Reactance and elastance as measures of small airways response to bronchodilator in asthma

Abstract

Bronchodilation alters both respiratory system resistance (Rrs) and reactance (Xrs) in asthma, but how changes in Rrs and Xrs compare, and respond differently in health and asthma, in reflecting the contributions from the large and small airways has not been assessed. We assessed reversibility using spirometry and oscillometry in healthy and asthma subjects. Using a multibranch airway-tree model with the mechanics of upper airway shunt, we compared the effects of airway dilation and small airways recruitment to explain the changes in Rrs and Xrs. Bronchodilator decreased Rrs by 23.0 (19.0)% in 18 asthma subjects and by 13.5 (19.5)% in 18 healthy subjects. Estimated respiratory system elastance (Ers) decreased by 23.2 (21.4)% in asthma, with no significant decrease in healthy subjects. With the use of the model, airway recruitment of 15% across a generation of the small airways could explain the changes in Ers in asthma with no recruitment in healthy subjects. In asthma, recruitment accounted for 40% of the changes in Rrs, with the remaining explained by airway dilation of 6.8% attributable largely to the central airways. Interestingly, the same dilation magnitude explained the changes in Rrs in healthy subjects. Shunt only affected Rrs of the model. Ers was unaltered in health and unaffected by shunt in both groups. In asthma, Ers changed comparably to Rrs and could be attributed to small airways, while the change in Rrs was split between large and small airways. This implies that in asthma Ers sensed through Xrs may be a more effective measure of small airways obstruction and recruitment than Rrs.

NEW & NOTEWORTHY This is the first study to quantify to relative contributions of small and large airways to bronchodilator response in healthy subjects and patients with asthma. The response of the central airways to bronchodilator was similar in magnitude in both study groups, whereas the response of the small airways was significant among patients with asthma. These results suggest that low-frequency reactance and derived elastance are both sensitive measures of small airway function in asthma.

INTRODUCTION

In asthma, airway obstruction primarily lies in the small airways (diameter <2 mm) and is thought to be largely responsible for most of the changes in respiratory system mechanics (56, 57). However, assessing small airways in mild or moderate asthma is challenging using spirometry because this region accounts for only a small portion of the total airway resistance (57).

A number of methods have been used to assess the role of small airways in asthma including inert gas washout (19, 26), oscillometry also known as the forced oscillation technique (FOT) (48), and functional imaging techniques such as hyperpolarized noble gas imaging (42), high-resolution computed tomography (25), and positron emission tomography (52). Among these methods, oscillometry directly probes the mechanics of moving air into and out of the lungs by evaluating respiratory system resistance (Rrs) and reactance (Xrs) (14, 33). The frequency dependence of Rrs (decrease in Rrs over 5 Hz to 19 or 20 Hz) is thought to arise from the development of heterogeneous small airway narrowing in asthma (31). This may be due also in part to the shunting of flow into compliant lower airway structures, as shown by Kaczka et al. (21, 22) over a lower bandwidth of frequencies.

There is increasing interest in using Xrs to assess changes in lung mechanics in disease (16, 24). At low frequencies, Xrs largely reflects the compliance of the lung parenchyma and can be used to estimate respiratory system elastance (Ers). In disease, airway and air space derecruitment occurs heterogeneously, which decreases the lung volume assessed by oscillometry, and Xrs becomes more negative and Ers increases (7, 13, 22, 32), changes that can be substantially reversed with a bronchodilator (BD) in asthma (12, 21).

Modeling can be used to help understand and attribute the role of central and peripheral airways to changes in Rrs and Xrs in obesity (1, 40), acute respiratory distress syndrome (2), and asthma (21, 30, 31, 48). However, the relative role of narrowing versus decrecruitment has not been quantitatively assessed comparing the response of these compartments in health and disease. Here we used a multibranch model to explicitly quantify the effect of small airway derecruitment with narrowing and to differentiate the mechanisms that underly the difference in response to a BD in health and asthma.

MATERIALS AND METHODS

Subjects

Inclusion criteria were age between 18 and 75 yr and never smokers or current or ex-smokers with less than 10 pack-years of smoking history. Subjects with asthma were diagnosed based on symptoms and/or airflow reversibility at least for 12 mo before the study procedures and had no changes or worsening of respiratory symptoms in the 6 wk before measurements. They also had no changes in their asthma medications in the 4 wk before the tests. Healthy subjects had no history of asthma or any other respiratory condition. The study was approved by the Nova Scotia Health Authority Research Ethics Board, and written informed consent was obtained from all participants before the study measurements.

Measuring Respiratory System Impedance and Lung Function

Respiratory system impedance was measured using a custom-made loudspeaker-based FOT device (9). Small amplitude pressure oscillations (approximately ±1 cmH₂O) were generated using a loudspeaker and applied at the subject’s mouth via a disposable antibacterial/antiviral filter (MicroGard; Viasys Respiratory Care, Palm Springs, CA). The subjects wore a nose-clip and sat upright with their cheeks and chin firmly supported with their palms while breathing on the FOT device. The pressure and flow changes at the subject’s mouth were recorded using a pressure transducer (TD-05-AS; SCIREQ, Montreal, Canada) and Pneumotachograph (Fleisch No. 2, Lausanne, Switzerland) connected to a differential pressure transducer (TD-05-AS; SCIREQ), respectively. The pressure and flow signals were amplified, filtered using a Bessel filter (SC24, SCIREQ cut off of 100 Hz), and sampled at 240 Hz with 16-bit resolution (DAQ 6036E; National Instruments, Austin, TX). The pressure transducer was calibrated using a U-tube fluid manometer, while the Fleisch pneumotachograph was calibrated using a calibrated 3-liter syringe by flow-integral method. The FOT device was validated using a standard test load of 5 cmH₂O·s·L⁻¹ (Hans Rudolph).

The loudspeaker was driven by a multifrequency sinusoidal signal containing three frequencies to maximize signals to noise in three frequency ranges (low, middle, and high using waveforms with 5, 15, and 20 Hz, which allowed for more rapid tracing of impedance or 4, 10, and 22 Hz). Twelve subjects (6 subjects with asthma and 6 healthy subjects) were measured at 5, 15, and 20 Hz/s. Twenty-four subjects (12 subjects with asthma and 12 healthy subjects) were measured at 4, 10, and 22 Hz to avoid the effects of harmonic interference between frequencies. Either signal permitted analysis of frequency dependence of Rrs and assessment of low-frequency Xrs (4 or 5 Hz), and there was no difference between groups for these results.

Spirometry was performed (Vmax Encore 20; Viasys Respiratory, Palm Springs, CA) according to American Thoracic Society/European Respiratory Society guidelines (35). The test results were expressed using the Global Lung Initiative reference values (41).

Study Design

Three 1-min FOT measurements separated by 15–20 s were collected at baseline, followed by spirometry. Bronchodilator (Salbutamol, 200 µg) was administered via metered dose inhaler with a valve-holding chamber device (CareStream Medical, Pickering, ON, Canada), and the measurements were repeated 12–15 min thereafter.

Signal Analyses

The three FOT recordings were concatenated, and the pressure and flow signals were digitally filtered by using a fast Fourier transform, removing components up to 1 Hz (most of the breathing signal). The signals were then inverse Fourier transformed to the time domain. This filtered signal was then analyzed using the periodogram approach with 1-s blocks with 50% overlap Hamming windowing to minimize nonstationarity and any residual edge artifacts, and impedance for each block was computed as the ratio of the Fourier transforms of pressure to flow. Impedance of the bias tubes, bacterial filter, and tubing between the subject and the bacterial filter was compensated (43), and real part was Rrs and imaginary part Xrs. Outlying impedance values >3 SD from the mean, usually resulting from coughs, swallows, and glottal closures were discarded, and the average values were computed. Impedance values were retained only if coherence was >0.95 and/or signal-to-noise ratio (SNR) of the pressure and flow signals was >20 dB (27). The coefficient of variation of the three FOT recordings was <15%. To estimate Ers, we used a three-parameter model of the lung consisting of linear resistive, inertial, and elastic elements in series (33), although for estimating of Ers only the two reactive parameters (inertial and elastic) were required. These were estimated by fitting Xrs to the model Xrs = 2πfIrs – Ers/2πf, using multiple linear regression by linear least squares where f were the oscillating frequencies (4, 10, and 22 Hz or 5, 15, and 20 Hz). The quality of the model fits was assessed from r² values, and Ers was discarded if r² was < 0.90.

Statistical Analyses

Data are presented as means (SD) unless otherwise specified. Normality of data was assessed using Shapiro-Wilk test. Differences in the baseline measures between the healthy and asthma subjects were assessed using a two-tailed, unpaired t-test or Mann Whitney rank sum test as appropriate. Changes in the measures following BD were compared using a one-tailed, paired t test or Wilcoxon signed rank test. Changes in the measures from baseline to post-BD between healthy and asthma subjects were compared using a mixed model repeated measures ANOVA with time and group as factors. Correlations between different measures were assessed by Pearson or Spearman correlation analysis. Statistical analyses were performed using SAS 5.1 (SAS Institute, Cary, NC), and significance was accepted at P < 0.05.

Modeling

Multibranch airway tree.

To help interpret the mechanics in vivo, and specifically, so we could more accurately incorporate airway derecruitment as well as airway narrowing separately and quantitatively, we developed a multibranch airway tree model (28) with the ability to reversibly obstruct a given fraction of airways. The model was based on an anatomically correct three-dimensional human airway geometry provided by Tawhai et al. (45) (Fig. 1A, airway tree shown with airway closures). It consisted of 26 generations and 64,896 airways. The model, up to the first eight airway generations, was generated using a host-specific volume derived from X-ray multidetector computed tomography imaging of the chest. The remaining generations were created using a volume filling algorithm maintaining daughter diameter ratios consistent with the established morphometry (46).

Fig. 1.

A: multibranch airway-tree model with multiple ventilation defects created by occluding 475 of 1,002 airways in the 10th airway generation. B: model respiratory resistance and reactance (Rrsm and Xrsm, respectively) estimated for the healthy and asthma subjects’ airway tree models. Solid and dotted lines indicate the single-compartment model fits to Rrsm and Xrsm, respectively. The r² values for the Xrs model fits were 0.99. See text for more details.

Because of the turbulent flow profile in some of the larger airways, we used Womersley flow rather than Poiseuille flow in the model (23). For the model, simulating the baseline condition in our control subjects (described in Simulations), we computed the Womersley number, α_a, for each airway branch given by,

$${\text{α}}_{\text{a}}=r_{\text{a}}\sqrt{\frac{2{\text{πρ}}_{\text{air}}\text{f}}{{\text{μ}}_{\text{air}}}}$$ (1)

where r_a is the radius of the airway; ρ_air is the density of air (1.16 kg/m³); μ_air is the dynamic viscosity of humid air at 37°C (1.85 × 10⁻⁵ Pa·s), and f is the oscillation frequency in Hertz. Accordingly, the complex impedance of a nonterminal airway (Z_a) was determined assuming Womersley flow (23) as follows:

$${\text{Z}}_{\text{a}}\left(\text{f}\right)=\frac{j2{\text{fρ}}_{\text{air}}{l}_{\text{a}}}{r_{\text{a}}^2}\left[1-\frac{2{\text{J}}_1\left({\text{α}}_{\text{a}}\sqrt{-\text{j}}\right)}{{\text{α}}_{\text{a}}\sqrt{-\text{j}}{\text{J}}_0\left({\text{α}}_{\text{a}}\sqrt{-\text{j}}\right)}\right]$$ (2)

where l_a is the length of the airway; and J₀ and J₁ are the complex Bessel functions of order 0 and 1, respectively; α_a is the Womersley number of the airway; and j is the unit imaginary number.

We included upper airway compliance as described below, and distributed the model lung elastance evenly among the terminal airways, with each terminal airway functionally serving as an alveolar compartment accounting for parenchymal stretch, surface tension, and any gas compression (49). This approach neglects any contribution from airway wall compliance or any gas compression within the airways, but this effect is much smaller than the effect of alveolar compartment (29, 34) in a healthy lung, owing largely to the small relative gas volume in the airways and the stiffer tissue of the airways. The impedance of a terminal airway (Z_t) was defined as

$${\text{Z}}_{\text{t}}={\text{Z}}_{\text{a}}-\text{j}\frac{{\text{E}}_{\text{t}}}{\text{ω}}$$ (3)

where E_t is the elastance of the terminal airway unit.

Since the model of Tawhai et al. (45) was obtained at total lung capacity (TLC), airway diameters and lengths were reduced to 80% of their original values, assuming a homogeneous isotropic volume change and maintaining the plethysmographically measured functional residual capacity (FRC) to TLC ratio of 0.5 from our healthy and asthmatic subjects. This ratio was also approximately equal to the upright FRC to TLC ratio of the model lung of Tawhai et al. (45).

The model impedance was calculated using a lumped element approach from the series and parallel network relations of airway impedances as described by Leary et al. (28). The tracheal and glottic resistance of 0.5 cmH₂O·s·L⁻¹ and the chest-wall resistance of 0.5 cmH₂O·s·L⁻¹ (4, 5, 37), which were not part of the tree of Tawhai et al. (45), were added to the model resistance to obtain the model respiratory system resistance. Furthermore, the chest-wall elastance of 9.3 cmH₂O/L (4) was added to the model elastance to obtain the model respiratory system elastance. Lastly, to account for the mechanics of compliant upper airway structures including the cheeks and soft palate, a viscoelastic upper-airway shunt impedance was added to the model in parallel extracting the required real and imaginary impedance components at our model frequencies from Cauberghs and Van de Woestijne (11). For most comparisons, we report model resistance (Rrsm) and reactance (Xrsm) at 4 Hz except where noted.

Simulations.

At baseline, the model impedance was computed with all airways open with their initial dimensions corresponding to an FRC-to-TLC ratio of 0.5 as stated above. Then, a slight scaling of the model by a further 30.7% narrowing of all airways was applied to match the mean baseline Rrs from our healthy subjects (2.64 cmH₂O·s·L⁻¹). Xrsm was then chosen to match the average Xrs obtained from the healthy controls (−2.17 cmH₂O·s·L⁻¹; Ers = 60.7 cmH₂O·s·L⁻¹) by distributing an elastance of 53 cmH₂O/L equally to all terminal units.

We then reproduced the mechanics from the asthmatic subjects as follows. Assuming initially only small airway derecruitment, we explored the effects of occluding by narrowing to 10% initial diameter (increasing their resistance 10,000-fold) a proportion of airways in the 9th, 10th, and 11th airway generations. Because the same derecruitment of the distal air spaces can be achieved by derecruiting the two daughter airways of a given generation, keeping the fraction of derecruitment of the distal lung the same, we select here the 10th airway generation for all subsequent comparisons. This was convenient as there were a sizable number of airways within this generation for better adjusting the fraction of derecruitment within a single generation compared with a larger airway generation and avoiding early terminations of some airways in more distal generations. Derecruitment thus accounted for the changes in Ers by a single variable parameter; the number of derecruited airways. We performed 10 repeated simulations of different amounts of random occlusions of 10th generation airways and computed average Rrsm and Ersm, choosing the number of airways with Ersm that best matched Ers from the subjects with asthma. Airway derecruitment would increase Rrsm but not sufficiently to account for the average baseline Rrs from the subjects with asthma. Thus we accounted for the remaining increase in Rrsm by homogenous narrowing of all remaining airways. The modest remaining narrowing required meant that this contribution to Rrsm was entirely dominated by central airways (approximately generation 5 and larger). The BD-induced changes in the respiratory mechanics were thus reproduced via dilation of the central airways and opening of the occluded 10th generation airways. To achieve this, we performed 10 simulations of random opening of the airways from 475 occluded airways ranging from 25 to 200 and computed Rrsm and Ersm for each simulation. We then computed percent decreases in Rrsm and Ersm for each simulation with respect to the baseline condition and averaged these decreases.

RESULTS

Demographics

Eighteen healthy subjects (11 women) and 18 patients with asthma (10 women) were enrolled (Table 1). There were no differences in age and height between the two groups. The patients with asthma were slightly heavier than the healthy subjects (P = 0.043, Table 1). The medication log for patients with asthma is reported in Table 2.

Table 1.

Subject demographics and lung function

	Controls (n = 18)	Asthma (n = 18)	P Value
Sex, men/women	8/10	7/11
Age, yr	35.2 (13.4)	35.9 (13.6)	0.84
Height, cm	169.2 (11.3)	168.8 (9.3)	0.92
Weight, kg	70 (16.3)	83.1 (20.9)	0.043*
BMI, kg/m2	24.4 (4.9)	29.0 (6.6)	0.01*
FEV1, %predicted
Baseline	96.8 (9.1)	83.0 (25.4)	0.21
Post-BD	100.4 (10.1)##	91.7 (19.1)##
%Change	3.7 (3.1)	16.3 (25.0)	0.054
FEV1 Z-score
Baseline	−0.3 (0.7)	−1.2 (1.8)	0.2
Post-BD	0.04 (0.8)##	−0.6 (1.4)##
Change	0.3 (0.3)	0.7 (0.8)	0.074
FVC, %predicted
Baseline	100.2 (13.5)	97.0 (20.4)	0.92
Post-BD	100.1 (13.6)	102.2 (14.2)
%Change	−0.2 (1.6)	8.4 (20.2)	0.06
FVC Z-score
Baseline	−0.02 (1.1)	−0.2 (1.6)	0.71
Post-BD	−0.03 (1.1)	0.2 (1.1)
Change	−0.01 (0.1)	0.4 (0.9)	0.06
FEV1/FVC, %
Baseline	80.8 (7.2)	69.9 (14.4)	0.007*
Post-BD	83.8 (6.0)#	74.2 (12.1)##
%Change	3.8 (2.4)	7.2 (9.5)	0.31
FEV1/FVC Z-score
Baseline	−0.33 (1.1)	−1.7 (1.7)	0.002
Post-BD	0.1 (1.0)#	−1.2 (1.4)##
Change	0.5 (0.2)	0.5 (0.6)	0.99

Data are represented as means (SD); n, number of subjects, BMI, body mass index, FEV₁, forced expiratory volume in 1 s percentage of predicted (34); FVC, force vital capacity as percentage of predicted (33); BD, bronchodilator.

^*Unpaired t-test between healthy subjects and subjects with asthma.

^#Difference between baseline and post-BD values within individual groups using the paired t-test.

^##Difference between baseline and post-BD values within individual groups using Wilcoxon signed rank test.

Table 2.

Asthma participants’ medications

Medications	No. of Subjects
Short-acting β-2 agonist (SABA)	4
SABA and inhaled corticosteroid (ICS)	2
SABA, ICS, and leukotriene receptor antagonist (LTRA)	1
SABA and a combination of long-acting β-2 agonist (LABA) and ICS	3
Combination of LABA and ICS	3
LTRA and a combination of LABA and ICS	1
ICS	1
No medication	3

Pre- and Post-BD Lung Function

There was no difference in baseline forced expiratory volume in 1 s (FEV₁) and forced vital capacity (FVC) between the heathy subjects and patients with asthma (Table 1). However, patients with asthma had smaller FEV₁/FVC than the healthy controls at baseline. Following BD, FEV₁ appeared to increase in both groups, but this did not reach statistical significance (ANOVA, P = 0.054). Furthermore, FEV₁/FVC increased following BD in both groups but with no differences between the two groups (P = 0.3), while FVC remained unaltered following BD in both groups.

Pre- and Post-BD Respiratory System Impedance

Baseline Rrs at the low- and mid-frequency range was higher in patients with asthma than in healthy subjects (Fig. 2A). Following BD, Rrs decreased significantly at all frequencies among patients with asthma (Wilcoxon signed rank test, P < 0.001 for low and mid frequencies, and P = 0.001 for high frequencies). However, healthy subjects only demonstrated a change in Rrs at the low- and mid-frequency range (one-tailed paired t test, P < 0.05). There was a 26.6 (20.9)% and 11.7 (20.5)% reduction in Rrs at low frequencies following BD among patients with asthma and healthy subjects respectively. Compared with healthy subjects, the reduction in Rrs at low and mid frequencies was larger in patients with asthma (ANOVA, P = 0.016 and P = 0.047 respectively).

Fig. 2.

A and B: baseline and postbronchodilator (post-BD) respiratory system resistance (Rrs; A) and reactance (Xrs; B) from 18 the healthy and 18 patients with asthma at low (L: 4 and 5 Hz), mid (M: 10 and 15 Hz), and high (H: 20 and 22 Hz) frequencies. Post-BD response bars (filled bars) are superimposed on the baseline data bars (empty bars). Error bars indicate means ± SE. *P < 0.05, significant change comparing pre- and post-BD values. P values indicate significant difference between the heathy and asthma subjects at baseline. Note the substantial reduction in Xrs in the asthma subjects with BD compared with lack of response in the healthy subjects.

There was no difference in baseline Xrs values at low-, mid-, and high-oscillation frequencies between the healthy group and patients with asthma (Fig. 2B). Following BD, Xrs at all frequencies increased (became less negative) in the patients with asthma (Wilcoxon signed rank test, P < 0.001 for all) but not in the healthy subjects. Also, the increases in Xrs were significantly larger at all frequencies in the group with asthma as compared with the healthy group (ANOVA, low: P = 0.006, mid: P = 0.007 and high: P = 0.005)

In four subjects (1 healthy and 3 with asthma), r² values for Xrs model fits to estimate Ers were <0.90 and excluded. In the remaining 17 healthy subjects and 16 patients with asthma, there were no difference between baseline Ers (Fig. 3). Following BD, Ers reduced by 23.2 (21.3)% among patients with asthma (Wilcoxon signed rank test, P < 0.001) but did not change significantly in the healthy subjects [3.9 (17.4)%, P > 0.05]. Also, the reduction in Ers was larger in the group with asthma than in the healthy group (ANOVA, P = 0.009).

Fig. 3.

A: respiratory system reactance (Xrs) measured using forced oscillation technique (diamonds) and the single-compartment model fit (dotted line) to Xrs from the asthma subjects measured at 4, 10, and 22 Hz (n = 11); r² for the model fit = 0.99. B: pre- and post-bronchodilator (BD) respiratory system elastance (Ers) from the healthy and asthma subjects (dark gray). Post-BD Ers values (filled bars) are superimposed on the baseline Ers values (empty bars). *P < 0.05, significantly different from baseline.

Correlations Between Ers and Spirometric Indexes of Small Airway Obstruction

We found a weak correlation between Ers and FVC % predicted (r² = 0.42, P = 0.003) and between reduction in Ers and increase in FVC following BD (r² = 0.36, P = 0.007) in patients with asthma. Furthermore, Ers was weakly correlated to predicted values of forced expiratory flow between 25 and 75% of the FVC (FEF25–75%; r² = 0.40, P = 0.004).

Model

Effect of BD on the healthy model.

Because there was no change in Ers with BD in the healthy subjects, to model the changes in lung mechanics following BD, all airways were dilated from 1 to 10%. As expected, Ers changed insignificantly, while Rrs decreased. A 7.5% dilation resulted in a 13.7% decrease in Rrsm and a 1.43% decrease in Ersm (Fig. 4A, arrow), which approximated the in vivo changes in lung mechanics.

Fig. 4.

Percent decreases in the model respiratory resistance (Rrsm) and elastance (Ersm) following simulated bronchodilation of the model for 2 conditions as follows. A: imposing central-airway dilation from 1 to 10% with no airway closures. The bars pointed indicate the model response that mimicked the in vivo bronchodilator (BD) response in the controls. B: effect of opening from 25 to 150 of the occluded airways. Combining the opening of 150 airways and 6.8% dilation of the central airways reproduced the in vivo BD response from the asthma subjects. Error bars indicate SD for 10 random simulations of airways opening.

Effect of BD on the asthma model.

To match Ersm to the average baseline Ers from the patients with asthma, we occluded 475 of 1,002 airways from the 10th airway generation from the healthy model. This also increased Rrsm at 4 Hz from 2.64 to 3.17 (0.06) cmH₂O·s·L⁻¹ but did not increase Rrsm sufficient to match baseline Rrs of 4.3 cmH₂O·s·L⁻¹. Thus we narrowed the remaining airways by 11.5%. This derecruitment and narrowing of the airways together produced Rrsm at 4 Hz of 4.27 (0.07) cmH₂O·s·L⁻¹ and Ersm of 110.1 (4.1) cmH₂O/L closely matching respiratory impedance from the patients with asthma. From this baseline asthma model, to account for the in vivo BD-induced change in Ers, we required opening 150 of the occluded airways, leaving 325 still occluded. This provided a percent decrease in Ersm of 20.5 (2.8)%. This level of derecruitment decreased Rrsm but not sufficient to account for the change in Rrs in the asthma subjects with BD, and we found that a 6.8% dilation of the central airways produced nearly similar decreases in Rrsm of 22.2 (1.3)% and Ersm of 21.8 (2.8)%, reproducing the in vivo response from the asthma subjects (Fig. 4B, arrow).

Effect of upper airway shunt.

Because shunt attenuates respiratory impedance particularly with airflow obstruction, we measured the effect using the model without shunt on Rrsm and Xrsm at baseline and post-BD, and the effect on the relative changes due to BD (Table 3). Inclusion of the upper airway shunt decreased baseline Rrsm slightly in a frequency-dependent manner in the healthy model at 4 and 10 Hz and increased it at 22 Hz. The effects of shunt on the asthma model were a little more pronounced at lower frequencies changing by as much as 15%, and the effects of shunt on post-BD Rrsm were similar. The effects in the asthma and healthy model on Rrsm however were much diminished when looking at the relative change due to BD. The difference in the percent changes due to BD due to shunt compared with without shunt was at most 1.9% at 22 Hz and in the asthma model <6%. However, examining Xrsm at 4 Hz (where elastic forces are dominant) shows it was less affected by shunt with changes at most 0.12 cmH₂O·s·L⁻¹at baseline in asthma. In addition, while the response of Xrsm at 4 Hz to BD without shunt was large at 25%, the difference caused by shunt was small at only 0.7%.

Table 3.

Effect of upper airway shunt on baseline and post-BD lung mechanics

	Rrsm, cmH2O·s·L−1 or %			Xrsm, cmH2O·s·L−1 or %
	4 Hz	10 Hz	22 Hz	4 Hz
Healthy
Baseline
Shunt	2.6	2.7	3.4	−2.0
No shunt	2.8	2.8	2.9	−2.0
%Change due to shunt	−7.8	−2.3	17.3	0.21
Post-BD
Shunt	2.3	2.4	2.9	−2.0
No shunt	2.5	2.4	2.5	−2.0
%Change due to shunt	−7.5	−2.7	14.7	−1.1
BD response
Shunt	−13.7	−13.6	−15.2	−0.5
No shunt	−13.9	−13.2	−13.3	0.8
Difference in %BD response due to shunt	0.3	-0.4	-1.9	-1.4
Asthma
Baseline
Shunt	4.3	4.3	4.9	−4.1
No shunt	5.0	4.7	4.8	−4.2
%Change due to shunt	−14.5	−9.1	2.4	−2.8
Post-BD
Shunt	3.3	3.4	4.1	−3.1
No shunt	3.7	3.6	3.7	−3.1
%Change due to shunt	−11.1	−5.6	10.3	−2.0
BD response
Shunt	−22.2	−21.1	−17.0	−24.5
No shunt	−25.2	−23.9	−23.0	−25.2
Difference in %BD response due to shunt	2.9	2.9	5.9	0.7

BD, bronchodilator; Rrsm, model respiratory system resistance; Xrsm, model respiratory system reactance.

DISCUSSION

Our principle findings are as follows: 1) from the patient data, with BD, while Rrs decreased in both healthy and asthma subjects, Ers decreased only in the asthma subjects, and in the asthma subjects, the percent decreases in Rrs and Ers were similar in magnitude; and 2) using this to guide our modeling, excluding recruitment of small airways, we found that that the relative changes in airway diameters with BD were similar between the healthy and asthma subjects and largely attributed to central airways’ influence on Rrs. However, what distinguished the asthma subjects from the healthy subjects was the recruitment response of the small airways, which was needed to describe the changes in Ers and only partially described the changes in Rrs. We also observed little frequency dependence of Rrs, which is often been attributed to be heterogeneity in the small airways. These findings suggest that rather than Rrs or its frequency dependence, Ers assessed by the forced oscillation technique is potentially a very clinically useful measure in asthma to assess the role of small airways.

Consistent with previous observations (12, 59), we found that Rrs was higher in the asthma subjects than in the healthy subjects and decreased in both groups with BD. Furthermore, in the healthy subjects, Rrs remained nearly constant over the oscillation frequencies (12, 33) with only a slight suggestion of any frequency dependence of Rrs (Rrs at 5 Hz larger than at 20 Hz), which is typically found with increased obstruction. Our subjects did not include severe asthma where frequency dependence is more prevalent (10, 13), and thus it may be that with higher severity of obstruction, there might be larger changes in Rrs attributed to the small airways than we observed. However, frequency dependence may arise from either time constant heterogeneities in ventilation attributable to small airways (39) or also to upper airway wall shunting (34) or both (6). Here we explicitly induced ventilation heterogeneity in the model via heterogeneous small airway narrowing, which accurately reproduced the in vivo Xrs data at low frequencies but was insufficient to markedly affect frequency dependence of Rrs in our frequency range. Our model can produce frequency dependence, exhibited at lower frequencies as others have observed (10, 30, 47, 48), indicating that frequency dependence of Rrs requires higher levels of heterogeneity or greater effects of upper airway shunt than we observed in our subjects, despite the heterogeneity present with derecruitment required.

In agreement with the modest level of obstruction in our subjects, there was no significant difference in Xrs between the healthy subjects and subjects with asthma at baseline. This was likely due to large variability in Xrs among the asthma subjects and an overlap in Xrs values between the two groups. Nevertheless, as found in previous studies (12, 51), in the asthma subjects, Xrs increased (became less negative) following BD likely due to the reduction in the stiffness of the respiratory system by airway opening and dilation. In healthy subjects, Rrs reduced with BD as we found, but changes in Xrs were almost negligible (38) in agreement with our observations. This implies that in healthy subjects, any changes in small airways diameter in response to BD are nonmeasurable and do not reach the threshold of recruitment likely as initial diameters are already dilated. In healthy subjects, small airways contribute so little to resistance that they do not contribute mechanically to Rrs in response to a BD, and only the response of the central airways is measured. We interpret that the reduction in Ers in the asthma subjects as indicative of an increase in the lung volume due to opening of previously occluded or closed airways leading to an increase in the observable lung volume. In addition to increases in elastance from closed airways or airways narrowed sufficiently to impede oscillatory flow and thus reduce the communicating parenchymal volume, airway constriction may also directly increase lung tissue stiffness. That is, even at baseline (prebronchodilator) tone in our subjects, alveolar tissue adjacent to airways may be stiffer with the stretch caused by the pull of adjacent airway walls (36) and contribute to Ers. This would tend to lower the required number of airways needed for our baseline model and its changes due to bronchodilator. However, ventilation defects in asthma observed by inhaled gas imaging and its correlation with changes in low frequency reactance are consistent with small airway derecruitment (58). Our findings also agree with observation from Cavalcanti et al. (12) showing an increase in compliance of the respiratory system (Crs) with BD in subjects with asthma. Cavalcanti et al. attributed the increases in Crs to the reduction in airway wall stiffness following BD (12). However, the airway wall is stiffer than lung parenchymal tissue due in part to higher wall tissue stiffness but largely due to the very small fraction of the available compliant tissue surface that contributes to the total Crs. Thus we believe that because of the highly parallel nature of the lung structure, changes in Ers mostly reflect events in the small airways, in agreement with current understanding and similar models of low frequency Xrs probed by oscillometry (7, 16, 17, 21). Other studies have shown that the decreases in Ers arise almost entirely from recruitment of peripheral airways (16, 21, 30).

The changes in Rrs from the subjects with asthma were also well accounted for by our model. Our simulations demonstrated that in the asthma subjects ~40% of the decrease in Rrs arose from opening of small airways while the remainder arose from the dilation of the remaining airways (Fig. 5). This remaining change in Rrs could be attributed to the central airways and came from a relatively modest change in airway diameter of 7.5%, a change in diameter shared by both asthma and healthy lung models. Thus, while the opening of small airways made the difference in differentiating the response from healthy to the asthma subjects in resistance, it accounted for only 40% of the difference in Rrs on top of the healthy response. While by comparison, the change in Ers was almost due entirely to airway opening, changing more than twofold times the relative contribution to Rrs. Thus, while the percent changes in Rrs and Ers are the same in asthma, and one might wish to say they are equivalently useful, the change in Ers is almost entirely due to the mechanism of small airway closure and reopening and appears to more distinctly differentiate asthma from health. Here we used a model to demonstrate that Ers, more than Rrs and its frequency dependence in the usual oscillometry frequency range, was a more direct, and likely a more useful, measure of small airway obstruction in asthma.

Fig. 5.

Percent decreases in the respiratory resistance and elastance measured from healthy and asthmatics subjects (Rrs and Ers) and in the model (Rrsm and Ersm) redrawn. Open bars represent healthy subjects and filled bars represent asthma subjects. The model response showed that in the asthma subjects nearly half of decreases in Rrs resulted from large airway dilation while the remaining half resulted from small-airway dilation; however, decreases in Ers were almost entirely due to small-airway opening. Error bars indicate means ± SE for the in vivo data and means ± SD for 10 random simulations for the model data.

One of our approaches that was different from previous methods was that we estimated Ers by fitting the single compartment model to Xrs versus frequency data, largely to take into account the contribution of inertive properties. Past studies have derived Ers or Crs from Xrs at a single low frequency, which is appropriate for very low frequencies such as <5 Hz as typically done in these studies where inertance is negligible (22). We found that the r² values for the model fits were >0.9 for all but four subjects, despite the heterogeneity needed to describe the mechanics, where perhaps a multicompartment model might be more appropriate. Thus in moderate to severe asthma, where Xrs is very negative, we believe that it would be appropriate to estimate elastance from 5-Hz Xrs as reported in other studies (12).

We found a modest association between Ers and the spirometric indexes of small airway narrowing, FEF25–75% and FVC. This could be because Ers reflects airway narrowing during normal breathing, where as a reduced FEF25–75% and FVC likely reflect airway closures or collapses during forced expiration.

Another technique to assess ventilation heterogeneity and that has been related to airway recruitment via modeling is multiple breath nitrogen washout (MBNW) (8, 18, 53, 54) Performed during normal breathing like oscillometry, it provides indexes that can be sensitive to heterogeneity. While it differs in time scale of measurement, and may thus represent different airways due to difference in time constant sensitivities, it would be interesting to examine if the changes we observe in airway decruitment in modeling Ersm would compare well with models of recruitment derived from MBNW.

This study has some limitations. First, as mentioned above, we assigned all lung compliance to the lung parenchyma assuming noncompliant airway walls. Airway wall and gas compression effects can contribute to mechanics particularly in severe obstruction as demonstrated in models of intubated canine animals with lung injury (3, 15). However, as described above, because the parenchymal volume is large, this effect is small particularly in adults with modest obstruction as in our study. Second, we included only binary derecruitment in our model similar to Tgavalekos et al. (48); that is, small airways were effectively closed by 90% airway obstruction only with no distribution in small airway narrowing. Including either airway wall shunt or more distributed narrowing would also broaden the time constant distribution in our model and thus could shift the balance of number of airways involved in recruitment versus central airways dilation. However, from impedance data alone, there is insufficient information to recover a more graded distribution, even though more complex models are possible (20). We also chose our models to be simple based on the stark lack of change in Ers in response to bronchodilation in healthy subjects, which dictated that only dilation was needed for explaining the mechanics in healthy subjects, and while distributed dilation is more likely, using a single relative change in diameter provides an indication of the magnitude of dilation required for typical bronchodilatory changes in respiratory mechanics, at least for the central airways. To match Ers in asthma and the response to BD, we restricted occlusions to the tenth generation. Similar results could be obtained with obstructions from other levels or combinations. However, these models would not be materially different in reproducing the changes in Ers, as long as the occluded volume, i.e., the unobservable parenchymal tissue beyond the obstruction, is similar. Closure of a ninth generation airway is same as closure of the two daughter airways, although the variation in Ers values that can be achieved becomes less flexible with closures of larger (parent) airways.

One of the interesting findings from this study is that in the model, the percentage of airway closure to account for the baseline data in subjects with asthma was much larger (~47%) than predicted by imaging studies. Previous hyperpolarized helium imaging studies showed that ventilation defects volume in subjects with asthma varied from 6% (mean) to 13% (median) of the total lung volume (44, 50), but depending on the disease severity (mild to severe), signal acquisition, and threshold setting. We think that the difference in defect volumes between our study and the imaging studies is likely due to the difference in effective time constant range for air movement measurable by the probing technologies used. In ³He or ¹²⁹Xe imaging, images are typically acquired over an 8- to 15-s breath hold, permitting more gas redistribution than oscillometry technique probes with probing frequencies >5 Hz typically. Thus, Ers estimated by oscillometry may be more sensitive to the effects of airway derecruitment than longer probing methods.

Conclusions

In conclusion, using a multibranch airway-tree model, we demonstrated that in patients with asthma elastance was more sensitive to peripheral airway derecruitment and its changes with bronchodilator than resistance. Our results suggest that elastance could be clinically useful measure to assess small airway dysfunction and response to bronchodilator therapy in patients with asthma.

GRANTS

This work was supported by Atlantic Innovation Fund, Natural Sciences and Engineering Research Council of Canada (NSERC), and the Lung Association of Nova Scotia. S. A. Bhatawadekar and U. Peters were supported by Atlantic Canada Opportunities Agency, V. Delange by NSERC, and D. Leary by a Canadian Thoracic Society scholarship.

DISCLOSURES

G. Maksym has <5% shares in Thorasys, Thoracic Medical Systems, Montreal, Inc. as a co-founder. None of the other authors has any conflicts of interest, financial or otherwise, to disclose.

AUTHOR CONTRIBUTIONS

S.A.B., D.L., and G.N.M. conceived and designed research; S.A.B., V.d.L., and S.F. performed experiments; S.A.B., D.L., and V.d.L. analyzed data; S.A.B., D.L., U.P., P.H., C.M., and G.N.M. interpreted results of experiments; S.A.B. prepared figures; S.A.B. drafted manuscript; S.A.B., D.L., U.P., P.H., C.M., and G.N.M. edited and revised manuscript; S.A.B., D.L., V.d.L., U.P., S.F., P.H., C.M., and G.N.M. approved final version of manuscript.