Abstract
Purpose
To compare titer reduction and delivery rate of active anti-tuberculosis bacteriophage (phage) D29 with three inhalation devices.
Methods
Phage D29 lysate was amplified to a titer of 11.8 ± 0.3 log10(pfu/mL) and diluted 1:100 in isotonic saline. Filters captured the aerosolized saline D29 preparation emitted from three types of inhalation devices: 1) vibrating mesh nebulizer; 2) jet nebulizer; 3) soft mist inhaler. Full-plate plaque assays, performed in triplicate at multiple dilution levels with the surrogate host Mycobacterium smegmatis, were used to quantify phage titer.
Results
Respective titer reductions for the vibrating mesh nebulizer, jet nebulizer, and soft mist inhaler were 0.4 ± 0.1, 3.7 ± 0.1, and 0.6 ± 0.3 log10(pfu/mL). Active phage delivery rate was significantly greater (p < 0.01) for the vibrating mesh nebulizer (3.3x108 ± 0.8x108 pfu/min) than for the jet nebulizer (5.4x104 ± 1.3x104 pfu/min). The soft mist inhaler delivered 4.6x106 ± 2.0x106 pfu per 11.6 ± 1.6 μL ex-actuator dose.
Conclusions
Delivering active phage requires a prudent choice of inhalation device. The jet nebulizer was not a good choice for aerosolizing phage D29 under the tested conditions, due to substantial titer reduction likely occurring during droplet production. The vibrating mesh nebulizer is recommended for animal inhalation studies requiring large amounts of D29 aerosol, whereas the soft mist inhaler may be useful for self-administration of D29 aerosol.
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Abbreviations
- g:
-
Gravitational acceleration
- i:
-
Nebulization cycle count
- log10 :
-
Base 10 logarithm
- MDR-TB:
-
Multidrug-resistant tuberculosis
- MOI:
-
Multiplicity of infection
- n:
-
Number of plates
- pfu:
-
Plaque-forming unit
- Phage:
-
Bacteriophage
- TB:
-
Tuberculosis
- TEM:
-
Transmission electron micrograph
- XDR-TB:
-
Extensively drug-resistant tuberculosis
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Acknowledgments and Disclosures
NC gratefully thanks the Natural Sciences and Engineering Research Council of Canada, Alberta Innovates, and the University of Alberta for scholarship funding. This includes a Michael Smith Foreign Study Supplement and an Education Abroad Individual Award allowing him to perform research in Sydney, Australia. The authors thank Arlene Oatway for help with the transmission electron micrograph and Jim Fink for providing Aerogen nebulizers and equipment. This work was financially supported in part by the Australian Research Council (Discovery Project DP150103953).
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Appendix
Appendix
Appendix Notation
- C d , p , i :
-
mass concentration of solute in the solvent droplets both exiting the mouthpiece and returning to the reservoir in the i th nebulization cycle, assumed to be equal
- C e , p , i :
-
mass concentration of solute in the solvent droplets exiting the mouthpiece in the i th nebulization cycle
- C n , p , i :
-
mass concentration of solute in the solvent exiting the nozzle in the i th nebulization cycle
- C p :
-
mass concentration of solute in the solvent
- C p , 0 :
-
mass concentration of solute in the solvent initially input to the reservoir
- C r , p , i :
-
mass concentration of solute in the solvent droplets returning to the reservoir in the i th nebulization cycle
- Cu(f e , i ):
-
fraction of the initial number of phage input to the jet nebulizer which have cumulatively exited the mouthpiece over i nebulization cycles
- Cu(i*X i ):
-
average number of nebulization cycles phage which exited the mouthpiece underwent
- f e , i :
-
fraction of the number of phage initially input to the reservoir, which exit the mouthpiece in the i th nebulization cycle
- i :
-
nebulization cycle count
- j :
-
a summation index for i in Cu(f e , i )
- k :
-
a summation index for i in X i
- L :
-
a summation index for i in Cu(i ∗ X i )
- \( {\dot{m}}_{e, s} \) :
-
mass flow rate of solvent in droplets exiting the mouthpiece
- \( {\dot{m}}_{h, s} \) :
-
mass flow rate of solvent exiting due to humidification of air supplied by the compressor
- \( {\dot{m}}_{n, s} \) :
-
mass flow rate of solvent exiting the nozzle
- \( {\dot{m}}_p \) :
-
mass flow rate of solute
- \( {\dot{m}}_{r, s} \) :
-
mass flow rate of solvent returning to the reservoir
- \( {\dot{m}}_s \) :
-
mass flow rate of solvent
- m 1p :
-
mass of a single phage
- N :
-
total number of nebulization cycles to complete aerosolization
- n e , p , i :
-
number of phage, either active or inactive, exiting the mouthpiece in the i th nebulization cycle
- n p , 0 :
-
number of phage initially input to the reservoir
- ρ s :
-
mass density of the solvent
- Q e , s :
-
volumetric flow rate of solvent in droplets exiting the mouthpiece
- Q h , s :
-
volumetric flow rate of solvent exiting due to humidification of air supplied by the compressor
- Q n , s :
-
volumetric flow rate of solvent exiting the nozzle
- Q r , s :
-
volumetric flow rate of solvent returning to the reservoir
- Q s :
-
volumetric flow rate of solvent
- t i :
-
time to complete the i th nebulization cycle
- V e , s , i :
-
volume of solvent in droplets exiting the mouthpiece in the i th nebulization cycle
- V F :
-
volume of solvent initially input to the reservoir, termed fill volume
- V h , s , i :
-
equivalent liquid volume of solvent exiting the device due to humidification of air supplied by the compressor in the i th nebulization cycle
- V n , s , i :
-
volume of solvent exiting the nozzle in the i th nebulization cycle
- V r , s , i :
-
volume of solvent returning to the reservoir in the i th nebulization cycle
- X i :
-
fraction of the cumulative number of phage which have exited the mouthpiece after aerosolization is complete, which exited the mouthpiece in the i th nebulization cycle
Nebulization Cycle Count Mathematical Model
A mathematical model was developed to estimate the average number of times that phage exited the nozzle and impacted the primary baffle of the jet nebulizer prior to exiting the mouthpiece.
The solvent, water in this study, can follow three paths after exiting the nozzle: 1) humidify the air supplied by the compressor and exit the nebulizer as vapor; 2) exit the mouthpiece as aerosol droplets; 3) impact the interior of the device and return (drip back) to the reservoir. By assuming no mixing between the reservoir fluid and returning fluid in the same nebulization cycle, conservation of mass for the solvent gives
where \( {\dot{m}}_{n, s} \) is the mass flow rate of the solvent exiting the nozzle, \( {\dot{m}}_{h, s} \) is the mass flow rate of solvent which will exit the device via humidification of the air supplied by the compressor, \( {\dot{m}}_{e, s} \) is the mass flow rate of solvent which will exit the mouthpiece of the device as aerosol droplets, and \( {\dot{m}}_{r, s} \) is the mass flow rate of solvent which will return to the reservoir to exit the nozzle in the next nebulization cycle.
The solvent mass flow rate is related to volumetric flow rate by
For water, ρ s can be considered constant during jet nebulization. Eq. (1) can thus be rewritten in terms of flow rates:
The flow rate exiting the nozzle, Q n , s , was determined experimentally using Tryptophan tracer assay, to be 17.64 mL/min. The flow rate exiting the mouthpiece of the device, Q e , s , was determined to be 0.12 mL/min from the mass captured on the filter during phage experiments. The flow rate lost to humidification, Q h , s , was calculated as the difference in flow rate determined based on mass loss from the nebulizer and mass captured on the outlet filter during phage experiments, and found to be 0.06 mL/min. This matched the theoretical amount of water required to fully humidify the air supplied by the compressor. The flow rate returning to the reservoir, Q r , s , was thus calculated using Eq. (3), to be 17.46 mL/min.
It is assumed that solute does not exit the inhaler via humidification losses. Mass conservation for the solute (phage) is then given by
The solute concentration in the solvent, C p , is related to the mass flow rate by
Assuming the solute remains in the droplets and reservoir fluid, Eqs. (4) and (5) can be combined to give
It is assumed that the humidification of the air supplied by the compressor occurs by evaporation of the droplets exiting the nozzle, which have a high air-liquid surface area to volume ratio, rather than from the liquid in the reservoir. The humidification due to evaporation of the primary and secondary droplets increases the solute concentration in the droplets. Let us assume that the increase in concentration in the droplets that exit the mouthpiece and that return to the reservoir is equal. Then, we can define the droplet concentration, C d , p , as
With each nebulization cycle, i, the concentration of the solute in the reservoir will increase. The concentration of solute in the reservoir in a specific cycle, i, is the same as the concentration of solute in the droplets in the previous cycle, i − 1, as we have assumed no mixing between the reservoir fluid and returning fluid in the same cycle:
Let us define
where C p , 0 is the input mass concentration of solute in solvent. Here, C n , p , 1 represents the concentration of solute in solvent exiting the nozzle during the first nebulization cycle, when i = 1.
By combining Eqs. (6) and (7), and assuming that the respective volumetric flow rates are independent of nebulization cycle,
and rearranging Eq. (11) gives
The value of \( \frac{Q_{n, s}}{\left({Q}_{e, s}+{Q}_{r, s}\right)} \) is a constant, equal to 1.0034 in the present study. This value quantifies the increase in concentration of solute in the droplets emitted from the nozzle with each nebulization cycle, due to loss of solvent associated with humidification of the air supplied by the compressor.
When i = 1, using Eqs. (8), (9), and (11), one finds that
For i = 2, Eq. (12) gives
Combining Eqs. (13) and (14), one finds that
One can continue to show that in general
This equation demonstrates how the solute concentration in the droplets of a specific nebulization cycle, i, is related to the initial solute concentration in the reservoir.
In order to estimate the number of phage exiting the mouthpiece in a specific nebulization cycle, volumes are evaluated for each nebulization cycle. The volume returned to the nebulizer, V r , s , in a specific cycle is equal to the volume exiting the nozzle, V n , s , in the following cycle:
Eq. (17) is valid for i = 2 → N. For i = 1, the volume exiting the nozzle is assumed to be equal to the fill volume, V F :
The time for a nebulization cycle to complete, t i , is specified by
The following volumes can then be obtained using t i and the known flow rates:
where V h , s , i is the equivalent liquid volume exiting the device due to humification in a specific nebulization cycle, V e , s , i is the volume exiting the mouthpiece of the device as droplets in a specific nebulization cycle, and V r , s , i is the volume returned to the reservoir in a specific nebulization cycle.
The number of phage, either active or inactive, exiting the mouthpiece in a specific nebulization cycle, n e , p , i , can be found according to
where m 1p is the mass of a single phage.
Similarly, the number of phage initially in the reservoir is
The fraction of the number of phage initially input to the reservoir that has exited the mouthpiece in a specific nebulization cycle, f e , i , can therefore be found using Eqs. (16), (23), and (24), as
The fraction of the number of phage initially input to the reservoir that have cumulatively exited the mouthpiece of the device over i nebulization cycles, Cu(f e , i ), is given by
where j is a summation index. To solve Eq. (26), for example, when i = 3,
The curve in Figure 4 represents the solution to Eq. (26) for every i from i = 1 to i = N, where N represents the number of nebulization cycles when V r , s , i is equal to the residual volume of the nebulizer after aerosolization is complete, which was experimentally determined to be 0.5 mL during phage measurements in this study. The fraction was converted to a percentage in the plot.
Also given in Figure 4 is the average number of nebulization cycles phage that exited the mouthpiece underwent. To determine this value, one must consider that some phage are left in the residual volume of the nebulizer after aerosolization is complete.
The fraction of the cumulative number of phage that have exited the mouthpiece after N nebulization cycles, that exited the mouthpiece in the specific nebulization cycle i, is termed X i , and is given by:
where k is a summation index.
It can be shown that the average number of nebulization cycles phage underwent prior to exiting the mouthpiece of the jet nebulizer, Cu(i ∗ X i ), is given by
where L is a summation index.
The average number of nebulization cycles the phage underwent prior to exiting the mouthpiece of the jet nebulizer was thus determined to be 96 in the present study, with the final phage exiting the mouthpiece having undergone N=269 nebulization cycles. Assuming that every time a phage exits the nozzle it impacts the primary baffle, the nebulization cycle count i corresponds to the number of baffle impactions the phage underwent.
Other parameters such as total nebulization time and total volumes lost to humidification and exiting the mouthpiece can also be obtained using summations from 1 to N.
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Carrigy, N.B., Chang, R.Y., Leung, S.S.Y. et al. Anti-Tuberculosis Bacteriophage D29 Delivery with a Vibrating Mesh Nebulizer, Jet Nebulizer, and Soft Mist Inhaler. Pharm Res 34, 2084–2096 (2017). https://doi.org/10.1007/s11095-017-2213-4
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DOI: https://doi.org/10.1007/s11095-017-2213-4