Deposition of Inhaled Ultrafine Aerosols in Replicas of Nasal Airways of Infants

Figures & data

FIG. 1 Nasal airways of one infant subject and two adult subjects (one male and one female) are shown.

TABLE 1 Adult subject parameters

Sub	Sex	V (mm^3)	A s (mm^2)	L (mm)
1	M	52338	28444	234
2	F	44567	28718	241
3	M	56218	31507	274
4	F	40410	26422	231
5	F	35857	23532	210
6	M	50125	31345	269
V, volume; As, surface area; L, length of the airways.

FIG. 2 Schematic diagram of the experimental setup.

FIG. 3 Pressure drop data points across six adult human nasal replicas as a function of inspiratory air flow rate compared with available in vivo and in vitro measurements in the literature.

FIG. 4 Deposition data for adults at a flow rate of 20 L/min compared to available in vivo and in vitro data.

FIG. 5 Pressure drop data for inspiratory flows in infant subjects.

TABLE 2 Summary of equations in the literature for predicting deposition of ultrafine particles in nasal airways of adults and their related R² values when fitted to our infant data

Deposition Equation		Comments	R^2	Reference
η=1−exp((−16.6)D ^0.5 Q ^−0.28)	[4]	Q (L/min)	0.58	Cheng (2003)
η=1−exp(−15.9D ^0.39 Q ^−0.28)	[5]	Q(cm^3/s)	0.32	Cheng, K. H. et al. (1996)
	[6]	Q(cm^3/s)	0.55	Cheng, K. H. et al. (1996)
η=1−exp(−11.8D ^0.5 Q ^−0.125)	[7]	Q(L/min)	0.55	Swift and Strong (1996)
η=1−exp(−12.65D ^0.5 Q ^−0.125)	[8]	Q(L/min)	0.64	Swift et al. (1992)
	[9]	Sc =υ/D	0.27	Cheng, Y. S. et al. (1996)
D, diffusion coefficient (cm^2/s); Q, flow rate (unit is specified in each study); As , total surface area of the nasal airway; A min , minimum cross-sectional area of nasal airway in a plane perpendicular to air flow; , average airway shape factor of the nasal turbinate region defined as the ratio of the airway perimeter to a reference perimeter that is the periphery of the rectangle bounding maximum horizontal and vertical boundaries of each 3 mm bilateral airway slice; , average cross-sectional area of nasal airway, which is calculated by dividing the volume of airways by the length of the centerline passing through the airways; dh , hydraulic diameter for calculating Reynolds; Re, Reynolds number; Sc, Schmidt number; , average perimeter of the nasal airways; v, kinematic viscosity.

FIG. 6 The correlation of Swift et al. (1992) developed for adults is shown with our infant deposition data. Error bars on our experimental data points are approximately the same size as the symbols and so are not shown.

FIG. 7 The correlation of Cheng et al. (1995) developed for older children (1.5-, 2.5-, and 4-year-olds) is shown with infant deposition data in this study.

FIG. 8 Comparison of deposition in infant replicas vs. particle diameter (dp) using tidal breathing (solid markers) and constant flow rate (empty markers).

FIG. 9 Comparison of deposition in adult replicas vs. particle diameter (dp) using tidal breathing (solid markers) and constant flow rate (empty markers).

TABLE 3 Characteristic diameters that are suggested in literature and tested in this study for calculation of dimensionless parameters to reduce intersubject variability

Characteristic diameter (dc )	Reference
V/As	Storey-Bishoff et al. (2008)
V/A min	Storey-Bishoff et al. (2008)
L	Storey-Bishoff et al. (2008)
As /L	Storey-Bishoff et al. (2008)
	Grgic et al. (2004)
	This study
	Cheng Y. S. (2003)
(0.0181 L nose/R nose)^4/19	Garcia et al. (2009)
4An /Pn	This study
	Cheng, Y. S. et al. (1996)
V, volume of the nasal cavity; L, length of the representative line passing through airway; L nose, length of the nasal airways from nostrils to the end of the septum; R nose, nasal resistance; An , surface area of nostrils; Pn , perimeter of nostrils. All the other parameters have been introduced in the caption of Table 2.

TABLE 4 R-squared values of Equation (12) fitted to infant data using different characteristic diameters

Deposition Parameter (X)	dc =V/As	dc = V/Amin	dc =L	dc =As /L
Sc^c	0.70	0.70	0.70	0.70	0.70
Re^b .Sc^c	0.77	0.78	0.72	0.73	0.75
Re^b .Sc^c.Wo^d	0.84	0.80	0.72	0.73	0.81
Re^b .Sc	0.84	0.80	0.72	0.73	0.81
Deposition Parameter (X)			dc =(0.0181  L nose/R nose)^4/19	dc = 4A n /Pn
Sc^c	0.70	0.70	0.70	0.70
Re^b .Sc^c	0.79	0.71	0.79	0.70
Re^b .Sc^c.Wo^d	0.82	0.71	0.89	0.71
Re^b .Sc	0.82	0.73	0.89	0.72
Deposition Parameter (X)
Sc^c	0.70
Re^b .Sc^c	0.71
Re^b .Sc^c.Wo^d	0.83
Re^b .Sc	0.83

TABLE 5 Values of constants in equations (12) and (13) for four diameters with the highest R ² values for infant data

Constant values	dc =(0.0181L nose/R nose)^4/19	dc =V/As
a	-4.58	-3.49	2.83	-2.14
b	0.04	0.05	0.01	0.14
c	-0.19	-0.22	-0.04	-0.32
d	-0.51	-0.59	-0.07	-0.45
e	3.51	2.59	-2.05	1.63
f	-0.20	-0.17	0.17	-0.10

FIG. 10 Deposition in infant replicas vs. non-dimensional deposition parameter using characteristic diameter defined as d_c =(0.0181L _nose/R _nose)^4/19.

TABLE 6 Nasal resistance dependent characteristic diameter of infants

	L nose	R nose×10^−8	dc
Subjects	(mm)	(Pa/(m^3/sec)^1.75)	(mm)
2	40.32	3.92	3.4
3	43.99	9.19	2.9
4	38.72	7.51	2.9
5	44.41	8.17	3.0
6	49.02	31.0	2.3
7	51.75	23.6	2.5
8	49.29	17.9	2.6
10	60.56	2.87	3.9
11	52.88	26.6	2.4
14	55.15	4.00	3.6

FIG. 11 Deposition in infant replicas vs. non-dimensional deposition parameter using characteristic diameter

.

TABLE 7 Nasal resistance dependent characteristic diameter of adults

	L nose	R nose×10^−8	dc =(0.0181L nose/R nose)^4/19
Subjects	(mm)	(Pa/(m^3/sec)^1.75)	(mm)
1	88.4	1.1256	5.2
3	87.8	2.5474	4.4
6	81.8	5.3457	4.3

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