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On the fate of inhaled particles in the human: A comparison of experimental data with theoretical computations based on a symmetric and asymmetric lung
Bulletin of. Mathematical Biology, Yol. 45, No. 3, pp. 409--424, 1983.
Printed in Great Britain.
0tD2-8240/83/03040%16503.00/0 Pergamon Press Ltd. 1~) 1983 Society for Mathematical Biology
ON THE FATE OF INHALED PARTICLES IN THE HUMAN: A COMPARISON OF EXPERIMENTAL DATA WITH THEORETICAL COMPUTATIONS BASED ON A SYMMETRIC AND ASYMMETRIC LUNG • T. MARTONEN'~ Inhalation Technology and Toxicology Section, Battelle, Pacific Northwest Laboratories, Richland, WA 99352, U.S.A. An analytical model is used .to describe the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simulate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree. Introduction. K n o w l e d g e of the sites of deposition of inhaled particulate matter within the tracheobronchial (TB) tree is of importance in assessing the health effects of atmospheric pollutants and in aerosol therapy p r o c e d u r e s w h e r e medicinal agents are administered to patients. Early experimental inhalation exposure studies established that particle deposition probabilities within the h u m a n respiratory system can be expressed as a function of the mass median a e r o d y n a m i c diameter (MMAD) and geometric standard deviation (~rg) of an inspired aerosol (Task Group on Lung Dynamics, 1966; L i p p m a n and Albert, 1969). A detailed experimental investigation of the regional dispersion of inhaled particles in the h u m a n c o n d u c t e d by L i p p m a n n et al. (1971) has shown that deposition in ciliated airways of the TB tree is related to an 'impaction parameter' defined in terms of particle parameters (size and density) and a breathing p a r a m e t e r (inspiratory flow rate). A theoretical model of aerosol behavior in the h u m a n respiratory tract that permits factors which influence deposition to be studied is presented here. The model requires definition of a system of deposition probability formulae and a description of h u m a n TB morphology. The system of equations describing the deposition efficiencies of the inertial impaction, t P r e s e n t a d d r e s s : N o r t h r o p S e r v i c e s , Inc., E n v i r o n m e n t a l S c i e n c e s , P.O. B o x 12313, R e s e a r c h Triangle P a r k , N C 27709, U.S.A.
409
410
T. MARTONEN
sedimentation and diffusion mechanisms proposed by Martonen (1982) is used. There are several morphologies available for use in such a theoretical aerosol deposition model. Different TB morphologies have been proposed by Weibel (1963), Horsfield et al. (1971) and Soong et al. (1979). The latter two will hereafter be referred to as the 'Horsfield' and 'Soong' geometries respectively. The Weibel and Horsfield descriptions are based on extensive anatomical measurements of the human lung. The Soong geometry is a Weibel-type TB morphology, with dimensions modified from the original to account for variation in lung dimensions among a population. The three TB descriptions were incorporated into the theoretical aerosol deposition model, and calculated particle losses within the different TB trees compared with the experimental data of Lippmann et al. (1971). Findings indicated that the symmetric, dichotomously branching pattern proposed by Weibel (1963), with airway dimensions modified by the statistical work of Soong, is a suitable description of the human lung for the study of aerosol behavior. H u m a n Tracheobronchial Morphology. The Weibel Model A morphology is the simplest TB description proposed for the human lung. It is a symmetric, dichotomously branching network of cylindrical tubes. There are 17 generations of conducting airways (tubes) numbered from 0 through 16, with generation I = 0 being the trachea and generation I = 16 the last unalveolated bronchiole. Each generation I consists of 21 identical airways. A description of the morphology is given in Table I. The dimensions given, which were measured from a cast of large-bore airways and histological sections of small-bore bronchioles, correspond to a lung volume of 3/4 total lung capacity (TLC), or 4800cm 3. The Weibel conception of the TB network, because of its simplicity and the fact that it is based on anatomical measurements, has been widely used in experimental (Ferron, 1977; Scherer et al., 1979) and theoretical (Gerrity et al., 1979; Martonen and Patel, 1981) studies of aerosol deposition in the human lung. The Soong branching scheme is identical to that of Weibel; airway dimensions, however, are different. Since Raabe et ai. (1976) discussed the significance of inter-subject differences in the structure and dimensions of the human TB tree, the Soong morphology, a statistical description, was intended to account for such variabilities. From morphometric measurements of airway lengths and diameters as functions of TB generation reported in the open literature, statistical parameters of each such distribution were determined. Mean airway dimensions /~ and coefficients of variation cr[~ of distributions of standard deviations cr are
411
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
TABLE I Description of the Weibel (1963) and Modified-Weibel (Soong et al., 1979) Symmetric Tracheobronchial Trees Airway Generation
Weibel Length Diameter (cm)
Modified-Weibel Length ~/~ Diameter o/~
(cm)
(cm)
0
12.000
1.800
10.494
0,I0
1.574
(cm) 0.I0
1
4.760
1.220
4.163
0.15
1.067
0.125
2
1.900
0,830
1.662
0.25
0.726
0.15
3
0.760
0.560
0.665
0.30
0.490
0.175
4
1.270
0.450
I.III
0.35
0.394
0.20
5
1.070
0,350
0.936
0.425
0.306
0.23
6
0,900
0.280
0.787
0.50
0,245
0.275
7 8
0.760
0.230
0.665
0.325
0.186
0.575 0.560 0.65
0.201
0.640
0.163
0.35
9
0,540
0.154
0.472 0.70
0.135
0.42
10
0,460
0,130
0,402 0.75
O.ll4
0.50
II
0,390
0.I09
0,341 0.80
0,095
0.575
12
0.330
0.095
0.289 0.81
0,083
0.66
13
0.270
0,082
0.236 0.775
0.072
0.675
14
0,230
0.074
0.201 0.725
0.065
0.60
15
0.200
0.066
0.175
0.058
0.50
~6
0.165
0.060
0,144 0.50
0.052
0.40
0.65
Mean airway dimension is denoted by p~, and tr is the standard deviation of the distribution of dimensions for each generation.
1
given in Table I. The dimensions correspond to a lung volume of ~ TLC, or 3200 cm 3, believed to be a more physiologically realistic condition for the human lung than the 3/4 TLC volume used by Weibel. The Horsfield description of the TB tree is very complicated. In it, airways are classified by 'order'. Airway lengths and diameters are given in Table II for a lung volume of 5000 cm 3. The measurements were obtained from a resin cast of a normal lung. The order 31 airway is the trachea, and order 6 airways are the smallest TB bronchioles. Airways of a given order do not necessarily have the same dimensions; there are, for example, three different order 27 airways. Branching within the Horsfield morphology is dichotomous, but four separate mathematical patterns are used to describe four different regions within the TB tree. Bifurcations from order 11 to 31 airways occur by a J - 1 and J - 4 pattern; that is, order 20 airways branch into order 19 and 16 airways. Branching from order 9 to 10 airways is defined by a J - 1 and J - 3 scheme, and from order 8 airways by a J - 1, J - 2 pattern. Order J = 7 airways branch only to order 6, J - 1 airways.
412
T. MARTONEN TABLE II Physical Parameters and Flow Distribution Characteristics of Horsfield et al. (1971) Airway Orders Order
Length
Diameter
(cm)
(cm)
Flow D i s t r i b u t i o n Coefficient
E
Fraction of Flow Entering Trachea
f
31
IO.O00
1.600
233,920
l.O00000
30
2.200
l.llO
128,576
.549658
29a
5.000
1.2OO
105,344
.450342
29b
2.600
0.890
84,320
.360465
28a
l.lOO
0.800
61,088
.261149
28b
0.800
0.640
61,088
.261149
27a
1.6OO
0.750
44,256
.189193
27b
1.560
0.730
44,256
.189193
27c
0.970
0.700
44,256
.189193
26
1.127
0.667
32,064
.137073
25a
2.1DO
0.520
23,232
.099316
25b
1.125
0.585
23,232
.099316
24
0.970
0.535
16~832
.071956
23
l.O81
0.427
12,192
.052120
22
0.953
0.349
8,832
.037756
21
0.857
0.347
6,400
.027360
20
0.988
0.309
4,640
.019836
19
0.796
0.288
3,360
.014364
18
0.918
0.277
2,432
17
0.818
0.267
1,760
7.5239 x lO-3
16
0.808
0.251
$,280
5.4720 x IO-3
15
0.774
0.235
928
3.9672 x lO-3
14
0.640
0.218
672
2.8728 x IO-3
13
0.627
0.200
480
2.0520 x IO-3
12
0.517
0.177
352
1.5048 x lO-3
II
0.477
0.156
256
1.0944 x IO-3
IO
0.422
0.135
192
8.2079 x lO -4
9
0.356
O.ll3
128
5.4720 x lO-4
8
0.312
0.095
96
4.1040 x IO-4
7
0.254
0.076
64
2.7360 x lO-4
6
O.llO
0.063
23
1.3680 x lO-4
.010397
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
413
A major significance of the Horsfield concept of the human lung is that it is structurally asymmetric because different airway orders comprise any given TB generation beyond the trachea. It was proposed, therefore, as a more realistic description of conducting airways than a symmetric network in which airways of a generation are identical. To effect a comparison of aerosol deposition efficiency calculations in the Weibel, Soong and Horsfield morphologies we will define the Horsfield TB tree as consisting of 26 generations, since there are 26 distinct airway orders in that description. The four different branching patterns previously discussed will be used to define the order composition of each TB generation. The trachea will be generation I = 0 and downstream generations numbered in a descending order. This morphological system was used in a previous, more focused work (Martonen and Gibby, 1982) and for completeness of this text is given in Table III. The number of airways per generation follows the 2 ~ formula proposed by Weibel only for generations 0-8. For generations 9-13, the number of conducting airways does not increase as rapidly, and beyond I = 14 the number of airways decreases.
Modeling of Aerosol Behavior. In this work, deposition of airborne particulate matter in conducting airways of the TB network is studied. Conducting airways are non-alveolated passages that do not participate in gas exchange. It is important to quantitate deposition in this compartment of the human respiratory tract in order to assess potential health hazards following inhalation of airborne contaminants. This applies to the general populace where the health effects of atmospheric pollutants are of concern and to personnel in the work environment exposed to occupational aerosols. Furthermore, in aerosol therapy, knowledge of factors affecting particle deposition would aid in successful treatment of patients with pulmonary diseases because particle sizes and breathing rates could be regulated so as to deposit medicinal agents more effectively at appropriate TB locations. For example, in the treatment of obstructive respiratory ailments like asthma, it is important to know the sites of action of bronchodilator agents. Before inhaled particulate matter can be deposited in the TB tree it must successfully penetrate proximal compartments of the human respiratory tract; namely, the oral and nasopharyngeal regions. Aerosol losses from mouth and nose breathing have been experimentally measured by Lippmann et al. (1971), Pattle (1961) and Heyder and Rudolf (1977) respectively. These upper compartments can be quite efficient filters of airborne particles, depending on specific particle sizes and inspiratory flow rates. In this work theoretical TB losses will be normalized to the inhaled aerosol mass that actually enters the trachea to be
414
T. MARTONEN
consistent with the manner in which the original laboratory TB data used for comparison (Lippmann et ai., 1971) were presented in the open literature. The most effective particle deposition mechanisms in the human TB tree are inertial impaction, sedimentation and diffusion (Findeisen, 1935). A system of formulae that describes particle deposition probabilities from
TABLE III Airway Order Composition of the Horsfield et aL (1971) Tracheobronchial Tree Airway Order
Generation 0
1 2
3 4
5 6
7
8
9
I0
II
12
13
14
15
16
17
18
19
20
21
22
2J
6
0
0
0
0
0
0
0
6
68
177
490
770
948
1230
I012
938
702
401
318
134
60
43
8
3
2
7
O 0 0 0
0
0
0
2
175 238 294 450
330
352 260
133
135
50
20
20
3
l
1
0
8
0 0 0
165
220
156
91
105
32
17
18
2
l
l
O
0
9
0 0 0 0
0 0
0
120 165
132
78
91
30
16
17
2
l
l
0
0
0
10
0
0
0
0
0
11
0
0
0
0
0
12
0
0
0
0
13
0
0
0
0
14
O 0
0
15
0
0
16
0 0
17
0 0 0
18
0 0
19
0
20
0
0
0
0 0
l
6
70
70
126 240
l
30
35
70
168
0
0 I0
15
35
112
84
120
0
2
5
15
70
56
84
90
0
0
1
5
40
35
56
72
0
0
1 20
20
35
56
36
0
0
0
8 10
20
42
28
0
0
2
4 I0
30
21
0 0
0
1 4 20
15
21
0
l 12 lO
15
0
0 0
O 0
16 36
II0
24 25
66
78
28
15
16
2
1
1
0
0
0
O
55
66
26
14
15
2
1
I
0
0
0
0
0
45
55
24
13
14
2
1
1
0
0
0
0
0
0
45
22
12
13
2
l
1
0
0
0
0
0
0
0
36
20
II
12
2
1
1
0
0
0
0
0
0
0
0
28
18
I0
II
16
9
I0
14
8
9
2
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
l
l
0
0
0
0
0
0
0
0
0
0
0
O 6
6 lO
12
7
8
2
1
l
0
0
0
0
0
0
0
0
0
0
0
0
0 0 0
2
3
6 lO
6
7
2
l
l
0
0
O
0
0
0
0
O
0
0
0
0
0
0 0
0
l
3 8
5
6
2
l
l
0
0
0
0
0
0
0
0
0
0
0
0
0
0
21
0 0 0
0
1
6 4
5
2
l
l
0
0
0
0
0
0
0
0
0
0
0
O
0
0
0
22
0
0 4
3 4
2
l
1
0
0
0
0
0
0
0
0
0
0
0
0
O
0
0
0
23
0 0 D 2 2
3
2
l
l
0
0
0
O
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0 0 0
l
2
2
l
1
O
0
0
0
0
0
0
0
0
0
0
0
O
0
0
0
0
0
25a
0 0 0
l
0
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25b
0
0 0
0
2
l
l
0
0
0
0
0
0
0
0
0
0
0
0
0
O
0
0
0
0
0
26
0 0 0
2
l
l
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27a
0 0
1 0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27b
0 0
1 0
O 0
0
0
0
0
0
0
0
0
0
O
0
0
0
0
0
0
0
0
0
0
27c
0 0 0
l
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
O 0
0
0
28a
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
28b
0 0 0
l
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29a
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29b
0 0
l
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
l
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
l
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
O 0
l
l
1 0
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
415
those mechanisms in a general branching network has been presented by Martonen (1982). The formulae may be used to compute aerosol losses in any particular TB morphology by using appropriate airway dimensions. Both stable and unstable air flow conditions were treated in the derivation of the formulae to simulate physiological conditions in the human. In fluid dynamics studies using replica casts of the upper TB tree, Dekker (1961) has demonstrated that a transition from laminar to turbulent flow at inspiratory flow rates as low as 6 1/min can be attributed to cartilaginous rings present in large-bore airways. Utilizing similar casts, West and Hugh-Jones (1959) have shown that the bifurcating pattern itself may induce flow irregularities in smooth-walled bronchioles. Other experimental work with airway models (Schroter and Sudlow, 1969) has substantiated the effect of branching. The effect of the larynx must also be included in a model of aerosol behavior. Schlesinger and Lippmann (1976) noted that turbulence induced at the restricted glottis opening at the entrance to the trachea may persist, and affect particle trajectories, in downstream generations. Furthermore, C h a n e t al. (1980) demonstrated that particles entrained in the laryngeal jet impact at a site immediately distal to the larynx, producing a 'hot spot' of deposition in the trachea. The empirical relation describing this enhanced deposition is:
p(t) = 2.536 Stk 1231.
(1)
The particle Stokes number, Stk, is defined by the equation S t k - pd2U 18nr '
(2)
where r = trachea radius, ~ = absolute air viscosity, U = airstream velocity, p = particle density and d = particle diameter. This work focuses upon deposition incurred during inspiration. It has been demonstrated (Lippmann and Albert, 1969) that for particles > 2.5/zm in size that are of primary therapeutic and risk assessment concern, nearly 100% of the inhaled aerosol mass entering the trachea may be deposited in the lung during the inspiratory phase of the respiratory cycle, Moreover, Widdecombe (1954) has established that airway carinae are ,locations within the TB tree where nerve endings and reflex receptors are concentrated. Experiments using human larynx-TB casts have demonstrated that bifurcation carinae can be sites of greatly enhanced particle deposition (Schlesinger et al., 1977; Martonen and Lowe, in press). Knowledge of such preferential losses, or 'hot spots',
416
T. MARTONEN
has obvious important implications in aerosol therapy and inhalation toxicology because of the high doses delivered to selected airway cells. Deposition is enhanced at such sites during inspiration, when the carina within a bifurcation functions as an airstream divider and particles of sufficient inertia traveling near the center line of the parent airway have trajectories that deviate from fluid streamlines and are deposited by impaction at the downstream carina. During expiration, however, a carina does not serve as a flow divider and particles may sweep past it, unless they have a fiber-like shape (for example, asbestos) and are collected by the interception deposition mechanism. Particle losses in an airway will be computed in the following manner (Martonen and Gibby, 1982). Fluid dynamics within the TB tree will be as described by Martonen (1982), and deposition probabilities of the inertial impaction, sedimentation and diffusion mechanisms written as p(i), p(s) and p(d) respectively. The branching angle between the two airways at a bifurcation within a generation is assumed to be 70 ° after the experimental measurements of Horsfield and Cumming (1967). In the trachea, enhanced losses by inertial impaction due to the laryngeal jet will be accounted for by including equation (1) in p (i). The total probability of deposition in an airway due to the action of all mechanisms p(T) will be determined from Landahl's (1950) equation:
p(T) = 1 - [1 - p(i)][1 - p(s)][1 - p(d)].
(3)
Aerosol dispersion within the Weibel and Soong TB geometries is facilitated by their simplicity. Since all airways within a given generation are identical, each individual airway receives 2-I of the total aerosol mass entering the generation. Hence deposition in a generation is that computed for one airway multiplied by 21. If the total aerosol mass entering generation I from the upstream generation ! - 1 is re(I), and the total deposition probability [equation (3)] in an airway of generation I is p(I), the aerosol mass that penetrates to the downstream generation I + 1 is:
m(I+l)=m(I)[1-p(I)].
(4)
Therefore, the aerosol mass entering the trachea, I = 0, that reaches generation I' where I' --_ 1 may be expressed as Irrl
M(I') = rn(O)- ~, m(I)p(I),
(5)
I=0
where m(0) is the original mass entering the trachea. The total dose
ON THE FATE OF I N H A L E D PARTICLES IN THE H U M A N
417
deposited in a symmetric TB tree, therefore, is simply 16
~, M(l)p(I).
(6)
I=0
Because of asymmetry, aerosol dispersion within the Horsfield geometry is more difficult to formulate than for the other TB patterns. The data under the E and f headings of Table II describe air distribution among different airway orders: [ is the fraction of inspired air entering a specific airway order and E defines the relative division of air at a bifurcation. The following equation is presented here for use in calculating~3the aerosol mass that enters order J airways of generation ! from order P 'parent' airways of the preceding ! - 1 generation: m ( L J, P ) = m ( I - 1 ) [ f ( P ) N ( I -
_r E(J)+E(S)] "
1, P)][1 - p ( I - 1, P ) ] I E ( J )
(7) For example, in generation I = 13, each of the 11 order-14 airways has an order-15 or an order-18 parent from the upstream I = 12 generation (Table III). Equation (7) has four major components. The aerosol mass that entered generation I - 1 [see equation (4)] is re(I-1). The number of order P parents in generation I - 1 is N ( I - 1 , P) and f(P) is the fraction of inspired aerosol reaching a parent P airway (Table II); their product is the fraction of aerosol mass of generation I - 1 in order P parent airways. The fraction of aerosol mass entering a parent P airway of generation I - 1 that penetrates it is [1 - p(I - 1, P)], where p(I - 1, P) is the deposition probability, as defined by equation (3), of the parent airway whose 'order' is defined in Table III. The division of aerosol at the bifurcation of two 'daughter' airways is defined by the last term of equation (7). E(J) and E(S) are the E values (Table II) for an airway order J and its 'sister', S. The aerosol mass deposited in all order J airways of generation ! from parents of either order can be written as D ( L J) = ~, m ( L J, P ) p ( J ) ,
(8)
P
where p(J) [equation (3)] is the deposition probability in an order J airway, and the summation is performed over the respective order P parents. For example, the aerosol mass deposited in order J = 20 airways of generation 8 is: [m(8, 20, 21)+ m(8, 20, 24)]p(20). The total aerosol
418
T. MARTONEN
mass deposited in generation I, D(I), is therefore the summation of D(I, J) over all order airways present:
D(I) = ~, D(I, J),
(9)
2
where the airway order composition for each TB generation is known (Table III). The fraction of the inspired aerosol mass deposited in the Horsfield TB tree can be computed in a manner similar to that for the symmetric Weibel and Soong geometries [equations (5) and (6)].
Results.
Theoretical aerosol deposition efficiencies in the human TB tree, as computed by three models using Martonen's (1982) deposition probability equations with Weibel, Soong and Horsfield TB geometries, were compared with experimental data from the extensive inhalation exposure tests of Lippmann et al. (1971). In the latter work, direct measurements of regional aerosol deposition in human subjects were made using 99mTc-labeled, insoluble monodisperse aerosols. TB deposition was measured with the aid of scintillation detectors. The experimental findings of these mouth-breathing tests, using both nonsmokers and ex-smokers, are presented in Figures 1, 2 and 3. TB losses are graphed as a function of an 'impaction parameter' defined as pdZQ, where Q (l/min) is the inspiratory flow rate and p (g/cm 3) and d (/zm) are the particle density and diameter respectively. The straight dashed line is the 'median' fit of Lippman et al. (1971) to their experimental data. The straight, dash-dot lines are the 'limit' lines to their data; all data lie within these 'limit' lines. Theoretical aerosol deposition calculations assumed an inspiratory flow rate of 301/min, and particle aerodynamic diameters Dae, where Dae = X/(p)d, ranged from 1 to 12/xm. Three different airway coefficients (AC), were used for each TB morphology to examine the effect of airway caliber upon deposition. The AC --- 1.00 curves plotted in Figures 1, 2 and 3 correspond to the airway dimensions given in Tables I and II respectively. The A C = 0 . 8 5 curves correspond to airway diameters that have been multiplied by 0.85 (decreased in bore by 15%). Similarly, the AC = 1.15 curves correspond to TB trees where airway diameters have been increased by 15%. Comparison of the three AC curves for TB geometry permit the effect of inter-subject differences on aerosol deposition to be assessed. It is apparent from Figures 1 and 2 that theoretical calculations of aerosol deposition using the symmetric Weibel TB morphologies are in very good agreement with the experimental data. It is clearly evident (Figure 3) that theoretical calculations assuming the asymmetric
ON THE FATE OF INHALED PARTICLES IN THE HUMAN 1.00
'
0.90
. . . . . . . . . .
0.80
'
I
....
I
'
,
,
I
MEANFIT TO DATA ENVELOPEOF DATA THEORETICALDEPOSITIONCURVES 0 AC : 1.00
....
419
I
/
/"
/"
/(t
0.70 z O
0.60
"
m.
0.50
//
0.40
/
0.30
I
i/ /l
/
l~
/ /
0.20
/
/
0.10 0.00i
10
102
103 2 IMPACTION PARAMETER, DaeQ , pm 2 Lmin-1
104
Figure 1. Comparison of experimental aerosol deposition measurements with calculations using the Weibel (1963) TB morphology.
Horsfield TB geometry for the human do not correlate well with experimental measurements; TB deposition is grossly underestimated. The Soong description, in particular, appears to be a suitable discription of the TB tree for aerosol studies• The AC = 1.00 curve in Figure 2, for pdZQ> 300, closely trails the median fit to the experimental data. This has special signifcance because the diameters given in Table I are mean airway values for a population• Decreasing airway diameters (the AC = 0,85 curves) in Figures 1 and 2 cause calculated deposition efficiencies to be increased. The opposite effect is noted for the AC = 1.15 curves. The systematic effect of a change in airway dimensions, that is, the translational shift of the curves on TB deposition suggests that inter-subject differences may be a significant factor influencing inhalation exposure data. The relative movements of the AC = 0.85 and AC = 1.15 curves away from the AC = 1.00 curve are consistent with the action of the inertial impaction deposition mechanism, because its efficiency will be markedly increased with an increase in airstream velocity that is produced by a reduction in airway cross-sectional area. Conversely, increasing an
420
T. MARTONEN 1.00 ~ 0.00
- --------
0.80
- -
. . . . .
-
MEAN
E N V E L O P E OF D A T A
THEORETICAL DEPOSITION CURVES
O Z 0
2
0.70
AC :
1,00
D
AC = 0.85
/ /
/
/'
0.60
~ /
/ /"
0
0.40
/
O.30
0.20
/
g~ AC = 1.15
0.50 ,,a:
/
FITTO DATA
/
!
/
/z
/
z
/
/
/
0.i0 0.00 i0
I00
i000
i0000
2 pm2 Lmin-1 IMPACI-IONPARAMETER,DaeQ Figure 2. Comparison of experimental aerosol deposition measurements with calculations using the Soong et al. (1979) TB morphology.
airway's diameter will decrease air velocity within it and, subsequently, reduce particle losses from inertial impaction. Lippmann et al. (1971) stated that the family of TB deposition curves for individual subjects, w h e n plotted on axes like Figures 1-3, were 'S-shaped' curves that appeared to be approaching asymptotes of ~ 20 and ~ 90% deposition values. Furthermore, the mid-regions of the Sshaped curves were reported as being quite linear, with the slopes of the linear portions having little variation between individual subjects. The families of theoretical curves in Figures 1 and 2 exhibit identical characteristics to the experimental curves, having sigmoidal shapes, although asymptotes appear to be at - 5 and ~-95% deposition, and are practically parallel within their mid-regions. The theoretical curves using the asymmetric Horsfield morphology (Figure 3) are not as compatible with experimental observations: they seem to be approaching a lower asymptote of -~ 0%, with only the AC = 0.85 curve appearing to have an upper asymptote, and the three curves are neither linear nor parallel in their mid-regions.
ON THE FATE OF INHALED PARTICLES IN THE HUMAN 1.00
,,I,,' I
,
O.90
'
' ' i .... I /
MEAN FIT TO DATA
0. 80
2
/
@
O AC -
0.70
J
1.00
/
/
i
r
/
.// ////
ii d
,"
0.60
/
,
/
• /
z~ AC-l.ls o AC-0.85
f I'''
/
.
THEORETICAL DEPOSITIONCURVES
'I
/
/
ENVELOPEOF DATA
Z 0 m I-,-
'
421
}
o.5Oo.4Oo.3o ,. y j /
o,o
0.I0 0.00
,
10
~
,
I
,
100
,
~
I
,
,LJl
,
,
1000
,
i
,
,,
10000
2 pm2 Lmin-1 IMPACTION PARAMETER, DaeQ,
Figure 3. Comparison of experimental aerosol deposition measurements with calculations using the Horsfield et al. (t971) TB morphology.
L i p p m a n n et al. (1971) noted that the upper limit line to their experimental data (the upper straight, dash-dot lines in Figures 1, 2 and 3) had a smaller slope than the lower limit line, and attributed that to the increasing contribution of deposition by sedimentation in peripheral TB airways at small pdEQ values. Since the change in slope was not too great, however, they proposed that the experimental data indicated that inertial impaction was the dominant deposition mechanism in the TB tree for the range of impaction parameters studied. The significant effect of the inertial impaction mechanism in the relative shifts of theoretical TB deposition values for AC =0.85, 1.00 and 1.15 curves, as previously discussed, is consistent with such an explanation of experimental data. Foord et al. (1978) have also measured the regional deposition of insoluble, 99mTc-labeled, monodisperse aerosols in man following mouth breathing. The test subjects were healthy, non-smoking males. Again, experimentally measured regional deposition was a function of pdEQ, suggesting that inertial impaction was the most significant mechanism of
422
T. MARTONEN
deposition in the TB tree. It was noted, however, that sedimentation may predominate in small conducting airways where airstream velocities are low. Indeed, Foord et al. (1978) suggested that experimental findings when pd2Q < 300 can be explained by sedimentation becoming increasingly more dominant over inertial impaction. It is important to note that (Figures 1 and 2) the theoretical aerosol deposition curves tail off very sharply precisely at pd2Q = 300. This indicates that the switch in relative effectiveness of the sedimentation and inertial impaction mechanisms is being accurately simulated in the theoretical models assuming a symmetric TB tree for the human. The tail-off is much more gradual in the model using the Horsfield geometry. Conclusions. Aerosol behavior in the human can be accurately predicted using the Martonen (1982) deposition model with a symmetric Weibel or Soong description of the TB tree. The theoretical findings are in excellent agreement with inhalation exposure data from human test subjects. Theoretical TB deposition curves predict: (1) the 'S-shaped' curves for individual human subjects measured by Lippmann et al. (1971); (2) the positions of asymptotes, and linear portions, of the Lippmann et al. (1971) data; (3) the median fit to experimental data (the straight, dashed line in Figures 1 and 2); (4) the influence of inter-subject differences on aerosol deposition measurements (the relative shifts in AC = 0.85, 1.00 and 1.15 curves in Figures 1 and 2); and (5) the tail-off in aerosol deposition within the TB tree when pd2Q < 300, experimentally measured by Foord et al. (1978). Symmetric TB models are in better agreement with experimental data than the asymmetric Horsfield model when airway dimensions as specifically reported in the open literature of the respective TB morphologies are used in aerosol deposition calculations. The data, however, do not suggest an asymmetric branching concept per se to be inappropriate for the human lung. The reason deposition calculated in the Soong model is in better agreement with laboratory findings than computations using the Weibel model is because the former has uniformly smaller airways. If the original Horsfield TB tree was adjusted to a lung volume of 2500 cm 3 and airway dimensions changed in proportion to the cube root of volume in the manner suggested by Hughes et al. (1972), new diameters would correspond to an airway coefficient of AC = 0.79. The theoretical deposition curve for such an asymmetric model would be in closer agreement with experimental results than the other theoretical curves of Figure 3. It is very important, therefore, to select carefully the TB parameters to be used in an aerosol deposition model because the deposition efficiencies of the inertial impaction, sedimentation and
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
423
diffusion mechanisms are functions of airway length, diameter and branching angle. This work was supported by Battelle, Pacific Northwest Laboratories Special Studies No. WBS 16-02. The author wishes to thank D. Gibby for valuable assistance in computer programming. LITERATURE Chan, T. L., R. M. Schreck and M. Lippmann. 1980. "Effect of the Laryngeal Jet on Particle Deposition in the Human Trachea and Upper Bronchial Airways." J. Aerosol Sci. 11,447--459. Dekker, E. 1961: "Transition Between Laminar and Turbulent Flow in Human Trachea." J. appl. Physiol. 16, 1060-1064. Ferron, G. A. 1977. "Deposition of Polydisperse Aerosols in Two Glass Models Representing the Up.per Human Airways." J. Aerosol Sci. 8, 409-427. Findeisen, W. 1935. "Uber das Absetzen kleiner, in der Luft suspendieter Teilchen in der menschlichen Lunge bei der Atmung." Pfliigers Arch. ges. Physiol. 236, 367-379. Foord, N., A. Black and M. Walsh. 1978. "Regional Deposition of 2.5-7.5 tzm Diameter Inhaled Particles in Healthy Male Non-smokers." J. Aerosol Sci. 9, 343-357. Gerrity, T. R., P. S. Lee, F. J. Hass, A. Marinelli, P. Werner and R. V. Lourenco. 1979. "Calculated Deposition of Inhaled Particles in the Airway Generations of Normal Subjects." J. appl. Physiol. 47, 867-874. Heyder, J. and G. Rudolf. 1977. "Deposition of Aerosol Particles in the Human Nose." In Inhaled Particles IV, Ed. W. H. Walton, pp. 107-126. Oxford: Pergamon Press. Horsfield, K. and G. Cumming. 1967. "Angles of Branching and Diameters of Branches in the Human Bronchial Tree." Bull. math. Biophys. 29, 245-259. - - , G. Dart, D. E. Olson, G. F. Filley and G. Cumming. 1971. "Models of the Human Bronchial Tree." J. appl. Physiol. 31,207-217. Hughes, J. M., F. G. Hoppin, Jr. and J. Mead. 1972. "Effect of Lung Inflation on Bronchial Length and Diameter in Excised Lungs." J. appl. Physiol. 32, 25-35. Landahl, H. D. 1950. "On the Removal of Airborne Droplets by the Human Respiratory Tract: I. The Lung." Bull. math. Biophys. 12, 43-56. Lippmann, M. and R. E. Albert. 1969. "The Effect of Particle Size on the Regional Distribution of Inhaled Aerosols in the Human Respiratory Tract." Am. Ind. Hyg. Ass. J. 30, 257-275. Lippmann, M., R. E. Albert and H. T. Peterson. 1971. "The Regional Deposition of Inhaled Aerosols in Man." In Inhaled Particles IlI, Ed. W. H. Walton, pp. 105-122. The Gresham Press, England: Unwin Bros. Martonen, T. B. 1982. "Analytical Model of Hygroscopic Particle Behavior in Human Airways." Bull. math. Biol. 44, 425-442. - and D. Gibby. 1982. "Computer Models of Aerosol Deposition in Two Human Tracheobronchial Geometries." Comput. Biomed. Res. 15, 425-433. - and J. Lowe. In press. "Assessment of Aerosol Deposition Patterns in Human Respiratory Tract Cases." In Proceedings of the International Symposium on Aerosols in the Mining and Industrial Work Environment. Ann Arbor: Ann Arbor Science Publishers. , - and M. Patel. 1981. "Modeling the Dose Distribution of H2SO4 Aerosols in the Human Tracheobronchial Tree." Am. Ind. Hyg. Ass. Jr. 42, 435-460. Pattle, R. E. 1961. "The Retention of Gases and Particles in the Human Nose." In Inhaled Particles and Vapours, Ed. C. N. Davies, pp. 302-309. Oxford: Pergamon Press. Raabe, O. G., H. C. Yeh, G. M. Schum and R. F. Phalen. 1976. "Tracheobronchial
424
T. MARTONEN
Geometry: Human, Dog, Rat, Hamster." LF-53, Lovelace Foundation for Medical Education and Research. NTIS, Springfield, VA. Scherer, P. W., F. R. Haselton, L. M. Hanna and D. R. Stone. 1979. "Growth of Hygroscopic Aerosols in a Model of Bronchial Airways." 2. appl. Physiol. 47, 544-550. Schlesinger, R. B. and M. Lippmann. 1976. "Particle Deposition in the Trachea: in Vivo and in Hollow Casts." Thorax 31,678-684. Schlesinger, R. B., D. E. Bohning, T. L. Chan and M. Lippmann. 1977. "Particle Deposition in a Hollow Cast of the Human Tracheobronchial Tree." J. Aerosol Sci. 8, 429--445. Schroter, R. L. and M. F. Sudlow. 1969. "Flow Patterns in Models of the Human Bronchial Airways." Respir. Physiol. 7, 341-355. Soong, T. T., P. Nicholaides, C. P. Yu and S. C. Soong. 1979. "A Statistical Description of the Human Tracheobronchial Tree Geometry." Respir. Physiol. 37, 161-172. Task Group on Lung Dynamics. 1966. "Deposition and Retention Models for Internal Dosimetry of the Human Respiratory Tract." Health Phys. 12, 173-208. Weibel, E. 1963. Morphometry of the Human Lung. Berlin: Springer-Verlag. West, J. B. and P. Hugh-Jones. 1959. "Patterns of Gas Flow in the Upper Bronchial Tree." J. appl. Physiol. 14, 753-759. Widdecombe, J. G. 1954. "Receptors in the Trachea and Bronchi of the Cat." J. Physiol. 123, 71-104. RECEIVED 12-1-81 REVISED 6-23-82
Printed in Great Britain.
0tD2-8240/83/03040%16503.00/0 Pergamon Press Ltd. 1~) 1983 Society for Mathematical Biology
ON THE FATE OF INHALED PARTICLES IN THE HUMAN: A COMPARISON OF EXPERIMENTAL DATA WITH THEORETICAL COMPUTATIONS BASED ON A SYMMETRIC AND ASYMMETRIC LUNG • T. MARTONEN'~ Inhalation Technology and Toxicology Section, Battelle, Pacific Northwest Laboratories, Richland, WA 99352, U.S.A. An analytical model is used .to describe the behavior of inhaled particulate matter in the human respiratory tract. Three different geometries, symmetric and asymmetric, are utilized to simulate the tracheobronchial (TB) tree. The suitability of each geometry for representing the human is evaluated by comparing calculated aerosol deposition probabilities with experimental data from inhalation exposure tests. A symmetric, dichotomously branching pattern is found to be a reliable description of the TB tree for studies of factors affecting aerosol deposition in the human lung. Calculations with the theoretical model are in excellent agreement with measured aerosol deposition efficiencies. Furthermore, the model accurately predicts experimentally observed features of inhalation exposure data, such as effects of inter-subject lung morphology differences and relative efficiencies of specific deposition mechanisms, on aerosol deposition patterns in the TB tree. Introduction. K n o w l e d g e of the sites of deposition of inhaled particulate matter within the tracheobronchial (TB) tree is of importance in assessing the health effects of atmospheric pollutants and in aerosol therapy p r o c e d u r e s w h e r e medicinal agents are administered to patients. Early experimental inhalation exposure studies established that particle deposition probabilities within the h u m a n respiratory system can be expressed as a function of the mass median a e r o d y n a m i c diameter (MMAD) and geometric standard deviation (~rg) of an inspired aerosol (Task Group on Lung Dynamics, 1966; L i p p m a n and Albert, 1969). A detailed experimental investigation of the regional dispersion of inhaled particles in the h u m a n c o n d u c t e d by L i p p m a n n et al. (1971) has shown that deposition in ciliated airways of the TB tree is related to an 'impaction parameter' defined in terms of particle parameters (size and density) and a breathing p a r a m e t e r (inspiratory flow rate). A theoretical model of aerosol behavior in the h u m a n respiratory tract that permits factors which influence deposition to be studied is presented here. The model requires definition of a system of deposition probability formulae and a description of h u m a n TB morphology. The system of equations describing the deposition efficiencies of the inertial impaction, t P r e s e n t a d d r e s s : N o r t h r o p S e r v i c e s , Inc., E n v i r o n m e n t a l S c i e n c e s , P.O. B o x 12313, R e s e a r c h Triangle P a r k , N C 27709, U.S.A.
409
410
T. MARTONEN
sedimentation and diffusion mechanisms proposed by Martonen (1982) is used. There are several morphologies available for use in such a theoretical aerosol deposition model. Different TB morphologies have been proposed by Weibel (1963), Horsfield et al. (1971) and Soong et al. (1979). The latter two will hereafter be referred to as the 'Horsfield' and 'Soong' geometries respectively. The Weibel and Horsfield descriptions are based on extensive anatomical measurements of the human lung. The Soong geometry is a Weibel-type TB morphology, with dimensions modified from the original to account for variation in lung dimensions among a population. The three TB descriptions were incorporated into the theoretical aerosol deposition model, and calculated particle losses within the different TB trees compared with the experimental data of Lippmann et al. (1971). Findings indicated that the symmetric, dichotomously branching pattern proposed by Weibel (1963), with airway dimensions modified by the statistical work of Soong, is a suitable description of the human lung for the study of aerosol behavior. H u m a n Tracheobronchial Morphology. The Weibel Model A morphology is the simplest TB description proposed for the human lung. It is a symmetric, dichotomously branching network of cylindrical tubes. There are 17 generations of conducting airways (tubes) numbered from 0 through 16, with generation I = 0 being the trachea and generation I = 16 the last unalveolated bronchiole. Each generation I consists of 21 identical airways. A description of the morphology is given in Table I. The dimensions given, which were measured from a cast of large-bore airways and histological sections of small-bore bronchioles, correspond to a lung volume of 3/4 total lung capacity (TLC), or 4800cm 3. The Weibel conception of the TB network, because of its simplicity and the fact that it is based on anatomical measurements, has been widely used in experimental (Ferron, 1977; Scherer et al., 1979) and theoretical (Gerrity et al., 1979; Martonen and Patel, 1981) studies of aerosol deposition in the human lung. The Soong branching scheme is identical to that of Weibel; airway dimensions, however, are different. Since Raabe et ai. (1976) discussed the significance of inter-subject differences in the structure and dimensions of the human TB tree, the Soong morphology, a statistical description, was intended to account for such variabilities. From morphometric measurements of airway lengths and diameters as functions of TB generation reported in the open literature, statistical parameters of each such distribution were determined. Mean airway dimensions /~ and coefficients of variation cr[~ of distributions of standard deviations cr are
411
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
TABLE I Description of the Weibel (1963) and Modified-Weibel (Soong et al., 1979) Symmetric Tracheobronchial Trees Airway Generation
Weibel Length Diameter (cm)
Modified-Weibel Length ~/~ Diameter o/~
(cm)
(cm)
0
12.000
1.800
10.494
0,I0
1.574
(cm) 0.I0
1
4.760
1.220
4.163
0.15
1.067
0.125
2
1.900
0,830
1.662
0.25
0.726
0.15
3
0.760
0.560
0.665
0.30
0.490
0.175
4
1.270
0.450
I.III
0.35
0.394
0.20
5
1.070
0,350
0.936
0.425
0.306
0.23
6
0,900
0.280
0.787
0.50
0,245
0.275
7 8
0.760
0.230
0.665
0.325
0.186
0.575 0.560 0.65
0.201
0.640
0.163
0.35
9
0,540
0.154
0.472 0.70
0.135
0.42
10
0,460
0,130
0,402 0.75
O.ll4
0.50
II
0,390
0.I09
0,341 0.80
0,095
0.575
12
0.330
0.095
0.289 0.81
0,083
0.66
13
0.270
0,082
0.236 0.775
0.072
0.675
14
0,230
0.074
0.201 0.725
0.065
0.60
15
0.200
0.066
0.175
0.058
0.50
~6
0.165
0.060
0,144 0.50
0.052
0.40
0.65
Mean airway dimension is denoted by p~, and tr is the standard deviation of the distribution of dimensions for each generation.
1
given in Table I. The dimensions correspond to a lung volume of ~ TLC, or 3200 cm 3, believed to be a more physiologically realistic condition for the human lung than the 3/4 TLC volume used by Weibel. The Horsfield description of the TB tree is very complicated. In it, airways are classified by 'order'. Airway lengths and diameters are given in Table II for a lung volume of 5000 cm 3. The measurements were obtained from a resin cast of a normal lung. The order 31 airway is the trachea, and order 6 airways are the smallest TB bronchioles. Airways of a given order do not necessarily have the same dimensions; there are, for example, three different order 27 airways. Branching within the Horsfield morphology is dichotomous, but four separate mathematical patterns are used to describe four different regions within the TB tree. Bifurcations from order 11 to 31 airways occur by a J - 1 and J - 4 pattern; that is, order 20 airways branch into order 19 and 16 airways. Branching from order 9 to 10 airways is defined by a J - 1 and J - 3 scheme, and from order 8 airways by a J - 1, J - 2 pattern. Order J = 7 airways branch only to order 6, J - 1 airways.
412
T. MARTONEN TABLE II Physical Parameters and Flow Distribution Characteristics of Horsfield et al. (1971) Airway Orders Order
Length
Diameter
(cm)
(cm)
Flow D i s t r i b u t i o n Coefficient
E
Fraction of Flow Entering Trachea
f
31
IO.O00
1.600
233,920
l.O00000
30
2.200
l.llO
128,576
.549658
29a
5.000
1.2OO
105,344
.450342
29b
2.600
0.890
84,320
.360465
28a
l.lOO
0.800
61,088
.261149
28b
0.800
0.640
61,088
.261149
27a
1.6OO
0.750
44,256
.189193
27b
1.560
0.730
44,256
.189193
27c
0.970
0.700
44,256
.189193
26
1.127
0.667
32,064
.137073
25a
2.1DO
0.520
23,232
.099316
25b
1.125
0.585
23,232
.099316
24
0.970
0.535
16~832
.071956
23
l.O81
0.427
12,192
.052120
22
0.953
0.349
8,832
.037756
21
0.857
0.347
6,400
.027360
20
0.988
0.309
4,640
.019836
19
0.796
0.288
3,360
.014364
18
0.918
0.277
2,432
17
0.818
0.267
1,760
7.5239 x lO-3
16
0.808
0.251
$,280
5.4720 x IO-3
15
0.774
0.235
928
3.9672 x lO-3
14
0.640
0.218
672
2.8728 x IO-3
13
0.627
0.200
480
2.0520 x IO-3
12
0.517
0.177
352
1.5048 x lO-3
II
0.477
0.156
256
1.0944 x IO-3
IO
0.422
0.135
192
8.2079 x lO -4
9
0.356
O.ll3
128
5.4720 x lO-4
8
0.312
0.095
96
4.1040 x IO-4
7
0.254
0.076
64
2.7360 x lO-4
6
O.llO
0.063
23
1.3680 x lO-4
.010397
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
413
A major significance of the Horsfield concept of the human lung is that it is structurally asymmetric because different airway orders comprise any given TB generation beyond the trachea. It was proposed, therefore, as a more realistic description of conducting airways than a symmetric network in which airways of a generation are identical. To effect a comparison of aerosol deposition efficiency calculations in the Weibel, Soong and Horsfield morphologies we will define the Horsfield TB tree as consisting of 26 generations, since there are 26 distinct airway orders in that description. The four different branching patterns previously discussed will be used to define the order composition of each TB generation. The trachea will be generation I = 0 and downstream generations numbered in a descending order. This morphological system was used in a previous, more focused work (Martonen and Gibby, 1982) and for completeness of this text is given in Table III. The number of airways per generation follows the 2 ~ formula proposed by Weibel only for generations 0-8. For generations 9-13, the number of conducting airways does not increase as rapidly, and beyond I = 14 the number of airways decreases.
Modeling of Aerosol Behavior. In this work, deposition of airborne particulate matter in conducting airways of the TB network is studied. Conducting airways are non-alveolated passages that do not participate in gas exchange. It is important to quantitate deposition in this compartment of the human respiratory tract in order to assess potential health hazards following inhalation of airborne contaminants. This applies to the general populace where the health effects of atmospheric pollutants are of concern and to personnel in the work environment exposed to occupational aerosols. Furthermore, in aerosol therapy, knowledge of factors affecting particle deposition would aid in successful treatment of patients with pulmonary diseases because particle sizes and breathing rates could be regulated so as to deposit medicinal agents more effectively at appropriate TB locations. For example, in the treatment of obstructive respiratory ailments like asthma, it is important to know the sites of action of bronchodilator agents. Before inhaled particulate matter can be deposited in the TB tree it must successfully penetrate proximal compartments of the human respiratory tract; namely, the oral and nasopharyngeal regions. Aerosol losses from mouth and nose breathing have been experimentally measured by Lippmann et al. (1971), Pattle (1961) and Heyder and Rudolf (1977) respectively. These upper compartments can be quite efficient filters of airborne particles, depending on specific particle sizes and inspiratory flow rates. In this work theoretical TB losses will be normalized to the inhaled aerosol mass that actually enters the trachea to be
414
T. MARTONEN
consistent with the manner in which the original laboratory TB data used for comparison (Lippmann et ai., 1971) were presented in the open literature. The most effective particle deposition mechanisms in the human TB tree are inertial impaction, sedimentation and diffusion (Findeisen, 1935). A system of formulae that describes particle deposition probabilities from
TABLE III Airway Order Composition of the Horsfield et aL (1971) Tracheobronchial Tree Airway Order
Generation 0
1 2
3 4
5 6
7
8
9
I0
II
12
13
14
15
16
17
18
19
20
21
22
2J
6
0
0
0
0
0
0
0
6
68
177
490
770
948
1230
I012
938
702
401
318
134
60
43
8
3
2
7
O 0 0 0
0
0
0
2
175 238 294 450
330
352 260
133
135
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ON THE FATE OF INHALED PARTICLES IN THE HUMAN
415
those mechanisms in a general branching network has been presented by Martonen (1982). The formulae may be used to compute aerosol losses in any particular TB morphology by using appropriate airway dimensions. Both stable and unstable air flow conditions were treated in the derivation of the formulae to simulate physiological conditions in the human. In fluid dynamics studies using replica casts of the upper TB tree, Dekker (1961) has demonstrated that a transition from laminar to turbulent flow at inspiratory flow rates as low as 6 1/min can be attributed to cartilaginous rings present in large-bore airways. Utilizing similar casts, West and Hugh-Jones (1959) have shown that the bifurcating pattern itself may induce flow irregularities in smooth-walled bronchioles. Other experimental work with airway models (Schroter and Sudlow, 1969) has substantiated the effect of branching. The effect of the larynx must also be included in a model of aerosol behavior. Schlesinger and Lippmann (1976) noted that turbulence induced at the restricted glottis opening at the entrance to the trachea may persist, and affect particle trajectories, in downstream generations. Furthermore, C h a n e t al. (1980) demonstrated that particles entrained in the laryngeal jet impact at a site immediately distal to the larynx, producing a 'hot spot' of deposition in the trachea. The empirical relation describing this enhanced deposition is:
p(t) = 2.536 Stk 1231.
(1)
The particle Stokes number, Stk, is defined by the equation S t k - pd2U 18nr '
(2)
where r = trachea radius, ~ = absolute air viscosity, U = airstream velocity, p = particle density and d = particle diameter. This work focuses upon deposition incurred during inspiration. It has been demonstrated (Lippmann and Albert, 1969) that for particles > 2.5/zm in size that are of primary therapeutic and risk assessment concern, nearly 100% of the inhaled aerosol mass entering the trachea may be deposited in the lung during the inspiratory phase of the respiratory cycle, Moreover, Widdecombe (1954) has established that airway carinae are ,locations within the TB tree where nerve endings and reflex receptors are concentrated. Experiments using human larynx-TB casts have demonstrated that bifurcation carinae can be sites of greatly enhanced particle deposition (Schlesinger et al., 1977; Martonen and Lowe, in press). Knowledge of such preferential losses, or 'hot spots',
416
T. MARTONEN
has obvious important implications in aerosol therapy and inhalation toxicology because of the high doses delivered to selected airway cells. Deposition is enhanced at such sites during inspiration, when the carina within a bifurcation functions as an airstream divider and particles of sufficient inertia traveling near the center line of the parent airway have trajectories that deviate from fluid streamlines and are deposited by impaction at the downstream carina. During expiration, however, a carina does not serve as a flow divider and particles may sweep past it, unless they have a fiber-like shape (for example, asbestos) and are collected by the interception deposition mechanism. Particle losses in an airway will be computed in the following manner (Martonen and Gibby, 1982). Fluid dynamics within the TB tree will be as described by Martonen (1982), and deposition probabilities of the inertial impaction, sedimentation and diffusion mechanisms written as p(i), p(s) and p(d) respectively. The branching angle between the two airways at a bifurcation within a generation is assumed to be 70 ° after the experimental measurements of Horsfield and Cumming (1967). In the trachea, enhanced losses by inertial impaction due to the laryngeal jet will be accounted for by including equation (1) in p (i). The total probability of deposition in an airway due to the action of all mechanisms p(T) will be determined from Landahl's (1950) equation:
p(T) = 1 - [1 - p(i)][1 - p(s)][1 - p(d)].
(3)
Aerosol dispersion within the Weibel and Soong TB geometries is facilitated by their simplicity. Since all airways within a given generation are identical, each individual airway receives 2-I of the total aerosol mass entering the generation. Hence deposition in a generation is that computed for one airway multiplied by 21. If the total aerosol mass entering generation I from the upstream generation ! - 1 is re(I), and the total deposition probability [equation (3)] in an airway of generation I is p(I), the aerosol mass that penetrates to the downstream generation I + 1 is:
m(I+l)=m(I)[1-p(I)].
(4)
Therefore, the aerosol mass entering the trachea, I = 0, that reaches generation I' where I' --_ 1 may be expressed as Irrl
M(I') = rn(O)- ~, m(I)p(I),
(5)
I=0
where m(0) is the original mass entering the trachea. The total dose
ON THE FATE OF I N H A L E D PARTICLES IN THE H U M A N
417
deposited in a symmetric TB tree, therefore, is simply 16
~, M(l)p(I).
(6)
I=0
Because of asymmetry, aerosol dispersion within the Horsfield geometry is more difficult to formulate than for the other TB patterns. The data under the E and f headings of Table II describe air distribution among different airway orders: [ is the fraction of inspired air entering a specific airway order and E defines the relative division of air at a bifurcation. The following equation is presented here for use in calculating~3the aerosol mass that enters order J airways of generation ! from order P 'parent' airways of the preceding ! - 1 generation: m ( L J, P ) = m ( I - 1 ) [ f ( P ) N ( I -
_r E(J)+E(S)] "
1, P)][1 - p ( I - 1, P ) ] I E ( J )
(7) For example, in generation I = 13, each of the 11 order-14 airways has an order-15 or an order-18 parent from the upstream I = 12 generation (Table III). Equation (7) has four major components. The aerosol mass that entered generation I - 1 [see equation (4)] is re(I-1). The number of order P parents in generation I - 1 is N ( I - 1 , P) and f(P) is the fraction of inspired aerosol reaching a parent P airway (Table II); their product is the fraction of aerosol mass of generation I - 1 in order P parent airways. The fraction of aerosol mass entering a parent P airway of generation I - 1 that penetrates it is [1 - p(I - 1, P)], where p(I - 1, P) is the deposition probability, as defined by equation (3), of the parent airway whose 'order' is defined in Table III. The division of aerosol at the bifurcation of two 'daughter' airways is defined by the last term of equation (7). E(J) and E(S) are the E values (Table II) for an airway order J and its 'sister', S. The aerosol mass deposited in all order J airways of generation ! from parents of either order can be written as D ( L J) = ~, m ( L J, P ) p ( J ) ,
(8)
P
where p(J) [equation (3)] is the deposition probability in an order J airway, and the summation is performed over the respective order P parents. For example, the aerosol mass deposited in order J = 20 airways of generation 8 is: [m(8, 20, 21)+ m(8, 20, 24)]p(20). The total aerosol
418
T. MARTONEN
mass deposited in generation I, D(I), is therefore the summation of D(I, J) over all order airways present:
D(I) = ~, D(I, J),
(9)
2
where the airway order composition for each TB generation is known (Table III). The fraction of the inspired aerosol mass deposited in the Horsfield TB tree can be computed in a manner similar to that for the symmetric Weibel and Soong geometries [equations (5) and (6)].
Results.
Theoretical aerosol deposition efficiencies in the human TB tree, as computed by three models using Martonen's (1982) deposition probability equations with Weibel, Soong and Horsfield TB geometries, were compared with experimental data from the extensive inhalation exposure tests of Lippmann et al. (1971). In the latter work, direct measurements of regional aerosol deposition in human subjects were made using 99mTc-labeled, insoluble monodisperse aerosols. TB deposition was measured with the aid of scintillation detectors. The experimental findings of these mouth-breathing tests, using both nonsmokers and ex-smokers, are presented in Figures 1, 2 and 3. TB losses are graphed as a function of an 'impaction parameter' defined as pdZQ, where Q (l/min) is the inspiratory flow rate and p (g/cm 3) and d (/zm) are the particle density and diameter respectively. The straight dashed line is the 'median' fit of Lippman et al. (1971) to their experimental data. The straight, dash-dot lines are the 'limit' lines to their data; all data lie within these 'limit' lines. Theoretical aerosol deposition calculations assumed an inspiratory flow rate of 301/min, and particle aerodynamic diameters Dae, where Dae = X/(p)d, ranged from 1 to 12/xm. Three different airway coefficients (AC), were used for each TB morphology to examine the effect of airway caliber upon deposition. The AC --- 1.00 curves plotted in Figures 1, 2 and 3 correspond to the airway dimensions given in Tables I and II respectively. The A C = 0 . 8 5 curves correspond to airway diameters that have been multiplied by 0.85 (decreased in bore by 15%). Similarly, the AC = 1.15 curves correspond to TB trees where airway diameters have been increased by 15%. Comparison of the three AC curves for TB geometry permit the effect of inter-subject differences on aerosol deposition to be assessed. It is apparent from Figures 1 and 2 that theoretical calculations of aerosol deposition using the symmetric Weibel TB morphologies are in very good agreement with the experimental data. It is clearly evident (Figure 3) that theoretical calculations assuming the asymmetric
ON THE FATE OF INHALED PARTICLES IN THE HUMAN 1.00
'
0.90
. . . . . . . . . .
0.80
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I
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I
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....
419
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103 2 IMPACTION PARAMETER, DaeQ , pm 2 Lmin-1
104
Figure 1. Comparison of experimental aerosol deposition measurements with calculations using the Weibel (1963) TB morphology.
Horsfield TB geometry for the human do not correlate well with experimental measurements; TB deposition is grossly underestimated. The Soong description, in particular, appears to be a suitable discription of the TB tree for aerosol studies• The AC = 1.00 curve in Figure 2, for pdZQ> 300, closely trails the median fit to the experimental data. This has special signifcance because the diameters given in Table I are mean airway values for a population• Decreasing airway diameters (the AC = 0,85 curves) in Figures 1 and 2 cause calculated deposition efficiencies to be increased. The opposite effect is noted for the AC = 1.15 curves. The systematic effect of a change in airway dimensions, that is, the translational shift of the curves on TB deposition suggests that inter-subject differences may be a significant factor influencing inhalation exposure data. The relative movements of the AC = 0.85 and AC = 1.15 curves away from the AC = 1.00 curve are consistent with the action of the inertial impaction deposition mechanism, because its efficiency will be markedly increased with an increase in airstream velocity that is produced by a reduction in airway cross-sectional area. Conversely, increasing an
420
T. MARTONEN 1.00 ~ 0.00
- --------
0.80
- -
. . . . .
-
MEAN
E N V E L O P E OF D A T A
THEORETICAL DEPOSITION CURVES
O Z 0
2
0.70
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/ /
/
/'
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0.50 ,,a:
/
FITTO DATA
/
!
/
/z
/
z
/
/
/
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I00
i000
i0000
2 pm2 Lmin-1 IMPACI-IONPARAMETER,DaeQ Figure 2. Comparison of experimental aerosol deposition measurements with calculations using the Soong et al. (1979) TB morphology.
airway's diameter will decrease air velocity within it and, subsequently, reduce particle losses from inertial impaction. Lippmann et al. (1971) stated that the family of TB deposition curves for individual subjects, w h e n plotted on axes like Figures 1-3, were 'S-shaped' curves that appeared to be approaching asymptotes of ~ 20 and ~ 90% deposition values. Furthermore, the mid-regions of the Sshaped curves were reported as being quite linear, with the slopes of the linear portions having little variation between individual subjects. The families of theoretical curves in Figures 1 and 2 exhibit identical characteristics to the experimental curves, having sigmoidal shapes, although asymptotes appear to be at - 5 and ~-95% deposition, and are practically parallel within their mid-regions. The theoretical curves using the asymmetric Horsfield morphology (Figure 3) are not as compatible with experimental observations: they seem to be approaching a lower asymptote of -~ 0%, with only the AC = 0.85 curve appearing to have an upper asymptote, and the three curves are neither linear nor parallel in their mid-regions.
ON THE FATE OF INHALED PARTICLES IN THE HUMAN 1.00
,,I,,' I
,
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'
' ' i .... I /
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0. 80
2
/
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0.70
J
1.00
/
/
i
r
/
.// ////
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,"
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.
THEORETICAL DEPOSITIONCURVES
'I
/
/
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Z 0 m I-,-
'
421
}
o.5Oo.4Oo.3o ,. y j /
o,o
0.I0 0.00
,
10
~
,
I
,
100
,
~
I
,
,LJl
,
,
1000
,
i
,
,,
10000
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Figure 3. Comparison of experimental aerosol deposition measurements with calculations using the Horsfield et al. (t971) TB morphology.
L i p p m a n n et al. (1971) noted that the upper limit line to their experimental data (the upper straight, dash-dot lines in Figures 1, 2 and 3) had a smaller slope than the lower limit line, and attributed that to the increasing contribution of deposition by sedimentation in peripheral TB airways at small pdEQ values. Since the change in slope was not too great, however, they proposed that the experimental data indicated that inertial impaction was the dominant deposition mechanism in the TB tree for the range of impaction parameters studied. The significant effect of the inertial impaction mechanism in the relative shifts of theoretical TB deposition values for AC =0.85, 1.00 and 1.15 curves, as previously discussed, is consistent with such an explanation of experimental data. Foord et al. (1978) have also measured the regional deposition of insoluble, 99mTc-labeled, monodisperse aerosols in man following mouth breathing. The test subjects were healthy, non-smoking males. Again, experimentally measured regional deposition was a function of pdEQ, suggesting that inertial impaction was the most significant mechanism of
422
T. MARTONEN
deposition in the TB tree. It was noted, however, that sedimentation may predominate in small conducting airways where airstream velocities are low. Indeed, Foord et al. (1978) suggested that experimental findings when pd2Q < 300 can be explained by sedimentation becoming increasingly more dominant over inertial impaction. It is important to note that (Figures 1 and 2) the theoretical aerosol deposition curves tail off very sharply precisely at pd2Q = 300. This indicates that the switch in relative effectiveness of the sedimentation and inertial impaction mechanisms is being accurately simulated in the theoretical models assuming a symmetric TB tree for the human. The tail-off is much more gradual in the model using the Horsfield geometry. Conclusions. Aerosol behavior in the human can be accurately predicted using the Martonen (1982) deposition model with a symmetric Weibel or Soong description of the TB tree. The theoretical findings are in excellent agreement with inhalation exposure data from human test subjects. Theoretical TB deposition curves predict: (1) the 'S-shaped' curves for individual human subjects measured by Lippmann et al. (1971); (2) the positions of asymptotes, and linear portions, of the Lippmann et al. (1971) data; (3) the median fit to experimental data (the straight, dashed line in Figures 1 and 2); (4) the influence of inter-subject differences on aerosol deposition measurements (the relative shifts in AC = 0.85, 1.00 and 1.15 curves in Figures 1 and 2); and (5) the tail-off in aerosol deposition within the TB tree when pd2Q < 300, experimentally measured by Foord et al. (1978). Symmetric TB models are in better agreement with experimental data than the asymmetric Horsfield model when airway dimensions as specifically reported in the open literature of the respective TB morphologies are used in aerosol deposition calculations. The data, however, do not suggest an asymmetric branching concept per se to be inappropriate for the human lung. The reason deposition calculated in the Soong model is in better agreement with laboratory findings than computations using the Weibel model is because the former has uniformly smaller airways. If the original Horsfield TB tree was adjusted to a lung volume of 2500 cm 3 and airway dimensions changed in proportion to the cube root of volume in the manner suggested by Hughes et al. (1972), new diameters would correspond to an airway coefficient of AC = 0.79. The theoretical deposition curve for such an asymmetric model would be in closer agreement with experimental results than the other theoretical curves of Figure 3. It is very important, therefore, to select carefully the TB parameters to be used in an aerosol deposition model because the deposition efficiencies of the inertial impaction, sedimentation and
ON THE FATE OF INHALED PARTICLES IN THE HUMAN
423
diffusion mechanisms are functions of airway length, diameter and branching angle. This work was supported by Battelle, Pacific Northwest Laboratories Special Studies No. WBS 16-02. The author wishes to thank D. Gibby for valuable assistance in computer programming. LITERATURE Chan, T. L., R. M. Schreck and M. Lippmann. 1980. "Effect of the Laryngeal Jet on Particle Deposition in the Human Trachea and Upper Bronchial Airways." J. Aerosol Sci. 11,447--459. Dekker, E. 1961: "Transition Between Laminar and Turbulent Flow in Human Trachea." J. appl. Physiol. 16, 1060-1064. Ferron, G. A. 1977. "Deposition of Polydisperse Aerosols in Two Glass Models Representing the Up.per Human Airways." J. Aerosol Sci. 8, 409-427. Findeisen, W. 1935. "Uber das Absetzen kleiner, in der Luft suspendieter Teilchen in der menschlichen Lunge bei der Atmung." Pfliigers Arch. ges. Physiol. 236, 367-379. Foord, N., A. Black and M. Walsh. 1978. "Regional Deposition of 2.5-7.5 tzm Diameter Inhaled Particles in Healthy Male Non-smokers." J. Aerosol Sci. 9, 343-357. Gerrity, T. R., P. S. Lee, F. J. Hass, A. Marinelli, P. Werner and R. V. Lourenco. 1979. "Calculated Deposition of Inhaled Particles in the Airway Generations of Normal Subjects." J. appl. Physiol. 47, 867-874. Heyder, J. and G. Rudolf. 1977. "Deposition of Aerosol Particles in the Human Nose." In Inhaled Particles IV, Ed. W. H. Walton, pp. 107-126. Oxford: Pergamon Press. Horsfield, K. and G. Cumming. 1967. "Angles of Branching and Diameters of Branches in the Human Bronchial Tree." Bull. math. Biophys. 29, 245-259. - - , G. Dart, D. E. Olson, G. F. Filley and G. Cumming. 1971. "Models of the Human Bronchial Tree." J. appl. Physiol. 31,207-217. Hughes, J. M., F. G. Hoppin, Jr. and J. Mead. 1972. "Effect of Lung Inflation on Bronchial Length and Diameter in Excised Lungs." J. appl. Physiol. 32, 25-35. Landahl, H. D. 1950. "On the Removal of Airborne Droplets by the Human Respiratory Tract: I. The Lung." Bull. math. Biophys. 12, 43-56. Lippmann, M. and R. E. Albert. 1969. "The Effect of Particle Size on the Regional Distribution of Inhaled Aerosols in the Human Respiratory Tract." Am. Ind. Hyg. Ass. J. 30, 257-275. Lippmann, M., R. E. Albert and H. T. Peterson. 1971. "The Regional Deposition of Inhaled Aerosols in Man." In Inhaled Particles IlI, Ed. W. H. Walton, pp. 105-122. The Gresham Press, England: Unwin Bros. Martonen, T. B. 1982. "Analytical Model of Hygroscopic Particle Behavior in Human Airways." Bull. math. Biol. 44, 425-442. - and D. Gibby. 1982. "Computer Models of Aerosol Deposition in Two Human Tracheobronchial Geometries." Comput. Biomed. Res. 15, 425-433. - and J. Lowe. In press. "Assessment of Aerosol Deposition Patterns in Human Respiratory Tract Cases." In Proceedings of the International Symposium on Aerosols in the Mining and Industrial Work Environment. Ann Arbor: Ann Arbor Science Publishers. , - and M. Patel. 1981. "Modeling the Dose Distribution of H2SO4 Aerosols in the Human Tracheobronchial Tree." Am. Ind. Hyg. Ass. Jr. 42, 435-460. Pattle, R. E. 1961. "The Retention of Gases and Particles in the Human Nose." In Inhaled Particles and Vapours, Ed. C. N. Davies, pp. 302-309. Oxford: Pergamon Press. Raabe, O. G., H. C. Yeh, G. M. Schum and R. F. Phalen. 1976. "Tracheobronchial
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