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Deposition of micrometer-sized aerosol particles in infant nasal airway replicas
Aerosol Science 39 (2008) 1055 – 1065 www.elsevier.com/locate/jaerosci
Deposition of micrometer-sized aerosol particles in infant nasal airway replicas John Storey-Bishoff, Michelle Noga, W.H. Finlay∗ University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, Alberta, Canada T6G 2G8 Received 29 March 2008; received in revised form 29 July 2008; accepted 30 July 2008
Abstract In vitro measurements of particle filtration were made for nasal geometries of 11 infants aged 3–18 months. The geometries were obtained from computed tomography (CT) scans of seven males and four female infants and replicas were built using rapid prototyping. Particles ranging in aerodynamic diameter from 0.8 to 5.3 m were passed through these replicas with simulated tidal breathing. Filtration was determined from particle counts upstream and downstream of the models using an electrical low pressure impactor (ELPI). Mathematical fits were constructed to predict the measured deposition based on the relevant parameters. The fractional deposition, , is found to depend on the Reynolds number of the flow (Re), the particle Stokes number (Stk), and an airway dimension D defined as airway volume divided by airway surface area. This dependence is well captured by the formula = 1 − (2.164 ∗ 105 /(2.164 ∗ 105 + (Re1.118 Stk 1.057 (D/Davg )−2.840 )))0.8510 . Here, Davg is the average value of the dimension D for the group studied and is equal to 1.20 mm. Re and Stk also use the dimension D as the length scale in their definitions. 䉷 2008 Elsevier Ltd. All rights reserved. Keywords: Nasal model; Human infant; Nasal aerosol deposition; Impaction; In vitro
1. Introduction Infants less than approximately 4–6 months of age are obligate nasal breathers since this facilitates breathing while breast feeding (Sasaki, Levine, Laitman, & Crelin, 1977). Nose breathing is also common during low activity at all ages (Bennett, Zeman, & Jarabek, 2008). For this reason, as well as reasons of compliance and practicality, face masks are used when administering pharmaceutical aerosols to infants. The nasal path is therefore important in determining lung drug dose for this age group (Everard, 2003). The filtering function of the nose is also important when an infant is exposed to environmental aerosols since it prevents some particles from entering the lung. A discussion of modeling aerosol deposition in this context including age effects is given by Phalen and Oldham (2001). In vivo measurement of aerosol deposition with infants is difficult due to issues of compliance, legitimate concerns over safety, and the non-voluntary nature of any participation. In vitro studies based on anatomical models of infant nasal geometries overcome most of these concerns and a limited number of such models have been constructed by other researchers (Cheng et al., 1995; Janssens et al., 2001; Swift, 1991). ∗ Corresponding author. Tel.: +1 780 492 4707.
E-mail addresses: [email protected] (J. Storey-Bishoff), [email protected] (W.H. Finlay). 0021-8502/$ - see front matter 䉷 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2008.07.011
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Nomenclature Re Stk D Q¯ V As Davg d Cc particle Dx Dxavg L
¯ Reynolds number ( Q/D) ¯ particle d 2 Cc/18D 3 ) Stokes Number ( Q length scale (V/As ) average volumetric flow rate airway volume airway surface average value of D for all subjects studied particle diameter Cunningham slip factor (1 + 2.52/d) is the fluid mean free path fluid density fluid viscosity particle density fraction not passed through replica √ length scale based on cross-sectional area ( V /L) average value of Dx for all subjects studied airway length
A large number of nasal studies exist in the literature where the focus is on adults or older children. For example, in vivo adult studies have been performed by Heyder, Gebhart, Rudolf, Schiller, and Stahlhofen (1986), Cheng (2003) and Rasmussen, Andersen, and Pedersen (2000), while in vivo studies of both adults and children have been performed by Becquemin, Swift, Bouchikhi, Roy, and Teillac (1991) and Bennett et al. (2008). A study that compares deposition in casts of a monkey nasal airway to that in an adult human airway is presented by Kelly, Asgharian, and Wong (2005). Recent computational fluid dynamics nasal modeling work includes that of Liu, Matida, Gu, and Johnson (2007), which highlights the importance of accurate turbulence modeling in the nose, and Kimbell (2006), which looks at inter-species differences in particle deposition in rats, monkeys and humans. While the existing literature allows a general understanding of nasal deposition in infants, the published data are insufficient to allow a straightforward predictive, quantitative understanding. For this reason, in the current study we have investigated 10 new infant nasal replicas constructed by us, as well as the SAINT model described in Janssens et al. (2001). A correlation which predicts nasal deposition in these 11 nasal replicas for micrometer-sized aerosol particles based on geometry specific Reynolds and Stokes numbers is then constructed which closely matches our measured data and allows quantitative prediction of infant nasal aerosol deposition. 2. Methods This study was conducted under the approval of the University of Alberta Health Research Ethics Board, file number 6432. Data from computed tomography (CT) scans of infants scanned for medical purposes were reused for this study. All subjects were deemed to have normal nasal structure and the original CT scans were not acquired because of any nasal or sinus problem. All scans were obtained with the patient in the supine position. Imaging was helical with reconstructed axial slices of 1.25 mm thickness and in plane resolution ranging from 291 to 430 m across subjects. The airways were identified in the CT based on gray level using the Mimics software package (Materialise, Ann Arbor, MI). An upper threshold of approximately −295 Hounsfield units was used. All airways extended from the nares to just past the larynx. Sinuses were kept if they were connected to the airway in the Mimics model. The airways were smoothed to eliminate surface roughness due to noise and discretization in the CT data. The area of the face from chin to forehead and including both cheeks was also identified in the CT data. Using the Magics software package (Materialise) these geometries were used to create models which could be built using a rapid proto-typer (Invision SR 3-D printer from 3D Systems, Rock Hill, SC).
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Table 1 Subject parameters. Sub
Age (M)
Sex
V (mm3 )
As (mm2 )
L (mm)
Amin (mm2 )
D (mm)
SAINT 2 3 4 5 6 7 8 10 11 14
9 3 3 4 5 6 7 8 16 18 15
F M M F F M M M M F M
8034 13 430 11 924 7913 8599 8723 11 789 10 342 18 583 10 754 14 304
7154 8723 8646 6760 7573 9641 10 241 10 142 13 693 9700 11 331
113.4 95.6 100.6 98.0 89.9 110.3 109.7 110.0 111.3 100.6 115.3
31.8 65.2 64.9 45.1 66.6 58.7 54.2 73.5 62.3 84.1 47.9
1.12 1.54 1.38 1.17 1.14 0.905 1.15 1.02 1.36 1.11 1.26
V is volume of airway, As is the surface area of airway lumen, L is a central path length through the model, Amin is the minimum cross-sectional airway taken perpendicular to expected airflow, D is the calculated dimension V /As .
The models were built in two parts with the face and throat built separately and later joined with bolts and sealed externally with putty. The build material was acrylic plastic and a wax support material was used. The support material was melted to expose the completed model segments. All models were subsequently CT scanned and a comparison was made of the airway parameters listed in Table 1 between the original subjects and the built models. Volume differed on average by 5.28%, airway surface by 5.24%, minimum cross-sectional area by 3.93%, the computed parameter D differed by 7.85% (tending to be larger in the models than the original CT data), while length remained unchanged. This indicates that the models accurately represent the subjects’ original nasal CT geometries and also that the error involved in model construction is small compared to the inter-subject variability of these parameters. The airways captured by CT scanning the completed models are shown in Fig. 1. Fig. 2 shows a completed model of subject 10 with views of the front and back of the model. In addition a SAINT replica of a 9 month old infant was purchased from Erasmus MC, Rotterdam, Netherlands. Details of the construction of the SAINT model can be found in Janssens et al. (2001). Parameters of each subject, such as the volume of the airway, the area of the surface lumen of the airway, the length of a central path through the airway and the minimum cross-sectional area of the airway perpendicular to the central path were measured from CT scans of the built replicas and are reported in Table 1 along with the ages and genders of each subject. In order to allow easy connection of the airway models to downstream tubing, each airway was appended with a distal 2 cm right prismatic extension. The pressure drop across the airway of each model was measured for a number of steady flow rates as an independent experiment. Flow was measured with a mass flow meter (4143 series, TSI, Shoreview, MN). Pressure drop was measured with a differential pressure meter (HHP-103, Omega, Stamford, CT) placed between the exit of the model and the room. A number of experiments to measure nasal deposition were carried out using the setup as shown in Fig. 3. From upstream to downstream the setup consisted of the following: • A six jet collision nebulizer (BGI, Inc. Waltham, MA) connected to filtered house air producing polydisperse aerosol of sunflower oil (=0.92 g/mL) with particles ranging in aerodynamic diameter from 0.8 to 5.3 m. Sampled aerosol MMAD was 3.2 m with a GSD of 2.4. • An unsealed chamber at room pressure, equipped with a mixing fan, housing the airway model and a blank sampling line of matched length. • A three-way valve to switch between the model and the blank sampling line. • An electronic low pressure impactor (ELPI) (Dekati Ltd., Tampere, Finland). • Filtered air-supply matched to the flow volume through the ELPI. • A mass flow meter (4143 series, TSI) measuring breathing flow. • One-way valve allowing only inhalation flow through the airway model. • Cyclic breathing machine, constructed in house, producing a sine wave breathing pattern.
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Fig. 1. Perspective views of the model airways used in this study. (A 2 cm straight extension at the exit of the airway is not shown but was included in all models except the SAINT.)
Flows through the ELPI are fixed at 30 L/min by critical flow at the outlet of the impactor. A filtered air-supply set to 30 L/min supplies the flow consumed by the ELPI through a relatively high resistance path. The cyclic breathing machine applies a varying pressure which results in flow primarily through the low resistance path which is either the sample line or nasal model depending on the position of the three-way valve. Deposition was measured by comparing the amount of aerosol that passed through the blank sample line to the amount that passed through the nasal model. No separate characterization of inhalability was performed and all measurements of deposition indicate the full fraction that did not pass through the model. Aerosol entered the replica naturally from the air surrounding the facial features of the replicas, so that the present results include both inhalability and internal nasal deposition, although inhalability is close to 100% for the flow rates and particle sizes considered here (Kennedy & Hinds, 2002). A single deposition experiment consisted of a 2 min sample drawn through the blank line followed by a 2 min sample through the model, and ended with another 2 min sample through the blank line. Each 2 min time interval was further
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Fig. 2. Photos of front and back of the built model of subject 10. 30 I/min input
aerosol
Flow Meter
ELPI
30 I/min output
Fig. 3. Experimental setup.
divided with a 40 s period at the beginning of the interval and a 5 s period at the end of each interval both being discarded to eliminate effects from settling of the instrument and errors in valve switching synchronization. This left a 75 s period of data which was actually used in each 2 min interval. This was sufficient to allow averaging of many breathing cycles. The ELPI provided an average particle count for size ranges corresponding to each stage of the impactor for each time interval. Nasal deposition for each impactor stage size range was calculated as the difference between the average number seen through the blank line at that stage and the average number seen through the model at that stage divided by the average number through the blank line at that stage.
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Table 2 Typical breathing patterns (inhalation only). Vt (cm3 )
bpm
Q¯ (cm3 /s)
60.9 113.8 107.3 87.9 186.2
45 30 45 57 30
91.3 113.8 161.0 167.1 186.2
Vt: tidal volume, bpm: breaths per minute, Q¯ : average flow rate during inhalation Q¯ = 2 ∗ Vt ∗ bpm ∗ 1 min /60 s.
Five repeats of this experiment were performed for each model using each of five breathing patterns and the results for each breathing pattern and model combination were individually averaged. A small number of validation runs were performed with an electrostatic neutralizer upstream of the model and compared to runs made without the neutralizer. The two differed negligibly in measured deposition in the models, confirming that electrostatic effects were insignificant. The breathing patterns used were half sinusoidal with only the inhalation portion of the curve being used. This was done to avoid many technical difficulties associated with using both the inhale and exhale flows given the small tidal volumes involved. In particular, the dead-space introduced by any length of sampling line would easily exceed the small tidal volumes being used, making proper sampling impossible. Balancing the volume of the model lines and sampling lines is also less critical if only the inhale flow is used. During in vivo breathing, there is a period of zero flow as exhalation stops and inhalation starts. The initial condition for inhalation is zero flow in both real breathing and in our patterns so it is not expected that using only the inhale flow will have had any effect on deposition. The average parameters for the breathing patterns are given in Table 2 while the actual parameters for each individual experiment were measured and used for all calculations. Periodic flow conditions were used in order to ensure a more physiologically realistic experiment. Previous studies, Haussermann, Bailey, Bailey, Etherington, and Youngman (2002) and Sosnowski, Moskal, and Gradon (2006), have shown differences in total deposition for periodic flows and steady flows of equal average velocity in airway replicas. Average weight for the infants in this study ranged from 6 to 11 kg based on age and gender (Centers for Diseae Control & Prevention, 2000). Resting tidal volume ranges from 5 to 8 mL/kg in infants and children(Chernick, Boat, Wilmott, & Bush, 2006). This gives a resting tidal volume range of 30–88 mL for the present subjects. Resting breathing rate ranges from 44 to 34 bpm with age from 2 to 18 months (Dozor, 2002). Rosenthal and Bush (2000) examined 23 children aged 8–10.5 yrs and found an increase in breathing rate of 97% from that at rest vs. maximum exercise for boys in this age group, while girls increased breathing rate on average by 79%. In the same study tidal volume was found to increase 185% for boys and 135% for girls under maximum exercise. The largest tidal volume used in the present study was a 112% increase from resting volume while the highest breathing rate was a 26% increase from resting range. Extrapolating from Rosenthal et al. (2000), the breathing patterns used in the present study represent states of moderate activity. All curve fitting was done using Levenberg–Marquardt nonlinear regression with a least squares objective function in the GNU Octave software package version 2.1.72 (www.octave.org). Multiple starting points in the parameter space were used to ensure a reasonably global solution. 3. Results and discussion ¯ where da is particle aerodynamic diameter, is shown Deposition for all subjects versus impaction parameter, da2 Q, in Fig. 4. A great deal of variability is evident across subjects and deposition for any individual subject is not captured, across breathing flow rates, by a single curve. Semi-empirical models to predict nasal deposition in individuals have been proposed based on pressure drop across the nose (Hounam, Black, & Walsh, 1969), maximum air velocity based on minimum airway cross-section area (Rasmussen et al., 2000) and Stokes number scaled using the minimum airway cross-sectional area (Cheng, 2003; Kelly et al., 2005; Swift, 1991). These models have been based on in vivo and in vitro measurements. In a study of various adult oral airways Grgic, Finlay, Burnell, and Heenan (2004) found the data collapsed well using a correlation involving Reynolds and Stokes number based on mean cross-sectional area to predict aerosol deposition.
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Fig. 4. Deposition vs. impaction parameter (standard error too small to display).
Table 3 r 2 of fits using different dimensions to define Reynolds and Stokes number. Fit, D= Stk, Re Stk, Re, D
V As
V Amin
0.887 0.930
0.745 0.778
L 0.545 0.588
As L 0.606 0.638
V L
0.792 0.813
√
Amin
0.495 0.590
P 0.351 0.901
1 P 0.753 0.901
Fits rely on either two term with Reynolds and Stokes (row 1) or three terms with Reynolds, Stokes and the dimension D (row 2).
In the present study subsequent results are presented as a function of Stokes and/or Reynolds numbers in order to express deposition in a way that collapses the inter-subject variability using the appropriate non-dimensionalization. The Reynolds number is a ratio of the convective and viscous terms of the equations governing fluid motion and is the main parameter used to characterize incompressible flows. The Stokes number relates the stopping distance of a particle in the flow to a characteristic length scale in the geometry. This indicates a particle’s ability to follow curves in the flow streamlines. A number of length scales were examined to non-dimensionalize the present infant deposition data. These included minimum cross-sectional area and average cross-sectional area. Trans-nasal pressure drop at 7 L/min of flow was also tried as a scale factor by using the inverse of pressure drop in place of the length scale in the definition of Stokes and Reynolds numbers. The length scale, D, that best collapsed the data was found to be airway volume divided by airway surface area. This can be seen by a comparison of r 2 values for fits using various scaling dimensions given in Table 3. Hydraulic diameter is often used as a scale dimension in non-circular geometries and is defined as Dh =
4 ∗ cross-sectional area perimeter
By comparison, our chosen dimension D has some analogy to the hydraulic diameter for these geometries with variable cross-section since it is equivalent to D=
average cross-sectional area average perimeter
The average flow rate for each breathing pattern was used in the definition of Re and Stk. It was found that the flow pattern could be fully characterized, for our purposes, by average flow rate, with patterns having similar average flow rate but different combinations of Vt and breaths per minute resulting in similar deposition. The dynamics of the nasal flows are, of course, changing through the breathing cycle and deposition may be happening at different rates during
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Fig. 5. Deposition vs. Stk (standard error too small to display).
Fig. 6. Deposition vs. f (Re, Stk) (standard error too small to display).
the cycle and at different locations within the nasal geometry. Despite this, average flow rate was successfully used to create a correlation for total deposition. A function of the form = 1 − (a/(a + x))b where a and b are fit parameters was used to match the overall shape of the deposition curve. In order to capture the deposition for all subjects as a single curve, the abscissa was taken variously as a function of Stokes number; Stokes and Reynolds numbers; or Stokes number, Reynolds number and length scale D. Attempts to express deposition versus only Stokes number resulted in distinct deposition curves for each flow rate and each individual as seen in Fig. 5. This suggests an additional dependence on flow rate. A better fit is obtained if Reynolds number is also included as in Fig. 6. This is consistent with the observed static pressure drop for these models i.e. when non-dimensionalized pressure drop is plotted versus Reynolds number, as in Fig. 7, we see that nondimensionalized pressure drop is not constant over the range of flow rates used. This suggests that the flow pattern is changing with flow rate over the range of flow rates used. This is similar to the results observed for the simpler system (stenosis) described in Itoh, Smaldone, Swift, and Wagner (1985).
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Fig. 7. Normalized pressure drop vs. Reynolds number.
Fig. 8. Deposition vs. non-dimensional parameter (standard error too small to display).
The fit function for deposition shown in Fig. 6 is =1−
1.007 ∗ 107 1.007 ∗ 107 + (Re1.526 Stk 1.015 )
1.126 (1)
While the nasal geometries of each infant have similar overall shape, the details of each geometry differ, as seen in Fig. 1. They are not scaled versions of the same structure so the use of the non-dimensional Stokes and Reynolds numbers is not expected to fully collapse the deposition data since it does not account for these intersubject differences. For this reason, a parametric correction was attempted which includes Reynolds, Stokes and the geometric scale factor D, as shown in Fig. 8. This results in a further collapse of the data. The fit function used in Fig. 8 is 0.8510 2.164 ∗ 105 (2) =1− 2.164 ∗ 105 + (Re1.118 Stk 1.057 (D/Davg )−2.840 )
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Fig. 9. Deposition vs. non-dimensionalized parameter based on
√
V /L (standard error too small to display).
where D = V /As , Davg = 1.20 mm. Eq. (2) allows quantitative prediction of nasal deposition in individual infant subjects. Comparing infant nasal deposition from Eq. (2) to that seen in adults (Cheng, 2003) for subjects at rest we find less nasal deposition in infants, e.g. for d = 2 m, Q¯ = 72 cm3 /s (4.3 L/ min, which is a typical resting flow rate for subjects in the age range of infants considered here), D = Davg and particle = 1000 kg/m3 , Eq. (2) gives = 2.0% for an infant, while the nasal deposition correlation of Cheng (2003) gives = 18.2% (assuming a resting adult flow rate of 15 L/min and taking average Amin of 2.08 cm2 as given). Much of this difference is attributable to the difference in resting flow rates. Bennett et al. (2008) also find lower nasal deposition in older children (6–10 yrs.) vs. adults, which supports our similar finding in infants. In order to provide a useful correlation for cases where the average cross-sectional area is known, perhaps through acoustic rhinometry, while the airway surface area is not known, Fig. 9 gives a parametric fit using Reynolds number and Stokes number instead defined using √ average cross-sectional length scale Dx with an additional term depending directly on Dx , where Dx is defined as V /L. Here V is the nasal airway volume and L is a nasal airway path length. The fit function shown in Fig. 9 is =1−
10.40 10.40 + (Re1.201 Stk 1.156 (Dx /Dxavg )−2.301 )
0.5201 (3)
√ where Dx = V /L, Dxavg = 10.3 mm. This correlation also reveals some differences between the oral geometries studied by Grgic et al. (2004) and the nasal geometries examined in the current study. While an excellent collapse of oral deposition was obtained by Grgic et al. using only Reynolds number and Stokes number based on V /L, Figs. 8 and 9 show that the quantity V /As provides better collapse of variability for the infant nasal geometries studied. Also in contrast with Grgic et al., we find here that a further dependence on a geometric factor beyond Reynolds number and Stokes number is required to obtain a tight collapse of the deposition data. These differences may be explained by two factors. First, the oral geometry is more circular in cross-section than the nasal geometry and therefore the square root of the average cross-sectional area is closer to the hydraulic diameter than is the case in the nasal geometry. Second, the oral geometries, being simpler, are apparently more easily modelled via the Reynolds number and Stokes number alone since their differences can be more accurately described by a volumetric scaling factor.
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4. Conclusions Our measurements of nasal deposition in replicas of infants indicate that there is considerable variability in nasal aerosol deposition between individual infants. Deposition within a single subject depends not only on Stokes number but also on Reynolds number. This is apparent from our deposition data and consistent with our static pressure drop measurements. A reasonable predictive equation for deposition in all 11 subjects was obtained by including both Stokes and Reynolds numbers scaled using total nasal air volume divided by surface area. An even tighter fit was obtained by including an additional direct dependence on volume over surface area. The resulting equation (Eq. (2)) allows estimation of nasal deposition in individual infants and is expected to be useful for those wanting to estimate the fraction of aerosol reaching the lungs through the nasal passage of infants during breathing. Acknowledgments The authors gratefully acknowledge the financial support of National Science and Engineering Research Council of Canada and the indispensable assistance of iRSM, the Institute for Reconstructive Sciences in Medicine. H. Janssens is also gratefully acknowledged for helpful suggestions in the preparation of this manuscript. References Becquemin, M., Swift, D. L., Bouchikhi, A., Roy, M., & Teillac, A. (1991). Particle deposition and resistance in the noses of adults and children. European Respiratory Journal, 4(6), 694–702. Bennett, W. D., Zeman, K. L., & Jarabek, A. M. (2008). Nasal contribution to breathing and fine particle deposition in children versus adults. Journal of Toxicology and Environmental Health, 71, 227–237. Cheng, Y. S. (2003). Aerosol deposition in the extrathoracic region. Aerosol Science and Technology, 37, 659–671. Cheng, Y. S., Smith, S. M., Yeh, H. C., Kim, D. B., Cheng, K. H., & Swift, D. L. (1995). Deposition of ultrafine aerosols and thoron progeny in replicas of nasal airways of young children. Aerosol Science and Technology, 23(4), 541–552. Chernick, V., Boat, T. F., Wilmott, R. W., & Bush, A. (2006). Kendig’s disorders of the respiratory tract in children. 7th ed., Saunders. Centers for Disease Control and Prevention (2000). Growth charts weight-for-age percentiles www.cdc.gov/growthcharts. Dozor, A. J. (2002). Primary pediatric pulmonology. Blackwell Publishing. Everard, M. L. (2003). Inhalation therapy for infants. Advanced Drug Delivery Reviews, 55, 869–878. Grgic, B., Finlay, W. H., Burnell, P. K. P., & Heenan, A. F. (2004). In vitro intersubject and intrasubject deposition measurements in realistic mouth–throat geometries. Journal of Aerosol Science, 35(8), 1025–1040. Haussermann, S., Bailey, A. G., Bailey, M. R., Etherington, G., & Youngman, M. (2006). The influence of breathing patterns on particle deposition in a nasal replicate cast. Journal of Aerosol Science, 33, 923–933. Heyder, J., Gebhart, J., Rudolf, G., Schiller, C. F., & Stahlhofen, W. (1986). Deposition of particles in the human respiratory tract in the size range 0.005–15 m. Journal of Aerosol Science, 17(5), 811–825. Hounam, R. F., Black, A., & Walsh, M. (1969). Deposition of aerosol particles in the nasopharyngeal region of the human respiratory tract. Nature, 221(5187), 1254–1255. Itoh, H., Smaldone, G. C., Swift, D. L., & Wagner, H. N. (1985). Quantitative evaluation of aerosol deposition in constricted tubes. Journal of Aerosol Science, 16(2), 167–174. Janssens, H. M., de Jongste, J. C., Fokkens, W. J., Robben, S. G., Wouters, K., & Tiddens, H. A. (2001). The sophia anatomical infant nose-throat (SAINT) model: A valuable tool to study aerosol deposition in infants. Journal of Aerosol Medicine, 14, 433–441. Kelly, J. T., Asgharian, B., & Wong, B. A. (2005). Inertial particle deposition in a monkey nasal mold compared with that in human nasal replicas. Inhalation Toxicology, 17(14), 823–830. Kennedy, N. J., & Hinds, W. C. (2002). Inhalability of large solid particles. Journal of Aerosol Science, 33(2), 237–255. Kimbell, J. S. (2006). Nasal dosimetry of inhaled gases and particles: Where do inhaled agents go in the nose?. Toxicologic Pathology, 34(3), 270–273. Liu, Y., Matida, E. A., Gu, J., & Johnson, M. R. (2007). Numerical simulation of aerosol deposition in a 3-D human nasal cavity using RANS, RANS/EIM, and LES. Journal of Aerosol Science, 38(7), 683–700. Phalen, R. F., & Oldham, M. J. (2001). Methods for modeling particle deposition as a function of age. Respiration Physiology, 128(1), 119–130. Rasmussen, T. R., Andersen, A., & Pedersen, O. F. (2000). Particle deposition in the nose related to nasal cavity geometry. Rhinology, 38, 102–107. Rosenthal, M., & Bush, A. (2000). Ventilatory variables in normal children during rest and exercise. European Respiratory Journal, 16(6), 1075–1083. Sasaki, C. T., Levine, P. A., Laitman, J. T., & Crelin, E. S., Jr. (1977). Postnatal Descent of the epiglottis in man. A preliminary report. Archives of Otolaryngology, 103, 169–171. Sosnowski, T. R., Moskal, A., & Gradon, L. (2006). Dynamics of oropharyngeal aerosol transport and deposition with the realistic flow pattern. Inhalation Toxicology, 18, 773–780. Swift, D. L. (1991). Inspiratory inertial deposition of aerosols in human nasal airway replicate casts: Implication for the proposed NCRP lung model. Radiation Protection Dosimetry, 38(1–3), 29–34.
Deposition of micrometer-sized aerosol particles in infant nasal airway replicas John Storey-Bishoff, Michelle Noga, W.H. Finlay∗ University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, Alberta, Canada T6G 2G8 Received 29 March 2008; received in revised form 29 July 2008; accepted 30 July 2008
Abstract In vitro measurements of particle filtration were made for nasal geometries of 11 infants aged 3–18 months. The geometries were obtained from computed tomography (CT) scans of seven males and four female infants and replicas were built using rapid prototyping. Particles ranging in aerodynamic diameter from 0.8 to 5.3 m were passed through these replicas with simulated tidal breathing. Filtration was determined from particle counts upstream and downstream of the models using an electrical low pressure impactor (ELPI). Mathematical fits were constructed to predict the measured deposition based on the relevant parameters. The fractional deposition, , is found to depend on the Reynolds number of the flow (Re), the particle Stokes number (Stk), and an airway dimension D defined as airway volume divided by airway surface area. This dependence is well captured by the formula = 1 − (2.164 ∗ 105 /(2.164 ∗ 105 + (Re1.118 Stk 1.057 (D/Davg )−2.840 )))0.8510 . Here, Davg is the average value of the dimension D for the group studied and is equal to 1.20 mm. Re and Stk also use the dimension D as the length scale in their definitions. 䉷 2008 Elsevier Ltd. All rights reserved. Keywords: Nasal model; Human infant; Nasal aerosol deposition; Impaction; In vitro
1. Introduction Infants less than approximately 4–6 months of age are obligate nasal breathers since this facilitates breathing while breast feeding (Sasaki, Levine, Laitman, & Crelin, 1977). Nose breathing is also common during low activity at all ages (Bennett, Zeman, & Jarabek, 2008). For this reason, as well as reasons of compliance and practicality, face masks are used when administering pharmaceutical aerosols to infants. The nasal path is therefore important in determining lung drug dose for this age group (Everard, 2003). The filtering function of the nose is also important when an infant is exposed to environmental aerosols since it prevents some particles from entering the lung. A discussion of modeling aerosol deposition in this context including age effects is given by Phalen and Oldham (2001). In vivo measurement of aerosol deposition with infants is difficult due to issues of compliance, legitimate concerns over safety, and the non-voluntary nature of any participation. In vitro studies based on anatomical models of infant nasal geometries overcome most of these concerns and a limited number of such models have been constructed by other researchers (Cheng et al., 1995; Janssens et al., 2001; Swift, 1991). ∗ Corresponding author. Tel.: +1 780 492 4707.
E-mail addresses: [email protected] (J. Storey-Bishoff), [email protected] (W.H. Finlay). 0021-8502/$ - see front matter 䉷 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2008.07.011
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Nomenclature Re Stk D Q¯ V As Davg d Cc particle Dx Dxavg L
¯ Reynolds number ( Q/D) ¯ particle d 2 Cc/18D 3 ) Stokes Number ( Q length scale (V/As ) average volumetric flow rate airway volume airway surface average value of D for all subjects studied particle diameter Cunningham slip factor (1 + 2.52/d) is the fluid mean free path fluid density fluid viscosity particle density fraction not passed through replica √ length scale based on cross-sectional area ( V /L) average value of Dx for all subjects studied airway length
A large number of nasal studies exist in the literature where the focus is on adults or older children. For example, in vivo adult studies have been performed by Heyder, Gebhart, Rudolf, Schiller, and Stahlhofen (1986), Cheng (2003) and Rasmussen, Andersen, and Pedersen (2000), while in vivo studies of both adults and children have been performed by Becquemin, Swift, Bouchikhi, Roy, and Teillac (1991) and Bennett et al. (2008). A study that compares deposition in casts of a monkey nasal airway to that in an adult human airway is presented by Kelly, Asgharian, and Wong (2005). Recent computational fluid dynamics nasal modeling work includes that of Liu, Matida, Gu, and Johnson (2007), which highlights the importance of accurate turbulence modeling in the nose, and Kimbell (2006), which looks at inter-species differences in particle deposition in rats, monkeys and humans. While the existing literature allows a general understanding of nasal deposition in infants, the published data are insufficient to allow a straightforward predictive, quantitative understanding. For this reason, in the current study we have investigated 10 new infant nasal replicas constructed by us, as well as the SAINT model described in Janssens et al. (2001). A correlation which predicts nasal deposition in these 11 nasal replicas for micrometer-sized aerosol particles based on geometry specific Reynolds and Stokes numbers is then constructed which closely matches our measured data and allows quantitative prediction of infant nasal aerosol deposition. 2. Methods This study was conducted under the approval of the University of Alberta Health Research Ethics Board, file number 6432. Data from computed tomography (CT) scans of infants scanned for medical purposes were reused for this study. All subjects were deemed to have normal nasal structure and the original CT scans were not acquired because of any nasal or sinus problem. All scans were obtained with the patient in the supine position. Imaging was helical with reconstructed axial slices of 1.25 mm thickness and in plane resolution ranging from 291 to 430 m across subjects. The airways were identified in the CT based on gray level using the Mimics software package (Materialise, Ann Arbor, MI). An upper threshold of approximately −295 Hounsfield units was used. All airways extended from the nares to just past the larynx. Sinuses were kept if they were connected to the airway in the Mimics model. The airways were smoothed to eliminate surface roughness due to noise and discretization in the CT data. The area of the face from chin to forehead and including both cheeks was also identified in the CT data. Using the Magics software package (Materialise) these geometries were used to create models which could be built using a rapid proto-typer (Invision SR 3-D printer from 3D Systems, Rock Hill, SC).
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Table 1 Subject parameters. Sub
Age (M)
Sex
V (mm3 )
As (mm2 )
L (mm)
Amin (mm2 )
D (mm)
SAINT 2 3 4 5 6 7 8 10 11 14
9 3 3 4 5 6 7 8 16 18 15
F M M F F M M M M F M
8034 13 430 11 924 7913 8599 8723 11 789 10 342 18 583 10 754 14 304
7154 8723 8646 6760 7573 9641 10 241 10 142 13 693 9700 11 331
113.4 95.6 100.6 98.0 89.9 110.3 109.7 110.0 111.3 100.6 115.3
31.8 65.2 64.9 45.1 66.6 58.7 54.2 73.5 62.3 84.1 47.9
1.12 1.54 1.38 1.17 1.14 0.905 1.15 1.02 1.36 1.11 1.26
V is volume of airway, As is the surface area of airway lumen, L is a central path length through the model, Amin is the minimum cross-sectional airway taken perpendicular to expected airflow, D is the calculated dimension V /As .
The models were built in two parts with the face and throat built separately and later joined with bolts and sealed externally with putty. The build material was acrylic plastic and a wax support material was used. The support material was melted to expose the completed model segments. All models were subsequently CT scanned and a comparison was made of the airway parameters listed in Table 1 between the original subjects and the built models. Volume differed on average by 5.28%, airway surface by 5.24%, minimum cross-sectional area by 3.93%, the computed parameter D differed by 7.85% (tending to be larger in the models than the original CT data), while length remained unchanged. This indicates that the models accurately represent the subjects’ original nasal CT geometries and also that the error involved in model construction is small compared to the inter-subject variability of these parameters. The airways captured by CT scanning the completed models are shown in Fig. 1. Fig. 2 shows a completed model of subject 10 with views of the front and back of the model. In addition a SAINT replica of a 9 month old infant was purchased from Erasmus MC, Rotterdam, Netherlands. Details of the construction of the SAINT model can be found in Janssens et al. (2001). Parameters of each subject, such as the volume of the airway, the area of the surface lumen of the airway, the length of a central path through the airway and the minimum cross-sectional area of the airway perpendicular to the central path were measured from CT scans of the built replicas and are reported in Table 1 along with the ages and genders of each subject. In order to allow easy connection of the airway models to downstream tubing, each airway was appended with a distal 2 cm right prismatic extension. The pressure drop across the airway of each model was measured for a number of steady flow rates as an independent experiment. Flow was measured with a mass flow meter (4143 series, TSI, Shoreview, MN). Pressure drop was measured with a differential pressure meter (HHP-103, Omega, Stamford, CT) placed between the exit of the model and the room. A number of experiments to measure nasal deposition were carried out using the setup as shown in Fig. 3. From upstream to downstream the setup consisted of the following: • A six jet collision nebulizer (BGI, Inc. Waltham, MA) connected to filtered house air producing polydisperse aerosol of sunflower oil (=0.92 g/mL) with particles ranging in aerodynamic diameter from 0.8 to 5.3 m. Sampled aerosol MMAD was 3.2 m with a GSD of 2.4. • An unsealed chamber at room pressure, equipped with a mixing fan, housing the airway model and a blank sampling line of matched length. • A three-way valve to switch between the model and the blank sampling line. • An electronic low pressure impactor (ELPI) (Dekati Ltd., Tampere, Finland). • Filtered air-supply matched to the flow volume through the ELPI. • A mass flow meter (4143 series, TSI) measuring breathing flow. • One-way valve allowing only inhalation flow through the airway model. • Cyclic breathing machine, constructed in house, producing a sine wave breathing pattern.
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Fig. 1. Perspective views of the model airways used in this study. (A 2 cm straight extension at the exit of the airway is not shown but was included in all models except the SAINT.)
Flows through the ELPI are fixed at 30 L/min by critical flow at the outlet of the impactor. A filtered air-supply set to 30 L/min supplies the flow consumed by the ELPI through a relatively high resistance path. The cyclic breathing machine applies a varying pressure which results in flow primarily through the low resistance path which is either the sample line or nasal model depending on the position of the three-way valve. Deposition was measured by comparing the amount of aerosol that passed through the blank sample line to the amount that passed through the nasal model. No separate characterization of inhalability was performed and all measurements of deposition indicate the full fraction that did not pass through the model. Aerosol entered the replica naturally from the air surrounding the facial features of the replicas, so that the present results include both inhalability and internal nasal deposition, although inhalability is close to 100% for the flow rates and particle sizes considered here (Kennedy & Hinds, 2002). A single deposition experiment consisted of a 2 min sample drawn through the blank line followed by a 2 min sample through the model, and ended with another 2 min sample through the blank line. Each 2 min time interval was further
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Fig. 2. Photos of front and back of the built model of subject 10. 30 I/min input
aerosol
Flow Meter
ELPI
30 I/min output
Fig. 3. Experimental setup.
divided with a 40 s period at the beginning of the interval and a 5 s period at the end of each interval both being discarded to eliminate effects from settling of the instrument and errors in valve switching synchronization. This left a 75 s period of data which was actually used in each 2 min interval. This was sufficient to allow averaging of many breathing cycles. The ELPI provided an average particle count for size ranges corresponding to each stage of the impactor for each time interval. Nasal deposition for each impactor stage size range was calculated as the difference between the average number seen through the blank line at that stage and the average number seen through the model at that stage divided by the average number through the blank line at that stage.
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Table 2 Typical breathing patterns (inhalation only). Vt (cm3 )
bpm
Q¯ (cm3 /s)
60.9 113.8 107.3 87.9 186.2
45 30 45 57 30
91.3 113.8 161.0 167.1 186.2
Vt: tidal volume, bpm: breaths per minute, Q¯ : average flow rate during inhalation Q¯ = 2 ∗ Vt ∗ bpm ∗ 1 min /60 s.
Five repeats of this experiment were performed for each model using each of five breathing patterns and the results for each breathing pattern and model combination were individually averaged. A small number of validation runs were performed with an electrostatic neutralizer upstream of the model and compared to runs made without the neutralizer. The two differed negligibly in measured deposition in the models, confirming that electrostatic effects were insignificant. The breathing patterns used were half sinusoidal with only the inhalation portion of the curve being used. This was done to avoid many technical difficulties associated with using both the inhale and exhale flows given the small tidal volumes involved. In particular, the dead-space introduced by any length of sampling line would easily exceed the small tidal volumes being used, making proper sampling impossible. Balancing the volume of the model lines and sampling lines is also less critical if only the inhale flow is used. During in vivo breathing, there is a period of zero flow as exhalation stops and inhalation starts. The initial condition for inhalation is zero flow in both real breathing and in our patterns so it is not expected that using only the inhale flow will have had any effect on deposition. The average parameters for the breathing patterns are given in Table 2 while the actual parameters for each individual experiment were measured and used for all calculations. Periodic flow conditions were used in order to ensure a more physiologically realistic experiment. Previous studies, Haussermann, Bailey, Bailey, Etherington, and Youngman (2002) and Sosnowski, Moskal, and Gradon (2006), have shown differences in total deposition for periodic flows and steady flows of equal average velocity in airway replicas. Average weight for the infants in this study ranged from 6 to 11 kg based on age and gender (Centers for Diseae Control & Prevention, 2000). Resting tidal volume ranges from 5 to 8 mL/kg in infants and children(Chernick, Boat, Wilmott, & Bush, 2006). This gives a resting tidal volume range of 30–88 mL for the present subjects. Resting breathing rate ranges from 44 to 34 bpm with age from 2 to 18 months (Dozor, 2002). Rosenthal and Bush (2000) examined 23 children aged 8–10.5 yrs and found an increase in breathing rate of 97% from that at rest vs. maximum exercise for boys in this age group, while girls increased breathing rate on average by 79%. In the same study tidal volume was found to increase 185% for boys and 135% for girls under maximum exercise. The largest tidal volume used in the present study was a 112% increase from resting volume while the highest breathing rate was a 26% increase from resting range. Extrapolating from Rosenthal et al. (2000), the breathing patterns used in the present study represent states of moderate activity. All curve fitting was done using Levenberg–Marquardt nonlinear regression with a least squares objective function in the GNU Octave software package version 2.1.72 (www.octave.org). Multiple starting points in the parameter space were used to ensure a reasonably global solution. 3. Results and discussion ¯ where da is particle aerodynamic diameter, is shown Deposition for all subjects versus impaction parameter, da2 Q, in Fig. 4. A great deal of variability is evident across subjects and deposition for any individual subject is not captured, across breathing flow rates, by a single curve. Semi-empirical models to predict nasal deposition in individuals have been proposed based on pressure drop across the nose (Hounam, Black, & Walsh, 1969), maximum air velocity based on minimum airway cross-section area (Rasmussen et al., 2000) and Stokes number scaled using the minimum airway cross-sectional area (Cheng, 2003; Kelly et al., 2005; Swift, 1991). These models have been based on in vivo and in vitro measurements. In a study of various adult oral airways Grgic, Finlay, Burnell, and Heenan (2004) found the data collapsed well using a correlation involving Reynolds and Stokes number based on mean cross-sectional area to predict aerosol deposition.
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Fig. 4. Deposition vs. impaction parameter (standard error too small to display).
Table 3 r 2 of fits using different dimensions to define Reynolds and Stokes number. Fit, D= Stk, Re Stk, Re, D
V As
V Amin
0.887 0.930
0.745 0.778
L 0.545 0.588
As L 0.606 0.638
V L
0.792 0.813
√
Amin
0.495 0.590
P 0.351 0.901
1 P 0.753 0.901
Fits rely on either two term with Reynolds and Stokes (row 1) or three terms with Reynolds, Stokes and the dimension D (row 2).
In the present study subsequent results are presented as a function of Stokes and/or Reynolds numbers in order to express deposition in a way that collapses the inter-subject variability using the appropriate non-dimensionalization. The Reynolds number is a ratio of the convective and viscous terms of the equations governing fluid motion and is the main parameter used to characterize incompressible flows. The Stokes number relates the stopping distance of a particle in the flow to a characteristic length scale in the geometry. This indicates a particle’s ability to follow curves in the flow streamlines. A number of length scales were examined to non-dimensionalize the present infant deposition data. These included minimum cross-sectional area and average cross-sectional area. Trans-nasal pressure drop at 7 L/min of flow was also tried as a scale factor by using the inverse of pressure drop in place of the length scale in the definition of Stokes and Reynolds numbers. The length scale, D, that best collapsed the data was found to be airway volume divided by airway surface area. This can be seen by a comparison of r 2 values for fits using various scaling dimensions given in Table 3. Hydraulic diameter is often used as a scale dimension in non-circular geometries and is defined as Dh =
4 ∗ cross-sectional area perimeter
By comparison, our chosen dimension D has some analogy to the hydraulic diameter for these geometries with variable cross-section since it is equivalent to D=
average cross-sectional area average perimeter
The average flow rate for each breathing pattern was used in the definition of Re and Stk. It was found that the flow pattern could be fully characterized, for our purposes, by average flow rate, with patterns having similar average flow rate but different combinations of Vt and breaths per minute resulting in similar deposition. The dynamics of the nasal flows are, of course, changing through the breathing cycle and deposition may be happening at different rates during
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Fig. 5. Deposition vs. Stk (standard error too small to display).
Fig. 6. Deposition vs. f (Re, Stk) (standard error too small to display).
the cycle and at different locations within the nasal geometry. Despite this, average flow rate was successfully used to create a correlation for total deposition. A function of the form = 1 − (a/(a + x))b where a and b are fit parameters was used to match the overall shape of the deposition curve. In order to capture the deposition for all subjects as a single curve, the abscissa was taken variously as a function of Stokes number; Stokes and Reynolds numbers; or Stokes number, Reynolds number and length scale D. Attempts to express deposition versus only Stokes number resulted in distinct deposition curves for each flow rate and each individual as seen in Fig. 5. This suggests an additional dependence on flow rate. A better fit is obtained if Reynolds number is also included as in Fig. 6. This is consistent with the observed static pressure drop for these models i.e. when non-dimensionalized pressure drop is plotted versus Reynolds number, as in Fig. 7, we see that nondimensionalized pressure drop is not constant over the range of flow rates used. This suggests that the flow pattern is changing with flow rate over the range of flow rates used. This is similar to the results observed for the simpler system (stenosis) described in Itoh, Smaldone, Swift, and Wagner (1985).
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Fig. 7. Normalized pressure drop vs. Reynolds number.
Fig. 8. Deposition vs. non-dimensional parameter (standard error too small to display).
The fit function for deposition shown in Fig. 6 is =1−
1.007 ∗ 107 1.007 ∗ 107 + (Re1.526 Stk 1.015 )
1.126 (1)
While the nasal geometries of each infant have similar overall shape, the details of each geometry differ, as seen in Fig. 1. They are not scaled versions of the same structure so the use of the non-dimensional Stokes and Reynolds numbers is not expected to fully collapse the deposition data since it does not account for these intersubject differences. For this reason, a parametric correction was attempted which includes Reynolds, Stokes and the geometric scale factor D, as shown in Fig. 8. This results in a further collapse of the data. The fit function used in Fig. 8 is 0.8510 2.164 ∗ 105 (2) =1− 2.164 ∗ 105 + (Re1.118 Stk 1.057 (D/Davg )−2.840 )
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Fig. 9. Deposition vs. non-dimensionalized parameter based on
√
V /L (standard error too small to display).
where D = V /As , Davg = 1.20 mm. Eq. (2) allows quantitative prediction of nasal deposition in individual infant subjects. Comparing infant nasal deposition from Eq. (2) to that seen in adults (Cheng, 2003) for subjects at rest we find less nasal deposition in infants, e.g. for d = 2 m, Q¯ = 72 cm3 /s (4.3 L/ min, which is a typical resting flow rate for subjects in the age range of infants considered here), D = Davg and particle = 1000 kg/m3 , Eq. (2) gives = 2.0% for an infant, while the nasal deposition correlation of Cheng (2003) gives = 18.2% (assuming a resting adult flow rate of 15 L/min and taking average Amin of 2.08 cm2 as given). Much of this difference is attributable to the difference in resting flow rates. Bennett et al. (2008) also find lower nasal deposition in older children (6–10 yrs.) vs. adults, which supports our similar finding in infants. In order to provide a useful correlation for cases where the average cross-sectional area is known, perhaps through acoustic rhinometry, while the airway surface area is not known, Fig. 9 gives a parametric fit using Reynolds number and Stokes number instead defined using √ average cross-sectional length scale Dx with an additional term depending directly on Dx , where Dx is defined as V /L. Here V is the nasal airway volume and L is a nasal airway path length. The fit function shown in Fig. 9 is =1−
10.40 10.40 + (Re1.201 Stk 1.156 (Dx /Dxavg )−2.301 )
0.5201 (3)
√ where Dx = V /L, Dxavg = 10.3 mm. This correlation also reveals some differences between the oral geometries studied by Grgic et al. (2004) and the nasal geometries examined in the current study. While an excellent collapse of oral deposition was obtained by Grgic et al. using only Reynolds number and Stokes number based on V /L, Figs. 8 and 9 show that the quantity V /As provides better collapse of variability for the infant nasal geometries studied. Also in contrast with Grgic et al., we find here that a further dependence on a geometric factor beyond Reynolds number and Stokes number is required to obtain a tight collapse of the deposition data. These differences may be explained by two factors. First, the oral geometry is more circular in cross-section than the nasal geometry and therefore the square root of the average cross-sectional area is closer to the hydraulic diameter than is the case in the nasal geometry. Second, the oral geometries, being simpler, are apparently more easily modelled via the Reynolds number and Stokes number alone since their differences can be more accurately described by a volumetric scaling factor.
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4. Conclusions Our measurements of nasal deposition in replicas of infants indicate that there is considerable variability in nasal aerosol deposition between individual infants. Deposition within a single subject depends not only on Stokes number but also on Reynolds number. This is apparent from our deposition data and consistent with our static pressure drop measurements. A reasonable predictive equation for deposition in all 11 subjects was obtained by including both Stokes and Reynolds numbers scaled using total nasal air volume divided by surface area. An even tighter fit was obtained by including an additional direct dependence on volume over surface area. The resulting equation (Eq. (2)) allows estimation of nasal deposition in individual infants and is expected to be useful for those wanting to estimate the fraction of aerosol reaching the lungs through the nasal passage of infants during breathing. Acknowledgments The authors gratefully acknowledge the financial support of National Science and Engineering Research Council of Canada and the indispensable assistance of iRSM, the Institute for Reconstructive Sciences in Medicine. H. Janssens is also gratefully acknowledged for helpful suggestions in the preparation of this manuscript. References Becquemin, M., Swift, D. L., Bouchikhi, A., Roy, M., & Teillac, A. (1991). Particle deposition and resistance in the noses of adults and children. European Respiratory Journal, 4(6), 694–702. Bennett, W. D., Zeman, K. L., & Jarabek, A. M. (2008). Nasal contribution to breathing and fine particle deposition in children versus adults. Journal of Toxicology and Environmental Health, 71, 227–237. Cheng, Y. S. (2003). Aerosol deposition in the extrathoracic region. Aerosol Science and Technology, 37, 659–671. Cheng, Y. S., Smith, S. M., Yeh, H. C., Kim, D. B., Cheng, K. H., & Swift, D. L. (1995). 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