Factors affecting distribution of airflow in a human tracheobronchial cast
Beverly S. Cohen, Robert G. Sussman 1 and Morton Lippmann Institute of Environmental Medicine, New York University Medical Center, New York, New York, USA
(Accepted 22 March 1993)
Abstract. Air velocity was measured at end airways of hollow replicate casts of the human tracheobronchial tree in order to determine the flow distribution within casts extending to 3 mm diameter airways. Measure- ments were made by hot-wire anemometry for constant inspiratory flow rates of 7.5, 15, 30 and 60 L.min -~. Average flow distribution among the lung lobes was as follows: right upper, 18.5 ~o; right middle, 9.2 ~o; right lower, 32.3%; left upper, 15.7%; and left lower, 24.3%. An empirical model derived from the experimen- tal flow distribution data demonstrated the effect of various morphometric parameters of the hollow cast on the distribution of airflow. Airway cross-sectional area, branching angle and total pathlength were found to have the greatest influence. As the tracheal flow rate decreased from 60 to 7.5 L'min -~, the influence of branching angle was reduced, while total pathlength became more influential. These results provide evidence
for the transition of flow regimes within the TB tree within normal physiological flow ranges.
Airflow, human airways, cast; Airways, cast; Distribution, airflow airways
Hollow casts of human tracheobronchial (TB) trees have frequently been used in studies of the intrabronchial deposition of particles (Lippmann, 1977; Schlesinger and Lippmann, 1976; Schlesinger et al., 1977; Martonen, 1983; Gurman et al., 1984; Cohen et al., 1990). Specific TB deposition cannot be adequately assessed unless flow through individual bronchi are known. Most theoretical models or experiments utilizing hollow TB casts assume that flow is proportional to the fraction of the total lung volume subtended by that airway (Horsfield etal . , 1971). However, flow distribution in a truncated cast may be different, and this 6tudy examined the influence of the morpho- metric variables of a truncated cast on the distribution of flow through that cast. Measuring flow distribution through the cast provided direct information on velocity, and permitted calculation of Reynolds number (a measure of the potential for turbu- lence in the airways). These parameters can both be important, since deposition rates depend on velocity, residence time and flow regime existing in the airways. The extent to which the flow distribution observed in the cast correspond to those in vivo depends
Correspondence to: Dr. B.S. Cohen, New York University Medical Center, Institute of Environmental Medicine, Long Meadow Road, Tuxedo, NY 10987, USA. 1 Present address: Warner-Lambert Company, 201 Tabor Road, Morrris Plains, NJ 07950, USA.
262
upon the extent to which alveolar pressures are uniform throughout the lung. Such pressures are likely to be uniform at the beginning of inspiration and throughout quiet breathing. In any case, the data in the cast can illuminate the factors affecting the distribution of flow.
Methods
Preparation of lung casts. One solid and several hollow TB casts were prepared for this study according to the method of Schlesinger et aI. (1982). The Silicone-rubber casts were made from the freshly excised lung of a 34-year-old male inflated to 75 7o of total lung capacity. The solid master was pruned back to the level of 3 mm diam- eter airways and replicate hollow casts were made of Silicone rubber using the mas- ter cast as a template.
The airways of the solid master cast were measured using an electronic digital cal- iper and a hand-held magnifier incorporating a protractor reticule. Measurements were recorded for airway length, midpoint diameter, and branching angle. These measure- ments were compared to other human casts prepared in the same manner (Nikiforov and Schlesinger, 1985).
Airwayflow measurements. A detailed examination of the distribution of airflow in the hollow cast was performed at constant inspiratory flow rates of 7.5, 15, 30 and 60 L 'min -1. These casts were used in deposition experiments under both constant and simulated cyclic inspiratory flow. Measurements of the distribution of flow at several different flow rates provided a basis for evaluating any redistribution of flow through the cast as tracheal flow rate changed. Direct measurement of cyclic flow through the cast was not feasible with the available recording device, due to the rapidly oscillat- ing inspiratory flow.
Total airflow through the cast was measured using a Fleisch pneumotachograph (Fig. 1). Pressure drop across the pneumotachograph was monitored with a Validyne MP-45 transducer connected to a Validyne carrier demodulator (Northridge, CA) and calibrated to read out directly in lpm. Velocity measurements at each open airway end were made to determine the distribution of tracheal flow into the various airway paths. The measurements were made using a TSI model 1260A-T1.5 hot wire anemometer probe in conjunction with a TSI series 1050 linearized anemometer (St. Paul, MN).
The anemometer was calibrated for each flow rate and sensitivity setting used. The 1260A-T1.5 probe is very sensitive and of sufficiently small size so that its
presence was not likely to interfere with flow at the end airway openings. The "hot- wire" portion of the probe was 1.25 mm long and 4/~m in diameter. Each end airway was measured at four different positions (Fig. 2). Readings were taken at the airway centerline as well as at the point of maximum velocity, in both cases with the probe aligned both perpendicular and parallel to the carinal ridge. The point of max velocity was found by traversing the airway. The mean of these four readings was used to re-
263
ot Wire Probe
Pneumotach Regulator ~ ,, ( ~ 4-- Air Supply
-L-L~Pressur e I Transducer
Amplifier ~
I Chart Recorder Anemometer
Fig. 1. Apparatus for measuring the distribution of flow through the cast.
present the average velocity in the airway. These four readings would be identical downwind of a long, straight cylindrical tube. However, due to the branching pattern of airways, the maximum velocity usually occurs off-center in an airway downstream of a bifurcation (Schroter and Sudlow, 1969) (Fig. 2b).
Results
CAST MORPHOMETRY
The results of the morphometric measurements are shown in Table 1. The trachea is considered generation 0 and the study cast extended to the 10 th generation along some paths. Airway diameters less than 3 mm first appeared in the 5 th generation. Since airways were pruned if smaller than 3 mm in diameter, only generations 0 through 4 were complete. The percentage of total airways present within a generation is shown in parentheses next to the number of remaining airways in that generation.
Before interpreting experimental results obtained using these casts and their possi- ble implications to corresponding distributions in intact lungs, a comparison of the dimensional measurements was made with a larger body of data on the morphome- try of human lungs. The data for the study cast was compared to the means of mea- surements made from eight casts of adult human right lungs (Nikiforov and Schlesinger, 1985). Two sample t-tests were performed between the two means, and the P-values of airway generations showing significant differences are noted on Table 1. The Niki- forov and Schlesinger data are more appropriate for this comparison than other data available in the literature because the casts in both studies were prepared using iden- tical methods. Because the Nikiforov and Schlesinger measurements were restricted to
264
a b
,C
Prof
Y T c
Profile C /
1::=,
Profile B
]::=,
Fig. 2. Position of anemometer probe during flow measurements: perpendicular to the carina at the airway centerline (a) and at the point of maximum velocity (b); and parallel to the carina at the airway centerline (c) and at the point of maximum velocity (d). Velocity profiles in a bifurcating tube are represented in (b). Profile A represents fully developed laminar flow in the parent airway. Profile B is the daughter velocity profile
in the plane of the figure. Profile C is the profile in the plane normal to the figure.
the right lung, there is a large d iscrepancy between the 1 st generat ion length measure-
ments. Normal ly , the left bronchus is approximate ly twice as long as the right bron-
chus. Therefore, we would expect the s tudy cast to have a mean approximate ly 1.5 t imes
the length of the popula t ion mean. The right bronchus of the s tudy cast measured 29.3
mm, which is much closer to the popula t ion mean of right lungs. The average of the
second generat ion airway lengths on the right side only is 18.9 mm. This also agrees
more closely with the mean of right lungs.
Other morphomet r ic differences lie in generat ions 6 through 8. In these generat ions,
the s tudy cast means are biased, since any airway smaller than 3 m m was removed.
The percentage of airways remaining after pruning decreases rapidly pas t the 5 th
generat ion. Since a great deal of variat ion is seen among the da ta of other investiga-
TABLE 1
Comparison of cast morphometry data from Nikiforov and Schlesinger; mean values + SD
265
Generation Number of airway Diameter (mm) Length (mm)
6 24(10090) 32.8 (100~o) 3.7+- 1.10 c 2.80+-0.97 10.9_+6.45 9.90+-5.4
7 20(12.59o) 46.8 (73~o) 3.4_+0.93 c 2.47+-0.88 8.9+-4.57 9.14+-4.7 8 12 (3.8~o) 49.1 (38~o) 3.5+1.01 c 2.26+-0.87 10.7 + 5.00 b 8.64+4.3
9 10 (1.6~o) 3.1 + 0.85 9.3 +- 5.09
10 6 (0.590) 2.9 + 0.23 9.7 +- 2.87
The following P values reflect the result of a two-sample t-test between the test cast and the N-S data: a 0.05; b 0.01 and
0.001. * N-S = Nikiforov and Schlesinger, 1985 (measurements made on right lung only).
tors (Weibel, 1963; Yeh and Schum, 1980; Soong etaL, 1979), and the airway mor- phometry is in good agreement with population means (Nikiforov and Schlesinger, 1985), we can conclude that this cast is representative of an average adult male.
AIRWAY F L O W M E A S U R E M E N T S
Distribution ofai~ow. Fig. 3 describes the nomenclature of the subsegmental bronchi. The results of the measurements of the distribution of flow in the study cast are shown in Fig. 4, as the percent of total flow in each airway for each tracheal flow rate. The data are also compared to the Horsfield flow distribution model (Horsfield et al., 1971), which assumes that flow is distributed in proportion to the fraction of the total lung volume subtended by that airway.
The overall distribution of flow was found to be 60 ~o to the right side and 40 ~o to the left. Average flow distribution throughout the lobes was as follows: right upper, 18.5~o; right middle, 9.2~o; right lower, 32.3~o; left upper, 15.7~o; and left lower, 24.3~o. Distributions for the four individual flow rates are shown in Table 2.
The airflow in the right and left upper lobes, as well as in the left lung overall, was consistently lower than that predicted by the Horsfield model. Likewise, flow into the right lower lobe, as well as in the right lung overall, was consistently higher than the prediction. Due to the vertical pressure gradient in the thorax, the lower lobes fill first
266
RIGHT LUNG ~ LEFT LUNG
Fig. 3. Nomenclature of the subsegmental bronchi.
in vivo, and are better ventilated at lower flow rates. The measurements appear to in-
dicate that the distribution of flow in the cast airways was similar to that in human
lungs.
TABLE 2
Flow distribution results
Region Percent total flow Mean Horsfield*
7.5 lpm 15 lpm 30 lpm 60 lpm
Left lower 24.5 23.8 23.9 25.0 24.3 24.9 Left upper 14.9 16.0 15.9 16.0 15.7 20.5 Right lower 32.1 33.5 32.4 31.2 32.3 23.2 Right middle 8.3 9.0 9.6 10.0 9.2 9.6 Right upper 20.2 17.7 18.2 17.8 18.5 21.7
Left lung 39.4 39.8 39.8 41.0 40.0 45.4 Right lung 60.6 60.2 60.2 59.0 60.0 54.6
* Horsfield et al., 1971.
267
70~
N ~ "
~ . ~ . I - -
1 0 "
Q
a
I Right Left
Main Bronchi
• : : ; I
Bronchus Posterior Anterior Apical Right Upper Bronchi
C
0 " : : Middle Bronchus Medial Lobe Lateral Lobe
Right Middle Bronchi
Right Lower Bronchi 25 e
2o
O. " " -- " " - Broqdlm StCerbr Polted0r Antedcr" A#cII L i a r Sl~erbr ~ " Bmnchm Brorch~ Lln~ar Llngubr
Left Upper Bronchi
f
2O
Left Lower BroNchi
Fig. 4. Distribution of flow: a, main bronchi; b, right upper bronchi; c, right middle bronchi; d, right lower bronchi; e, left upper bronchi; f, left lower bronchi.
Velocity maxima measured at the airway ends usually occurred at or near the air- way centerline. However, in recently bifurcated airways, the measured maxima were generally towards the inside wall of the bifurcation as shown in Fig. 2b.
The chart recorder measured unsteady velocities at 30 and 60 lpm at the level of 3 mm diameter airways (fifth to tenth generation). At 7.5 and 15 lpm, the anemometer output remained smooth. There were deviations from constant velocity readings as flow rate increased.
Factors affecting flow distribution. The measurements in Table 2 shows that flow dis- tribution in the various lobes does not change much as tracheal flow rate changes, with the exception that the percent of total flow into the right middle lobe increases as the tracheal flow rate increases. However, in most individual airways, the percent of tra- cheal flow undergoes either small increases or decreases as the tracheal flow rate changes. Overall, the uncertainty in these measurements based on calibration and flow averaging is estimated at less than 10~o.
268
In order to analyze for redistribution of flow in the individual airways, the data were fitted by linear regression to a power curve equation (Cohen and Briant, 1989):
y = ax b
where: y = flow rate in the individual airway, x = tracheal flow rate, and a and b = constants.
When b = 1, the constant "a" represents the fraction of the tracheal flow passing through that airway and the equation reduces to the linear relationship of y = ax. This means that the fraction of total flow in an individual airway does not change with tracheal flow. For cases where b > 1, as tracheal flow increases, so does the fraction of flow in the individual airway. Conversely, when b < 1, the fraction of flow in the individual airway decreases as tracheal flow increases. The results of the regression are in Table 3. The b value for each end airway was examined and assigned a value o f " - " if the distribution decreased with increasing flow rate, " + " if the distribution increased with increasing flow and "0" if there was no change. No change was considered to be 0.95 < b <1.05.
Flow distribution through the cast was analyzed with respect to airway diameter, length and branching angle, to determine the effect of morphometric variables on distribution at the various flow rates. Additional variables (airway cross-sectional area, surface area, and volume) were generated from the original morphometric measure- ments and were examined as well. The cumulative measurements (~) of all these variables were also examined to test the effect of "morphometric history" on the dis- tribution of flow.
Kruskal-Wallis tests were then performed between the morphometric variables and the signed variable. The results (Table 4) show that the variables angle, ~ length, Z angle, lg surface area, and lg volume have a significant effect on the redistribution of flow in the cast as the total flow changes. Many of these variables are intercorrelated (Table 5). By selecting the variables with the greatest effect on distribution and the least amount of intercorrelation, stepwise regression could be performed to determine the influence of each variable on the distribution of flow. Cumulative surface area is highly correlated with Z length, and was therefore not included.
A stepwise regression analysis was performed using the percent distribution for each flow rate as the dependent variable, and the remaining morphometric variables (cross- sectional area, final branching angle, cumulative branching angle, and total pathlength) as the independent variable. The resulting flow models (Table 6) show that as the total flow rate through the cast increases, the total pathlength becomes relatively less im- portant, and the cross-sectional area and branching angle becomes relatively more important, in determining the distribution of flow through the cast.
Right upper 0.2151 0.9495 0.9975 - Right middle 0.0699 1.0900 0.9999 + Right lower 0.3402 0.9829 0.9992 0 Left upper 0.1432 1.0299 0.9994 0 Left lower 0.2362 1.0092 0.9940 0
Right lung 0.6216 0.9884 1.0000 0 Left lung 0.3795 1.0172 1.0000 0
a Values are shown for the fight upper lobe, for the five lung lobes and two lungs. A full table of values may be obtained from the authors upon request.
Discussion
Flow distribution. Studies involving the pattern of gas flow in human airways were
performed in 1915 by Rohrer (translation, 1975). He suggested that the distribution of
flow might be due to regional differences in flow resistance caused by the irregularity
of branching. He also suggested that the pressure drop in the airways was a function
of frictional plus inertial forces. The latter was assumed to have minimal influence, since
flow in the airways was thought to be largely laminar.
Pedley et aL (1972) suggested that with increasing flow there would be a redistribu-
tion of ventilation from the lower to upper lobes. This was demonstrated in vivo by Bake
et al. (1974) and was attributed to differences in airway geometry. Gran t et al. (1974)
showed that although lungs start filling from the basal region, as flow rate increases,
so does ventilation to the apical regions.
Cohen and Briant (1989) made flow distribution measurements on human airway
casts extending to 1 mm airways and smaller. They f ound that flow redistributed to
lower lobes as tracheal flow rate increased, and attributed this to an increase in flow
270
TABLE 4
KruskaI-Wallis analysis for morphometry on flow distribution
Variable Mean
Group 1 Group 2 Group 3
P value
Angle 48.9 36.9 23.5 0.001
2 length 28.2 27.8 47.5 0.001
l~ angle 42.5 43.8 25.9 0.003
1~ S-area 30.4 27.1 45.8 0.003
Y volume 32.1 27.2 44.2 0.016
Z diameter 35.5 26.0 41.7 0.057
Diameter 41.4 26.5 35.9 0.079
X-area 41.4 26.5 35.9 0.079
Z X-area 36.7 25.9 40.6 I).079
Length 30.3 35.0 41.9 0.106
S-area 33./) 32.9 40.3 0.337
Volume 34.9 31.2 39.5 0.422
Group 1: Airway flow decreased with increasing tracheal flow ( n - 27). Group 2: Airway flow remained unchanged with increasing tracheal flow Group 3: Airway flow increased with increasing tracheal flow (n = 29). X-area = cross-sectional area; S-area = surface area; Y = cumulative.
(n = 15).
stream inertia. Since the upper lobes have more acute angles, the results were consistent with the hypothesis that effective resistances of angles is flow dependent, increasing as angle increases (Slutsky et al., 1980). In the current study, the upper right lobe of the cast tended to receive a lower percentage of tracheal flow as tracheal flow increased. The right middle lobe, on the other hand, tended to receive a higher percentage of the tracheal flow. However, in most of the lobes there is little evidence of redistribution of flow. Caution should be used on extrapolating these results obtained in cast studies to in vivo lungs.
Flow distribution was measured both with and without a larynx in the Cohen and Briant (1989) study. Differences of less than 5 ~o were seen. Dekker (1961) found that the critical flow for the onset of turbulence was only one third to one fourth as high if the cast was preceded by a larynx. Use of a larynx is considered critical in deposi- tion studies using TB casts. Experiments by Chan et al. (1980) showed that tracheal deposition patterns in casts were altered by the inclusion of a larynx. Deposition in the trachea is enhanced by the laryngeal jet and more closely represents tracheal deposi- tion in vivo. The use of a larynx during the measurement of flow distribution, however, does not appear to be as important.
The production of turbulent eddies is normally a random occurrence in parcels of fluid moving through a pipe. Larger eddies break down into smaller eddies until the disturbances are so small that they are damped by the viscosity of the fluid. When turbulent flow is fully developed, the rate of production of eddies equals the rate of their
The numbers in each column are the variable coefficients. The numbers in parentheses below are the P values for each coefficient.
decay. In the TB tree, the larynx produces large scale d is turbances which move down
the bronchi until they reach airways that are smaller than the d is turbances themselves,
where they break up into smaller eddies. In small airways with low Reynolds number
(Re), these smaller eddies rapidly dissipate.
The flow regime that exists in the TB cast is largely de termined by the Re. This
d imensionless pa ramete r is the rat io of inertial to viscous forces. When the rat io is high,
the fluid mot ion is in the turbulent regime. At lower Re, viscous forces are more im-
por tan t and the fluid is in the laminar regime.
R e - m
poUD poQD 4poQ 1~ # A nl~D
where:
Po = fluid density,
U = airway velocity,
D = airway diameter ,
/~ = viscocity of air,
Q = airway flow rate, and
A = airway cross-sect ional area.
In straight, smooth walled tubes, the Re normal ly associa ted with the different re-
gimes are as follows: Re < 2000, laminar flow; Re > 10000, fully deve loped turbulent
flow; and 2000 < R e < 10000, t ransi t ion regime. In the TB tree, as air travels down
the generat ions, the d iameters decrease but the total cross sect ional area of the airways
increases. As Re decreases in straight tubes with smooth walls, Re < 2 0 0 0 should
signify the t ransi t ion to laminar flow. However , in the TB tree, a series of short, rough
walled, bifurcat ing tubes; fully developed laminar flow may require much lower values
of Re. A measure of the d is tance usually required for fully developed parabol ic lami-
273
nar flow to be established within a tube is called the "entrance length" (Le) (Olson et al.,
1970).
L e = 0.02875. D . Re
If the length of a tube does not equal or exceed this measure, laminar flow will not be established. Fig. 5 shows L e as a function of generation for the four flow rates measured. The airway lengths in the TB tree are much less than the required Le for all flow rates except 7.5 lpm. Only at this lowest flow rate is L~ exceeded by airway length in the fifth to tenth generations. Therefore, complex flow patterns arising at a bifurcation generally do not dissipate before the next bifurcation (Clarke et aL, 1972). Re for the fifth to tenth generations at 7.5 lpm ranges from 50 to 75. Re as a function of generation is shown for the four flow rates examined (Fig. 6).
Thus, Re alone is not a good indicator of flow regime in lung airways. As noted in the results section, the velocity measurements for the two higher flow rates, as displayed by the anemometer output, showed a mean velocity superimposed with a fluctuating component. If the Re alone is considered, the flow should be laminar (Re ~ 200 to 500). However, L e for these airways is greater than the length of the airways themselves (L~ ~ 2 to 7 cm). Non-laminar flow has been observed in the trachea as low as 4.3 lpm
10 3
A
E 10 2 0
¢..
C
,,.,.I 101
o C L_
C 100 UJ
[ ]
0 • 0
• 0
[ ] • 0 I I
[ ] • 0 • •
[ ] • 0 0
[ ] • •
[ ] [ ]
7.5 Ipm
15 Ipm
30 Ipm
60 Ipm
• •
0 0 0
• •
[ ] [ ] [ ]
10 "1 , , , 0 2 4 6 8
G e n e r a t i o n
Fig. 5. Entrance length (cm) as a function of generation.
10
274
10 4
L .
,,D
E
Z
"0 0 =,= >,,
n"
10 3
10 2
101
0
[]
O . . . . . . . . . . . . .
• o • •
o •
[] • o o • o
[] • • [] •
[] [] []
i i i
2 4 6
G e n e r a t i o n
Fig. 6. Reynolds number as a function of generation.
[ ]
0
0
[ ]
75 Ipm
15 Ipm
30 Ipm
60 Ipm
O
[ ]
10
(Re = 300) (Dekker, 1961). Clarke et al. (1972) question whether pure laminar flow ever exists in branching systems, even at a Re of unity. Unstable flows have been observed in the sublobar bronchi at Re below 100 (Olson et al., 1973).
The airstream velocity profile downstream of a bifurcation is asymmetrical. The peak velocity occurs near the inner wall of the daughter branches in the plane of the bifur- cation. Centrifugal force caused by flow encountering a bend in the airway leads to an increased pressure on the inside wall which skews the velocity profile and causes a separation of streamlines in from the outer wall in a disturbance referred to as sec- ondary flow. Secondary flow has been observed (Clarke et al., 1972) at Re as low as 100.
Skewed velocity profiles as well as unsteady flows were observed when the velocity was measured near the open end of recently bifurcated airways in these experiments. The streamlines of higher velocity are skewed toward the inner wall of the daughter airway (Fig. 2b). This also affects the distribution of flow in the following daughters since the flow profile being split by the second bifurcation has been skewed by the first.
The flow in the TB cast was measured at a constant flow rate. The effects of pul- satile flow on the persistence of turbulence cannot be ignored (Pedley et al., 1970). The Womersley parameter (c 0 is a measure of the impact of oscillatory flow on turbulence in an airway (Womersley, 1955).
275
D X/2 rrf
e = 2 v
where: D = airway diameter (cm), f = oscillatory frequency (Hz), and v = kinematic viscosity (cm2/sec)
The degree of departure from parabolic flow increases with ~ and frequency effects may become important in straight tubes when c~ > 1. Womersley number is plotted as a function of airway generation in Fig. 7. For conditions of these experiments, ~ drops below one somewhere between the third and fourth generation.
FLOW MODEL
Current deposition models are not able to incorporate the effects of flow patterns in the upper airways which contribute to the nonhomogeneity of deposition demonstrated in the cast system. The flow regimes that exist in TB casts can determine which mechanisms will govern deposition. By knowing more about the elements involved in
10
I _ .
en
E Z
x . _
E O
Generation Fig. 7. Womersley number as a function of generation.
10
276
the transition of flow from the laminar to turbulent regimes, more accurate predictions of deposition efficiency can be made.
One of the physical factors in the determination of flow distribution in the human lung is the pressure drop across the airways. The pressure drop is due to several an- atomical features of the TB tree. According to Olson, et al. (1970), the most important feature is the short lengths of the airways. The shortness of the airways causes the flow to be distributed such that more energy loss per unit length occurs as friction against the tube wall than would be the case in longer conduits. This friction depends upon the flow regime of the fluid and the roughness of the wall. The energy lost to frictional forces or "head loss", is the product of the kinetic energy of the fluid and the resis- tance factor, which is an empirically derived quantity (Olson et al., 1970).
Branching angle is also important because it causes flow to change direction and velocity profiles to become asymmetric. For fully developed turbulent flow as measured in a simple model of branching tubes (Clarke et al., 1972), the Re required for unsteady ftow is approximately equal to 1000 at 35 °, the mean branching angle in the study cast.
Changes in cross-sectional area is the last mechanism discussed by Olson et al. The flaring of an airway as it approaches a bifurcation causes the fluid to rapidly deceler- ate and streamlines to separate (Chanet al., 1980).
It therefore appears that morphometry can influence the distribution of flow in air- ways. If an idealized airway branched into two airways of unequal diameter at iden- tical 45 ° angles, more air would pass through the airway with the greater cross-sectional area. Similarly, when two airways of equal diameter have branching angles of 10 ° and 80 ° , more air flows down the airway with the smaller branching angle. Finally, if the two daughters are of equal diameter and branching angle, but unequal lengths, airflow will prefer the shorter path.
In realistic lung models, airways have different combinations of diameters, lengths, branching angles, and even upstream "morphometric histories". Therefore, the path of least resistance is less obvious. By examining the regression based flow models (Ta- ble 6), the influence of some of the morphometric parameters on the redistribution of flow throughout the cast may be estimated.
At the higher flow rates used (30 and 60 lpm), unsteady flow penetrated the end airways of the cast, as noted before. Such penetration indicates the presence of non- laminar flow throughout the cast. Inertial forces may be more important than frictional forces at these flow rates. In addition to cross-sectional area, which is significant at all flow rates, the influence of branching angles becomes significant at the higher flow rates, indicating that high velocity streamlines undergo less directional change. At 60 lpm, both final and cumulative branching angle are important in determining flow distribu- tion. As the flow decreases to 30 lpm, the final branching angle is no longer a signif- icant morphometric parameter and cumulative branching angle becomes less signifi- cant. At 15 and 7.5 lpm, the total path length is more influential on frictional losses in the airway. Total path length and cumulative branching angle have negative coeffi- cients, indicating that longer and sharper branching airways are less likely to receive a portion of the total flow. Frictional coefficients are much greater in the laminar re-
277
gime than in the turbulent regime. In addit ion, inertial forces are less impor tan t and
the influence of fr ict ional losses increases.
Summary and conclusions
Hollow replicate casts of a human TB tree were used to analyze the flow regimes in
the bronchi in order to evaluate the influence of flow related factors on the deposi t ion
of fibers and other part icles. The da ta presented for the dis tr ibut ion of airflow in the
human cast are consis tent with previous da ta on flow distr ibut ion in vivo during the
initial stages of inspirat ion. The alveoli in the lower lobes open before those in the upper
lobes due to a thoracic pressure gradient. Therefore, the lower lobes are better venti-
lated than the upper lobes. The actual dis tr ibut ions of airflow in t r immed casts of the
human TB tree are different from those predic ted by the Horsfield model , but are closer
to the dis tr ibut ion of flow that is seen in vivo.
The empirical flow models that were derived from the experimental flow distr ibution
da ta demons t ra te the effects of morphomet r ic parameters on the dis tr ibut ion of airflow.
Airway cross-sect ional area, branching angle and total pathlength were found to have
the greatest influence on airflow distr ibution. As the t racheal flow rate decreased from
60 to 7.5 L .min -1 , branching angle became less influential and total pathlength became
more influential. These results provide evidence for the t ransi t ion of flow regimes within
the TB tree within normal physiological ranges. When flow in the airways is turbulent,
inertial forces domina te and flow distr ibut ion is influenced by airway angles. On the
other hand, as the flow becomes less turbulent, frictional forces become more impor-
tant and flow distr ibut ion is influenced by total path length.
Acknowledgements. This research was supported by Grant ES 00881 from the National Institute of Envi- ronmental Health Sciences (NIEHS). It is part of a Center program supported by Grants ES 00260 from NIEHS and CA 13343 from the National Cancer Institute.
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