Theoretical framework

We characterize the interplay between the airway wall and its surrounding parenchyma in terms of the relationship between outer airway cross-sectional area (A_o) and the degree of surrounding (peribronchial) parenchymal expansion (E_pb) elevated to the ^2/3 power (E_pb^2/3) to preserve dimensionality. A_o is the sum of inner luminal cross sectional area, A_i, plus the cross sectional area of the airway wall, A_w. E_pb is defined as the volumetric ratio of gas to parenchyma tissue within a spherical region adjacent to the airway [13–17] as detailed in the supporting material (S1 Fig). To account for size differences in among different airways, the relationship is expressed as a plot where A_o and E_pb^2/3 are normalized by their respective values measured at total lung capacity (TLC) or: (A_o/A_o,T) vs (E_pb/E_pb,T)^2/3 (Fig 1). In such a plot lung expansion from mean lung volume (MLV) to TLC for a given airway, follows a path with a cord slope that defines the distensibility of the airway relative to that of the peribronchial parenchyma, RD: (1) Airways with RD < 1 are relatively stiffer, and thus expands less than the surrounding parenchyma as lung volume is increased to TLC. Conversely, airways with RD > 1 expand relatively more than the surrounding parenchyma and those with RD = 1 have a stiffness equivalent to that of the parenchyma.

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Fig 1. Empirical framework, (for explanation see text).

https://doi.org/10.1371/journal.pone.0208337.g001

Examples for the behavior of three hypothetical airways are presented in Fig 1. All three airways start with a fully relaxed state at baseline (point B) but are submitted to different degrees of smooth muscle activation during broncho-provocation. It is also assumed that lung volume increases following broncho-provocation such that the peribronchial parenchyma increases normalized expansion (E_pb/E_pb,T)^2/3 from 0.62 to 0.7. Depending on their degree of smooth muscle activation, the states of the three airways should follow paths to different equilibrium states following bronchial challenge. If the smooth muscle force is not affected by the MCh challenge, the airway state can be expected to follow the non-linear path such as that for a fully relaxed airway [18] reaching an equilibrium state at P1, with A_o,P1/A_o,T > A_o,B/A_o,T. With further expansion of the lung to TLC, the airway becomes stiffer than the parenchyma (RD < 1), as it approaches its maximum passive circumference. In a second airway, the force generated by the airway smooth muscle (ASM) after MCh is just enough to balance the force exerted by the expanded parenchyma, and A_o/A_o,T remains unchanged, reaching its new state P2. In a third airway, the ASM force greatly exceeds the forces generated by the expansion of the surrounding parenchyma, and A_o/A_o,T becomes smaller in state P3 or, A_o,P3/A_o,T < A_o,B/A_o,T. Further elevations of lung volume to TLC for these last two airways results in paths of higher RD (slope) than that for the first airway.

Assuming linearity for the A_o,P/A_o,T vs. (E_pb/E_pb,T)^2/3 relationship for each airway, one can estimate the outer cross-sectional area that any airway would have reached (A*_o/A_o,T), had the peribronchial lung expansion remained unchanged after MCh. Such an assumption seems reasonable for constricted airways based on CT imaging observations of canine lungs by Brown et al. [18] (S7 Fig).

However, Brown et al. [18] also showed that for a relaxed airway the slope of the relationship decreases with lung inflation and thus for those airways A*_o,1/A_o,T would over-estimate the expected value of the airway that should have remained equal to that at baseline A_o,B/A_o,T.

Nonetheless, for airways with constricting ASM, such as those in conditions P2 and P3, the extrapolated values of A*_o /A_o,T would be lower than at baseline, A_o,B/A_o,T, and post MCh, A_o,P/A_o,T. Note also that for an airway with very high ASM force, in a condition like P3, the extrapolated value A*_o may be less than A_w, or (A*_o,3/A_o,T < A_w,P/A_o,T). Since the luminal area A_{i =} A_o + A_w, this would predict a negative value for A_i or:

Clearly, a negative luminal area would be physically impossible. However a negative value of A*_i,3/A_o,T would represent a state where ASM force more than exceeds the distending force opposed by the parenchyma distended at baseline conditions, and thus the airway lumen would be completely shut, and the excess in ASM force would be balanced by compression forces on airway wall tissues central to the ASM band. In this case, as the airway would remain closed as lung volume increases until peribronchial expansion exceeds a critical value (E_pbCrit,3/E_pb,T)^2/3.

Evaluation of the critical peribronchial expansion for each segmental airway of the tree and assuming that the airway wall areas remain unchanged during an expiratory forced vital capacity (FVC), allows estimation of the volume of the subtended lung that would be trapped by closing airways during the expiratory maneuver. The sum of these estimated trapped volumes during a FVC maneuver would be an approximation of the contribution of these closing segmental airways to the reduction in FVC after bronchoconstriction.

In summary, in this report we used the empirical framework described above for the following objectives: 1) Analyze experimental imaging data from normal and asthmatic lungs in conditions where the subjects are allowed to choose their mean breathing volume before and after bronchoconstriction. 2) Evaluate whether closure of individual segmental airways could have occurred if lung volume was not elevated following MCh bronchoconstriction (were there airways with values of A*_i,3/A_o,T <0 ?). 3) Test whether the elevation of lung volume by each subject following bronchoconstriction resulted in peribronchial expansion around segmental airways that matched or exceeds the critical value for closure. And 4) estimate the volume of gas expected to be trapped behind closed segmental airways during a forced vital capacity maneuver and compared it with the changes in FVC observed for each subject. Specific imaging protocols, analysis of the imaging data, and methods for comparison of predicted against measured values for each subject are presented below.

Subjects

This study analyzed HRCT scans of subjects that were imaged with PET/CT as part of published research protocols [19,20]. Data was collected under a Massachusetts General Hospital IRB approved protocol. Scans from seven subjects with demonstrated reversible obstruction and mild-moderate asthma (AS) and nine healthy controls (NA) were analyzed. AS subjects were selected according to the criteria of the NIH Global Initiative for Asthma [21]: airways hyperresponsiveness, a history of intermittent airway obstruction, less than daily symptoms, forced exhaled volume within 1 sec (FEV₁) or forced vital capacity (FVC) ≥80% predicted, and peak flow or FEV1 variability of ≤30%.

At the time of the study all subjects were either non-smokers or had a pack-year smoking history ≤ 10. Other exclusion criteria were: known cardiopulmonary disease or chronic respiratory disorder other than asthma, pregnant or nursing women (confirmed via serum beta-HCG test), upper and lower airway respiratory infection or emergency visits or hospitalizations in the month prior to screening, previous exposure to more than half the radiation dose for the study in the past year (3.75 mSv, or equivalent), or had taken oral steroids in the past year for their asthma. No systemic or inhaled corticosteroids had been used within one week prior to enrollment.

Study design

Subjects attended two separate visits. Short- and long-acting bronchodilator medications were stopped 8 and 48 hours respectively, prior to the visits. In a screening visit, baseline spirometry was acquired in the erect position (Satellite Spirometer, Jones Medical Instrument, USA) followed by a standard five-breaths MCh challenge test with a jet nebulizer (Rosenthal dosimeter) according to ATS guidelines [22]. AS subjects were given MCh at increasing concentrations to estimate the value that caused a 20% reduction in FEV₁ (PC20). For AS subjects PC20 dose ranged form 0.116 to 4.9 mg/ml. In NA subjects the absence of airway hyperresponsiveness was ascertained when a MCh challenge with a maximum concentration of 25 mg/ml failed to reduce FEV1 by 20% from baseline. During a second (imaging) visit, the subject was positioned supine in the PET/CT scanner and a baseline (B) full-chest HRCT scans was obtained during a short breath-hold (~12 sec) at a lung volume equal to the mean lung volume (MLV) measured during a 30 sec of stable tidal breathing prior to the scan.

In order to determine the values of MLV, and ensure constant volume during the breath-holds, impedance plethysmography (SomnoStarPT, SensorMedics, USA) was used to monitor dynamic lung volume in real time. The SomnoStarPT output signal was plotted in real time with a laptop computer and the screen presented to the subject via a head mount display (Argo Cinema 2 Goggles, Welton Electronics Inc, Hong Kong). MLV was estimated by averaging the volume signal over 30 seconds of stable breathing, and presented to the subject as a reference line superimposed on the real time lung volume signal.

Following the baseline scan (B), the MCh challenge was given at a concentration equal to the previously determined PC20 for the AS subjects, and equal to 25 mg/ml for the NA subjects.

After allowing 10 minutes to establish bronchoconstriction, a second post MCh HRCT scan (P) was obtained at a lung volume equal to the subject’s new spontaneous MLV. Finally, and still during bronchoconstriction, a third HRCT scan (T) was acquired with the lungs at total lung capacity (Fig 2). Spirometry was performed after B and P scans with the subject remaining supine within the scanner.

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Fig 2. Study protocol.

With the subjects in the supine position, HRCT images were acquired during a short breath hold (~12 s) under three consecutive conditions: 1) at baseline (B) and imaged at mean lung volume (MLV), where MLV was defined as the average lung volume during stable tidal breathing; 2) following five deep breaths of MCh at his/her previously determined PC20 dose and imaged at the subject’s spontaneous MLV (P); and 3) post MCh and imaged at total lung capacity (T). Colored regions of the lung correspond to 3 of the ~19 parenchyma segmental regions studied in each lung.

https://doi.org/10.1371/journal.pone.0208337.g002

In order to standardize the lung volume history and facilitate the breath-hold during imaging, prior to the B and P scans, the subjects were asked to take a deep inspiration and exhale out stopping at the MLV value shown at the head mount display.

Analysis showed no difference in lung function at baseline between the two groups although the AS group was, by definition, hyper-responsive, as indicated by a PC20 < 4 mg/ml [22]. FEV₁ and FVC values were influenced by the change in posture between the screening visit (seated) and the imaging day (supine) with FEV₁ significantly higher in the screening visit both the asthma (p<0.05) and control groups (p<0.001) (Table 1).

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Table 1. Subject characteristics.

https://doi.org/10.1371/journal.pone.0208337.t001

Imaging and regional analysis

The HRCT scans were obtained using a Siemens Biograph 64 PET-CT scanner. The scanner was used in a helical mode with 64 slices per rotation, 0.6 mm collimation, a pitch of 1, 120 kV peak, and 80 mA. The image reconstruction was done using the B31 kernel with a slice thickness of 0.75 mm, 0.5 mm slice increment and 0.25 mm overlap (as recommended by VIDA Diagnostics, IA, USA).

Airway and parenchymal segmentation and measurements.

Image analysis included quantification of airway dimensions and regional parenchymal expansion (Fig 3). Airways and parenchymal regions were rendered, segmented and characterized from the HRCT scans using the Pulmonary Workstation 2.0 (PW2) software (VIDA Diagnostics, IA, USA). Airway dimensions were extracted from PW2 for 19 anatomically defined segmental airways for each of the three conditions [23]. The following parameters were imported into MALTAB (Mathworks, Natick, MA) for each airway: 1) lumen (A_i) and 2) outer (A_o) cross-sectional areas, 3) length (L), 4) centerline, 5) branching point information (between mother and daughter airways for each bifurcation), and 5) anatomical labeling. Both A_i and A_o corresponded to the average across sections of the middle third of the airway length, as defined by PW2 [23]. By inspection, airways with centerline not perpendicular to the airway cross-section and/or showing software segmentation errors were excluded (typically one airway per scan). Only airways that could be identified and characterized in each of the three scans were included in the analysis.

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Fig 3. Methodology overview.

Airway and parenchymal segmentation were performed to the HRCT images at the three different conditions. Using VIDA software, values of inner (A_i), outer (A_o) and wall (A_w) cross-sectional areas were obtained for each of the 19 segmental airways. A spherical region of diameter four times the outer airway diameter was defined around each airway center point. Intersection of the sphere with the parenchymal mask defined a peribronchial (pb) ROI, and its average expansion (E_pb) normalized by its value at TLC (E_pb /E_pb,T), was plotted vs A_o normalized by the outer airway area at TLC (A_o /A_o,T). The data shown in the plot are averages for all AS (black) and NA (red) subjects. (One graphical element on this Fig is a modified version from original in http://image.diku.dk/exact/).

https://doi.org/10.1371/journal.pone.0208337.g003

Using PW2 on the HRCT images, we also defined masks of the lung pleural surfaces, airway tree, vessel tree and the 19 segmental sub-lobar regions (subtended by the 19 identified segmental airways, Fig 3). The rendered airways and segmental sub-lobar regions were visual inspected for completeness and accuracy. Manual editing of improper segmentation was performed when necessary.

A lung parenchyma mask was obtained after subtracting from the lung surface masks voxels including airway and pulmonary vessel trees, and applying a threshold including voxels between -950 to -400 Hounsfield units (HU). This excluded bronchial, pulmonary vessel, and lymphatic tissues, (especially those located within the interlobular septa), and nerves, that were obvious by close inspection. For each voxel the fractional air content or gas fraction (F_gas) is calculated as in reference [24] using the equation With HU_blood = 65 and HU_air = -1,000, and HU in Hounsfield Units.

Segmental parenchyma ROI’s were defined as the intersection of the segmental regions with the lung parenchymal mask.

Peribronchial parenchyma ROI’s were defined for segmental airways as follows. First, the location of the center point (CP) along the axis of each segmental airway was defined. For the B condition, a spherical region, centered at the CP, was defined with a diameter equal to four times that of an equivalent circle with area A_o. The intersection of this sphere with the parenchyma mask defined a peribronchial ROI. The relative diameter of the sphere was defined based on modeling studies showing non-uniform parenchymal deformation within this region during lung inflation [25]. For the P and T conditions, the diameter of the sphere was adjusted iteratively, until the total parenchymal tissue volume within the ROI was within 5% of that measured at B. This ensured that approximately the same tissue was evaluated for the three conditions.

For each airway, the following parameters were also determined: 1) The relative vertical-distance (Δh) between the airway’s CP and the corresponding geometric center of the subtended segmental parenchymal ROI normalized by the lung maximal dorso-ventral height. 2) The parenchyma expansion of the subtended segment (E_SL) and the peribronchial parenchyma expansion (E_pb), both estimated as the ROI’s voxel average of: F_gas /(1-F_gas), which correspond to the average voxel gas-to-tissue volume ratio. 3) The sampled volume by the peri-bronchial parenchyma ROI (Fs), as a fraction of the theoretical ROI volume (the volume of the sphere minus that of an intersecting cylinder of cross-sectional area A_o).

For each condition, the global lung expansion (E_Lung) was estimated as the voxel average of gas-to-tissue volume ratios within the global lung parenchymal mask.

Change in mean lung volume and forced vital capacity after MCh

To evaluate the gas volume trapped behind each closing airway using Eqs 3a or 3b, it was necessary to account for a measured difference ΔE_mean between segment’s distal parenchyma, E_SL, and its local peribronchial expansions E_pb, using the empirical relationship obtained between ΔE_mean and E_Lung presented in Fig 4, as: (4)

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Fig 4. Mean difference between sub-lobar and peribronchial parenchyma expansion, adjusted by height difference, ΔE_mean plotted for each subject vs. average lung expansion, E_Lung, in three conditions for the group of subjects without asthma (NA, left) and with asthma (AS, right).

The conditions are Baseline at MLV (Green), post MCh at MLV (Red), and post at TLC (Blue). Points for each subject are connected with dashed lines. There is no apparent difference in the behavior of both groups.

https://doi.org/10.1371/journal.pone.0208337.g004

For each subject we calculated an expected change in lung volume between baseline and that at which the first segmental airway would have closed (ΔV_C). To do that, we selected the airway with the lowest value of (A_i*/A_o,T) and estimated its critical peribronchial expansion E_pbCrit/E_pb,T, using the empirical relationship between peribronchial and segmental expansion for that subject (Eq 4), ΔV_C was estimated as: (5) TLC normalized values of ΔV_C were plotted against the change those MLV measured for each subject (see Results).

Finally, to estimate the total sum of air volume trapped behind closing airways (V_Tr) during a FVC maneuver, we considered the sum of volumes behind each airway (j) expected to close during a forced vital capacity, or those behind airways with E_pbCrit > E_pb at RV (): (6) were the residual volume at RV post MCh, RV_P, was calculated as the difference between TLC (measured from the CT) and FVC, assed by spirometry post MCh in the supine position.

was then plotted against the fractional reduction of FVC measured between baseline and post MCh.

Statistical analysis

Data are expressed as mean ± SD and statistical analysis was completed using MATLAB. Significance was accepted at P < 0.05. Paired T-tests were used for assessing differences between conditions, or between peribronchial and segmental measures for each subject, and unpaired T-tests were used to assess differences in demographic and measurements between the asthma and control groups.

Differences between peribronchial and segmental expansion

Histograms of voxel gas-to-tissue volume fraction (E) values within peribronchial and segmental ROI’s showed a shift to the right as lung volume increased from baseline to post MLV and to TLC (S2 Fig).

In average MLV as a fraction of TLC increased from 0.53±0.78, at baseline, to 0.66±0.11 after bronchoconstriction (p<0.01) in NA and from 0.55±0.97 to 0.68±0.12 in AS (p<0.05), but these changes were not significantly different between groups (Tables 2 and 3). Consistent with the changes in lung volume, the average values of E_pb and E_SL, also increased after MCh challenge, and further increased with lung inflation to TLC. The changes in E_SL for the subtended segment’s peripheral parenchyma were systematically greater than those in peribronchial E_pb of the feeding airway (S3 Fig).

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Table 2. Differences between peribronchial and segmental parenchymal expansion ΔE.

https://doi.org/10.1371/journal.pone.0208337.t002

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Table 3. Differences between peribronchial and segmental parenchymal expansion ΔE (Continued).

https://doi.org/10.1371/journal.pone.0208337.t003

This difference in parenchymal expansion between average subtended segment parenchyma and peribronchial parenchyma ROIs, was heterogeneous between segments but presented a systematic dependency with the vertical-distance between the respective ROI’s geometric centers for all conditions (S4 Fig): ΔE = E_SL-E_pb was greater for segmental airways feeding non-dependent parenchyma (Δh>0) and lower for airways feeding more dependent parenchyma (Δh<0).

The average difference between segmental and peribronchial expansion, after de-trending for the vertical location dependence ΔE_mean, was highly dependent on the average expansion of the whole lung (E_Lung), for each subject and condition and for both AS and NA subjects. No significant differences between AS and NA were found in this dependence but ΔE_mean tended to be higher for AS at TLC.

Note that for both groups, ΔE_mean was around zero in the subjects-conditions with the lowest values of E_Lung, and that ΔE_mean increased monotonically as E_Lung increased (represented in figures of section ‘changes in luminal cross-sectional area, mean breathing lung volume and forced vital capacity with methacholine’).

Behavior of airways and peribronchial parenchyma during bronchoconstriction

There was no difference between the AS and NA groups for average values of E_pb/E_pb,T and A_o/A_o,T at baseline (Fig 5). There was a general increase in mean lung volume (V_L) following MCh (Tables 2 and 3), as well as in average E_pb/E_pb,T that increased significantly in both AS and NA groups of subjects (p<0.05 and p<0.01, respectively). Broncho-provocation with MCh left average A_o/A_o,T unchanged in AS, but caused a minor reduction in NA. Also, the average values of A_o/A_o,T and E_pb/E_pb,T for the P*, P and T states fell along the same line for both AS and NA groups, as expected for the similarity in average RD between the two groups. Average RD 0.75+/-0.48 for AS and 0.75+/-0.55 for NA.

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Fig 5. Effects of broncho-provocation with MCh (B to P) and inhalation to TLC (P to T), on average airway cross-sectional outer area (A_o), vs the corresponding averages of peribronchial parenchymal expansions, E_pb.

Plots present the relationship between, A_O normalized by the equivalent area at TLC (A_o,T) and E_pb normalized by E_pb at TLC (E_pb,T) elevated to the ^2/3 power, at baseline (B), post MCh (P) and TLC (T) of all segmental airways for all subjects with asthma (AS in in black) and those without asthma (NA in red). The data are presented as mean +/- SEM. The slope of the relationship between P and T corresponds to the relative distensibility (RD) of the average airway. corresponds to the value of the airway outer area, A_o, as estimated by extrapolation assuming constant RD, that would have been expected had there been no change peribronchial expansion, E_pb, following bronchoconstriction. Also shown are the values of airway wall area A_w normalized by A_o,T (A_w/A_o,T) for the three states B,P and T, and the difference between A_o*/A_o,T and A_w/A_o,T corresponds to the average luminal area had peribronchial lung expansion remained the same as at baseline (A_i*/A_o,T).

https://doi.org/10.1371/journal.pone.0208337.g005

RD of individual airways was highly heterogeneous among airways and subjects (S6 Fig). RD varied from close to zero in some airways to as high as three in others including values above and below unity.

Average values of airway wall area A_w normalized by A_o,T (A_w/A_o,T) were similar between B and P but were significantly greater at T in both groups (P<0.001).

Changes in luminal cross-sectional area (Ai), mean breathing lung volume (MLV) and forced vital capacity (FVC) with methacholine (MCh)

There were no statistical differences between AS and NA in the relative degree of obstruction caused by MCh, estimated as the fractional change in airway luminal area between B and P (A_i,B-A_i,P)/A_i,B. However, the average (A_i,B-A_i,P)/A_i,B for each subject, was inversely correlated with ΔV_L/TLC, (R = -0.63, P<0.01 for all subjects, Fig 6). Thus the increase in lung volume between B and P was not greater for the subjects showing the greatest degree of airway narrowing after MCh. On the contrary, the relative reduction in airway lumen caused by MCh occurred in subjects showing the lowest increases in lung volume.

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Fig 6. Measured values of ΔV_L/V_TLC for each subject vs. average change in luminal airway among segmental airways following MCh, for subjects with (AS, blue) and without (NA, red) asthma.

Although it was relatively weak, the negative association (R = -0.63, P<0.01 for all subjects) between the variables indicates that subjects with the greatest relative reduction in average airway luminal cross-sectional area, (highest degree of narrowing), tended to be those with the lowest changes in lung volume Post MCh, or inversely: the subjects with greater increases in lung volume Post MCh tended to have an increase in average luminal airway or, (A_i,B-A_i,P)/A_i,B <0.

https://doi.org/10.1371/journal.pone.0208337.g006

ΔV_L/ V_TLC after MCh, was also inversely correlated (R = -0.83, P < 0.001 for all subjects) with the lowest value of A*/A_o,T of each subject among his segmental airways (A*/A_o,T)min (Fig 7, left).

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Fig 7.

LEFT: Plot of the relative change in mean lung volume (ΔV_L/V_TLC) chosen for breathing after MCh by each subject, vs the corresponding minimum value of A_i*/A_o,T, amongst all segmental airways of each subject (A_i*/A_o,T)min. This illustrate an inverse association between the variables (R = -0.83, P<0.001 for all subjects). Each data point corresponds to a subject of the AS (blue) and NA, (red) groups. RIGHT: Plot showing the Inverse association (R = 0.76, P<0.001 for all subjects) between ΔV_C/V_TLC and the critical change in lung volume causing for first airway to close (ΔV_Crit/V_TLC) in both groups. Note that the relative change in MLV for each subject after MCh was always at least 15% higher of that for predicting the onset of the first airway closure in each subject.

https://doi.org/10.1371/journal.pone.0208337.g007

Similarly, ΔV_L/V_TLC, was significantly associated (R = 0.76, P<0.001 for all subjects) with the critical change in lung volume for closure of the first airway normalized by V_TLC (ΔV_C/ V_TLC) (Fig 7, right). Note that the change in mean lung volume chosen by each subject for breathing after MCh, was at least 15% higher than the critical change in volume estimated for closure of the first airway of that subject.

Finally, the change in force vital capacity relative to TLC by MCh (ΔFVC_(P-B)/FVC_B) for each subject was higher than but correlated with the volume of gas estimated to be trapped behind closed segmental airways (V_Tr /FVC_B) during a FVC (Fig 8). There were large differences in ΔFVC_(P-B)/FVC_B among subjects raging from 3% to 32% of baseline in NA, and from 10% to 50% in the AS group. By enlarge, the measured changes in FVC were equal, or greater, than those predicted by our analysis for all subjects ΔFVC_(P-B)/FVC_B ≥ ΔV_Tr/ FVC_B.

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Fig 8. Measured relative drop in FVC from baseline to post MCh (ΔFVC_(P-B)/FVC_B) plotted as a function of the sum of volumes estimated to be trapped behind closing segmental airways during a force vital capacity maneuver (V_Tr /FVC_B).

Each data point corresponds to a subject of the AS (blue) and NA, (red) groups.

https://doi.org/10.1371/journal.pone.0208337.g008

In the NA subjects ΔFVC_(P-B) increased in the same proportion of the estimated trapped gas volumes (slope = 0.97) and was ~ 7% higher than ΔV_Tr (intercept = 0.07). In the AS subjects, the values ΔFVC_(P-B) were substantially greater for the same range of estimated ΔV_Tr and followed a regression line with an intercept (0.15) twice as high and a slope (1.74) 74% higher than those for the NA subjects. For each subject the difference between the measured ΔFVC_(P-B)/FVC_B and the estimated ΔV_Tr/FVC_B corresponds to the fraction of the reduction in FVC in addition to that caused by closure of segmental airways. Such fraction was significantly (P<0.05) greater in AS compared with NA subjects.

Expansion of the peribronchial and segmental parenchyma

Average peribronchial parenchyma expansion around constricted segmental airways (E_pb) was generally different than that of the subtended parenchyma (E_SL). Such a difference depended in part on the relative vertical distance between center of gravity of the segmental parenchyma and the peribronchial ROI center (S4 Fig). Such a vertical dependence is consistent with the well known vertical gradient in lung expansion for human lungs in the supine position [41–46]. Indeed, at baseline conditions and once the vertical dependence was accounted for, sub-lobar and peribronchial parenchyma were equally expanded (E_SL- E_pb~0). However, as lung volume increased after bronchoconstriction, expansion of the peribronchial parenchyma was less than that of the subtended parenchyma, (E_SL- E_pb>0) with a difference that was correlated with the global degree of lung expansion (E_Lung): for either a subject or condition the greater E_Lung the greater (E_SL- E_pb) (Fig 4). This means that, except for the expected gravitational differences in lung expansion, under normal breathing conditions the parenchyma is uniformly expanded across iso-gravitational planes the lung. However, as the breathing lung volume increased with broncho-constriction, E_pb increased less than E_SL generating the differences observed in parenchymal expansion. A possible cause for this difference could be a local effect of the stiffer airway and vascular trees as predicted by theoretical modeling studies [20] for parenchyma within 4 diameters of the airways.

Airway-parenchyma interdependence of individual airways and changes in mean lung volume during breathing after MCh challenge

The findings of heterogeneity in parenchymal expansion within the lung may have implications for understanding airway narrowing and for disease diagnosis. Distention of the airways by the parenchyma has been identified as a potent bronchodilator, at least in normal human lungs. Lai-Fook and colleagues [47] evaluated Wilson’s model of airway-parenchyma interdependence [48] and showed that the radial traction exerted by the surrounding parenchyma was the mechanism by which intrapulmonary airways are expanded during a deep inhalation.

The present study evaluated dimensions of individual airways in spontaneously breathing subjects before and after broncho-constriction. By protocol, we allowed the subjects to chose their breathing pattern and mean lung volume both at baseline and after MCh. This not only made the conditions of the study more physiologically relevant, but also allowed us to test whether differences in the change in lung volume among subjects between baseline and post MCh, (ΔV_L), could be associated to the average degree of airway constriction (dynamic hyperinflation) or related to the prevention of airway closure by the interdependent behavior between airways and their surrounding parenchyma.

If the elevation of ΔV_L for a subject was merely a passive phenomena of dynamic hyperinflation, one would have expected that ΔV_L /V_TLC, would have been positively correlated with de average degree of luminal airway narrowing between baseline and post MCh ([A_i,B—A_i,P]/A_i,B). In contrast we found that ΔV_L /V_TLC was inversely correlated with [A_i,B—A_i,P]/A_i,B (Fig 7). Thus, our data is inconsistent with the hypothesis that the elevation of V_L during bronchoconstriction was caused by an increase in airway resistance. Instead, the data showed that the subjects with the greatest degree of luminal narrowing were those that did not increase V_L and, conversely, that subjects with the highest ΔV_L /V_TLC had negative values of [A_i,B—A_i,P]/ A_i,B corresponding to an average segmental airway dilation post MCh.

If the elevation in lung volume post MCh was not associated with passive dynamic hyperinflation, then what could explain it? Our data showed that the values of ΔV_L/V_TLC for both AS and NA subjects were inversely associated with the minimal value of A_i*/A_o,T among all segmental airways of each subject (A_i*/A_o,T)_min. Virtually identical results were obtained when the minimal A_i*/A_o,T was calculated as the mean minus two standard deviations of the A_i*/A_o,T distribution for all segmental airway of each subject (S8 Fig). As discussed in the empirical framework, the value of A_i* is a theoretical estimate of the luminal area that the airway would have reached, had the peribronchial parenchyma expansion remained unchanged after MCh, assuming a constant relative distensibility for that constricted airway. In an airway with A_i* = 0 the elevation in smooth muscle force by MCh would be just enough to bring it to closure if peribronchial parenchyma expansion had remained constant after constriction. Similarly, in an airway with A_i*<0 the smooth muscle force would be greater than that by the parenchyma opposing its closure and as a result, if lung volume had not increased after MCh, the airway not only would have become fully closed, but it would have also remained closed until the peribronchial expansion had exceeded the critical value of peribronchial parenchyma expansion (E_pb,Crit). Our data shows that all subjects had their mean lung volume following bronchoconstriction at levels that were at least 15% greater than those for closure of the first segmental airway on each subject. This remarkable finding could suggest that the behavior of individual airways, and not that of the average airway, may have affected lung volume during breathing after bronchoconstriction. This result derived for airways > = 2mm in diameter, together with previous observations of inspiratory muscle activation during exhalation [3], would be consistent with an active control mechanism aimed at preventing the onset of airway closure during spontaneously breathing, possibly mediated by vagal sensory neurons such as those recently identified in murine airways [49]. However, our findings cannot rule out the presence of other mechanisms. For example air trapping behind airways too small to be measured with CT could have affected lung volume during spontaneous breathing. If that was the case, the behavior of larger airways would have been a marker for that of deeper airways.

Air trapping and changes in FVC following broncho-constriction

We observed large inter-subject differences in the reduction in FVC during MCh bronchoconstriction (Fig 8). The values of ΔFVC/FVC_B in both groups were associated with, but greater than, the fraction of FVC_B expected to become trapped behind closing segmental airways during a forced exhalation from TLC to RV (ΔV_C/FVC_B). In NA subjects that difference ΔFVC/FVC_B increased in the same proportion as the predicted difference in ΔV_C (slope of the regression line ~1) and was, in average, only slightly higher than ΔV_C (intercept ~ 7%). In the AS subjects, however, the intercept value of ΔFVC/FVC_B was 15% greater than ΔV_C/FVC_B, for subjects with minimal ΔV_C, and increased 74% more than ΔV_C/FVC_B. These findings show that in subjects with healthy lungs the reduction in FVC during MCH bronchoconstriction is closely related to the amount of gas entrapped behind specific segmental airways. In the asthmatic lungs, however, the estimated gas trapped behind closed segmental airways explains only a fraction of the reduction in FVC. This suggests that in the asthmatic lung a substantial part of the reduction in FVC by MCh may be attributed to gas trapping behind airways more peripheral than the segmental airways.

Relative airway distensibility, RD

RD is the ratio between the fractional change in cross-sectional area of an airway and the fractional change in peribronchial parenchymal expansion to the power of ^2/3 (to make RD dimensionless). Airways with RD = 1 expand in the same proportion of their surrounding parenchyma not causing any shear distortion of parenchyma. Most of the airways (78%) had RD ≤ 1 and thus expanded less than the surrounding parenchyma, thus resulting in shear distortion of the parenchyma during lung expansion. The rest of the airways had values of RD > 1 and thus expanded more than the surrounding parenchyma. This can only take place when the airway wall tissue is very compliant, which is unexpected for segmental airways, or when the peribronchial parenchyma around a severely constricted airway generates forces greater than those of by ASM, resulting in brisk airway dilation. This behavior has been described as fluidizing of a frozen smooth muscle by expanding forces [50]. In average RD was less than unity and not different between AS and NA subjects (S6 Fig). This means that MCh-constricted segmental airways in average distend less than the surrounding parenchyma during a deep inhalation to TLC and that airway distensibility does not differentiate mild-to-moderate asthmatic from healthy lungs. This finding is consistent with that from Brown et al [34] and Williamson et al [51] and thus supports the concept that the lack of a bronchodilatory effect of deep inhalations may not be related to a difference in distensibility of the airways or the parenchyma, at least up to the level of segmental airways imaged in this study. In contrast, other studies assessing global airway distensibility indirectly have shown reduced distensibility in subjects with asthma [30,52]. The cause for this apparent disparity in results may be that indirect measurements of distensibility include a contribution from the small airways (less than 2mm² in area), which are not measured using HRCT. It is also possible that the ASM of asthmatics may recover differently from a stretch than NA [34]. However it is unlikely that this disparity will be resolved until the direct measurement of the distensibility of much smaller airways becomes feasible.

In both subjects with asthma and healthy controls values of RD varied between -1 (minimum) and 3 (maximum). When airways have distensibility different from unity, they expand differently than peribronchial parenchyma when lung volume is changed, thus generating increased shear stresses on the parenchyma in the vicinity of the airway [48]. When RD < 1, the airway is relatively stiffer than the surrounding parenchyma. This may occur when parenchymal tethering forces are unable to overcome the airway smooth muscle forces or when the airway is already near full expansion at MLV. This past behavior is consistent with the reduction in airway lumen distensibility following albuterol observed in AS subjects [30]. Although a few airway with RD < 0 were observed, these were airways that their outer area, measured at MLV after MCh, was higher than that measured at TLC. Because most of these airways had minimally changed their area after MCh, this could be caused by imaging or segmentation errors but they could also reflect and unlikely effect of airway constriction in response to the lung expansion to TLC.

The RD of individual airways was found to be highly heterogeneous within and between subjects. Previous studies measuring the distensibility of individual airways with HRCT [33,53], recognized they could be potentially important as they were affected by differences in trans-pulmonary pressure, and their transmission within the lungs via the fibrous and elastic stroma, and modified by disease processes [26]. Thus those measures of airway distensibility could be affected by heterogeneity in peribronchial parenchyma expansion amongst airways and by differences in the degrees of lung inflation at TCL and FRC among subjects. Past studies have attempted to control the lung volume during imaging at FRC [36–38] to minimize these effects. However, even if the accurate control of lung volume was possible, regional difference in parenchymal expansion within the lung could still contribute to the heterogeneity in airway distensibility observed.

Methodological considerations and study limitations

Other methodological differences in our measurements of distensibility compared with those by others are: 1) Airway dimensions and lung expansion were referenced to those measured at TLC instead the less reproducible FRC [54]. 2) We used outer airway cross-sectional area (A_o) instead of luminal area (or inner diameter) because it is the dimension directly affecting and/or being affected by the surrounding parenchyma. 3) Airway cross-sectional areas were measured objectively by the PW2 software package, as the average across the middle third of their respective length. This allowed us to assess most segmental airways in all subjects objectively in three conditions B, P, and T. Early measures of airway %distensibility were limited to airways running perpendicular to the CT cross-sections that could have been affected by longitudinal heterogeneity of airway luminal area [19]. Estimation of %distensibility of bronchoconstricted airways (that is between A_i,P and A_i,T) gave average values and heterogeneities consistent with those previously reported for studies in asthmatics post MCh [31,55].

Other methodological details are worth mentioning. Parenchymal Expansion, E, was defined as the average gas-to-tissue volumes ratio within the region and was calculated for individual ROI’s from the CT scans. Taking the tissue volume as a surrogate of the number of alveolar units within the ROI, E would represent the average degree of gas inflation per alveolar unit.

The resolution of the HRCT scanner could have affected the results. However, airway area measurements using Pulmonary Workstation 2.0 have been validated using phantom tubes with a cross-sectional area greater than 3.1mm² for all scan directions [23] and all airways analyzed within the current study had lumen areas greater or equal to 4.2 mm². Also, partial volume effects could have resulted in underestimation of parenchymal tissue expansion in peribronchial ROI’s because of their smaller dimensions compared with those of the distal segmental ROI’s. However, this is unlikely because the value of ΔE increased with lung inflation and the potential partial volume effects should have been greatest at baseline mean lung volume where airway dimensions were the lowest. Nonetheless, it was precisely at low lung expansion where that peribronchial parenchymal expansion approached that of the distal regions (i.e. ΔE ~ 0).

We imaged the airways at each subject’s spontaneous MLV both before and after the MCh challenge allowing the evaluation of A_o during physiological conditions. This also removed the need to enforce a breathing pattern and breath-holds at volumes lower than that chosen by the subject after the administration of MCh. Indeed, analysis of the CT scans showed most subjects in both groups increased their MLV following MCh, an outcome that has an independent influence on airway cross-sectional area. In order to account for that effect, based on the relative distensibility of each airway, we estimated the value of (A_o*) as the A_o that would have been measured, had the peribronchial expansion remained unchanged after the MCh challenge. RD was calculated assuming that relationship between A_o/A_o,T and the relative changes in peribronchial expansion (to the ^2/3 power) was linear. This seems to be a reasonable assumption, for bronchoconstricted airways, based on the measurements by Brown et al. in dogs after aerosol challenge [18], as shown in S7 Fig. Although the linearity assumption is only an approximation, as mentioned above, the impressive correlation between the behavior of specific airways and the response of the system as a whole suggests that such assumption may be a reasonable for broncho-constricted airways.

Measuring E and defining parenchymal ROI’s

Our definition of E is similar to the specific gas volume (SV_g) [56,57] defined as volume of gas per gram of tissue (ml/g) but it is dimensionless. The quantity of average voxel gas-to-tissue volume ratio (average E_voxel), given for lung (E_Lung), segment (E_SL) and peribronchial region (E_pb), represents a measure of parenchymal distension, if one assumes that all alveolar units have the same mass and that it does not change with lung inflation. Clearly changes in blood volume within parenchymal ROI’s could affect the results. We restricted the peribronchial ROI size to be a spherical region with a diameter equal to four times the outer diameter of the airway based on models of parenchyma deformation and airway-airway interaction [25,48]. Given that the outer diameter of the airways changed with the different conditions, we defined the peribronchial ROI at baseline and iteratively adjusted the diameter of the peribronchial ROI for other conditions to include the same amount of tissue than at baseline. However, we repeated the analysis defining the peribronchial ROI’s with a diameter equal to 4 times the outer airway diameter for each condition and that did not change the findings or conclusions of our study.

Physiological and clinical implications

In a heterogeneously expanding lung a regional reduction in lung expansion decreases parenchymal recoil [58] reduce stretching forces on the airway wall and increase the constriction created by the airway smooth muscle [59]. This can potentiate a positive feedback mechanism promoting further decrease in airway lumen and airflow until the airway becomes unstable and closes [58], contributing to the formation of ventilation defects or VDef’s [44]. The redistribution of airflow to regions away from VDef’s increases their tidal expansion, dilating and stabilizing the corresponding branches of the airway tree. During bronchoconstriction these competing effects result in a bi-stable behavior of airway lumen that leads to the self-organized formation of VDef’s [9]. The heterogeneous behavior of RD and A* amongst a subject’s airways is consistent with the above model.

In practical terms, assessing individual airway RD and A* could be important in diagnostics, assessment of disease progression and response to therapy, as well as pre-interventional planning [60,61]. HRCT can allow assessment of the contributions of airway and parenchymal changes, and evaluate how these measures relate to symptoms and to pulmonary function [26]. Although our study did not include patients with COPD, we could extrapolate them to this group of patients where the loss of airway attachments and elastic parenchyma recoil result in dynamic collapse of airways during expiration. Wille and Petersen [62] observed a markedly reduced global distensibility of airways in patients with severe COPD. Because our measurement of RD includes the effect of distending forces of the surrounding parenchyma, we speculate that this measurement could provide a more sensitive indicator of the disease than that of absolute distensibility. Another potential application of our methodology could be for personalized treatment of severe asthmatics by selecting airways for bronchial thermoplasty treatment [60] based on their values of RD or A_i*/A_o,T.