Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition

Transcription

1 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 010

2 ii Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition Abstract Wallace Wee Masters of Health Science Clinical Engineering, Institute of Biomaterials and Biomedical Engineering University of Toronto 010 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.

3 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.

4 iv 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 Introduction... 1 Background Patient Respiration Particle Distributions Particle Distributions Inertial Impaction Gravitational Sedimentation Diffusion Jet Nebulizers Conventional Unvented Jet Nebulizer Breath-Enhanced Jet Nebulizer Breath-Actuated Jet Nebulizer Chapter Predicting Inhaled Mass Materials and Methods Mathematical Modelling Experimental Setup Experimental Procedure... 3

5 v Steady State Conditions Dynamic Conditions Experimental Results... 5 Chapter 3 Predicting Pulmonary Drug Deposition Materials and Methods Mathematical Modelling Inhaled Mass Model Pulmonary Drug Deposition Model Experimental Setup Experimental Procedure Steady State Conditions Experimental Results Chapter 4 Discussions In Vitro Results: Predicting Inhaled Mass In Vivo Results: Predicting Pulmonary Drug Deposition Chapter 5 Conclusions References Appendix A Inhaled Mass Model Derivation... 53

6 vi List of Tables Table 1: Coefficients of the Quadratic Equations (y = a + b x c x ) 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 Table : Coefficient of Variation of breath-enhanced nebulizers... 8 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 V T =0.6 L, Ti/Te = 0.4/0.6 and 15 BPM Table 4: Subject breathing patterns and physical characteristics.... 4

7 vii List of Figures Figure1: Poisson distribution... 7 Figure : Lognormal distribution... 8 Figure 3: Deposition Processes... 9 Figure 4: Inertial Impaction Figure 5: Gravitational Sedimentation... 1 Figure 6: Unvented Jet Nebulizer Figure 7: Bernoulli Effect Figure 8: Breath-enhanced Jet Nebulizer (LC Star) Figure 9: Breath-actuated Jet Nebulizer (AeroEclipse) Figure 10: Previously reported characterization curves for various nebulizers Figure 11: Equating flows... 0 Figure 1: Scenarios... 1 Figure 13: Dynamic conditions setup... 5 Figure 14: Sample characterization curves... 7 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... 9 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

8 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... 9 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 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 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 coefficients. Bias represented in blue and 95% Confidence Interval is in red Figure 0: 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 coefficients. Bias represented in blue and 95% Confidence Interval is in red Figure 1: 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... 3 Figure : 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... 3

9 ix Figure 3: Nebulizer characterization curves with RF for the Breath-Enhanced (A) LC Star and (B) LC Plus Figure 4: Visual representation of drug delivered to the patient (white) after eliminating aerosol trapped in the dead space (black) Figure 5: Particle size distribution measurement setup using the Malvern Mastersizer X Figure 6: 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 Figure 7: 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 Figure 8: 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 Figure 9: 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

10 x List of Appendices Appendix A: Inhaled Mass Model Derivation

11 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

12 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 effects 3. 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 deposition 4. 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 r 3 ) 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

13 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 cords. 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 optimal. 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 agents 6;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 exhalation 7. 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

14 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 nebulized 11. 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 devices 6. 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 accuracy 1;13. These include the selection of an appropriate

15 4 radioactive label, accommodation of different tissue attenuations and D 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 device 14. 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 pattern 15. 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

16 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 ) and cystic fibrosis patients (Chapter 3), pediatric and adult, where both pattern of breathing through a nebulizer and drug deposition is known. 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.

17 6.1 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.. 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 (σ g ) measures the extent of how polydisperse the Poisson distribution is, where a larger σ g implies greater polydispersion.

18 7 Figure1: Poisson distribution 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 3 rd power of the radius (r 3 ). 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.

19 8 Figure : Lognormal distribution 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 unitdensity 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

20 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..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 Processes 1

21 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 turns 1. 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 [

22 11 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..3. 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

23 1 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..3.3 Diffusion Figure 5: Gravitational Sedimentation [ 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 (T i ). 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

24 13 amount of drug carried is proportional to r 3 ) 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..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)..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

25 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. Low Pressure Figure 6: Unvented Jet Nebulizer ρ = density υ = velocity z = change in height p = pressure g = gravity 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

26 15 the jet stream is insignificant in comparison to the gas velocity. As a result, the velocity and pressure are inversely proportional..4. 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. Inspiration Expiration Figure 8: Breath-enhanced Jet Nebulizer (LC Star)

27 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..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 inspiration 6. A schematic of the AeroEclipse II breath-actuated jet nebulizer is shown in figure 9.

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

29 18 Chapter 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: VTωi V ' pt( t) = sin ( ω t),[l/min] i ω = i Π T i,[rad/min] Where V T is the tidal volume in liters, ω i is the frequency of inspiration in radians per second, t is time in seconds, T i is the total inspiration time, T e is the total expiration time and T tot

30 19 is the sum of inspiration and expiration. For patients breathing from nebulizers the typical breathing pattern has a T i /T tot around 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. O' tot ( V ' ent( t) ) = a+ bv ' ent( t) cv ' ent( t),[mg/min] 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 / L ] characterize the drug-device combination. Figure 10: Previously reported characterization curves for various nebulizers 6 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:

31 0 ( t) = V ' ( t) V ' ent( t),[l/min] V ' pt N + Where V N is the nebulizer flow (compressor flow) in lpm. Entrained Flow Patient Flow Compressor Flow 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 1).

32 1 Beginning of Inspiration Inspiration End of Inspiration 0 t 1 t Figure 1: 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 Otot = V T a V ' N V V ω t t T T 1 ( 1 cos( ωt )) + A( t t ) B [ cos( ωt ) cos( ωt )] + C,[mg/breath] Breath-Actuated Nebulizers ( ωt ) sin( ωt ) BVT CVT ω t t1 sin 1 Otot= A( t t1) [ cos( ωt ) cos( ωt1) ] +,[mg/breath] 4 4 ω

33 1. 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 flowcalibration 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 losses 4 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.

34 3 1.3 Experimental Procedure 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.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 (V r ) 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 prenebulization and after post-nebulization weighing. In each case a 0 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

35 4 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. Otot f ( V ' ent( t) ) = D V C,[mg] i r i osm osm i Otot O ' tot = ( V ' ent( t) ),[mg/min] t run Where D i is the initial dose in mg, V r is the residual volume in milliliters, C i is the initial drug concentration in milligrams per milliliter, osm is the osmolalilty in milliosmols and t run is the runtime. The initial dose of salbutamol was 4 mg at a concentration of 0.65 mg/ml 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.

36 5 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 8 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. 1-way Filters Nebulizer Compressor Breathing Simulator Connectors 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 ). 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

37 6 independently to observe how the model accommodates varying breathing patterns. Tidal volume variations included 0. 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 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 0 due to the short range of x-axis values. Overall when all data points are consolidated onto the same Bland and Altman plot (figure ), 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).

38 7 A Output Rate [mg/min] LC Star A Characterization Curve y = x x R = Entrained Flow [L/min] B AeroEclipse II Characterization Curve Output Rate [mg/min] y = x x R = Entrained Flow [L/min] Figure 14: Sample characterization curves (A) breath-enhanced nebulizer (B) breath-actuated nebulizer

39 8 Table 1: Coefficients of the Quadratic Equations (y = a + b x c x ) 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.e e -.3e Pari LC Plus e e e AeroEclipse II 1.69e e -.98e Table : Coefficient of Variation of breath-enhanced nebulizers Type n Coefficient of Variation [%] at Varying Entrained Flows [lpm] Pari LC Star Pari LC Plus

40 9 LC Star Inhaled Mass for Varying Tidal Volumes with 4 minute Runtime Inhaled Mass - Model [mg] Average Inhaled Mass [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 LC Star Inhaled Mass for Varying Duty Cycle with 4 minute Runtime Inhaled Mass - Model [mg] Average Inhaled Mass [mg] 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 coefficients. Bias represented in blue and 95% Confidence Interval is in red.

41 30 LC Star Inhaled Mass for Varying BPM with 4 minute Runtime 0.0 Inhaled Mass - Model [mg] Average Inhaled Mass [mg] 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 LC Star Inhaled Mass for Varying Parameters with 4 minute Runtime Inhaled Mass - Model [mg] Average Inhaled Mass [mg] 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.

42 31 LC Plus Inhaled Mass for Varying Tidal Volumes with 4 minute Runtime 0.10 Inhaled Mass - Model [mg] Average Inhaled Mass [mg] 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 coefficients. Bias represented in blue and 95% Confidence Interval is in red. LC Plus Inhaled Mass with Varying Duty Cycle with 4 minute Runtime 0.06 Total Inhaled Mass - Model [mg] Average Inhaled Mass [mg] Figure 0: 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 coefficients. Bias represented in blue and 95% Confidence Interval is in red.

43 3 LC Plus Inhaled Mass for Varying BPM with 4 minute Runtime 0.04 Inhaled Mass - Model [mg] Average Inhaled Mass [mg] Figure 1: 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. LC Plus Inhaled Mass for Varying Parameters with 4 minute Runtime Inhaled Mass - Model [mg] Average Inhaled Mass [mg] Figure : 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.

44 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 V T =0.6 L, Ti/Te = 0.4/0.6 and 15 BPM Device Breathing Pattern Inhaled Mass [mg] Error [%] In Vitro Model A Standard C Standard

45 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 breathenhanced jet nebulizers and therefore the following sections will focus on the derivation of breath-enhanced models Inhaled Mass Model Please refer to Chapter Section.1 for the derivation of this model Pulmonary Drug Deposition Model

46 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 patients 4. 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.

47 36 A LC Star W-1 Characterization y = x x R = Output Rate [mg/min] y = x x R = Entrained Flow [L/min] B LC Plus A Characterization y = x x R = Output Rate [mg/min] y = x x R = Entrained Flow [L/min] Figure 3: 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. ml of volume per kg of weight 7. In addition, the amount of aerosol that is trapped in the dead space occurs during the end of inspiration.

48 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: V deadspace t = V ' pt( t) dt = t i t i t VTωi sin ( ω t) dt,[l/min] i cos -1 V t= deadspace VT + ω i cos( ωiti),[min] 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 3, below. 0.5 Nebulizer Output During Inspiration Aerosol caught in dead space 0. Output [mg/min] Aerosol delivered to patient Time [min] Figure 4: Visual representation of drug delivered to the patient (white) after eliminating aerosol trapped in the dead space (black).