Vol. 83, Issue 5, 1595-1601, 1997

Mechanical impedance of the lung periphery

Z. Hantos¹, F. Peták¹, Á. Adamicza², T. Asztalos¹, J. Tolnai¹, and J. J. Fredberg³

Departments of ¹ Medical Informatics and ² Experimental Surgery, Albert Szent-Györgyi Medical University, H-6720 Szeged, Hungary; and ³ Department of Environmental Health, Harvard School of Public Health, Boston, Massachusetts 02115

ABSTRACT

INTRODUCTION

MATERIALS AND METHODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENTS

FOOTNOTES

REFERENCES

ABSTRACT

Hantos, Z., F. Peták, Á. Adamicza, T. Asztalos, J. Tolnai, and J. J. Fredberg. Mechanical impedance of the lung periphery. J. Appl. Physiol. 83(5): 1595-1601, 1997.The mechanics of the regional airways and tissues was studied in isolated dog lobes by means of a modified wave-tube technique. Small-amplitude pseudorandom forced oscillations between 0.1 and 48 Hz were applied through catheters wedged in 2-mm-diameter bronchi in three regions of each lobe at translobar pressures (PL) of 10, 7, 5, 3, 2, and 1 cmH₂O. The measured regional input impedances were fitted by a model containing the resistance (R₁) and inertance (I) of the regular (segmental) airways, the resistance of the collateral channels (R₂), and the damping (G) and elastance (H) of the local tissues. This model gave far better fits to the data on impedance of the lung periphery than when G and H were replaced by a single tissue compliance, which explains why interruption of segmental flow did not lead to monoexponential pressure decay in previous studies. The interlobar and intralobar variances of the parameters were equally significant, and poor correlations were found between the airway parameters R₁ and R₂ and between any airway and tissue parameter (e.g., R₁ and H). R₂ was on average ~10 times higher than R₁, although the R₂-to-R₁ ratios and their dependencies on PL were regionally highly variable. However, for the total of 33 regions studied, the PL dependence was the same for R₁ and R₂, which may reflect similar morphological structures for the regular and collateral airways. The dependencies of G and H on PL showed high interregional variations; generally, however, they assumed their minima at medium PL values (~5 cmH₂O).

collateral airways; collateral resistance; airway resistance; pulmonary elastance; lung tissue resistance

INTRODUCTION

THE RESISTANCE of the collateral airways (Rcoll) has been measured extensively to characterize the properties of the small airways. The most common approach to the measurement of Rcoll is the use of a fiber-optic bronchoscope wedged in bronchi 5-6 mm in diameter, with one channel to lead constant airflow (coll) into the periphery and another to measure the pressure at the bronchoscope tip (Pb) (10). This technique has been used to establish the baseline variability of Rcoll (15, 22, 25), the dependencies of Rcoll on gas composition (19) and lung volume (11, 12, 23, 26), the changes in Rcoll in response to various constrictor agents (1, 7, 12-15, 24), and the difference in Rcoll between normal and asymptomatic asthmatic subjects (25). However, the fundamental question of whether the behavior of Rcoll is similar to that of the resistance of small bronchi of the "regular" airway tree remains controversial (14, 23). In addition, we know little about the dynamic properties of the structures associated with the collateral pathways: the only dynamic approach addressed the mechanical responses to the interruption of constant coll (11, 14, 24, 26).

The purpose of the present study was to develop a technique for the measurement of the input impedance of the lung periphery (Zp), as seen at the distal end of a catheter wedged in a 2-mm-diameter peripheral bronchus. We demonstrate that, from the Zp data of an appropriate frequency range, parameters characterizing 1) the distal regular airway tree, 2) the local tissue compartment, and 3) the collateral channels leading to adjacent converging airways can be estimated separately.

MATERIALS AND METHODS

RESULTS

An example of Zp data obtained at different levels of PL is presented in Fig. 2. With decreasing PL, the real part of Zp (Re_p) progressively increased, and the imaginary part of Zp (Im_p) assumed more negative values at medium and low frequencies. Overall, the frequency dependencies of Zp were different for the different lobes and for the different regions within one lobe at the same PL, and they were greatly affected by the PL values in all regions. We considered the frequency dependencies to be characteristic when Re_p was of a sigmoid shape, delineating plateaus toward both the lowest and highest frequencies, and when this was associated with Im_p first falling and then increasing with frequency. In these cases, the model fitting gave stable and unique parameter estimates, whereas from some Zp data either the zero-frequency Re_p (= R₁ + R₂), corresponding to Rcoll in the constant-flow technique, or, conversely, the high-frequency Re_p (= R₁) was not well determined, i.e., multiple sets of parameters with comparable F-values were found. Because of the lack of a characteristic frequency dependence, we had to discard the measurements at PL of 10 cmH₂O in two regions and at PL of 10 and 7 cmH₂O in another two regions. As substantiated by high impedance magnitudes (>10⁶ cmH₂O · s · l¹) and irregular frequency dependencies, airway closures near the tip of the catheter occurred at 1 cmH₂O in eight regions and at 2 cmH₂O in a further five regions. In addition, the measured data were retained only for those regions where Zp was interpretable in terms of model parameters at 4 levels of PL. Eventually, with regard to the 13 lobes and the corresponding 39 regions, there were 7 and 6 lobes where 3 and 2 regions, respectively, were studied successfully; of the 33 regions, 16 remained where model parameters could be derived at all PL levels.

There was a consistent difference in fitting quality between the two models (Fig. 3). The model including the tissue parameters G and H (model b) gave excellent fits to the data in most cases [the average F-value was 3.05 ± 1.28 (SD) % for all Zp data], whereas the fitting of the model with shunt C (model a) always resulted in higher F-values (10.00 ± 4.17% for all Zp data), reflecting significant systematic deviations from Zp, as shown in Fig. 3. Therefore, the parameters of the latter model are not reported here.

We found marked differences in the parameters estimated in the different regions of the same lobe. This is exemplified in Fig. 4, where the values of R₁ and R₂ are plotted against PL for the five regions of two lobes. The interlobar and intralobar differences were comparable in both the values of R₁ and R₂ and the slopes of their PL dependence. All the individual dependencies appeared linear in the log-log plot. The dissipative and elastic parameters of the local tissues, obtained in the same regions as in Fig. 4, are plotted against PL in Fig. 5. These graphs illustrate that, in addition to the equally significant interlobar and intralobar variabilities of G and H at a given PL, marked differences may exist in the value of PL at which these parameters assume their minimum. At higher values of PL, the changes in G and H are more interrelated, as indicated by the fairly constant values of . The analysis of variance, performed on the parameter values obtained at PL of 5 cmH₂O, resulted in values of Wilks's lambda ranging from 0.46 to 0.60; these figures indicate that, for every parameter, approximately one-half of the total variance is explained by the intralobar variance.

Data obtained in the 16 regions where the parameter values were available at all PL levels are pooled in Figs 6 and 7. The relationships between PL and the mean values of the airway parameters are closely linear on a log-log scale (Fig. 6), which corresponds to power functions of the form a(PL)^b. It is noteworthy that the values of exponent b are almost the same for R₁ and R₂ (1.79 and 1.78, respectively). We note, however, that the individual values of b for R₁ and R₂ were not correlated (r² = 0.223). The values of a (3.49 and 4.57, respectively) show that, on average, the R₂ values were ~10 times higher than the R₁ values. The dependence of I on PL appears similar, although at high PL levels the mean values of I are close to zero and unreliable because of the great scatter in the data. The average tissue parameters, shown in Fig. 7, display characteristic PL dependencies: both G and H exhibit their minimum values at medium PL (between 4 and 6 cmH₂O). Nevertheless, the increase in G toward low PL values is steeper than that in H, in accordance with the augmented increase in  at the lowest PL values.

These relationships do not change much if data collected from all 33 regions are considered. The individual log-log regressions between R₁ and PL and R₂ and PL resulted in similar values of exponent a: 1.96 ± 0.58(SD) and 1.84 ± 0.40, respectively (statistically not significantly different). These individual regressions were characterized by high correlation coefficients (r² = 0.942 ± 0.042 and 0.975 ± 0.032, respectively, P < 0.001). Again, R₂ was on average ~10 times higher than R₁.

The interdependence of the model parameters was studied for data obtained at PL of 5 cmH₂O. Interestingly, the parameters R₁ and R₂ were uncorrelated (r² = 0.0012), and very weak positive correlations were observed between H and R₂ (r² = 0.180), H and R₁ (r² = 0.293), and I and R₁ (r² = 0.288). The only close relationship was found between G and H (r² = 0.724).

DISCUSSION

The purpose of this study was to estimate the parameters characterizing the regular segmental airways, the collateral pathways, and the local parenchymal tissues on the basis of the mechanical response of isolated dog lung regions to broad-band forced oscillations. We used the modified wave-tube method to determine the mechanical input impedance of peripheral lung units belonging to small (~2-mm-diameter) bronchi. The Zp data measured at PL values between 1 and 10 cmH₂O exhibited a characteristic frequency dependence in most regions, and this resulted in stable parameter estimates with low and nonsystematic F-values.

Through a comparison of the R₁ and R₂ values derived from our measurements, a key problem of collateral ventilation is addressed. The Rcoll values determined with the wedged bronchoscope technique are widely regarded as a measure of small airway resistance, although the morphological background of Rcoll contains some hypothetical elements (17), and there is still some controversy concerning the similarity in mechanical behavior of the segmental (regular) and collateral airways. Most authors conclude that both airway compartments display similar dependencies on PL or lung volume (12, 19) and respond similarly to constrictor stimuli (1, 12, 13, 17), whereas others find the segmental airway resistance to be negligible in comparison with Rcoll (14), or even independent of lung volume (11). In the present study, stable values of R₁ were estimated from the frequency-domain measurements at all PL levels in most regions, and the mean value of the R₁-to-R₂ ratios (R₁/R₂) at PL of 5 cmH₂O (0.115) falls into the wide variety and range of data reported previously: from 0.01 to 0.1 (23), 0.15 (11), and from 0.11 to 0.2 (6). However, it is equally notable that the range of our individual R₁/R₂ values extends from 0.012 to 0.497. The latter wide range results primarily from the scatter in the R₂ data, i.e., the considerable interregional variability in the number and size of collateral channels belonging to a given segment. This variability was also demonstrated by the airway casts, in which the segmental airways forming a dense network and the sparse fragments of the adjacent segmental airway systems, filled through the collateral channels, were clearly distinguishable (Fig. 8). The number of secondary casts belonging to a primary segment varied between one and five. However, the geometry of the collateral channels determining the R₂ values remained unknown because, as in the study by Sasaki et al. (23), the dense cast did not allow us to identify the junctions between the primary and secondary casts.

In addition to R₁/R₂, wide ranges characterized all relationships between any parameter pairs except G and H: their ratio, reflecting the hysteresivity of the local parenchyma (5), was relatively stable. The lack of correlations between the parameters points to the huge variability in the segmental architecture within the lung. Our data indicate that not only can the tissue impedances and the Rcoll belonging to a given R₁ and a PL level be extremely variable but also their patterns of PL dependence can similarly exhibit high interregional differences (see Figs. 4 and 5). In view of these purely mechanical properties, it is not surprising that the responses to constrictor stimuli are characterized by a significant interregional variability (15).

The peripheral lung unit, the input impedance of which we measured, can be conceived as a tiny and leaky lung. Indeed, the ratio of the "regular" airway resistance (R₁) to the local tissue elastance (H) at a PL of 5 cmH₂O was, on average, 0.021 s, a value comparable to the range found for the total airway resistance-to-tissue elastance ratios (0.007-0.019 s) when small-amplitude oscillations were applied in open-chest dogs and isolated dog lungs (21). We consider it very noteworthy, however, that finite R₂ values characterized all Zp data until Zp suddenly became huge and irregular at a low PL level. There was only a single measurement at PL of 2 cmH₂O in one region where the frequency dependence of Zp corresponded to that of a miniature lung without leaks (the value of R₂ was identified as >10¹⁴ cmH₂O · s · l¹). These observations suggest that with decreasing lung volume the collateral channels remain patent as long as the regular airways are open. The similar mechanical behavior of these two airway systems, extending to the near-closure states, supports Mitzner's (17) conclusion that the main pathways for coll are pairs of normal airways from neighboring segments, connected at the level of a joint alveolar duct.

In a discussion of our parameter values in the context of data obtained with the wedged bronchoscope technique, two questions must be addressed. First, there were differences in the sizes of the regions measured with these methods because the usual diameter of the bronchoscope (5-6 mm) determines larger segments than those accessed in the present study. Accordingly, the R₁ + R₂ values we obtained at PL of 5 cmH₂O [6,950 ± 2,903 (SE) cmH₂O · s · l¹] are considerably higher than the baseline Rcoll values reported from wedged bronchoscope studies, which generally fall in the range from 200 to 2,000 cmH₂O · s · l¹ (6, 11, 14, 15, 24-26).

Second, from a methodological point of view, the wave-tube oscillation of the lung region can be regarded as the frequency-domain counterpart of the combined techniques of wedged bronchoscope and flow interruption. The difference between the two dynamic measurements lies in the amount of information extractable from transient analysis vs. multifrequency oscillations, particularly in the presence of corrupting noise. The sudden drop in Pb after the interruption of flow may be difficult to read, and this might have contributed to the contradictory reports on the value of segmental airway resistance (i.e., R₁) in some studies (11, 14, 24). Traditionally, the whole decay in Pb has been considered to be an exponential (mono- or multiexponential) process (11, 14, 22, 24, 26) and analyzed accordingly in terms of time constants (Tcoll). Ludwig et al. (14) found that at low values of interrupted flow the decay process was well described by a single exponential, whereas at higher flow rates biexponential fitting was required; they concluded that this behavior was consistent with the response of a single nonlinear mechanical compartment.

Our frequency-domain study demonstrates that, even within the limits of linear behavior, the peripheral lung unit cannot be described by a single Tcoll, i.e., the product of Rcoll and the segmental compliance (C). Indeed, the F-values decreased by 69% on average, and the systematic impedance misestimations disappeared when C, representing the tissues, was replaced by a constant-phase impedance (Fig. 3). In terms of time-domain behavior, we introduced the power function pressure-relaxation process of the form t^k, where k is a function of  and H (8, 9), in place of the exponential function e^t/Tcoll. This clearly indicates that from the exponential analysis of the model a fittings one can obtain an ideal compliance characterizing the size or the effective elasticity of the tissue unit (14, 22, 26) but not the viscoelastic properties thereof. In contrast, from the fitting of model b both G and H are available. Our results reveal that the estimates of both the elastance and viscous damping parameters (i.e., G and H, respectively) are reasonable (see Fig. 7): they have minimum values at medium or physiological values of PL (i.e., between 3 and 8 cmH₂O), and the corresponding values of  agree with data obtained previously for parenchymal hysteresivity (5, 8, 9, 16). However, the unrealistically high values of  estimated at low PL, still associated with a good fitting performance of the model, suggest that  and G include components of not real tissue origin. These virtual components might be due to increased heterogeneity in the most peripheral segmental airways and/or among multiple collateral pathways, via a mechanism analogous to that suggested for the case of the constricted lung (8) and confirmed experimentally in recent work (16).

In summary, from the broad-band peripheral impedance data obtained with a modified wave-tube technique in isolated dog lobes at different PL, we estimated the resistances of the segmental and collateral airways separately, in addition to the elastic and viscous parameters of the surrounding parenchyma. Although the parameters and their relationships were characterized by a high interregional variability, the segmental and collateral airways exhibited the same overall mechanical behavior, suggesting common morphological properties for these pathways.

ACKNOWLEDGEMENTS

The authors thank Dr. Krisztina Boda for statistical advice and I. Kopasz and L. Vígh for excellent technical assistance.

FOOTNOTES

Address for reprint requests: Z. Hantos, Dept. of Medical Informatics, Albert Szent-Györgyi Medical Univ., PO Box 2009, H-6701 Szeged, Hungary (E-mail: hantos{at}dmi.szote.u-szeged.hu).

Received 21 January 1997; accepted in final form 1 July 1997.

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