Journal of Applied Physiology
Vol. 82, No. 4, pp. 1098-1106, April 1997
GAS EXCHANGE, MECHANICS, AND AIRWAYS

Respiratory tissue properties derived from flow transfer function in healthy humans

W. Tomalak, R. Peslin, and C. Duvivier

Unité 14 de Physiopathologie Respiratoire, Institut National de la Santé et de la Recherche Médicale, Université H. Poincaré Nancy I, 54500 Vandoeuvre-les-Nancy, France; and National Institute for Tuberculosis and Lung Diseases, Pediatric Division, 34700 Rabka, Poland

ABSTRACT

INTRODUCTION

MATERIALS AND METHODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENTS

FOOTNOTES

REFERENCES

ABSTRACT

Tomalak, W., R. Peslin, and C. Duvivier. Respiratory tissue properties derived from flow transfer function in healthy humans. J. Appl. Physiol. 82(4): 1098-1106, 1997.Assuming homogeneity of alveolar pressure, the relationship between airway flow and flow at the chest during forced oscillation at the airway opening [flow transfer function (FTF)] is related to lung and chest wall tissue impedance (Zti): FTF = 1 + Zti/Zg, where Zg is alveolar gas impedance, which is inversely proportional to thoracic gas volume. By using a flow-type body plethysmograph to obtain flow rate at body surface, FTF has been measured at oscillation frequencies (f_os) of 10, 20, 30 and 40 Hz in eight healthy subjects during both quiet and deep breathing. The data were corrected for the flow shunted through upper airway walls and analyzed in terms of tissue resistance (Rti) and effective elastance (Eti,eff) by using plethysmographically measured thoracic gas volume values. In most subjects, Rti was seen to decrease with increasing f_os and Eti,eff to vary curvilinearly with f_os², which is suggestive of mechanical inhomogeneity. Rti presented a weak volume dependence during breathing, variable in sign according to f_os and among subjects. In contrast, Eti,eff usually exhibited a U-shaped pattern with a minimum located a little above or below functional residual capacity and a steep increase with decreasing or increasing volume (30-80 hPa/l²) on either side. These variations are in excess of those expected from the sigmoid shape of the static pressure-volume curve and may reflect the effect of respiratory muscle activity. We conclude that FTF measurement is an interesting tool to study Rti and Eti,eff and that these parameters have probably different physiological determinants.

respiratory mechanics; forced oscillations; mechanical inhomogeneity; volume dependence; effective elastance; respiratory muscles

INTRODUCTION

THERE EXIST INSTANTANEOUS DIFFERENCES between flow rate at the airway opening (ao) and at the body surface (bs) that are due to changes in inspired and expired gas temperature and water pressure (P_H2O) (2, 11), to departure from unity of the respiratory exchange ratio (17, 30), to gas compression within the chest (1, 12), and, to a small extent, to gas compression within the abdomen (8). During spontaneous breathing and, more generally, when the respiratory system is driven at the body surface, flow differences induced by gas compression inside the lung are related to airway impedance (Zaw) and to alveolar gas impedance (Zg): assuming that alveolar pressure is homogeneous [T-network model of DuBois et al. (13) (Fig. 1)], the flow transfer function (FTF) bs/ao = 1 + (Zaw/Zg) (15); this relationship, which forms the basis for airway resistance measurements by body plethysmography, simply states that bs is distributed between the airway and the gas-compression pathway according to the ratio of their impedances. Symmetrically, when the respiratory system is driven by pressure oscillations at the airway opening (Fig. 1), airway flow is distributed between the tissues and the gas-compression pathway, and the FTF = (ao/bs) is given by

(1)

where Zti is the impedance of the lung and chest wall tissues. In that instance, FTF is independent of Zaw, because it is implicitly assumed in the model that there is no flow loss through the airways (rigid airways and negligible gas compression). As Zg may easily be obtained from thoracic gas volume (TGV) [Zg = j · (PB  P_H2O)/(TGV · ), where j is the unit imaginary number, PB the barometric pressure, and  = 2 ·  · f, with f being the frequency], Eq. 1 provides a noninvasive way to study respiratory tissue properties. FTF data in humans in the 4- to 40-Hz frequency range have been incidentally reported in two studies (21, 25) devoted to respiratory input (Zin) and transfer (Ztr) impedances (FTF = Ztr/Zin). In this investigation, we have measured the FTF of healthy humans at 10, 20, 30, and 40 Hz, both during quiet breathing and during large tidal volume maneuvers. The results have been analyzed by using Eq. 1 to obtain the real part [Re(Zti) or tissue resistance (Rti)] and the imaginary part [Im(Zti)] of Zti. The study revealed strikingly different volume dependencies of Rti and of tissue effective elastance (Eti,eff) [Eti,eff = Im(Zti) · ], which suggests that these properties have different physiological determinants.

MATERIALS AND METHODS

The study was performed in eight healthy subjects (5 men, 3 women), recruited from the laboratory staff, all trained to perform respiratory maneuvers. Their biometric characteristics and lung volumes are shown in Table 1.

Table 1. Biometric characteristics and lung volumes of the subjects Subject No. Gender Age, yr Height, cm Weight, kg FRC, liters VC, liters TLC, liters 1 M 50 171 92 1.96 5.13 6.12 2 M 58 168 66 3.28 4.27 5.70 3 F 34 171 70 2.82 4.33 5.94 4 M 65 168 71 2.69 4.84 6.31 5 F 40 155 48 3.12 3.54 5.13 6 F 40 160 60 2.60 3.80 5.38 7 M 58 178 55 5.39 5.09 7.43 8 M 34 187 84 3.45 6.10 7.53 M, male; W, female; FRC, functional residual capacity; VC, vital capacity; TLC, total lung capacity.

Equipment. The subjects were seated in a 350-liter flow-type body plethysmograph (Emerson, Cambridge, MA) equipped with two layers of metal screen (area 144 cm², resistance 0.083 hPa · s · l¹) and breathed outside the box. bs was derived from box pressure measured with a Validyne MP45 ±2-hPa differential transducer (Validyne, Northridge, CA) with respect to the pressure in a small reference chamber. The plethysmograph had a time constant (screen resistance × gas compressibility) of ~18 ms. ao was measured with a heated Fleisch no. 2 pneumotachograph connected to a similar pressure transducer. Airway opening pressure (Pao) was also measured with a similar transducer and used, as indicated in Data analysis, to correct the FTF for the motion of upper airway walls. The responses of the three transducers were matched within 1% of amplitude and 2° of phase up to 40 Hz. The data were corrected for the relative frequency response of the plethysmograph and of the Fleisch pneumotachograph (see Data analysis). Before each series of measurements, ao and bs were calibrated by the integral method using a 1-liter syringe, and Pao was calibrated with a slanted fluid manometer.

Pressure oscillations at the airway opening were applied by using a 100-W loudspeaker enclosed in a box and connected to the pneumotachograph. The loudspeaker was supplied through a power amplifier with computer-generated sinusoidal signals. The subject breathed through a low-resistance high-inertance side tube branched in parallel with the loudspeaker. The distal end of the tube was connected to a small open reservoir where the gas was conditioned to BTPS so as to eliminate the component of the FTF related to the warming and humidification of inspired air in the airways.

bs, ao, and Pao were digitized at a rate of 360 Hz by a 486-type personal computer equipped with a 12-bits analog-to-digital conversion board (PC-Lab, Digimétrie, Perpignan, France).

Protocol. Measurements were performed in triplicate with superimposed pressure oscillations at oscillation frequencies (f_os) of 10, 20, 30, and 40 Hz in random order. To facilitate the maneuvers, ao and inspired volume (V), obtained by online digital integration of ao, were displayed on the computer screen in front of the subject who supported his/her cheeks firmly with his/her palms. Each measurement included the recording of a few cycles of quiet breathing, followed by five to seven deeper breaths with three to four times larger tidal volumes and, finally, by a slow vital capacity (VC) maneuver. Zero-flow offsets were also recorded as well as the flow signals when the subject was off the mouthpiece, which provided the FTF of the equipment. In most subjects, satisfactory measurements of the FTF could not be obtained during VC maneuvers because of glottic closure near total lung capacity (TLC) and/or near residual volume; then, VC maneuvers were only used to provide a volume reference.

Two additional measurements were also performed in all subjects. First, to correct the FTF for the motion of upper airway walls (see Data analysis), their impedance (Zuaw) was obtained by measuring the relationship between Pao and ao at the same four frequencies during Valsalva maneuvers (20) while the subject supported his/her cheeks. Second, TLC was measured in triplicate by using a constant-volume body plethysmograph; this permitted computing TGV and Zg at any time during the measurements using the recorded VC maneuvers.

Data analysis. To correct for any difference in gain between the two flow channels and/or for small departures from BTPS conditions of inspired gas, the slope of the relationship between ao and bs during the slow VC maneuvers was assessed by linear regression after filtering out the superimposed oscillations (digital low-pass filter at 1 Hz); ao data were then divided by the slope, which ranged from 0.996 to 1.040 (mean 1.021 ± 0.008).

After elimination of their low-frequency breathing component (14), ao and bs were submitted to Fourier analysis on a cycle-per-cycle basis, and their Fourier coefficients were combined to obtain the FTF. The later was corrected for the FTF of the equipment derived from the signals recorded when the subject, still sitting in the box, was off the mouthpiece.

As the head of the subject was inside the plethysmograph, some of the flow through the pneumotachograph was shunted directly to the box by the vibrations of upper airway walls (mouth floor, pharynx, residual motion of supported cheeks). The effect of the shunt is to bias the measured FTF (FTFm) toward unity, and its magnitude is related to the ratio of Zuaw to respiratory system Zin (Zin = Pao/ao). Zin values were, therefore, similarly computed from Pao and ao on a cycle-per-cycle basis and used to correct the FTF with the following relationship

(2)

where H = Zin/Zuaw. The real (Re) and imaginary (Im) parts of the corrected FTF and instantaneous TGV were used to compute Rti and Im(Zti) from Eq. 1 according to

(3)

(4)

Im(Zti) was expressed in terms of tissue effective elastance [Eti,eff = Im(Zti) · ]. Also, combining the values of Eti,eff at different frequencies and assuming mechanical homogeneity of the tissues, tissue compliance (Cti) and inertance (Iti) were computed by linear regression of Eti,eff vs. ² according to

(5)

RESULTS

Time plots of ao, V, Re(FTF), and Im(FTF) in a representative subject are shown in Fig. 2. All variables have been low-pass filtered with a cut-off frequency of 1 Hz to eliminate the superimposed oscillations on ao and V and smooth the FTF data. It may be seen that both Re(FTF) and, to a lesser extent, Im(FTF) undergo systematic variations during the breathing cycle, which are clearly related to the amplitude of the tidal volume. Re(FTF), Im(FTF), and the derived Rti and Eti,eff were averaged over the whole respiratory cycles during the periods of quiet breathing (QB) and of deep breathing (DB). Mean data in the group are shown in Table 2, and individual values of Rti as a function of f_os and of Eti,eff as a function of ² during QB are shown in Fig. 3. Eti,eff is shown as a function of ², rather than as a function of f_os, because it is expected to be linearly related to ² if the tissues behave homogeneously (Eq. 5). Rti decreased with increasing frequency in all subjects, and the trend was statistically significant in the group. Eti,eff, which includes both the elastance and a negative frequency-dependent inertial component (Eq. 5), decreased considerably as expected from 10 to 40 Hz. In two subjects, however, it increased slightly from 10 to 20 Hz. The tissue resonant frequency (Eti,eff = 0) was between 20 and 30 Hz in all but one subject (Fig. 3). When Eti,eff was analyzed by linear regression according to Eq. 5, Cti ranged from 0.019 to 0.060 l/hPa (mean ± SD 0.032 ± 0.016 l/hPa) and Iti ranged from 0.09 to 0.33 Pa · s² · l¹ (mean ± SD 0.21 ± 0.10 Pa · s² · l¹). Slightly but significantly larger values of Rti were found during DB than during QB. Eti,eff was also significantly larger during DB, and the corresponding Cti and Iti were slightly lower, averaging 0.025 ± 0.014 l/hPa and 0.19 ± 0.10 Pa · s² · l¹, respectively.

Table 2. Mean values of FTF and derived tissue properties during quiet and deep breathing fos, Hz Quiet Breathing Deep Breathing Re(FTF) Im(FTF) Rti, hPa · s · l1 Eti,eff, hPa/l Re(FTF) Im(FTF) Rti, hPa · s · l1 Eti,eff, hPa/l 10 1.086 ± 0.030  0.283 ± 0.070  1.23 ± 0.46  22.5 ± 8.8  1.129 ± 0.026 0.326 ± 0.059 1.38 ± 0.45* 31.0 ± 8.4* 20 1.046 ± 0.051  0.429 ± 0.155  0.94 ± 0.41  13.1 ± 14.7  1.110 ± 0.054* 0.505 ± 0.131 1.06 ± 0.37  24.7 ± 16.0 30 0.889 ± 0.058  0.503 ± 0.142  0.73 ± 0.26   33.5 ± 21.6  0.972 ± 0.060 0.569 ± 0.151 0.82 ± 0.30  13.4 ± 18.7* 40 0.662 ± 0.128  0.685 ± 0.237  0.73 ± 0.29   97.2 ± 49.8  0.756 ± 0.145 0.722 ± 0.254  0.78 ± 0.31   75.4 ± 54.9* P <0.0001 0.0004 0.03 <0.0001 <0.0001 0.0005 0.01 <0.0001 Values are means ± SD of average values over breathing cycles in 8 subjects. fos, oscillation frequency; Re and Im, real and imaginary parts of flow transfer function (FTF), respectively; Rti, tissue resistance; Eti,eff, tissue effective elastance. P values denote statistical significance of differences among frequencies (1-way analysis of variance); paired t-test for differences between quiet and deep breathing: * P < 0.05,  P < 0.01.

The variations of Rti during the respiratory cycle were, in general, weak and varied among subjects, as illustrated in Fig. 4 by the data obtained at 20 Hz. In four subjects, Rti decreased with increasing lung volume at all frequencies during QB, whereas in others it varied very little and in either direction, depending on frequency. The results were similar during DB, except for a more frequent and stronger negative volume dependence of Rti below normal FRC. On average, the slopes of the Rti-V relationships, obtained by linear regression over the entire respiratory cycle, were negative (Table 3), did not vary significantly with the f_os, and tended to be steeper, although not significantly so, during DB than during QB (Table 3). The Rti-V relationship also exhibited in most instances some degree of counterclockwise hysteresis, with slightly larger values of Rti at the same volume during the expiratory than during the inspiratory phases; at midinspiration, the differences averaged 8.6% during QB and 10.5% during DB.

Table 3. Volume dependence and hysteresis of Rti and Eti,eff during quiet and deep breathing fos Rti Eti,eff Quiet breathing Deep breathing Slope EI Diff Slope EI Diff Quiet breathing slope Deep breathing slope 10  0.112 ± 0.168  11.7 ± 5.4   0.215 ± 0.099  8.7 ± 10.8  59.2 ± 25.2  42.0 ± 20.4* 20  0.061 ± 0.247   8.0 ± 4.4   0.127 ± 0.107  5.3 ± 7.4  62.8 ± 27.1  38.4 ± 10.6* 30  0.082 ± 0.118   9.1 ± 2.5   0.145 ± 0.100  14.5 ± 8.7  84.3 ± 43.4  64.1 ± 28.8 40  0.145 ± 0.102   5.7 ± 3.5   0.192 ± 0.089  13.6 ± 8.0* 98.2 ± 44.7  71.5 ± 31.5 P NS 0.049 NS NS NS 0.025 Values are means ± SD in 8 subjects. Slope, regression coefficient of Rti (hPa · l2 · s) and Eti,eff (hPa/l2) as a function of volume; for Eti,eff, it is the slope of that part of the relationship with a positive volume dependence. EI Diff, %difference between expiratory and inspiratory Rti values at mid-tidal volume. P values denote statistical significance of differences among frequencies (1-way analysis of variance); NS, not significant. Paired t-test for differences between quiet and deep breathing: * P < 0.05,  P < 0.01.

The variations of Eti,eff during the respiratory cycle were stronger and much more systematic than those of Rti (Fig. 5). In all subjects and at all frequencies, Eti,eff was higher at end inspiration than at end expiration during QB. In several subjects, however, the Eti,eff-V relationship was U shaped, exhibiting a minimum a little above FRC. A U-shaped relationship was also seen in six out of eight subjects during DB. In some instances, particularly at low frequencies during QB, the Eti,eff-V relationship also exhibited some degree of clockwise hysteresis, with larger Eti,eff values at the same lung volume during inspiration than during expiration; in most cases, however, the relationships were eight shaped with clockwise looping at high lung volume and counterclockwise looping at low lung volume; this was systematically the case when the relationship was U shaped (Fig. 5). We measured by linear regression the slopes of the right part of the loops, over the volume range where Eti,eff exhibited a positive volume dependence during both respiratory phases. These slopes tended to be a little larger during QB than during DB and increased significantly with frequency during DB (Table 3).

DISCUSSION

In a previous study from the same laboratory (25), Re(FTF) and Im(FTF) had been found in 10 healthy men to average 1.068 and 0.286, respectively, at 10 Hz; 1.095 and 0.490, respectively, at 20 Hz; and 1.008 and 0.610, respectively, at 30 Hz during QB. These numbers are similar to those observed in this study (Table 2), except for Re(FTF) at 30 Hz, which was slightly and significantly larger (P < 0.01). In contrast, the values of bs/ao (1/FTF) observed by Mishima et al. (21) correspond to substantially larger Re(FTF) (1.19 and 0.88 at 10 and 40 Hz, respectively) and to larger Im(FTF) at high frequency (0.83 at 40 Hz) than seen in this study. These differences may be related in part to methodological differences: BTPS conditions of the inspired air were not fully achieved in our previous work (25) or, presumably, in the work by Mishima et al. (21), where the inspired gas only passed through a heated pneumotachograph. In this study, we solved the problem both by conditioning the inspired air to BTPS and by correcting the ao data for any residual difference between the low-frequency components of the two flows. More importantly, Mishima et al. did not correct their data for the upper airway shunt. The influence of this factor is illustrated in Table 4, which shows corrected and uncorrected data in two representative subjects. It may be seen that the effect of the correction is weak at low frequency but becomes quite substantial at 30 and 40 Hz. Specifically, the uncorrected upper airway shunt is responsible for an overestimation of both Re(FTF) and Im(FTF), which could explain the larger values found by Mishima et al. at high frequency. Although correction for the upper airway shunt appears necessary, one should point out, however, that the correction used in this study may be less than perfect; indeed, it has been shown that Zuaw, as measured during Valsalva maneuvers, is slightly overestimated, probably because of the active contraction of the muscles in the face and neck (24); then, our FTF could be slightly undercorrected.

Table 4. FTF in 2 representative subjects, uncorrected and corrected for upper airway shunt Subject No. fos (10 Hz) fos (20 Hz) fos (30 Hz) fos (40 Hz) Re(FTF) Im(FTF) Re(FTF) Im(FTF) Re(FTF) Im(FTF) Re(FTF) Im(FTF) 4   Uncorrected 1.078 0.277 1.061 0.473 0.912 0.623 0.641 0.837   Corrected 1.066 0.281 1.009 0.469 0.833 0.594 0.582 0.738 5   Uncorrected 1.110 0.209 1.074 0.381 0.994 0.520 0.944 0.694   Corrected 1.102 0.215 1.044 0.374 0.937 0.487 0.863 0.606

The values of Rti derived from Im(FTF) have the same order of magnitude as those obtained by analyzing the frequency dependence of respiratory Ztr of healthy adults with DuBois' six-coefficient model (12): 0.70 ± 0.28 (18), 1.01 ± 0.26 (26), 1.10 ± 0.35 (27), 1.03 ± 0.17 (29), and 0.62 ± 0.19 hPa · s · l¹ (31). This is noteworthy, since the two methods are fundamentally different: indeed, contrary to the approach used in this study, the analysis of Ztr data requires specific assumptions concerning the properties of the airway and tissue compartments and the additional assumption that the coefficients are not frequency dependent. Also, our Rti data are but a little larger than the values of chest wall resistance (Rw) derived from chest wall impedance measurements around 4 Hz (6, 16, 22, 28) or measured with the interruption technique (9); this is not surprising, since tissue resistance of human lungs has been shown to get extremely small above a few hertz at normal distending pressures (28, 32). Similarly, Cti and Iti, derived from the frequency dependence of Eti,eff (Eq. 5), are in good agreement with the data obtained by other forced-oscillation approaches on the same frequency range in healthy humans: for instance, mean values of Iti and Cti derived from Ztr data range from 0.10 to 0.21 Pa · s² · l¹ and 0.021-0.035 l/hPa, respectively (18, 26, 27, 29, 31).

An advantage of the FTF over the usual Zin or Ztr is that Rti and Eti,eff may be obtained noninvasively at any frequency. As shown in Fig. 3, Rti exhibited a substantial degree of negative frequency dependence in most subjects, which is in agreement with previous observations (21, 25, 28); in addition Eti,eff tended to vary curvilinearly with ², with a larger negative frequency dependence above than below 20 Hz. These data are inconsistent with the simple resistance-inertance-compliance model (Eq. 5) but may be explained by a two-compartment, six-coefficient (bitissular) model (25) accounting for the asynchronous deformation of different parts of the chest wall documented above 3 Hz (4-6, 13). The number of frequencies recorded in this study is too low for accurate analysis of the data with a six-coefficient model. An example, however, chosen among the subjects who departed most from homogeneous behavior, is shown in Fig. 6. It may be seen that the association in parallel of a pathway with a low resonant frequency and of a pathway with a large resonant frequency gives a very good fit to the data. This is in agreement with our previous observations (25).

The most interesting piece of information in this study is the fact that tissue properties varied systematically during the respiratory cycle in a volume-dependent manner and that these variations were quite different for Rti and Eti,eff. Variations of tissue properties during the respiratory cycle may be expected on several grounds. One should first rule out, however, artifactual variations. Conceivably, errors on plethysmographically measured TLC could be responsible for absolute errors on Rti and Eti,eff and for small variations during the cycle. Indeed, both properties are computed by using instantaneous values of TGV (Eqs. 2 and 3) derived from TLC and integrated ao; for a given absolute error on TLC, the relative error in TGV would vary systematically during the cycle, provoking some volume dependence of Rti and Eti,eff. The variations, however, would be similar for the two parameters, which does not fit our findings, and would not exceed a few percent per liter of tidal volume for a 10% error on TLC.

Provided that alveolar pressure is homogeneous, mechanical inhomogeneity of the tissues, as discussed above, could not be responsible for artifactual volume dependence of Rti and Eti,eff if the local properties are constant. However, it may conceivably influence the data in two ways. First, some artifactual variations may be expected in a system with several lung compartments in parallel if the inspired gas distribution between the compartments, and, therefore, the ratio of the local TGVs vary systematically during the cycle. Indeed, the "weight" of each compartment in the overall FTF depends on its TGV; if, for instance, compartment 2 has a much lower elastance than compartment 1 and takes most of the inspired volume, one may expect Eti,eff to decrease with increasing lung volume. Would the two compartments breathe out of phase, this mechanism could also explain some looping in the Rti-V and Eti,eff-V relationships. We did some computer simulation with a model including two T networks in parallel, with the same airway resistance, airway inertance, Rti, and FRC (1.0 hPa · s · l¹, 0.02 hPa · s² · l¹, 1.0 hPa · s · l¹, and 2 liters, respectively), which only differed by their Cti (0.1 and 0.01 l/hPa, respectively). With a tidal volume of 1 liter and a breathing frequency of 0.25 Hz (91% of the tidal volume in compartment 1), Eti,eff decreased with increasing volume with a slope of 3 to 4 hPa/l², depending on the f_os, which is one order of magnitude less than the observed Eti,eff slopes (Table 3). It is, therefore, quite unlikely that inhomogeneous inspired gas distribution is responsible for much of the observed volume dependence of tissues properties. Second, if two compartments with similar or different properties have different volume dependencies of these properties, the volume dependence of the global Eti,eff may have little to do with that of the local elastances; it could even happen that the increase of a local elastance paradoxically results in a decrease of Eti,eff at some frequencies. This is due to the fact that the imaginary part of the impedance of two resistance-inertance-elastance pathways does not increase monotonously with frequency and may present a wavy pattern between the resonant frequencies of the two compartments (25); then, the increase of a local elastance may shift the curve in such a way that, at a given frequency, Eti,eff will be decreased. We have not found situations where this would also be the case for Rti. Although this factor may have influenced our Eti,eff volume dependencies, it is unlikely that it was of much importance for two reasons: 1) the Eti,eff-V loops were not different in the two subjects who exhibited a strong negative frequency dependence of Rti and a strong nonlinearity of the Im(Zti)-² relationship (1st and 2nd subjects of 1st row in Fig. 5); and 2) although the Eti,eff-V slopes tended to increase with increasing frequency (Table 3), the changes were moderate, and in all subjects the right part of the loops had a positive slope at all frequencies.

In most subjects, Eti,eff was seen to present a minimum at some volume slightly above (3 cases) or below (3 cases) FRC. One may assume that in the two other subjects the minimum was located below the volume range explored during the maneuvers. Eti,eff increased rather sharply with decreasing or increasing volume on either side of the minimum. Eti,eff depends on tissue elastance (Eti = 1/Cti) and Iti, and its volume dependence reflects that of both properties; there is little reason, however, to expect that Iti (which is related to the mass of the tissues) will vary much with lung volume. To test that expectation, we computed separately Eti and Iti by combining the data obtained at different f_os values using Eq. 5 in the six subjects in whom that equation appeared to be an acceptable model [almost linear decrease of Im(Zti) with ²]; Eti and Iti were obtained by linear regression of Eti,eff vs. ² by using the values of Eti,eff at different times of ensemble-averaged breathing cycles (32 points/cycle). A representative example of the Eti-V and Iti-V loops obtained in that manner is shown in Fig. 7. It may be seen that the volume dependence of Iti is very weak during both QB and DB and that the variations of Eti are very similar to those of Eti,eff (Fig. 5, 3rd subject in lower row). In the part of the loops with a positive volume dependence, the slopes in the six subjects averaged 56.1 ± 31.9 hPa/l² for Eti, compared with 56.4 ± 28.8 hPa/l² for Eti,eff at 10 Hz during QB; the corresponding numbers during DB were 33.3 ± 13.5 hPa/l² for Eti and 40.7 ± 23.7 hPa/l² for Eti,eff at 10 Hz. Most of the variations of Eti,eff, therefore, reflect changes in lung and chest wall elastic properties.

A first obvious cause for these variations is the sigmoid shape of the respiratory static pressure-volume curve. From the model and the data of Paiva et al. (23) in healthy humans, the change in lung elastance would be ~10%/l for a 1-liter volume change on either side of FRC and 25%/l for a 2-liter volume change; even if the same degree of nonlinearity was present in the chest wall, the corresponding slope of the Eti,eff-V relationship would only be ~3-8 hPa/l², which is much lower than actually observed (Table 3). The static pressure-volume curve reflects respiratory tissues elasticity during muscular relaxation. Elastic loading experiments suggest that the effective total respiratory elastance may be substantially larger during active breathing, in relation to the force-length relationship of respiratory muscles and to chest wall distortion from its passive configuration (7, 19). In addition, there is direct evidence that sustained respiratory muscle contraction increases both Rw and chest wall elastance (3): a muscular effort of 10 hPa in either direction would double Rw and increase chest wall elastance by a factor of five or more. Whereas these variations are much larger than those expected from elastic loading experiments (7), they would well explain the large volume dependence of Eti,eff observed in this study: most of the pressure developed by respiratory muscles at usual breathing frequencies being in phase with volume, so would be the resulting variations of Eti,eff. The U-shaped characteristic of the Eti,eff-V relationship could reflect inspiratory muscle activity above normal FRC and expiratory muscle activity at lower volume. This mechanism would also explain the observation of higher Eti,eff during the active inspiratory phase than during expiration. This interpretation, however, remains hypothetical. Indeed, from the data of Barnas et al. (3), one would also expect Rti to exhibit some volume dependence in relation to respiratory muscles contraction. This was not observed, which could mean that Rti has something to do with the state of respiratory muscles when measured with low oscillation frequencies [4 Hz, Barnas et al.] but not when measured at the frequencies used in this study. Although there is evidence that Rti is mostly located in the chest wall (28), its precise physical meaning remains to be established.

If one assumes that the cyclic variations of Eti,eff observed in this study are largely related to the activity of respiratory muscles, one may wonder about their physiological significance. A mechanism by which they may play an important role during breathing has been pointed out by Barnas et al. (3). The rib cage and abdomen-diaphragm pathways act like parallel pumps operating on the lung to produce flow; to behave properly, such a system requires that the internal impedance of both pumps be large compared with that of the lung; indeed, if one of the pumps had a comparatively low impedance, it would be driven by the other and decrease the total flow output instead of increasing it. The same reasoning applies to parts of the chest wall which, at a given time, are not acting as a pump but must offer a high enough impedance to simply resist the changes in intrathoracic pressure; this increased impedance may be provided by the contraction of muscles acting as fixators (10). Whether the changes seen in Eti,eff reflect an increased internal impedance of the muscles as they contract or the stiffening by fixators of some part of the chest is open to question. Whatever the case, the observed variations of tissue elastance may be beneficial and prevent paradoxical motion when intrathoracic pressure is lowered during inspiration or increased at low lung volumes: an increase in elastance by 30 hPa/l, as we have seen to occur in our subjects during a quiet inspiration (Fig. 5), corresponds to an increase in impedance by 20 hPa · s · l¹ at a breathing frequency of 15 breaths/min; that change is sufficiently large compared with normal lung impedance at the same frequency (~5 hPa · s · l¹) to be a very effective stabilizing mechanism. Whereas a high internal impedance of the pumps may be beneficial, it is also costly in term of energy expenditure; the corresponding work, however, does not appear in the conventional pressure-volume diagrams because it is performed inside the pressure generator itself; it only contributes to lowering what is measured as the efficiency of respiratory muscles. It is one of the merits of approaches in which external generators are used, such as the forced-oscillation method, to reveal otherwise inapparent mechanical features of the respiratory system.

In summary, we have developed and tested a noninvasive method to measure respiratory tissue properties. The method does not assume that the tissues behave homogeneously, and the data are little influenced by inspired gas maldistribution. The method is well suited to study the frequency dependence of tissues properties as well as their time, volume, or flow dependence. We have also observed a volume dependence of Eti,eff to be much larger than expected from the passive properties of the respiratory system, which may reflect the effect of respiratory muscles activity. In contrast, Rti varied little with lung volume, which suggests that the two properties have different physiological determinants.

ACKNOWLEDGEMENTS

The authors are grateful to B. Clement for typing the manuscript and to M. C. Rohrer for the illustrations.

FOOTNOTES

Address for reprint requests: R. Peslin. Unité 14 INSERM, Physiopathologie Respiratoire, CO n°10, 54511 Vandoeuvre-les-Nancy cedex, France (E-mail: rpeslin{at}u14.nancy.inserm.fr).

Received 2 July 1996; accepted in final form 2 February 1996.

REFERENCES