INTRODUCTION

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THE MEASUREMENT of respiratory input impedance (Zrs,in) by forced oscillations and the indirect measurement of alveolar pressure (PA) by body plethysmography were described by DuBois and co-workers (3, 5) more than 40 years ago. To our knowledge, these two investigations have never been combined to investigate respiratory mechanics. In a few studies, plethysmographic measurements of chest flow have been associated with forced oscillations to compute respiratory transfer impedance (Zrs,tr) or the transfer function between flows at the airway opening (ao) and at the chest (bs) (16, 19, 24, 29). Also, Finucane and Mead (6) measured bs and ao during forced oscillations at the airway opening with a piston pump and computed PA from their difference. Never, however, has the plethysmograph been used in the so-called differential mode, i.e., with the subject breathing inside the box, which may be expected to provide a much easier and accurate measurement of the very small difference between ao and bs related to PA variations. The rationale of measuring Zrs,in and PA simultaneously is that it provides a way to obtain airway impedance (Zaw) and tissue impedance (Zti) separately without specific modeling of these impedances. This is of interest in many clinical and experimental situations to partition the effects of disease or drugs on the airways and tissues. It is particularly interesting in view of the recent experimental studies which have shown that bronchomotor drugs may have a large effect on lung tissue properties (1, 9, 25). The method consists in applying pressure oscillations at the airway opening of a subject placed into, and breathing inside, a body plethysmograph. The oscillator is also placed inside the box, so that box, subject, and oscillator form a closed system, and box pressure only reflects changes in gas condition within that system. The analysis is based on the usual monoalveolar T-network model (5), which features Zaw and Zti separated by a shunt impedance (Zg) corresponding to alveolar gas compressibility (Cg)

(1)

(2)

where j is the unit imaginary number,  is the circular frequency (2 ·  · f), TGV is thoracic gas volume, PB is barometric pressure, and PH₂O is alveolar water vapor pressure. Equation 2 assumes that alveolar gas compression is isothermal. When a pressure input is applied at the airway opening (Pao), Zg and Zti are arranged in parallel, and both are in series with Zaw. Then Zrs,in, the relationship between Pao and ao, is given by

(3)

The two terms on the right in Eq. 3 correspond to airway impedance

(4)

and "alveolar" impedance, the impedance of the tissues and alveolar gas in parallel

(5)

Provided the volume variations detected by the plethysmograph (Vpl) are freed from any thermal or gas exchange component (rebreathing of BTPS gas) (3, 6)

(6)

Equation 6 also assumes that gas compression in the abdomen and dead space (including instrumental dead space) is negligible. In what follows, we denote Hpl as the relationship between Vpl and ao

(7)

From Eqs. 6 and 5

(8)

where ZA is alveolar impedance. So the relationship between the plethysmographic signal and airway flow is just the product of ZA and Cg. From Eqs. 3, 5, and 8 

(9)

(10)

The aim of this study was to assess whether reliable estimates of Zaw and Zti could be obtained by this approach. For this we measured Zrs,in and Hpl from 4 to 29 Hz in healthy subjects rebreathing BTPS gas.

	METHODS

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Fifteen healthy subjects (10 men, 5 women), aged 25-66 yr, were recruited from the laboratory staff.

Equipment. The subjects were seated in a 370-liter constant-volume body plethysmograph made in the laboratory from metal and Plexiglas (Fig. 1). Pressure variations at the airway opening were applied by a loudspeaker (model TS-W201, Pioneer Electronic) connected to the airways through a Fleisch no. 2 pneumotachograph, a shutter valve, and a mouthpiece. During the measurements the subject rebreathed through a side tube connected to a reservoir covered with a thin bag, where the gas was conditioned to BTPS by a thermostated water bath (Polystat 5, Bioblock, Ilkirch, France). All the tubing from the reservoir to the mouth was heated to avoid cooling and condensation. Box pressure (Pbox), Pao, and the pressure drop across the pneumotachograph were measured with transducers (type MP15 ±50 hPa for Pao and type MP45 ±2 hPa for Pbox and ao, Validyne, Northridge, CA) matched within 1% of amplitude and 2° of phase up to 30 Hz. In addition, a fourth pressure transducer was used to assess whether gas compression occurred within the air conditioner reservoir; it was always found to contribute negligibly to Vpl oscillations and was not corrected for. The common mode rejection ratio of the flow transducer was >60 dB. Pao was calibrated using a slanted fluid manometer and ao by the integral method using a 1-liter syringe. The plethysmograph had a comparatively short time constant (3 s) to minimize thermal pressure drift during the measurements; Pbox was calibrated in terms of Vpl with a small reciprocating pump at a frequency of ~2 Hz.

View larger version (25K): [in this window] [in a new window]   Fig. 1.   Experimental setup. Pao and ao, airway opening pressure and flow; Vpl, volume change detected by plethysmograph; P Amplifier, power amplifier; LS, loudspeaker; Ac, gas conditioner.

Protocol. The subject, wearing a noseclip, was asked to take the mouthpiece and firmly support his/her cheeks with the palms. After Pbox had steadied, the forced oscillation data were collected for 33 s (the longest time allowed by our program). Then the oscillations were stopped, the shutter was closed, and the subject was asked to pant for 5 s against the occlusion for measurement of TGV. Finally, the shutter was reopened, and the subject was asked to continue panting for another 5 s for measurement of airway resistance (Raw,pl) by the usual approach (3). Five to six such measurements were made at 2- to 3-min intervals, with the air conditioner being thoroughly washed with fresh air between successive measurements. In a few subjects additional measurements were performed in various experimental conditions, as described in RESULTS.

Data analysis. Vpl was corrected for the mechanical time constant (T) of the plethysmograph, which is the product of the resistance of the leak (Rpl) and the compliance of the gas inside the box (Cpl). These two elements being in parallel

(11)

where leak is the flow of gas through the leak and Vpl° is the uncorrected plethysmographic signal. The volume lost through the leak is, therefore, the integral of the measured volume divided by the time constant. The correction was implemented digitally using

(12)

where subscripts i and j designate the ith and jth samples and dt is the reciprocal of the sampling frequency. T was obtained from recordings of the exponential decrease of Pbox after a step volume input.

(13)

(14)

1

1

	RESULTS

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An example of the Zrs,in and Hpl frequency spectra obtained from one single measurement in a representative subject, along with between-block standard deviations and ², is shown in Fig. 2. The variability of both functions was larger and the ² was lower at the lowest frequencies; the variability was also usually slightly less for Zrs,in than for Hpl. In 12 of 15 subjects, ² was <0.9 at 4 Hz for Zrs,in and/or Hpl in three or more of the five to six successive measurements. This was the case for only two subjects at 5 and 6 Hz and never occurred at larger frequencies. As commonly done in forced oscillation studies, we have discarded all the data with ² <0.9 and do not report the 4-Hz data, because all measurements were rejected in many subjects.

View larger version (24K): [in this window] [in a new window]   Fig. 2.   Real (Re, ) and imaginary (Im, ) parts of input impedance (Zrs,in, top) and of relationship between plethysmographic signal and flow (Hpl, middle) as a function of frequency (f). Values are means ± SD of 30 data blocks from a single measurement in a representative subject (subj. 1). Bottom: coherence function of Zrs,in (×) and Hpl ().

As explained above (Eq. 8), Hpl is the product of Cg (a constant term) times ZA, the association of Zti and Zg in parallel. Zg being much larger than Zti (because gas compliance is much less than tissue compliance), ZA is very close to Zti. Thus the Hpl spectrum mainly reflects the resistive and elastic properties of the respiratory tissues.

Figure 3 shows Zaw and Zti derived from the five successive measurements in the same representative subject. In general, the variability of Zaw was similar to that of Zrs,in, and the variability of Zti was somewhat smaller.

View larger version (17K): [in this window] [in a new window]   Fig. 3.   Real () and imaginary () parts of airway impedance (Zaw, top) and tissue impedance (Zti, bottom). Values are means ± SD (not shown when smaller than symbol) from 5 consecutive measurements in a representative subject (subject 1).

Mean data and standard errors in the group are shown in Fig. 4. For the sake of brevity, the real parts of impedances are thereafter termed resistances (denoted R) and the imaginary parts are termed reactances (denoted X) with suffixes rs, aw, and ti for the total respiratory system, airways, and tissues, respectively. Rrs exhibited a small negative frequency dependence, falling by ~12% from 5 to 29 Hz. Raw and Rti had roughly the same magnitude, but with opposite frequency dependences, Raw increasing by 25% and Rti decreasing by 43% over the observed frequency range. Rrs may be substantially lower than the sum of Raw and Rti because of the alveolar gas shunt pathway (Eq. 3). Xrs exhibited the usual pattern and was partitioned into an airway component, which increased almost linearly with frequency, and a negative tissue component, which increased hyperbolically toward zero.

View larger version (16K): [in this window] [in a new window]   Fig. 4.   Real (R, open symbols) and imaginary (X, filled symbols) parts of respiratory input (rs), airway (aw), and tissue (ti) impedance. Values are means ± SE in 15 subjects.

Whereas the qualitative features observed in the group were seen in all subjects, substantial quantitative differences were noted among them. The results of two subjects with very different Rrs are shown in Fig. 5. The analysis revealed that the larger Rrs of subject 5 was due to a larger Raw and a larger Rti. Subject 5 also had a larger Xaw and a wavy Xti, features clearly present in three other subjects.

View larger version (25K): [in this window] [in a new window]   Fig. 5.   Real (open symbols) and imaginary (filled symbols) parts of respiratory (top), airway (middle), and tissue (bottom) impedance of 2 subjects [subjects 2 (triangles) and 5 (circles)] with very different resistances.

The mean values of Raw and Rti in all subjects over the 5- to 29-Hz frequency range are presented in Table 1, along with the values of airway inertance (Iaw) and tissue elastance (Eti). Iaw was obtained by linear regression of Xaw vs.  (r > 0.99 in all instances) and Eti by linear regression of Xti ·  vs. ²: modeling the tissues as an elastance and an inertance (Iti) arranged in series, Xti ·  = Iti · ²  Eti. The latter analysis was not performed in the four subjects exhibiting a wavy Xti; Iti values are known to be unreliable in that frequency range (10, 17) and are not presented. On average, Rti was only slightly lower than Raw with Rti-to-Raw ratios of 0.46-1.46. The interindividual variability of Raw was almost twice as large as that of Rti. Forced-oscillation Raw was also compared with plethysmographic Raw obtained during panting at the end of each recording (Raw,pl). On average, Raw was similar to Raw,pl at 5 Hz (1.29 ± 0.51 vs. 1.29 ± 0.53 hPa · s · l¹) and larger at 29 Hz (1.56 ± 0.61 hPa · s · l¹, P < 0.001). The two estimates were significantly correlated at all oscillation frequencies, the highest correlation being seen at 29 Hz (r = 0.81).

To test the quality of the partitioning of Zrs,in into Zaw and Zti, measurements were performed in one subject when chest wall elastance was increased by stretching two elastic bands around his rib cage and waist, respectively. The load decreased mean TGV from 3.73 to 2.97 liters. Compared with control conditions, the load induced a small increase in Rrs at low frequency (Fig. 6), which the analysis attributed to Rti and which could be due to the viscoelastic properties of the elastic bands; the analysis also showed a significant increase in Raw (1.07 vs. 0.86 hPa · s · l¹ for the means from 5 to 29 Hz). As for the reactances, the load substantially decreased Xrs at all but the largest frequencies, which appeared almost entirely due to the tissue component; Eti, computed as above, increased from 21.4 to 75.2 hPa/l, whereas Iaw did not change (0.0131 vs. 0.0126 hPa · s² · l¹). Measurements were also performed in two subjects breathing at different lung volumes. In the instance shown in Fig. 7, breathing at a higher lung volume slightly decreased Rrs and Raw, did not modify Rti and Iaw, and lowered Xti at all frequencies (Eti = 42.0 hPa/l vs. 30.8 hPa/l at normal TGV). Breathing at a lower lung volume decreased Xti to a larger extent (72.6 hPa/l), did not modify Iaw, and increased Raw and Rti. The results were qualitatively similar in the other subject, except Iaw was also increased during breathing at the lower lung volume.

View larger version (24K): [in this window] [in a new window]   Fig. 6.   Real (open symbols) and imaginary (filled symbols) parts of respiratory (top), airway (middle), and tissue (bottom) impedance of a subject in control condition (circles) and during loading of chest wall with elastic bands stretched around rib cage and abdomen (triangles).

View larger version (25K): [in this window] [in a new window]   Fig. 7.   Real (open symbols) and imaginary (filled symbols) parts of respiratory (top), airway (middle), and tissue (bottom) impedance of a subject at usual lung volume [circles, mean thoracic gas volume (TGV) = 5.6 liters] and at higher (triangles, TGV = 6.7 liters) and lower (inverted triangles, TGV = 4.8 liters) lung volumes.

Finally, measurements during induced bronchoconstriction were performed in two subjects. Bronchoconstriction was induced by having the subject inhale an aerosol of methacholine (MCh; De Vilbiss model 5610 D nebulizer) at a dose that decreased forced expiratory volume in 1 s by ~20%; measurements were also performed after the effect of MCh was reversed by an aerosol of fenoterol and ipratropium bromide (Bronchodual, Boehringer; 3 puffs). The effects of bronchoconstriction were similar in the two subjects and are illustrated in Fig. 8: MCh induced a large increase and a negative frequency dependence of Rrs, which appeared almost entirely related to the airway component; MCh also induced a shift to the right of Xrs that seemed to involve the airway and the tissue components. Subsequent bronchodilation completely reversed the changes in Xrs and its components and decreased Rrs and Raw below their control values.

View larger version (26K): [in this window] [in a new window]   Fig. 8.   Real (open symbols) and imaginary (filled symbols) parts of respiratory (top), airway (middle), and tissue (bottom) impedance of a subject in control condition (circles), after an aerosol of methacholine that decreased forced expired volume in 1 s by 20% (triangles), and after subsequent bronchodilation (inverted triangles).

	DISCUSSION

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A number of approaches may be used to partition noninvasively lung and respiratory impedances into their airway and tissue components. Several of them imply the use of models in which specific assumptions are made concerning the properties of the two components. Among these are the analysis of Zrs,tr using the DuBois (5) six-coefficient model (10, 22); the analysis of low-frequency Zrs,in using a model where airway resistance is Newtonian, whereas the tissues are viscoelastic (8, 11, 13); and the analysis of combined time-frequency domain data during bronchoconstriction with a model in which airway properties are inhomogeneous and tissue properties are nonlinear (28). In contrast, other approaches do not require any specific assumptions concerning the properties of the airways and the tissues; they simply use the more general assumption that airways and tissues are separated by a shunt pathway corresponding to alveolar gas compliance (monoalveolar T-network model). These alternative approaches require measuring simultaneously (16, 19) or separately (26) Zrs,in and Zrs,tr or the relationship between ao and bs (24, 29), which is equivalent. The method described here belongs to that category, the use of differential body plethysmography providing the required relationship between ao and bs (dVpl/dt = ao  bs). Provided the partitioning is accurate, an obvious advantage of the second type of approach over the first is that no a priori model is forced on Zaw and Zti. It is only after the separation is made and after the respective frequency dependences of the components are known that models may be proposed to account for them; this may allow more sophisticated modeling, such as analysis of Zti with a two-compartment model (19).

Our observations suggest that the combination of Zrs,in measurements and body plethysmography provides reliable estimates of Zaw and Zti in normal subjects. Before these results are discussed in more detail, several methodological and theoretical issues deserve a few comments.

An important condition for accurately estimating PA by using Eq. 5 is that Vpl be freed from any thermal- or gas-exchange component (3, 6). When a normal subject inspires ambient air in a body plethysmograph, the part of Vpl corresponding to the warming and humidification of the gas in the airways is commonly 10 times as large as the part of Vpl related to PA changes (20). Instantaneous differences between O₂ uptake and CO₂ output in the lung vary along the respiratory cycle (4) and are also responsible for respiratory variations of Vpl (3). The first of these factors decreases with increasing frequency but, on the basis of a thermal-time constant of 100 ms (21), should still be important at the lowest frequencies explored in this study. In a preliminary series of measurements performed without gas conditioning, we observed a poor separation of Zaw and Zti below 10 Hz, resulting in an underestimation of Xaw: in a group of eight healthy subjects, Xaw was negative at 4 Hz in seven instances; it was still negative at 5 Hz in two subjects, averaging 0.105 hPa · s · l¹, whereas it should have been 0.31-0.93 hPa · s · l¹ for the expected Iaw of 0.01-0.03 hPa · s² · l¹ (10, 22). This underestimation is consistent with the effect of the thermal factor and disappeared after the inspired gas was conditioned to BTPS (Xaw = 0.544 ± 0.045 hPa · s · l¹ in our 15 subjects). Another advantage of having the subject rebreathe from a gas conditioner is that it also decreases the variations of CO₂ output during the respiratory cycle (7).

Another methodological problem, always present during Zrs,in measurement at comparatively large frequencies, is the fact that part of the measured ao is shunted through the compliant extrathoracic airway walls (cheeks, mouth floor, pharynx); this is responsible for a frequency-dependent systematic error on Zrs,in and, in our approach, on Hpl as well. To minimize the error, both spectra were corrected as indicated in METHODS. To evaluate the influence of this factor, the data were reanalyzed in subjects 1-5 without correction. Although Rrs was slightly modified, uncorrected Raw and Rti were progressively overestimated (+17.7% at 29 Hz) and underestimated (31.4% at 29 Hz), respectively, above 13 Hz. Iaw was practically unchanged (0.0124 vs. 0.0118 hPa · s · l¹), but uncorrected Xti was lowered by 0.20-0.25 hPa · s · l¹ over the entire frequency range. It, therefore, appears that correcting for the upper airway shunt is important in accurate partitioning of Zrs,in.

In the T-network hypothesis used to partition Zrs,in into Zaw and Zti, it is implicitly assumed that 1) PA is homogeneous and 2) airway walls are rigid, so that all the gas entering the airways reaches the alveolar space. These two assumptions are also made in the methods involving a priori modeling of Zaw and Zti, except for the method recently described by Suki et al. (28), which allows for mechanical inhomogeneity of the airways. Lutchen et al. (11, 12) recently showed, both theoretically and experimentally, that the analysis of Zrs,in based on a model with a Newtonian Raw and viscoelastic tissues provided erroneous estimates of Zti in the presence of severe inhomogeneities and airway wall shunting. We performed some computer simulation to assess the influence of these two assumptions on the partitioning of Zrs,in with our approach. Concerning the assumption of mechanical inhomogeneity, first, it is required by the theory that PA be homogeneous but not that the whole respiratory system be homogeneous. For instance, the equations remain valid if Zti consists of a number of compartments in parallel with different properties, provided this does not make PA inhomogeneous. We generated numerically at the 10 usual frequencies Zrs,in and Hpl data corresponding to a system made of two T networks in parallel with a common resistive (Rc = 1.0 hPa · s · l¹) and inertive (Ic = 0.01 hPa · s² · l¹) central airway. Each T network included a resistive (Raw_i) and inertive (Iaw_i) airway, a resistive (Rti_i), elastic (Eti_i), and inertive (Iti_i) tissue compartment, and an elastic alveolar shunt (Cg_i). Starting from the homogeneous situation (Raw₁ = Raw₂ = 2 hPa · s · l¹, Iaw₁ = Iaw₂ = 0.01 hPa · s² · l¹, Cg₁ = Cg₂ = 0.002 l/hPa, Rti₁ = Rti₂ = 2 hPa · s · l¹, Eti₁ = Eti₂ = 50 hPa/l, Iti₁ = Iti₂ = 0.002 hPa · s² · l¹), we examined the effect of different types of mechanical inhomogeneity on the computed Zaw and Zti. Increasing Raw₂ by a factor of 5 increased Raw, as expected, and made it slightly frequency dependent (2.4% from 4 to 29 Hz); it also decreased Xaw at low frequencies below the expected value (0.159 vs. 0.377 hPa · s · l¹ at 4 Hz). However, it did not modify Rti and Xti. Increasing Iaw₂ by a factor of 5 influenced Raw, which exhibited a strong positive frequency dependence but, similarly, did not modify Zti. Symmetrically, increasing Rti₂ slightly modified Xti, and increasing Eti₂ made Rti frequency dependent, but these tissue inhomogeneities did not influence Zaw. Finally, changing the distribution of alveolar gas between the compartments (Cg₁ and Cg₂ = 0.001 and 0.003 l/hPa, respectively) minimally modified Raw, Xaw, and Rti (<3% at all frequencies) but slightly decreased Xti. From these results, we conclude that the type of inhomogeneity represented in this model creates some interference between the resistance and reactance of the inhomogeneous component but, depending on the situation, influences very little or not at all the partitioning of Zrs,in into Zaw and Zti in our frequency range. Extending the simulation to frequencies an order of magnitude lower (0.4-2.9 Hz), where mechanical inhomogeneities have a greater influence on Zrs,in (18), we observed the same lack of effect of airway inhomogeneity of Zti estimates and of tissue inhomogeneity on Zaw estimates.

Compliant intrathoracic airway walls shunt some of the flow oscillations directly to the intrathoracic space, so that the flow entering the alveoli is less than ao. This type of shunting, described by Mead (14), is important only when the impedance of the peripheral lung is no longer much lower than that of airway walls. To assess the influence of that situation on our analysis, we used a model including a central airway, as described above, a resistive peripheral airway (Rp), an elastic lung tissue (El = 10 hPa/l), the usual Cg (0.004 l/hPa), and a resistive (Rw = 1 hPa · s · l¹), elastic (Ew = 10 hPa/l), and inertive chest wall (Iw = 0.001 hPa · s² · l¹). Airway wall properties were modeled as an elastic bridge (Cb) shunting the peripheral airway and lung tissue. Zrs,in and Hpl were computed for different combinations of Rp (0.2-5 hPa · s · l¹) and Cb (0.001-0.005 l/hPa) and analyzed as usual. The influence on Zaw and Zti of increasing Rp from 0.2 to 1.0 hPa · s · l¹ with Cb = 0.005 l/hPa is shown in Fig. 9. Airway wall shunting greatly increased Raw at low frequency and made it frequency dependent. It also shifted Xaw substantially to the right; the same effect has been described by Mishima et al. (16) for the approach combining Zrs,in and Zrs,tr. On the other hand, it affected Xti negligibly and lowered Rti by just a few percent. With Rp = 5 hPa · s · l¹, Raw became extremely frequency dependent and Xaw was negative below 20 Hz, but Rti was only moderately underestimated (19 and 5% at 4 and 29 Hz, respectively) and Xti only slightly increased. We conclude that airway wall shunting makes the usual resistance-inertance model of the airways totally inadequate but does not compromise to a great extent the recovery of Zti.

View larger version (19K): [in this window] [in a new window]   Fig. 9.   Computer simulation of effect of airway wall shunting on airway (top) and tissue (bottom) impedance. Open symbols, real parts; filled symbols, imaginary parts. Circles, low airway peripheral resistance (Rp; 0.2 hPa · s · l1); triangles, increased Rp (1.0 hPa · s · l1). Xti is almost unaffected by Rp. See DISCUSSION for description of model used in simulation.

Our results in unchallenged subjects have much in common with those obtained in studies using a different experimental approach, the measurement of Zrs,in and Zrs,tr but the same basic assumption, i.e., the monoalveolar T-network model. In particular, the positive frequency dependence of Raw and the negative frequency dependence of Rti, as well as the linear increase of Xaw with frequency, characteristic of inertial reactance, were seen by Peslin et al. (19), Rotger et al. (27), and Mishima et al. (16). This is also the case for the increase of Xti with increasing frequency, characteristic of elastic-inertive systems. In 4 of 15 subjects, Xti (and Xrs) clearly presented a wavy pattern, as illustrated by subject 5 in Fig. 5; this feature was also previously observed and has been shown to be consistent with the association in parallel tissue compartments with different resonant frequencies (19). Although the similarity of our data to those in studies that used the same basic assumptions does not really demonstrate the reliability of the method under study, it proves at least that the measurements of Zrs,in and Hpl (and those of Zrs,in and Zrs,tr in the other studies) were technically correct. Our values of Raw and Iaw (Table 1) are also similar to those found by Kaczka et al. (8), who analyzed lung impedance spectra from 0.18 to 8.1 Hz obtained in nine healthy humans with a model featuring a viscous tissue compartment (Raw = 1.67 ± 0.61 hPa · s · l¹, Iaw = 0.016 ± 0.006 hPa · s² · l¹).

Besides the good agreement between Raw values observed with our approach and with the usual panting technique, more direct evidence of the quality of the partitioning is provided by the results obtained when the experimental conditions were varied. During elastic loading of the chest accompanied by a reduction in lung volume (Fig. 6), the analysis showed the expected effect, namely, a marked decrease in Xti at all frequencies, corresponding to a large increase of Eti. Interestingly, Xaw was almost unchanged, although it represented at low frequencies only a small part of the total reactance; this is in agreement with observations showing that Iaw varies little with lung volume (17) and strongly supports a very good separation between the two components. Elastic loading also significantly increased Raw, which is consistent with the decreased TGV. The expected effect of lung volume on Raw was also clearly present in the two subjects who were studied during voluntary breathing at different TGVs. Decreasing and increasing TGV were seen to increase Eti; this is consistent with the sigmoidal shape of the static pressure-volume curve of the respiratory system and also with the effect of respiratory muscle contraction on respiratory mechanics (24, 29). The latter factor may also explain the associated changes in Rti at low lung volume. Finally, increasing TGV did not modify Xaw, but decreasing TGV had opposite effects in the two subjects. In one of the subjects (Fig. 7), it slightly decreased Xaw at low frequency, which may reflect some degree of Raw inhomogeneity or airway wall shunting, as discussed above. In the other subject (not shown), who breathed very close to residual volume, it substantially increased Xaw and Iaw (0.0215 vs. 0.0117 hPa · s² · l¹ at his normal TGV), suggesting a decrease in the caliber of the large airways. Finally, bronchoconstriction and bronchodilation (Fig. 8) strongly changed Raw but had almost no effect on Rti. This finding is consistent with the data of Kaczka et al. (8), who observed larger changes in Raw than in lung tissue damping during mild bronchoconstriction in humans. In our study, bronchoconstriction slightly lowered Xti (increased Eti), which may be due to a genuine effect of MCh on lung tissue, as seen by others after the administration of various bronchomotor drugs (1, 9, 25), or to the increased activity of respiratory muscles (24, 29). The second mechanism is supported by the absence of change in lung tissue elastance during mild bronchoconstriction in the study of Kaczka et al. Unexpectedly, bronchoconstriction also markedly shifted Xaw to the right (Fig. 8); from our computer simulation (Fig. 9), airway wall shunting seems a likely explanation for this finding. The data Kaczka et al. obtained during more severe bronchoconstriction were also consistent with that mechanism.

In this study the lowest frequency was set at 4 Hz, because with use of small-amplitude forced oscillations it is difficult to obtain satisfactory impedance data at lower frequencies in spontaneously breathing subjects. We even had to discard the 4-Hz data, because ² was frequently <0.9. At these comparatively high oscillation frequencies, respiratory impedance contains virtually no information on the viscoelastic properties of the lung, which have been shown to represent ~40% of lung resistance at typical breathing frequencies in humans (8). The applicability of our approach at lower frequencies, using an adapted pressure input such as the "optimal ventilator waveform" (8), remains to be investigated.

In summary, we have tested a method to partition Zrs,in into its Zaw and Zti components by combining 4- to 29-Hz forced oscillations and body plethysmography. The method is similar, in principle, to that proposed by Finucane and Mead (6), but, being based on differential plethysmography, rather than on separate measurements of ao and bs, it is easier and probably much more accurate. The results obtained in 15 healthy subjects were in agreement with previous findings. In addition, the analysis of data in various experimental conditions, some of them strongly modifying lung mechanics, provided Zaw and Zti spectra that were mostly in agreement with the expected effects; there was no evidence of interference between Zaw and Zti changes. Computer simulation suggests that the partitioning of Zrs,in is unaffected by substantial degrees of mechanical inhomogeneity and only moderately affected by airway wall shunting.