pattern variation by particle size under 7 L/min inlet flowrate 28 Figure 2-13: Li (2012) employed 3 different extra-thoracic region models to compare inspiratory airflow pattern during different respiratory modes - (a) Circular model (b) Realistic model (c) Elliptic model...... 29

Figure 2-14: Mid-plane velocity vectors, static pressure, cross sectional axial velocity contours, secondary velocity vectors and static pressure with 30 l/min respiratory intensity at different times: (a) 0.2 s; (b) 0.4 s (Chen, et al., 2012) ...... 30 Figure 2-15: Particle deposition in ten-generation bronchial tube model. (a) Colour map for particle destination map, (b) particle destination map and (c) FTLE map. (Soni & Aliabadi, 2013) ...... 31 Figure 2-16: Particle (dp=10 μm) deposition comparisons in bifurcating airway model G3-G6 using two-way coupling DDPM-DEM (a) St=0.037 (b) St=0.125 (Feng & Kleinstreuer, 2013) ...... 31 Figure 2-17: Comparison between respiratory airflow streamline and particle trajectories in idealised airway model were conducted by Augusto et al. (2016). (a)~(c) are comparison between fluid streamline and 1 &10 µm particle trajectories during sleep condition, whereas (d) ~ (f) are comparison between fluid streamline and 1&10 µm particle trajectories during heavy activity condition...... 33 Figure 2-18: Particle deposition enhancement factors were presented by Longest & Holbrook (2012) in upper tracheobronchial region during inhalation flowrate of 30 L/min - (a) 40 nm, and (b) 4 µm particles (Xi, et al., 2008) ...... 34 Figure 2-19: Comparison of predicted total upper tracheobronchial deposition fractions with experimental deposition data for both nano- and micro-particles. (Xi, et al., 2008) ...... 35 Figure 2-20: Dynamic comparisons of flow field between airways with and without larynx were presented by Xi et al. (2008). Mid-plane velocity vectors, contours of velocity magnitudes, and in-plane streamlines of secondary motion for a constant inspiratory flow rate of 15 l/min in TB models with the laryngeal approximation (A), and without the larynx (B)...... 36 Figure 2-21: Particle deposition efficiency analysis: Regional comparison Deposition fraction vs Particle deameter (Kleinstreuer, et al., 2008) ...... 37 Figure 2-22: Comparison between computed and measured η (Stokes number) data for the first bifurcation of a symmetric double bifurcation (Comer, et al., 2000) ...... 37 Figure 2-23: Comparison of pharmaceutical aerosol deposition– (a) Novolizer® inhalation under 99 L/min inlet flowrate condition, and (b) Respimat® inhalation under 41 L/min inlet flowrate condition (Tian, et al., 2015)...... 39 Figure 3-1: KG7 geometry overview ...... 43 Figure 3-2: (a) mesh overview (b) mesh view on inlet (c) mesh view on outlet ...... 44 xii

Figure 3-3: discretization scheme Residuals plot of – (a) 1st order upwind and; (b) 2nd order upwind ...... 47 Figure 3-4: (a) Maximum pressure and (b) maximum fluid velocity in KG7 model plotted against number of mesh elements for grid independence test ...... 50 Figure 3-5: (a) Replica model of main bronchus airway experimental apparatus used by Chang and Osama (1982) to examine axial velocity of inspiratory airflow and; (b) Corresponding measurement positions defined in computational domain for model validation ...... 51 Figure 3-6: (a) Inlet diameter to position diameter ratio comparison between CFD domain and experimental apparatus constructed by Chang and Osama (1982) and (b) Inlet velocity to position velocity ratio comparison between CFD and experimental results ...... 52 Figure 3-7: Particular positions defined for data measurement. Note that generation 0 corresponds to the position 1...... 54 Figure 3-8: Reynolds number variation comparison between CFD results and conceptual lung models during (a) Inhalation condition (b) Breathing condition ...... 55 Figure 3-9: Flowrates variations were plotted against critical position. Note that generation 0 corresponds to the particular position 1 in Figure 3-7...... 56 Figure 3-10: Overview of pressure contour during (a) inhalation condition; (b) breathing condition ...... 57 Figure 3-11: Velocity contours of inhalation condition at positions 1~8...... 59 Figure 3-12: Velocity contours of breathing condition at positions 1~8...... 60 Figure 3-13: Inlet-to-critical positions velocity ratios were plotted against critical position. Note that generation 0 corresponds to critical position 1. Note that inlet velocities are 7.15 m/s and 2.14 m/s for inhalation and breathing condition respectively...... 61 Figure 3-14: Comparison of (a) mean pressures; and (b) turbulence kinetic energy plotted against critical positions during inspiratory conditions...... 62 Figure 3-15: 3D respiratory airflow streamline during (a) inhalation condition (b) breathing condition in KG7 airway model ...... 64 Figure 3-16: Particle trajectory variations comparison under inhalation and breathing condition...... 65 Figure 3-17: Particle deposition variations during inhalation and breathing condition. . 66

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Figure 4-1: (a) Dimension of idealised airway model presented by Augusto et al. (2016) (b) Creation of finite volume of tetrahedral mesh with prism layers near the wall ...... 72 Figure 4-2: The airway models used for Kim & Fisher (1999)’s experiment are shown above. Note that the experimental data of model (A) in the left hand side was used to validate simulation model...... 73 Figure 4-3: Deposition efficiency percentage plotted against Stokes number based on (a) experimental data conducted by Kim and Fisher (1999); and (b) the current CFD simulation...... 75 Figure 4-4: Velocity vector field at (a) first bifurcation during inhalation condition (20L/min) (b) first bifurcation during breathing condition (5.75 L/min) (c) second bifurcation during inhalation condition (d) second bifurcation during breathing condition ...... 76 Figure 4-5: 2D flow-field contour in velocity under (a) inhalation condition (b) breathing condition...... 77 Figure 4-6: Two dimensional velocity contours during inhalation condition at cross section of selected airway positions are shown...... 78 Figure 4-7: Two dimensional velocity contours during breathing condition at cross section of selected airway positions are shown...... 78 Figure 4-8: Mesh overview of (a) KG7 model; (b) KG11 model; and (c) WM model. . 81 Figure 4-9: 3D velocity vector field in KG7 model during (a) inhalation condition (b) breathing condition...... 84 Figure 4-10: 3D velocity vector field in WM model during (a) inhalation condition (b) breathing condition...... 85 Figure 4-11: 3D velocity vector field in KG11 model during (a) inhalation condition (b) breathing condition...... 86 Figure 4-12: 3D respiratory airflow streamline during (a) inhalation condition (b) breathing condition in WM model ...... 88 Figure 4-13: WM model particle trajectory variations...... 89 Figure 4-14: 3D respiratory airflow streamline during (a) inhalation condition (b) breathing condition in KG11 model ...... 91 Figure 4-15: KG11 model particle trajectory variations...... 92 Figure 4-16: WM model particle deposition variations...... 94 Figure 4-17: KG11 model particle deposition variations...... 96

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Figure 4-18: Deposition efficiency plotted against particle size (diameter) assuming that the shape of injected particles is spherical...... 97 Figure B-1: Comparison of drag force applied to 1 µm particles during inhalation and breathing conditions. Note that the flow velocity is in µm/s...... 110 Figure B-2: Comparison of drag coefficient during inhalation and breathing condition ...... 110

LIST OF TABLES

Table 3-1: Summary of dimension – KG7 model ...... 43 Table 3-2: Maximum velocity, maximum pressure, maximum back pressure and maximum turbulence kinetic energy of each discretization schemes were compared. ... 47 Table 3-3: Dimension comparison between Finlay, Weibel and KG7 model ...... 54 Table 4-1: Comparison overview – key differences between geometries ...... 79 Table 4-2: Data summary of CFD simulation including comparison of three different airway models employed for the study of particle deposition and its efficiency is shown...... 81 Table A-1: Dimension comparison of Finaly Lung model and Weibel Lung model (Finlay, et al., 2000; Weibel, 1963) ...... 108 Table A-2: Bifurcation growth at each generation ...... 109

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Chapter 1

1. INTRODUCTION

In order to treat disease of the human pulmonary system such as asthma, bronchitis or airway stenosis, direct drug inhalation or targeting deposition technique through pulmonary airways is acknowledged as a safe and efficient method in comparison to the other drug transportation techniques.

Currently a few inhalation techniques along with intake equipment have been developed for the human pulmonary system disease treatment in the past few decades. For example, electric nebulizer is the earliest invention of a modern drug inhalation technology and it was developed in 1930s (Nikander & Sanders, 2010). Then a pharmaceutical dry powder inhaler (DPI) was introduced by Aerohaler in 1949 (Frea, 2012), In 1950s, metred dose inhaler (MDI) was introduced and commercialised in the pharmaceutical market by Riker Lab, one of 3M Corporation subsidiary (Purewal & Grant, 1997). DPI is currently classified as the most efficient way of taking pharmaceutical therapeutic agents into the pulmonary region for lung diseases treatment among the other inhalation devices. The main advantage of DPI is that its usage does not require any external propellant to transport the particle into the required region. Also, DPI can better suppress bacterial growth than other solutions. Furthermore, the superiority of chemical stability is proven for dry powder aerosols inhalation.

However, the complex structure of the human respiratory system leads to the profound effect of the air flow and particle deposition. It is globally concerned that the health issues related to the pulmonary diseases due to the particle deposition are continually increasing and rarely resolved. In accordance to those facts, in other words, the efficiency improvement of the particle deposition in the respiratory tract is currently a significant pharmaceutical issue. In fact, particle deposition in the respiratory tract can cause the severe pulmonary disease such as a chronic obstructive pulmonary disease (COPD), airway stenosis or even a cancer. COPD, according to the World Health Organization, was the fourth major factor of lung disease death globally in 2008 and

will predictably be stepping up to the third leading factor of death due to lung disease by 2030 (WHO, 2008).

Another major circumstance causing respiratory diseases can be occurred due to the bad quality of ambient air which is drastically becoming worse in accordance to countries’ level of commercial exploitation and industrial development. According to the data shared by Australian Bureau of Statistics (ABS), majority of Australian death-causes are mostly shared by various acquired diseases (ABS, 2015). Australian death due to respiratory diseases was continuously ranked on 3rd in the past few decades. However, it is remarkable to observe that the fluctuation of their growth rates is relatively greater in comparison to the other utmost death causes. Furthermore, according to the data posted by WHO, approximately 31 million people are being fallen victim solely due to respiratory diseases (WHO, 2013).

Global air quality dilemma, improvement failure of respiratory disease death and demand of pharmaceutical aerosol inhaler technology consequently led to increase a rigorous research interest on the particle deposition in human pulmonary system. However, the prospects for coming years remain still dismal due to projections of futurists on this problem. Currently many of particle deposition in silico model using simplified lung geometries have been conducted showing local deposition phenomenon of discrete part of the lung. Diversified approaches are highly required to study this problem and many different ideas need to be attempted. Therefore, this research will directly support pharmacodynamical improvement of DPI, targeting deposition technology, development of oral filtration equipment and the study of COPD treatment.

This project has the objective to understand how inhaled particles deposit in the respiratory tract. Through having insight of geometry of the respiratory tract, fluid dynamics and the particle trajectory in the respiratory tract, such understandings can be achieved. The specific aims include:

 To understand the natural phenomenon of flow field of the inhaled/inspired air in the respiratory tract; then,  To observe how the particle behave to deposit in the respiratory tract when the particle is suspended in the flowing fluid; and  To investigate the particle deposition efficiency variation.

This project was conducted using the computational fluid dynamics (CFD) simulation which is able to provide detailed flow and particle dynamics under various conditions.

The thesis consists of the following chapters: In Chapter 2, literature review of mechanism of particle deposition and recent research in relation to the particle deposition in respiratory tract are discussed.

In Chapter 3, the CFD model development is mainly focused on, including comparison of viscous model, grid independence test, boundary conditions, model validation and initial results of CFD simulation.

In Chapter 4, another two different airway models are adopted in order to compare with original airway model employed in the previous chapter. Inspiratory airflow field, particle trajectory and particle deposition of three different models are compared.

In Chapter 5, key outcomes of CFD results in adopted airways model are outlined and the possible future works are suggested.

Chapter 2

2. LITERATURE REVIEW

The objective of this chapter is to review the fundamental mechanisms of particle motion in correlation to the inspiratory airflow through the respiratory tract during inspiratory condition. Since the complex geometry of human airways is a significant factor of the particle deposition, this review begins with the discussion of the respiratory tract structure, followed by fluid dynamics in the respiratory tract. Then, motion of particles in human airways during inspiratory conditions and deposition factors are reviewed. Furthermore, the previous studies of CFD simulations of particle deposition in the respiratory tract are discussed.

2.1 Theoretical characterisation of flow and particle deposition in respiratory tract

2.1.1 The structure of respiratory tract Particle deposition and their transportation are significantly influenced by the geometry of respiratory tract (Hussain, et al., 2011).

Figure 2-1 shows a schematic of human respiratory system which consists of trachea, main bronchus, lobe bronchus and terminal bronchus. Human pulmonary system can be divided into the upper respiratory tract and the lower respiratory tract by its orientation. The respiratory tract consists of multiple airways, and the air transports through hollow airways into the distal part of the lung and alveolus where the phase exchange of the air occurs. Those multiple structures are classified as particular regions depending on their functions: the extra-thoracic, tracheobronchial and alveolar regions, which will be discussed briefly below. Generation number as shown in Figure 2-1 is a scheme creation for identifying the ramification of the human airways by numbering each bifurcation from the trachea (generation 0) to terminal alveoli in alveolus (generation 23), thus the portion of the airways between two bifurcation is called generation (Weibel, 1963; Finlay, 2001; Augusto, et al., 2016).

Figure 2-1: Generation creation in respiratory system (Kleinstreuer, et al., 2008)

 Extra-thoracic Region The extra-thoracic region is the entrance of the human respiratory tract being the earliest protecting region against the inhalation of toxic particulate matters (Cheng, 2003). It was previously found that the pharmaceutical aerosol deposition in this region from devices such as DPI or MDI can cause adverse transport efficiency and drug dosage (Clark, et al., 1998; Cheng, et al., 2001a; Cheng, et al., 2001b).

 Tracheobronchial Region Tracheobronchial region consists of the trachea and main bronchus followed by continuous bifurcations. The cross-sectional shape of conducting airways is similar to the cylindrical pipe and the cross sectional diameter gradually becomes narrower towards alveolar region.

 Alveolar Region Together with bronchial branches, alveolar region is called the lung consisting alveolar ducts and alveolus which are entirely covered by alveoli. The gas exchange occurs in this region; so the alveoli cells change the inspired oxygen to carbon dioxide.

2.1.2 Conceptual respiratory tract models To investigate the particle deposition and the air flow characteristic and the respiratory tract it needs to be parametrized. The human respiratory tract is classified into three anatomical regions.

The airway bifurcations starting from the trachea (main bronchus) to the alveoli can be divided up to 23 generations, as shown in Figure 2-1. Weibel (1963) has developed a numerical concept of human lung through his morphological study of respiratory tract, suggesting volume and cross-sectional diameter of airways in each generations as shown in Table A-1 of Appendix A. In his morphometric investigation of human lung, it was assumed that human airways continuously bifurcate from trachea to the alveoli. The concept of generation number is employed to approximate total number of bifurcations in human lung. Finlay (2001) has further studied about human lung morphology based on Weibel’s investigation and has introduced a smoothened conceptual airway model as shown in Table A-1 of Appendix A. In his work, the data of airway volume in each generation are idealised from Weibel’s lung model. Finlay’s conceptual lung model is an idealised model having smoothened dimensions while keeping original structures and volumetric data of Weibel’s lung model. Figure 2-2 shows the concept of bifurcation generation comparison between Finlay and Weibel’s lung models. In this figure, plot of bifurcation number growth of Finlay and Weibel’s idealised airway models against generation numbers are presented. Total number of bifurcated airway branches of Finlay’s lung model is approximately 70 million showing a rapid growth rate at generation 15. Similarly, total number of bifurcated airway branches in Weibel’s lung model is approximately 58 million indicating an abnormal growth rate between generations 18 to 19.

The lung capacity can be varied from individual to individual depending on the age, medical condition, gender and height and/or weight. However, both Finlay and Weibel’s lung model assume that the average volumetric capacity of typical adult human lung during normal breathing condition is approximately 3000 cc. This excludes the volume of the extra-thoracic region. Generation 0 is the trachea at the end of larynx in upper respiratory tract. A cross sectional area of typical adult man’s larynx has a nozzle shape and is relatively small as it is approximately 1 cm2 , and diameter is approximately 0.5~1.0 cm (Cheng, et al., 1997; Stapleton, et al., 2000). This is because,

as the entrance of airways start at larynx and during inspiration or expiration, epiglottis can be either closed or opened to prevent foods entering through the oral cavity that may cause blockage of the airway. The airway diameter becomes 50% larger at the trachea, and is gradually narrowed as the generation number is increased. 1.0E+08 Weibel model

1.0E+07 Finlay model 1.0E+06

1.0E+05

1.0E+04

1.0E+03

1.0E+02

Number of Bifurcations ofNumber 1.0E+01

1.0E+00 1 3 5 7 9 11 13 15 17 19 21 23 Generation Figure 2-2: Bifurcation growth comparison between Finlay and Weibel's conceptual lung model

The number of bifurcated daughter airways in each generation is calculated based on the data of accumulative volume and dimension of each generation, which is shown in Table A-1 and Table A-2 of Appendix A.

2.1.3 Flow Dynamics in the Respiratory System Based on Weibel and Finlay’s models, the fluid characteristics in the respiratory tract can be analysed. In the analysis, the density of air is assumed to be constant throughout the inspiratory condition. The atmospheric condition is at 1 atmospheric pressure and the temperature is normally between room temperature and human body temperature.

Experimental measurements were conducted by Cheng et al. (1997) to determine inspiratory flowrates during inhalation and breathing conditions. Steady-state flowrates of inhalation and normal tidal breathing conditions are assumed to be 60 L/min and 18 L/min respectively (Finlay, 2001). Figure 2-3 shows velocity variation in the two lung models plotted against each generation. Inlet velocity in the Finlay model during inhalation and breathing conditions at trachea are 3.76 m/s and 1.13 m/s respectively. Similarly, inlet velocity in Weibel model during inhalation and breathing conditions at trachea are 5.38 m/s and 1.61 m/s respectively. The velocity of outlets in generation 23 alveoli in Finlay model during inhalation and breathing conditions are 5.81 × 10−4m/s

and 1.74 × 10−4 m/s respectively. Also, the velocity of outlets in generation 23 alveoli in Weibel model during inhalation and breathing conditions are 3.29 × 10−4m/s and 9.88 × 10−5m/s respectively.

In both models, the fluid velocity tends to gradually decrease toward the alveolar region during both respiratory conditions. Fluid velocity is higher at the upper tracheobronchial region, since the number of bifurcation is the least and cross sectional area of a single airway is larger than the one at distal part of the lung. Therefore, fluid velocity in the respiratory tract is inversely proportional to the number of bifurcation growth and the fluid velocity is the lowest at which the number of bifurcation of bronchial airway is the highest.

Velocity decrease rate is the highest at the upper tracheobronchial region followed by the lower tracheobronchial region and the alveolar region. Target efficiency of particle delivery is expected to be comparatively low if targeting deposition is required at the alveoli, due to the weakness of the fluid velocity. In other words, harmful particulate matter such as fine dusts or soot particles can be highly deposited at the lower tracheobronchial region or entrance of alveolar region. Fluid velocities at the alveoli of both inhalation/breathing conditions are relatively low in comparison to the inlet fluid velocity at the trachea.

1.0E+01 Inhalation (Finlay)

Breathing (Finlay) 1.0E+00 Inhalation (Weibel)

Breathing (Weibel) 1.0E-01 Upper tracheo-

bronchial region Alveolar region

m/s 1.0E-02 Lower tracheobronchial region

1.0E-03

1.0E-04 0 4 8 12 16 20 24 Generation Figure 2-3: Fluid velocity comparison between Finlay and Weibel airway model during inhalation and breathing conditions

Three dimensionless numbers can be used to characterise the flow: Reynolds number, Strouhal number and Womersley number.

Reynolds number is the ratio of inertia force and viscous force given by

휌푈퐷 푅푒 = (2-1) 휇 where 휌 and 휇 are fluid density and viscosity respectively. Reynolds number is also used to determine whether the flow is turbulent or laminar.

Strouhal number is a dimensionless number of the ratio of centrifugal force and inertia force. Therefore, it determines fluid flow oscillation and is a measurement of significance of unsteady term in relation to the convective term, given by

휏푈 푆푡 = (2-2) 퐷 where τ is the inhalation time or inspiration time that represents the period of inhalation or inspiration, depending on the inspiratory condition. By assuming that breathing period is typically 3 to 5 seconds, 5 seconds of τ is selected to calculate Strouhal number. U and D are velocity of the fluid and cross-sectional diameter of the airway respectively.

Womersley number is to determine the significance of the unsteadiness in comparison to the viscosity of the fluid flow (Womersley, 1955), given by

푅푒 훼 = √ ⁄푆푡 (2-3) where Re and St are Reynolds number and Strouhal number respectively.

Figure 2-4 shows Reynolds number, Strouhal number and Womersley number variations through each generations of bifurcation for both models using velocity data obtained from inhalation and breathing flowrates.

Figure 2-4 – (a) shows Reynolds number variation in both models under two respiratory conditions. Since turbulent flow likely occurs at Reynolds number of greater than 2000, both Finlay and Weibel’s lung model manifested that the flow is turbulent in upper

tracheobronchial region where generation number is between 0–8 during inhalation condition. Maximum Reynolds number of inhalation condition at trachea of Finlay and Weibel’s lung model are approximately 4000 and 5000 respectively. Transition between turbulent and laminar flow in both Finlay’s and Weibel’s model is shown in generations 2 to 3. Maximum Reynolds number of breathing condition at trachea in Finlay and Weibel’s lung model are approximately 1200 and 1500 respectively. Therefore, since the influence of turbulent flow is comparatively insignificant during inhalation condition at trachea, turbulence of airflow in the extra-thoracic region is also insignificant during breathing condition. Rate of decrease of Reynolds number is also the highest at this region.

In fact, experimental observation of flow characteristic in the respiratory tract has indicated that the turbulent flow generated at the extra-thoracic region to trachea drastically decays due to the convection into the distal part of the lung (Simone & Ultmann, 1982; Ultmann, 1985). Also, Finlay has verified that the turbulence of flow is originally generated at the extra-thoracic region and continues until the trachea, and then it may be convected into the entrance of the lung at lower tracheobronchial region (Finlay, 2001). Thus the decay of Reynolds number towards the distal part of the lung is valid.

Figure 2-4 – (b) shows comparison of Strouhal number under inhalation and breathing condition in both Finlay and Weibel’s lung models. In Finlay’s lung model the highest Strouhal number is manifested at lower tracheobronchial region. Strouhal number is high in the region of trachea, and therefore it is predictable that Strouhal number at the extra-thoracic region is comparatively higher than Strouhal number at the alveolar region, but not as high as at lower tracheobronchial region. Also, unsteadiness of the fluid flow is seemed to be insignificant at tracheobronchial region, since comparatively high Strouhal number can be observed.

In Weibel’s lung model, the highest Strouhal number is observed at upper tracheobronchial region. Strouhal number is then gradually decreased as generation number is increased. Variation of inhalation and breathing condition are the same in both Finlay and Weibel’s lung model. Unsteadiness of the fluid flow by inhalation or breathing condition flowrate is significant in the alveolar region since relatively low Strouhal number can be observed. However, it is previously noted that the unsteady

term in NS Equation is relative to the convective term, and since Reynolds number at the alveolar region is also comparatively lower than Reynolds number at tracheobronchial region (both upper and lower regions), unsteadiness of the flow at alveolar region also can be insignificant. Rather than that, viscosity of the flow in relation to the unsteadiness of the flow can be more significant in the alveolar region.

The increase of daughter airways bifurcated in each generations directly influences to the increase of sum of cross sectional diameter of airways in each generation. Also, the fluid velocity of inhaled air continuously decreases with generation due to the nature of exponential growth of number of daughter airways. Therefore, the fluid velocity and sum of cross sectional diameter variations in each generation consequently affect to the Strouhal number decrease.

Figure 2-4 – (c) shows Womersley number variation of both Finlay and Weibel’s lung models. The highest Womersley number can be observed at the upper tracheobronchial region, and so is predictable that high Womersley number is likely to be at the larynx in the extra-thoracic region. Maximum Womersley number in Finlay’s lung model is approximately 2 whereas in Weibel’s lung model it is approximately 1.7. On the other hand, minimum Womersley number of Finlay’s lung model is approximately 0.0007 whereas of Weibel’s lung model is approximately 0.0015.

Therefore, the unsteadiness of the flow in the respiratory tract is insignificant during inhalation or breathing condition in comparison to the viscous or convective term of both lung models. In other words, unsteady term of the air flow is not significant for aerosol inhalation of DPI, if compared with an influence of viscosity or convection of the flow, and this can be a primary fact of particle deposition participation in the human respiratory system in accordance to the fluid dynamics.

1.0E+04 Inhalation (Finlay) 1.0E+03

Breathing (Finlay) 1.0E+02 Inhalation (Weibel) Breathing (Weibel) 1.0E+01 Upper tracheo-bronchial region 1.0E+00 1.0E-01 Lower tracheo-bronchial

region Reynolds number Reynolds 1.0E-02 Alveolar region 1.0E-03 0 4 8 12 16 20 24 Generation (a)

1.0E+04 Inhalation (Finlay)

Breathing (Finlay)

1.0E+03 Inhalation (Weibel) Breathing (Weibel) 1.0E+02 Upper tracheo-bronchial Lower tracheo-bronchial region region

1.0E+01 Strouhal number Strouhal

Alveolar region 1.0E+00 0 4 8 12 16 20 24 Generation (b)

2 Finlay Model

Weibel Model

Lower tracheo-bronchial region 0.2 Alveolar region

Upper tracheo-bronchial

region Womersley number Womersley

0.02 0 4 8 12 16 20 24 Generation (c)

Figure 2-4: Comparison of dimensionless number variation against generation in the Finlay and Weibel's lung models – (a) Reynolds number; (b) Strouhal number; and (c) Womersley number

2.2 Particle Deposition in the Respiratory System When pharmaceutical aerosols or particulate matters inhaled through the respiratory system, particles traveling through the airways do not always follow the streamline of the fluid flow, and consequently certain amount of particles undergo deposition. There are several factors causing particle deposition. Particles in the respiratory tract are most likely influenced by inspiratory air flow pattern.

Furthermore, the size of particles from therapeutic aerosol can vary due to the atmospheric condition such as rapid change of surrounding temperature or humidity, since the particle in therapeutic aerosol in the inhaler once is at a room temperature and suddenly temperature and surrounding humidity change when those are inhaled. In fact, the size of aerosol powder particles such as Cromolyn Sodium in DPI observed to be raised approximately 76.5% when atmospheric condition rapidly changed from room condition to the body temperature, ambient pressure and saturated with water vapour condition, since particles in the pharmaceutical aerosol are hygroscopic and it is heterodisperse in size (Smith, 1980; Hiller, 1980).

2.2.1 Particle Dynamics in the Respiratory System In order to investigate particle deposition in the respiratory tract, motion of particle trajectory is required to understand. There are two assumptions that need to make prior to discuss the particle trajectory. Firstly, although shapes of most artificial particles are not spherical, the shape of the particle is assumed to be spherical (Kleinstreuer & Feng, 2013). Secondly, density of particle is greater than the density of fluid (Barton, 1995; Crowe, et al., 1998).

As shown in Figure 2-5, the motion of micron is a function of gravitational force, drag force and electro-static force. The term 푚푔 is gravitational force, 퐹푑푟푎푔 is drag force,

퐹푒푙푒푐푡푟푖푐 is electric force and 퐹푒푙푒푐푡푟표−푠푡푎푡푖푐 is electro-static force exerted on the particle.

Figure 2-5: Schematic diagram of Particle motion in fluid flow (Finlay, 2001)

Aerodynamic effect is significant for particle motion as drag force plays a major role of particle transportation in the respiratory tract. Drag force is only non-negligible aerodynamic force on the particle. Also, the body force is only gravity and is only valid for the microns. Drag force on a particle is given by

1 퐹 = 휌 푣2 퐴퐶 (2-4) 푑푟푎푔 2 푎푖푟 푟푒푙 푑 where 휌푎푖푟, 푣푟푒푙, 퐴 and 퐶푑 are density of the air, velocity of particle relative to the fluid velocity, cross-sectional area of the particle and drag coefficient. By Crowe’s assumption based on experimental data (Crowe, et al., 1998), the drag coefficient can be calculated as

24 퐶 = (1 + 0.15푅푒0.687) (2-5) 푑 푅푒

The high drag coefficient is observed in alveolar region. Tracheobronchial region, where high Reynolds number observed, have shown that the range of drag coefficient between 0.3 to 27 under inhalation condition and 0.4 to 100 under breathing condition. Therefore drag force of the particle with 1 µm diameter in the respiratory tract have shown the highest force at the entrance of tracheobronchial region and seems to lose the force along with bifurcation generations. Drag force and drag coefficient variations against generation number are shown in Figure B-1 and Figure B-2 of Appendix B.

Electric force and electro-static force exerted the particle due to space charge is given by;

푞2 (2-6) 퐹푖푛푡푒푟푝푎푟푡푖푐푙푒 = 2 푥 16휋휀0 and,

푞1푞2 퐹푝푎푟푡푖푐푙푒−푤푎푙푙 = 2 (2-7) 푟 4휋휀0

−12 2 −1 −2 where휀0is the permittivity of free space constant, 푖. 푒. 8.85 × 10 퐶 . 푁 . 푚 , 푥 is distance between particle with charge q and the respiratory tract wall, r is the distance between particles and 푞1, 푞2 or 푞 are electric charge of particle 1 and particle 2 respectively. The electrostatic force between particle and the inner wall of respiratory tract can be occurred by charged particle itself and an electric field induced by the particle. Such an induced electric field causes the molecules in the tissues in the respiratory tract to have the dielectric effect (Finlay, 2001).

There are five different factors causing particle deposition; sedimentation, inertial impaction, diffusion, electrostatic force and interception. For microscopic particles, majority of deposition can be caused by three factors including impaction due to inertia, sedimentation and gravitational settling. If the particle size is in nano-scale then Brownian diffusion is another significant factor of particle deposition.

 Gravitational settling Gravitational settling mainly occurred due to the particle density when it is relatively larger than the fluid density. Possibility of gravitational settling may increase if size of particles is large but drag force generated by inspiratory airflow is relatively weak. If drag force is not powerful enough to carry particle agglomerates then such particles are likely deposited due to gravitational settling (Finlay, 2001).

 Impaction Another major deposition factor for micron particle is an impaction and it can be occurred by high momentum of the particle. Trajectory of particle does not always ideally follow the streamline of the fluid when direction of the fluid suddenly changed.

It is predictable that inertial impaction of the particle is likely occurred at airway bifurcation regions of the respiratory tract where the change of flow direction occurs. High deposition rate of particle deposition due to inertial impaction may be observed at the carinal ridge area of the extra-thoracic region (Finlay, 2001).

 Diffusion Brownian diffusion of the particle, an irregular motion of nano-particles that can be observed in the fluid can also be observed from sub-micron particles. Diffusion is a physical motion of particles in nano-scale that collide with randomly moving gas molecules so that a nondeterministic random walk is undergone (Finlay, 2001).

 Electro-static Force Particle deposition by electro-static force can be caused by induced electrical charge that is charged on to the inhaled particle. Electro-static force becomes significant factor in lower tracheobronchial region or distal part of the lung where inertia force is comparatively weaker than upper regions of the lung. However, similar to diffusion, this deposition factor is also relatively insignificant in comparison to sedimentation or inertial impaction for micron particles. This is because more than 43 elementary charges are needed per particle if electro-static induced charge is effective to the particle deposition (Finlay, 2001).

 Interception Interception can be occurred by the physical contact of the particle with the surface of the wall inside of respiratory tract. The particle actually follows the streamline of the fluid flow and as a result, all other particle deposition factors are negligible (Bezemer & Pieters, 2009). Thus interception is independent particle deposition factor and cannot be coupled with other factors.

2.2.2 Stokes Number & Froude Number Figure 2-6 – (a) and Figure 2-6 – (b) shows Stokes number and Froude number variations in Finlay’s and Weibel’s model respectively when aerodynamic diameter if particle is 1 µm. Stokes number is a dimensionless figure representing the particle behaviour which is embedded in the fluid flow. Particle deposition due to inertial impaction, a leading deposition factor for microscale particles in the respiratory tract, can be predicted through Stokes number. If Stokes number is greater than 1 then inertial

impaction occurs and deposition on the wall is likely to be caused. If Stokes number is less than 1 then the particle follows the streamline of the flow. In this case, gravitational settling is also negligible thus particle deposition due to sedimentation can be avoided. It is impossible to verify neither the exact position of particle deposition nor sedimentation status if Stokes number is greater than 1. Stokes number equation is shown below.

2 휏 푈 휌푝푎푟푡푖푐푙푒푈0푑 퐶푐 푠푡푘 = 푟푒푙 0 = (2-8) 퐷 18휇퐷 where, 푈0 is fluid velocity, 푑 is particle diameter, 휌푝푎푟푡푖푐푙푒 is particle density, 휇 is dynamic viscosity of fluid and,

2 휌푝푎푟푡푖푐푙푒푑 퐶푐 휏 = 푝푎푟푡푖푐푙푒 푟푒푙푎푥푎푡푖표푛 푡푖푚푒 = (2-9) 푟푒푙 18휇 and,

휆 퐶 = 퐶푢푛푛푖푛푔ℎ푎푚 푠푙푖푝 푓푎푐푡표푟 = 1 + 2.52 [푓표푟 푑 > 0.1 휇푚] (2-10) 푐 푑

Stokes number can be increased by longer particle relaxation time or smaller geometry of respiratory tract which can be found at distal part of the lung such as lower tracheobronchial region or alveolar region. However, as fluid velocity is lowest at alveolar region, matter of inertial impaction deposition in accordance to Stokes number is not significant. In the respiratory tract Stokes number is the highest at lower tracheobronchial region. Although the fluid velocity is the highest at the extra-thoracic region and upper tracheobronchial region, its Stokes number is low in comparison to Stokes number at lower bronchial region. When the fluid flow is slower the Stokes number still can increase only if the cross-sectional diameter of daughter airway in particular generation is relatively small. Furthermore, particle deposition status due to sedimentation can be predicted by Froude number. Froude number is defined as

푈2 Fr = 0 (2-11) 퐷푔 where D is cross sectional diameter of airway, and g is gravitational constant. High Froude number represents the negligibility of sedimentation conveying that a factor of

micron deposition is mainly due to inertial impaction. On the other hand, sedimentation is a main factor of particle deposition at low Froude number showing that inertial impaction is comparatively weak to be a primary factor of particle deposition in such respiratory tract regions.

1.0E-02 Aerodynamic diameter of particle = 1 µm 1.0E-03 Alveolar region 1.0E-04 Upper tracheo-bronchial region Lower tracheo-bronchial 1.0E-05 Finlay (Inhalation) region

Stokes number Stokes Finlay (Breathing) Weibel (Inhalation) 1.0E-06 Weibel (Breathing) 0 4 8 12 16 20 24 Generation (a) 1.0E+04 Aerodynamic diameter

1.0E+02 of particle = 1 µm

1.0E+00 Upper tracheo-bronchial region 1.0E-02 Lower tracheo-bronchial Finlay (Inhalation) region 1.0E-04 Finlay (Breathing)

Weibel (Inhalation) Froude number Froude 1.0E-06 Weibel (Breathing) Alveolar region 0 4 8 12 16 20 24 Generation (b)

Figure 2-6: Comparison of dimensionless numbers variation against generation in Finlay and Weibel's lung model – (a) Stokes number (b) Froude number

2.2.3 Deposition Efficiency Particle deposition efficiency is also known as deposition fraction, and it is a simple ratio of deposited particle or target reached particle against total input particle. Fundamental concept of particle deposition efficiency can be written as

퐷푒푝표푠푖푡푒푑 푃푎푟푡푖푐푙푒 휂 = (2-12) 푑푒푝표푠푖푡푖표푛 퐼푛푗푒푐푡푒푑 푃푎푟푡푖푐푙푒

The ideal case of deposition efficiency is obviously zero in upper regions of respiratory tract, where no particle deposition should have been occurred and therefore unit number or certain volume of agglomerated particles reached into the target area should be the

same as their values of injected particle. According to Zhu et al. (2014), similarly, deposition efficiency can be calculated as below.

푛 휂 = 1 − (2-13) 푑푒푝표푠푖푡푖표푛 푁

Note that n is a unit number of particles entered into the target area and N is a total number of injected particles. This equation shows the same fundamental concept as it represents the deposition fraction in percentage. The goal of using this deposition fraction is to find out what the ranges of deposition efficiencies are in the respiratory tract and where about or which region the deposition efficiencies are high or low. Also, the ultimate goal for determining the deposition efficiency would be that which deposition factors are most likely to occur at where about in the respiratory tract for certain investigation of the particle deposition efficiency. Since theoretical calculation has a limitation to define those significant information of particle deposition, in vivo, in vitro and in silico models of particle deposition in the respiratory tract is very useful. So the main purpose of this project can be narrowed down to develop and implement in silico model for investigating particle deposition efficiency, deposition factors and suspicious regions of the respiratory tract where the most inefficient deposition occurred.

2.3 CFD Modelling Observation of aerosol deposition in the respiratory tract is possible to conduct either by in vitro experiment (Chang & Osama, 1982; Kim & Fisher, 1999) using replica models of tracheobronchial airways or in vivo experiments (Griesenbach, et al., 2008; Albuquerque-Silva, et al., 2014) which a living body and external observation devices are required. Data and results obtained through those experiments may be the most trustworthy but there are absolute limitations for conducting such experiments and therefore their results can be very confined. This is because, firstly, there is a geometry scale limitation in the respiratory tract model generation to conduct in vitro, since creating a lower generations airways and observation of deposition in the microscale replica is hard to construct. Secondly, it is hard to apply various boundary conditions into replica model similar to the actual respiratory conditions. Thirdly, it is unable to characterise the flow field of the fluid or particle deposition in the respiratory tract of a living body for both in vitro and in vivo experiment. Moreover, in vivo experiments may have legal restrictions and therefore it makes hard to conduct. However, in silico

modelling of particle deposition in the respiratory tract has indisputable benefits over in vitro or in vivo experiments. Most of limitations from in vitro or in vivo experiments including limitations mentioned above can be enabled through in silico modelling. Additionally, costs and time consumption can be much saved in comparison to in vitro and in vivo experiments. Also, it is possible to carry on 3-Dimensional characterisation in in silico model, making easier to understand the behaviour of the fluid and particle in the respiratory tract during any inspiratory conditions. Flexibility is another benefit of simulation, as various experimental condition or boundary condition can be applied into it.

2.3.1 Governing Equations The fluid flow in the respiratory tract is a Newtonian fluid – an incompressible and steady channel flow with constant viscosity. The CFD governing equation, Navier Stokes (NS) equations are widely employed to solve momentum and continuity equations of Newtonian fluid in the respiratory tract.

NS equations can be transformed in various forms in accordance to the scope of application and flow conditions. The NS equations are derived from Newton’s second law; when certain force is applied to the object then its rate of change of velocity changes. In other words, the fluids’ rate of change of momentum is the same as the force exerted on the fluid. It is important to understand how NS equations can be applied to simulate the fluid flow in the respiratory tract. Also, each term comprising NS equations are required to understand how each term may influence to other terms to get an idea of the fluid characteristic. For simplicity, the vector term of incompressible flow NS equations and continuity equation in Cartesian co-ordinate system are shown. It is noted that the velocity divergence is negligible with constant properties and can be expressed as

퐷휌 = 0 (2-14) 퐷푡

휕푣 1 휇 + 푣. 훻푣 = − 훻푝 + 훻2푣 (2-15) 휕푡 휌 휌

휕푣 where 푣. 훻푣 is a convective term of the fluid and the rate of change of velocity is an 휕푡 expression of a state of the fluid, therefore the unsteady term. This term is relevant to

the Strouhal number, one of dimensionless figure that can be an index of the fluid 휇 characteristic. Similarly, 훻2푣 is the viscous term where it can be a function of 휌 Reynolds number. According to Finlay, viscosity of the fluid may be negligible at high Reynolds number, as Reynolds number determines the importance of the viscous term in relation to the convective term (Finlay, 2001). Convection of the fluid flow may also be negligible at low Reynolds number due to the proportionality of each term. Furthermore, unsteadiness of the flow in relation to the convection may be negligible at high Strouhal number, since Strouhal number determines the importance of the unsteady term in relation to the convective term. Fluid dynamics in the respiratory tract can be therefore theoretically analysed in accordance to such mechanical interpretations, which is originally derived from NS equations in terms of dimensionless numbers correlated to each term, using calculated data of Reynolds number, Strouhal number and Womersley number.

The density of inhaled air is constant and the fluid flow is well within subsonic. Thus the flow in the upper respiratory tract is considered as incompressible and turbulent flow whereas the lower respiratory tract is incompressible and laminar flow. Direct Numerical Simulation (DNS) can be employed to simulate particle depositions in the respiratory tract but DNS is defined not to be suitable for the turbulent flow analysis in complex geometry including flow field simulations using respiratory tract model, since the unsteady motion is solved to approximate all scales of turbulent flow (Cengel & Cimbala, 2006). Reynolds-Averaged Navier-Stokes (RANS) model is the time averaged NS equations to analyse turbulent flow and is widely employed to numerically analyse the turbulent flow. Two equation models such as k-ɷ model or k- model based on RANS are often used to simulate turbulent flow. However, problematic issues such as inaccuracy due to information loss are observed when RANS based models are utilized in the respiratory tract simulation. According to Ruzycki, those issues arisen by the use of RANS modelling can be reduced by employing large eddy simulation (LES) as small-scale turbulent eddies are only casted (Ruzycki, et al., 2013). It is also demonstrated that the accuracy of LES is better over the RANS model in which is used to simulate the fluid flow in accordance to the particle deposition (Matida, et al., 2003; Matida, et al., 2006).

CFD modelling of particle deposition in the respiratory tract is now widely conducted in order to investigate particle deposition factors. According to their results and observation, the particle deposition is most likely occurred in bifurcation regions, or at a stagnation point and carinal ridge, where the fluid velocity or pressure is zero and the direction of the flow rapidly changes. The result of stagnation effect is mainly observed at upper regions of respiratory tract, and the deposition factor is mainly due to sedimentation or inertial impaction. The particle deposition by diffusion or sedimentation is mainly observed at the alveolar region.

The most effective region of respiratory tract in terms of therapeutic purposes to treat COPD or asthma is tracheobronchial region where the most airway generations exist (Dolovich & Labiris, 2003). Therefore it is important to observe patterns of particle deposition as well as particle transportation and penetration through upper respiratory tract. Hence some previous CFD simulations of upper respiratory tract (i.e. the extra- thoracic region) are firstly reviewed followed by review of CFD simulations of bifurcating airways (i.e. tracheobronchial region).

2.3.2 Simulation of extra-thoracic region Sung and Ryou (2012) observed the flow field at the extra-thoracic region with two different flowrates which are 125 L/min and 254 L/min as shown in Figure 2-7. Idealised model of human airways is utilised in order to investigate the velocity distribution, secondary flow and turbulence kinetic energy. The secondary flow and turbulence kinetic energy are increased as the inspiratory flow rate is increased. On the other hand, the secondary flow is dissipated as the inspiratory flow rate is increased. However, their results have shown shortcomings of using idealised airway models.

Figure 2-7: Streamline at Pharynx Plane, 1D from G Plane and whole airway in (a) 125 L/min case (b) 254 L/min case (Sung & Ryou, 2012)

Similarly, Longest and Holbrook (2012) have simulated the particle deposition in the airways of the extra-thoracic region connected to upper tracheobronchial region. Figure 2-8 shows trajectories of the particle in this region compared with the particle deposition status with various size of the particle. Particles with diameter between 1.5~2.5 µm have mostly deposited at the upper tracheobronchial region by inertial impaction. Deposition efficiency of 1.31 % is recorded at this region. At lower airways, combination of particles with various sizes is deposited and the deposition efficiency has recorded the highest as 38 %. Since the velocity is expected to be much reduced in comparison to the upper region, it is predictable that the particle deposition is chiefly due to sedimentation for particles with larger diameter and/or Brownian diffusion for particles with smaller diameter (Longest & Holbrook, 2012).

Figure 2-8: Enhanced condensational growth delivery of an initially 900 nm aerosol with a humidity stream temperature of 39 °C in terms of (a) trajectories and (b) deposition locations contoured according to droplet size (Longest & Holbrook, 2012).

Rahiminejad et al. (2016) have used realistic the extra-thoracic region model including nasal and the oral cavity to simulate respiratory airflow and pressure field under various sneezing conditions. Figure 2-9 shows the geometrical scope for this simulation from

nasal and the oral cavity (2 outlets) to the entrance of trachea (1 inlet) where the entrance of main bronchus starts.

In their work, flowrate of sneezing condition is between 400 and 570 L/min for simulation so the respiratory airflow is defined as turbulent. The k-ɷ turbulence model was adopted and several sneezing cases including case of nose blockage, case of sneezing while mouth close, and both mouth and nose open sneezing case are simulated accordingly. Two dimensional airflow and pressure fields at particular positions of the extra-thoracic region are visualized.

Figure 2-9: Schematic of geometry utilized by Rahiminejad et al. (2016) to simulate respiratory airflow and pressure field during sneezing condition. Note that alphabet a ~h represent for cross section of 2D contour visualizations. Their main observations are the pressure and airflow velocity during sneezing. The maximum pressure reached in the extra-thoracic region during sneezing are approximately 8000 Pa, and the maximum velocity at trachea is reached to 100 m/s. The magnitude of pressure and velocity during sneezing is comparatively higher than magnitudes during inhalation or breathing condition. Also, two dimensional velocity

magnitude contours, as shown in Figure 2-10, is significant to observe, because turbulence of respiratory flow field in the extra-thoracic region directly affects possibility of particle penetration.

In terms of cross sectional shape, the extra-thoracic region has greater complexity and inconsistency in comparison to cross sectional shapes of airways in tracheobronchial region (Rahiminejada, et al., 2016). Fluid velocity is greater near the oral cavity than near nasal cavity during sneezing, if blockage is occurred neither at nose nor mouth. Fluid velocity is accelerated at position d where cross sectional area becomes narrowed, and the velocity at the oral cavity outlet is reduced in comparison to the inlet and position d. Cross sectional flow field at the extra-thoracic region is generally inconsistent as great velocity gradients are observed at each positions. Though flow field and particle deposition in upper tracheobronchial region which starts from the trachea is a major interest and concern, flow field and pressure field variation observation in the extra-thoracic region during sneezing condition is worth to consider for the purposes of simulating particle deposition as it suggests ideas of particle penetration.

Figure 2-10: This shows a 2D velocity magnitude contours at particular positions presented in Figure 2-30 during normal sneezing condition for the flowrate of 470 L/min (Rahiminejada, et al., 2016). Naseri et al. (2014) have developed the male mannequin containing realistic the extra- thoracic region of respiratory tract model (shown in Figure 2-11) to simulate deposition pattern of various size of airborne particles during several calm breathing conditions. Various particle sizes including 2, 5, 10, 20, 30 and 50 µm are tracked under different

breathing conditions with flowrates of 7, 10 and 15 L/min (Naseri, et al., 2014). The extra-thoracic geometry is subdivided to measure particle deposition fractions at each part of sub-divisions.

Figure 2-11: The male mannequin including realistic extra-thoracic region airway model was developed by Naseri et al. (2014) – (a) schematic of the computational domain (b) model of the mannequin with the attached upper airway (c) the developed 3D model of the upper airways In their study, the key observation is the particle deposition fraction variation along the position of the extra-thoracic region. The extra-thoracic region is segmented in accordance to the actual structure of human respiratory tract. Furthermore, this consists of Vestibule, Nasopharynx, Oropharynx, Larynx and Trachea. Particularly during 7 L/min inlet flowrate breathing condition, as shown in Figure 2-12, deposition fraction is significantly varies as size of particles is changed, and majority of particles greater than 10 µm are not able to pass through Larynx of the extra-thoracic region. 20 µm particles are successfully passed through Nasopharynx region where cross-sectional area is mostly narrow, but majority of 20 µm particles are deposited near nasal valve area. 30 and 50 µm particles are mainly deposited near nasal valve area but even less number of such particles are successfully reached in Nasopharynx region. Naseri et al. (2014) have clearly demonstrated particle deposition pattern in the extra-thoracic region in

accordance to the size of particle by determining deposition fraction measurements at each sub-divisional parts of the extra-thoracic region which helps to understand particle penetration through upper respiratory tract.

Figure 2-12: Deposition pattern variation by particle size under 7 L/min inlet flowrate (Naseri et al., 2014)

Another CFD simulation using the extra-thoracic region model has done by Li (2012). Particle deposition in the extra-thoracic region is numerically investigated by comparing inspiratory airflow and deposition pattern in 3 different airway models as shown in Figure 2-13. Since the purpose of Li’s work is for comparing very low inhalation profiles, 3 different inlet flowrates are employed, including 1.05, 1.65 and 15 L/min in the simulations. Low Reynolds Nnumber k-ω model is only applied to simulate 15 L/min inlet condition in accordance to the previous statement of Zhang and Kleinstreuer which reported that the respiratory airflow may change from laminar to turbulent via transitional flow near the trachea (Zhang & Kleinstreuer, 2004). Particles size range

between 0.001~5 µm are employed to observe deposition pattern during various low profile inhalation conditions. Brownian motion of particle in airway during respriatory conditions is considered particularly for submicrons by solving Brownian force into particle transport equation:

2 2 휉푗 2푘퐵 푇 (2-16) 퐹퐵푟표푤푛푖푎푛 = √ 푚푝 퐷̃푑푡 where 휉푗 is a zero mean variant form that could be calculated from the Gaussian probability density function, 푚푝 is the mass of particle, 푘퐵 is the Boltzmann constant, T is temperature, dt is the time interval for particle integration and 퐷̃ is the molecular diffusion coefficient (Li, 2012). The key finding of the work is that, for number of particles in different sizes, the highest deposition fraction could be in either circular or realistic models due to the multiple effects of the Brownian motion as well as drag force and/or gravity. Also, it is observed that greater number of submicron particles is deposited during lower flowrate as particles have occupied the oral-tracheal airway longer and therefore, more deposition is occurred due to the Brownian motion.

Figure 2-13: Li (2012) employed 3 different the extra-thoracic region models to compare inspiratory airflow pattern during different respiratory modes - (a) Circular model (b) Realistic model (c) Elliptic model

2.3.3 Simulation of tracheobronchial region Chen et al. (2012) clearly demonstrated the stagnation point of the airway bifurcation by visualising the pressure field using CFD-DPM method as shown in Figure 2-14.

Discrete phase model (DPM) is coupled with CFD in order to determine the particle motion and fluid-particle interaction. The velocity field in the airway are also shown for the observation of velocity vector variation and secondary flows.

Figure 2-15: Particle deposition in ten-generation bronchial tube model. (a) Colour map for particle destination map, (b) particle destination map and (c) FTLE map. (Soni & Aliabadi, 2013)

Feng and Kleinstreuer have introduced DEM coupling with a Dense Dispersed Phase Model (DDPM) simulation to show the interactions between the fluid, particles and wall surfaces in the respiratory tract (Feng & Kleinstreuer, 2013). Generation 3 to 6 of Weibel’s lung model is chosen for their DDPM-DEM coupled simulation to observe deposition of dense particles suspended in the air flowing in the respiratory tract. This method demonstrated the most accurate particle dynamics of high density suspension in the air which the one-way coupling of Euler-Lagrangian method cannot clearly demonstrate. Figure 2-16 shows the particle depositions with different Stokes number.

Figure 2-16: Particle (dp=10 μm) deposition comparisons in bifurcating airway model G3-G6 using two-way coupling DDPM-DEM (a) St=0.037 (b) St=0.125 (Feng & Kleinstreuer, 2013) Augusto et al. (2016) have employed DPM to simulate particle trajectory through idealised airway model as shown in Figure 2-17. Several different inspiratory conditions are adopted for the purposes of comparing variation of inspiratory airflow pattern as well as particle trajectories including sleep, resting, light activity and heavy activity condition. In their study, correlation between deposition pattern and respiratory airflow field in random portion of airways in upper tracheobronchial region are shown by comparing particle trajectory, two dimensional velocity magnitude contour and fluid

streamline. The idealised airway model, however, are designed based on Weibel (1963)’s study of human lung morphology and are widely utilized to investigate particle deposition pattern as well as respiratory flow field by many researchers, even though the absence of realistic human airway features. Such an airway is identical to the one Feng and Kleinstreuer (2013) have used for their DDPM simulation which is formerly discussed. The scope of such airway consists of generation 3 to generation 6 airways in tracheobronchial region. Results have shown that larger size of particles are more deposited than smaller size of particles during any inspiratory conditions, and the movement of particles are similar to streamlines of respiratory airflow during sleep and heavy activity conditions. Airway penetration of 6 µm or greater size particles are preferentially occurred in the first bifurcation and are likely deposited in third bifurcation region. Particles smaller than 6 µm are not successfully penetrated through the first bifurcation and are mostly deposited in the first bifurcation. One shortcoming of Augusto and their colleagues work is that if particle deposition position has been visualized in the adopted airway model then it could be more beneficial and clarified to investigate where the most particle deposition occurs in the airway.

Figure 2-17: Comparison between respiratory airflow streamline and particle trajectories in idealised airway model were conducted by Augusto et al. (2016). (a)~(c) are comparison between fluid streamline and 1 &10 µm particle trajectories during sleep condition, whereas (d) ~ (f) are comparison between fluid streamline and 1&10 µm particle trajectories during heavy activity condition.

Longest and Holbrook (2012) have discussed particle deposition investigation based on the CFD simulation results using the simplified patient specific airway model which was previously conducted by Xi et al. (2008). In their study, deposition enhancement factors for a steady state inhalation flowrate of 30 L/min were visualized with 2 different particle sizes; 40 nm and 4 µm, as shown in Figure 2-18. Particle deposition enhancement factor, which quantifies the amount of local deposition within a defined area in relation to a total deposition in the entire region, has shown that nanoscale particle generally has higher chance to be deposited on the surface of the airway than micro particles (Longest & Holbrook, 2012). Definition of deposition enhancement

factor that is initially introduced by Xi et al. (2008) and presented in Longest and Holbrook (2012) is

퐷퐸푗/퐴푗 퐷퐸퐹푗 = 푁 푁 (2-17) ∑푗=1 퐷퐸푗 / ∑푗=1 퐴푗 where 퐴푗 is the local area, 퐷퐸푗 is the regional deposition efficiency which is defined as the ratio of deposition of particles in a particular region to the particles entering into that region.

Brownian force acting on nano particles could be dominant during inhalation condition and is significant in relation to deposition factors in upper tracheobronchial region. Also, significant local deposition enhancement are been observed at the maximum stagnation region where the first bifurcation of daughter airways occurs in both nano size submicron and micron transportations. Difference of deposition enhancement factor between 40 nm and 4 µm are the factor of 95 since deposition enhancement factor of 40 nm aerosol is 25 whereas deposition enhancement factor of 4 µm is 110.

Figure 2-18: Particle deposition enhancement factors were presented by Longest & Holbrook (2012) in upper tracheobronchial region during inhalation flowrate of 30 L/min - (a) 40 nm, and (b) 4 µm particles (Xi, et al., 2008) Xi et al. (2008) have conducted CFD simulation with Lagrangian particle tracking method to observe pattern of particle deposition using the patient specific upper tracheobronchial airway model. Inlet flowrates of 15 and 30 L/min are determined as turbulent flow and therefore LRN k-Ɛ turbulence model was employed for their simulation. They have compared CFD results with experimental data obtained from

works of Cohen et al. (1990) and Gurman et al. (1984) by plotting deposition fractions against particle diameter as shown in Figure 2-19. Selected inhalation flowrates for CFD simulation are 15 L/min and 30 L/min, and numerical results of such inlet flowrates are compared with experimental results of 16, 18, 32 and 34 L/min inlet flowrates conditions. Generally, log scale plot of deposition fraction against the range of particle diameter between 1 nm and 10 µm has shown the positive parabolic pattern. Pattern of CFD results and experimental results are observed to be similar within submicron (i.e. approx. 10−2~ 10−1µm) and 10 µm of particle diameter range. CFD results however have shown that deposition fractions are rapidly grown when particle diameters are smaller than 10−2 µm. This indicates that the deposition factor of Brownian force could be dominantly caused particles to be deposited as submicron particles including nano particles affected by the Brownian diffusion. Minimum deposition fractions are observed between 100 nm and 10 µm in both CFD and experimental results. Deposition fractions increase when particle size becomes greater than 5 to 6 µm.

Figure 2-19: Comparison of predicted total upper tracheobronchial deposition fractions with experimental deposition data for both nano- and micro-particles. (Xi, et al., 2008) Another significant observation presented by Xi et al. (2008) is the effectiveness of induced laryngeal jet to the inspiratory flow field. This is determined by comparing inspiratory airflow flow-field between airways with and without larynx, including velocity profile vector variation and two dimensional velocity contour with in-plane streamlines of secondary motion as shown in Figure 2-20.

Figure 2-20: Dynamic comparisons of flow field between airways with and without larynx were presented by Xi et al. (2008). Mid-plane velocity vectors, contours of velocity magnitudes, and in-plane streamlines of secondary motion for a constant inspiratory flow rate of 15 l/min in TB models with the laryngeal approximation (A), and without the larynx (B). Xi and colleagues have observed that larynx leads inspiratory flow-field during inhalation to be inconsistently distributed in upper tracheobronchial region as induced laryngeal jet and asymmetric geometry of airway cause velocity profile to be leaned to one side in main bronchus. It is comparable since the velocity profile in main bronchus is symmetrically distributed in airway model without larynx whereas the velocity profile in main bronchus is asymmetrically distributed in airway model with larynx. The primary cause of velocity profile distribution variation as well as skewness of velocity contours between two different airways is the generation of laryngeal jet.

Kleinstreuer et al. (2008) have observed particle deposition rate at each regions in the respiratory tract. As shown in Figure 2-21, particle deposition fraction is plotted against the particle diameter, showing that the most efficient particle size in terms of avoiding deposition is between 0.01µm and 1 µm in the extra-thoracic region and upper airways.

Figure 2-21: Particle deposition efficiency analysis: Regional comparison Deposition fraction vs Particle deameter (Kleinstreuer, et al., 2008) Post 1 µm diameter particles have high deposition fraction throughout the respiratory tract, and particle deposition due to inertial impaction is predictable for this size of particles. Also, particles with diameter of 0.01µm or smaller have high deposition fraction, especially at nasal and the oral cavity of the extra-thoracic region.

Comer et al. (2000) has approached to see particle deposition by plotting deposition rate against Stokes number as shown in Figure 2-22. Deposition efficiency gradually increases as Stokes number increases, showing that deposition efficiency is an exponential function of Stokes number. Different Reynolds numbers are also plotted on the same graph, showing that higher Reynolds number leads to lower deposition efficiency at the first bifurcation in upper tracheobronchial region. Comer et al. (2000) also has compared in silico data with in vitro and other in silico.

Figure 2-22: Comparison between computed and measured η (Stokes number) data for the first bifurcation of a symmetric double bifurcation (Comer, et al., 2000)

Tian et al. (2015) have compared deposition fractions in upper tracheobronchial region between two cases of pharmaceutical aerosols inhalation: when Novolizer inhaler is used and when Respimat inhaler is used. Novolizer and Respimat inhalers are DPI and SMI respectively, and details of devices are not mentioned for brevity. The realistic model of airways that is relevant to the upper tracheobronchial region is employed for the purposes of simulating two different aerosol inhalation cases using Novolizer and Respimat. LRN k-Ɛ turbulence model with Lagrangian method of particle tracking were employed for their CFD simulation. Figure 2-23 shows that the size of majority particles in Novolizer are determined to be smaller than the size of particles generated by Respimat.

Peak inspiratory flowrates (PIFR) are predetermined and PIFR for the use of Novolizer and Respimat are measured to be 99 L/min and 41 L/min respectively. CFD simulation results are successfully compared with in vivo experimental results obtained by Stahlhofen et al. (1989) as the percent relative error of the computational simulations is 9.9% compared with the experimental in vivo data (Tian, et al., 2015). Various size of particles, the range between 1 to 11 µm are employed in monodispersed injection to measure depositon fraction at each specified regions of the airway model.

Even though PIFR are lower in Respimat in comparsion to PIFR of Novolizer, greater number of particles is deposited in the entrance of throat when Novolizer is used, as deposition fraction at the mouth throat is reached to 67% during use of Novolizer whereas 39.5% of deposition fraction is observed during use of Respimat. However, greater number of larger size particles are successfully reached into distal part of the lung when Respimat is used, as deposition fraction in use of Respimat is greater than the deposition fraction in use of Novolizer. A gradational variation of deposition fractions are measured, which have shown that the status of local deposition at each regions of the airways is varied depending on the size of particles as well as which inhaler device has been used.

Figure 2-23: Comparison of pharmaceutical aerosol deposition– (a) Novolizer® inhalation under 99 L/min inlet flowrate condition, and (b) Respimat® inhalation under 41 L/min inlet flowrate condition (Tian, et al., 2015) 2.4 Summary A literature review was conducted to understand the particle and fluid dynamics in the respiratory tract when pharmaceutical aerosol or toxic particulate matter is inhaled / breathed into the human pulmonary system. Complex human pulmonary system geometry was discussed followed by the discussion of fluid dynamics, particle trajectory, particle deposition factors and their efficiency. Current CFD models and their combination with other methods such as DPM or DEM were also discussed to initiate the scope of this project. It is understood that the particle deposition in airways is a vital phenomenon during respiratory condition due to several factors causing particle deposition by dense particles suspended in the air during respiratory condition through the pulmonary airways. Complexity of respiratory tract, respiratory flowrate, airway size and size of the particle are all key considerations for determining deposition factors. Previous results have shown that there is a possibility of retaining controllability of particle deposition which can be useful for induced targeting deposition technique that could be employed for therapeutic purposes.

Observation of the particle deposition in the respiratory tract is a major aim of this project. This could be an underpinning research task for obtaining controllability of deposition efficiency – the purpose of targeting deposition. It is obvious that the flow

rate intensity control has limitation to induce a complete targeting deposition by nature. However, it is also examined that variation of few parameters can increase the controllability of deposition efficiency. Firstly, particle size can be one of parameters which enable to increase controllability, since the size of particle is directly relevant to the most effective particle deposition factor, that is, inertial impaction. Secondly, particle shape also can be a parameter to control deposition efficiency. Spherical shape of particle is most likely assumed in the past research. But since drag force is dominant force acting on the particle transportation, creation of effective aerodynamic shape or employing a certain level of aspect ratio to the particle dimension creating smoother streamlines in respiratory airflow (i.e. less turbulence) may minimise inertial impaction or sedimentation. Finally, as particle deposition is a function of particle density, variation of such density may be useful to observe, in terms of the deposition efficiency controllability.

CHAPTER 3

3. CFD MODEL DEVELOPMENT OF THE RESPIRATORY TRACT SIMULATION

3.1 Introduction In this chapter, CFD model development for simulation of particle deposition in the respiratory tract is expressed. Realistic airways model is employed for CFD model development, and two different inspiratory conditions are adopted to compare differences of flow field, particle trajectory and deposition pattern.

Recently many different approaches are attempted to accurately demonstrate the characteristic of airflow pattern in correlation to the particle deposition characteristic in human respiratory tract. Li (2012) has brought three different oral-tracheal airway models to simulate flow patterns in order to determine deposition fraction in relation to the particle diameter. The results show the effect of different inner oral shapes during smoking, inhalation and normal breathing. Feng and Kleinstreuer (2014) simulated particle deposition by comparing DDPM–DEM and DPM using Weibel’s triple generations airway geometry (Weibel, 1963) to observe deposition phenomenon and its efficiencies. Oakes et al. (2014) have used Magnetic Resonance Image (MRI) derived geometry of rat’s respiratory airway bifurcation for simulating complex air flow-field with respect to the particle deposition pattern in order to compare CFD data to in vivo data. The result of this project is consequently exposed to an accuracy of CFD simulation of inspiratory airflow fields in the respiratory tract confirming high computational reliability as well as limitation of respiratory model simulation. Similarly, Tian et al. (2015) have compared CFD prediction of pharmaceutical aerosol deposition in mouth-throat respiratory model with in vivo data in the aims of supplementing previous results of their CFD simulations. In this paper the CFD simulation of stochastic individual pathway are also implemented and directly compared with the whole lung in vivo model data, validating that the characteristic differences of deposition between dry powder inhaler and soft mist inhaler. Augusto et al. (2016) have discussed comparison of fluid streamline and particle pathways in Weibel’s triple

generation airway model that is relevant to Generation 3 to Generation 6 of upper tracheobronchial region under several different breathing conditions. Physical mechanism of fluid-particle coupled flow is analysed by CFD simulation. Also, Sung and Ryou (2012) have used the idealised model of human oropharynx airway geometry in CFD simulation under different inlet conditions in order to investigate the difference of velocity distribution, secondary flow and turbulence kinetic energy in the vicinity of the oral cavity inlet. In their work, turbulent flow in the upper respiratory tract is mainly focused to implicitly show how turbulent airflow at the upper region of respiratory system influences particle deposition in the lower regions. Similarly, Longest and Holbrook (2012) have simulated the particle deposition in the airways in upper tracheobronchial region by comparing trajectories of particles in different sizes with respect to the particle deposition characteristic. On the other hand, Chen et al. (2012) clearly demonstrated the stagnation point of the bifurcation region in airways model by visualising the pressure field using CFD-DPM coupling in order to determine the particle motion and fluid-particle interaction. Furthermore, Soni and Aliabadi (2013) have simulated particle deposition and fluid flow of Steady-state and unsteady inhalation in the first 10 generations of the respiratory tract. Finite-time Lyapunov exponent diagnosis is implemented for their CFD simulation for the purposes of clearly visualizing deposition pattern of particles in complex airway geometry under different boundary settings.

Unsolved confinement of advanced CFD models of particle deposition include: firstly, difficulty of the entire lung geometry employment due to the exponential growth bifurcation of airway generation; Secondly, determination of diversified particle physics and; finally, computational expenses. In addition, it is required to complement a lacking of flow-field information in correlation to the particle deposition in more realistic airway geometry.

3.2 Numerical Model

3.2.1 Respiratory tract geometry and discretisation

 Geometry Figure 3-1 shows the overview of employed airway model. The CFD simulation employed the three dimensional human respiratory tract model developed by Kitaoka et

al. (Kitaoka, et al., 1999; Kitaoka, et al., 2013). Such an airway model is based on the computed tomography scans of male adult’s common 3,000 cc size pulmonary system (Kitaoka, 2011). In order to create this model, the software called Lung4Cer was adopted and the initial geometry was converted into the appropriate geometry file by using a commercial 3D CAD software package. A Kitaoka respiratory tract model corresponding from generation 0 to 7 (KG7) features continuous three dimensional bifurcations of daughter airways. This model provides robust simulation of inspiratory airflow by allowing realistic structural features including continuous bifurcations in upper tracheobronchial region. Table 3-1 shows dimension of computational domain. The KG7 model consists of main bronchus, lobe bronchus and daughter airways, which is equivalent to generation 0 to 7. Cross-sectional diameters from trachea to generation 7 of the KG7 model decrease by the factors range between 0.3 to 3.3 mm.

Figure 3-1: KG7 geometry overview

Table 3-1: Summary of dimension – KG7 model Geometrical scope Upper TB region Number of branches 67 Number of outlets 34 Min. outlet diameter 2.43 mm Inlet area 139.79 mm2 Inlet diameter 13.34 mm Total outlet area 307.10 mm2 Total outlet diameter 19.77 mm

 Mesh generation For the preservation of geometrical complexity as well as considering limitation of number of mesh elements, unstructured tetrahedral mesh with prism layers is employed. Unstructured mesh enables to preserve the realistic features of the KG7 airway geometry. Also unstructured mesh provides higher optimisation for selected respiratory tract geometry in terms of the geometrical characteristic.

Figure 3-2 shows some details of generated mesh. ANSYS 14.5 Workbench Mesh has been utilized to generate mesh. Since the computational domain is employed as a faceted 3D geometry, virtual topology generation is applied in order to eliminate curves disturbing creation of optimised mesh shapes. To keep the consistency of cell shape, body sizing is applied to the geometry. 6 inflation layers with 30% growth rate are applied for inlet and outlets boundaries to increase accuracy of the velocity profile development. Advanced size function on proximity is also applied to adjust cell sizes in vicinity of proximities.

Figure 3-2: (a) mesh overview (b) mesh view on inlet (c) mesh view on outlet Tetrahedral mesh quality improvement is achieved via TUI command in FLUENT using mesh repair quality-improve function. The minimum orthogonal quality of the mesh achieved up to 0.1.

3.2.2 CFD models The behaviour of fluid flow is governed by Navier-Stokes equations, given by 퐷휌 = 0 (3-1) 퐷푡

퐷퐯 휌 = −훻푃 − [훻 ∙ 흉] + 휌품 (3-2) 퐷푡

Equations 3-1 and 3-2 can be solved directly in CFD for laminar flow. For turbulent flow, different turbulence models have been developed and the Reynolds averaged Navier-Stokes (RANS) model is mostly widely used, defined as

퐷(휌퐯̅) = −∇푃̅ − [ ∇ ∙ 흉̅ ] − [∇ ∙ 휌퐯̅̅′̅퐯̅̅′] + 휌품 (3-3) 퐷푡 where 흉̅ is time averaged viscous stress and 휌퐯̅̅′̅퐯̅̅′ is Reynolds stress tensor. It is previously provided that implementation of the RANS turbulence models including series of k-Ɛ models, k-ɷ or Reynolds stress model for the transitional – turbulent inspiratory airflow simulation using respiratory tract model is mandatory (Kleinstreuer & Zhang, 2010; Ball, et al., 2008; Menon, et al., 1984; Zhang & Kleinstreuer., 2003a; Zhang & Kleinstreuer, 2003b). Low-Reynolds Number (LRN) k-epsilon model has previously been verified as a reasonable turbulence model for the inspiratory airflow simulation in the respiratory tract (Kleinstreuer & Zhang, 2010). Realizable two equations k-epsilon model is also considered to be a suitable turbulence model for such simulation as it gave a good agreement in previous simulation results in comparison to experimental data (Kadota, et al., 2016).

Four equations transition SST model is recognized to be optimized for transitional flow simulation particularly for inhalation condition simulation. Transition SST model additionally solves intermittency and transition onset criteria in terms of momentum- thickness Reynolds number by coupling with classical k-ω SST model to seek significant differences of the airflow characteristic. The default four-equations are based on the two-equation SST-2003 model, augmented by two additional equations to describe the laminar-turbulent transition process (NASA, 2016). Thus the default values of transition length function, critical momentum thickness Reynolds number and transition onset momentum thickness Reynolds number are applied as those are suitable for the simulation condition. Range of Reynolds number in the respiratory tract

from generation 1 to 23 is approximately 0.001~10,000 and is predictable that the inspiratory airflow in airways is combination of turbulent – transitional – laminar flows.

The boundary Reynolds numbers of the KG7 model is between 1000 and 6000 during inhalation condition. Accordingly, transition SST turbulence model is selected for simulating inhalation condition and considered to be the most appropriate turbulence model for this project.

The flow status is determined to be transitional during inhalation condition, whereas during breathing condition it is determined to be laminar. Appropriate turbulent intensities, 퐼푡푢푟푏푢푙푒푛푐푒 for transitional flow in both inlet and outlets are given by (Russo & Basse, 2016)

2 ′ √ 푘 1 푢 3 − 퐼푡푢푟푏푢푙푒푛푐푒 = = = 0.16푅푒푑ℎ 8 (3-4) 푈 2 2 2 √푈푥 + 푈푦 + 푈푧 where 푢′ is the root-mean-square of the turbulent velocity fluctuations, U is the mean velocity, k is the turbulent kinetic energy and 푅푒푑ℎis the Reynolds number of airway diameter. The term in the right hand side of Equation 3-4 is an approximation of turbulence intensity in accordance to Reynolds number, where the internal flow in airways is assumed to be fully developed.

 Discretization Schemes Figure 3-3 compares residual plots of 1st order and 2nd order discretization scheme. Transition SST turbulence model is employed for discretization scheme. Since the model consists of unstructured tetrahedral mesh elements, it is worthwhile to compare those two discretization schemes. Using the optimized mesh model, second order upwind discretization scheme and first order upwind discretization scheme are simulated under inspiratory flow of inhalation inlet condition (inlet velocity = 7.15 m/s). Stability of the model is shown approximately at 16000 iterations onward for second order upwind discretization scheme. On the other hand, first order upwind discretization scheme model has shown instability of the model even solution iterations have exceeded 25000 times and the residuals level decreases continuously. Table 3-2 shows comparison between 1st and 2nd order discretization scheme.

Figure 3-3: discretization scheme Residuals plot of – (a) 1st order upwind and; (b) 2nd order upwind

Table 3-2: Maximum velocity, maximum pressure, maximum back pressure and maximum turbulence kinetic energy of each discretization schemes were compared. 1st order 2nd order Var. Iterations 25,000 20,000 - vmaximum (m/s) 10.43 10.95 5% Pmaximum (Pa) 60.14 58.69 2% Pback (Pa) 36.21 31.16 16% ktur,max (J/kg) 7.78 7.41 5%

Regions where maximum velocity, maximum pressure and maximum back pressure occur are the same in both discretization scheme models and their variance differences are in range of 2%~16%. This has proved that the higher order discretization scheme gives stable convergence and second order upwind discretization scheme is more robust in comparison to the first order upwind discretization scheme for the inspiratory airflow simulation in the respiratory tract.

 Convergence All model convergences are monitored by the level of residuals for each discrete equation. The residual values are required to reduce down to 1 × 10−10 in order to achieve convergence. This is because second order discretization scheme solver setting and multi equations turbulence model employment led slower convergence with lower level of residuals. Although monotone upstream centred schemes for conservation laws (MUSCL) discretization scheme setting gives higher accuracy for unstructured mesh, the combination of such a discretization scheme setting with some other pressure- velocity coupling and interpolation methods for face pressure settings are inappropriate for this model. Model stability has shown that pressure based second order upwind

discretization scheme with semi-implicit method for pressure-linked equations (SIMPLE) pressure-velocity coupling and standard interpolation methods for face pressure setting are consequently well converged in 10−10 residuals level. Under relaxation factors are set to 0.1 in order to avoid any divergences. The CFD simulation with employment of transition SST turbulence model has well converged prior to 20,000 iterations, whereas simulations under LRN k-epsilon turbulence model employment required up to 30,000 iterations to attain the model convergence at 1 × 10−10 residuals level.

3.2.3 Simulation Conditions Flowrates of inhalation and breathing conditions are primarily selected in accordance to Finlay (2001), which are 60 L/min and 18 L/min, respectively.

Based on two inlet flowrates condition, boundary Reynolds numbers in inlet and outlet of the KG7 model during inhalation and breathing conditions are calculated. Reynolds number at inlet during inhalation and breathing conditions are 5896 and 1779, respectively. Therefore the airflow in the respiratory tract is expected to be laminar flow during stable tidal breathing condition, whereas turbulent-laminar transitional flow can be expected during inhalation condition.

In order to analyse the flow pattern of the model, the steady state three dimensional mass conservation and momentum equations are solved by finite volume method (Kadota, et al., 2016; Milenkovic, et al., 2013; Chen, et al., 2013; Gemci, et al., 2008). The model airflow is assumed to be viscous, isotropic and incompressible Newtonian fluid with constant properties. Pressure based solver is chosen as this takes momentum and pressure as a major variables and for discretization method second order upwind is set in order to achieve higher order accuracy. Similarly, Semi implicit method for pressure linked equations is set for pressure and velocity coupling setting interpolation methods for face pressure is set to standard. The computational time is taken up to approximately 7 hours in 64-bit OS and 3.2GHz Intel quad core i5 CPU computer with 8 GB of RAM.

Lagrangian particle tracking is adopted by employment of DPM coupling with CFD simulation. In-house UDF code is applied to obtain coordinates of particle deposition in the KG7 model. Escape boundary condition type is applied to both inlet and outlets with

UDF particle trap application on the wall. Number of particles is injected through the inlet in normal direction from the inlet surface. Initial velocity of particles is set to the same as inlet boundary condition. Several different sizes of particles are adopted to observe the effect of particle size in terms of deposition rate. Particle trajectories and depositions are observed under two selected inspiratory conditions; inhalation and breathing condition.

3.3 Results and discussion

3.3.1 Grid independence test Several different numbers of mesh elements are generated for convergence comparison. Figure 3-4 represents the grid independence test for obtaining an optimised mesh density.

Maximum pressure variations versus mesh density in Figure 3-4 – (a) is shown that the finer the mesh gives higher maximum pressure value. 6 different numbers of mesh densities are attempted for the grid independency check and plotted in correlation to the maximum pressure. For this grid independence check inhalation condition is applied to the inlet boundary condition.

The initial result has indicated that the highest pressure occurs at the first bifurcation region where the stagnation spot exist. The mesh density comparison in relation to the maximum pressure indicated that the finer mesh gives higher pressure, until the number of elements reached approximately 479000. The maximum pressure at 479436 mesh elements is 64.6 Pa whereas the maximum pressure at 510210 mesh element is 64.69 Pa. 30774 mesh elements difference indicating less than 1% difference of the maximum pressure has shown a good agreement that the post number of 479436 mesh elements result in the grid independency for this model.

Figure 3-4 – (b) shows the plot of maximum velocity variation against different number of mesh elements for the grid independency check. Similar to the maximum pressure variation, the maximum velocity is increased as mesh becomes finer. This indicates that the maximum velocity tends to be consistent after post 479000 elements. Therefore, the grid independency checks through the maximum pressure and velocity have proved that the mesh density with 479000 elements gives the optimized mesh element size.

62 60 58 56 54

Max. Pressure (Pa) Pressure Max. 52 50 4.E+04 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 Number of mesh elements (a) 10.3

10.2

10.1 10 9.9 9.8 9.7

Max. velocity (m/s) velocity Max. 9.6 9.5 4.E+04 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 Number of mesh elements (b) Figure 3-4: (a) Maximum pressure and (b) maximum fluid velocity in the KG7 model plotted against number of mesh elements for grid independence test

3.3.2 Model validation Airways of Tracheobronchial regions was previously experimented by developing in vitro model to investigate respiratory airflow characteristic in human pulmonary airways using physical apparatus of replica respiratory tract.

Figure 3-5 – (a) shows experimental apparatus constructed by Chang and Osama (1982). Their experimental model consists of 3:1 scale rigid replica airways of tracheobronchial region up to generation 2 and has used to investigate an axial velocity profile of inspiratory airflows under two different flowrates (24 L/min and 102 L/min). Similarly, Menon et al. (1984) have utilised the same rigid replica airway model for developing in vitro model for inspiratory airflow investigation in the aims of observing the oscillatory velocity profile.

Figure 3-5 – (b) shows corresponding positions of experiment apparatus defined in computational domain in accordance to the experimental measurement positions specified in Figure 3-5 – (a) for validation procedure. The comparison of corresponding dimensions indicates that the dimensions of Chang and Osama (1982) and computational domain are not identical, as the scale ratio of those two geometry dimensions is approximately 3.5:1.

Figure 3-5: (a) Replica model of main bronchus airway experimental apparatus used by Chang and Osama (1982) to examine axial velocity of inspiratory airflow and; (b) Corresponding measurement positions defined in computational domain for model validation Figure 3-6 – (a) shows geometrical comparison between computational domain and experimental apparatus, by measuring inlet to position diameter ratio. Geometrical variance between experimental apparatus and computational domain is between 0%~50%.

Figure 3-6 – (b) shows the plot of inlet to position velocity ratio comparison between CFD results and experimental data. Velocities at each corresponding positions are measured at particular positions in computational domain and compared with experimental velocity data. Experimental velocity data at two different inspiratory flowrates (24 L/min and 102 L/min) obtained by Chang and Osama (1982) are compared with the CFD data. Fluid velocities in each position in experimental apparatus are relatively higher in comparison to velocities of computational domain. Higher inlet air flowrate has shown greater range of velocity variances between experimental data and computational data as 102 L/min inlet flowrate condition shows velocity variances

between 5%~59% whereas 24 L/min condition shows velocity variances between 2%~49%. The highest velocity in experimental apparatus is observed at position-h whereas the highest velocity in computational domain is observed at position-c in both 24 L/min and 102 L/min inlet flowrate conditions. However, the position of lowest velocity is the same in both experimental apparatus and computational domain as it is observed at position-g under 24 L/min and 102 L/min inlet conditions. 1.2 CFD domain 1

Exp. Apparatus

0.8

0.6

diameter Ratio diameter 0.4 Inlet diameter to position to diameter Inlet

0.2 0 1 2 3 4 5 6 7 8 9 10 a b c d e f g h i Measurement positions (a) 1.8 24 litre/min (CFD) 102 litre/min (CFD) 1.4 24 litre/min (Chang et al.) 102 litre/min (Chang et al.)

velocity Ratio velocity 0.6 Inlet velocity to position to velocity Inlet

0.2 0 1 2 3 4 5 6 7 8 9 10 a b c d e f g h i Measurement positions (b)

Figure 3-6: (a) Inlet diameter to position diameter ratio comparison between CFD domain and experimental apparatus constructed by Chang and Osama (1982) and (b) Inlet velocity to position velocity ratio comparison between CFD and experimental results

Difference between experimental velocity ratio and computational velocity ratio at each point is able to be predictable since there is a major geometrical and dimensional heterogeneity between those two models. Consistency of velocity change is observed in both models as those models have shown the similar gradient change of inspiratory airflow to the fluid velocity in continuous bifurcating geometry. Continuous bifurcation

and cross-sectional dimension properties change and the inspiratory condition such as inspiratory flowrate are the major influences to the airflow characteristic in human pulmonary airways and both models have well indicated the inspiratory characteristic.

3.3.3 Fluid Flow field Fluid velocity variation along each generation in the KG7 model is compared with Finlay and Weibel’s airway model. Finlay et al. (2000) have introduced conceptual lung model for paediatric ages, which geometrically unnecessary uncertainties are eliminated providing a tolerant analysis (Finlay, et al., 2000). In addition, Finaly has expressed a comparison with his conceptual lung model to Weibel’s lung model (Weibel, 1963). Dimensions of conceptual lung model are mean values so it is assumed that cross- sectional diameter and length of the airways associated in each generation are the same. This assumption is also valid since the conceptual model is an idealised model and is neither realistic nor patient specific. However, the geometrical shape of the KG7 model and its dimensions of airways in each generation are inhomogeneous. Reynolds number are measured in each generation where a particular line passing through the airway from inlet to the outlet in right side of the KG7 geometry under normal x-z direction as shown in Figure 3-7. Cross sectional surfaces are created at particular positions in each generation. Definition of each critical position in CFD domain is assumed to be corresponding to each generation in conceptual lung model.

Figure 3-7 shows particular positions at each generation in the KG7 model. Particular positions are defined along the selected airway path as shown for the purposes of obtaining CFD data. Table 3-3 shows comparison of corresponding cross-sectional diameters of Finlay, Weibel model with the cross-sectional diameters of particular positions in the KG7 airway model.

Figure 3-7: Particular positions defined for data measurement. Note that generation 0 corresponds to the position 1.

Table 3-3: Dimension comparison between Finlay, Weibel and the KG7 model

Cross-sectional diameter (mm) Position Finlay (conceptual) Weibel (conceptual) KG7 (CFD) 0th generation 18.1 15.4 13.3 1st generation 14.1 10.4 10.0 2nd generation 11.2 7.1 9.2 3rd generation 8.9 4.8 8.2 4th generation 7.1 3.9 7.9 5th generation 5.7 3.0 7.4 6th generation 4.5 2.4 7.4 7th generation 3.6 2.0 4.6

Figure 3-8 shows Reynolds numbers comparison in each generation during inhalation and breathing condition to Reynolds number variation in Finlay and Weibel’s conceptual lung models. Reynolds number comparison between CFD results and

calculations on conceptual lung models have shown that both cross-sectional diameter and maximum velocity of inspiratory airflow passing through the airway are gradually decreased towards the distal part of the lung. As a result, Reynolds number also gradually decreases as generation number increases showing that the inspiratory airflow eventually becomes laminar as geometrical complexity of airways intensifies. During inhalation condition, inspiratory airflows in both conceptual models and CFD model are turbulent-transitional throughout the upper tracheobronchial region. During breathing condition, inspiratory airflows in both conceptual models and CFD model are laminar throughout the upper tracheobronchial region.

8000 Finlay model (conceptual) 7000

Weibel model (conceptual) 6000 Kitaoka model (CFD) 5000

4000

3000

Reynolds number Reynolds 2000

1000

0 0 1 2 3 4 5 6 7 Generation (a) 2500 Finlay model (conceptual)

2000 Weibel model (conceptual)

Kitaoka model (CFD) 1500

1000 Reynolds number Reynolds 500

0 0 1 2 3 4 5 6 7 Generation (b)

Figure 3-8: Reynolds number variation comparison between CFD results and conceptual lung models during (a) Inhalation condition (b) Breathing condition

Figure 3-9 shows flowrate variation against each generation. During inspiratory condition, drastic reduction of flowrate is observed between position 0 and position 1 (i.e. between generation 0 and generation 1) where the first major bifurcation of daughter airways occurs. Flowrates then gradually decrease towards distal part of the airways model.

70 Inhalation 60 Breathing

Inspiratory flowrate (litre/min) flowrate Inspiratory 10

0 Inlet 0 1 2 3 4 5 6 7 Generation Figure 3-9: Flowrates variations were plotted against critical position. Note that generation 0 corresponds to the particular position 1 in Figure 3-7. Rapid flowrate drop occurs in both respiratory conditions. This is predictable as the geometrical change due to bifurcation is the major cause of rapid flowrate drop in this region. Multi generation of airway branches causes dispersion of inspiratory flowrate and as a result airflow velocity gradually reduces causing higher risk of particle sedimentation in deeper regions of respiratory tract.

Figure 3-10 shows pressure contours during (a) inhalation and (b) breathing condition. High pressure zones are likely developed on the wall where bifurcation of airways is formed in each generation. Also the highest pressure stagnation point is likely occurred at the same location where inspiratory air velocity is zero. Maximum pressures at the stagnation point during inhalation and breathing inspiratory conditions are approximately 52 Pa and 7 Pa respectively. Maximum back pressure is observed between generation 0 and generation 1 at the left-hand-side airway generations. Direction of the fluid rapidly changes in the location and the fluid are undergone rapid expansion causing back pressure. Such a phenomenon is observed both inspiratory

conditions. Absolute magnitudes of back pressures during inhalation and breathing condition in this region are approximately 28 Pa and 1 Pa respectively.

Figure 3-10: Overview of pressure contour during (a) inhalation condition; (b) breathing condition Figure 3-11 and Figure 3-12 show the series of contour plots of velocity distributions in each particular position mentioned in Figure 3-7. Asymmetry of velocity distribution is observed as wider area of higher velocity field is shown in right-hand-side airway generation. This phenomenon occurred in both inspiratory condition and asymmetry of velocity distribution is greater when inlet velocity condition is lower as shown in breathing condition velocity contour in position 1.

The highest velocity is observed between position 1 and position 3 during both inspiratory conditions. As a result wider high-velocity distribution (i.e. wider area of higher velocity area in velocity contour) is occurred in position 2 showing greater range of velocity field across the cross-sectional area. It is notable that the velocity stagnation is observed in position 2 on near upper wall. Back pressure zone is also observed in such location during both respiratory conditions. High velocity distribution is most likely occurred near the bottom wall of the airway after first bifurcation. Furthermore, higher velocity distribution is gradually reduced as position number increases (i.e. toward distal part of the lung).

Position 1 Position 2

Position 3 Position 4

Position 5 Position 6

Position 7 Position 8 Figure 3-11: Velocity contours of inhalation condition at positions 1~8.

Position 1 Position 2

Position 3 Position 4

Position 5 Position 6

Position 7 Position 8 Figure 3-12: Velocity contours of breathing condition at positions 1~8. Figure 3-13 shows comparison of inspiratory airflow velocity variation between inhalation and breathing conditions. Velocity ratio of each position to inlet is calculated and plotted against critical positions. An overall ratio of inhalation condition is relatively higher than overall ratio of breathing condition. Ratios in generation 1 and 5 (i.e. position 2 and 6 equivalent in Figure 3-7) are higher than their previous positions in both respiratory conditions showing the venturi effect of airway geometry.

The inlet-to-position velocity ratio however decreases toward lower generations, while the mean velocity also reduces as generation number increases. The highest velocity is observed at the airway after first bifurcation. High deposition density can be expected in this region if particles are entered under inhalation condition. This expectation is valid since micro-sized particles experience inertial impaction when they are transported

through the airways with continuous change of direction of airflows. The KG7 model consists of heterogeneous direction of airways so the inhaled particles are likely to be deposited in stagnation regions and the bottom wall of airway between generation 0 and generation 1.

1.0

0.9 0.8 0.7 0.6 0.5

0.4 position velocity ratio velocity position

- 0.3 to - 0.2 Inhalation 0.1 Inlet Breathing 0.0 Inlet 0 1 2 3 4 5 6 7 Generation Figure 3-13: Inlet-to-critical positions velocity ratios were plotted against critical position. Note that generation 0 corresponds to critical position 1. Note that inlet velocities are 7.15 m/s and 2.14 m/s for inhalation and breathing condition respectively. In Figure 3-14 – (a), mean pressure plot against the critical position indicated that the largest pressure drop occurs at generation 1 from inlet during both inspiratory conditions. This is because since the volume of respiratory tract rapidly expands after the generation 0, the pressure rapidly drops in generation 1. The mean pressure then gradually increases until generation 4 and drops in generation 5 under inhalation condition. Large pressure drop is occurred due to the back pressure at those regions. The pressure however gradually decreases towards the distal part of the lung. Mean turbulence kinetic energy, as shown in Figure 3-14 – (b), is the highest at vicinity of the inlet. It then largely drops before first bifurcation region and is tended to continuously increase until generation 3 under inhalation condition.

30 Inhalation

25 Breathing (Pa) 20

10 Mean pressure pressure Mean

0 Inlet 0 1 2 3 4 5 6 7 Generation

(a) 0.5 Inhalation 0.4 Breathing 0.4

0.3

(J/kg) 0.2

0.2

0.1

0.1 Mean turbulence kinetic energy energy kinetic turbulenceMean 0.0 Inlet 0 1 2 3 4 5 6 7 Generation (b)

Figure 3-14: Comparison of (a) mean pressures; and (b) turbulence kinetic energy plotted against critical positions during inspiratory conditions.

3.3.4 Particle trajectory and deposition Following the respiratory flow field discussion, number of different size of particles is applied using DPM in Lagrangian frame with stochastic particle tracking through the employed realistic airway model. As inertia is a dominant factor of particle transportation in upper regions of respiratory tract, the pressure gradient force, the lift force and the mass force applied by gravity are assumed to be negligible. As a result, the governing equations for the particles can be defined as follow.

1 퐅 = 휌 |퐯 − 퐯 |(퐯 − 퐯 )퐴퐶 (3-5) 푑푟푎푔 2 푓 푓 푝 푓 푝 푑 where 퐯푓 is the fluid velocity, 퐯푝 is the particle velocity, 휌푓 is the fluid density and 퐶푑 is the drag coefficient which can be determined by using Equation 2-5.

Particle diameter of 2, 6 and 10 µm are stochastically tracked and compared with the respiratory airflow streamlines: respiratory airflow streamline during inhalation and breathing condition are shown in Figure 3-15 – (a) and (b) respectively, followed by 2 µm, 6 µm and 10 µm particle trajectories during inhalation and breathing conditions are shown in Figure 3-16. It is noted that to clearly present maximum number of streamlines and trajectories are set to 75.

Swirling trajectories of the particles are observed at the first bifurcation of daughter airway in generation 1 in all cases, indicating that rapid volume increase of airway causes stagnation effect and particle movement. Particle trajectories have shown that the particle deposition significantly increases as particle size increases. Also, the deposition of particle is greater during inhalation condition than during breathing condition.

Fluid streamlines and particle trajectories of inspiratory airflow in the airway are similar, considering that drag force acting on particles are dominant causing its transportation through the airway in upper tracheobronchial region.

Most of particles are escaped through outlets during breathing condition especially for smaller particle size; i.e. 2 µm and 6 µm particles. 10 µm particles however are markedly deposited during both inhalation and breathing condition in comparison to the smaller particle deposition status as increase of particle trajectory discontinuations are observable. During inhalation condition, only few particles exit through downward outlets but there are no particles escaped out through upward outlets in generation 3 ~ 4. Similarly, greater number of particles is successfully exited through downward outlets, and smaller number of particles is successfully exited through upward outlets during breathing condition.

(a)

(b)

Figure 3-15: 3D respiratory airflow streamline during (a) inhalation condition (b) breathing condition in the KG7 airway model

2 µm

6 µm

10 µm

Inhalation (60 L/min) Breathing (18 L/min)

Figure 3-16: Particle trajectory variations comparison under inhalation and breathing condition. Figure 3-17 shows the particle deposition position in the KG7 during two inspiratory conditions demonstrating deposition concentration and pattern characteristic under various sizes of particles and different inspiratory conditions. Note that dots in red color in the figure represent particles deposited on the wall of airways.

Similar to the particle trajectories, 2, 6 and 10 µm particles are selected for comparing deposition status of inhalation and breathing conditions. Deposition concentration is

found on the wall of bifurcation of daughter airways at each generation. Concentration of particle deposition is clearly visible in 10 µm particles during both inspiratory conditions as greater number of particles have deposited. Particle deposition near the inlet gradually increased as particle size is increased particularly during inhalation condition. This phenomenon is a significant concern as there are no advantages of particles to be deposited on the wall of main bronchus.

2 µm

6 µm

10 µm

Inhalation (60 L/min) Breathing (18 L/min)

Figure 3-17: Particle deposition variations during inhalation and breathing condition.

 Deposition rate Deposition rate is a ratio of deposited particle to the total injected particle in particular region of the respiratory tract. Particle deposition rate is also recognized as deposition efficiency and can be calculated by

퐷푒푝표푠푖푡푒푑 푃푎푟푡푖푐푙푒 휂 = (3-6) 푑푒푝표푠푖푡푖표푛 퐼푛푗푒푐푡푒푑 푃푎푟푡푖푐푙푒

During inhalation condition, 6.6% of 2 µm particles are deposited. No particles are deposited on the wall of main bronchus and are started to deposit after generation 1. Majority of deposited 2 μm particles are observed in stagnation regions in generations 5-7 in lower airways, as shown in Figure 3-17. Only few deposited particles are observed in stagnation regions in generations 1-4. During breathing condition, 2.9% of 2 µm particles are deposited. Most 2 µm particles are successfully exited through outlets and few particles are deposited on the wall of main bronchus and some of daughter airways. For 6 µm particles, 60.7% are deposited during inhalation condition. Particles are started to deposit near the inlet. Few particles are deposited on the wall of main bronchus as well as stagnation areas before the bifurcation of generation 1. Concentration of particle deposition is visible at most of bifurcation regions in each generation. On the other hand, 9.0% of 6 µm particles are deposited during breathing condition. Comparatively less number of particles is deposited during breathing condition. However, particle deposition near the inlet of main bronchus is still a significant concern as no particles should beneficially be deposited in such area. Particles are deposited due to the direct inertial impaction or sedimentation where the airflow becomes stagnated. Furthermore, 91.5% of 10 µm particles are deposited during inhalation condition. Only few particles could successfully come out through outlets. Relatively less number of particles is deposited near upward outlets. However, concentration pattern of particle deposition has clearly showed that the dominant deposition factor is inertial impaction. During breathing condition, 44.9% of 10 µm particles are deposited. Markedly less number of particles is deposited in comparison to the deposition during inhalation condition. Concentration of particle deposition pattern is similar to the one during inhalation condition as most particles are deposited on the wall of bifurcated daughter airways in each generation.

3.4 Conclusion In this chapter, A CFD model has been developed to simulate inspiratory airflow under different conditions. Based on the simulation results, the air and particle flow were analysed. The main findings of the work can be summarised as:

 The CFD model based on the Kitaoka model from generations 0-7: Two types of flow conditions, breathing (18L/min) and inhalation (60 L/min) were adopted. The transition SST turbulence model was used to simulate the inhalation condition. The CFD model was validated by comparing fluid velocity variation along the generation with experimental data. The realistic in vitro model in the scale of 3.5:1 dimension ratio was utilized for CFD validation.  Evaluation of flow field in upper tracheobronchial airways shows that the high pressure zones are likely generated at every bifurcation regions in each generation of the airways. The high density of particles deposition occurred on the wall of those regions. Higher velocity in comparison to the inlet boundary condition is observed at 1st generation of main bronchus where cross-sectional diameter of the airway is smaller than the inlet diameter. Back pressure is also observed at this zone. Intensity of turbulence kinetic energy is also increased as flowrate is increased, showing that at stronger inspiratory conditions the higher risk of particle deposition is expected at upper pulmonary regions including the nasal/oral cavity, the extra-thoracic region and main bronchus of tracheobronchial region due to inertial impaction. Fluid velocity is gradually decreased towards the outlet indicating that the inspiratory flow is gradually become laminar flow towards the lower regions of pulmonary system. Intensity and range of turbulence or transition flows are directly dependent on intensity of inlet flowrate.  In upper tracheobronchial region, drag force acting on inhaled particles is dominantly caused inertial impaction. As a result large volume of particles is deposited particularly at bifurcation region in each generation during inhalation condition. Based on Lagrangian particle track, it is observed that the stronger inhalation inspiratory condition led to the farther transportation of the particle at the upper regions of pulmonary system but higher risk of turbulent flow which ultimately causes the higher inertial impaction. Particle deposition rate is exponentially increased as particle size and fluid velocity are increased, showing

that the deposition rate variation between inhalation and breathing condition for 2 µm is 4% whereas for 6 µm and 10 µm are 58% and 47% respectively. Furthermore, inertial impaction is dominant factor of particle deposition in upper tracheobronchial region particularly during inhalation condition, where the status of inspiratory airflow is transitional – laminar. Dense deposition is observed with greater particle size under higher inlet flowrate; i.e. rate of deposition is higher during inhalation than during breathing condition.

Furthermore, the KG7 model gives geometrical advantage as it characterises with a realistic tracheobronchial airway features. The KG7 model also has enabled to observe flow-field and particle motion in upper tracheobronchial region at a glance. However, complexity of human lung geometric composition seems to prevent smooth streamline of the airflow causing higher number of high pressure and back pressure zones. Moreover, such a geometrical complexity disturbed the inspiratory airflow profile to be fully developed in each airway generation due to the relative shortage of physical length.

CHAPTER 4

4. COMPARISON OF THE RESPIRATORY TRACT MODELS

4.1 Introduction In chapter 3, the CFD model has been developed to simulate the fluid flow fields, particle trajectory and particle deposition in an airway model introduced by Kitaoka (Kitaoka, et al., 2013; Kitaoka, 2011). Most common respiratory condition i.e. inhalation and breathing conditions (Finlay et al. 2001), were selected to investigate particles behavior. Through the CFD simulations, it was found that inhaled micro particles were dominantly influenced by the fluid streamline as it travels by following inspiratory airflow. As a result, it was proved that the inertial impaction is a governing factor in upper tracheobronchial region of the respiratory tract, during inspiratory conditions.

The model in Chapter 3 is much more complicated and realistic than an idealized airway model which was proposed by Weibel (Weibel, 1963) that has been widely used to investigate airway particle deposition (Zhang & Kleinstreuer, 2003b; Augusto, et al., 2016; Weibel, 1963). Realistic features of Kitaoka model (KG7) has enabled to observe dominant deposition factor of particle more concisely. For example, a radical change of airflow direction due to airway bifurcation caused less density of particle deposition in upper region of geometry where outlets face upward. Also, the flow pattern differences are clearly demonstrated in asymmetrical geometry which is unable to observe idealised airways model such as Weibel or Finlay model assuming geometry is symmetric from left to right. Furthermore, the KG7 model has enabled to discover pattern of particle deposition in upper tracheobronchial region at a glance. The KG7 simulation results have shown that the inertial impaction is dominantly causing particle deposition particularly during inhalation condition. Deposition efficiency is higher during breathing condition than inhalation condition. Dense deposition is observed at the most of bifurcation regions in each generation. Swirling motion of particles is observed where backpressure and low velocity area occurred.

The KG7 model consists of 64 daughter branches and 34 outlets, which corresponds to 7th generations from trachea in tracheobronchial region of human respiratory tract. This model applies to approximately 1 percent of the male adult lung size if lung capacity of 3,000 cubic centimeters is assumed. So it is unclear if a model with higher degree of complexity having greater number of airway daughter branches, outlets and higher generation number is required to be representative of real human respiratory tracts.

This Chapter aims to compare fluid flow and particle deposition behavior with different respiratory tract models: Weibel idealized airway model (WM) and two Kitaoka models (KG7 and KG11) with different degrees of complexities. The comparisons of the results under the identical and/or relevant boundary conditions can clarify the effect of respiratory condition in relation to the particle deposition in the respiratory tract. This also gives rise to observing any numerical or computational error if existed.

In the following sections, the flow in Weibel model is validated and discussed first. Then the fluid flows in the three models are compared. Simulations are also conducted using ANSTS Fluent 14.5 and the discrete phase method is coupled with CFD to predict particle trajectories in various particle sizes. An in-house UDF code is implemented in order to obtain particle positions where depositions have occurred on the wall of airways.

4.2 Flow in Weibel idealised airway model

4.2.1 Geometry creation and simulation conditions The model was initially developed by Weibel (1963) in the study of human respiratory tract morphology. In that work, a conceptual scheme of human respiratory airway was proposed in order to determine ramifications of respiratory tract by classifying generation number at each bifurcation. Zhang et al. (2002), Zhang and Kleinstreuer (2002), Xi and Longest (2007), Longest and Vinchurkar (2007) and Augusto et al. (2016) have implemented such Weibel’s scheme to develop similar airway model in the aims of simulating particle deposition and comparing with experiment data under various respiratory conditions.

Figure 4-1 – (a) shows detailed dimensions of the model (Augusto et al. 2016). The geometry is created using Wildfire 5.0 Pro/Engineer. Combination of various section

sweep tool and swept blend tool are utilized to create such geometry. Figure 4-1 – (b) shows the mesh created using ANSYS Meshing. Similar to the mesh generation of the previous model, finite volume tetrahedral mesh with prism layers near the wall is created. Mesh comparisons between Weibel model and Kitaoka model will be discussed later.

Figure 4-1: (a) Dimension of idealised airway model presented by Augusto et al. (2016) (b) Creation of finite volume of tetrahedral mesh with prism layers near the wall Simulation condition applied for the WM model is similar to the KG7 model. In the WM model, single velocity–inlet and 8 zero pressure–outlets are assigned for computational domain boundary. Solid wall with no slip condition is applied. Since the inlet of the WM model corresponds to generation 3 in upper tracheobronchial region, inlet flowrates for selected inspiratory conditions are re-calculated based on the KG7 model simulation result. Accordingly, 20 L/min and 5.75 L/min inlet flowrates conditions are applied for inhalation and breathing conditions respectively. Reynolds number has shown that the airflow under breathing condition is laminar. On the other hand, respect Reynolds number under inhalation condition is combination of turbulence–transitional flow, thus RANS 4 equations transition SST turbulence model is adopted for the inhalation condition simulation. Backflow turbulent intensity is calculated in accordance to Equation (3-4 for both inlet and outlets for inhalation

conditions. SIMPLE pressure-velocity coupling with second order upwind discretization scheme is applied for solution method. The model is well converged prior to 20,000th iterations.

4.2.2 Model validation To validate the current model, experimental data produced by Kim and Fisher (1999) is adopted. The experimental data have been used previously to validate CFD simulations including Zhang et al. (2002; 2004), Longest and Vinchurkar (2007) and recently it is used by Augusto et al. (2016) for their particle trajectory model validation.

In the experiment, observation of particle deposition efficiency is conducted using a Weibel airway model corresponding to generations 3 to 5, as shown in Figure 4-2. The monodispersed oleic acid droplets tagged with uranine is used for deposition investigation which its aerosolized solutions are prepared by dissolving oleic acid into 90% isopropyl alcohol and 10% of an uranine-water solution (Kim & Fisher, 1999). In the experiment, various inlet flowrate conditions as well as particle sizes are applied.

Figure 4-2: The airway models used for Kim & Fisher (1999)’s experiment are shown above. Note that the experimental data of model (A) in the left hand side was used to validate simulation model. Kim and Fisher (1999) have determined particle deposition efficiency by calculating the ratio of uranine content deposited in a section to the amount of uranine injected to the

airway section. The data are then fitted to a logistic function of deposition efficiency, given by

1 퐷퐸 = 100 (1 − ) (4-1) 푎 × 푠푡푘푏 + 1 Where stk is Stokes number, given by

2 휏 푈 휌푝푎푟푡푖푐푙푒푈0푑 퐶푐 푠푡푘 = 푟푒푙 0 = (4-2) 퐷 18휇퐷 where 푈0 is a mean-velocity in the airway, D is a diameter of airway, 휌푝푎푟푡푖푐푙푒 is a particle density, d is a particle diameter, 퐶푐 is a Cunningham factor, 휇 is the absolute viscosity of air and 휏푟푒푙 is a relaxation time of the particle.

Figure 4-3 shows the comparison of deposition efficiency as a function of Stokes number obtained from the experiments and simulations. The pattern of CFD simulation results and experiment results show a good agreement: deposition efficiency exponentially increases with Stokes number, indicating that the higher Stokes number causes greater inertial effect to moving particles. Thus the particles are likely deposited to the wall of airway dominantly due to its inertial forces exerted by the drag force when Stokes number increases. The good agreement suggests that the current simulations can be utilized in the aims of simulating the particle deposition and their trajectory along with the flow field.

(a)

50 CFD simulation result

Deposition Efficiency Deposition % %

0 0.01 0.1 0.5 Stokes number, Stk

(b)

Figure 4-3: Deposition efficiency percentage plotted against Stokes number based on (a) experimental data conducted by Kim and Fisher (1999); and (b) the current CFD simulation. 4.2.3 Flow fields Figure 4-4 and Figure 4-5 show the flow-field during inspiratory conditions in vector and velocity contour plot respectively. Fluid velocity at the distal part of the lung is comparatively low in comparison to the fluid velocity in upper regions of the lung. As a result, particle depositions due to inertial impaction are less important in such region.

A brief discussion of flow field in the WM model during the inhalation and breathing conditions are introduced prior to the analysis of respirable particle behavior. One of the geometrical characteristic of human airway is in complexity due to continuous bifurcation of daughter airway. Direction of such bifurcations also continuously varies so the direction of the flow changes as shown in Figure 4-4. The vector field of fluid has shown that after bifurcation the airflow attached to the wall of airway where the primary airflow strikes. Flow detachment, however, consequently has occurred at the opposite side of the wall causing the backflow.

Direction of the fluid flow vector in this region is inconsistent and eddy flow is observed. Such an eddy flow is defined by two dimensional velocity contour as shown in Figure 4-5. Velocity in eddy flow regions is comparatively lower than regions where attached flow occurred. This could be observed under both inhalation and breathing condition, showing that the appearance of eddy flow and flow attachment are

independent of flow velocity. Low velocity zones are observed at two upper walls in first bifurcation of airway and near outlets in third bifurcation, during both inspiratory conditions. A stagnation points are also observed during inspiratory condition particularly where bifurcation starts. High velocity is observed along the vertical axis of geometry, causing fluid velocity at 4 outlets towards horizontal axis is relatively lower in comparison to the fluid velocity at other 4 outlets. These phenomena show that the airflow direction change highly influences strength of fluid velocity in the airways.

Furthermore, particular positions representing each generation are selected and shown in Figure 4-5 – (b), in order to present two dimensional velocity contours. The first position (a) corresponds to generation 3, second position (b) corresponds to generation 4, and the last position (c) and (d) correspond to generation 5 respectively. Since the geometry is symmetric, only right hand side half of model is considered. The fluid flow from entrance of the airway is separated after bifurcation occurs.

(a) (b)

Figure 4-4: Velocity vector field at (a) first bifurcation during inhalation condition (20L/min) (b) first bifurcation during breathing condition (5.75 L/min) (c) second bifurcation during inhalation condition (d) second bifurcation during breathing condition

Figure 4-5: 2D flow-field contour in velocity under (a) inhalation condition (b) breathing condition Cross section of two dimensional velocity contours in critical positions during inhalation and breathing conditions are shown in Figure 4-6 and Figure 4-7 respectively. The flow field is inconsistent after the airway bifurcation. High velocity of the fluid is focused to the airway wall where direction of airflow is not greatly changed from initial direction of the flow. In contrast, low velocity of the fluid is focused to other side of the wall and flow separation and detachment is clearly observed. Such flow phenomena are observed under both inspiratory conditions.

(a) (b)

(c) (d) Figure 4-6: Two dimensional velocity contours during inhalation condition at cross section of selected airway positions are shown.

(a) (b)

(c) (d) Figure 4-7: Two dimensional velocity contours during breathing condition at cross section of selected airway positions are shown.

4.3 Comparison of flow in different models

4.3.1 Geometry and mesh In this section, the flow and particle deposition in three different models will be compared: Weibel model (WM) and two Kitaoka models with 7 and 11 generations (KG7 and KG11), respectively. Geometry comparison overview is shown in Table 4-1.

Table 4-1: Comparison overview – key differences between geometries

(a) KG7 (b) KG11 (c) WM

Number of outlets 34 129 8 Lung-to-volume 0.78 % 1.00 % 0.093 % ratio Volume 23494 푚푚3 29884 푚푚3 2779 푚푚3 Generational scope Trachea to gen. 7 Trachea to gen. 11 Generation 3 to 6

The key differences between these three models include the volume, inlet and outlet boundary conditions, relevant generation numbers, symmetry and the number of branches, as shown in Table 4-1. The KG7 and KG11 have the same inlet conditions, as its domain generations both start from the trachea (i.e. generation 0) of tracheobronchial region. Both are asymmetric as real human lung airways are. Main difference between the two models is their correspondence of respiratory generation number: The KG7 as introduced in the previous chapter corresponds to generation 7 whereas the KG11 corresponds to generation 11. The number of branches is different and the KG11 has more branches and consequently has a greater numbers of outlets. Sizes of those two airway models are also different as the KG11 has larger volume.

On the other hand, the WM is from generation 3 to generation 6 so it is a part of airway model in the upper tracheobronchial region in the respiratory tract. This model consists of a single inlet and 8 outlets. The volume of WM is comparatively smaller than the KG7 and KG11 models. Unlike Kitaoka airway models, the orientation and direction of daughter airways and outlets are symmetry along top and bottom.

Figure 4-8 is a mesh overview of each model and shows geometry comparison. Tetrahedral element containing prism layers are selected to generate meshes. 6 inflation layers are created for each model. The number of mesh elements for the KG7, KG11

and WM model are 479436, 509313 and 222421 respectively, whereas number of nodes are 194529, 211873 and 95563 respectively.

Constant body sizing is applied in the aims of obtaining consistent fine mesh elements that could reduce numerical errors caused by differences between proximities, and curvatures. Consistent fine mesh also prevents separation of numerical results between near the inlet and outlets in this particular model. Since ratio of number of outlets to the number of inlet is large, such a sizing method is comparatively efficient for such a complex computational domain.

(a)

(b)

(c)

Figure 4-8: Mesh overview of (a) KG7 model; (b) KG11 model; and (c) WM model.

4.3.2 Simulation conditions Summary of simulation conditions for 3 models are shown in Table 4-2. Two different respiratory conditions are adopted in order to observe behavior of inhaled particles – inhalation condition (60 L/min) and breathing condition (18 L/min) at trachea.

Table 4-2: Data summary of CFD simulation including comparison of three different airway models employed for the study of particle deposition and its efficiency is shown.

Properties KG7 (KG11) WM Respiratory condition Inhalation Breathing Inhalation Breathing Flowrate 60 18 20 5.75 (L/min) Velocity (m/s) 7.15 2.14 10.55 3.03 Area (푚푚2) 139.79 28.14 Inlet Reynolds 5896 1769 3740 1075 number Turbulent 5.34 N/A 5.721 N/A intensity (%) Ʃ Area (푚푚2) 307.10 (452.44) 76.84 Reynolds 3978 (3277) 1193 (983) 901 259 Outlet number Turbulent 5.61 (5.74) N/A 6.84 N/A intensity (%)

Simulation conditions for model comparisons are adopted in full from the KG7 and WM model simulation conditions. With the 2 inspiratory conditions, their Reynolds numbers indicates whether the flow through airways is turbulent or not. Under inhalation condition the flow status is turbulent-transitional whereas during breathing condition the flow status is determined to be laminar. Appropriate turbulent intensities for transitional flow in both inlet and outlets are calculated based on Equation 3-1. Velocity inlet with zero pressure outlets and no slip condition on the all are set for boundary condition. 4 equations transition SST turbulence model is adopted to solve turbulence of transitional flow in inhalation condition. 2nd order upwind discretization scheme is selected for solving equations. For DPM setting, inert particles are injected from the inlet in normal direction. Discrete phase boundary condition type is set to escape in both inlet and outlets and in-house UDF code is employed to measure where particles trapped in the geometry. Initial velocity of injected particles is set to the same as inlet velocity.

Solid particle density of 1425 kg/푚3 is assumed in the simulations. Temperature difference between ambient and body is considered, so appropriate air density and air viscosity are applied accordingly. 9 different particle sizes are employed to determine deposition efficiency variation in upper tracheobronchial region. Range of particle size is 1 ~ 20 µm with the increment of 2 or 3.

4.3.3 Comparison of flow fields Figure 4-9 to Figure 4-11 show the 3D velocity vector fields of both inhalation and breathing conditions. The pattern of fluid flow during both respiratory conditions is similar in both realistic airway models and the idealised airway model. Fluid velocity decreases as generation number of airway increases, showing that the cross sectional area of airways gradually increases toward the distal part of the lung.

Figure 4-9 shows 3D vector fields in the KG7 model. Fluid velocity is gradually decreased toward outlets, and fluid velocity at downward outlets is relatively higher than fluid velocity at upward outlets. Maximum fluid velocity is observed at 1st bifurcation reached up to 10.64 m/s during inhalation condition. Several stagnation spots are observed at bifurcating zone where daughter airways are generated. Similar to the vector field during inhalation condition above, fluid velocity at downward outlets is relatively higher than that of upward outlets, indicating that inconsistency of fluid

direction due to the direction change of daughter airway bifurcation highly affected intensity of fluid velocity near outlets. As a result, stagnation spots occurred at such bifurcation regions is relatively larger than bifurcation regions near downward daughter airways. Maximum fluid velocity observed at 1st bifurcation has reached up to 3.41 m/s during breathing condition.

3D vector fields in the WM model are shown in Figure 4-10. Pattern of the airflow during inhalation condition is observed to be similar to realistic airway models. But since the direction of outflow is not sharply changed, the respiratory airflow during inhalation condition is observed to be consistent. Stagnation zones are observed to be relatively larger than the one in realistic airway models as well as one in the WM model during breathing condition. The maximum velocity is reached at generation 5. During the breathing condition, the maximum fluid velocity of 4.05 m/s is observed at generation 5. There are total 7 stagnation zones where daughter airways bifurcation occurs.

3D vector fields in the KG11 are shown in Figure 4-11. The KG11 enabled to simulate the whole upper tracheobronchial region in the respiratory tract. Inlet starting from the main bronchus, the respiratory airflow during inhalation condition has shown that the overall outflow pattern is inconsistent as the flow pattern of airway near downward outlets is observed to be different to the flow pattern of airway near upward outlets.

(a)

(b)

Figure 4-9: 3D velocity vector field in the KG7 model during (a) inhalation condition (b) breathing condition

(a)

(b)

Figure 4-10: 3D velocity vector field in the WM model during (a) inhalation condition (b) breathing condition

(a)

(b)

Figure 4-11: 3D velocity vector field in KG11 model during (a) inhalation condition (b) breathing condition Respiratory airflow eddies are also likely observed where direction of respiratory outflow rapidly changes in the KG11 model. Flow pattern during inhalation condition is observed to be similar to the one during breathing condition in the KG11 model. The maximum velocity, 10.58 m/s of the fluid is observed at generation 1. Similarly, the maximum velocity is observed to be 3.32 m/s at generation 1. As more weakened outflow near upward outlets, sedimentation and interception are expected to be a

dominant factor of particle deposition. Size of airflow eddies is observable to be larger than the one during inhalation condition.

4.3.4 Comparison of particle trajectory and deposition Comparisons of respiratory airflow streamline and particle trajectory under two respiratory conditions obtained from simulations are shown from Figure 4-12 to Figure 4-15. Both inhalation and breathing conditions are applied to the KG11 model and WM model for flow streamline and particle trajectory comparisons. 3 particular particle sizes are selected to present particle trajectories; 2, 6 and 10 microns – to clearly demonstrate trajectory differences between particles. Fluid streamlines of the WM model are presented in Figure 4-12 followed by particle trajectories Figure 4-13. Also, fluid streamlines of the KG11 model are presented in Figure 4-14 followed by particle trajectories in Figure 4-15. For simulation condition, the assumption is made that individual particles successfully penetrate through the extra-thoracic region so that majority of particles have entered into entrance of tracheobronchial region. Therefore, dense particles are injected normal from the inlet surface of each airway model. Approximately 150 and 420 particles are injected from the surface of inlet in normal direction from the WM and KG11 model respectively, depending on their inlet grid status. Initial velocity of injected particles is assigned to be the same as inlet boundary condition, i.e. inlet fluid velocity. For the purposes of magnifying visual clarification, maximum number of trajectory threads representing fluid streamline and particle trajectory of the WM and KG11 model are set to 50 and 100 points respectively.

As shown in Figure 4-12 and Figure 4-13, both fluid streamline and particle trajectory are steadfast at high velocity areas in the WM model. This stood out from the entrance of the airway to inner walls of airways at generation 4and inner walls of left and right airways at generation 5. Steadfast streamline and particle trajectory are observed during both inhalation and breathing condition. Unsteadiness of particle movement are conspicuously observed during breathing condition near outer walls of airways at each generation, where the velocity of inspiratory airflow is relatively weaker than main airway near inlet or near inner walls of airways at generation 4. Swirling movement or eddy motion of 2 µm particles is most likely to occur during breathing condition, whereas 2 µm particles during inhalation condition are less swirling following well with the airflow streamline.

(a)

(b) Figure 4-12: 3D respiratory airflow streamline during (a) inhalation condition (b) breathing condition in the WM model However, particle trajectories have shown that during breathing condition all size of particles are more penetrable throughout the airway model, as greater number of trajectory threads during breathing condition exit through outlets. 6 µm particles are highly deposited during inhalation condition and only few particles are penetrated through daughter airways in generation 6.

2 µm

6 µm

10 µm

Inhalation (60 L/min) Breathing (18 L/min)

Figure 4-13: The WM model particle trajectory variations.

More particles are likely to exit through downward daughter airways (toward left-right- left outlet and right-left-right outlet) in comparison to other daughter airways in generation 6. Pattern of particle movement during breathing condition is similar to the one with 2 µm injection, as few particles are swirlingly transported through daughter airways in generation 6. Furthermore for 10 µm particles, lots of particles are deposited on the wall of first bifurcation particularly during inhalation condition. Only few

particles have exit through downward outlets and there is no particle delivery to the other outlets in generation 6. On the other hand, greater number of particles is exit through outlets during breathing condition.

Such results have proven that the dominancy of particle deposition due to inertial impaction rises if velocity of respiratory airflow in the airway and/or aerodynamic diameter of particle increases. This is because fluid velocity and size of particle are two key factors causing the increase of drag force acting on individual particles. The WM model comparison between the fluid streamline and particle trajectory during two different respiratory conditions have shown that the most of particles tend to follow fluid streamline but inertial impaction has caused deposition when flow direction changes.

Fluid streamlines and particle trajectories in the KG11 model under two inspiratory conditions are shown in Figure 4-14 and Figure 4-15 respectively. Greater number of fluid streamlines is observed toward downward outlets as shown in Figure 4-14. Similarly, as particle size gets larger, higher number of particles are deposited during both respiratory conditions and only a few number of particles are successfully penetrated through downward outlets as shown in Figure 4-15. In terms of particle penetration through the airway model, breathing condition is more efficient in comparison to inhalation condition.

(a)

(b)

Figure 4-14: 3D respiratory airflow streamline during (a) inhalation condition (b) breathing condition in the KG11 model

2 µm

6 µm

10 µm

Inhalation (60 L/min) Breathing (18 L/min)

Figure 4-15: The KG11 model particle trajectory variations. Pattern comparison between a fluid streamline and particle trajectories are similar. The major findings from particle trajectories of the KG11 model is that, injected particles have been inhaled through the oral cavity, individual particle cannot be transported through every single daughter airways in upper tracheobronchial region. In other words, movement of particles are random and particles could be delivered by any daughter airways but realistically it seems to be difficult to select particular airways or airway route for particle to be transported. This fact can be significant especially for drug delivery of therapeutic purposes such as treatment of COPD or asthma. For example, if

some of respiratory airways in patients’ pulmonary system already suffer from airway stenosis due to respiratory diseases, particles could be more likely transported through other airways where respiratory airflow is smoother while inhaling pharmaceutical aerosol. It is inferable that transportation momentum of particles is relatively weaker in stenosed pulmonary airways. Furthermore, as it is already observed in the result of the KG7 and WM model, velocities of respiratory airway near upward outlets and their corresponding daughter airways are comparatively lower than downward outlets and its daughter airways.

In the aims of supplementing commentation of particle trajectory, particle deposition is discussed. Range of particular particle sizes, as same as particle trajectories discussion that formerly presented, are selected to see how different respiratory conditions, sizes of particles and different scope of airway model affects deposition rate.

Figure 4-16 and Figure 4-17 show series of particle deposition plots in the WM model and KG11 model respectively. Deposition plots have shown that deposition fraction, which is a ratio of particle deposited on the wall of airway to the total number of particle entered through inlet, is generally higher during inhalation than during breathing condition. Deposition fraction also is observed to gradually increase as particle size increased.

 Deposition rate of WM model As Weibel airway model shown in Figure 4-16, total 154 particles are injected through the inlet and 9.7 % and 3.2 % of total number of 2 µm particles are deposited during inhalation and breathing condition respectively. Few particles are deposited on the wall of both daughter airways in generation 4 during inhalation condition whereas, during breathing condition, some particles are mostly deposited near the entrance of both daughter airways in generation 5.

For 6 µm particles injection case, deposition fractions during inhalation condition and breathing condition are 38.3% and 15.6% respectively. It is clearly presented that the particle deposition is concentrated on the wall of bifurcation regions particularly during inhalation condition. Under breathing condition, greater number of particles among deposited particles is penetrated through generation 4, but these are mostly deposited near the entrance of generation 5.

Concentration of particle deposition is more clearly presented in 10 µm particles injection case. Deposition fraction of 10 µm particles is marked to 97.4 % under inhalation condition, whereas deposition fraction is 56.2 % under breathing condition.

2 µm

6 µm

10 µm

Inhalation (60 L/min) Breathing (18 L/min)

Figure 4-16: The WM model particle deposition variations. Figure 4-17 shows particle deposition status in the KG11 model. The KG11 model has enabled an observation of global deposition concentration pattern in upper tracheobronchial region at a glance. Assuming that the most particles inhaled are

successfully penetrated through the extra-thoracic region to get into tracheobronchial region, 424 particles are injected from the inlet.

 Deposition rate of KG11 model In 2 µm particles injection case, deposition fractions are 30.9 % and 16.2 % during inhalation and breathing condition respectively. Most of particles are deposited on the wall of main bronchus followed by daughter airways in lower generations during inhalation condition, whereas only a few particles are deposited near the inlet and main bronchus of airway during breathing condition.

In 6 µm particles injection case, deposition fraction is reached 80.1 % under inhalation condition whereas deposition fraction is 24.4 % under breathing condition. Number of particle deposited during breathing condition is not drastically increased although size of the particle is trebly increased. In contrast to breathing condition, however, fewer particles are deposited near the inlet during inhalation condition, but deposition pattern is extensive throughout the generation. Scope of local deposition is wider during inhalation condition in comparison to breathing condition. Deposition concentration in bifurcation regions is clear during inhalation condition in 6 µm particles injection.

Furthermore, particle depositions of 10 µm particles injection during inhalation and breathing condition are presented in Figure 4-17. Number of particles deposited is greater when 10 µm particles are injected in comparison to smaller particle sizes, and deposition fractions are approximately 99.8 % and 62.6 % under inhalation and breathing condition respectively. Main bronchus is the dominant region of particle deposition during both respiratory conditions, followed by bifurcation zones at all generations. Particle deposition near the inlet is also significant as quantity of particles deposited in this region is gradually increased as particle size increased. Particle deposition near the inlet is greater during breathing condition than inhalation condition.

2 µm

6 µm

10 µm

Inhalation (60 L/min) Breathing (18 L/min)

Figure 4-17: The KG11 model particle deposition variations.

4.3.5 Deposition Efficiency Figure 4-18 shows particle deposition efficiencies against particular particle sizes (1– 20µm) in two particular inspiratory conditions. To calculate deposition efficiency, equation introduced by Zhu et al. (2014) is employed:

푛 휂 = 1 − (4-3) 푑푒푝표푠푖푡푖표푛 푁

where n is number of particle deposited within the airway, and N is total number of particle injected through the inlet.

Trend of deposition efficiency is generally decreased by increasing size of the particle. Deposition efficiency is higher during breathing condition than during inhalation condition, indicating that less viscous respiratory airflow through the airway induces less deposition phenomenon. Also, variation of deposition efficiency in relation to the particle size is non-linear, and a radical variation (decrease) of deposition efficiencies exist between the particle size of 6 – 13 µm during inhalation condition and between 2 – 10 µm during breathing condition.

In terms of efficiency of particle penetration through the airway, the KG7 airway model is more efficient in comparison to the WM or KG11 model. The highest deposition efficiency is 97 % which is calculated based on 2 µm particles in the KG7 model. In terms of particle transportation, 2 µm particles are the most efficient particle size during both inhalation and breathing condition within generation 0 to generation 7 of upper tracheobronchial region. This is appeared through both the KG7 and WM model, except for the WM model during inhalation condition, as such deposition efficiency is smaller than deposition efficiency of 1 µm particle. In the KG11 model during inspiratory conditions and the WM model during inhalation condition, 1 µm particles are the most efficient particle size in terms of particle transportation, as deposition efficiencies are reached to 70 %, 84 % and 92 % respectively. 100% KG7 (Inhalation)

8 µm KG7 (Breathing)

75% KG11 (Inhalation) KG11 (Breathing) 2 µm 10 µm WM (Inhalation) 50% WM (Breathing) 4 µm 13 µm 25%

Deposition Efficiency Deposition 17 µm 20 µm 0% 1 6 11 16 21 Particle size (µm) Figure 4-18: Deposition efficiency plotted against particle size (diameter) assuming that the shape of injected particles is spherical.

4.4 Conclusion Three different airway models under two different respiratory conditions are simulated in order to compare particle trajectory, particle deposition and deposition efficiency. CFD-DPM is employed to observe flow field in airways of upper tracheobronchial region in the Eulerian frame as well as to track particle trajectories in the Lagrangian frame. Under the same (between KG7 and KG11 models) or relevant (between KG7 or KG11 and WM model) conditions, results are compared particularly for the particle trajectories and deposition pattern to observe variation of deposition efficiency in relation to the effect of particle size. The main assumption, which dominant particle deposition factor in upper tracheobronchial region is inertial impaction is proved as transportation of particles in such region is dominantly influenced by drag force of respiratory airflow during inspiratory conditions.

Major finding of the simulation is that the inhalation, an induced inspiratory condition which its flowrate is generally measured as 60 L/min is less efficient in terms of particle penetration through upper tracheobronchial in comparison to the normal breathing condition which its flowrate is measured to be 18 L/min, since deposition fraction of inhalation condition is comparatively lower than the deposition fraction of breathing condition. Particle deposition is concentrated on the walls of bifurcation of daughter airways at each generation during both respiratory conditions.

If particle deposition is desirable in upper tracheobronchial region rather than penetrating such region, inhalation would be more capable. Also, if particle transportation into the distal part of the lung such as particle deposition into alveolar region is mainly concerned, inspiratory flowrate should be controlled under 60 L/min as flowrates exceeding 60 L/min cause null efficiency of particle deposition at upper tracheobronchial region. In this connection, however, observation through further study and simulation using airway models consisting of lower generation (i.e. greater generation numbers) would require to reliably or confidently discuss.

CHAPTER 5

5. SUMMARY AND FUTURE WORK

In this project, the flow-field of the air and behaviour of inhaled particles in airway models corresponding to upper tracheobronchial region of human pulmonary system under two different inspiratory conditions were investigated by numerical simulations based on CFD. Inhalation and normal breathing inspiratory conditions were particularly adopted for such numerical investigation. The steady state fluid dynamics and prediction of particle transportation in employed realistic and idealised airway models were simulated by applying Eulerian – Lagrangian method. ANSYS Fluent package including discrete phase model was utilized for the purposes of performing models employment, meshing, simulation and particle track. All simulation models were validated through comparing with physical experiments by applying similar boundary conditions with respect to flow-field, Reynolds number, Stokes number and deposition efficiencies. Based on the numerical results, flow properties, particle trajectory variation, particle deposition concentration and deposition efficiencies in different inspiratory conditions and particle size were systematically studied. The major findings of this project are listed as below.

 Breathing inspiratory condition was shown to be better in terms of deposition efficiency in comparison to inhalation inspiratory condition in upper tracheobronchial region. Inlet flowrate of breathing condition is approximately one-third lower than the flowrate of inhalation condition. However greater number of particles was observed to be penetrated through airways in upper tracheobronchial region during breathing condition regardless of aerodynamic diameter of particles. The flow-field during inhalation condition was transitional flow whereas during breathing condition was laminar flow, causing increase of inconsistency of particle trajectories due to the turbulence during inhalation condition.  With the particle density of 1425kg/푚3, the aerodynamic diameter of particles between 1 ~ 4 µm was observed to be the most efficient size in terms of

deposition efficiency in upper tracheobronchial region. Particles larger than 4 µm were largely deposited in comparison to smaller particles in both inspiratory conditions. Deposition rate differences between 4 µm and 6 µm were approximately 30 % whereas rate differences between 6 µm and 8 µm were approximately 15 %. Drastic drop of deposition rate between 4 µm and 6 µm was more significant during inhalation condition. The highest deposition efficiency was 97 % observed in 2 µm particles during breathing condition in the KG7 and WM airway model.  Inertial impaction dominantly caused particle deposition in upper region of the airways geometry, causing particles to be deposited on the wall of upper tracheobronchial airways especially in airway bifurcation regions. Deposition density in regions of daughter airway bifurcation was observed to be increased by increase of particle size and inlet flowrate. The greatest deposition density in bifurcation region was observed in generation 1 where the first bifurcation occurs. Particle deposition due to sedimentation also observed in the lower generations of the KG11 but was not as much as deposition due to the inertial impaction.  Rapid change of inspiratory airflow direction and gravity were observed to be dominantly causing particle motion. Due to the inertia of particle, trajectories of particles were less observed in airways toward the upward outlets. As a result, majority of particles transported through airways toward downward outlets. Density of particle deposition in such regions was also observed to be less than lower parts of upper tracheobronchial region, since only few particles were observed to be deposited in upper parts.  Employment of realistic and idealised airway models has both cons and pros. In terms of deposition efficiency measurement, both KG series and the WM airway models have shown similar results including patterns of inspiratory air flow- field, particle trajectory and particle deposition and deposition efficiency. KG series models however enabled to observe pattern of particle deposition at a glance by showing global deposition status in whole upper tracheobronchial region. On the other hand, the WM airway model enabled to measure detailed local concentration of particle deposition in particular areas of upper tracheobronchial region. Furthermore, realistic features presented in KG airway

100

models provide numerical results with better reliability over idealised airway models.

This project has demonstrated the ability of Euler-Lagrangian method for simulating inspiratory air flow-field and particle trajectory to observe pattern of particle deposition under different inspiratory conditions in particular area of human respiratory tract by using CFD-DPM model. Additional future works over this project could be considered as follow.

 Employment of CFD-DEM coupling in multiphase-flow model to investigate interactions between particle to particle as well as particle to wall under inspiratory conditions.  Employment of realistic respiratory tract model consisting of the extra-thoracic together with tracheobronchial regions. This will enable to observe particle penetration from nasal or the oral cavity through upper airways to reach therapeutically effective regions of the respiratory tract at a glance.  Employment of dynamic realistic environmental conditions as a boundary condition of simulation can be studied to improve our understandings of atmospheric or environmental effects causing respiratory disease as well as therapeutic solutions.

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Appendix A

Data of conceptual respiratory tract models

Table A-1: Dimension comparison of Finaly Lung model and Weibel Lung model (Finlay, et al., 2000; Weibel, 1963) Finlay Model Weibel Model Length Diameter Cumulative Length Diameter Cumulative Generation (m) (m) Volume (m) (m) Volume (푚3) (푚3) 0 0.120456 0.0181 0.00003205 0.1026 0.01539 0.00001907 1 0.03614 0.01414 0.000043401 0.0407 0.01043 0.00002564 2 0.02862 0.01115 0.000054572 0.01624 0.0071 0.00002864 3 0.02281 0.00885 0.000065786 0.0065 0.00479 0.0000295 4 0.0178 0.00706 0.000076918 0.01086 0.00385 0.0000317 5 0.01126 0.00565 0.000085948 0.00915 0.00299 0.00003376 6 0.00897 0.00454 0.000095237 0.00769 0.00239 0.00003595 7 0.00828 0.00364 0.000106236 0.0065 0.00197 0.00003839 8 0.00745 0.00286 0.000118458 0.00547 0.00159 0.00004114 9 0.00653 0.00218 0.000130922 0.00462 0.00132 0.00004439 10 0.00555 0.00162 0.000142711 0.00393 0.00111 0.00004826 11 0.00454 0.00121 0.000153381 0.00333 0.00093 0.00005301 12 0.00357 0.00092 0.000163119 0.00282 0.00081 0.00005914 13 0.00277 0.00073 0.000172644 0.00231 0.0007 0.00006626 14 0.00219 0.00061 0.00018313 0.00197 0.00063 0.00007714 15 0.00134 0.00049 0.000204967 0.00171 0.00056 0.0000907 16 0.00109 0.00048 0.000239898 0.00141 0.00051 0.0000907 17 0.00091 0.00039 0.000284101 0.00121 0.00046 0.00013932 18 0.00081 0.00037 0.000357893 0.001 0.00043 0.00019061 19 0.00068 0.00035 0.000474046 0.00085 0.0004 0.00028817 20 0.00068 0.00033 0.000689872 0.00071 0.00038 0.00051295 21 0.00068 0.0003 0.00106777 0.0006 0.00037 0.00092525 22 0.00065 0.00028 0.001742742 0.0005 0.00035 0.00169417 23 0.00073 0.00024 0.003 0.00043 0.00035 0.003

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Table A-2: Bifurcation growth at each generation

Number of Bifurcation Increase Rate Sub-Region Generation Finlay Weibel Finlay Weibel Model Model Model Model Trachea 0 1 1 - - 1 2 2 ▲93.4% ▲89.1% 2 4 5 ▲99.9% ▲147.0% 3 8 7 ▲99.9% ▲57.4% Upper Tracheo- 4 16 17 ▲99.9% ▲137.0% bronchial region 5 32 32 ▲100.2% ▲84.3% 6 64 63 ▲100.0% ▲98.0% 7 128 123 ▲99.6% ▲94.0% 8 255 253 ▲100.0% ▲105.6% 9 511 514 ▲100.3% ▲103.0% 10 1,031 1,018 ▲101.5% ▲98.0% 11 2,044 2,100 ▲98.3% ▲106.4% Lower Tracheo- 12 4,103 4,218 ▲100.8% ▲100.9% bronchial region 13 8,216 8,009 ▲100.2% ▲89.9% 14 16,384 17,717 ▲99.4% ▲121.2% 15 86,418 32,196 ▲427.5% ▲81.7% 16 177,097 168,797 ▲104.9% ▲424.3% 17 406,622 253,319 ▲129.6% ▲50.1% 18 847,288 519,823 ▲108.4% ▲105.2% 19 1,775,397 913,362 ▲109.5% ▲75.7% Alveolar region 20 3,710,882 2,791,530 ▲109.0% ▲205.6% 21 7,860,694 6,390,999 ▲111.8% ▲128.9% 22 16,865,802 15,983,989 ▲114.6% ▲150.1% 23 38,070,553 31,564,013 ▲125.7% ▲97.5%

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Appendix B

Drag force and Drag coefficient applied to 1 µm particles in Finlay and Weibel’s conceptual lung model during selected inspiratory conditions

1.E+01 Aerodynamic diameter of particle = 1 µm 1.E+00

1.E-01

1.E-02 Upper tracheo-

Drag bronchial region F

1.E-03 Lower tracheobronchial region Finlay (Inhalation) 1.E-04 Finlay (Breathing) Weibel (Inhalation) Alveolar region Weibel (Breathing) 1.E-05 0 4 8 12 16 20 24 Generation Figure B-1: Comparison of drag force applied to 1 µm particles during inhalation and breathing conditions. Note that the flow velocity is in µm/s.

1.E+05 Alveolar region

1.E+04

1.E+03 Lower tracheobronchial region

Upper tracheo-

1.E+02

D bronchial region C

1.E+01

1.E+00 Inhalation

Breathing 1.E-01 0 4 8 12 16 20 24

Generation Figure B-2: Comparison of drag coefficient during inhalation and breathing condition

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