Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition · ii Modelling Jet Nebulizers to Estimate Pulmonary Drug Deposition Wallace Wee Masters of Health Science Clinical
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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
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.
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.
30
LC Star Inhaled Mass for
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
Average Inhaled Mass [mg]
Inhaled Mass - Model [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
-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
Average Inhaled Mass [mg]
Inhaled Mass - Model [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.
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
Average Inhaled Mass [mg]
Inhaled Mass - Model [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
-0.04
-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
Average Inhaled Mass [mg]
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
coefficients. Bias represented in blue and 95% Confidence Interval is in red.
32
LC Plus Inhaled Mass for
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
Average Inhaled Mass [mg]
Inhaled Mass - Model [mg]
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.
LC Plus Inhaled Mass for
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
Average Inhaled Mass [mg]
Inhaled Mass - Model [mg]
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
Entrained Flow [L/min]
Output Rate [mg/min]
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
Entrained Flow [L/min]
Output Rate [mg/min]
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%
Confidence Interval is in red.
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%
Confidence Interval is in red.
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
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