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Vol. 83, Issue 5, 1721-1732, 1997
1 Department of Environmental
and Occupational Medicine, University of Aarhus, DK-8000 Aarhus C,
Denmark; 2 University Hospital for
Children and Youth "Wilhelmina Children's Hospital", ABSTRACT Pedersen, O. F., H. J. L. Brackel, J. M. Bogaard, and K. F. Kerrebijn. Wave-speed-determined flow limitation at peak flow in
normal and asthmatic subjects. J. Appl.
Physiol. 83(5): 1721-1732, 1997.
peak expiratory flow; peak flow-determining factors
INTRODUCTION PEAK EXPIRATORY FLOW is defined as the highest flow
achieved at the mouth during a maximally forced vital capacity (FVC)
maneuver, starting at full inspiration (1, 19).
As first pointed out by Fry et al. (6), there is a unique relationship
among transpulmonary pressure, expiratory flow, and lung volume so
that, during a forced expiration, flow reaches a maximal value before
pressure does. When flow has become maximal, that is, when flow at a
given lung volume does not increase further when pressure increases,
the expiratory flow has been defined as "effort independent."
Hyatt et al. (9) initially estimated the effort-independent part of the
maximum expiratory flow-volume curve to begin at ~50% of vital
capacity (VC). This estimate was later increased to 60% (8). Mead et
al. (15) demonstrated levels of 70% VC or higher in five normal
subjects.
Van de Woestijne and Zapletal (23), requiring at least five points to
define a plateau after a maximum on an isovolume pressure-flow curve,
found that the effort-independent portion extended to 82% and that PEF
was found at 88% VC in the examined subjects. This indicates that PEF
may indeed be obtained at near-flow-limiting conditions. This is
supported by Volta et al. (26), who applied a negative pressure pulse
at the mouth and found no change in PEF in nine normal subjects
applying maximal efforts.
A different approach can be made by applying the analysis by Dawson and
Elliott (2). This approach shows that flow ( If PEF is limited by the wave speed, then it should occur when the
velocity of the accelerating flow reaches wave speed at some point in
the airway. At that point, the speed index (SI = As described in studies in dogs (16), The purpose of the present study was to measure SI during FVC maneuvers
at different locations in the airway of healthy and stable asthmatic
subjects to obtain support for the hypothesis that PEF is determined by
the wave-speed flow-limiting mechanism.
MATERIALS AND METHODS
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
The purpose of
this study was to examine whether peak expiratory flow is determined by
the wave-speed flow-limiting mechanism. We examined 17 healthy subjects
and 11 subjects with stable asthma, the latter treated with inhaled
bronchodilators and corticosteroids. We used an esophageal balloon and
a Pitot-static probe positioned at five locations between the right
lower lobe and midtrachea to obtain dynamic area-transmural pressure
(A-Ptm) curves as described (O. F. Pedersen, B. Thiessen, and S. Lyager. J. Appl.
Physiol. 52: 357-369, 1982). From these curves we
obtained cross-sectional area (A)
and airway compliance (Caw = dA/dPtm) at PEF, calculated flow at wave speed {
ws = A[A/(Caw*
)0.5],
where is density} and speed index is (SI = /ws). In 13 of 15 healthy and
in 4 of 10 asthmatic subjects, who could produce satisfactory curves,
SI at PEF was >0.9 at one or more measured positions. Alveolar
pressure continued to increase after PEF was achieved, suggesting flow
limitation somewhere in the airway in all of these subjects. We
conclude that wave speed is reached in central airways at PEF in most
subjects, but it cannot be excluded that wave speed is also reached in
more peripheral airways.
) through
an airway segment becomes maximal when the linear velocity reaches the
speed of a pressure-wave propagation through the airway. Wave-speed
flow (ws) depends on the cross-sectional area
(A), airway compliance (Caw = dA/dPtm), which is the slope of the
curve describing A as a function of
distending transmural pressure (Ptm), and the density () of the gas,
according to the equation
It can be seen that
![<A><AC>V</AC><AC>˙</AC></A>ws = <IT>A</IT>[<IT>A</IT>/(&rgr;∗Caw)]<SUP>0.5</SUP>](/content/vol83/issue5/fulltext/1721/img001.gif)
ws will decrease, when
A becomes smaller, and Caw and become larger. ws indirectly depends on the lung
elastic recoil pressure (Pel) and the pressure loss (Pfr) upstream from
the flow-determining segment, which Dawson and Elliott (2)
called the "choke point" because a decreased pressure head (J = Pel 
Pfr) will make the distending
pressure (Ptm) smaller and, accordingly, make A
smaller.
/ws) will be equal to one.
ws can be
measured at different locations in the airways from data obtained with a Pitot-static probe, an esophageal balloon, and expiratory flow.
-2 agonist, which resulted in maximal bronchodilatation
during a dose-response curve obtained 1 wk before the prednisolone
course.
Plat,
J = PT Ppl, and Ptm = Plat Ppl, where Pca is the pressure needed for convective
acceleration, i.e., for acceleration of the gas molecules so that they
can pass a given cross section of the airway at a given flow.
J is a fluid mechanical term defined
as the pressure head, and Ptm is the transmural pressure. The pressures
were calibrated daily with a mercury manometer providing ±10 kPa.
Mouth flow (m) was measured by a nonheated Fleisch
no. 3.5 pneumotachograph. The pressure drop across the flow head was measured with a Validyne MP45 transducer (Northridge, CA) fitted with a
2-kPa diaphragm and connected to a Validyne amplifier. Flow was
calibrated by the integration procedure (24), introducing 9 liters of
air through the flow head with a 1-liter syringe. The amplification was
adjusted so that the integrated flow signal provided the same output as
an integrated 1-s pulse reference flow, which was then by definition 9 l/s. The geometry of the inlet to the flow head was optimized so that
the deviation from linearity was <5% up to 15 l/s.
m and the pressure signals, Pca, Ptm, and Ppl, were
visible on-line on an AT computer (Olivetti PCS-286 with a 80287 mathematical coprocessor). In this way it was possible to assess the
results directly. Especially, it was possible to detect malfunctioning of the Pitot-static probe, as in case of obstruction of one or more of
the holes. The signals of approved maneuvers were saved for subsequent
calculations.
Tuning of catheters.
The Pitot-static probe and the esophageal balloon were enclosed in an
airtight tube to which a sine pump could be attached and deliver
pressure swings of ~10 kPa. The three pressure differences were
displayed on an oscilloscope. With the pump running at the slowest
possible speed (~1 Hz), the amplifications were adjusted so that
the differences between them were zero. Then, the speed of
the pump was increased to its maximum (~8 Hz), and the resistance and
length of the individual catheters were adjusted to minimize the
excursions. In this way, the error in the pressure differences could be
reduced to <1% of the pressure swings. The 90% rise time to a
square-wave pressure input was <10 ms.
An x-y oscilloscope was finally used to tune the Pca pressure signal to
the m signal. Via a Y tube, the Pitot-static probe was positioned in an ~15-mm-inner diameter rigid tube connected to
the pneumotachograph. According to the Bernoulli equation, Pca equals
(/A)2/2,
where A is the cross-sectional area.
For a blunt flow profile and a constant
A, Pca and must
be in phase. The pneumotachograph was supplied with catheters identical
to those of the Pitot-static probe, and the length of these was
adjusted until the x-y recording showed a closed loop as a response to
a peak flow maneuver through the tube.
Test of Pitot-static probe.
Figure 1 shows results of testing the
Pitot-static probe for accelerating and decelerating flows. Measured
areas for different straight tubes are drawn against Pca. The true
dimensions of the tubes are given at the corresponding horizontal
lines. Because the probe measures the area around it, a slight but
constant underestimation of the tube dimension is expected. This is
important especially for the narrowest tube, where, in Fig. 1, the
dashed line is the true area minus 0.07 cm2, the area occupied by the
probe. Except for the largest areas, the accuracy is in the range
of ±10%.
Experimental procedure. Initial lung function tests were performed on a separate day before the Pitot study. These included measurements of FEV1, FVC, PEF, total lung capacity (TLC), and maximum expiratory flow-volume curves. Furthermore, quasi-static pressure-volume curves were measured according to Zapletal et al. (28). The balloon was introduced via one nostril to a position in the esophagus where the pressure was most negative during maximal inspiration. The balloon was filled with 1.5 ml of air and stayed in situ throughout the experiment. On the day of the Pitot study the subject was premedicated with 0.5 mg atropine intramuscularly 1 h before the introduction of the Pitot-static probe to minimize mucous production and prevent a vasovagal reaction. No sedatives were used. Local anesthesia was given as follows: mouth and pharynx, 10% Xylocaine or 4% lidocaine spray; vocal cords, trachea, and bronchial tree: 0.5% novesine solution, 20 ml maximally, or lidocaine 1%, 10 ml maximally. Anesthesia was given on demand through the bronchoscope. A cuffless endotracheal (ET) tube was placed over the bronchoscope. After introduction of the bronchoscope into the trachea, the ET tube was passed between the vocal cords, and the bronchoscope was pulled back. The Pitot-static probe with its two catheters was placed into the trachea through the ET tube, which was then removed. Subsequently, the bronchoscope was reintroduced and the Pitot-static probe was placed at the most peripheral position ( position 0), with the tip of the probe just above the entrance to the right lower lobe (the left lower lobe in one subject). After the position of the two catheters was checked, the Pitot-static probe was pulled back until four other positions were reached. These were, respectively, middle-lobe entrance, mid-main stem bronchus, 1 cm above the main carina, and midtrachea (Fig. 2). The distance between the positions was determined individually by measuring, at the mouth, the distance the catheter was pulled back between positions. Next, the Pitot-static probe was repositioned in its most peripheral position, the bronchoscope was carefully withdrawn, and the two catheters were pushed through and secured in two tightly fitting side holes in the specially designed mouthpiece. Finally, the free ends of the catheters were connected to the pressure transducers, and the mouthpiece was connected to the pneumotachograph.
The subjects were measured while sitting upright in a chair and wearing a noseclip. Before each measurement the two Pitot-probe catheters were each flushed forcefully with at least 2 × 50 ml of air to remove secretions from the end and side holes of the probe. Most of the subjects were asked to perform two types of forced expiratory maneuvers from TLC to residual volume. One was an ordinary FVC maneuver, the other a "huff" maneuver, with performance of a number of sequential peak flows without closing the vocal cords. Some of the healthy subjects were also asked to perform relaxed expirations from TLC (sighs). At each position, starting with the most peripheral, each procedure was repeated until acceptable results were obtained or a maximum of 4-5 maneuvers was performed. Calculations. The data acquisition and calculation applied Asyst software (version 3.10, Asyst Software Technologies, Rochester, NY). From the inputs,
m, Pca, Ptm, and Ppl, the parameters in
Table 1 were calculated at PEF of the
maximum expiratory maneuvers and for the first peak of the huff
maneuvers. Caw was calculated as dA/dt
divided by dPtm/dt by using a Asyst
software routine applying a first-order differentiation of a
second-degree polynomial fitted to three points corresponding to the
peak.
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m.
Equations 4-15 define derived
variables. A few of the equations can be commented on. In
Eq.
9, gas density at the probe
PB was calculated
as the weighted density at 37°C of expired gas from data presented
by Radford (20) to be 1.13 kg/m3,
by use of Boyle's law. In Eq. 10,
flow at the probe was similarly calculated by use of Boyle's law. In
Eq. 11, to correct for the effect of
gas compression (10), especially in the matching of dynamic volumes
with volumes measured quasi-statically during determination of the
static Pel, the expired volume from TLC was corrected for the influence
of Ppl only. At PEF, this represents the largest part of alveolar
pressure (PA), which ideally
should have been used in the correction. This correction was only done for positive Ppl. Equation 12 calculated A from the Bernoulli equation under the assumption of blunt velocity profile.
Equation 15 was derived from
Eqs. 12 and 14. m was not
corrected to BTPS conditions, and no
attempt was made to correct for the difference between the composition
of air and the alveolar gas. That correction will introduce a small,
but systematic, error considered to be of no significance in the
present study.
, flow; PT,
impaction pressure; Pfr, pressure loss (upstream);
PA, alveolar pressure; Plat,
lateral airway pressure; J, pressure
head; Ptm, transmural pressure; Ppl, pleural pressure; Pel, elastic
recoil pressure.
Selection criteria. Curves with obvious errors (evidence of blocked holes in or wedging of the Pitot-static probe) were not saved. In the unselected data, there was a considerable variation in Caw, with many negative values that cannot be used in calculation of SI (Eq. 15 in Table 1). This scatter was considerably decreased only if values of Caw for Pca > 1.3 kPa were selected, but negative values of Caw were still found. We therefore excluded curves with extreme values of (Caw <
10 and Caw > 5 cm2/kPa) and with SI > 1.3, or rather
SI2 > 1.69 that could be
calculated also for negative values of Caw (cf.
DISCUSSION). The criterion Pca > 1.3 kPa was not used for examination of the distributions of the
variables (except Caw) within the airways.
Statistics.
The maximum SI in the airway of a subject was determined by first
choosing the curve with the highest PEF (or first huff peak) among
repeated measurements (replications) with the same maneuver and at the
same position of the probe, and next the highest SI among positions was
determined.
Group means were compared by nonparametric tests. Multivariate analysis
of variance and regression analysis were applied to provide estimates
of differences between groups stratified for disease, gender, and probe
position. P < 0.05 was chosen as the significance level.
RESULTS
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10 < Caw < 5 cm2(kPa)
1
and SI2 < 1.69, 97.2% of the
curves could be used. By use of the further requirement of Pca > 1.3 kPa, this figure was reduced to 45% in the healthy subjects and 47%
in the asthmatic subjects.
Measurements in subjects.
Figures 4-6 show examples of recordings of different types of expiratory maneuvers
from a healthy subject with the Pitot-static probe positioned in the
lower part of the trachea.
Figure 4 describes curves obtained during a maximum expiratory flow-volume maneuver. In Fig 4A, flow at the Pitot-static probe (i.e.,
Plat),
pressures, and SI are plotted vs. VPpl, which is an
approximation of the thoracic gas volume change (see
Calculations). It can be seen that SI is
smaller than one (subcritical conditions) before PEF is reached and
close to one at PEF. After PEF, SI apparently becomes >1
(supracritical conditions).
In Fig. 4B, A at the probe is plotted vs. Ptm. Because this curve is slightly irregular, a fourth-degree polynomial fit was applied for calculation of Caw, which is the slope of the curve, and this Caw was subsequently used in the calculation of SI, shown in Fig. 4A, bottom. During expiration, Ptm decreases (see Fig. 4A, top) and A decreases. At the A-Ptm curve, PEF is reached at the arrow (Fig. 4B).
Figure 4C shows that PA continues to increase when PEF is reached, forming a closed loop for the entire expiration. Figure 5 shows a set of curves obtained during a submaximal expiration in the same subject with the same position of the Pitot-static probe as in Fig. 4. The curve has no clear peak, lower flow than the maximal expiration, and SI < 1 during the upper 40-50% of the FVC. At some point, however, SI becomes unity, and the flow-volume curve follows the course of the maximal curve, as seen by comparison with Fig. 4, indicating that flow limitation has now occurred at the given position. This happens at a lower Ptm and A and at a lower PA than in Fig. 4. The shape of the
-PA curve
is different. After the maximum flow is reached,
PA and both
decrease until SI equals one (Fig. 5C,
arrow). Then, PA increases again
with decreasing flow, just as was the case in Fig. 4 when SI > 1.
Figure 6 shows results from a huff flow-volume maneuver of the same
subject and the same position as in Figs. 4 and 5. There are five peaks
in the series of huffs. During each huff, SI increases abruptly and
becomes unity near the peak. The curves in Fig. 6, B and
C, show a clear volume dependence of
both the A-Ptm and -PA curves.
Similar curves could be obtained from asthmatic subjects, but in these
subjects, SI in the trachea, especially at lower lung volumes, was
generally smaller than in the healthy subjects.
In Fig. 7, the maximum SI among probe
positions for each subject is plotted for the healthy and asthmatic
subjects (one data point for each subject). Two healthy women (with SI < 0.6) and one asthmatic woman (with SI = 0.77) showed evidence of
submaximal effort, with pressure-flow patterns as shown in Fig. 5. They
could not produce Pca > 1.3 kPa, and therefore their data were not
included in Fig. 7. The remaining subjects included 15 healthy subjects (6 women and 9 men) and 10 asthmatic subjects (3 women and 7 men). Among the healthy subjects, 13 of 15 had SI 
0.9, but the same was
true for only 4 of 10 asthmatic subjects
(P = 0.22, Fisher test). The
distribution of maximum SI among probe positions was not different
between healthy and asthmatic subjects, although only 3 of 15 healthy
subjects compared with 5 of 10 asthmatic subjects had maximum SI
peripheral to the trachea (P = 0.13, Fisher test).
) and
asthmatic subject (+).
Analysis of data from the two groups described in Fig. 7 is presented in Table 3. The only significant difference between the two groups was an apparently smaller SI in the asthmatic subjects. A similar analysis (not shown), including values only from the most peripheral probe position ( position 0), showed no significant differences between the two groups. Five healthy subjects (1 woman and 4 men) were compared with eight asthmatic subjects (3 women and 5 men).
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DISCUSSION
The purpose of the present study was to examine whether peak expiratory flow is determined by the wave-speed flow-limiting mechanism (2) and whether the mechanics of the forced expiration differs between healthy and stable asthmatic subjects. For that purpose we used a method previously applied in dogs (16). We used a Pitot-static probe as originally used by Macklem and Wilson in 1965 (14). As pointed out by these authors, this method is technically difficult, and therefore it should be discussed.
Technical problems. The crucial points are the measurements Pca = PT Plat with the
Pitot-static probe and Ptm = Plat Ppl by further use of the
esophageal balloon. Figure 2 shows that the area in stiff tubes could
be measured reasonably well, even for small values of Pca. Areas >2
cm2, however, may have been
overestimated by 10-15%. About 18% of the measured areas were
>2 cm2 and were mostly found in
tall healthy men. The position of the probe should be axial in the
airway. With the given design of the probe, we found in the previous
study (16) that an angle up to 20° changed measured
A < 10% in a single experiment. In that study we also found that, in a converging part of the airway, the
area is measured rather accurately but, because of separation of flow
from the airway walls, the area in a diverging airway may be
underestimated if the probe is in the middle of the lumen or
overestimated if the probe is near the wall. In the present study we
found decreasing areas when the probe was moved up in the trachea
(Table 4), and therefore the measurements may be more accurate than
indicated in Fig. 1.
The measurements in the bronchial tree supply a "functional"
cross-sectional area related to the total cross-section of the airway.
It is assumed that all airways at the same level behave like the airway
containing the probe. On the other hand, analysis of overall airway
behavior is necessary for determination of the overall flow limitation.
Nonhomogeneous emptying of the lungs will probably influence total flow
very little because as soon as flow limitation occurs in one airway,
flow through the others will speed up (21). Consequently, SI may be
large in one parallel airway and small in another one. SI determined by
the present method is a weighted value that assumes that all parallel
airways behave similarly. In the present study, the asthmatic and the
healthy subjects did not differ a great deal, and we believe that
nonhomogeneous emptying is of minor importance for the interpretation
of the results of the bronchial measurements.
Another factor that may influence interpretation is that the probe will
move toward the periphery during the expiration, when the airways
shorten. This was examined by having the subjects perform a slow vital
capacity expiration with the bronchoscope in a fixed position. The
relative motion was less than the distance between two cartilage rings.
With the probe in a very peripheral position, Ptm includes
transparenchymal pressure, and we do not know the significance of this.
In the present study all positions were extrapulmonary, but
intrathoracic. Therefore, we believe that the measured Ptm reflects
transmural pressure only.
Interpretation of results.
We believe that PEF is reached when SI equals one for the first time
somewhere in the airway, and we define the flow-determining site as the
most upstream point in the airway where this happens. In theory, SI at
PEF cannot be >1 because at supracritical velocities (SI > 1) flow
becomes less than maximal (16) and hence less than flow at an SI of one
that necessarily must precede flow at SI > 1. Later, during the
expiration, the velocity may become supracritical, but only downstream
of the flow-determining site. With this in mind, we found it
justifiable to discard values of SI > 1.3 at PEF.
Repeated measurements of the same subjects at the same positions showed
a large variation of SI. However, the performance varied greatly
between individual tests, which is only natural because of the
inconvenience of the catheters. This is reflected in a large
variability of Pca, Caw, and A, which
are all determinants of SI (Eq. 15 in
Table 1). This was especially marked when Pca < 1.3. Typical problems
were coughing by subjects, mucus blocking the holes of the probe, and
occasional wedging of the probe, especially at the most peripheral
positions. Because Caw was determined as a quotient of two slopes, it
is especially sensitive to noise in the measurement. As seen in Figs.
4, 5, 6, SI changes rapidly near PEF, which means that small changes
in flow around PEF are associated with large changes in SI. This is an
additional source of variation. With the given coefficient of
variation, we estimated that a measured SI > 0.9 would not be
different from an SI of one.
Despite the technical difficulties, the results in Figs. 4, 5, 6
clearly support the hypothesis that SI at PEF in the central airways in
a normal subject is very close to unity. This means that at PEF the air
velocity reaches wave speed. We also found that with submaximal effort,
SI at PEF will be <1, when the peak of flow occurs before the
perimeter of the maximum expiratory flow-volume curve is reached. With
slightly less initial effort, the peak in Fig. 5 (defined as the
maximum flow during the expiration) might have been reached at the
perimeter where SI equals one, but at a much lower lung volume. PEF is
clearly effort dependent, but if it is reached at the perimeter of the
maximum expiratory flow-volume curve, it is determined by the wave
speed.
The fact that PEF is close to wave-speed flow in the central airways
does not necessarily imply that the flow is determined in the central
airways. We believe that PEF is reached at the moment when air velocity
for the first time during the expiration just reaches wave speed at
some point in the airway, i.e., before dynamic compression occurs and
before frictional pressure losses because of dynamic compression can be
detected. If the flow-determining site is defined as the most upstream
point in the airway where SI first becomes unity, we cannot be sure
that we have reached the flow-determining site with the probe, even if
SI equals one.
There may be two reasons for a local SI < 1 at PEF. First, the effort
may be too small so that wave speed is not reached anywhere in the
airway. In the case of flow limitation at PEF, we saw that PA continued to increase after
PEF was reached (Fig. 4). The explanation for this is that
when flow limitation occurs, the resistance
(PA/) and the driving
pressure (PA) increase
proportionally, keeping unchanged at the given lung
volume. If we consider a short interval encompassing PEF, then the
volume will not change very much within that interval, and we can
consider the pressure-flow curve within the interval equal to a segment
of an isovolume pressure-flow curve. If this curve has a maximum at
PEF, so that decreases for increasing pressure after
PEF is reached, then PEF can be considered a maximal flow. If we expand
the interval around PEF, the decrease of after PEF
is related to the decrease in maximum flow with volume.
If PEF is reached with submaximal effort and no flow limitation, this
phenomenon will not take place. When
declines after PEF is reached, pressure
will also decrease like in a stiff tube. However, as the resistance of
the airways increases with decreasing lung volume, the curve in Fig. 5
will not completely follow the same path down. When the decreasing
eventually reaches the flow-volume perimeter
(arrow), SI becomes unity. Flow and pressure will no longer be in
phase, and flow decreases more rapidly than pressure.
The reason why previous investigators did not find flow limitation at
PEF may have to do with the definition of flow limitation. According to
the classic definition, flow limitation occurs when flow reaches the
maximum or plateau of an isovolume pressure-flow curve. It is very
difficult to construct isovolume pressure-flow curves near TLC, and
flow limitation at PEF is difficult to demonstrate in this way. Fry and
Hyatt (7), however, believed that if a subject is able to create a
sufficient intrathoracic pressure, such a maximum could be
demonstrated. In the present study, assuming that flow limitation
occurs at wave speed, we can get around this problem because SI can be
determined during the actual forced expiration.
As pointed out by Fry and Hyatt (7), the addition of an external
resistance will move the maxima of the isovolume pressure-flow curves
toward higher pressures. Addition of an external resistance may
therefore lead to insufficient pressure for maximal flow. This is
illustrated in Fig. 8 (O. F. Pedersen,
unpublished observations), where data in
A and
B were obtained in a healthy subject
performing forced expirations through a 13- and a 6.5-mm
orifice, respectively. The subject was sitting in a volume-displacement
body plethysmograph equipped to measure
PA. In Fig. 8,
C and
D, similar curves were obtained with a
servo-controlled piston pump replacing the subject. In the piston pump,
dynamic compression cannot occur, and the pressure-flow curves are
alone determined by the two orifices and the driving pressures. For the
human subject blowing through the 13-mm orifice, peak flow occurs
before peak pressure, indicating dynamic compression at PEF. The 6.5-mm
orifice, however, imposes a resistance so large that flow limitation is
not reached at PEF. The flow follows closely the pressure-flow curve of
the orifice. Peak flow and peak pressure are reached simultaneously,
just as with use of the piston pump. With decreasing flow after PEF,
flow initially follows the pressure-flow curve for the orifice, but at
some point dynamic compression of the airways or volume-related changes
in the airways cause the resistance to increase and flow to deviate
from the curve for the orifice. At the point where the flow-volume
curve indicates flow limitation, the deviation is marked. The pattern
in Fig. 5 is not as clear but indicates the same phenomenon. We
therefore believe that when PA
continues to increase markedly after PEF is reached, it is a sign of
flow limitation at PEF somewhere in the airway, whereas simultaneous pressure and flow peaks indicate that flow limitation at PEF may not
have occurred.
The second reason for SI < 1 at PEF may be that the flow-determining site is not within reach of the probe. We found SI < 1 at all positions in some subjects, mostly asthmatic subjects. This could be explained by a location of the flow-determining segment peripheral to the most upstream position of the probe. In that case, SI at the probe may be <1 but the PA will continue to rise after PEF is reached, as we found for all subjects in Fig. 7. The finding that the upstream Pfr was not increased in these cases is probably because of PEF just being reached and dynamic compression not yet having been fully established. The huff curves (Fig. 6) show that SI equals one not only at the first peak corresponding to PEF but also at subsequent peaks. The PA-flow curves indicate flow limitation at the three last peaks, but not clearly at the first two peaks at the higher lung volumes, where inspiration was initiated as soon as flow became maximal. Figure 6 also shows that the relationship between A and Ptm, i.e, the "tube law," is volume dependent, mostly at higher lung volumes. For a given Ptm, A becomes smaller with decreasing volume, and the slope of the curve becomes smaller. This is in agreement with the findings of Macklem and Wilson (14). The smaller A with decreasing lung volumes could be explained by decrease of dilating forces because of changes in axial tension, and the smaller compliance by stiffening of the airways when the cartilages approach each other with shortening of the airways, as shown for calf tracheae (22). Figure 7 shows that the position of the highest measured SI, which most closely reflects the flow-determining site at PEF, is not different between healthy and asthmatic subjects, although SI appears smaller in the asthmatic subjects, in whom there is a slight tendency for a more peripheral location. Table 3 shows that this smaller SI most likely is because of a smaller Caw (Eq. 15 in Table 1), but Table 4, which also includes data for positions with less than maximal SI, does not support this. Table 4 displays some significant differences between the healthy and the ashmatic subjects. In the following we try to explain these differences. If, as a first approach, we assume that flow is determined in the central airways in both groups, the following differences are consistent: a smaller Pel and a larger Pfr in the asthmatic subjects will decrease J (Table 1, Eq. 7), and a decreased J will decrease the maximal flow via a decreased Ptm, leading to a smaller A. The finding of a larger driving pressure (PA = Ppl + Pel) at PEF in the asthmatic subjects is interesting and contrary to what should immediately be expected. Studies by Campbell et al. in 1957 (3) clearly indicated that airway obstruction with flow limitation caused the esophageal pressure at PEF (maximal effective intrathoracic pressure) to decrease. This is supported by studies of flow maxima of isovolume pressure-flow curves of Potter et al. (17). On the other hand, increased downstream resistance will increase PA at PEF by moving the flow maxima toward higher pressures (7). In that case, an increased PA at PEF in the asthmatic subjects would most likely be because of an increased downstream pressure drop due to dissipation of the excess pressure, but this could not be demonstrated. The downstream resistance, however, was slightly, although not significantly, larger in the asthmatic subjects (P = 0.07). Because of the difficulties in determining Caw, especially in the healthy subjects, with a larger fraction of negative values, a proper statistical evaluation of Caw could not be performed, and it could not be determined whether the finding of the lower SI in Table 3 could be because of a generally lower Caw among the stable asthmatic subjects. Stiffer central airways could explain not only smaller SI but also a more upstream location of the flow-determining sites in the asthmatic subjects compared with the healthy subjects, findings that were only indicated in the present study. It is noteworthy that Pfr upstream of the most peripheral positions and the pressures here were identical in the two groups of subjects and that the differences between the groups only became evident at more downstream positions (Table 4). Therefore, peripheral airway obstruction is unlikely to play a part in the observed difference between the groups. The slightly smaller Pel, however, might contribute. The smaller Pel found at PEF for the asthmatic subjects in the multivariate analysis could be because of a larger expired volume at PEF. Table 4 showed that, when the value is measured in absolute terms, this was not the case. Measured relative to FVC, the fraction was 0.14 ± 0.05 in the healthy subjects and 0.15 ± 0.04 in the asthmatic subjects. This is very close to the median value in a population study by Lebowitz et al. (12). The absence of a difference in volume to PEF indicates that the smaller Pel in the asthmatic subjects most likely is because of other factors. A possible explanation could be related to the bronchodilator treatment and subsequent relaxation of the alveolar ducts (25) or maximal bronchodilatation (4, 5). In our attempt to compare asthmatic subjects with healthy subjects, we realize that the interpretation might have been easier if the healthy subjects had also received bronchodilator treatment, but the present study design was chosen to give a more realistic comparison. It is interesting that SI at PEF can be close to one at many locations in the airway, even at different lung volumes. This may be more than a coincidence because in that way local strain is minimized and the airways are better protected against damaging effects of severe local dynamic compression. Evolution may have played a part by favoring airways with the most appropriate structure. Modeling of expiratory flow. Lambert et al. (11) made a fluid mechanical analysis of the maximum expiratory flow. The analysis was partly based on airway properties obtained from excised human lungs and partly from data of Weibel (27). They predicted that the most proximal locations of the flow-determining site at high lung volumes were in the main or lobar bronchi and that Ptm at flow limitation would be slightly positive or close to zero. This means that the flow-determining sites were upstream to or at the equal pressure points. We found that at PEF the SI was equal to unity in the trachea in most cases, supporting flow limitation in the trachea, but we could not exclude that SI would be unity also at more upstream locations. We found Caws different from those, on which the computational model was based. Contrary to our expectations, we did not find that the compliance at PEF increased significantly with peripheral motion of the probe, but Ptm increased. At Ptm measured in our study, the Caw read from the curves presented by Lambert et al. (11) had almost the same value in the trachea, but in the lobar bronchi it was much larger. This may explain why they did not find flow limitation in the trachea at high lung volumes but in the bronchi instead (cf. Eq. 15 in Table 1). Other factors may contribute: our curves were measured during dynamic conditions, in which invagination of the membranous parts of the airways and axial tension may change the A-Ptm curves in a way that is not accounted for in the model. Main conclusions and implications. The main conclusion of the present work is that when PEF is reached the SI is close to unity in the central airways of most subjects. Among those with SI < 1 in the measured airways (mostly asthmatic subjects), the shape of the PA-flow curves usually indicated that flow limitation at PEF took place at some point in the airway. This may be in more peripheral airways, beyond the reach of the probe. Therefore, this work supports that PEF in general is determined by the wave-speed flow-limiting mechanism. If PEF is obtained with submaximal effort, it is determined by the wave-speed flow-limiting mechanism, if PEF is reached at the perimeter of the maximum expiratory flow-volume curve. These findings have consequences for the interpretation of PEF. If PEF is determined by the wave-speed flow-limiting mechanism, it will be determined by three main factors: Pel, upstream Pfr, and relationship between distending pressure (Ptm) and A at the most upstream positions where SI equals one. PEF will be large when Pel is large, Pfr is small, A is large, and Caw is small. PEF will increase with increasing effort because wave speed is reached at a higher lung volume (higher Pel and smaller upstream Pfr). In the present study, stable asthmatic subjects had smaller maximum SI in the measured airways than did healthy subjects. This might be related to decreased Caw, but this could not be confirmed.
ACKNOWLEDGEMENTS
T. F. Pedersen is acknowledged for Asyst programming that made the study possible, and Dr. Neil Pride is acknowledged for contribution of valuable literature references. Drs. H. Matthys and B. Thiessen are acknowledged for their contribution to the very first studies in Freiburg, Germany, in 1979.
FOOTNOTES
Address for reprint requests: O. F. Pedersen, Institute of Environmental and Occupational Medicine, Bldg. 180, Univ. of Aarhus, DK-8000 Aarhus N, Denmark (E-mail: ofp{at}mil.aau.dk).
Received 14 February 1997; accepted in final form 15 July 1997.
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