J Appl Physiol 96: 137–142, 2004;
10.1152/japplphysiol.00504.2003.
Deep breath reversal and exponential return of
methacholine-induced obstruction in asthmatic and nonasthmatic subjects
Andrew C. Jackson,1 Margaret M. Murphy,1 John Rassulo,2
Bartolome R. Celli,2 and Roland H. Ingram, Jr.3
1
Biomedical Engineering Department, Boston University, Boston 02215; 2Pulmonary and Critical Care Medicine,
St. Elizabeth’s Hospital, Boston, Massachusetts 02135; and 3Emory University, Atlanta, Georgia 30365
Submitted 13 May 2003; accepted in final form 9 September 2003
that airways in asthmatic
subjects are hyperresponsive to bronchial provocation compared with nonasthmatic subjects. It is also well accepted that
nonasthmatic and asthmatic subjects respond differently to a
deep breath (DB) during induced obstruction, but the magnitude of the asthmatic subject response has been controversial.
In healthy subjects with experimentally induced airway obstruction, a DB transiently reverses the obstruction (e.g., Refs.
1, 14). In asthmatic subjects with experimentally induced
obstruction, a DB has been said to transiently reduce the
obstruction (9, 14) or to have little if any effect (4, 15). The
underlying mechanisms(s) responsible for airway hyperresponsiveness in asthmatic subjects as well as the differences in their
DB responses have not been well elucidated. Possible candidate mechanisms include ones that are based on mechanical,
biochemical, and/or neurological processes, the dynamics of
which can theoretically be described by differential equations
of some order of complexity. Evidence of the complexity of
these mechanisms, although not necessarily the nature of the
mechanism, could be provided by the response of the system to
disturbances in the time and/or frequency domain.
Two studies have reported the transient changes in airway
caliber after a DB, i.e., a time-domain response (9, 14). Lim et
al. (9) reported that, after a DB, asthmatic subjects who were
pharmacologically obstructed had an immediate decrease in
airway caliber followed by a rapid, exponential reestablishment of baseline airway caliber. Changes in airway caliber
were quantified once every 5–10 s for 2 min after the DB by
using plethysmographically determined specific airway conductance. More recently, Pellegrino et al. (14) studied the time
course of changes in lung resistance after a DB in asthmatic
and nonasthmatic subjects who were experimentally bronchoconstricted. They reported that lung resistance dramatically
and consistently decreased in both groups. However, they
reported that the recovery of the bronchoconstriction was a
linear function of time and that the slope of the lung resistance
vs. time plot was steeper in the asthmatic compared with the
nonasthmatic subjects. Pellegrino and coworkers made measurements for only 1 min after the DB, which was not long
enough to determine whether lung resistance vs. time was truly
exponential, as reported by Lim et al. Because of the relative
short time of the post-DB measurements in the Pellegrino
study, they were unable to determine the longer term consequences of the DB, i.e., whether the level of constriction after
the DB was less than, greater than, or equivalent to the pre-DB
level. More recently, Jensen et al. (5) reported airway resistance (Raw) after a DB with high time resolution (8 Hz) in
methacholine (MCh)-obstructed asthmatic subjects and healthy
subjects. Like Pellegrino et al. and Lim et al., they reported that
the post-DB recovery of Raw occurred faster in the asthmatic
subjects. However, they did not monitor Raw for a long enough
period (only for several breaths, or ⬃15–20 s) to establish
whether the recovery was linear or exponential.
The goal of the present study is to measure Raw in nonasthmatic and asthmatic subjects with pharmacologically induced
obstruction before and after a DB. The transient changes in
airway caliber were determined by making post-DB measurements with sufficient time resolution to determine how quickly
the constriction returned and for a long enough period to
determine whether the constriction returned to a greater, lesser,
Address for reprint requests and other correspondence: A. C. Jackson,
Biomedical Engineering Dept., Boston Univ., 44 Cummington St., Boston,
MA 02215 (E-mail: [email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked “advertisement”
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
airway resistance; transfer impedance; respiratory system impedance
IT HAS BEEN WELL DEMONSTRATED
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Jackson, Andrew C., Margaret M. Murphy, John Rassulo,
Bartolome R. Celli, and Roland H. Ingram, Jr. Deep breath
reversal and exponential return of methacholine-induced obstruction
in asthmatic and nonasthmatic subjects. J Appl Physiol 96: 137–142,
2004; 10.1152/japplphysiol.00504.2003.—A deep breath (DB) during
induced obstruction results in a transient reversal with a return to
pre-DB levels in both asthmatic and nonasthmatic subjects. The time
course of this transient recovery has been reported to be exponential
by one group but linear by another group. In the present study, we
estimated airway resistance (Raw) from measurements of respiratory
system transfer impedance before and after a DB. Nine healthy
subjects and nine asthmatic subjects were studied at their maximum
response during a methacholine challenge. In all subjects, the DB
resulted in a rapid decrease in Raw, which then returned to pre-DB
levels. This recovery was well fit with a monoexponential function in
both groups, and the time constant was significantly smaller in the
asthmatic than the nonasthmatic subjects (11.6 ⫾ 5.0 and 35.1 ⫾
15.9 s, respectively). Obstruction was completely reversed in the
nonasthmatic subjects (pre- and postchallenge mean Raw immediately
after the DB were 2.03 ⫾ 0.66 and 2.06 ⫾ 0.68 cmH2O䡠l⫺1 䡠s,
respectively), whereas in the asthmatic subjects complete reversal did
not occur (2.29 ⫾ 0.78 and 4.84 ⫾ 2.64 cmH2O䡠l⫺1 䡠s, respectively).
Raw after the DB returned to postchallenge, pre-DB values in the
nonasthmatic subjects (3.78 ⫾ 1.56 and 3.97 ⫾ 1.63 cmH2O䡠l⫺1 䡠s,
respectively), whereas in the asthmatic subjects it was higher but not
significantly so (9.19 ⫾ 4.95 and 7.14 ⫾ 3.56 cmH2O䡠l⫺1 䡠s, respectively). The monoexponential recovery suggests a first-order process
such as airway wall-parenchymal tissue interdependence or renewed
constriction of airway smooth muscle.
138
RESISTANCE AFTER A DEEP BREATH WITH INDUCED OBSTRUCTION
or equivalent level. The study included nine nonasthmatic
subjects and nine asthmatic subjects.
METHODS
Table 1. Subject physical data
Subject
Age,
yr
NA1
NA2
NA3
NA4
NA5
NA6
NA7
NA8
NA9
Means ⫾ SD
57
22
19
28
33
20
23
21
21
27⫾12
A1
A2
A3
A4
A5
A6
A7
A8
A9
Means ⫾ SD
26
29
24
26
38
25
25
20
20
26⫾5
Gender
Height,
cm
Weight,
kg
FRC,
liters
77
82
66
75
66
68
73
66
69
71⫾6
3.60
2.79
2.33
3.17
3.59
3.65
4.08
3.49
4.17
3.43⫾0.59
50
58
70
82
116
68
64
52
75
71⫾20
2.92
3.18
3.97
3.39
3.16
2.96
3.62
2.61
3.86
3.30⫾0.45
Nonasthmatic subjects
M
M
F
M
F
M
M
F
M
178
178
170
168
178
172
180
179
188
177⫾6
Asthmatic subjects
F
F
M
M
M
M
F
F
M
160
166
178
173
178
163
179
155
178
170⫾9
FRC, functional residual capacity.
J Appl Physiol • VOL
RESULTS
The baseline data indicate that the two groups were comparable in anthropometric terms (Table 1) and had equivalent
baseline Raw (Table 2). It is also apparent that the asthmatic
subjects had mild disease that was well controlled without
chronic medication.
MCh-induced changes in Raw. As expected, both groups
responded to MCh and the asthmatic subjects had a greater
degree of obstruction at all doses above 0.025 mg/ml as
determined by either FEV1 or Raw (Tables 2 and 3, respectively). All the nonasthmatic subjects received the maximum
MCh dose. Regarding the asthmatic subjects, the responses to
albuterol showed a return to baseline values in both groups.
The maximum dose of MCh was 2.5 mg/ml in two of the
asthmatic subjects (A1 and A2), 10 mg/ml in two subjects (A3
and A4), and 25 mg/ml in the remaining five subjects (A5, A6,
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Measurements were made on nine nonasthmatic subjects and nine
intermittent, mild asthmatic subjects (Table 1). The asthmatic subjects
were diagnosed and the level of disease was established on the basis
of criteria of the National Institutes of Health (12). The asthmatic
subjects were all clinically stable at the time of the measurements and
none had routinely used bronchodilators or steroids or had taken any
medication within 24 h before testing. The protocol was approved by
the Institutional Review Boards for Human Studies at Saint Elizabeth’s Medical Center and Boston University. All subjects completed
and signed an informed consent form.
Respiratory system transfer impedance measurement. Transfer impedance (Ztr) measurements were made while the subjects were seated in
a head-out partial body box with a partial seal around the neck (10). Two
loudspeakers were mounted on each side of the body chamber. The
speakers were driven with a broad-spectrum, pseudo-random forcing
function constructed of multiple sine waves (2–64 Hz, in 2-Hz increments) with equal magnitudes and randomized phases. Pressure within
the body box (Pbs) was measured with a pressure transducer (Sensym,
SCXL05). Flow at the airway opening (V̇ao) was determined by measuring the pressure drop across a screen-type pneumotachometer with a
pressure transducer (Sensym, SCXL05). The Pbs signal was amplified,
band-pass filtered (high-pass cutoff at 2 Hz and low-pass cutoff at 64 Hz),
and digitized with a sampling frequency of 256 Hz. The V̇ao signal was
filtered into two components representing the separate oscillatory (V̇osc)
and tidal flows (V̇tidal). The subjects’ V̇tidal was obtained by low-pass
filtering the measured flow signal (cutoff frequency at 2 Hz). The
V̇osc was obtained by band-pass filtering the measured flow signal
(high-pass cutoff at 2 Hz and low-pass cutoff at 64 Hz). The Pbs and
V̇osc signals were digitally compensated to match their magnitude
and phase responses as well as to compensate the analog-to-digital
multiplexer delay. Respiratory system Ztr was computed from the
Fourier transforms of the Pbs and V̇osc signals either by using the
method described by Michaelson et al. (11) or by computing the ratio
of Pbs(␻) (where ␻ is frequency in rad/s) and V̇osc(␻) for each
individual spectrum. The former method was used to analyze the
pre-DB Ztr in six 20-s blocks from which mean ⫾ SD of Raw was
computed. Because multiple estimates of Pre-DB Raw were made, we
were able to compare the baseline and post-MCh values for each dose
in each subject. The latter method was used to analyze Ztr after the
DB because Raw was time dependent owing to the recovery from the
DB. Because the major goal of this study was to examine the
characteristics of the transient response to the DB, Raw estimates with
the highest level of time resolution were used, i.e., from each individual spectrum.
System identification. Estimates of Raw were extracted from the Ztr
data by using system-identification methods described elsewhere (10).
The Ztr data were fit with the DuBois six-element model of the
respiratory system by using a global optimization procedure (3) that
minimized the root-mean-square error between the experimental data
and the model-predicted spectra. The six elements in this model are
Raw, airway inertance, gas compression compliance, tissue resistance
(Rti), tissue inertance, and tissue compliance (Cti).
Protocol. Ztr and spirometry were measured at baseline and after
inhalations of MCh in increasing doses (0.025, 0.25, 2.5, 10, and 25.0
mg/ml) separated by ⬃10-min intervals. Aerosolized MCh was administered with a pressure-activated dosimeter during five normal
tidal volumes. During baseline and after each MCh dose, the subjects
were instructed to breathe normally and not take a deep inhalation
until Ztr had been measured for 2 min. After this 2-min period, the
subjects were instructed to inspire slowly to total lung capacity then
relax to functional residual capacity and continue to breathe normally
while the Ztr measurements continued for another 2 min. The DB was
done slowly so that several measurements could be made during the
inspiratory and expiratory phases. Spirometric measurements were
made on completion of the Ztr measurements. If the subject’s forced
expiratory volume in 1 s (FEV1) did not decrease by ⬎20% from
baseline, the next higher dose of MCh was administered and the
measurement protocol was repeated. If the subject’s FEV1 did decrease by ⬎20%, no higher doses of MCh were administered and the
subject was treated with a fast-acting bronchodilator (3 ml of nebulized 0.083% albuterol) after the Ztr and spirometric measurements.
Statistical analysis. From Raw vs. time [Raw(t)] plots, glottal
closures were identified and manually removed. Glottal closures were
easily detected as points where Raw became exceedingly large (⬎3
standard deviations above the mean) and V̇tidal rapidly went to zero
for a short period of time. The Raw(t) data were low-pass filtered by
use of a 15-point running average (SigmaPlot, SPSS, Chicago, IL).
The Raw(t) transients after the DB were fit to a single exponential
function (see Eq. 1 below) by using SigmaPlot.
All results are presented as means ⫾ SD. Statistical significance
was determined by nonpaired or paired Student’s t-tests. Differences
between groups were considered statistically significant at P ⬍ 0.02.
139
RESISTANCE AFTER A DEEP BREATH WITH INDUCED OBSTRUCTION
Table 2. FEV1 as percent predicted at baseline and increasing doses of MCh as well as after albuterol
Subject
BL
0.025 mg/ml
NA1
NA2
NA3
NA4
NA5
NA6
NA7
NA8
NA9
Means ⫾ SD
96
82
100
125
98
80
97
112
98
99⫾14
96
79
98
124
102
81
95
111
97
98⫾14
0.25 mg/ml
2.5 mg/ml
10 mg/ml
25 mg/ml
Albuterol
94
76
93
124
97
78
92
99
90
94⫾14*†
91
76
87
122
93
77
93
95
90
92⫾13*†
96
82
96
109
95
93⫾10
72
59
59
78
68
67⫾8*†
117
91
98
70
84
74
81
92
81
88⫾14
Nonasthmatic subjects
96
88
100
126
100
81
95
111
95
99⫾13†
95
76
96
125
97
78
94
106
93
96⫾14*†
91
80
Asthmatic subjects
110
89
103
71
81
75
74
99
85
87⫾14
107
89
101
73
79
75
69
100
82
86⫾14
101
80
100
74
80
78
75
100
79
85⫾12†
72
71
90
60
79
66
73
99
82
77⫾12*†
82
50
74
64
69
88
72
71⫾12*†
FEV1, forced expiratory volume in 1 s; MCh, methacholine; BL, baseline. *Within group; significant difference (P ⬍ 0.02) compared with BL. †Between
groups; significant difference (P ⬍ 0.05) at same dose.
A7, A8, and A9). The responses to MCh, as measured by FEV1
and Raw, were compared as the percent change from baseline
where the asthmatic subjects were grouped by their maximum
MCh dose (Fig. 1). There was a significantly larger response in
the asthmatic subjects compared with the nonasthmatic subjects at the second and all higher MCh doses (Tables 2 and 3).
The relative magnitudes of the percent changes in Raw were
significantly larger compared with the percent changes in FEV1
at the second and all higher doses in both groups.
DB-induced changes in Raw. Figure 2 presents Raw after the
DB for one of the five asthmatic subjects who received the
highest MCh dose (A7), contrasted with a representative
nonasthmatic subject (NA1). There are several visual differences between the asthmatic subject’s DB response in Raw
compared with that of the nonasthmatic subject, including
that the magnitude of the response to MCh was greater;
there was much greater variability in Raw; the DB reversal
was greater in magnitude; and finally, the return to the
Table 3. Airway resistance at baseline and increasing doses of MCh as well as after albuterol
Subject
BL
0.025 mg/ml
0.25 mg/ml
2.5 mg/ml
10 mg/ml
25 mg/ml
Albuterol
2.67†
7.08†
3.06†
1.87
2.80†
4.81†
2.43†
4.63†
2.44†
3.53⫾1.66†
3.67†
6.67†
3.53†
2.34†
3.94†
6.52†
2.70†
4.12†
2.24†
3.97⫾1.63†
2.10†
1.30†
1.95⫾0.46
8.46†
12.90†
13.91†
5.00†
4.11†
8.88⫾4.46*†
1.79
1.73
1.24
2.72
3.68†
1.64†
3.27
1.99
1.85†
2.20⫾0.83
Nonasthmatic subjects
NA1
NA2
NA3
NA4
NA5
NA6
NA7
NA8
NA9
Means ⫾ SD
1.71
3.46
1.68
1.91
1.75
2.80
1.39
1.87
1.67
2.03⫾0.66
1.84
3.29
2.13†
1.77
2.19
2.83
1.45
1.91
1.50
2.10⫾0.44
1.66
3.71†
1.86†
1.59
2.05
2.73
1.94
1.95
1.49†
2.11⫾0.70†
1.85†
4.25†
1.91†
1.86
2.67†
4.23†
1.64†
2.85†
2.06†
2.59⫾1.02†
1.97†
2.67†
1.66
2.02†
Asthmatic subjects
A1
A2
A3
A4
A5
A6
A7
A8
A9
Means ⫾ SD
2.99
1.57
1.29
2.86
2.81
2.60
3.24
1.97
1.30
2.29⫾0.76
3.92†
2.12†
1.92†
3.76†
3.44†
2.42
3.34
2.09
1.77†
2.70⫾0.91†
6.66†
2.56†
3.16†
4.39†
6.10†
2.96
4.42†
2.06
2.42†
3.76⫾1.77*†
11.7†
3.15†
4.99†
7.50†
7.12†
5.22†
5.97†
2.10
1.65†
4.68⫾2.24*†
5.45†
6.34†
10.2†
10.5†
8.26
4.50†
2.46†
5.50⫾3.31*†
Airway resistance units are in cmH2O䡠l⫺1 䡠s. *Significantly different, P ⬍ 0.02, comparing between groups; †significantly different, P ⬍ 0.02, compared with
BL.
J Appl Physiol • VOL
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A1
A2
A3
A4
A5
A6
A7
A8
A9
Means ⫾ SD
140
RESISTANCE AFTER A DEEP BREATH WITH INDUCED OBSTRUCTION
Table 4. Parameters estimated by fitting Raw(t) data after
DB taken at maximum MCh dose with Eq. 1
Raw0, cm
H2O䡠l⫺1 䡠s⫺1
Subject
␶, (s)
Rawmax, cm
H2O䡠l⫺1 䡠s⫺1
Regress.
Coff.
4.08
7.07
3.78
2.79
2.31
5.00
2.11
4.08
2.79
3.78⫾1.56
0.94
0.87
0.83
0.78
0.93
0.88
0.83
0.93
0.69
0.85⫾0.08
12.3
4.31
N/A
7.25
12.9
14.2
15.1
4.14
3.29
9.19⫾4.9*
0.62
0.58
N/A
0.87
0.77
0.87
0.81
0.69
0.69
0.74⫾0.11
Nonasthmatic subjects
NA1
NA2
NA3
NA4
NA5
NA6
NA7
NA8
NA9
Means⫾SD
2.19
2.92
2.43
1.55
1.40
3.11
1.38
2.19
1.35
2.06⫾0.68
A1
A2
A3
A4
A5
A6
A7
A8
A9
Means ⫾ SD
7.89
2.60
N/A
4.35
4.70
6.34
8.82
1.87
2.14
4.84⫾2.63*
54.0
35.7
24.4
38.2
52.8
23.6
21.5
54.1
11.7
35.1⫾15.9
Asthmatic subjects
obstruction was faster. The similarities in the DB response
in the two groups was that Raw decreased immediately after
the DB and subsequently increased exponentially to a plateau. The Raw data after the DB were fit to a three-parameter
exponential equation
Raw(t) ⫽ Raw0 ⫹ A(1 ⫺ e
⫺t/␶
)
(1)
where Raw0 is an estimate of the minimum value of the
parameter immediately after the DB and ␶ is the time constant,
i.e., the time required for Raw to return to 67% of its maximum
level. The sum of Raw0 and A is the maximum Raw value that
is asymptotically approached with increasing time (Rawmax).
Fig. 2. Raw deep breath (DB) transients at maximum MCh dose in a nonasthmatic (NA1) and an asthmatic subject (A7) with fits to Eq. 1 and their mean
(⫾SD) pre-DB Raw.
J Appl Physiol • VOL
Raw (t), airway resistance (Raw) vs. time; Raw0, estimate of minimum Raw
value immediately after deep breath (DB); ␶, time constant; Rawmax, maximum
Raw value that is asymptotically approached with increasing time; Regress.
Coff., regression coefficient. In subject A3, transients after DB at maximum
MCh dose could not be reliably fit with exponential function. *Significantly
different, P ⬍ 0.02, between groups. All P values for the regression coefficients were ⬍0.001.
The Raw data were fit well with Eq. 1 in the nonasthmatic
subjects as well as the asthmatic subjects (regression coefficients, R ⫽ 0.85 ⫾ 0.08 and 0.74 ⫾ 0.11, respectively) (Table
4). There were significant differences in the mean ␶ (35.1 ⫾
15.9 and 11.6 ⫾ 05.0 s), Raw0 (2.06 ⫾ 0.68 and 4.84 ⫾ 2.63
cmH2O䡠l⫺1 䡠s), and Rawmax (3.78 ⫾ 1.56 and 9.19 ⫾ 4.9
cmH2O䡠l⫺1 䡠s) between the nonasthmatic and asthmatic subjects, respectively (Table 4). The transient response in one
asthmatic subject (A3) could not be fit with Eq. 1 because he
exhaled all the way to residual volume after the DB and his
Fig. 3. Raw (mean ⫾ SD) in nonasthmatic and asthmatic subjects: at baseline,
maximum MCh dose before DB, immediately after DB (Raw0), and the
maximum Raw value that is asymptotically approached with increasing time
(Rawmax).
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Fig. 1. Forced expiratory volume in 1 s (FEV1) and airway resistance (Raw)
as a function of methacholine (MCh) dose and albuterol as percent of baseline
(BL). Asthmatic subjects are grouped according to their maximum MCh dose.
5.8
12.6
N/A
12.5
7.14
11.4
11.7
9.35
22.2
11.6⫾5.0*
RESISTANCE AFTER A DEEP BREATH WITH INDUCED OBSTRUCTION
DISCUSSION
Pharmacologically induced obstruction in mild asthmatic
subjects is uniformly reversed by a DB, yet the time course for
reestablishing pre-DB resistance levels is quite rapid and
would likely have been missed if measurements were not made
almost continuously. It is probable that previous studies that
found no or minimal reversibility of induced obstruction in
asthmatic subjects failed to make sufficiently rapid measurements after the DB. The method used in the present study to
quantify changes in airway obstruction provides sufficient time
resolution to track the DB-induced transients. It is also
important to note that Raw extracted from Ztr data is significantly more sensitive to changes in airway caliber compared
with FEV1.
The more rapid return to pre-DB resistance levels that is
seen in asthmatic subjects compared with nonasthmatic subjects confirms the data of Pellegrino et al. (14) and Jensen et al.
(5). In contrast to the data of Pellegrino et al., which were
analyzed as a linear function of time, our data indicate an
exponential time course in both groups. The exponential time
course also agrees with the asthmatic reversibility data of Lim
et al. (9), as does the magnitude of the time constants.
Asthmatic smooth muscle has been shown to be hyperresponsive in terms of velocity of contraction (14), which fits
nicely with the time course differences between asthmatic
subjects and healthy subjects found in this study. Moreover, in
vitro measurements of airway smooth muscle shorting vs. time
reported by Jiang et al. (6) suggest a monoexponential process.
However, those data were from a canine model of allergic
airway hyperresponsiveness with artificial mechanical loads,
which gave much shorter time constants than seen in our
asthmatic subjects. The hyperresponsiveness of asthmatic airways, in general, is probably due to a complex interplay among
inflammation (cells, mediators, edema), airway geometry, and
neural factors, perhaps with some contribution by altered
smooth muscles. Any of these factors, as well as the load on
J Appl Physiol • VOL
airway smooth muscle due to mechanical interdependence with
parenchyma, could explain the delayed return to pre-DB levels
in our patients.
Our results indicate that a DB taken by obstructed nonasthmatic subjects totally and transiently reverses the obstruction,
but the obstruction is not totally reversed in asthmatic subjects,
which is in agreement with Jensen et al. (5). Peribronchial
edema has been proposed as a mechanism for decreasing the
degree of mechanical interdependence between airways and
parenchyma in asthmatic subjects. The failure to achieve complete
reversal at peak dilation in asthmatic subjects could represent
some degree of uncoupling. The complete reversal seen in nonasthmatic subjects could represent greater airway-parenchymal
interdependence compared with the asthmatic subjects.
A combination of elevated mechanical coupling and slower
smooth muscle shortening velocity could explain the uniformly
longer time constants found in nonasthmatic subjects; greater
smooth muscle velocity and a lesser degree of mechanical
interdependence in asthmatic subjects could explain their more
rapid reestablishment of pre-DB resistance levels.
The monoexponential recovery of obstruction suggests a
mechanism whose dynamics is described by a first-order differential equation or an overdamped second-order differential
equation. An example of a first-order mechanical system is one
consisting of a resistance and compliance in series. A possible
second-order mechanical system would be one consisting of a
series combination of a resistance, compliance, and inertance.
Airway wall and lung tissue interdependence could be a firstorder system if the effective resistance and compliance were
important, or it could be a second-order system if the effective
inertance was also important. Considering the magnitude of the
time constants as well as the low breathing frequencies, airway
wall mass or inertance is unlikely to be influential, which
suggests a first-order mechanical system. As discussed above,
the contraction of excised airway smooth muscle also exhibits
an exponential transient response. Therefore, return of smooth
muscle tone in response to MCh still present in the tissues or
a transient due to airway-parenchymal interdependence appears to be the most likely first-order process.
GRANTS
This study was funded by National Heart, Lung, and Blood Institute Grant
HL-65401.
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