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Deep breath reversal and exponential return of methacholine-induced obstruction in asthmatic and nonasthmatic subjects

¹Biomedical 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

	ABSTRACT

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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·l^-1·s, respectively), whereas in the asthmatic subjects complete reversal did not occur (2.29 ± 0.78 and 4.84 ± 2.64 cmH₂O·l^-1·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·l^-1·s, respectively), whereas in the asthmatic subjects it was higher but not significantly so (9.19 ± 4.95 and 7.14 ± 3.56 cmH₂O·l^-1·s, respectively). The monoexponential recovery suggests a first-order process such as airway wall-parenchymal tissue interdependence or renewed constriction of airway smooth muscle.

airway resistance; transfer impedance; respiratory system impedance

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, or equivalent level. The study included nine nonasthmatic subjects and nine asthmatic subjects.

	METHODS

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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 (ao) 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 ao signal was filtered into two components representing the separate oscillatory (osc) and tidal flows (tidal). The subjects' tidal was obtained by low-pass filtering the measured flow signal (cutoff frequency at 2 Hz). The osc 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 osc 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 osc 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 osc() 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 tidal 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.

	RESULTS

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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, 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.

View larger version (25K): [in this window] [in a new window]   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.

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 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

(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 (Raw_max).

View larger version (32K): [in this window] [in a new window]   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.

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·l^-1·s), and Raw_max (3.78 ± 1.56 and 9.19 ± 4.9 cmH₂O·l^-1·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 Raw immediately returned to the pre-DB level. The data in Tables 3 and 4 are summarized in Fig. 3. As noted above, there was no significant difference in baseline Raw in the two groups. Pre-DB Raw at the maximum MCh dose was significantly higher in the asthmatic compared with the nonasthmatic subjects. The DB in both groups resulted in a significant decrease in Raw. The mean Raw₀ in the nonasthmatic subjects was not significantly different from their baseline values, whereas in the asthmatic subjects Raw₀ was still significantly elevated compared with their baseline values. After the DB, Raw in the nonasthmatic subjects returned to a mean value (Raw_max) that was not significantly different from their pre-DB Raw, whereas in the asthmatic subjects it was higher than the pre-DB Raw, although this difference was not significant.

View larger version (18K): [in this window] [in a new window]   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).

Changes in other parameters of the six-element model. The only parameters of clinical interest other than Raw are Rti and Cti. Because the resonant frequency of most subjects occurred at such low frequencies, there were only one or two frequencies below the resonant frequency, and as a consequence reliable estimates of Cti were not obtained. Reliable estimates of Rti were obtained, but the changes due to MCh, a DB, and the bronchodilator were inconsistent and relatively small, and thus we have not included Rti or Cti data.

	DISCUSSION

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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 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 first-order 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.

	ACKNOWLEDGMENTS

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GRANTS

This study was funded by National Heart, Lung, and Blood Institute Grant HL-65401.

	FOOTNOTES

 

Address for reprint requests and other correspondence: A. C. Jackson, Biomedical Engineering Dept., Boston Univ., 44 Cummington St., Boston, MA 02215 (E-mail: ajax{at}bu.edu).

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.

	REFERENCES

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