DEVELOPING COMPUTATIONAL METHODS TO PREDICT THE...

DEVELOPING COMPUTATIONAL METHODS TOPREDICT THE FATE OF INHALED PARTICLES IN THE

LUNG

TEODOR ERNGREN

A THESIS SUBMITTED IN FULFILLMENT FOR THE

DEGREE MASTER OF SCIENCE IN BIOMEDICAL

ENGINEERING WITH MASTERS IN

BIOMEDICAL MODELLING AND SIMULATION

IN THE

DEPARTMENT OF BIOMEDICAL ENGINEERING

LINKÖPING’S INSTITUTE OF TECHNOLOGY

LIU-IMT-TFK-A–17/545—SE

EXAMINER: GUNNAR CEDERSUND

JUNE 2017

Abstract

The respiratory system can be targeted by many different types of diseases, for example asthmaand cancer. The drug delivery method by inhaling substances for treating diseases only startedin the 1950s with the treating of asthma, considered also for many other diseases. Mathematicaldosimetry models are used in drug development to predict the deposition of particles in the lungs.This prediction is not easily achieved experimentally, and therefore these mathematically modelsare of high importance. Monkeys are often used in the late stages of drug development due to theirresemblance in humans. A good model for predicting the deposition pattern in monkeys is thereforeuseful in the development of drugs. However, there is at the moment no developed deposition modelfor monkeys. In this thesis both a static model and the first dynamic deposition model was developedusing the data on the breathing pattern from respiratory inductance plethysmography (RIP) bands.This dynamic model provides regional and time resolved information on the particle deposition in thelungs of monkeys and can be used to get a deeper understanding of the fate of inhaled particles. Thismodel can also determine inter-animals differences which have not been achieved before. An extensiveimplementation of these time resolved deposition models could be used to increase understandingabout deposition in a variety of species and help the field to move forward.

3

Preface

This master thesis is for fulfillment of the degree master of science in biomedical engineering with master

in biomedical modelling and simulation. The master thesis was conducted at AstraZeneca in Mölndal and

consists of a literature study and development of different computational models in MATLAB.

Acknowledgements

Firstly I would like to thank AstraZeneca and especially my supervisor Elin Boger for the opportunity to

conduct this thesis and all the support I have got during the thesis work. Elin’s support in both writing

and problem solving have been invaluable. A big thank you to Steven Oag at AstraZeneca as well, for

his input and help. Also thanks to my examiner Gunnar Cedersund and my supervisor William Lövfors

for their support and guidance. Finally a big thank you to my friends and family that have served as my

support group during the thesis. Without all of you the thesis result would not have been the same.

- Teodor Erngren

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Contents

List of Figures 7

1 Introduction 91.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Theoretical background 112.1 Respiratory system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Generating airflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.2 Respiratory system of rhesus and cynomolgus monkeys . . . . . . . . . . . . . . 13

2.1.3 Breathing parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Depositions factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Impaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2 Sedimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.3 Brownian diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Respiratory inductance plethysmography . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Material and methods 173.1 Airway geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Static model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Results 274.1 Static model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2.1 Regional deposition for 1 m particles . . . . . . . . . . . . . . . . . . . . . . . 29

4.2.2 Whole breathing cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2.3 Deposition fraction for 2 µm particles over time . . . . . . . . . . . . . . . . . . 34

5 Discussion and analysis 355.1 Static model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2 Dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3 Model comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Ethical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5

6 Conclusion 43

7 Future research 45

A Figures 47

Bibliography 59

6

List of Figures

2.1 A schematic picture of the airway structure . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 A spirogram, showing the different breathing parameters, adapted from [9] . . . . . . . . . . 13

2.3 A schematic picture of the major deposition mechanism, adapted from [25]. . . . . . . . . . 15

2.4 An example of a summed filtered RIP signal acquired with dual-belt system. . . . . . . . . . 16

3.1 A segmented breath from the RIP signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Schematic figures over the filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 A schematic picture of the output structure, with permission from the creator [26]. . . . . . . 25

4.1 Graphs over the regional deposition during inspiration and breath-hold. . . . . . . . . . . . 27

4.2 Graphs over the regional deposition for expisation and the total deposition. . . . . . . . . . . 28

4.3 Total deposition fraction for different particle sizes. . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Graphs over the total deposition for different regions of the lung. . . . . . . . . . . . . . . . 29

4.5 Deposition fraction over time in different generations of the lung for 1 µm particles, during

the inspiratory phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29


breath holding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


the expiratory phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.8 Total deposition fraction over time in different generations for 0.1 µm particles. . . . . . . . 31

4.9 Total deposition fraction over time in different generations for 0.5 µm particles. . . . . . . . 31

4.10 Total deposition fraction over time in different generations for 1 µm particles. . . . . . . . . 32



4.13 Total deposition fraction for 2 µm particles over time. . . . . . . . . . . . . . . . . . . . . . 34

4.14 Graphs over the fraction of particles that gets trapped in the nose and lungs. . . . . . . . . . 34

A.1 Deposition fraction over time in different generations of the lung for 0.1 µm particles, during




A.3 Deposition fraction over time in different generations of the lung for 2 µm particles, during


7




breath holding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


breath holding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


breath holding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


breath holding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51









A.13 Total deposition fraction for different particle sizes for different breaths. . . . . . . . . . . . 53

A.14 Total deposition fraction for different particle sizes for different breaths,

with static breathing parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

A.15 Total deposition fraction for different particle sizes for different breaths

in the tracheobronchial (TB) region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54


in the tracheobronchial (TB) region, with static breathing parameters. . . . . . . . . . . . . 55


in the pulmonary (PUL) region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55


in the pulmonary (PUL) region, with static breathing parameters. . . . . . . . . . . . . . . . 56

A.19 Fraction of particles that gets trapped in the nose for different particle sizes

for different breaths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A.20 Fraction of particles that gets trapped in the nose for different particle sizes

for different breaths, with static breathing parameters. . . . . . . . . . . . . . . . . . . . . . 57

A.21 Fraction of particles that gets trapped in the lung for different particle sizes

for different breaths, after spontaneous nasal breathing . . . . . . . . . . . . . . . . . . . . 57

A.22 Fraction of particles that gets trapped in the lung for different particle sizes

for different breaths, with static breathing parameters, after spontaneous nasal breathing . . . 58

A.23 Graphs from [3] for comparison with the models output . . . . . . . . . . . . . . . . . . . . 58

8

Chapter 1

Introduction

The respiratory system can be affected by many different types of diseases, with different severity and

targeting different parts of the respiratory system. Everything from chronic diseases as chronic obstructive

pulmonary disease (COPD) and asthma, to infection such as pneumonia and also cancer. Many of these

diseases can be very problematic for the patients if left untreated, and a good treatment can have a high

impact on the quality of life of the patients.

Inhaling substances for treating diseases has only begun to be used in modern medicine. In the 1950s

asthma started to be treated by inhaled drugs and inhalation is now considered for a number of lung

conditions and other diseases. Modern discoveries have led to a rise of interest of systemic delivery

of drugs by inhalation [6]. Monkeys or nonhuman primates have been used to investigate the benefits

and risks of inhaled exposure to different compounds in humans. Due to similarities between humans

and monkeys, some biological responses found in monkeys can be expected to occur in humans as well.

Prediction of drug exposure and deposition is hard to determine experimentally and therefore it is of

interest to investigate the potential usage of mathematical dosimetry models [3]. However, there is at the

moment no developed deposition model for monkeys. Such a model could be used to predict the drug

deposition for preclinical studies and also to see if monkeys can be used as a predictor for the deposition

in human lungs. Such models needs to account for and handle the complexity of the respiratory system

and especially the lungs.

The lungs are a part of the complex respiratory system, which is crucial for all mammals survival.

In collaboration with the cardiovascular system, it does not only supply the body with oxygen, but also

eliminates the by-product carbon dioxide from the body. The respiratory system consists of the nose,

pharynx, larynx, trachea, bronchi and the lungs. The bronchi and the lungs are subdivided into primary

bronchi, secondary bronchi, tertiary bronchi, bronchioles, terminal bronchioles, respiratory bronchioles,

alveolar ducts, alveolar sac and alveoli [9]. All this builds up a rather messy tree structure.

9

In modelling, the structure is simplified and divided into smaller parts called generations. These

generations of the respiratory tree starts in the nose and ends in the alveoli, and are indexed from 1 to

∼25. Parts of these generation indices are coupled together to form three main regions, the extrathoractic

region (ET), tracheobronchial region (TB) and alveolar region (AL). The ET region reaches from the nose

down to the start of the trachea and are defined as generation 1. The TB region reaches from the trachea

all the way down to the bronchioles, e.g. generation 2-18. The bottom of the lung tree is called the AL

region which reaches from the terminal bronchioles to the alveoli e.g. generation 19 -∼25 [5].

As of today a conventional way to calculate the predicted dose in an inhalation study is given by:

Dose = DdeposcAVttfmin (1.1)

where Ddepos is the deposition fraction,e.g. the fraction of the inhaled particles that gets trapped in the

chosen region, cA is the particle concentration in the inhaled air, Vt is the tidal volume, t is the exposure

time and fmin is the breathing frequency [7]. The values of the tidal volume and breathing frequency are

mean values of the exposure time and are measured by, for example, RIP bands (respiratory inductance

plethysmography). The deposition fraction is in the best case calculated according to species, body weight,

particle size distribution and average breathing pattern based on empirically derived equations, but are

sometimes only taken from a table. This way of calculating the dose assumes a fixed breathing pattern

and it can thus significantly deviate from the truth. The tidal volume differs between each breath and the

breathing frequency varies as well. Clearly, the deposition fractions are dependent of tidal volume and

flow rate, which means that they will also vary from breath to breath.

It would be of interest to use the time resolved flow signal from RIP bands and thereby make the

the deposition modelling time resolved. This would give a more precise prediction of the dose and

also enable tracking of the deposition in the monkey over the exposure time. An extension of this kind,

would closer resemble the ideal situation and thus provide a prediction of the particle deposition. CFD

(computational fluid dynamics) would also be an attractive option, as such modelling approach would

account for different flow profiles in the airways.

1.1 Aims

The aims of this master thesis are :

- To develop a computational model for the particle deposition in the lungs of monkeys.

- To integrate the volumetric flow data from RIP bands to extend the model and make it time resolved.

1.2 Limitations

The models will be developed in MATLAB and using a variety of MATLAB’s toolboxes. This means

that the models will be dependent of MATLAB to be used. In the models, no clearing factors such as

mucociliary clearance will be accounted for.

10

Chapter 2

Theoretical background

In order to construct these deposition model in both man and monkeys (mainly rhesus (Macaca Mulatta)

and cynomolgus (Macaca Fascicularis) monkeys [12]) one need to have a deep understanding on how the

respiratory system functions. If one understands the structure and the functionality of the upper and lower

respiratory tract, one can then construct suitable models to enable prediction of the particle deposition.

The particles will travel down into the lungs by the inhaled air and on must understand how the air behaves

in the lungs. The lungs reside in the thoracic cavity and are separated by, for example, the heart. Because

of the hearts placement, the left lung is approximately 10 % smaller than the right. The most peripheral

part of the lungs is the alveoli, which is the site of gas exchange in the lungs. At the alveoli the oxygen in

the air diffuse into the blood and the carbon dioxide diffuses from the blood to the lungs [9].

2.1 Respiratory system

The respiratory system helps the body to contain homeostasis by enable the exchange of oxygen and

carbon dioxide between the air, blood and cells in the body. By doing this, it also contributes to a stable

pH level in the body fluids. The respiratory system reaches all the way from the nostrils down to the

alveoli. It is usually divided into two main parts; 1) the upper respiratory system which includes the nose,

nasal cavity, pharynx with their associated structures, and 2) the lower respiratory system, which includes

the larynx, trachea, bronchi and the lungs. The different parts of the lower respiratory system are divided

in a variety of sub-parts as can be seen in Figure 2.1 [9].

11

Figure 2.1: A schematic picture of the airway structure

The main function of the upper respiratory system is to warm, moisten and filter the incoming air,

which is mainly preformed in the nasal cavity. When air is inhaled through the nostrils, it passes by skin

lined with coarse hairs, which is designed to capture large particles in the air. While the air is traveling

through the upper respiratory tract, it is warmed by the blood in the capillaries in the airways. Throughout

the air’s path down towards the lungs mucus is secreted from the goblets cells that help moisten the air, but

also traps dust particles. The trapped particles are transported to the pharynx by the cilia where it can be ei-

ther swallowed or spat out [9]. The air will then continue down the trachea and down throughout the lungs.

At the carina, the trachea divides into the right and left primary bronchus, which connects the trachea to

the lungs. The right bronchus is more vertical, shorter and wider than the left one, which means that an

inhaled object is more prone to enter the right bronchus than the left. From these primary bronchus the

airways branches out more and more, as shown in Figure 2.1 [9]. Throughout the airways branching there

are mucous and cilia that help trapping foreign objects and transporting them up to the pharynx for removal.

The particles travels to all part of the lung by the airflow in the lungs and this airflow is of course

driven by the ventilation of the lungs by the act of breathing. The process of breathing is a rather complex

mechanism in the body with many different contributors which work together in order to get air in and out

of the lungs.

2.1.1 Generating airflow

The breathing is driven purely by pressure differences between the atmospheric pressure and the pressure

in the lungs. In order to achieve this pressure difference and allow air to flow in and out of the lungs, the

muscles surrounding the lungs work to change the volume of the lungs, which thus leads to changes in

the pressure in the lung. The main contributor to the increased lung volume is the diaphragm, which is a

dome-shaped muscle that basically is the floor of the thoracic cavity. During inhalation the diaphragm

contracts and by doing that it flattens, which increases the lung volume and thus decreases the pressure.

Not only the diaphragm is contracting during inhalation, the external intercostals also contract and elevate

the ribs [9].

12

In order to empty the lungs during exhalation, the body has to decrease the lung volume and there-

fore increase the pressure. The exhalation begins when the contracted muscle at inhalation starts to relax.

Due to the elasticity of the muscles, they will spring back to their original shape and position and by doing

that the lung volume decreases. This process is active during relaxed breathing and does not require any

real effort from the body. It is only at forceful expiration that the abdominal muscles and the intercostals

start working to increase the expiratory flow rate, which might be needed when playing a wind instrument

for example [9].

2.1.2 Respiratory system of rhesus and cynomolgus monkeys

Detailed information about the airways and the breathing pattern of maraque monkey are very sparse. But

similarities between the maraque and humans have been established, for example the bifurcation of the

airways. The number of airway generations is roughly the same in the majority of mammalian species,

but the actual bifurcation is rather unique in primates, including humans. The airways is branching out at

45 degrees and are almost uniformly in size, and is called dichotomous branching [13]. Other similarities

has been found, in both architectural, morphological and development patterns. The lungs of non-human

primates are also more similar in number of airway generations, number of alveoli and the type of the

distal airways than any other laboratory animals [14].

2.1.3 Breathing parameters

At rest, an adult human breathe with a frequency of about 12 breaths/min and the inhaled and exhaled

volume are approximately 500 mL. This volume is called the tidal volume (Vt) and if one multiply

this volume by the breathing frequency, one get the minute volume which is the total inhaled/exhaled

volume during a minute. The Vt is individual and varies a lot between different persons, but also in

the same person at different times. To investigate these parameters and also to measure other relevant

volumes of the lung, one can use a spirometer to produce a spirogram, which can be seen in Figure 2.2 [9].

Figure 2.2: A spirogram, showing the different breathing parameters, adapted from [9]

13

These additional parameters are related to forceful breathing, e.g. when putting more effort into the

breathing to inhale/exhale more air. The extra air that a person is able to inhale under a breath is called the

inspiratory reserve volume (IRV) and by adding this to the Vt one get the inspiratory capacity (IC). With

the same logic applied, the volume a person can exhale is called the expiratory reserve volume (ERV)

and if adding this to the IC one get the vital capacity (VC) of the lungs. The volume that resides in the

lungs after a person has exhaled the maximum amount of air possible, is the residual volume (RV). This

volume is impossible to exhale due to the subatmospheric intrapural pressure that keeps the alveoli slightly

inflated. By adding up all these volumes of the spirogram, one get the total lung capacity (TLC), which is

the maximum volume of the lung [9].

All of these parameters will impact the number of particles deposited in different parts of the airways. But

to understand how and where the particles will end up in the lungs, one need to have an understanding on

how the particles deposit and what influences these deposition factors.

2.2 Depositions factors

Predicting the fate of inhaled particles in the lung is a multidisciplinary task that includes solving a

complex physical problem within a biological system. With the use of mathematical equations and

accounting for biological factors, one can describe the deposition of particles in the lungs. The biological

system in question, the lungs, are described by building up a morphology consisting of cylindrical tubes

that branches out and represents the different airway generations. The respiratory parameters are of

great importance, because they decide the flow rate and velocity of the inhaled air and therefore also the

particles’ velocity in the airways. Deposition models should strive to achieve two main goals: firstly,

the assumptions made should be as anatomically and physiologically realistic as possible. Secondly,

they must allow numerical or analytical solutions to the mathematical expressions describing the air flow

patterns, deposition and the biological system [5].

Aerosols suspended in inhaled air will be subject to different physical mechanisms, which will re-

sult in the aerosols leaving the airstream of the inhaled air and finally deposit in the surrounding area. The

three main mechanisms ( which can be seen in Figure 2.3) that will affect the aerosols and contribute to

the deposition are 1) Brownian diffusion, 2) sedimentation due to gravity, and 3) impaction due to inertial

forces. Other factors like deposition due to phoretic forces, electrical charge and cloud settling may occur

for specific aerosols and conditions [5].

14

Figure 2.3: A schematic picture of the major deposition mechanism, adapted from [25].

2.2.1 Impaction

Impaction is mostly present in the upper airways due to the higher air velocities compared to the peripheral

lung regions [5]. Impaction comes from when a particle sticks to its original trajectory in the airways,

instead of following the curvature of the actual airway. For this phenomenon to occur, the particles

momentum needs to be high enough for the centrifugal forces to force the particle out from the turbulent

airstream and impact on the nearby airway walls. This is mostly present in the first 10 generations of the

airways where the speed is sufficiently high and the flow is predominately turbulent [15]. Impaction also

occurs more for larger particles and for fast breathing, due to the increase in air flow velocities [5].

2.2.2 Sedimentation

The slower air velocities in the distal regions of the lung lead to longer residence times. As the longer

residence times allow the particles with sufficiently high masses to deposit due to gravitational forces, de-

position due to sedimentation will predominantly occur in the last five generations of the bronchioles [15].

Clearly, it also follows that a slower breathing pattern will increase the deposition due to sedimentation as

the decreased air velocity leads to longer residence times [5].

2.2.3 Brownian diffusion

The particle deposition due to diffusion is the main deposition mechanism in the lower airways and in

the alveoli. The particles are moving around randomly in the inhaled air and are depositing on the walls

of airways, this motion of the particles is called Brownian motion [16]. Brownian motion is a stochastic

process of particle motion suspended in a fluid. The particle, which is much larger than an air molecule,

will hit the air molecules repeatedly and will then appear the be moving randomly in the air. Diffusional

deposition is more prominent for smaller particles with a diameter of 0.5 µm or less. If the particles are

even smaller, down to nm size, the particles will also be trapped in the upper airways.

15

2.3 Respiratory inductance plethysmography

RIP is a non-invasive method to measure lung volumes and is performed by measuring the movement

of the chest and abdomen induced by breathing. Many breathing parameters can be extracted using RIP,

such as respiratory rate, tidal volume, peak inspiratory/expiratory flow and work of breathing index.

The RIP system consists of an elastic band with a coiled wire inside. This belt is worn either around the

chest or abdomen (single-band system) or both (dual-band system). An alternating current is applied to

the coiled wire, which will create a magnetic field. The RIP system works of the principle from Faraday’s

law [21], that a current through a loop will generate a magnetic field orthogonal to the orientation of the

loop. The change of area of the enclosed loop will then generate an opposing current proportional to the

change of area of the loop according to Lenz’s law ("The direction of the induced current is such as to

create a magnetic field which opposes the change of magnetic flux" [21]). When breathing, the raising

and lowering of the chest/abdomen will result in a change of the cross-sectional area of the subject’s

body and therefore the enclosed area of the loop. This change in area will thus change the magnetic field

that is generated by the loop and the change will then induce an opposing current in the wire that can be

measured. This is usually done by measuring the change in frequency of the applied alternating current

[20].

The signals generated both from the chest and abdomen can either be presented independently or as

a mathematical summation between the two. To handle amplitude differences, the signals are usually

normalized before the summation. The summed RIP signal is a good measurement of the subject’s

breathing, a typical RIP signal can be seen in Figure 2.4, but different factors may affect the quality of the

signal. For instance how firmly the belt is attached can play an important role, if too tight the belt itself

can restrict the breathing and therefore the area change of the loop. If the belt is too loose the belt can

start sliding and the two bands can even overlap. Also the belt placement is of great importance, if placed

down at the hips for example, very little change in area will occur when breathing [20].

Time [s]

0 5 10 15 20 25

Volu

me[m

l]

-60

-40

-20

0

20

40

60

80 Filtred RIP-signal

Figure 2.4: An example of a summed filtered RIP signal acquired with dual-belt system.

16

Chapter 3

Material and methods

The approach of building the models started off by defining a geometry and with that starting point trying

to find expressions for the deposition of drug particles/aerosols in the different generations of the lung

tree. Due to lacking data from the deposition in different lung generations quite a few approximations

had to be done. All approximations in the models were either confirmed by literature or were deemed

to be reasonably coherent with anatomical and physiological knowledge of the airways. From here on

monkey will refers to both rhesus and cynomolgus monkeys, because literature shows no major difference

between the species. In all the equations, SI units is assumed unless stated otherwise.

3.1 Airway geometry

In the models, the airway geometry of the monkey and the deposition in the nose were given from [3].

Unfortunately this article was the only one that provided a full description of the airways and the article

only included data from one monkey (six months old male weighing 1.79 kg). This meant that the lung

geometry had to be scaled according to body weight (BW) and breathing parameters to be able to handle

monkeys of different sizes. The breathing parameters used were total lung capacity (TLC), functional

residual capacity (FRC), tidal volume (VT ), upper respiratory tract (URT) minute volume and breathing

frequency. The breathing frequency was determined to be independent of BW and sex and was set to be

39 breaths/min. The other parameters were scaled according to BW with the following equations:

Minute volume = −0.44051 + 3.8434Log(BW ) (3.1)

For males with a BW ≤ 4 kg.

Minute volume = −2.5302 + 1.7744BW − 0.15866BW 2 (3.2)

For females with a BW ≤ 4 kg.

Minute volume = 1.9108− 24.7378e−1.2479BW (3.3)

For both sexes with a BW > 4 kg.

TLC = −51.304 + 104.02BW − 3.6788BW 2 (3.4)

For both sexes with a BW ≤ 15 kg.

17

FRC = −52.593 + 68.651BW − 2.2103BW 2 (3.5)

For both sexes with a BW ≤ 15 kg.

VT = −23.818 + 26.093BW − 2.1946BW 2 (3.6)

For males with a BW < 5.5 kg.

VT = −61.578 + 45.391BW − 4.3842BW 2 (3.7)

For females with a BW < 4.5 kg.

VT =1000 ∗ Minute volumeBreathing frequency

(3.8)

For males with a BW ≥ 5.5 kg and for females with a BW ≥ 4.5 kg [3].

The lungs are modeled like cylindrical tubes, with a given length and diameter representing the air-

ways and each airway is then branching out to two daughter branches in adjacent generations. An "airway"

refers to one cylinder in the model, with a given length and diameters depending on the airway generation.

If summing up the volume of each cylindrical shaped airway in the model, calculating them with the

corresponding length and diameter, the total calculated volume would be be far less than the real volume.

This is because the cylindrical volume only makes up a part of the total lung volume, as the alveoli volume

is unaccounted for by this cylindrical airway structure. The alveolar volume is therefore added to the

volume of the last seven generations [3]. The method of adding the alveolar volume was developed by

Weibel [24] and is dependent on the number of alveoli in the given generation. After adding the alveolar

volume in a way that the accumulative volume of the lungs equals TLC, the volumes are subsequently

scaled to reflect the lungs at FRC, because a typical breath starts at FRC [24]. This was done for the

monkey lung tabulated in [3] in order to create a "normalized" lung or "lung zero". The produce of adding

and scaling was then preformed again to re-scale "lung zero" according to BW.

To further scale the morphology to be more coherent to reality the length and diameters are scaled

with a factor fARLV given by:

fARLV =

(FRC + 0.5VT

TLC

) 13

(3.9)

and the volumes were scaled by α, according to:

α =FRC + VTFRC

(3.10)

The scaling fARLV is used because the dimensions of the airways given in [3] are acquired at, or near,

TLC with alveolar volumes added. This will result in a morphology that will not correspond to a realistic

respiratory lung volume. By scaling the dimensions by fARLV and α, you get an average respiratory lung

volume over an entire breathing cycle. Also the URT was subtracted from the ingoing tidal volume to

account for the volume trapped in the nose and will therefore not effect the lung deposition.

18

3.2 Static model

The static model was developed by building up a lung morphology using the data from the article by

[3], and implement the scaling according to BW with the equations given in section 3.2.1 and adding the

corresponding alveolar volumes [3]. To get a more realistic lung volume over an entire breathing cycle

the airway morphology was subsequently scaled with fARLV and α. When a suitable morphology had

been created, the particle loss in the nose was modeled. Due to the high flow velocity in the nose, the

two dominating factors for particle loss are inertial impaction for particle sizes of 1µm > and Brownian

diffusion for particles < 1µm.

The particle loss due to Brownian diffusion was given by Yeh et al [10] and then modified by [3]

to enable scaling according to BW:

ηd = 1− e−13.3

(S/VS0/V0

)−0.219

D0.543Q−0.219

(3.11)

where ηd is the particle loss efficiency due to Brownian diffusion in the nose, D is the particles diffusion

constant in cm2

s and Q is the flow rate in litersmin . S/V is the surface-to-volume ratio of the BW of the

monkey that is evaluated. The S0/V0 is the S/V ratio of the measurements done by [10] (a monkey with a

BW of 8.5 kg) and both ratios is calculated by equation:

S/V = 6.23 + 30.306e−0.2658BW (3.12)

The particle loss due to inertial impaction was given by Kelly et al [11], and yet again the equation

was modified to enable BW scaling [3]:

ηi = 1− e

−

(3.227∗10−4

(S/VS0/V0

)ρd2Q

)2.162

(3.13)

where ηi is the deposition efficiency due to inertial impaction, S/V and S0/V0 is calculated in the same

way as for the Brownian diffusion but S0/V0 was calculated for a monkey with a BW of 10 kg from [11].

ρ is the particle density given in gcm3 , d is the particle diameter in µm and Q is the flow rate in cm3

s [11].

Even though the two different particle loss processes occur primarily for different particles sizes, it is safe

to assume the net particle loss, e.g. the fraction of particles that gets trapped in the nose, can be written as

the sum of the two particle loss processes [3]:

ηnet = ηd + ηi (3.14)

where ηnet is the total deposition efficiency in the nose.

The ηnet can also be written as [11]:

ηnet = 1− CoutCin

(3.15)

where Cin is the concentration of the air inhaled through the nostrils and Cout is the concentration that

will travel down into the respiratory tree. By rearranging Equation 3.15 one can calculate Cout:

Cout = (1− ηnet)Cin (3.16)

19

This calculated Cout is then used as input in the dose calculations in the lungs.

The rest of the airway system (from the trachea and down to the alveoli) were modeled by using

components from the models described by Lee et al [4] and Schmid et al [7]. The basic idea is to calculate

a probability that a particle will be deposited in a given lung generation, if not deposited in a generation,

the particle will simply exit the lung during exhalation. The probability of deposition will depend on three

different factors; 1) diffusion of particles, 2) inertial impaction, and 3) gravitational sedimentation in the

airways. Together these factors contribute to a probability given by:

Pi = 1− (1−DIFi)(1− IMPi)(1− SEDi) (3.17)

The calculations for the gravitational sedimentation (SEDi) was given by [7]:

SEDi =2

π(2ε(1− ε2/3)1/2 − ε1/3(1− ε2/3)1/2 + arcsin(ε1/3)) (3.18)

where ε is given by:

ε =3vgticosφi

4Di(3.19)

where ti is the mean residence time of the air in given airway generation i, φi is the angle that forms

between the tube in the given airway and the gravity of the earth. Di is the diameter of the airways

in generation i and vg is the settling velocity of a particle due to gravitation and is described by Equa-

tion 3.20 [4]:

vg =ρpd

2gC(d)

18η(3.20)

where ρp is the inhaled particle density, d is the particle aerodynamic diameter, g is the gravitational

acceleration constant, η is the viscosity of air at ambient conditions. The difference from the equation

in [4] is the use of a sin term instead of cos, that is due to the rat’s lung orientation with respect to the

gravitation field of the earth and C(d) is the Cunningham correction factor given by Equation 3.21 [4]:

C(d) = 1 +λ

d

[2.514 + e−0.55 d

λ

](3.21)

where λ is the mean free path of air molecules at ambient conditions [4].

The deposition due to inertial impaction in the airways (IMPi) was described as:

IMPi = 0.768θiStk (3.22)

where Stk is the Stokes number of the flow given by Equation 3.23 and θi is the bend angle, which is

given by Equation 3.24 [23].

Stk =ρ0d

2uiC(d)

9ηDi(3.23)

where ρ0 is the unit particle density and ui is the flow velocity in the given airway generation.

θ =Li4Di

(3.24)

20

The deposition due to Brownian diffusion during inhalation and exhalation (DIFi) is given by [4]:

DIFi = 1− 0.819e−14.63µ − 0.0976e−89.22µ − 0.0325e−228µ − 0.0509e−125.9µ2/3 (3.25)

where µ is given by Equation 3.26 for inhalation and exhalation.

µ =DmolLiuiD2

i

(3.26)

where Dmol is the Brownian diffusion constant calculated by Equation 3.27, Li is the length of the airway

in a given generation [4] and ui is the mean velocity of the air in a given airway [7].

Dmol =kTC(d)

3πηd(3.27)

k is the Boltzmann constant and T is the temperature in Kelvin [4]. For breath holding, the deposition due

to Brownian diffusion is given by:

DIFi = 1− e

−5.784kTCt

6πµdi2 D

2i (3.28)

where t is the breath-hold time in a given airway.

By using these factors for deposition, one can calculate the probability that a particle will deposit

in a given generation during the three different parts of the breathing cycle; 1) inhalation, 2) breath holding

and 3) exhalation according to Equation 3.17. With these probabilities for deposition, one can calculate

the deposition fractions for the different parts of the breathing cycle.

The deposition fraction during inhalation (DE(i)in) is given by:

DE(i)in = fiPini

imax∑j=i

Vj (3.29)

where i denotes the airway generation, V the total volume of the airway generation, imax is the last

ventilated airway generation, e.g. the last generation penetrated by the tidal volume and the factor f is

given by [4]:

fi =i−1∏j=1

(1− P ini ) (3.30)

The factor f is the fraction of the aerosols in the inhaled air that travels to a given generation without

being deposited [22]. Deposition during breath holding (DE(i)bh) is given by [7]:

DE(i)bh = fi(1− P ini )P bhi Vi (3.31)

And finally the deposition during exhalation (DE(i)ex) is given by:

DE(i)ex = fi+2Vi+1Pexi + P exi

imax∑j=i+2

fj+1Vj(1− P bj )

j−1∏l=i+1

(1− P exl ) (3.32)

By summing up these deposition factors for all generations of the lung and for the three different parts of

the breathing cycle, one can get a total deposition factor (DEi) for the lung for that particle size [4]. This

is done according to [7]:

21

DEi = DEini +DEbhi +DEexi (3.33)

By using the calculated deposition factors, one can estimate the deposited dose in the lungs during a

selected time period. The estimated dose is dependent on the concentration that enters the lungs, the

deposition factor calculated in Equation 3.33 and the minute volume. The estimated dose is calculated

according to Equation 1.1 [7], which also can be written as:

Dose = DE ∗ Cout ∗Minutevolume (3.34)

3.3 Dynamic model

The basic idea of the dynamic extension of the deposition model was to account for differences in the

breathing pattern during the exposure time. Because the deposition of the lungs is highly dependent on

the breathing pattern, it is safe to assume that the deposition will vary with varying breathing parameters.

Changes in flow rate and tidal volume will have a big impact on the deposition fraction. The static model

does not account for asymmetry in the breathing, e.g. if the inhalation is faster than the exhalation etc.

In order to make the model dynamic, one need measurements of the breathing pattern to use as input to

the model. RIP bands are often used to measure the breathing in monkeys during inhalation studies and

the measurements from RIP bands are used in this model to make it dynamic. The dynamic model is

actually the static model that is run over and over again with different breathing parameters as input for

each run. Such RIP data have been collected by AstraZeneca with emka RIP band system and processed

with thier iox2 software, the data was then imported into MATLAB. The data needed to be calibrated and

the calibration coefficient was extracted from emka’s software ECGauto.

The relevant breathing parameters to be extracted were the tidal volumes for inhalation and exhala-

tion, breath holding time and flow rate for inhalation and exhalation. To enable extraction of these

parameters, the signal had to be processed and filtered to reduce noise and artifacts. The signal has

a sample frequency of 200 Hz, but the relevant information, the breathing, has a frequency around 1

Hz. This means that a lot of the samples carries the same information. In order to avoid unnecessary

calculations, the signal was decimated/down sampled to a frequency of 40 Hz.

22

To account for some movement artifacts and baseline wandering of the signal, the signal was high-

pass filtered using a high-order high-pass filter with an empirically decided cut-off frequency to get a

satisfactory result, e.g a result which minimized the noise without loosing any information. The built in

convolution function filtfilt in MATLAB was used to ensure that no phase-shift was introduced in the

signal. The same procedure was used to remove the high frequency noise that is partly introduced due to

movement of the monkey but also due to bad placement and/or movement of the bands, e.g. sliding down.

The high-pass filtered signal was filtered again by a high-order low-pass filter with an empirically decided

cut-off frequency which produced a satisfactory result, e.g a result which minimized the noise without

loosing any information. Yet again the MATLAB function filtfilt was used to ensure that no phase-shift

was introduced in the signal. An example of a filtered signal can be seen in Figure 2.4.

The idea behind the extraction of breathing parameters can be seen in Figure 3.1 which shows a typical

breath from the RIP data. The result of the filtering processes can be seen in Figure 3.2a and 3.2b.

Figure 3.1: A segmented breath from the RIP signal.

23

Samples

0 200 400 600 800 1000

Volu

me[m

l]

-80

-60

-40

-20

0

20

40

60

80High-pass filtering

(a) An example of the high-passfiltering of the RIP signal, the red signal is after filteringand the blue is before the filtering.

Samples

0 200 400 600 800 1000

Volu

me[m

l]

-80

-60

-40

-20

0

20

40

60

80Low pass filtering

(b) An example of the low-passfiltering of the RIP signal, the red signal is after filteringand the blue is before the filtering.

Figure 3.2: Schematic figures over the filtering.

To be able to extract the relevant breathing parameters from the filtered RIP signal, the MATLAB

command findpeaks was used to find the points in the signal that are marked by the circles and crosses

in Figure 3.1. The circles and crosses denote the start and end of inhalation of a breath, and start and

end of the exhalation of a breath. By looking at the amplitude differences between the start of inhala-

tion/exhalation and the end of inhalation/exhalation one can calculate the tidal volume going in and out the

lungs. The idea behind the calculation of tidal volumes can be seen in the spirogram shown in Figure 2.2.

To extract the flow rate of the inhalation and exhalation, a gradient vector between the start and end of

inhalation/exhalation was created and the flow rate was set as the mean of the gradient vector. The last

parameter to be extracted was the breath holding time between inhalation and exhalation. In order to

calculate the breath holding time, the difference between the ten adjacent samples from both sides of the

peak at end of inhalation were investigated. As long as the difference between two adjacent samples was

less than 2 mL, the signal were considered to be flat. Meaning that there is no change in volume of the

lungs, e.g. the subject is holding its breath. By measuring the number of samples when the signal is flat,

one can decide the breath holding time by converting the number of samples to seconds.

Some error handling were implemented to account for when the calculated breathing parameters took

unreasonable values. This was achieved by checking if either the flow rates or tidal volumes were

unreasonably high or low. If one of theses parameters were outside the defined normal range of values,

the whole breath associated with that parameter was deemed bad and replaced with a predefined standard

breath. This was to ensure that no unrealistic asymmetry of a breath occurred.

24

When the relevant breathing parameters had been extracted from the RIP signal, these were used

as input to the rest of the model. Firstly the nose deposition was calculated, and the calculations were

preformed in the same way as in the static model. Two loss factors were calculated, one depending on

impaction (Equation 3.13) and one depending on diffusion (Equation 3.11), and the outgoing concentration

was subsequently calculated according to Equation 3.16. The nose deposition, or nose filtering, is highly

dependent on flow rate, which means that the filtering efficiency of the nose will vary for the same particle

size, but with different breathing parameters. By running the nose algorithm for each breath with the

corresponding flow rate, and for all simulated particle sizes, the generated output from the nose filtering

will be a 2D-array with outgoing concentration for each breath and for each particle size. This array was

later used to predict the deposited dose in the lungs.

The deposition fraction is clearly dependent on the airway geometry and the airway scaling of TLC

and FRC according to BW is the same as in the static model. However, since the other breathing pa-

rameters that are used as input to the model are varying between each breath, the airway geometry will

be scaled slightly different for each breath. This is evident from the equations describing the scaling

factors (Equation 3.9 and Equation 3.10), where the breath-varying parameter Vt is used as input. All

these different scaling factors are used in the scaling for each breath. Also the tidal volumes needs to be

adjusted to account for the part of the tidal volume that gets trapped in the URT. The variation in lung

geometry because of the variation of breathing parameters will of course have even more impact on the

deposition fraction. Not only will the RIP data introduce variations in the lung geometry between breaths,

but also, the variation in breathing pattern will effect the impaction, sedimentation and diffusion in the

lungs. Both the tidal volume and the flow rate influence the deposition mechanism. The tidal volume

decides how far the particles will penetrate in the lungs, and the flow rate decides the particles velocity in

the airways.

When all the scaling factors and breathing parameter vectors were established, all of them were used

as input to the actual deposition fraction calculation. The deposition calculation itself is more or less

identical to the static model, but now the algorithm is run over and over again for each breath and each

particle size. Each simulated particle size is run through the model with the varying breathing parameters

and scaling factors for the corresponding breath. This means that the static model is run for each breath

and each particle size with the corresponding breathing parameters. Hence, this results in a rather complex

output. Rather than to get one deposition fraction for each part of the breathing cycle, and one total for

each generation of the lung tree, the resulting output instead becomes several outputs for each breath. The

basic structure of the output can be seen in Figure 3.3.

Figure 3.3: A schematic picture of the output structure, with permission from the creator [26].

25

The deposition algorithm will generate three 3D-arrays, one for each part of the breathing cycle, with

deposition fractions. The rows in the arrays corresponds to a lung generation, the columns corresponds to

each breath and finally the different pages of 2D-arrays correspond to the different particle sizes simulated.

These arrays are what makes the model dynamic. Since the model works breath by breath, one can use

these arrays and reduce the Equation 1.1 to the following:

Dose = DDepos(t)CA(t) (3.35)

By incorporating the time dependence in the concentration and in the deposition fraction, there is no need

of having the Vt, exposure time and fmin in the dose calculations. By subsequently manipulating these

3D-arrays, one can choose which parts of the lung or at which time one wants to look at the deposition

fraction.

26

Chapter 4

Results

This section contains a selection of outputs from both models. The outputs have been chosen to emphasize

the differences between the static and the dynamic model. Also, a partial validation of the output will be

presented. The deposition fractions in the graphs are assumed to be with endotracheal breathing unless

stated otherwise. Endotracheal breathing means that the particle loss in the nose is not accounted for,

the model only considers air going in to the trachea. The other mode of breathing is spontaneous nasal

breathing which is the most common way of breathing in monkeys, meaning that the breath through their

nose and particle loss in the nose is accounted for.

4.1 Static model

The output from the static model was simulated with a BW of 1.79 kg and with breathing parameters

scaled according to BW. The BW was chosen to resemble the monkey, which was used to generate the

morphology data in [3]. By doing that, one can validate the output by comparing the results from that paper.

Figure 4.1 and 4.2 show regional deposition fractions for a variety of particle sizes. The graphs show the

fraction of particles of a given sizes that will deposit in a given generation. Figure 4.3 and 4.4 show the

total deposition for a spectrum of particles sizes for the whole lung, the TB region and PUL region.

Lung generation

0 5 10 15 20 25

De

po

sitio

n f

ractio

n

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1Deposition during inspiration

0.1 µm

0.5 µm

1 µm

2µm

3µm

(a) Deposition fraction during inspiratory phasein the different lung generations.

Lung generation

0 5 10 15 20 25

De

po

sitio

n f

ractio

n

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04Deposition during breath holding

0.1 µm

0.5 µm

1 µm

2µm

3µm

(b) Deposition fraction during breath holdingin the different lung generations.

Figure 4.1: Graphs over the regional deposition during inspiration and breath-hold.

27

Lung generation

0 5 10 15 20 25

De

po

sitio

n f

ractio

n

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02Deposition during expiration

0.1 µm

0.5 µm

1 µm

2µm

3µm

(a) Deposition fraction during expiratory phasein the different lung generations.

Lung generation

0 5 10 15 20 25

De

po

sitio

n f

ractio

n

0

0.02

0.04

0.06

0.08

0.1

0.12Total deposition during the breathing cycle

0.1 µm

0.5 µm

1 µm

2µm

3µm

(b) Total deposition fractionin the different lung generations.

Figure 4.2: Graphs over the regional deposition for expisation and the total deposition.

Particle diameters [m]

10-8 10-7 10-6 10-5

Depositio

n fra

ction

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Deposition factor for different particle diameters

Figure 4.3: Total deposition fraction for different particle sizes.

28


10-8 10-7 10-6 10-5

Depositio

n fra

ction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Deposition factor for different particle diameters, tracheobronchial (TB) region

(a) Total deposition fraction for differentparticles sizes in the tracheobronchial (TB) region.


10-8 10-7 10-6 10-5

Depositio

n fra

ction

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35Deposition factor for different particle diameters, pulmonary (PUL) region

(b) Total deposition fraction for differentparticle sizes in the pulmonary (PUL) region.

Figure 4.4: Graphs over the total deposition for different regions of the lung.

4.2 Dynamic model

The outputs from the dynamical model were simulated with a BW of 3 kg, because it is similar to the

average weight of the monkeys used in the study were the RIP data was extracted from. It was also

simulated with a BW of 1.79 kg and with static breathing parameters from the static model to highlight

the differences between the models. Figure A.1 to Figure 4.12 show the regional deposition for different

particle sizes over time, during the different parts of the breathing cycle.

4.2.1 Regional deposition for 1 m particles

25

20

Deposition fraction in different generations for 1 µm particles, during the inspiratory phase

15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.03

0.025

0.02

0.015

0.01

0.005

0

0.035

0

Depositio

n fra

tion

0

0.005

0.01

0.015

0.02

0.025

0.03

Figure 4.5: Deposition fraction over time in different generations of the lung for 1 µm particles, duringthe inspiratory phase.

29

25

20

Deposition fraction in different generations for 1 µm particles, during breath holding

15

10

Lung generation

5

025

20

15

Time [s]

10

5

2

4

6

8

0

0

×10-3

Depositio

n fra

tion

×10-3

0

1

2

3

4

5

6

7

Figure 4.6: Deposition fraction over time in different generations of the lung for 1 µm particles, duringbreath holding.

25

20

Deposition fraction in different generations for 1 µm particles, during the expiratory phase

15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.03

0.025

0.02

0.015

0.01

0

0.005

0

Depositio

n fra

tion

0

0.005

0.01

0.015

0.02

0.025

Figure 4.7: Deposition fraction over time in different generations of the lung for 1 µm particles, duringthe expiratory phase.

30

4.2.2 Whole breathing cycle

25

20

15

Total deposition fraction in different generations for 0.1 µm particles

Generation

10

5

025

20

15

Time (s)

10

5

0.07

0.02

0.06

0.05

0.08

0.01

0

0.04

0.03

0

Depositio

n fra

tion

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Figure 4.8: Total deposition fraction over time in different generations for 0.1 µm particles.

25

20

15


10

Lung generation

5

025

20

15

Time [s]

10

5

0.01

0.015

0.02

0.025

0

0.005

0

Depositio

n fra

tion

0

0.005

0.01

0.015

0.02

Figure 4.9: Total deposition fraction over time in different generations for 0.5 µm particles.

31

25

20

15

Total deposition fraction in different generations for 1 µm particles

10

Lung generation

5

025

20

15

Time [s]

10

5

0.03

0.05

0.02

0.01

0

0.06

0.04

0

Depositio

n fra

tion

0

0.01

0.02

0.03

0.04

0.05

Figure 4.10: Total deposition fraction over time in different generations for 1 µm particles.

25

20

15


10

Lung generation

5

025

20

15

Time [s]

10

5

0

0.02

0.04

0.06

0.1

0.12

0.14

0.08

0

Depositio

n fra

tion

0

0.02

0.04

0.06

0.08

0.1

0.12


32

25

20

15


10

Lung generation

5

025

20

15

Time [s]

10

5

0.15

0.1

0.05

0

0

Depositio

n fra

tion

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14


33

4.2.3 Deposition fraction for 2 µm particles over time

Figure 4.13 and Figure 4.14 shows deposition fraction over time for 2 µm particles. Both the total

deposition fraction (e.g. the sum of the nose and lung deposition) and also the fraction of particles that

gets trapped in the nose and in the lung.

Time [s]

0 5 10 15 20 25

De

po

sitio

n f

ractio

n

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9Total deposition fraction

Figure 4.13: Total deposition fraction for 2 µm particles over time.

Time [s]

0 5 10 15 20 25

Fra

ctio

n

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26Fraction of particles deposited in the nose

(a) Fraction of 2 µm that gets stuck inthe nose over time.

Time [s]

0 5 10 15 20 25

Fra

ctio

n

0.6

0.62

0.64

0.66

0.68

0.7

0.72Fraction of particles deposited in the lung

(b) Fraction of 2 µm that gets stuck inthe lung over time.

Figure 4.14: Graphs over the fraction of particles that gets trapped in the nose and lungs.

34

Chapter 5

Discussion and analysis

Both models are capable of modeling the particle deposition in a sufficient way, but the two approaches

yield different results. Therefore an evaluation gives a deeper understanding of the output and how the

output is generated, and also if the output and the models behavior is coherent with reality. Because of the

usefulness mathematical dosimetry models in drug development and the increased usage of inhalation as

a drug delivery method, a well developed model can be ground breaking. With a dynamical extension of

the deposition models on can get more precise prediction of the particle deposition and therefore a better

understanding.

5.1 Static model

The static model is the more conventional way of modelling particle deposition and this kind of models

are already implemented for different species such as [4][7] for rodents. The logic used in these models

has also laid the foundation for the models created specifically for monkeys. The model describe all parts

of the lung as cylindrical tubes, which the particles deposit in, either by impaction, sedimentation or

diffusion. Since the models in [4] and [7] are built upon deposition of particles in cylindrical tubes, it

follows that the same equations with some modification can be implemented for deposition in monkeys as

well. The equations are well known and heavily cited, which strengthens the use of them in the model.

The model is more or less divided into two parts. One part that calculates the concentration of par-

ticles in the air that goes down in the the trachea. Meaning that the algorithm calculates the filtering

efficiency of the nose, i.e. the number of particle that gets trapped in the nose. The two factors for particle

loss in the nose, diffusion and impaction, are both empirically derived by simulating the airflow in casts of

the URT of monkeys. For the studies that evaluated the URT deposition in monkey, an animal with a BW

of 12 kg [11] and one with 8.5 kg BW [10] was used for the impaction and diffusion study, respectively.

As the constants in the Equations 3.11 and 3.13 are empirically derived, the BW scaling implemented

from [3] might not be as accurate when interpolating down to a BW of around 3 kg for example. The two

factors that impact the filtering in the nose are dominant for different particle sizes. Diffusion is present

for particles < 1 µm and inertial impaction is present for particles > 1 µm. But there is a "grey area"

where both the diffusion and impaction is very low and the nose filtering are very low in total, e.g. the

majority of the particles will travel down to the lungs. The "grey area" is roughly between 0.1 µm - 2.5 µm.

As there is only one monkey morphology available, given in [3], interpolation is required to enable

35

BW scaling of the lung morphology. The same goes for the breathing parameters such as TLC, FRC etc.

Because of the limited sample size, the breathing parameters were only measured in 121 monkeys, the

regression analysis has limited strength. Also when constructing the airways in the model, the alveolar

volumes are added according to Weibel’s method [24] and then it is assumed that the branching pattern

and alveolating pattern is the same in monkeys as in humans. This assumption is fairly good because

similarities has been documented between the lungs in maraques and humans [14]. This limitation in the

morphology and scaling to other BW is one of the Achilles’s heel of the model. But as of today there

are not any more available data and one has to rely on this kind of interpolation and the assumption of

similarities in humans, and therefore this is the best solution at the moment. The nose filtering has the

same limitation as the equations need to be scaled to a lower BW, the same problems occur when scaling

the breathing parameters. Since the regression analysis was performed on a data set collected from 121

monkeys with a BW < 4 kg, the scaling if the breathing parameters might be less accurate at higher BWs.

Despite these limitations in the airway morphology and scaling, the model provides satisfactory re-

sults and the model’s behavior corresponds to the expected behavior in reality. This can be highlighted

in Figure 4.1 and 4.2. As one can see in the graphs the larger particles deposit in the upper generations

and the smaller particles in the lower generations. This is an expected behavior because impaction is

more present in the upper generations, and larger particles are also more prone to impact in the upper

bifurcations. With the same logic, one can expect that the smaller particles are more prone to deposit in

the lower generations since diffusion is the predominating deposition factor in the lower generations and

also the smaller particles are very prone to diffuse.

Another thing that is worth mentioning is the high differences in deposition fraction in the different

parts of the breathing cycle. These differences are mainly caused by the different deposition factors that

dominate different parts of the breathing cycle. During inhalation, impaction will dominate the upper

generations due to the high air velocities and relatively many bifurcations. As the air travels down in the

lung tree, the air velocity decreases and therefore the deposition due to impaction will decrease as well.

The decreasing air velocity will also increase the deposition due to gravitational sedimentation. This is

because the streamlines in the airways will be weaker meaning that the gravitational force will be able to

pull the particles down towards the walls of the airways. Also at increasingly lower generations, the airway

diameter decreases which means that the distance the gravitational force need to pull the particle will be

shorter and shorter. When the air reaches the most distal airways, diffusion will be the main deposition

mechanism and therefore one can see that the deposition fractions are higher for smaller particles because

they are more prone to diffuse.

36

The deposition during breath-hold is a lot lower than for inhalation and the regional deposition pattern

is different as well. The regional deposition pattern can be seen in Figure 4.1b and one thing to mention

is that almost no particles deposit in the upper generations. This is because in the upper generations,

impaction is the dominating deposition mechanism and during breath-holding the air stands still in the

airways. This means that the particles will not flow by the bifurcations, therefore no deposition will

occur due to impaction. Therefore sedimentation and diffusion are the only factors that influence the

deposition. As a result, the deposition during breath-hold is highly dependent on the tidal volume and

the breath holding time. The tidal volume decides how deep the air will penetrate in the lungs and since

diffusion and sedimentation is more present in lower generations, the deposition during breath-hold will

increase with higher penetration. Also with longer breath-holding time, the deposition will increase

because of the particles have more time to sediment and diffuse before the air turns and the exhalation

start. Clearly, another factor contributing to the lower deposition during breath-hold and exhalation, it that

many particles have already deposited during the inspiratory phase. With that exception, the same logic

applies to exhalation, e.g. larger particles are more prone to deposit in the upper generations and vice versa.

Another common representation of the output is to look at the total deposition fraction over a spec-

trum of particle sizes. As can be seen in Figure 4.3, this motivates the selection of particle sizes for the

simulations shown in Figure 4.1 and 4.2. In the particle size region of 0.1 - 3 µm, the deposition fraction

changes a lot and therefore it is more interesting to look at, this is highlighted in Figure A.13. Also in a

typical inhalation study in monkeys, the size range of the inhaled particles is roughly between 1 - 3 µm.

Different deposition mechanism are expected to be dominant for different particle sizes, which clearly was

reflected in the models output. Because as the particles get smaller, they are more prone to diffuse. Hence,

as the particles get smaller , the deposition increases and this can be seen for 0.1 µm in Figure 4.2b. The

same logic applies for larger particles, because larger particles are more prone to impact and therefore the

deposition fraction will increase as the particle size increase, this can be seen for 3 µm in Figure 4.2b.

To validate the model, Figure 4.4 was generated showing the the deposition fraction for different regions

of the lung for endotracheal breathing. This Figure, when compared to the Figures A.23 from [3], it

shows good agreement. The differences might be caused by the different modelling approach that was

used in the article, where they use mass conservation equations. This comparison serves as validation of

the static model, i.e. it follows the expected behavior.

37

5.2 Dynamic model

As mentioned before, the dynamic model is basically the static model run over and over again with

varying breathing parameters. This means that the particles will exhibit identical behaviours in the two

models. The key difference is that the dynamic output has a third dimension; time. Rather than to have a

static output for a given generation and particle size, the deposition factor will vary over time. As one

can see in Figure A.1, the overall shape of the 3D-plot is similar to the ones found in Figure 4.1a. As

stated previously, the crucial difference is the variation in time, which can be seen in the 3D-plots in the

appendix. The many peaks that are shown in the graph are caused by the varying breathing parameters,

which are derived from the RIP data. These peaks depend on parameters such as tidal volume that decides

how deep the air will penetrate in the lung and therefore the deposition in the lower generations. The

peaks that can be seen in the upper generations in Figure A.2 depend on the flow rate, as a higher flow rate

will increase the deposition due to impaction in the upper generations. One interesting thing to highlight

is that if there is a peak in the upper generations, there is also a valley in the lower generations. This is

because that higher flow rate will increase the impaction, but also decrease the sedimentation and diffusion

because less particles will reach the distal airways.. Also the deposition fraction is higher in the dynamic

model, mostly because in the static model the breathing parameters are derived from anethezised animals.

Anaesthesia is know to alter the breathing pattern [3] and these animals are expected to breath slower and

not take as big breaths as animals that are awake and also in a stressful situation. Also the dynamic output

where simulated with a BW of 3 kg, which can contribute to the differences.

38

During breath-holding one can clearly see the impact of different breathing parameters, in this case

the breath-holding time. In the Figures that show the breath-holding, e.g. Figure 4.6 and the ones in teh

appendix A.8, one can see a distinct peak at the same location for all particle sizes. It is because the

breath-holding time is longer in that particular breath and therefore the deposition fractions are higher for

that breath. If one looks at the amplitude of the breath-holding graphs, the deposition fraction is very low

and the breath-holding will not have as much impact on the total deposition. Nevertheless these graphs

highlight the differences over time of the deposition fraction.

During exhalation, the same behavior seen in the static model for different particle sizes and differ-

ent generations. The shape of the curves in Figure 4.7 are similar to the shapes found in Figure 4.2a, but

with the same variations as can be seen during inhalation. As one can see in these graphs, peaks and

valleys occur because of the varying breathing parameters from the RIP data. The same pattern observed

during inhalation can also be found during exhalation. Breaths with high peaks in lower generations have

a valley in the upper generations and vice versa, and this occurs for the same reasons as for inhalation.

Also when looking at the amplitude of the exhalation graphs, one can see that amplitude here is lower

than for inhalation, but higher than for breath-holding. This means that the main contributor to the total

deposition fraction is the deposition which comes from the inhalation phase. This does not mean that

the exhalation and breath-holding is redundant, they still contribute to regional deposition and should

not be neglected. One can still see the contributions from exhalation and, for some particles sizes, the

contribution from breath-holding in the graphs for total deposition, Figure 4.8 to 4.12. One can see that

there is constructive interference between the different parts of the breathing cycle and together builds up

the shape of the total deposition.

Clearly it is of interest in the dynamical model to check the total deposition fraction for endotracheal

breathing for different particle sizes, this can be seen in Figure A.13. The surface of the 3D-plot is very

uneven and this is caused by the varying breathing parameters. This is in line with the behaviour shown in

the regional deposition graphs, where the deposition varies with time. It is thus logical that the output

in Figure A.13 follows the same pattern. For the same reason as in the static model, it is of interest to

divide the deposition fraction into the TB and PUL region to enable comparison of the output to the

corresponding output generated in [3]. The overall shapes of the graphs in Figure A.15 and A.17 are very

much alike the one found in [3], but with some amplitude differences for the different particles sizes. This

difference is primarily dependent on two things: 1) like mentioned before, the model used to generate the

output in [3] use equations based on mass conservation to calculate the deposition fraction, 2) the output

in the article was simulated using breathing parameters from anesthetized animals, while in Figure A.15

and A.17 the breathing parameters were derived from the RIP data. Still the results from the paper and the

dynamic model are similar and the output from the model is deemed reasonable.

39

As mentioned before, the filtering efficiency of the nose is variable and highly dependent on particle

size and the velocity of the ingoing air. This behavior can be seen in Figure A.19, which shows the

fraction of particles that gets trapped in the nose for different particle sizes and breaths. As one can see,

in the range from roughly 0.1 - 2 µm almost all particles go down to the lungs. But for larger particles,

the filtering efficiency rapidly increases. If one takes this into account, the fraction of particles that gets

trapped in the lung changes as well. With endotracheal breathing the fraction for different particles was

shown in Figure A.13. If one instead assumes spontaneous nasal breathing and account for the filtering of

the nose, the fraction is shown in Figure A.21. This fraction is basically the fraction in A.13 with the nose

filtering fraction subtracted. The result is shown in Figure A.21, and here one can also see the uneven

surface the occurs because of the varying breathing parameters.

As the output from the dynamical model is in 3D, the visualization is somewhat problematic. 3D-

plots can be hard to interpret in 2D, but there is not a better way of showing the output. One can see that

the surfaces are uneven but it is still hard to distinguish the real differences. Therefore, for visualization

purposes it can be preferable to choose a particle size to asses how its deposition fraction varies over

time. Figure 4.13 show the deposition fraction for 2 µm particles over time. From this Figure, it is clear

that the fraction varies a lot with the varying breathing parameters. The same pattern can be seen in

Figure A.23a and A.23b, which highlight that the different breathing parameters have a high impact on the

deposition fraction. Even though these variations from the RIP data provide valuable information about

the deposition, it also introduces error factors. If the RIP signal is too noisy, it is impossible to extract any

valid information about the breathing pattern. The solution is to replace an invalid breath with a standard

breath with predefined breathing parameters. This is of course hard to generalize for all different situations

and subjects, and unfortunately this occurs often during the exposure time. This is because inhalation

constitutes a stressful situation for the monkey, which therefore will move a lot during the exposure time

and thereby introduce movement artifacts in the RIP signal, which are hard to handle.Therefore, probably

the most reasonable way of handling this noise is to replace breaths with a standard breath, but choose the

predefined parameters with care.

40

5.3 Model comparison

Static models are the standard way to model particle deposition,to the best of the author’s knowledge, and

the dynamical model is the first time resolved model that has been developed until this day. Therefore

it is hard to validate the model without conducting further experiments, but one can still compare the

static way to the dynamical way.This comparison can easily be done since the dynamic model is only an

extension of the static model and basically is the static model ran over and over again. One can then use

the validation of the static model and therefore validate the dynamic model as well, assuming that the

breathing parameters are true. The comparison between the models outputs and the output from [3] are

the only validation steps that were done. In that comparison one could see that the outputs are similar

enough and seem reasonable. Therefore the outputs from the static and dynamic model seem reasonable

as well. With this established, one can start comparing the static approach to the dynamic approach in

more detail to assess the gain of the dynamic extension.

As one can see in Figure A.13 to A.22 in the appendix, all output from the dynamical model have

been replicated with static breathing parameters, derived from the static model. Here, the differences

between the models are obvious and as one can see the shape between both outputs are equal but with the

difference that the dynamical outputs are uneven and varying over time. The uneven surface shows the

gain of time resolved modelling instead of static modelling, it shows that the deposition fraction varies and

it is more reasonable to think that the deposition fraction will vary. Not many animals or humans breath

with static breathing parameters and one can easily see in the static model that the deposition fraction

changes when the breathing parameters changes. Therefore it is logical to model dynamically if one

want to get a model that is more coherent with reality. There are also amplitude differences between the

models, there are cases when the dynamical model provides higher deposition fraction and cases where

the static provides higher deposition. This is easily seen in the graphs for the regional deposition during

breath-holding. The general pattern is that the RIP data provides higher tidal volumes, higher flow rates,

but when these parameters are higher then the breath-holding time usually gets lower. This will result in a

lower deposition during breath-holding which can be seen in the graphs.

Even though the dynamic model provides more detailed information about the deposition over time, one

can argue that the dynamic model is not as reliable as the static one. Because with the static model,

output is not depending on the quality of an externally acquired signal, which has a high impact on the

deposition. Because the static model uses interpolated BW scaling, one will get the same result for the

same monkey, or at least monkeys of the same size and sex, for all different exposures. That is also a

drawback with the static model, it is not reasonable to think that monkeys of the same size and sex will

breath equally, and especially not in a stressful situation, but one can of course argue that the differences

can be neglected. The beauty of the dynamical model is that one can actually check the difference between

monkeys and then have a more solid argument if one can neglect the difference or not. But this requires

that the RIP signal from both monkeys are of good quality. It is a risk and reward with both models, they

have their strengths and weaknesses and different limitations. The static model can be seen as the easy

way out because one is not confined to the limitation of the flow measurements. But the dynamic model

provides more opportunities to investigate variations over time and might be able to explain things that

the static model can not. In the long run the dynamic model will provide more valuable information and a

continuous work towards this kind on modelling will only strengthen the model.

41

For many particle sizes there is not a high variability in the deposition due to breathing parameters,

as can be seen in Figure A.13 for very large particles. This is mainly due to inhalability of the particles,

and in these particle ranges it might be unnecessary to use a dynamic model because it is somewhat more

computationally heavy. Also one can argue from Figure 4.13 that the deposition fraction varies a lot, but

during a one hour exposure time the accumulated dose might converge towards roughly the same value

as in the static case. Even so, the regional deposition, and thus the local free drug concentrations that

drive the pharmacological effect, might be different. This may potentially affect the pharmacological

response of the drug, i.e the aim of treatment, further highlighting the need to describe drug deposition as

accurately as possible. The idea of the dynamic modelling is that the model itself should converge towards

reality, the "optimal" model should describe reality as good as possible and this dynamic extension is one

step in the right direction.

5.4 Ethical issues

When working with projects that includes animal studies, one has to think about the ethical questions

that arise. Always when using animals in studies, one has to consider if that particular study is necessary

and/or it can be done differently and still generate the wanted data. Therefore all studies on animals need

to be approved by an ethics committee that decides if it is reasonable and ethically defensible to conduct

the study. In this decision, the committee takes into account the gain from the study and what strain it will

put on the animal. Because animal studies puts a strain on the animal, the committee tries to make sure

that the strain is hold to a minimum.

Monkeys are often used in the later stages of drug discovery, due to their resemblance with humans [?].

But because of this resemblance and the intellectual level of the monkeys , one need to think about how

the monkey will experience the study and try to minimize the strain. Animal studies is a crucial part of

drug discovery to ensure that the developed drugs are safe to use for humans, therefore animal testing is a

natural part of the work flow.

Computational models need animal studies to be able to validate the models and one of their main

usages at the moment is to interpret the data from studies. But with the increasing complexity of the

models and higher understanding of what happens with inhaled particles, the models could potentially

replace the animal studies. Because if one could instead simulate a specific compound and by the analysis

of the models output, achieve the same results as from a animal study. then one could simply use the

model instead of putting unnecessary strain on an animal. The usage of models is also more time and cost

efficient, because one only need to run a simulation instead of conducting a whole study. One could also

much more efficiently screen more compounds without the need of animal usage. Not only could this

save time, money and reduce the number of animal studies, but it would also result in better medicines for

humans. The process of discovering a new drug would potentially go faster and therefore be able to help

more people and improve the health of the population.

42

Chapter 6

Conclusion

Modelling is not only useful to predict particle deposition, it is also a useful tool in drug development.

It can be used to get a deeper understanding of what happens when a compound is inhaled. Delivering

drugs by inhalation is a fairly new way of treating diseases and in order to develop useful drugs, one

need to have knowledge of what happens with the inhaled particles. The existing deposition models are

static and does not provide any information on how the deposition changes over time and with varying

breathing parameters. In order to achieve this deeper understanding of the particle deposition a foundation

containing a static deposition model for monkey, and then add time resolution. The time resolution come

from adding the flow measurements from RIP signal, which makes the model work breath-by-breath. This

dynamic extension give information on the deposition over time and also allows to investigate differences

between subjects in a more extensive way. The idea and approach to the dynamic model is implementable

in more deposition models and can be used to add time resolution in modelling in other species than

monkeys.This kind of modelling approach will hopefully be acknowledged in the field and help develop

and increase the understanding of what happens with inhaled particles during the exposure time.

43

Chapter 7

Future research

Because there are no time resolved deposition models at the moment except the one developed in this

thesis, it would be of interest to conduct experiments for validating the model further. One approach

to validate the model could be to use imaging techniques with radioactive markers to track the regional

deposition in the lung and check if it corresponds to the predicted deposition pattern from the model. Also

by doing more extensive comparisons of the achieved dose and the predicted dose from an inhalation

study one could use that comparison to validate the model. The beauty of the dynamic part of the model

is that it can be implemented for different species, it just needs a flow signal from the subject’s breathing

pattern. It would be of interest to try this dynamical extension in other deposition models developed for

other species to see the gain of the dynamical extension in these models as well.

There are limitations in the model and one of the big bottle necks is the quality of the flow measurements.

The data does not get any better than the signal itself. Both more sophisticated signal processing, but

foremost further development of the measurement hardware and measuring techniques would increase

the accuracy of the model. Also, with better hardware and continuous work with the signal acquisition,

one could extend the model to work in real-time during the actual exposure time. If the hardware and the

model could be developed and improved in a way that it would work in real-time, one could track the

predicted dose during the exposure time and therefore get more precise dosing. An other bottle neck is the

limited amount and the quality of the available morphology data. To increase the accuracy of the model,

it would be necessary to get a better geometry of the lung that correspond more to reality. One way of

achieving this is by using imaging techniques to get morphology data from more subjects to strengthen the

interpolation to all BWs. There are resolution limitations, which makes it hard to distinguish the alveolar

regions, but with increasingly better imaging techniques it might be possible to distinguish the alveolar

region.

With this improved morphology, a new opportunity becomes possible. That opportunity is CFD, which is

a collection of computational methods to solve physical problems that involves fluid flows. CFD problems

is handled by defining a geometry with physical bounds, this is often done with the help of computer

aided design (CAD) programs. With better imaging one could develop these CAD models that are crucial

to be able to use CFD. If one could extract these lung geometries from the images, one big piece of the

CFD-puzzle is put in place. The geometry is also subdivided into smaller element in a mesh structure.

With a defined geometry and mesh, governing equations is established along with boundary conditions.

These governing equations is then solved iteratively as a steady-state or transient solution.

45

CFD can be used to extend the typical symmetric dosimetry models to increase the accuracy and address

the problem of asymmetry in the lungs. But in order to use CFD in an efficient way, two major problems

need to be solved. Firstly, the geometry need to be established. To adress that, High-resolution computer

tomography (HRCT) could be used to segment out the airway tree from the generated 3D-images [17].

But like mentioned before, limitations in resolution will decide how many airways that can be distin-

guished and therefore segmented out [18]. The second big limitation is the avaiable computational power.

From a study in 2008 the run time when using CFD on the upper 17th generations in a human lung, the

computational time on a super computer was 50 hours [17]. The computational power is a big bottle neck

that is hard to solve, and it is a long way before that kind of computational power will be easily accessed.

But CFD is probably the future for deposition calculations, it is more precise than the existing deposition

models and a leap towards a model that is as close to reality as possible.

46

Appendix A

Figures

Inspiratory phase

25

20

15


10

Lung generation

5

025

20

15

Time [s]

10

5

0.02

0.06

0.08

0.04

0

0

Depositio

n fra

tion

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Figure A.1: Deposition fraction over time in different generations of the lung for 0.1 µm particles, duringthe inspiratory phase.

47

25

20

Deposition fraction in different generations for 0.5 µm particles, during the inspiratory phase

15

10

Lung generation

5

025

20

15

Time [s]

10

5

0

0.005

0.01

0.015

0

Depositio

n fra

tion

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Figure A.2: Deposition fraction over time in different generations of the lung for 0.5 µm particles, duringthe inspiratory phase.

25

20


15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.06

0.1

0.08

0.04

0.02

0

0

Depositio

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0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Figure A.3: Deposition fraction over time in different generations of the lung for 2 µm particles, duringthe inspiratory phase.

48

25

20


15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.12

0

0.02

0.14

0.1

0.08

0.06

0.04

0

Depositio

n fra

tion

0

0.02

0.04

0.06

0.08

0.1

0.12

Figure A.4: Deposition fraction over time in different generations of the lung for 3 µm particles, duringthe inspiratory phase.

Breath-holding phase

25

20

Deposition fraction in different generations for 0.1 µm particles, during breath holding

15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.005

0

0.015

0.02

0.025

0.03

0.01

0

Depositio

n fra

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0

0.005

0.01

0.015

0.02

0.025

Figure A.5: Deposition fraction over time in different generations of the lung for 0.1 µm particles, duringbreath holding.

49

25

20

Deposition fraction in different generations for 0.5 µm particles, during breath holding

15

10

Lung generation

5

025

20

15

Time [s]

10

5

6

4

3

2

1

0

5

0

×10-3

Depositio

n fra

tion

×10-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Figure A.6: Deposition fraction over time in different generations of the lung for 0.5 µm particles, duringbreath holding.

25

20


15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.014

0

0.002

0.004

0.006

0.008

0.01

0.012

0

Depositio

n fra

tion

0

0.002

0.004

0.006

0.008

0.01

0.012

Figure A.7: Deposition fraction over time in different generations of the lung for 2 µm particles, duringbreath holding.

Expiratory phase

50

25

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15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.012

0.01

0.008

0.004

0.006

0.002

0

0

Depositio

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tion

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

Figure A.8: Deposition fraction over time in different generations of the lung for 3 µm particles, duringbreath holding.

25

20

Deposition fraction in different generations for 0.1 µm particles, during the expiratory phase

15

10

Lung generation

5

025

20

15

Time [s]

10

5

0

0.005

0.01

0.015

0.02

0.025

0.03

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Depositio

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0

0.005

0.01

0.015

0.02

0.025

Figure A.9: Deposition fraction over time in different generations of the lung for 0.1 µm particles, duringthe expiratory phase.

Figure A.13 to Figure A.22 are graphs generated with both RIP data and static breathing parameters for

comparison between static output and dynamic output. Figure A.19 to Figure A.22 are with spontaneous

nasal breathing mode.

51

25

20

Deposition fraction in different generations for 0.5 µm particles, during the expiratory phase

15

10

Lung generation

5

025

20

15

Time [s]

10

5

0

0.002

0.004

0.006

0.008

0.01

0.012

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Depositio

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0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

Figure A.10: Deposition fraction over time in different generations of the lung for 0.5 µm particles, duringthe expiratory phase.

25

20


15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.01

0

0.02

0.05

0.03

0.04

0

Depositio

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0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Figure A.11: Deposition fraction over time in different generations of the lung for 2 µm particles, duringthe expiratory phase.

Graphs for comparison from [3]

52

25

20


15

10

Lung generation

5

025

20

15

Time [s]

10

5

0.025

0.015

0.01

0.005

0

0.02

0

Depositio

n fra

tion

0

0.005

0.01

0.015

0.02

Figure A.12: Deposition fraction over time in different generations of the lung for 3 µm particles, duringthe expiratory phase.

10-5

10-6

3D plot of deposition fractions of different particle sizes

10-7

Particle size [m]

10-8

0

5

10

15

Time [s]

20

0.6

0.7

0.8

0.9

1

0.2

0.1

0.3

0.4

0.5

25

Depositio

n fra

tion

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure A.13: Total deposition fraction for different particle sizes for different breaths.

53

10-5

10-6

3D plot of deposition fractions of different particle sizes

10-7

Particle size [m]

10-8

0

5

10

15

Time [s]

20

0.5

0.4

0.3

0.2

0.1

0.6

0.7

0.8

0.9

1

25

Depositio

n fra

tion

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure A.14: Total deposition fraction for different particle sizes for different breaths,with static breathing parameters.

10-5

10-6

Deposition fraction in the tracheobronchial region

10-7

Particle size [m]

10-8

0

5

10

15

Time [s]

20

0

0.8

0.6

0.4

0.2

1

25

Depositio

n fra

tion

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure A.15: Total deposition fraction for different particle sizes for different breathsin the tracheobronchial (TB) region.

54

10-5

10-6

Deposition fraction in the tracheobronchial region

10-7

Particle size [m]

10-8

0

5

10

15

Time [s]

20

0

1

0.8

0.2

0.4

0.6

25

Depositio

n fra

tion

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure A.16: Total deposition fraction for different particle sizes for different breathsin the tracheobronchial (TB) region, with static breathing parameters.

10-5

10-6

Deposition fraction in the pulminary region

10-7

Particle size [m]

10-8

0

5

10

15

Time [s]

20

0.4

0.3

0.2

0.1

0

0.5

0.7

0.6

25

Depositio

n fra

tion

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure A.17: Total deposition fraction for different particle sizes for different breathsin the pulmonary (PUL) region.

55

10-5

10-6

Deposition fraction in the pulminary region

10-7

Particle size [m]

10-8

0

5

10

15

Time [s]

20

0.15

0.05

0.2

0.25

0.3

0

0.1

25

Depositio

n fra

tion

0.05

0.1

0.15

0.2

0.25

Figure A.18: Total deposition fraction for different particle sizes for different breathsin the pulmonary (PUL) region, with static breathing parameters.

10-5

10-6

Fraction of particles deposited in the nose

10-7

Particle size [m]

10-8

25

20

15

Breath number

10

5

1

0.6

0.4

0.2

0.8

1.2

0

Depositio

n fra

tion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure A.19: Fraction of particles that gets trapped in the nose for different particle sizesfor different breaths.

56

10-5

10-6

Fraction of particles deposited in the nose

10-7

Particle size [m]

10-8

25

20

15

Breath number

10

5

0.4

0

0.2

1

0.6

0.8D

epositio

n fra

tion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure A.20: Fraction of particles that gets trapped in the nose for different particle sizesfor different breaths, with static breathing parameters.

10-5

10-6

Fraction of particles deposited in the lung

10-7

Particle size [m]

10-8

25

20

15

Breath number

10

5

0.4

0.2

0

0.8

1

0.6

Depositio

n fra

tion

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Figure A.21: Fraction of particles that gets trapped in the lung for different particle sizesfor different breaths, after spontaneous nasal breathing

57

10-5

10-6

Fraction of particles deposited in the lung

10-7

Particle size [m]

10-8

25

20

15

Breath number

10

5

0.5

0.3

0.2

0.8

0.1

0.7

0

0.4

0.6

Depositio

n fra

tion

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Figure A.22: Fraction of particles that gets trapped in the lung for different particle sizesfor different breaths, with static breathing parameters, after spontaneous nasal breathing

(a) Output from [3] showing the deposition fraction in thetracheobronchial region.

(b) Output from [3] showing the deposition fraction in thepulminary region.

Figure A.23: Graphs from [3] for comparison with the models output

58

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