INTRODUCTION

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Recently, we successfully partitioned airway resistance (Raw) and lung tissue resistance (Rti) from total lung resistance (RL) and elastance (EL) data in healthy humans before and after methacholine-induced bronchoconstriction (1). Our approach was to measure lung impedance over several frequencies surrounding the breathing rate. Because the airway and lung tissue impedances have distinct frequency responses, it is possible to partition Raw and Rti noninvasively using this technique (2). We reported that in healthy humans, Rti constituted approximately 40% of total RL, including upper airway structures. This estimate is much higher than that previously reported in plethysmographic studies of humans (3, 4). Moreover, during methacholine-induced bronchoconstriction in healthy humans, our data suggest that changes in Raw are responsible for most of the increase seen in RL. This contrasts with alveolar capsule studies in animals, which have reported that the increase in Rti may be equal to or greater than the increase in Raw during bronchoprovocation (5, 6).

Asthma is considered to be an inflammatory airway disease. However, the relative contributions of the airways and lung tissues to the changes seen in RL and EL in asthma have not been well characterized. The lung tissues comprise most of the intrathoracic resistance in healthy lungs (1). A reasonable concern is whether Rti becomes elevated in asthma or whether it varies with the severity of obstruction and inflammation. Plethysmographic studies in asthmatics have suggested that Rti is higher than that in healthy subjects (7). However, plethysmography can be prone to significant error because of thermal effects (10), and factors such as serial and parallel airway heterogeneity may confound the partitioning of airway and tissue properties with this technique, particularly at physiologic breathing frequencies (11). Information about the magnitudes of Raw and Rti in asthma may be useful to distinguish between asthmatics whose disease involves primarily airway smooth muscle constriction from those with a more inflammatory component that may alter the mechanical properties of the lung tissues.

The goal of this present study was to determine the relative contributions of Raw and Rti to RL in asthmatics with varying degrees of obstruction at baseline, and how these properties change after bronchodilation with albuterol. In addition, we examined whether changes in our estimates of airway and tissue mechanical properties after bronchodilation could be correlated with traditional spirometric and plethysmographic measurements of lung function.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Subjects

Measurements were made in 21 asthmatic subjects (9 male and 12 female) at baseline and after -agonist-induced bronchodilation. Inclusion criteria were a prior clinical diagnosis of asthma by a physician, current use of an inhaled bronchodilator at least once per day, and a FEV₁  90% of predicted or FEV₁/FVC  85% on the day of the study. Subjects ranged from 18 to 49 yr of age (29 ± 10 yr). Nine of the 21 subjects received combination inhaled corticosteriods and ₂-selective agonists daily (one of them also received cromyln sodium), and the other 12 received -agonists alone. Subjects were asked to abstain from inhaled corticosteriods for 24 h before measurements, and from inhaled -agonists and caffeine for at least 6 h. The study was approved by our institutional research committees, and informed consent was obtained from each subject. Physical data, current medications, and baseline FEV₁ values for all patients are presented in Table 1. All subjects were nonsmokers with the exception of Subjects 11, 19, and 21, who were occasional smokers.

Optimal Ventilator Waveform

To measure RL and EL, we used an optimal ventilator waveform (OVW), a broad-band flow input forcing designed to estimate lung impedance (ZL) while simultaneously delivering a volume consistent with tidal-like excursions (12). The energy of this waveform is concentrated only at specific frequencies such that the output pressure waveform is minimally distorted by nonlinearities. Three different OVWs were used in this study. Two of them (OVW-A and OVW-B) have been described previously (1). Both of these waveforms contain energy from 0.156 to 8.1 Hz, but they differ by where the maximum energy is placed. The frequency of maximum energy determines the physiologic breathing rate for the subject. This breathing rate occurs at 0.156 Hz in OVW-A and at 0.391 Hz in OVW-B. Both of these OVWs were periodic over 12.8 s. For the newer OVW-C, the primary physiologic breathing rate was located at 0.43 Hz, with lower frequency modulations at 0.078 and 0.195 Hz. Although this waveform did allow us to probe the mechanics at a lower frequency than either OVW-A or -B, it was periodic over 25.6 s. Thus, it required considerably longer subject cooperation time (see PROTOCOL section below).

Experimental Measurements

The experimental system was used to generate the OVW flow forcings has been described previously (1). Briefly, a discretized OVW displacement (volume) signal was generated from a D/A board (Data Translations DT-2811, Marlboro, MA) at a shift frequency of 40 Hz. The volume signal was low-pass-filtered at 10 Hz (4 pole Butterworth; Frequency Devices, Haverhill, MA) and presented to a servo-amplifier that drove a linear motor (Infomag Model 15, Goleta, CA) connected to a piston/cylinder arrangement. After passing through a soda lime scrubber, the airway flow was measured with a pneumotachograph (Model 4700A; Hans Rulolph, Kansas City, MO) connected to a Celesco pressure transducer (Model LCVR, 0-2 cm H₂O; Celesco Instruments, Canoga Park, CA). Esophageal pressure was obtained with a 10-cm latex balloon containing ~ 0.5 ml air and positioned in the lower half of the esophagus. Transpulmonary pressure was estimated as the difference between airway opening and esophageal pressures measured across a single Celesco 0-50 cm H₂O LCVR pressure transducer. All signals were low-pass-filtered at 10 Hz (4 pole Butterworth; Frequency Devices) and sampled at 40 Hz (Data Translations DT-2811 A/D board). The phase distortion caused by sampling delays between A/D channels was corrected in real-time by a third-order Lagrange polynomial interpolation technique (13). A small bias flow of 100% O₂ (about 0.5 L/min) was introduced into the pump to compensate for leaks in the system. This bias flow and soda lime scrubber helped prevent stimulation of breathing because of hypercapnia and/ or hypoxia.

Protocol

Prior to placing the esophageal balloon, baseline values of FEV₁ were measured, after which a 15- to 20-min training period on the OVW system was allowed so that the subject would become accustomed to relaxing their respiratory muscles during the flow forcing. During this training period, airway pressure was closely monitored on an oscilloscope since this signal would become highly erratic if any breathing efforts were made by the subject. The training period also allowed us to establish which OVW (A, B, or C) was the most comfortable for the subject. Usually only one OVW was applied to a given asthmatic subject after the esophageal balloon was placed, but we previously confirmed that all three OVWs produced consistent results in two healthy control subjects.

The nasopharynx of each subject was then anesthetized with atomized lidocaine (1%), and the esophageal balloon was inserted transnasally and positioned in the lower half of the esophagus. Each subject sat in a chair positioned slightly away from vertical to facilitate relaxation of the chest wall muscles. After a few breaths, the subject exhaled passively to FRC and placed the mouth tightly around a mouthpiece while firmly supporting the cheeks. The linear motor was then started such that the subject received an OVW inspiration from FRC. Most subjects could remain fairly confortable on the system for 60 to 90 s. Two to three separate OVW measurements were made at baseline, after which two puffs of aerosolized albuterol were administered. After 2 min, two to three more OVW measurements were made. The esophageal balloon was then removed and spirometry repeated.

In seven of the subjects, prealbuterol and postalbuterol estimates of Raw were obtained using standard pressure plethysmography (BP/ PLUS; Warren E. Collins, Braintree, MA) during panting (rates of 1.0 to 1.5 Hz). The plethysmographic measurements were made just prior to the balloon insertion and immediately after the balloon withdrawl.

Data Processing

Total lung impedance (ZL) is defined as the complex ratio of transpulmonary pressure to flow as a function of frequency (f). The ZL and its coherence function (²) were determined using the approach described by Daroczy and Hantos (14). The ZL spectra were computed using either a 12.8-s rectangular window (for OVW-A and OVW-B) or a 25.6-s rectangular window (for OVW-C), both with 83% overlap. After neglecting the first three transient breaths in the data record, between four and 12 overlapping windows were used to calculate ZL for each subject. The total lung resistance was thus determined as the real (Re) part of ZL only at those frequency f_k where input flow energy was placed: RL(f_k) = Re[ZL(f_k)]. The effective lung elastance was calculated from the imaginary (Im) part: EL(f_k) = 2 f_k Im[ZL(f_k)]*. For several subjects, energy from cardiogenic oscillations in the esophageal pressure signal often corrupted one or more frequencies between 1 and 3 Hz. Typically, any frequency point for which ² < 0.95 was discarded.

Data Analysis

Airway and tissue properties were partitioned by model analysis of the ZL data. In relatively healthy lungs, these data are very well described by a simple model in which a homogeneous and rigid airway compartment containing an airway resistance (Raw) and inertance (Iaw) leads to a viscoelastic tissue compartment (Figure 1A) (1, 16, 17). The tissues are characterized by two properties: a tissue damping (G) and a tissue elastance (H), such that Rti and dynamic EL (Edyn) are given by:

(1)

View larger version (13K): [in this window] [in a new window]   Figure 1.   Various pulmonary models used to describe lung impedance data in asthmatic subjects. (A) Homogeneous airway model consisting of a rigid-walled airway compartment with parameters for airway resistance (Raw) and inertia (Iaw) followed by a viscoelastic tissue compartment with parameters for tissue damping (G) and tissue elastance (H). The effective tissue resistance and dynamic elastance can be computed from G and H according to Equation 1. (B) Airway shunt model consisting of an additional parameter for airway wall compliance (Caw). (C ) Inhomogeneous airway model consisting of two separate airway pathways (Raw1 and Raw2), both leading to identical viscoelastic tissue compartments. Each pathway shares a common Iaw. (D) Interregional flow model with an additional collateral resistance (Rcol) in parallel with the tissues.

where  = (2/)tan¹(H/G) and tissue hysteresivity (18) is given by  = G/H. Partitioning ZL data into airway and tissue components with this approach provides results consistent with (or more accurate than) data obtained from alveolar capsules, even after inducing mild-to-moderate bronchoconstriction (2, 17).

During asthmatic conditions, different patterns of airway obstruction can result in additional frequency dependence of RL and EL that is not due solely to the tissue viscoelasticity described by Equation 1. With severe peripheral airway obstruction, the flow may be shunted into the central airway walls, which results in an excessive positive frequency dependence in EL (1, 19, 20). In this case, more accurate partitioning of airway and tissue properties is achieved by modifying the model of Figure 1A such that the homogeneous airway compartment is no longer considered rigid and now includes a shunt airway wall compliance (Caw) (Figure 1B) (1). When ZL data are influenced by airway wall shunting, applying the homogeneous rigid airways model would cause an artifactual increase in the estimated tissue damping (1).

In theory, two other airway mechanisms can contribute to frequency dependence of RL and EL: parallel constriction inhomogeneities (21) and collateral ventilation (22, 23). To compensate for parallel inhomogeneities, the model of Figure 1A could also be modified to contain two separate airway resistance pathways, both leading to identical viscoelastic tissue compartments (Figure 1C). To investigate effects of collateral ventilation on RL and EL, one could use the model recently proposed by Hantos and colleagues (23) (Figure 1D), which adds an additional collateral resistance (Rcol) in parallel with the tissue compartment to account for interregional flows.

In our previous study (1), only the airway shunt model was necessary to describe the ZL data after induced constriction in healthy subjects. Nevertheless, for each ZL data set in the present study, the parameters of all models were estimated using a nonlinear gradient search technique that minimized the sum of squared differences between the actual ZL and model predicted ZL (24). All model fits were performed both with and without inclusion of the inertial parameter Iaw. The relevant model for a given ZL data set was established by either: (1) choosing the model with the minimum root mean squared error for models with equal number of parameters; or (2) using paired F tests for models with a different number of parameters (25). We considered only those model fits in which all parameters were physically sensible (i.e., positive).

Statistical Analysis

The results will indicate that two distinct groups of asthmatics were observed. A one-way analysis of variance (ANOVA) of three levels was used to compare airway and lung tissue parameter values among the two groups (during either their baseline asthmatic state or after albuterol inhalation) along with a healthy control group whose data were reported previously (1). If significance was obtained with ANOVA, post hoc analysis using the Tukey HSD procedure was performed (26). Within each asthmatic group, parameter comparisons (prealbuterol and postalbuterol) were made using two-tailed paired t tests; p < 0.05 was considered statistically significant.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Two distinct patterns of RL and EL were observed in these asthmatic subjects. Representative examples from each of the two patterns are shown in Figure 2. Eleven of the subjects were classified as Type A asthmatics since they demonstrated EL data typical of healthy subjects (1), with EL becoming negative at higher frequencies because of the effects of airway inertia. However, their RL was mildly elevated compared with that in healthy subjects (1). After albuterol inhalation in Type A subjects, RL decreased at all frequencies, but EL showed no change. The other 10 subjects, classified as Type B asthmatics, demonstrated a baseline EL that increased sharply with increasing frequency, especially over the range of 2 to 8 Hz. In addition, their baseline RL was far more elevated at all frequencies compared with the Type A subjects. After albuterol inhalation in Type B subjects, the positive frequency dependence in EL disappeared, and RL decreased at all frequencies.

View larger version (20K): [in this window] [in a new window]   Figure 2.   Examples of RL and EL versus frequency for two representative types of asthmatics. Shown are the data before (open circles) and after (closed circles) albuterol inhalation, as well as the homogeneous airways (solid lines) and airway shunt (dashed lines) model fits.

For the Type A asthmatics, both their baseline and postalbuterol data were always best described by the homogeneous rigid airway model with the Iaw parameter, and applying any other model did not significantly improve the quality of fit. For the Type B subjects, the airway shunt model without Iaw always described the baseline data significantly better than any other model. For these subjects, inclusion of an Iaw parameter did not significantly improve the quality of the model fit to the baseline data. This is consistent with their EL data not showing any tendency to decrease with frequency even by 8 Hz (Figure 2). However after albuterol inhalation, the homogeneous airways model with Iaw always yielded the best fit for Type B subjects.

The prealbuterol and postalbuterol homogeneous airways model parameters for all Type A subjects are reported in Table 2. The prealbuterol airway shunt model parameters and postalbuterol homogeneous airway model parameters for all Type B subjects are reported in Table 3. All subjects demonstrated large decreases in Raw (17 to 61% for Type A, 22 to 72% for Type B) and tissue damping G (13 to 71% for Type A, 9 to 80% for Type B) after albuterol. The  values dropped in all of the Type A subjects (11 to 62%) and eight of the 10 Type B subjects (6 to 67%). Most Type A subjects showed very little change in tissue elastance H, whereas five of the Type B subjects showed substantial (> 20%) decreases in H. 

A summary of percent predicted FEV₁ and the airway and lung tissue properties (from the most appropriate model fits) for the Type A and Type B subjects before and after albuterol inhalation, along with data from nine healthy subjects reported previously (1), is shown in Figure 3. Recall that patient classification as Type A or B was not based on spirometry. Nevertheless, at baseline the Type B subjects had a significantly lower % pred FEV₁ compared with either the Type A group or the healthy group, as well as significantly higher Raw (p < 0.001). Although the Type A group demonstrated a significantly lower % pred FEV₁ at baseline compared with our previous healthy group (p < 0.05), there was no significant difference between their Raw. ANOVA did detect a significant effect of the baseline state on G (F = 3.480, p = 0.0452), but the post hoc Tukey HSD comparison of G among Type A, Type B, and healthy groups did not indicate significant pairwise differences. ANOVA yielded no significant differences in baseline H or . A paired t test showed highly significant reductions in Raw (p < 0.0001) and G (p < 0.002) after albuterol inhalation for both the Type A and Type B groups, but only the Type B group demonstrated a significant drop in H (p = 0.027). Both groups demonstrated significant decreases in  (p < 0.01). After albuterol, Type B subjects still demonstrated significantly higher Raw compared with either Type A postalbuterol or healthy subjects at baseline (p < 0.05), as well as significantly lower % pred FEV₁ (p < 0.05).

View larger version (16K): [in this window] [in a new window]   Figure 3.   Summary of % predicted FEV1 ± SD and model parameters ± SD for the 11 Type A asthmatics (closed bars) and the 10 Type B asthmatics (open bars) before and after albuterol inhalation. For comparison, data from nine healthy subjects reported previously (1) are also shown (hatched bars). *Significantly different from baseline condition using the two-tailed paired t test (p < 0.05). Significantly different from healthy group using ANOVA and the Tukey HSD test (p < 0.05). Significantly different from Type A group under same condition (either baseline or postalbuterol) using ANOVA and the Tukey HSD test (p < 0.05).

Both groups showed significant increases in FEV₁ after albuterol (p < 0.001, paired t test). On the basis of spirometric criteria, the Type A subjects appear to have mild asthma (prealbuterol FEV₁ = 87 ± 3% predicted), whereas the Type B group suffers from moderate-to-severe asthma (prealbuterol FEV₁ = 70 ± 12% predicted). Also, the Type B group demonstrated a significantly greater improvement in FEV₁ after albuterol compared with the Type A group (%FEV₁ = 25 ± 17% versus 9 ± 4%, p = 0.011). We examined whether changes in our estimated airway and lung tissue properties could be correlated with these spirometric indices. Both baseline % predicted FEV₁ and % change in FEV₁ versus absolute changes in Raw, G, and H for all 21 subject are shown in Figure 4. Significant negative correlations were observed between % predicted FEV₁ and changes in Raw (r = 0.80, p < 0.001) and G (r = 0.68, p < 0.001), but none for either H or . Significant positive correlations were observed between %FEV₁ and Raw (r = 0.66, p < 0.01), G (r = 0.59, p < 0.01), and H (r = 0.62, p < 0.01), but none for . The data indicate that the Type B asthmatics drive the significance of most of these correlations.

View larger version (20K): [in this window] [in a new window]   Figure 4.   Changes in model parameters versus baseline percent predicted FEV1 and postalbuterol percent change in FEV1 for the 11 Type A asthmatics (closed circles) and 10 Type B asthmatics (open circles). Regression lines are drawn only for significant correlations (p < 0.05).

Our model-based estimates of Raw are compared with estimates of Raw obtained from plethysmography for seven of the asthmatic subjects (four Type A, three Type B) (Table 4). For all of these subjects, the model-based estimates were consistently and significantly higher than the plethysmographic estimates (prealbuterol, p = 0.01017; postalbuterol, p = 0.0009).

	DISCUSSION

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Asthmatic Conditions Consistent with ZL Data

There are a number of etiologies that can contribute to the occurrence of bronchoconstriction in asthma. Nevertheless, this study has distinguished two different patterns of asthmatics solely on the basis of pulmonary impedance spectra. These differences may or may not reflect distinct pathologies. The Type A group demonstrated mildly elevated RL but EL similar to that seen in healthy subjects (1), but the Type B group showed a highly elevated RL and pronounced positive frequency dependence in EL, especially from 2 to 8 Hz. Spirometric data further suggests that these two types of asthmatics differ in terms of the severity of obstruction. Because it is primarily the difference in the frequency dependence of EL that makes the two types of asthmatics distinct, a thorough discussion is warranted regarding the mechanisms contributing to this frequency dependence of and how these mechanisms may be affected in asthma.

Three distinct mechanisms have been shown to contribute to a positive frequency dependence in EL: tissue viscoelasticity (27), parallel time constant inhomogeneties (21), and airway wall shunting (19, 20, 28). However, several studies now indicate each of these mechanisms affect EL with varying degrees and over different frequency ranges (19, 28). Hildebrandt (27) demonstrated that tissue viscoelasticity causes EL to increase slightly with frequency from 0 to 1 Hz, and such an increase is compatible with our modeling analysis (Equation 1). A recent morphometric modeling study by Lutchen and Gillis (28) showed that in the absence of airway wall shunting, frequency-dependent increases in EL caused by parallel airway heterogeneity occurs predominantly from 0 to 2 Hz followed by a decreasing EL above 2 Hz. Moreover, such a pattern becomes evident only when a few airways become highly constricted or nearly closed. Neither the Type A nor the Type B subjects showed such an EL profile below 2 Hz, which argues against parallel airway heterogeneity being the sole (or even dominant) mechanism influencing their baseline data. Conversely, Lutchen and Gillis also demonstrated that the phenomenon of airway wall shunting will alter the frequency dependence of EL in a manner more consistent with our data in Type B subjects. Specifically, when there is substantial constriction throughout (but not necessarily limited to) the lung periphery, airway wall shunting will occur and cause EL to increase at higher frequencies (2 to 8 Hz), similar to that seen in our Type B subjects. This is not to say that the Type A subjects had no constriction in their lung periphery; rather, their constriction was probably not severe enough to result in airway wall shunting. Likewise, we do not suggest that the constriction is limited only to the periphery and is perfectly homogeneous in the Type B subjects. We simply suggest that the peripheral constriction is severe enough such that airway wall shunting dominates the frequency-dependent profile of EL. This conclusion is consistent with the spirometric data which revealed that Type A subjects had mild asthma, whereas Type B subjects had moderate-to-severe asthma.

Our hypothesis about the nature of the airway constriction in these subjects is also compatible with the modeling analysis. The prealbuterol and postalbuterol RL and EL data from the Type A group was always best described by a model assuming homogeneous rigid airways and viscoelastic tissues. However, the Type B group at baseline had results best described by a model that incorporated the shunting of flow into an airway wall compliance, a concept originally introduced by Mead (20). With the exception of one subject (Subject 1), the values of airway wall compliance for these Type B subjects (Caw = 0.005 ± 0.002 cm H₂O/L, excluding Subject 1) were very consistent with Mead's estimates. The fact that the inhomogeneous airways and interregional flow models never yielded a statistically better fit to the data before or after albuterol does not rule out their contributions to the frequency-dependent features of RL and EL; rather, it is just unlikely they make a strong contribution to the data.

In the seven subjects in which both measurements were made, we found that model estimates of Raw were significantly higher than estimates obtained using pressure plethysmography. For the Type A subjects, the discrepancy between the two measures was similar to that previously reported in healthy subjects (1), and it is consistent with measurements made by Stanescu and colleagues (31) who demonstrated that panting lowers plethysmographic estimates of Raw by widening glottal aperture. The greatest discrepancies occurred for the Type B subjects before albuerol inhalation. In these subjects, it is reasonable that plethysmographic Raw estimates may be further lowered because of central airway wall shunting and the failure of pressure fluctuations at the mouth to accurately reflect changes in alveolar pressure (11), whereas our modeling analysis reduces this effect by explicitly incorporating the impact of Caw on RL. It is unlikely that these mechanisms can completely account for the large differences between the two techniques, and a complete explanation for the discrepencies is not apparent to us at present.

Airway and Lung Tissue Mechanics in Asthma

Both groups of asthmatic subjects demonstrated significant decreases in Raw, G, and , but only the Type B group demonstrated a significant decrease in H. A decrease in Raw after administration of a -agonist is expected and easily explained by increases in airway caliber caused by airway smooth muscle relaxation (32). Other investigators have reported decreases in lung tissue resistance and dynamic elastance at the levels of the parenchymal strip (33) and whole organ (9, 34) following -agonist exposure. Possible mechanisms for the decreases in G and H we observed may include the opening of previously closed lung units (28), an increase in the volume of air contained in the peripheral airways (35), a decrease in the hysteresis of airway and alveolar duct smooth muscle (33, 36, 37), or a decrease in parallel airway heterogeneity (19, 29).

In the absence of significant collateral ventilation, airway opening and alveolar recruitment would increase communication to more lung tissue and thus decrease the apparent lung tissue resistance and dynamic elastance. This is certainly consistent with the significant drops in both G and H we observed in the Type B subjects. However, if airway reopening was the sole mechanism for the decreases in G and H, one would expect both tissue parameters to decrease by an equal percentage after albuterol, so that remained constant (18). However, for nearly all subjects, the drop in G was greater than the drop in H, so that  decreased significantly.

A portion of the decrease in H observed in the Type B subjects may also be due to an increase in the caliber of peripheral airways after albuterol, with a corresponding increase in their volume. As demonstrated by Woolcock and colleagues (35), peripheral airway constriction can cause appreciable decreases in lung volume and a rightward shift in the quasi-static pressure-volume loop. In principle, this will cause a change in the pressure-volume relationship of the lungs measured under static or dynamic conditions (35).

Decreases in G and  may be a reflection of a decrease in the hysteresis of airway and alveolar duct smooth muscle (36). The hysteresis of parenchymal strips and isolated airway smooth muscle has been shown to decrease after -agonist exposure (33, 36). It has been recently argued that a substantial fraction of this hysteresis is due to the detachments of stretched myosin heads bound to actin filaments in the parenchymal contractile apparatus, and that  is really a reflection of cross-bridge cycling rate (33, 37). After smooth muscle experiences -agonist-induced relaxation, the number of attached cross bridges and their rate of cycling would be expected to decrease (32). To the extent that the hysteresis of contractile elements contributes to the overall hysteresis of lung tissue, it is possible that a change in the kinetics of these elements is a contributing mechanism for the decreases in G and  we observed (18).

Finally, it is possible that our baseline estimates of G were artifactually high because of heterogeneous airway constriction, and that the albuterol decreased such heterogeneity. Several experimental and modeling studies have shown that if bronchoconstriction is highly inhomogeneous, estimates of G (and consequently Rti) determined using a homogeneous airway model will be biased (2, 19, 29). However, as noted above, parallel airway heterogeneity causes an excessive frequency-dependent increase in EL predominantly over the 0 to 2 Hz range (28). The fact that our subjects did not show such EL profiles below 2 Hz and that the simple two-parallel-pathway model of Figure 1C never yielded a statistically better fit compared with the homogeneous or airway shunt model suggests that estimates of G are probably not significantly biased by parallel airway heterogeneity.

Regardless of the mechanisms for the observed decreases in G and H, the relative contributions of Raw and Rti to RL in our asthmatics did not significantly change after albuterol. Rti and Raw versus frequency simulated from the mean airway and tissue parameters of the Type A and B groups (before and after albuterol) and the healthy group reported previously (1), are shown in Figure 5. Also shown are the corresponding percent contributions of Raw and Rti to RL. For both the Type A and Type B asthmatics, Raw makes up a larger fraction of RL at breathing frequencies (approximately 70 to 80% at 0.25 Hz) compared with healthy subjects (~ 60% at 0.25 Hz). However, after -agonist-induced bronchodilation, the Raw and Rti change by nearly equal amounts for both the Type A and Type B asthmatics. That Rti and Raw decrease by nearly equal amounts at all frequencies after -agonist exposure is remarkably consistent with observations by Vettermann and colleagues (34). Thus, it appears that the percent of RL caused by Rti is independent of the severity of smooth muscle constriction.

View larger version (23K): [in this window] [in a new window]   Figure 5.   Upper panels show the effective airway (squares) and tissue (triangles) resistances versus frequency predicted from averaged model parameter values from Tables 2 and 3 before (open symbols) and after (closed symbols) albuterol inhalation for Type A and Type B asthmatics. Also shown are predictions from nine healthy subjects reported previously (1). Tissue resistance was calculated according to Equation 1. Airway resistance was obtained from the Raw parameter of the homogeneous airways model, except for the baseline Type B asthmatics whose airway resistance was computed as Raw(f) = Re[ZL(f)]  Rti(f). Note that for the Type B asthmatics, whose prealbuterol data are best described by the airway shunt model, the influence of Caw produces some mild frequency dependence in effective Raw. Corresponding percent contributions of Raw and Rti to RL are shown in the bottom panels.

In summary, this study has demonstrated that under baseline conditions, asthmatics have distinct frequency-dependent profiles of RL and EL. These profiles most likely reflect the degree of airway constriction in the lung periphery. The subjects with mild baseline asthma suffer from mild airway constriction that appears to influence tissue properties only minimally. Subjects with more severe baseline asthma present with widespread peripheral airway constriction, which produces a large increase in the frequency dependence of lung elastance because of shunting of flow into the central airway walls. Decreases in apparent tissue resistance and elastance after albuterol inhalation may reflect the opening of previously closed airways, an increase in the volume of the peripheral airways (neither of which constitutes an explicit alteration in lung tissue rheology), and/or a decrease in the energy dissipation of airway smooth muscle. For either group of subjects, analysis of the data suggests that airway resistance in asthma comprises the majority (> 70%) of their total lung resistance at breathing frequencies, and that both airway resistance and lung tissue resistance are responsive to -agonist-induced bronchodilation.