1 Introduction

In respiratory diseases such as asthma and chronic obstructive pulmonary disease (COPD), airflow limitation is one of the main correlates of symptom severity, morbidity, and mortality [18–20]. Airflow limitation occurs due to abnormal airway function, namely, reduced airway lumen area [24] and reduced airway compliance [1, 7, 31, 33]. Abnormal airway function may result from altered smooth muscle dynamics [17], airway remodeling [25], and/or reduced parenchymal tethering on the airways [21]. As such, measurements of airway function, particularly airway compliance, are essential for understanding the pathophysiology and progression of obstructive lung diseases.

Airway compliance is defined as the change in airway dimensions that result from changes in transmural pressure. In vivo measurement of airway compliance in the form of airway diameter–pressure relationships have been made in animal models [2, 3, 6, 12]. Brown et al. [2, 3] demonstrated in dogs that airway compliance was decreased, or increased, in association with smooth muscle contraction, or relaxation, respectively. The curvilinear shape of the airway diameter–pressure relationship in these animal studies suggests that, rather than being a constant, airway compliance varies across the entire range of physiological transpulmonary pressures. The ability to quantify airway compliance at any transpulmonary pressure, i.e., instantaneous airway compliance, has the potential to provide additional insight into the physiological and clinical significance of airway mechanical properties.

In humans, direct measurement of airway compliance is difficult, and an indirect or surrogate measure of airway compliance, known as airway distensibility, has been developed [5, 7, 14, 31, 33]. Airway distensibility refers to the change in airway dimensions due to altered lung volume which is an important measurement in a number of diseases such as asthma. However, a limitation of the distensibility technique is that decreased airway distensibility may not be due to decreased airway compliance only, but also to increased lung compliance [8]. In patients with asthma, it was shown that airway distensibility, measured by the forced oscillation technique, was not related to lung elastic recoil [7]; however, it is not known whether the same is true for patients with COPD who have more extensive lung tissue abnormalities. In order to confidently attribute deficiencies in airway compliance to an airway abnormality rather than a lung tissue abnormality, it is necessary to measure changes in airway size with respect to changes in airway distending pressure [8]. However, there is currently no method to directly assess in vivo airway compliance in humans.

In this study, we used high resolution computed tomography (HRCT) measurements of airway diameter, and pressure–volume recordings to generate airway diameter–pressure relationships for airways of varying size, and presented them as a continuous 3D surface. This surface allows the determination of specific airway compliance at any transpulmonary pressure (instantaneous compliance) for airways of varied size. Our method is a novel tool that may elucidate more detailed information about changes in airway mechanics with diseases such as asthma and COPD.

2 Methods

2.1 Subjects

Subjects were recruited from advertisements at the Woolcock Institute of Medical Research (Sydney, Australia). Subjects were free of asthma and other respiratory or cardiac illnesses, current non-smokers with a less than ten pack year smoking history, and free of symptoms of acute respiratory infection. The study was approved by the Human Ethics Committee of The University of Sydney (Protocol No. X03-0222) and subjects gave written, informed consent.

2.2 Experimental design

The subjects were tested on three separate days. During visit one, subjects completed spirometry and lung volume testing. The second visit included spirometry and partial HRCT scans while breathing on a pneumotach. HRCT scans were obtained during a voluntary breath-hold of approximately 15 s at the lung volumes FRC, TLC, and a volume approximately 50% between FRC and TLC (MID), referred to as V FRC, V TLC, and V MID, respectively. Subjects were instructed to breath-hold at the appropriate lung volume by a trained scientist who had visual feedback via a real-time spirogram. Breath-holds were rehearsed prior to the scan. Subjects inhaled maximally to TLC and breath-held during the TLC scan. Scans at MID were obtained by inhalation to TLC then exhaling to a predetermined volume and scans at FRC through a breath-hold at end expiration from a normal tidal breath. Breath-holds were followed by maximal inhalation to TLC to allow verification of the lung volume at which they were scanned. On the third visit subjects completed esophageal pressure–volume measurements.

2.3 Equipment and measurements

Spirometry was performed using a Vmax 20c spirometer (Sensormedics Corporation Yorba Linda, CA, USA) and a Spiropro® hand-held spirometer (Viasys Healthcare GmbH, Hoechberg, Germany) during visit one and two, respectively. Lung volumes were measured using an Autobox 6200 DL plethysmograph (Sensormedics Corporation, Yorba Linda, CA, USA). Spirometry and lung volumes were performed to meet the ATS/ERS acceptability and repeatability criteria [23, 30]. Predicted values described by NHANES III [13] and Crapo [10] were used for spirometry and lung volumes, respectively.

HRCT scanning was completed using a Sensation 16 slice CT Scanner (Siemens AG Berlin, Germany), using settings of 120 kVp and 100 mAs with a slice thickness of 1.0 mm and a rotation of 0.75 s with a table speed of 13 mm s−1. HRCT images were reconstructed using a high spatial frequency algorithm and a 30-cm field of view to a 512 × 512 matrix yielding a voxel dimension of 0.58 × 0.58 × 1.0 mm. Esophageal pressure–volume (P–V) curves were measured according to the method described by Brown et al. [7], where a 10-cm long thin latex balloon was swallowed to predetermined depth [9], filled with 0.5 ml of air, and transpulmonary pressure measured during a deflation maneuver. Individual P–V curves for each subject were characterized by the expression V = x − ye −zP [9] using MATLAB (The Mathworks, Natick, MA, USA). The P–V curves were determined from the change in pressure (P el) from FRC and lung volume represented as %TLC. Individual curve fits for each subject were generated, and the mean P–V curve determined by averaging the coefficients of the individual P–V curves.

2.4 HRCT image analysis

On each HRCT scan, airway segments were identified and matched across several digital image (DICOM format) slices, between scans, and at different lung volumes, using airway bifurcations as anatomical landmarks. An airway segment was defined as a section of airway lying between two consecutive airway branch points.

On each image, mean lumen area was measured using a semi-automated analysis program (WinImageBase, version 1.8.3), which has been previously validated against excised lung as a calibration standard [11]. In brief, airway cross sections were identified on each HRCT image. Radial vectors extending from the centroid to the boundary of the region of interest were generated at equal angles (Fig. 1a). Each radial vector was analyzed to determine the points at which the greatest change in pixel intensity occurred, defining the air–tissue barrier. Airway lumen area was calculated from the number of pixels within the lumen perimeter, and averaged across each slice. Since airway size is commonly described by diameter [2, 16, 27], mean airway lumen cross-sectional area was translated to idealized airway diameter, assuming a circular lumen [11]. No corrections were made for the airway angle.

Fig. 1
figure 1

The four step process to generate specific airway compliance. a HRCT identified airway, spiral vectors determine airway lumen edge and subsequently calculate lumen diameter. b Exponential regression results for the normalized change in diameter (D n) at V FRC (solid line), V MID (dotted line) and V TLC (dashed line), \( D_{{{\text{n}}_{\text{FRC}} }} \)(D FRC), \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC) and \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC), respectively. c Mean pressure–volume (P–V) regression curve (V = 103.76 − 55.53e −0.1261P) generated from subject 1 (open squares) and subject 2 (open circles) data. HRCT volume measurements V FRC (solid line), V MID (dotted line), and V TLC (dashed line) translated to change in lung elastic pressures (P el) P FRC, P MID, and P TLC. d Regression results \( D_{{{\text{n}}_{\text{FRC}} }} \)(D FRC), \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC) and \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC), placed along the third P el axis at P FRC, P MID, and P TLC. e Iterative curve fitting between \( D_{{{\text{n}}_{\text{FRC}} }} \)(D FRC), \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC), and \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) along the P el axis allows the relationship D n(P el) to be described continuously. f Iterative curve fitting from 1e allows the A and K coefficients to be described with respect to D FRC for a complete description of airway compliance with respect to pressure and airway size, D n(D FRC, P el). Note that the x-axis in b and f are reversed for consistency with d and e

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2.5 Determination of airway compliance surface

Airway lumen diameters (D) were measured from HRCT at three lung volumes, FRC (D FRC), MID (D MID), and TLC (D TLC), during deflation. The change in diameter with lung volume was assessed for significance through comparisons of the D FRC, D MID, and D TLC data sets. In order to enable comparison between airways of different sizes, measurements of D FRC, D MID, and D TLC, for each airway, were normalized (n) to their corresponding D FRC measurement and referred to as \( D_{{{\text{n}}_{\text{FRC}} }} \), \( D_{{{\text{n}}_{\text{MID}} }} \), and \( D_{{{\text{n}}_{\text{TLC}} }} \) [29], such that \( D_{{{\text{n}}_{\text{FRC}} }} \) therefore equals 1. \( D_{{{\text{n}}_{\text{MID}} }} \) and \( D_{{{\text{n}}_{\text{TLC}} }} \) data points for both subjects at each lung volume were then grouped and plotted together against absolute diameter D FRC. Subsequently, nonlinear regression was performed on the data using the exponential expression \( y = a + be^{ - kx} \) to determine two relationships: (1) the increase in diameter from FRC to MID with respect to diameter at FRC, \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC), and (2) the increase in diameter from FRC to TLC with respect to the diameter at FRC, \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) (Fig. 1b). The exponent k was determined from the \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) relationship, where the greatest degree of expansion occurred, and was maintained throughout the subsequent regressions. Notably, the \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC) regression using the fixed exponent did not exhibit a significant loss of strength (Fisher Z test, p = 0.34). The difference between regression curves for \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC) and \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) was assessed based on differences between the coefficients a and b.

In order to generate a 3D representation of specific airway compliance, where compliance is described as specific because the change in airway diameter is represented as normalized change, airway diameter measurements were combined with the mean P–V curve. In particular, this involved three steps. First, the change in P el associated with the absolute change in diameter that occurred between each volume (V FRC, V MID, V TLC) was determined by translating the breath-hold volumes during the HRCT scans (V FRC, V MID, and V TLC) to the corresponding change in lung elastic pressure from FRC (P FRC, P MID, and P TLC) using the mean P–V curve (Fig. 1c). Based on the assumption that airway pressure is equal to lung elastic pressure [28], the lung elastic pressures (P FRC, P MID, and P TLC) were used to distribute the \( D_{{{\text{n}}_{\text{FRC}} }} \)(D FRC), \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC), and \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) regression curves on a third axis of P el (Fig. 1d). Second, in order to determine pressure–diameter relationships, D n(P el), for airways of each diameter (D FRC), curve fitting was employed to interpolate between the three values of D n(P el) for each airway size using the expression \( 1 + A\left( {1 - e^{{\left( {KP_{\text{el}} } \right)}} } \right) \), based on Colebatch [9] (Fig. 1e). This process effectively generated a pressure–diameter curve, with coefficient values A and K, for each airway size (Fig. 1f). In order to develop a continuous description of the specific compliance of airway diameter with respect to D FRC and P el, D n(D FRC, P el), changes in A and K with respect to D FRC were described continuously using exponential equations sufficient to achieve R 2 > 0.9999 (Table 2). Finally, a complete set of expressions for the description of specific airway compliance is given by;

$$ D_{\text{n}} \left( {D_{\text{FRC}} , \, P_{\text{el}} } \right) = 1 + A\left( {D_{\text{FRC}} } \right)\left( {1 - e^{{( - K(D_{\text{FRC}} )P_{\text{el}} )}} } \right) $$
(1)

where A(DFRC) and K(DFRC) describe the change of the coefficients for the pressure–diameter curves D n(P el) for varying airway size. The final 3D representation (Fig. 2) reflects diameter–pressure curves for each airway size, plotted together, where the gradient of the surface with respect to P el represents the compliance.

Fig. 2
figure 2

Airway compliance with respect to pressure (P el) and airway size (D FRC), D n(D FRC, P el). This surface shows small airways undergo a larger fractional increase in diameter (D n) with increasing pressure than larger airways. The contour of the surface represents specific airway compliance with changing pressure. A steep contour indicates high compliance, and a gentle contour a low compliance

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The relationships, A(D FRC) and K(D FRC), characterize the features of the diameter–pressure curves at each airway diameter. A(D FRC) represents the maximum degree of expansion from the initial value. K(D FRC) describes the curvature, whereby a larger value equates to a smaller pressure required to increase D n from the initial value to the asymptote (1 + A(D FRC)). The plateau pressure, P p, defined as the pressure at which 95% of the expansion of the airway has occurred can be determined from, P p = 3/K(D FRC) (Fig. 3a). Finally, the derivative of the D n(D FRC, P el) relationship (Eq. 1) allows specific airway compliance (C n) to be described for any airway size at any P el (Eq. 2).

$$ C_{\text{n}} \left( {D_{\text{FRC}} ,P_{\text{el}} } \right) = K\left( {D_{\text{FRC}} } \right)A\left( {D_{\text{FRC}} } \right)e^{{( - K(D_{\text{FRC}} )P_{\text{el}} )}} $$
(2)
Fig. 3
figure 3

Plateau pressure (P p) and compliance (C n) at P FRC, P MID, and P TLC determined from 3D compliance surface. P p is proportional to airway size (a). Compliance at P FRC and P MID are inversely proportional to airway size and greater than the compliance at P TLC, respectively

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2.6 Statistical analysis

Data are shown as means with standard errors unless otherwise stated. In order to assess the change in diameter between V FRC, V MID, and V TLC, one way RM ANOVA with Student–Newman–Keuls post-hoc analysis were performed on consecutive data sets D FRC, D MID, and D TLC. The T statistic was used to assess differences between the individual P–V curve fits and between the coefficients of the curve fits for D FRC(\( D_{{{\text{n}}_{\text{FRC}} }} \)), D FRC(\( D_{{{\text{n}}_{\text{MID}} }} \)), and D FRC(\( D_{{{\text{n}}_{\text{TLC}} }} \)).

3 Results

Two male subjects took part in the study. Subject demographics and lung function results, which were within normal limits, appear in Table 1. From the HRCT scans, 22 individual airway segments were identified from the intermediate and lower lobe bronchi. Airways identified at only one lung volume or not identified at FRC were excluded, leaving 14 airways (Subject 1: 3 airways; Subject 2: 11 airways) included in the analysis ranging from 1.4 to 7.7 mm. The breath-hold volumes during the HRCT scans were averaged, due to similarity of the lung volumes, with the following results, V FRC (51.6% TLC), V MID (75.9% TLC), and V TLC (99.6% TLC). P FRC (0 cm H2O), P MID (3.96 cm H2O), and P TLC (17.92 cm H2O) were calculated using the mean P–V curve (Fig. 1c).

Table 1 Anthropometric characteristics and lung function results for Subject 1 and 2
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3.1 Specific airway compliance

Airway diameters at V MID (mean \( D_{{{\text{n}}_{\text{MID}} }} \) = 1.20 ± 0.05) and V TLC (mean \( D_{{{\text{n}}_{\text{TLC}} }} \) 1.30 ± 0.06) were significantly greater than at V FRC (p < 0.001), however, the difference between MID and TLC did not reach significance (p = 0.09). Normalized diameter data for \( D_{{{\text{n}}_{\text{FRC}} }} \)(D FRC), \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC), and \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) are shown in Fig. 1b. \( D_{{{\text{n}}_{\text{TLC}} }} \) was greater in the smaller sized airways compared to the larger sized airways, which demonstrates that specific compliance increases with decreasing airway size. The equation coefficients, R 2 and p values for these regressions are included in Table 2. Each Regression was statistically significant (p < 0.05). Comparison of the coefficients between \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC) and \( D_{{{\text{n}}_{\text{TLC}} }} \)(DFRC) showed no significant differences in a (p = 0.09) or b (p = 0.76).

Table 2 Regression coefficients for \( D_{{{\text{n}}_{\text{TLC}} }} \)(D FRC) and \( D_{{{\text{n}}_{\text{MID}} }} \)(D FRC) along with regression equations for the continuous description of A(D FRC) and K(D FRC)
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The normalized change in diameter (D n) as a function of airway diameter at FRC (D FRC) and pressure (P el), referred to as D n(D FRC, P el), is presented continuously as a 3D surface (Fig. 2) which quantifies how the pressure–diameter curve changes with airway size. Changes in the shape of the pressure–diameter curve are characterized by the coefficient relationships A(D FRC) and K(D FRC), which fall progressively with increasing airway diameter (Fig. 1f). Based on these coefficients, we observed that airway plateau pressure P p increases progressively with increasing airway diameter. We found that P p is greater for larger airways and lower in smaller airways (Fig. 3a). Calculation of the instantaneous compliance at P FRC, P MID, and P TLC, showed greater compliance at P FRC compared to P MID and P TLC, and that compliance at P FRC and P MID was inversely related to airway size (Fig. 3b).

4 Discussion

This study describes a novel method to determine in vivo airway diameter–pressure curves for airways of varying size in humans. In addition, the method allows specific compliance to be determined at any transpulmonary pressure for a range of different sized airways. The method incorporates HRCT measurements of airway diameter with pressure–volume recordings to generate a unique description of specific airway compliance over a range of distending pressures. We found that smaller airways expand to a greater extent than larger airways, consistent with previous studies in animals [1, 29]. In addition, specific airway compliance is greatest at low pressures (FRC) and decreases with increasing airway size. This corresponded to airway plateau pressure increasing progressively with airway size.

Several methodological issues warrant discussion, which include assumptions used, technical limitations, and sample size. The assumptions of the study were: (1) That data obtained from both subjects were comparable and therefore grouping these data was appropriate. This was considered reasonable as subject anthropometrics were similar and, at the lung volumes measured during HRCT scans, individual P–V regressions were also similar; (2) That the gravitational effect on pleural pressure was negligible, and therefore corrections for variations in pleural pressure with gravity [22] were not included; (3) That changes in the esophageal pressure corresponded to changes in the airway transmural pressure, which is valid during breath-hold maneuvers [28], such as those completed during the HRCT scanning. In the presence of parenchymal uncoupling [21] this assumption may be invalid, although unlikely in this study due to the use of normal healthy subjects, in whom lung tissue abnormalities would not be expected. The potential effect of a loss of airway-parenchymal tethering in disease would be reduced airway distension during lung inflation. Therefore, airways would appear less compliant, if measured using the current method; yet it would be unclear whether this was due to airway stiffening or impaired transmission of airway distending forces. This will remain an issue until better methods of measuring airway-parenchymal tethering are developed.

Technical limitations include: (1) The postural mismatch between volume and pressure measurements. Lung volume [32], lung compliance, and P FRC [32] will be reduced in the supine position, during HRCT scans, compared to the upright position. This is a common issue in HRCT studies and we have attempted to minimize its impact, by measuring relative lung volume changes, from maximal lung inflation, during the supine HRCT scans. Maximal lung inflation, measured during HRCT, was matched to TLC, which was measured in the upright position. However, the important measurement is the relative change in lung volume during the scan, which was measured supine. The reduction in lung compliance in the supine position is not accounted for in this study, but the likely effect would be an overall reduction in airway compliance. (2) It has been reported that HRCT measurements of airway lumen area are underestimated in small airways [4, 34], which would result in an overestimation of compliance. However, the magnitude of effect between different airway sizes is difficult to estimate. Importantly, in this study, we used a lumen measurement method [11, 15] where although precision is reduced in the smaller airways, we validated the method to be specifically bias free, avoiding potential errors in calculated compliance.

The sample size of the study and hence the power of the 3D surface could be improved by the addition of more airway measurements by either increasing the number of subjects in the study or making airway dimension recordings at a fourth or fifth lung volume. However, the small sample size was sufficient to demonstrate the functionality of the method while minimizing radiation exposure to the subjects.

Despite the limitations of the study, the foundation of the surface was a statistically strong set of regression curves. More importantly, the method enables a description of specific airway compliance to be developed from in vivo, human data, which has not previously been possible.

The 3D surface model generated in this study suggests that airways do not dilate isotropically with lung inflation. The airway diameter–pressure curves vary with airway size, which would not have occurred with isotropic lung expansion. This finding is in agreement with similar work in dogs [2]. Based on our 3D surface model, our study found for the first time in adult humans that small airways are more compliant than large airways which is in agreement with prior studies in mice [29] and have lower plateau pressures than larger airways. The mechanism for the increased specific compliance of small airways is likely due to differences in airway wall composition, specifically decreased or absent cartilage in small airways compared with large airways [26]. The greater specific compliance and lower plateau pressure in the smaller airways may also be of major importance for minimizing airflow resistance during breathing.

In conclusion, we have described a new method for determining in vivo airway diameter–pressure relationships in humans, in a manner which allows quantification of specific airway compliance for any transpulmonary pressure across a range of airway sizes. The measurement of specific airway compliance has many potential applications in studies of airflow limitation. It will allow realistic in vivo airway compliance values for mathematical assessment of airflow resistance during breathing to be determined. It has the potential to examine, in detail, changes in airway mechanics during the transition from mild disease to chronic and life threatening airflow limitation, which is still poorly understood.