Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition · ii Modelling Jet Nebulizers to...

Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition

by

Wallace Bo-Neng Wee

A thesis submitted in conformity with the requirements for the degree of Masters of Health Science

Clinical Engineering, Institute of Biomaterials and Biomedical Engineering University of Toronto

© Copyright by Wallace Wee 2010

ii

Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition

Wallace Wee

Masters of Health Science

Clinical Engineering, Institute of Biomaterials and Biomedical Engineering

University of Toronto

2010

Abstract

Administration of medication directly to diseased lungs reduces adverse systemic side

effects. For cystic fibrosis, jet nebulizers are the standard aerosol delivery system since they can

aerosolize drugs that require relatively large volumes of liquid. Selection of the appropriate

nebulizer for a given drug is crucial to ensure delivery of the therapeutic dose. This selection,

ideally, requires knowledge of the pulmonary drug deposition (PDD). The gold standard for

accurately measuring PDD is nuclear medicine techniques, which exposes the subject to

radiation and therefore cannot be used repeatedly to test multiple devices. An alternative is to

characterize the nebulizer using in vitro experiments and estimate the device’s in vivo

performance. However these techniques are time-consuming and can only collect data for one

breathing pattern and drug-device combination. Therefore this study is to formulate

mathematical models for jet nebulizers that can estimate PDD based on the drug-device

combination and patient’s breathing patterns.

iii

Acknowledgments

I am deeply grateful to Dr. Allan Coates for his guidance, patience and encouragement

throughout this project. His insightful advice and support has made my experience in aerosol

science eye-opening and exciting, and has played a substantial part in my development as a

medical researcher.

I am very appreciative to Kitty Leung for teaching me the lab techniques necessary to becoming

an aerosol scientist and having the serenity and fortitude to explain these complex concepts.

I would like to thank my thesis committee Prof. Tom Chau, Dr. Joseph Fisher and Dr. James

Duffin for offering their insight and advice during the project.

I am also very thankful to my family for their inspiration, motivation and continual support.

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Table of Contents

Acknowledgments.......................................................................................................................... iii

Table of Contents ........................................................................................................................... iv

List of Tables.................................................................................................................................. vi

List of Figures ...............................................................................................................................vii

List of Appendices .......................................................................................................................... x

List of Abbreviations...................................................................................................................... xi

Chapter 1 Overview ........................................................................................................................ 1

1 Introduction ................................................................................................................................ 1

2 Background ................................................................................................................................ 5

2.1 Patient Respiration .............................................................................................................. 6

2.2 Particle Distributions........................................................................................................... 6

2.3 Particle Distributions........................................................................................................... 9

2.3.1 Inertial Impaction .................................................................................................. 10

2.3.2 Gravitational Sedimentation.................................................................................. 11

2.3.3 Diffusion................................................................................................................ 12

2.4 Jet Nebulizers .................................................................................................................... 13

2.4.1 Conventional Unvented Jet Nebulizer................................................................... 13

2.4.2 Breath-Enhanced Jet Nebulizer............................................................................. 15

2.4.3 Breath-Actuated Jet Nebulizer .............................................................................. 16

Chapter 2 Predicting Inhaled Mass ............................................................................................... 18

1 Materials and Methods ............................................................................................................. 18

1.1 Mathematical Modelling ................................................................................................... 18

1.2 Experimental Setup ........................................................................................................... 22

1.3 Experimental Procedure .................................................................................................... 23

v

1.3.1 Steady State Conditions ........................................................................................ 23

1.3.2 Dynamic Conditions.............................................................................................. 24

1.4 Experimental Results......................................................................................................... 25

Chapter 3 Predicting Pulmonary Drug Deposition ....................................................................... 34

1 Materials and Methods ............................................................................................................. 34

1.1 Mathematical Modelling ................................................................................................... 34

1.1.1 Inhaled Mass Model .............................................................................................. 34

1.1.2 Pulmonary Drug Deposition Model ...................................................................... 34

1.2 Experimental Setup ........................................................................................................... 38

1.3 Experimental Procedure .................................................................................................... 39

1.3.1 Steady State Conditions ........................................................................................ 39

1.4 Experimental Results......................................................................................................... 40

Chapter 4 Discussions ................................................................................................................... 45

1 In Vitro Results: Predicting Inhaled Mass................................................................................ 45

2 In Vivo Results: Predicting Pulmonary Drug Deposition......................................................... 46

Chapter 5 Conclusions .................................................................................................................. 49

References ..................................................................................................................................... 50

Appendix A – Inhaled Mass Model Derivation ............................................................................ 53

vi

List of Tables

Table 1: Coefficients of the Quadratic Equations (y = a + b x – c x2) for the Rate of Output and

Regression Coefficient (r), where x is the entrained flow through the devices and n is the number

of devices characterized. ............................................................................................................... 28

Table 2: Coefficient of Variation of breath-enhanced nebulizers ................................................ 28

Table 3: Breath-Actuated AeroEclipse II in vitro data – Aerosol collected on the inspiratory

filter compared to the model’s predicted inhaled mass. The standard patient breathing pattern is

VT =0.6 L, Ti/Te = 0.4/0.6 and 15 BPM........................................................................................ 33

Table 4: Subject breathing patterns and physical characteristics. ................................................ 42

vii

List of Figures

Figure1: Poisson distribution ......................................................................................................... 7

Figure 2: Lognormal distribution................................................................................................... 8

Figure 3: Deposition Processes ...................................................................................................... 9

Figure 4: Inertial Impaction ......................................................................................................... 10

Figure 5: Gravitational Sedimentation ......................................................................................... 12

Figure 6: Unvented Jet Nebulizer ................................................................................................ 14

Figure 7: Bernoulli Effect ............................................................................................................ 14

Figure 8: Breath-enhanced Jet Nebulizer (LC Star)..................................................................... 15

Figure 9: Breath-actuated Jet Nebulizer (AeroEclipse) ............................................................... 17

Figure 10: Previously reported characterization curves for various nebulizers ........................... 19

Figure 11: Equating flows............................................................................................................ 20

Figure 12: Scenarios..................................................................................................................... 21

Figure 13: Dynamic conditions setup .......................................................................................... 25

Figure 14: Sample characterization curves .................................................................................. 27

Figure 15: Bland and Altman limits of agreement plot of the difference between drug collected

on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Stars with varying

tidal volumes and the model’s predicted output using the device-drug specific characterization

coefficients. Bias represented in blue and 95% Confidence Interval is in red............................. 29



viii

duty cycles and the model’s predicted output using the device-drug specific characterization

coefficients. Bias represented in blue and 95% Confidence Interval is in red.............................. 29



respiration rates and the model’s predicted output using the device-drug specific characterization

coefficients. Bias represented in blue and 95% Confidence Interval is in red.............................. 30

Figure 18: Bland and Altman limits of agreement plot of the difference between the drug

collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Stars

with varying parameters (tidal volume, duty cycle and respiration rates) and the model’s

predicted output using the device-drug specific characterization coefficients. Bias represented in

blue and 95% Confidence Interval is in red. ................................................................................. 30


on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Pluses with

varying tidal volumes and the model’s predicted output using the device-drug specific

characterization coefficients. Bias represented in blue and 95% Confidence Interval is in red. .. 31



varying duty cycles and the model’s predicted output using the device-drug specific




varying respiration rates and the model’s predicted output using the device-drug specific




varying all parameters (tidal volume, duty cycle and respiration rates) and the model’s predicted

output using the device-drug specific characterization coefficients. Bias represented in blue and

95% Confidence Interval is in red................................................................................................. 32

ix

Figure 23: Nebulizer characterization curves with RF for the Breath-Enhanced (A) LC Star and

(B) LC Plus.................................................................................................................................... 36

Figure 24: Visual representation of drug delivered to the patient (white) after eliminating aerosol

trapped in the dead space (black). ................................................................................................. 37

Figure 25: Particle size distribution measurement setup using the Malvern Mastersizer X........ 39

Figure 26: Bland and Altman limits of agreement plot of the difference between the in vivo

inhaled mass data and the model’s predicted inhaled mass for normal subjects. Bias represented

in blue and 95% Confidence Interval is in red. ............................................................................. 43

Figure 27: Bland and Altman limits of agreement plot of the difference between the in vivo PDD

data and the model’s predicted PDD for normal subjects. Bias represented in blue and 95%

Confidence Interval is in red. ........................................................................................................ 43

Figure 28: Bland and Altman limits of agreement plot of the difference between the in vivo

inhaled mass data and the model’s predicted inhaled mass for CF patients. Bias represented in

blue and 95% Confidence Interval is in red. ................................................................................. 44

Figure 29: Bland and Altman limits of agreement plot of the difference between the in vivo PDD

data and the model’s predicted PDD for CF patients. Bias represented in blue and 95%

Confidence Interval is in red. ........................................................................................................ 44

x

List of Appendices

Appendix A: Inhaled Mass Model Derivation

xi

List of Abbreviations

BPM: Breathes Per Minute

DPI: Dry Powder Inhalers

LPM: Liters Per Minute

MDI: Metered Dose Inhalers

MMAD: Mass Median Aerodynamic Diameter

MMD: Mass Median Diameter

PDD: Pulmonary Drug Deposition

RF: Respirable Fraction

UV: Ultraviolet

1

Chapter 1 Overview

1 Introduction

Lung diseases, like asthma and cystic fibrosis, are conditions that can affect the patient’s

ability to breathe, exchange gases and/or become prone to lung infections. Therefore, where

possible, it makes sense to deliver medications directly to the lungs in the treatment of

respiratory diseases, as this will minimize systemic exposure and adverse side effects3. The ideal

situation would be to achieve successful delivery, which by definition, is noninvasively

overcoming the protective mechanisms and barriers of the airway for distal lung deposition4.

The anatomical barriers that may need to be overcome include the nose, posterior pharynx and

the various airway bifurcations. As a result, successful treatment can be accomplished by

generating an aerosol that can provide sufficient drug deposition but also bypass anatomical

barriers. While smaller aerosol particles are less likely to be trapped by the airway defence

mechanisms, the tradeoff is that these small particles would carry little drug since the particle

volume is proportional to radius cubed (volume α r3)3.

For the clinician to ensure that the patient is receiving adequate medication they require

information about the aerosol particle size and the drug administration route (orally or nasally)5.

The particle size of most medical aerosols follow a Poisson distribution and can be described by

the mass median diameter. Aerosols inhaled orally encounter different anatomical structures as

opposed to those administered nasally. For normal adults, aerosols inhaled through the nose

2

experience greater turbulent flow at the level of nasal turbinates which filters the particle size

significantly in comparison to oral administration where particles greater than 5 µm are filtered,

usually at the posterior pharynx and vocal cords2. The respirable fraction (RF) is defined as the

fraction deposited in the lungs in relation to the total amount that entered the airway opening.

Aerosol devices like the metered dose inhalers (MDI) and dry powder inhalers (DPI) are

devices widely used in asthma management. However these devices are highly dependent on the

properties of the drug being aerosolized and are limited to high potency medications such as

powders, suspensions and solutions. Specifically, high potency for asthma medication refers to

drugs active in the microgram range. For inhaled drugs such as antibiotics which are only

effective in the milligram range, these convenient and efficient delivery systems are less

optimal2.

The jet nebulizer, on the other hand, is the standard aerosol delivery system for cystic

fibrosis since it is able to aerosolize drugs like antibiotics and mucolytic agents6;7

. There are

many classes of jet nebulizers that range from unvented to breath-enhanced to breath-actuated.

Briefly, the unvented nebulizer generates aerosols based solely on the compressor, independent

of the patient’s breathing pattern. More efficient nebulizers, like the breath-enhanced and

breath-actuated devices, are able to minimize the amount of drug generated and lost during

exhalation7. While many of these devices may offer similar outputs, selecting the appropriate

nebulizer for a given drug is crucial to ensure that the patient receives the therapeutic dose.

Unlike intravenous administration, where the clinician knows the exact dose administered to the

3

patient, aerosol medication delivery varies markedly. Although higher technology devices

approach 30% efficiency, the old unvented ones have typical values hovering around 5%8;9

. In

infant patients using a facemask the nebulizer efficacy drops even more to about 1%10

. This

implies that without proper selection of the device and drug combination the delivery could be

less than the therapeutic range or in the worst case cause toxicity in the patient. Another reason

to select the appropriate nebulizer for a given drug is that many of the drugs are expensive, a

factor that favours efficient delivery.

The selection of a suitable nebulizer should, ideally, be based on measurements of

pulmonary deposition. However, this is difficult for three reasons. First, there is a lack of

characterization data for a given device and agent combination. Secondly, nebulizer

performance data by most manufacturers are determined using a saline solution. For aqueous

based drug solutions this does not pose a significant problem for the particle size distribution,

however this still does not provide an accurate indication of the drug output because the output is

often highly dependent on the physical properties (viscosity and surface tension) of the agent

being nebulized11

. Lastly, the sheer number of nebulizers on the market from unvented to

breath-enhanced to breath-actuated and the variations in efficiency within each class of

nebulizers makes it hard to systematically compare devices6.

The current gold standard for accurately measuring pulmonary drug deposition is to use

nuclear medicine techniques. However this technique is not only time consuming but also faces

a number of challenges affecting its accuracy12;13

. These include the selection of an appropriate

4

radioactive label, accommodation of different tissue attenuations and 2D images to infer

deposition in a 3D structure. On top of this, the nuclear medicine technique is only able to

collect data on one patient with a given device and drug combination at a time and at the expense

of exposing the patient to radiation. This also becomes more complicated when dealing with

tests on pediatric patients. Therefore nuclear medicine techniques are not conducive for

evaluating multiple nebulizers for use in patients groups who vary widely in size.

An alternative method is to characterize jet nebulizers using in vitro experiments and then

estimate the in vivo performance of the device14

. These in vitro experiments can be grouped into

two phases. In the first phase the device is evaluated with a known drug to determine the output

particle size distribution at a given entrained flow. The second phase incorporates the dynamic

situation with a patient breath simulator, typically using a double half sinusoidal breathing

pattern15

. Other equipment utilized for these experiments include the electronic balance,

osmometer, ultraviolet (UV) spectrophotometer and laser diffraction particle sizer.

Unfortunately, while the in vitro methodology provides a method of evaluating the device it is

also time-consuming and again is only able to collect data for one breathing pattern, device and

drug combination.

A better solution for evaluating and comparing different nebulizers is to use a

mathematical model that is built upon the patient’s breathing pattern, nebulizer and drug

combination. Although not entirely independent of in vitro experiments, the mathematical model

will only require the steady state information collected in the first phase of the in vitro

5

experiments, which would reduce experimental time. Moreover the model is more flexible,

providing the clinician with the ability to alter any parameter, allowing them to observe trends,

by providing more than 1 data point. Lastly the model can incorporate additional concepts like

the respirable fraction, which is lacking in the in vitro experiments, thus giving more accurate

data for comparison.

As a result the focus of this thesis project is to formulate a mathematical model to bridge

the gap presented by the in vivo and in vitro experiments. This model will provide the means to

effectively determine the amount of pulmonary drug deposition in a patient by taking into

account the nebulizer and drug combination and the patient’s breathing pattern. The validity of

the model will be established from data gathered in both normal adults (Chapter 2) and cystic

fibrosis patients (Chapter 3), pediatric and adult, where both pattern of breathing through a

nebulizer and drug deposition is known.

2 Background

The goal of aerosol treatment is to successfully delivery aerosolized medication directly

to the lungs. To accomplish this requires an understanding of aerosol physics, pulmonary

physiology and technologies. The main concepts that will be touched upon in this section include

patient patterns of breathing, particle size distribution, deposition processes and nebulizer

performance.

6

2.1 Patient Respiration

When a normal individual breathes, air flows in and out of the lungs because of the

pressure differential between the atmosphere and the lungs. The pressure gradient is achieved

either by expanding the lungs during inspiration creating a drop in pressure in the lungs causing

air to flow inwards or vice-versa by contracting the lungs during expiration causing air to flow

outwards. When air travels to the alveoli, during inspiration, it experiences different resistances

and obstructions as it travels through various cavities and airway tracts, which help to filter

unwanted particulate matter. For example air inhaled through the nose experiences greater flow

resistance and turbulence as opposed to air being inhaled through the mouth.

2.2 Particle Distributions

Previously it has been indirectly mentioned that the successful delivery of medical

aerosols is in part dependent on the particle size. This is because the size determines how much

drug is carried and whether the particle will deposit in the lungs. Generally aerosols can be

classified as either monodisperse (particles having all the same size) or polydisperse (aerosol

particles with varying sizes). In practice most medical aerosols are polydisperse and follow the

Poisson distribution, shown in figure 1, which relates particle size with the particle number of an

aerosol. The geometric standard deviation (σg) measures the extent of how polydisperse the

Poisson distribution is, where a larger σg implies greater polydispersion.

7

Figure1: Poisson distribution2

The Poisson distribution, however, does not provide the full picture because small

particles carry little drug. Recall that the particle’s volume is proportional to the 3rd

power of the

radius (r3). Therefore the convention is to express the particle size distribution on a logarithmic

scale of the diameter. Most medical aerosols fit this scale to generate a lognormal distribution,

shown in figure 2.

8

Figure 2: Lognormal distribution2

Additionally, these distributions can be described using a number of different methods.

Two useful statistical values include the mass median diameter (MMD) and mass median

aerodynamic diameter (MMAD). The MMD by definition is the diameter at which one half of

the total mass of spherical particles of unit density is attributed to particles larger than the MMD.

The MMAD is similar to the MMD but is used to describe aerosol particles of non-spherical

and/or different densities. By definition the aerodynamic diameter is the diameter of a unit-

density sphere having the same terminal settling velocity as the particle in question.

From past research studies the ideal aerosol particle size ranges for pulmonary deposition

in normal adults (inhaled orally) is from 1 to 5 µm, but if administered nasally this range

decreases. In addition, there is evidence that the smaller the size of the patient (i.e. pediatric

9

patients) the particle size required for deposition drops even more. The respirable fraction

accounts for the discrepancy between the nebulizer drug output and the amount that deposits in

the lungs is the concept. By multiplying the respirable fraction by the inhaled mass, one can

more accurately determine the amount of drug delivered. The inhaled mass, by definition, is the

amount of aerosol delivered to the mouth of the patient. For in vitro experiments the inhaled

mass corresponds to the mass of aerosol collected on the inspiratory filter, which is the “mouth”

of a mechanical breath simulator.

2.3 Particle Distributions

Aerosolized medication delivered to the patient is deposited in the lungs by one of three

processes; inertial impaction, sedimentation and diffusion (shown in figure 3).

Figure 3: Deposition Processes1

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2.3.1 Inertial Impaction

Large aerosol particles (greater than a few micrometers in diameter) have increased

inertia and as a result are less able to follow a column of air as it turns1. Another way to describe

this process is that these particles cannot navigate around sharp corners (like the airway

bifurcation) and will continue along their original path, illustrated in figure 4. Since inertia is

defined as the resistance of an object to a change in its state of motion, “inertial impaction”

occurs when the particle fails to make a turn and exits the “column of air” carrying it into the

lungs. Inertial impaction against baffles within a nebulizer removes particles too big for lung

deposition and determines the particle size distribution of the device output.

Figure 4: Inertial Impaction

[http://www.biologicalcontrols.com/800400.shtml]

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Three factors that influence a particle’s probability of undergoing inertial impaction are

the particle size, flow speed and aerosol path. The first two factors can be thought of as follows,

the larger or faster a particle is the more time it requires to negotiate around a turn, which

increases the likelihood of inertial impaction. Since the particle is moving at the same speed as

the column of air, in which it is suspended, speed and flow are closely linked.

The last factor is the path that the aerosol takes to reach the lungs. The reason for this is

that depending on where the aerosol travels it will encounter a number of different anatomical

barriers. A prime example is the administration of an aerosol nasally or orally. The anatomical

structures of the nose increase flow resistance and turbulence, which traps more drug in the nasal

pharynx before it can enter the lungs. This is because one of the functional purposes of the nose

is to remove particulate matter from inhaled air before it can deposit in the lungs and it does this

job well, preventing many infections.

2.3.2 Gravitational Sedimentation

In gravitational sedimentation the aerosol particles begin to “rain out”, due to gravity, and

deposit themselves in the lungs, illustrated in figure 5. This deposition process is time-dependent

and therefore is proportional to the time the drug spends in the lungs. In other words the longer

the drug has to dwell in the lungs the greater the amount of deposition. This follows that the

amount of aerosol deposition increases with slow breathing and breath holding because the

aerosolized medication has more time to travel along the respirable tract and sediment. The

12

typical range of particle size diameters that experience sedimentation are from 1 to 5µm.

Particles ≤ 1µm have a high surface area to weight ratio and remain suspended for longer periods

than their larger “sibling”. This time of suspension can be such that they are exhaled before

deposition.

Figure 5: Gravitational Sedimentation

[http://www.argus-group.com/images/sediment.gif]

2.3.3 Diffusion

Diffusion is the primary deposition mechanism for small aerosol particles (diameters less

than 1 µm). For this deposition process, the particles can be modeled as small spheres that

follow the kinetic theory of gases and the concept of Brownian motion. This is where the

particles move about randomly, colliding with other gas molecules until they eventual impact

with the airways of the lungs. The main intermolecular force that contributes to diffusion is

electrostatic. As in the case with gravitational sedimentation, the rate of diffusion deposition is

inversely proportional the patient’s breathing rate, specifically the inspiratory time (Ti). The

slower the patient breathes the more time these small particles have to randomly hit the walls of

the lungs. However the amount of drug carried by these tiny particles is so small (since the

13

amount of drug carried is proportional to r3) that diffusion plays a minor role in drug delivery.

The exception is in the field of air pollution with very potent agents like diesel particulate matter.

2.4 Jet Nebulizers

The current nebulizers on the market utilize three aerosol generation techniques;

ultrasound, jet nebulization and vibrating membrane. This section will focus on the jet nebulizer

as it is the basis for the models. Within this nebulizer class there are significant differences in

the aerosol particle size distribution, cost and design of the different jet nebulizer types (i.e.

unvented vs. breath enhanced vs. breath actuated).

2.4.1 Conventional Unvented Jet Nebulizer

Conventional unvented jet nebulizers are inexpensive and disposable. These devices

generate aerosols by passing compressed gas through a small orifice above the drug solution, as

shown in figure 6. Passing a gas through a small hole creates a high velocity jet, and based on the

Bernoulli Effect (figure 7), will cause a drop in pressure. This pressure differential draws the

drug solution up adjacent capillary tubes towards the jet stream. When the drug reaches the jet

stream it is sheared into an aerosol and travels toward the outlet of the device. A baffle system

located above the orifice filters the particulates to generate a specific particle size distribution.

Larger aerosols that are unable to navigate through the baffles will impact these baffles and fall

14

back down into the original drug solution. In addition, since the only air entering the nebulizing

chamber comes from the compressor, nothing the patient does influences output.

Figure 6: Unvented Jet Nebulizer2

Figure 7: Bernoulli Effect

The above equation of the Bernoulli Effect explains the process in which the drug

solution is pulled towards the jet stream. Although the equation is comprised of multiple

parameters, for simplicity, it can be assumed that ρgz is equal to 0 since the change in height of

ρ = density z = change in height

υ = velocity p = pressure

g = gravity

Low Pressure

15

the jet stream is insignificant in comparison to the gas velocity. As a result, the velocity and

pressure are inversely proportional.

2.4.2 Breath-Enhanced Jet Nebulizer

More sophisticated jet nebulizers are the breath-enhanced and breath-actuated nebulizers.

These nebulizers are more efficient because they are able to minimize the amount of drug

expelled during exhalation.

The breath-enhanced nebulizer generates aerosols in a manner similar to the conventional

unvented nebulizer. However the output of the device can be broken down into two stages based

on the patient’s inspiration and expiration phases. A schematic of a breath-enhanced nebulizer in

operation is shown in figure 8.

Figure 8: Breath-enhanced Jet Nebulizer (LC Star)

Inspiration Expiration

16

From the above figure, it can be seen that the aerosol is continually generated by a high

velocity jet that shears the medication into particulates. During inspiration, the nebulizer’s vent

(entrained flow valve) opens, allowing entrained air to enter the nebulizer and carry aerosolized

medication around the baffles to the patient. During expiration, the vent closes as the expiratory

valve opens. This allows the patient’s expired air to escape to the atmosphere instead of entering

the nebulizer. This stops the expired air from carrying drug out of the vent thereby reducing

drug loss since most of the drug generated during expiration either impacts on the baffles or

“rains out” back into the nebulizer reservoir. Relating this back to modelling the devices, the

amount of aerosol generated during the patient’s expiratory phase is minute in comparison to the

dose delivered during inspiration and therefore can be considered negligible.

2.4.3 Breath-Actuated Jet Nebulizer

While the breath-actuated nebulizer follows the same principles in generating the aerosol,

this device performs slightly better than the breath-enhanced nebulizer by generating medication

only during inspiration6. A schematic of the AeroEclipse II breath-actuated jet nebulizer is

shown in figure 9.

17

Figure 9: Breath-actuated Jet Nebulizer (AeroEclipse)

18

Chapter 2

Predicting Inhaled Mass

1 Materials and Methods

1.1 Mathematical Modelling

The output of breath-enhanced and breath-actuated devices is dependent on the patient’s

respiration cycle (breathing pattern) and drug-device combination.

The breathing pattern can be described using the patient’s flow, V’pt(t), which is divided

into two phases; inspiratory and expiratory. Inspiration is the phase of interest since the device is

delivering aerosol to the patient. This phase can be modeled as a half sinusoidal function, shown

below:

( ) [L/min] , sin2

)(' tV

tptV iiT ω

ω=

[rad/min] , i

iT

Π=ω

Where VT is the tidal volume in liters, ωi is the frequency of inspiration in radians per

second, t is time in seconds, Ti is the total inspiration time, Te is the total expiration time and Ttot

19

is the sum of inspiration and expiration. For patients breathing from nebulizers the typical

breathing pattern has a Ti/Ttot around 0.415

.

The characterization of the drug-device combination is based on the jet nebulizer’s rate of

output versus entrained flow. This relationship can be modeled by a quadratic formula shown

below. Examples of characterization curves are shown in figure 10.

( )( ) ( ) ( ) [mg/min] , ''''2

tentcVtentbVatentVtotO −+=

Where O’tot is the rate of output in milligram per second, V’ent is the entrained flow in liters per

minute and coefficients a [mg/min], b [mg/L], c [mg x min / L2] characterize the drug-device

combination.

Figure 10: Previously reported characterization curves for various nebulizers6

The operation of the nebulizer (illustrated in figure 11) needs to be incorporated to relate

the rate of output to the patient’s breathing pattern. Since the device has negligible height and air

is a Newtonian fluid, one can assume the summation of flows into and out of the device is

approximately 0 liters per minutes (lpm). This is described in the following equation:

20

( ) ( ) ( ) [L/min] , ''' tentVtVtptV N +=

Where V’N is the nebulizer flow (compressor flow) in lpm.

Figure 11: Equating flows

An added complexity accounted in the model is the time when the inspiratory valve

opens. For the breath-enhanced nebulizers this occurs when the patient flow is equal to the

compressor flow. For the breath-actuated nebulizers is when the inspiratory effort reaches the

manufacturer’s specified flow. In general, this creates three operation scenarios; beginning of

inspiration, inspiration and end of inspiration (as illustrated in figure 12).

Entrained Flow

Compressor Flow

Patient Flow

21

Figure 12: Scenarios

The total output of the devices can be derived for one inspiration phase based on the

above equations. The detailed derivation can be found in Appendix A.

Breath-Enhanced Nebulizers

( )( ) ( ) ( )[ ] ][mg/breath , 24

coscos2

)(cos1'

12

22

12121

−+−−−+−=

ttVCtt

VBttAt

V

aVOtot TT

N

T

ωωωω

Breath-Actuated Nebulizers

( ) ( ) ( )[ ] ( ) ( )][mg/breath ,

4

2sin2sin

24coscos

2

1212

22

1212

−−

−+−−−=

ωωωω

ωωttttCV

ttBV

ttAOtot TT

t1 t2

End of Inspiration Inspiration Beginning of Inspiration

0

22

1.2 Experimental Setup

Three reusable jet-nebulizer types were chosen for this project and are as follows:

• Breath-enhanced Pari LC Star (Pari Respiratory Equipment)

• Breath-enhanced Pari LC Plus (Pari Respiratory Equipment)

• Breath-actuated AeroEclipse II (Trudell Medical International)

The number of devices evaluated varied for each nebulizer type. Nebulizers were tested on their

performance under steady-state and dynamic conditions.

In each experiment the nebulizers were driven by compressors at the manufacturer’s

recommended flows. The breath-enhanced nebulizers used the Pari Proneb Ultra compressor

(flow of 4.1 L/min) and the breath-actuated device was driven by the Invacare Mobilaire (flow of

7.1 L/min). Flows were measured and verified at the start of each experiment using a flow-

calibration instrument (TSI) placed at the mouth piece of the device. Compressors were utilized

over the hospital dry gas source in order to mimic the home environment, reduce evaporative

losses4 and generate enhanced output with correct particle sizes.

The active ingredient Salbutamol (Ventolin Respirator Solution) was selected for the in

vitro experiments. The reasoning for this is that Salbutamol is water soluble and undergoes

almost identical nebulization characteristics to other water soluble drugs currently in use or being

investigated for treatment of cystic fibrosis such as tobramycin, hypertonic saline, denufosol. In

addition, this drug solution is not only less costly compared to tobramycin but also contains a

chromophore which lends itself to ultraviolet (UV) spectroscopy, which is used for measuring

concentration.

23

1.3 Experimental Procedure

1.3.1 Steady State Conditions

As mentioned above the jet nebulizer’s rate of output with respect to entrained flow can

be modeled using a quadratic formula. These characterization curves were obtained by in vitro

testing of each device under steady state conditions with varying entrained flows (ranging from 0

to 35 L/min). For each experiment the nebulizers were vertically clamped.

The device output was determined after 4 minutes (for the breath-enhanced nebulizers LC

Star and LC Plus) and 2.5 minutes (for the breath-actuated device AeroEclipse II) of

nebulization. The reason for the different runtimes is that the AeroEclipse II, when operated at

high entrained flows, reached end-nebulization around 3 minutes. Therefore to keep the initial

dose and fill volume the same, the runtimes were reduced. Furthermore a set duration was

selected, as opposed to letting the device run till ‘end nebulization’, in order to calculate rate of

output.

The output of the device was determined by gavimetrically weighing the device dry, after

filling, and after nebulization. The residual volume (Vr) was measured, which is defined as the

change in device weight before and after nebulization. To account for evaporative effects and

the resulting change in concentration of the drug solution, osmolality was obtained before pre-

nebulization and after post-nebulization weighing. In each case a 20 microliter sample was

assayed for osmolality by vapour pressure osmometry (Advanced Micro-Osmometer 330).

With the device’s change in weight and osmolality, the total drug output can be

determined. The nebulizer output was calculated based on the initial dose (initial fill volume

multiplied by the drug concentration) minus the mass of the drug left in the well of the nebulizer

24

at the end of nebulization (residual volume multiplied by the initial concentration) multiplied by

the ratio of final-to-initial osmolality, to take into account evaporative effects. Subsequently the

rate of output is calculated to be the total output divided by the runtime.

( )( ) [mg] , 'i

f

iriosm

osmCVDtentVOtot −=

( )( ) [mg/min] , ''runt

OtottentVtotO =

Where Di is the initial dose in mg, Vr is the residual volume in milliliters, Ci is the initial

drug concentration in milligrams per milliliter, osm is the osmolalilty in milliosmols and trun is

the runtime. The initial dose of salbutamol was 4 mg at a concentration of 0.625 mg/ml.

1.3.2 Dynamic Conditions

To determine how the nebulizers would perform during a patient’s respiration cycle, each

device was tested under dynamic conditions. These conditions tested the device’s performance

under an idealized patient respiration cycle with varying duty cycles, volumes and breathing

frequencies. The nebulizer was connected to a T-connector attached to an inspiratory filter and

an expiratory filter with a unidirectional valve. The ‘mouth’ of the above setup was connected to

the Harvard pump. This pump is a Harvard Model 613 Volume-controlled Large Animal

Ventilator (Harvard Apparatus Canada, US) capable of generating half sine-wave patterns of

breathing. The overall setup is shown in figure 13.

25

After each 4 minute run was performed, aerosol generated was trapped on the inspiratory

filter, expiratory filter and connector. The total drug output was then determined as the amount

of drug left in the nebulizer and trapped in the filters/connectors. The concentration of drug

collected on the filters and connector was determined from UV spectroscopy at an absorbance

wavelength of 228 nm. The data provided information about the total device output and inhaled

mass (amount of drug on inspiratory filter). In addition the respirable mass was determined

based on the drug collected on the inspiratory filter multiplied by the respirable fraction.

Compressor

Connectors

Nebulizer

1-way Filters

Breathing Simulator

Figure 13: Dynamic conditions setup

1.4 Experimental Results

The characterization of the jet nebulizers is crucial in obtaining the performance

coefficients for the model. The quadratic fits used to model the output rate of the device show a

high correlation (r > 0.95) with the in vitro steady state performance data, as shown in figure 14

and in table 1. In addition comparison of the steady state output rates for breath-enhanced

devices of the same type using the coefficients of variation showed similar performance (table

2).

The next step is to evaluate the models prediction with dynamic in vitro data. The

models for the LC Star and LC Plus were tested with breathing patterns that varied the tidal

volume, duty cycle and respiration rate. The standard breathing pattern is a tidal volume of 0.6

L, duty cycle of 40/60 and respiration rate of 15 BPM. The above parameters were varied

26

independently to observe how the model accommodates varying breathing patterns. Tidal

volume variations included 0.2 L, 0.4 L and 0.6 L. Duty cycle was tested at 40/60 and 50/50.

Previous studies suggest that patient breathing patterns have a 40/60 duty cycle, whereas the

European standard uses a 50/50 duty cycle. The respiration rates tested included 15 BPM and 30

BPM. This range was chosen to observe how the increased respiration rates affect the maximum

flows into the device and the subsequent drug output to the patient.

Figures 16 to 18 are the Bland and Altman limits of agreement between the dynamic in

vitro inhaled mass of the LC Stars with the model’s predicted inhaled mass using device specific

coefficients. These experiments were tested on 4 devices, with each device experimented 3

times. All figures show biases around zero with tight 95% confidence intervals. Figure 18

(which is the consolidation of data points for all parameter variations) illustrates the strong

agreement between the model and the in vitro data.

Similarly for the LC Plus, figures 19 to 22 are the Bland and Altman limits of agreement

between the dynamic in vitro inhaled mass of the LC Pluses with the model’s predicted inhaled

mass using device specific coefficients. These experiments were tested on 3 devices, with each

device experimented 3 times. All figures show biases around zero and tight 95% confidence

intervals, with the exception of figure 20 due to the short range of x-axis values. Overall when

all data points are consolidated onto the same Bland and Altman plot (figure 22), it demonstrates

the strong agreement between the model and in vitro data.

Due to a lack of in vivo data for the AeroEclipse II, the model for this device was only

tested on the standard breathing pattern (tidal volume of 0.6 L, duty cycle of 40/60 and

respiration rate of 15 BPM).

27

LC Star A Characterization Curve

y = -0.000187x2 + 0.011863x + 0.091398

R2 = 0.994203

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40

Entrained Flow [L/min]

Output Rate [mg/min]

Figure 14: Sample characterization curves

(A) breath-enhanced nebulizer (B) breath-actuated nebulizer

AeroEclipse II Characterization Curve

y = -0.000298x2 + 0.016196x + 0.169230

R2 = 0.968654

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 5 10 15 20 25 30 35 40


Output Rate [mg/m

in]

B

A

B

28

Table 1: Coefficients of the Quadratic Equations (y = a + b x – c x2) for the Rate of Output and Regression Coefficient (r), where x is the entrained flow through the devices and n is the

number of devices characterized.

n a b c r

Pari LC Star 4 9.22e-2

1.34e-2

2.23e-4

0.993

Pari LC Plus 3 1.13e-1

1.57e-2

3.33e-4

0.966

AeroEclipse II 2 1.69e-1

1.62e-2

2.98e-4

0.969

Table 2: Coefficient of Variation of breath-enhanced nebulizers

Type n Coefficient of Variation [%] at Varying Entrained Flows [lpm]

0 5 10 15 20 25 30 35

Pari LC Star 4 18.23 12.20 5.33 9.05 8.55 7.80 5.73 5.43

Pari LC Plus 3 15.37 13.34 7.22 5.95 3.95 6.00 4.69 7.94

29

LC Star Inhaled Mass for

Varying Tidal Volumes with 4 minute Runtime

-0.10

-0.05

0.00

0.05

0.15 0.20 0.25 0.30 0.35 0.40 0.45

Average Inhaled Mass [mg]

Inhaled Mass - Model [mg]

Figure 15: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Stars with varying tidal volumes and the model’s predicted output using the device-drug specific characterization

coefficients. Bias represented in blue and 95% Confidence Interval is in red.


Varying Duty Cycle with 4 minute Runtime

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49



Figure 16: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Stars with varying duty cycles and the model’s predicted output using the device-drug specific characterization


30


Varying BPM with 4 minute Runtime

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48



Figure 17: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Stars with varying

respiration rates and the model’s predicted output using the device-drug specific characterization coefficients. Bias represented in blue and 95% Confidence Interval is in red.


Varying Parameters with 4 minute Runtime

-0.10

-0.05

0.00

0.05

0.10

0.15

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55



Figure 18: Bland and Altman limits of agreement plot of the difference between the drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Stars with varying parameters (tidal volume, duty cycle and respiration rates) and the model’s predicted output using the device-drug specific characterization coefficients. Bias represented in blue and

95% Confidence Interval is in red.

31

LC Plus Inhaled Mass for

Varying Tidal Volumes with 4 minute Runtime

-0.05

0.00

0.05

0.10

0.20 0.25 0.30 0.35 0.40



Figure 19: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Pluses with varying tidal volumes and the model’s predicted output using the device-drug specific characterization


LC Plus Inhaled Mass with

Varying Duty Cycle with 4 minute Runtime

-0.04

-0.02

0.00

0.02

0.04

0.06

0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60


Total Inhaled Mass - Model [mg]

Figure 20: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Pluses with varying duty cycles and the model’s predicted output using the device-drug specific characterization


32


Varying BPM with 4 minute Runtime

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49 0.51



Figure 21: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Pluses with varying

respiration rates and the model’s predicted output using the device-drug specific characterization coefficients. Bias represented in blue and 95% Confidence Interval is in red.


Varying Parameters with 4 minute Runtime

-0.10

-0.05

0.00

0.05

0.20 0.25 0.30 0.35 0.40 0.45 0.50



Figure 22: Bland and Altman limits of agreement plot of the difference between drug collected on the inspiratory filter from in vitro experiments of the Breath-Enhanced LC Pluses with varying all parameters (tidal volume, duty cycle and respiration rates) and the model’s predicted output using the device-drug specific characterization coefficients. Bias represented in blue and 95%

Confidence Interval is in red.

33

Table 3: Breath-Actuated AeroEclipse II in vitro data – Aerosol collected on the inspiratory filter compared to the model’s predicted inhaled mass. The standard patient breathing pattern is VT

=0.6 L, Ti/Te = 0.4/0.6 and 15 BPM

Device Breathing Pattern Error [%]

In Vitro Model

A Standard 0.3884 0.4220 8.6509

0.3819 0.4220 10.5001

0.3761 0.4220 12.2042

C Standard 0.5508 0.5560 0.9441

0.5854 0.5560 -5.0222

0.5314 0.5560 4.6293

Inhaled Mass [mg]

34

Chapter 3 Predicting Pulmonary Drug Deposition

1 Materials and Methods

1.1 Mathematical Modelling

The mathematical models derived in the previous chapter provided the foundation to

predict the inhaled mass (the amount of aerosol delivered to the mouth of the patient) generated

by jet nebulizers. This model was validated using the in vitro experiments that tested the jet

nebulizer’s output during dynamic conditions.

The next step is to test the model against in vivo nuclear medicine studies on a wide range

of patients, from normal to cystic fibrosis adults. The in vivo data set was conducted on breath-

enhanced jet nebulizers and therefore the following sections will focus on the derivation of

breath-enhanced models.

1.1.1 Inhaled Mass Model

Please refer to Chapter 2 Section 2.1 for the derivation of this model.

1.1.2 Pulmonary Drug Deposition Model

35

The inhaled mass model provided the means to predict the amount of aerosol delivered to

the mouth of the patient. Enhancing this model to estimate PDD requires integrating the RF,

patient’s dead space, nebulizer output cut-off and the plateau effect.

For the model to predict the PDD, it is necessary to include the respirable fraction (RF),

the fraction of aerosol particles ≤ 5 µm in diameter. This cutoff diameter was chosen as these

particles are likely to deposit in the central region of the lungs for adult patients4. The respirable

fraction varies with respect to the entrained flow (V’ent) through the device. Therefore to

integrate the RF, the fraction of particles ≤ 5 µm in diameter was multiplied against the

nebulizer’s output rate at each level of entrained flow. The resulting RF characterization curves

are shown in the figure 31 below.

36

LC Star W-1 Characterization

y = -0.000194x2 + 0.012520x + 0.111872

R2 = 0.984633

y = -0.000151x2 + 0.010507x + 0.055973

R2 = 0.989904

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 10 20 30 40 50 60



LC Plus A Characterizationy = -0.000198x2 + 0.012741x + 0.115474

R2 = 0.911294

y = -0.000115x2 + 0.008715x + 0.062771

R2 = 0.975714

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 10 20 30 40 50 60



Figure 23: Nebulizer characterization curves with RF for the Breath-Enhanced (A) LC Star and (B) LC Plus.

The model was further enhanced by incorporating the patient’s dead space, the portion of

the patient’s airway where inhaled aerosol is immediately exhaled before impaction can occur.

Previous studies have suggested that for normal patient’s dead space can be approximated as 2.2

ml of volume per kg of weight27

. In addition, the amount of aerosol that is trapped in the dead

space occurs during the end of inspiration.

B

A

37

Calculating the amount of aerosol caught in the patient’s dead space, requires the time

during inspiratory phase when the dead space volume is being filled. The mathematical

derivation is shown below:

( ) [L/min] ,dt sin2

dt )(' ∫∫ ==ii t

t

iiT

t

t

deadspace tV

tptVV ωω

( )[min] ,

cos2

cos

1-

i

iiT

deadspace tV

V

tω

ω

+=

After solving for the time, the amount of aerosol in the dead space can be calculated and

subtracted from the predicted amount. A visual representation of this is shown in figure 32,

below.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350

0.05

0.1

0.15

0.2

0.25

Time [min]

Output [mg/min]

Nebulizer Output During Inspiration

Figure 24: Visual representation of drug delivered to the patient (white) after eliminating aerosol trapped in the dead space (black).

Aerosol caught in dead space

Aerosol delivered to patient

38

Two more empirical modifications were made to improve the model’s prediction; plateau

effect and output cutoff. The plateau effect is the situation when the nebulizer’s output has

reached its maximum, at a given entrained flow, and for all greater flows the output is

approximated to be the maximum output. This plateau effect can be seen in the above in the

device characterization respirable fraction curves. There are two reasons for this approximation.

The first is that with increasing entrained flows, there is increased aerosol generation with larger

particles impacting the baffles. Therefore at lower flows the amount of aerosol delivered to the

patient is mostly carried in larger particles. However for higher entrained flows these larger

particles impact the baffles and the output is substituted by more numerous smaller particles,

hence the plateau in output. The second reason is based on the quadratic fit. The quadratic fit is

a good approximation for the nebulizer’s output for lower flows. However for higher flow

quadratic coefficient dominates and prematurely drops off. This results in an under-prediction of

the nebulizer’s output.

The output cutoff is the estimation that corrects for the situation when the nebulizer

output drops to zero when extremely high flows are reached, typically around 60 lpm. The

rationale for this is that the nebulizer, when high entrained flows are delivered, experienced

increased turbulence which resulted in the drug solution being swished around and no output was

visible.

1.2 Experimental Setup

The experimental setup is similar to Chapter 2 Section 2.2. In this section only two specific

reusable breath-enhanced jet-nebulizers (1 LC Star and 1 LC Plus) were tested because these

devices were utilized in the in vivo testing of the ‘normal’ subjects.

39

1.3 Experimental Procedure

1.3.1 Steady State Conditions

The steady-state characterization procedure is similar to that in Chapter 2 Section 2.3.1 with an

added step that measures the particle size distribution (described below).

Particle size measurements, for determining the RF, were made using the Malvern

Mastersizer X (Malvern Instruments, Worcestershire, UK) according to Mie Theory. Details and

validation of this technique have been previously published26

. The nebulizer was situated so that

the aerosol perpendicularly passed the laser’s path. In addition the nebulizer was placed to

ensure no vignetting or aerosol deposition on the sensor occurred. Furthermore care was taken to

ensure that sufficient aerosol passed through the laser to achieve an obscuration factor of >0.05

at all flows. A schematic of the setup is shown below. Measurements were made after 2 min of

nebulization, allowing nebulizing conditions to stabilize.

Figure 25: Particle size distribution measurement setup using the Malvern Mastersizer X.

Detector

Nebulizer

Laser

Vacuum

Laser Path

Aerosol

Vacuum

40

Based on the particle size distribution the RF was determined as the fraction of aerosol

particles with diameters ≤ 5µm. Therefore for a given entrained flow the respirable output is:

( )( ) [mg/min] , ''' RFtotOtentVO RF ×=

1.4 Experimental Results

The in vivo data was collected using from 4 ‘normal’ subjects and 12 cystic fibrosis

patients using nuclear deposition studies. The breathing patterns and physical characteristics of

these subjects are listed in table 3. The estimated dead space for all subjects was calculated

based on the approximation of 2.2 ml per kg of body mass.

The in vivo data for the 4 ‘normal’ subjects was collected using the LC Star and LC Plus.

The drug utilized in the LC Star studies was saline (AddiPak) with a concentration of 15 mg/ml

whereas for the LC Plus studies the drug was tobramycin with a concentration of 300 mg/ml.

Figures 26 and 27 show the agreement between the model and in vivo data for inhaled mass and

PDD, respectively. Both figures show biases around 0, narrow confidence intervals and

concentration of data points at the extremes. This suggests that the model is able to predict the

inhaled mass and PDD.

The in vivo data for the 12 CF patients was collected using only the LC Plus with the

drug tobramycin (concentration of 300 mg/ml). In these studies, each subject used their own LC

Plus. Using the CF patient’s breathing pattern, the model was tested to estimate the inhaled mass

and PDD. The Bland and Altman agreement plots in figures 28, 29 show that the consistently

over-predicts both the inhaled and PDD, represented by a large negative bias. In addition the

41

plots have negative 95% confidence intervals and a distribution of points that form a box.

Overall this indicates that there is no agreement between the model and in vivo data.

42

Table 4: Subject breathing patterns and physical characteristics.

Subject VT

[L]

Duty Cycle

(Ti/TTot)

Respiration

Rate

[BPM]

Weight

[kg]

Estimated

Dead Space

[L]

Normal 1 0.704 1.78/4.40

13.6

77

0.169

Normal 2 1.048 3.11/7.43

8.1

80

0.176

Normal 3 0.948 2.03/5.12

11.7

90

0.198

Normal 4 0.977 1.16/2.94 20.4 81 0.178

CF Patient 1 0.382 1.00/2.16 27.8 58 0.128

CF Patient 2 0.479 1.88/3.80 15.8 62 0.137

CF Patient 3 0.525 1.27/3.00 20.0 78 0.172

CF Patient 4 1.197 1.88/5.44 11.0 86 0.189

CF Patient 5 0.321 0.84/1.80 33.3 52 0.115

CF Patient 6 0.879 1.84/4.24 14.2 73 0.161

CF Patient 7 0.936 1.96/3.76 16.0 80 0.176

CF Patient 8 0.657 1.72/3.36 17.9 57 0.126

CF Patient 9 0.433 1.36/3.16 19.0 73 0.161

CF Patient 10 0.390 1.36/3.04 19.7 75 0.165

CF Patient 11 0.573 1.40/2.64 22.7 40 0.088

CF Patient 12 0.713 0.80/1.80 33.3 47 0.103

43

In Vivo Inhaled Mass for Normal Subjects

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14

Average Inhaled Mass Charge Rate [ml/min]

In Vivo Inhaled Mass - Model Charge Rate [ml/min]

Figure 26: Bland and Altman limits of agreement plot of the difference between the in vivo inhaled mass data and the model’s predicted inhaled mass for normal subjects. Bias

represented in blue and 95% Confidence Interval is in red.

In Vivo PDD For Normal Subjects

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04 0.05 0.06 0.07 0.08 0.09 0.1

Average PDD Charge Rate [ml/min]

In Vivo PDD - Model Charge Rate [ml/min]

Figure 27: Bland and Altman limits of agreement plot of the difference between the in vivo PDD data and the model’s predicted PDD for normal subjects. Bias represented in blue and 95%


44

In Vivo Inhaled Mass for CF Patients

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15

Average Inhaled Mass Charge Rate [ml/min]

In Vivo Inhaled Mass - Model Charge Rate [ml/min]

Figure 28: Bland and Altman limits of agreement plot of the difference between the in vivo inhaled mass data and the model’s predicted inhaled mass for CF patients. Bias represented in

blue and 95% Confidence Interval is in red.

In Vivo PDD for CF Patients

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Average PDD Charge Rate [ml/min]

In Vivo PDD - Model Charge Rate [ml/min]

Figure 29: Bland and Altman limits of agreement plot of the difference between the in vivo PDD data and the model’s predicted PDD for CF patients. Bias represented in blue and 95%


45

Chapter 4 Discussions

1 In Vitro Results: Predicting Inhaled Mass

The Bland and Altman limits of agreement plots, in Chapter 2 Section 2.4 figures 15 to

22, demonstrate the strong agreement between the in vitro data and the model. In addition these

figures also show the model’s ability to accommodate changes in breathing patterns and drug-

device combinations.

For the LC Star models, the plots (figures 15 to 18) show a slight negative bias. This

negative bias indicates that the model slightly over-predicts the amount of aerosol delivered to

the inspiratory filter. This may have resulted from the inability to fully recover all aerosol

particulates from the filters during experimentation. Another explanation for the bias is that the

model’s does not account for evaporative losses on the wall of the nebulizer. To minimize the

effects of evaporation, the experiments utilized a wet gas compressor as opposed to dry hospital

gas. While the dry hospital gas is dried and has virtually no water vapour, the standard nebulizer

air compressors do not remove water vapor. When the room air is drawn into the compressor, it

is pressurized using a piston and then cooled to room temperature. This may cause the partial

pressure of water vapor to equal the saturated vapor pressure, thus making the gas wet28

.

The Bland and Altman plots for the LC Plus models (figures 19, 21 and 22) have a slight

positive bias, which indicates the model’s under-prediction of aerosol collected on the

inspiratory filter. This bias may result from low tidal volumes (VT = 0.2 L) as shown in figure

19 (the in vitro data for varying tidal volumes) where a cluster of points on the left of the plot are

all positive. A possible rationale is that for low tidal volumes there is a decrease in entrained

flows through the devices and this causes increased aerosol density in the connectors. In other

words, the aerosol density is calculated as the amount of aerosol generated divided by air flow

46

through the device29

. For lower tidal volumes the flow through the device is less, therefore the

ratio of aerosol generated to the air flow is greater, which creates the positive bias seen in figure

19. Subsequently the increase in aerosol density results in more aerosol being delivered to the

inspiratory filter and thus generating the positive bias. For the Bland and Altman plot for

varying duty cycles (figure 21), the dynamic range (x-axis) is small and therefore the plot is

inconclusive to demonstrate agreement between the model and in vitro data.

The breath-actuated nebulizer (AeroEclipse II) was only tested on the standard breathing

pattern (VT = 0.6, Ti/Te = 40/60, 15 BPM) to provide proof of concept. The preliminary results

on table 2 show that the modified model can predict the inhaled mass to within 10%. This model

was not studied further due to a lack of in vivo data. Additional testing of the AeroEclipse II is

necessary to test the robustness of this model.

The main limitation in this part of the study was the restriction in the maximum tidal

volume of the breathing simulator, which is 0.6 L. For pediatric patients who have smaller tidal

volumes, this does not pose a problem. However for larger patients, who have VT > 0.6 L, there

is a lack of in vitro data to test the model.

2 In Vivo Results: Predicting Pulmonary Drug Deposition

The purpose of this section of the study was to validate the model based on in vivo

nuclear deposition studies. The model was modified to incorporate a respirable fraction (≤5 µm)

and dead space volume (approximation of 2.2 ml per kg of weight), described in Chapter 3

Section 2. The modified model was tested on two subject groups; ‘normal’ subjects and cystic

fibrosis patients. The subjects breathing patterns and estimated dead space volumes are listed in

table 4. Figures 26 to 29 are Bland and Altman plots that compare the models prediction to the

47

in vivo data based on charge rates, nebulizers initial charge volume over time. The use of charge

rates was used to account for the difference in drug concentration used in the in vivo experiments

and those used in the in vitro characterization of the nebulizers.

Normal subjects completed nuclear deposition studies for both the LC Star and LC Plus.

The results, shown in figure 26 and 27, represent the ‘normal’ subjects inhaled mass and PDD

for both these devices. Overall these figures demonstrate the model’s ability to predict the

amount of aerosol delivered, with a slight over-estimation. The model’s accuracy is, in part,

attributed to the derivation of various modelling parameters, like the respirable fraction. On the

other hand, the CF patient in vivo studies were conducted using only the LC Plus. The model’s

prediction of the inhaled mass and PDD for these subjects (figure 28 and 29, respectively) is less

accurate with a consistent over prediction of both inhaled mass and PDD. This may be due to

the inability to derive several modeling parameters and relying on estimations for RF. This has

been supported by past literature30

, where it was shown that CF patients breathing through a

nebulizer generate patterns of breathing that differ from the sinusoidal inspiratory pattern used to

model normal breathing. The study also demonstrates that ‘normal’ sinusoidal patterns of

breathing used to model the CF patient’s breathing pattern had parameters (e.g. VT and

respiratory rate) that were generally higher. These inflated estimations of CF patient breathing

parameters subsequently resulted in the model’s over-prediction of the inhaled mass and

pulmonary drug deposition.

Possible explanations of this discrepancy are that the model currently utilizes three

generalized approximations for all subject; respirable fraction, dead space approximation and the

idealized breath. In terms of the respirable fraction the ≤ 5 µm diameter cutoff will vary across

subjects and may decrease for younger subjects or those with cystic fibrosis. In addition the

dead space approximation of 2.2 ml per kg of weight may not be valid for CF patients because

bronchiectasis, which is very much a part of the disease, increases the patient’s anatomical dead

space. Lastly, the model is based on an idealized sinusoidal breathing pattern. While the

sinusoid may be a good approximation for the subject’s inspiration15

, it assumes that the patient’s

breathing pattern is consistent throughout the experiment, it is prone to variation.

48

The two technical limitations of the in vivo study involve the characterization of the

nebulizers. The first limitation was obtaining the respirable fraction using particle sizing device

(Malvern Mastersizer X). It was found that in order to generate an obscuration > 0.05, the

maximum entrained flow through the nebulizer was 50 lpm. This resulted in a reduced

characterization range of the nebulizers. Secondly, the in vivo data for the CF patients utilized

LC Pluses that were not previously characterized, which may introduce performance variations

not accounted for in the model.

49

Chapter 5 Conclusions

Models were developed to predict the inhaled mass and pulmonary drug deposition, and

provide another method for evaluating nebulizers. In addition these models were successfully

derived to accommodate a wide range of patient breathing patterns and device-drug

combinations. Overall the models have achieved the in vitro goal of the study and show strong

agreement with the in vitro nebulizer performance across varying breathing parameters.

Moreover the model has demonstrated it’s effectiveness in predicting the amount of aerosol

delivered to ‘normal’ subjects, whose modelling parameters can be derived. However the model

is less accurate when applied to in vivo data of subjects with the presence of disease, in part,

because these subjects may not have patterns of breathing that have been used in the model for

normal subjects and because anatomical variations due to disease may lead to inaccuracies in

assumptions made with RF. This would suggest that physical models routinely used in

laboratories to predict device performance may not be as accurate when predicting drug

deposition in the presence of disease.

The next step of this study is to further develop the model by incorporating additional

nebulizer parameters like aerosol concentrating effects and more robust anatomical models that

can account for anatomical variations due disease like the dead space volume and respirable

fraction.

50

References

1. Coates, A. L. 2008. Guiding aerosol deposition in the lung. N Engl J Med 358:304-305.

2. Coates, A. L. and S. L. Ho. 1998. Drug administration by jet nebulization: State of the Art.

Pediatr Pulmonol 26:412-423.

3. Katz, S. L., I. Adatia, E. Louca, K. Leung, T. Humpl, J. T. Reyes, and A. L. Coates. 2006.

Nebulized therapy for childhood pulmonary hypertension: an In vitro model. Pediatr

Pulmonol 41:666-673.

4. Coates, A. L. and C. O'Callaghan 2006. Drug administration by aerosol in children. In V.

Chernick, T. E. Boat, R. W. Wilmott, and A. Bush, editors Kendig's Disorders of the

Respiratory Tract in Children,7th ed. Saunders Elsevier, Philadelphia. 268-279.

5. Newman, S. P. and S. W. Clarke. 1983. Therapeutic aerosols 1- Physical and practical

considerations. Thorax 38:881-886.

6. Leung, K., E. Louca, and A. L. Coates. 2004. Comparison of Breath Enhanced to Breath

Actuated Nebulizers for Rate, Consistency and Efficiency . Chest 26:1619-1627.

7. Ho, S. L., W. T. J. Kwong, and A. L. Coates. 2001. Evaluation of four breath-enhanced

nebulizers for home use. J Aerosol Med 14:467-475.

8. Coates, A. L., P. D. Allen, C. F. MacNeish, S. L. Ho, and L. C. Lands. 2001. Effect of size

and disease on expected deposition of drugs given by jet nebulization to children with

cystic fibrosis. Chest 119:1123-1130.

9. Ilowite, J. S., J. D. Gorvoy, and G. C. Smaldone. 1987. Quantitative deposition of

aerosolized gentamycin in cystic fibrosis. Am Rev Respir Dis 136:1445-1449.

10. Chua, H. L., G. G. Collis, A. M. Newbury, K. Chan, G. D. Bower, P. D. Sly, and P. N.

LeSouëf. 1994. The influence of age on aerosol deposition in children with cystic fibrosis.

Eur Respir J 7:2185-2191.

11. McCallion, O. N. M., K. M. G. Taylor, M. Thomas, and A. J. Taylor. 1996. The influence

of surface tension on aerosols produced by medical nebulisers. Inter J Pharm 129:123-136.

12. Coates, A. L., M. Green, K. Leung, E. Louca, M. Tservistas, J. Chan, N. Ribeiro, and M.

Charron. 2007. The challenges of quantitative measurement of lung deposition using 99m

Tc-

DTPA from delivery systems with very different delivery times. J Aerosol Med 20:320-

330.

13. Coates, A. L., M. Green, K. Leung, J. Chan, N. Ribeiro, E. Louca, F. Ratjen, M. Charron,

M. Tservistas, and M. Keller. 2008. Rapid Pulmonary Delivery of Inhaled Tobramycin for

Pseudomonas Infection in Cystic Fibrosis: A Pilot Project. Pediatr Pulmonol 43:753-759.

51

14. Bosco, A. P., R. Rhem, and M. B. Dolovich. 2005. In vitro estimation of in vivo jet

nebulizer efficiency using actual and simulated tidal breathing patterns. J Aerosol Med

18:427-438.

15. Coates, A. L., C. F. MacNeish, P. D. Allen, S. L. Ho, and L. C. Lands. 1999. Do sinusoidal

models of respiration accurately reflect the respiratory events of cystic fibrosis patients

breathing on nebulizers? J Aerosol Med 12:265-273.

16. Nikander, K., M. Turpeinen, and P. Wollmer. 1999. The conventional ultrasonic nebulizer

proved inefficient in nebulizing a suspension. J Aerosol Med 12:47-53.

17. Brain, J. D. and J. D. Blanchard 1993. Mechanisms of particle deposition and clearance. In

F. Moren, M. B. Dolovich, M. T. Newhouse, and S. P. Newman, editors Aerosols in

Medicine:Principles diagnosis and therapy,2nd ed. Elsevier, Amsterdam,London,New

York, Tokyo. 117-156.

18. Clay, M. M., D. Pavia, S. P. Newman, and S. W. Clarke. 1983. Factors influencing the size

distribution of aerosols from jet nebulisers. Thorax 38:755-759.

19. Newman, S. P., P. G. D. Pellow, M. M. Clay, and S. W. Clarke. 1985. Evaluation of jet

nebulisers for use with gentamycin solution. Thorax 40:671-676.

20. Coates, A. L., C. F. MacNeish, L. Dinh, T. Rollin, S. Gagnon, S. L. Ho, and L. C. Lands.

2000. Accounting for radioactivity before and after nebulization of tobramycin to insure

accuracy of quantification of lung deposition. J Aerosol Med 13:169-178.

21. Wildhaber, J. H., N. D. Dore, J. M. Wilson, S. G. Devadason, and P. N. LeSouëf. 1999.

Inhalation therapy in asthma: Nebulizer or pressurized metered-dose inhaler with holding

chamber? In vivo comparison of lung deposition in children. J Pediatr 135:28-33.

22. Geller, D. E., W. H. Pitlick, P. A. Nardella, W. G. Tracewell, and B. W. Ramsey. 2002.

Pharmacokinetics and bioavailablility of aerosolized tobramycin in cystic fibrosis. Chest

122:219-226.

23. Janssens, H. M., J. C. Jongste, W. J. Fokkens, S. G. F. Robben, K. Wouters, and H. A. M.

Tiddens. 2001. The Sophia anatomical infant nose-throat (Saint) model: A valuable tool to

study aerosol deposition in infants. J Aerosol Med 14:433-441.

24. Mitchell, J. P. and M. W. Nagel. 2004. Particle size analysis of aerosols from medicinal

inhalers. Kona-Powder and Particle (In press)

25. MacNeish, C. F., D. Meisner, R. Thibert, S. Kelemen, E. B. Vadas, and A. L. Coates. 1997.

A comparison of pulmonary availability between Ventolin (Albuterol) nebules and

Ventolin (Albuterol) Respirator Solution. Chest 111:204-208.

26. Mitchell, J. P., M. W. Nagel, S. Nichols, and O. Nerbrink. 2006. Laser diffractometry as a

technique for rapid assessment of aerosol particle size from inhalers. J Aerosol Med

19:409-433.

52

27. Chernick, V. and J. B. West 2006. The functional basis of respiratory disease. In V.

Chernick, T. E. Boat, R. W. Wilmott, and A. Bush, editors Kendig's Disorders of the

Respiratory Tract in Children,7th ed. Saunders Elsevier, Philadelphia. 29-64.

28. Coates, A. L., C. F. Macneish, L. C. Lands, A. Smountas, D. Meisner, S. Kelemen and E.

B. Vadas. 1998. Factors influencing the rate of drug output during the course of wet

nebulization. J Aerosol Med 11:101-111.

29. Vecellio, L., P. Kippax, S. Rouquette and P. Diot. 2009. Influence of realistic airflow rate

on aerosol generation by nebulizers. Internation Journal of Pharmaceutics 371:99-105.

30. Coates, A. L., C. F. Macneish, P. D. Allen, S. L. Ho and L. C. Lands. 1999. Do sinusoidal

models of respiration accurately reflect the respiratory events of patients breathing on

nebulizers? J Aerosol Med 12:265-273.

53

Appendix A – Inhaled Mass Model Derivation

Breathing Pattern - Inspiration

( ) [L/min] , sin2

)(' tV

tptV iiT ω

ω=

[rad/min] , i

iT

Π=ω

Where VT is the tidal volume in liters, ωi is the frequency of inspiration in radians per second, t is

time in seconds, Ti is the total inspiration time and Ttot is the sum of inspiration and expiration.

For patients breathing from nebulizers the usual breathing pattern is a Ti/Ttot around 0.4.

Jet Nebulizer - Modeling

Entrained flow

( )( ) ( ) ( ) [mg/min] , ''''2

tentcVtentbVatentVtotO −+=

54

Where O’tot is the rate of output in milligram per second, V’ent is the entrained flow in liters per

minute and coefficients a [mg/min], b [mg/L], c [mg x min / L2] characterize the drug-device

combination.

( ) ( ) ( ) [L/min] , ''' tentVtVtptV N +=

Where V’N is the nebulizer flow (compressor flow) lpm.

Figure A1: Scenarios

Beginning of Inspiration (0 < t ≤ t1):

t1 t2

End of Inspiration Inspiration Beginning of Inspiration

0

55

( ) [L/min] , '' NVtentV −=

Where t1 is the total time for the beginning of inspiration and is derived below.

( ) ( ) [L/min] , sin2

'' 11 tV

tptVV TN ω

ω==

[min] ,

'2sin 1

1 ω

ω

=

−

T

N

V

V

t

Inspiration (t1 < t ≤ t2):

( ) ( ) [L/min] , ''' NVtptVtentV −=

Where t2 is the time when the end of inspiration starts. Since the patient’s flow is a quadratic and

symmetrical therefore the entrained flow will also be symmetrical. Solving for t2:

[min] , 12 tTt i −=

[min] ,

'2sin 1

2 ω

ω

−=

−

T

N

i

V

V

Tt

56

End of inspiration (t2 < t ≤ Ti):

( ) [L/min] , '' NVtentV −=

Breath-enhanced nebulizer model

The above equations can now be used to derive the total output from the device during one

breath. Analyzing the device operation during each scenario, one obtains the following.


Since V’pt(t) < V’N we can take V’ent = -V’N. Therefore the output of the device is the density of

drug generated multiplied by the volume output by the nebulizer.

( )( ) [mg] , cos1'2

1tV

aVOtot

N

T ω−=

Inspiration (t1 < t ≤ t2)`:

57

Substituting the patient flow into the jet nebulizer output equation one gets:

( )( ) ( ) ( ) [mg/min] , ''''2

tptCVtptBVAtptVtotO ++=

[mg/min] , ''2

NN cVbVaA +−=

[mg/L] , '2 NcVbB −=

]Lmin / x [mg , 2cC =

Therefore the total output during inspiration is:

( ) ( ) ( )[ ] ( ) ( )[mg] ,

4

2sin2sin

24coscos

2

1212

22

1212

−−

−+−−−=

ωωωω

ωωttttCV

ttBV

ttAOtot TT

Based on past studies it was noted that the overwhelming majority of patients had an inspiration

time of ≤ 2 seconds which makes ω equal 1.57 [rad/sec], making the final term insignificant. In

addition with more rapid breathing the ω would continue to increase making the final term

vanishingly small. As a result, the final term can be ignored and gives

( ) ( ) ( )[ ] [mg] , 24

coscos2

12

22

1212

−+−−−=

ttCVtt

BVttAOtot TT ω

ωω

58


Since the model is quadratic, it is symmetrical making this situation identical to the beginning of

inspiration.

( )( ) [mg] , cos1'2

1tV

aVOtot

N

T ω−=

Total Output

The total output for one respiratory cycle is the summation of the 3 equations above and this

gives the following:

( )( ) ( ) ( )[ ] ][mg/breath , 24

coscos2

)(cos1'

12

22

12121

−+−−−+−=

ttVCtt

VBttAt

V

aVOtot TT

N

T

ωωωω

Breath-actuated nebulizer model

59

The derivation of the breath-actuated mathematical model is similar to the breath-enhanced

algorithm. The main difference is that the generation and output of aerosol only occurs when a

minimum inspiratory effort is achieved. In the case of the AeroEclipse II, the minimum

inspiratory effort is 15 liters per minute. The adjusted derivations are as follows:


[mg] , 0=Otot

[min] ,

30sin 1

1 ω

ω

=

−

TVt

Where t1 is the time when the patient’s inspiratory flow reaches 15 lpm.

Inspiration (t1 < t ≤ t2):

Substituting the patient flow equation in to the rate of output equation results in:

( )( ) ( ) ( ) [mg/min] , ''''2

tptCVtptBVAtptVtotO ++=

60

[mg/min] , ''2

NN cVbVaA +−=

[mg/L] , '2 NcVbB −=

]Lmin / x [mg , 2cC =

The resulting total output is calculated to be:

( ) ( ) ( )[ ] ( ) ( )[mg] ,

4

2sin2sin

24coscos

2

1212

22

1212

−−

−+−−−=

ωωωω

ωωttttCV

ttBV

ttAOtot TT

For this model the final term cannot be ignored because the operation of the device occurs during

high flows, where this term is no longer insignificant.

Similarly, since the patient’s flow is symmetrical gives t2 as:`

[min] ,

30sin 1

2 ω

ω

−=

−

T

i

VTt


61

[mg] , 0=Otot

Total Output

The total output for one respiratory cycle is the summation of the 3 equations above and this

gives the following:

( ) ( ) ( )[ ] ( ) ( )][mg/breath ,

4

2sin2sin

24coscos

2

1212

22

1212

−−

−+−−−=

ωωωω

ωωttttCV

ttBV

ttAOtot TT

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