INTRODUCTION

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ALTHOUGH SOME SYSTEMATIC errors have been demonstrated in patients with severe airway obstruction (2, 25, 26), the reference method to estimate thoracic gas volume (TGV) is that proposed by DuBois et al. (6), namely, the plethysmographic measurement of body volume changes (Vpl) during breathing efforts against a closed airway. A drawback of the method, however, is that it requires some degree of active cooperation from the subject to correctly perform the maneuver. Several successive inspiratory and expiratory efforts of uniform amplitude are, in our experience, necessary to detect the presence of a drift in Vpl and correct the data for it (20). Thus it may be difficult to obtain satisfactory recordings in young children, in patients with dyspnea and, more generally, in uncooperative subjects. The purpose of this study was to assess the reliability of an alternative method that would not require any active cooperation from the subject. It is based on the combination of alveolar pressure (PA) measurements by body plethysmography and of measurements of total respiratory mechanical impedance (Zrs) by forced oscillation; it also uses an assumption about mechanical properties of airways. The method was tested in healthy subjects by reference to the standard plethysmographic technique.

	PRINCIPLE

When a subject rebreathes BTPS gas in a body plethysmograph, Vpl is proportional to PA and to TGV (6)

(Eq. 1)

where K is the absolute pressure of dry gas in the alveoli [barometric pressure  water vapor pressure (PH₂O)]. On the other hand, in the frequency domain, airways impedance (Zaw) is the complex ratio of the pressure drop from the airway opening (Pao) to the alveoli (Pao  PA) to gas flow (). Taking PA from Eq. 1

(Eq. 2)

where Pao/ is respiratory input impedance (i.e., Zrs), the relationship between a pressure input at the airway opening and the resulting flow. Zaw is a complex variable that includes a resistive component [airway resistance (Raw)], and an out-of-phase component or reactance (Xaw). Provided airway walls are relatively stiff and airway properties are homogeneous, Xaw at comparatively low frequencies (<50 Hz in humans) is expected to be dominated by gas inertance (Iaw) and to increase linearly with frequency

(Eq. 3)

where  is the circular frequency ( = 2 ·  · f with f the frequency). Such a linear relationship has indeed been observed in studies in which Zrs has been partitioned into its airway and tissue components (17, 22). The method described herein relies heavily on Eq. 3 and assumes that Xaw/ is constant (i.e., independent of ). By using that assumption and considering the out-of-phase components of Pao/ (total total respiratory reactance; Xrs) and of Vpl/ (plethysmographic reactance; Xpl) in Eq. 2

(Eq. 4)

On the basis of Eq. 4, measurements of Xrs and Xpl at two frequencies (indexes 1 and 2) are sufficient to compute TGV

(Eq. 5)

If measurements at more than two frequencies are available, the value of TGV that minimizes the variance of Xaw/ may be obtained by

(Eq. 6)

where index i designates the measurement, n is the number of measurements, A_i = Xrs_i/_i and B_i = Xpl_i/_i. One may point out that the method does not impose any specific condition on Xpl and on the reactance of the tissues. It should be clear, however, that the very definition of Zaw as (Pao  PA)/ contains the implicit assumption that PA is homogeneous. The consequences of mechanical inhomogeneity are examined in DISCUSSION.

	MATERIALS AND METHODS

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The method was tested by using measurements of Xrs and Xpl obtained in 15 healthy subjects for a different purpose [separation of airway and tissue components of Zrs by using the standard plethysmographic TGV (TGV_st)(16)]. The subjects (10 men, 5 women) were aged 25-66 yr and were recruited among the laboratory staff.

Equipment. The subjects were seated in a 370-liter constant-volume body plethysmograph and connected, via a mouthpiece, shutter, and Fleisch no. 2 pneumotachograph, to a forced oscillation setup placed inside the box. Pressure variations at the airway opening were applied by a loudspeaker (Pioneer TS-W201, Pioneer Electronic), and the subject rebreathed through a side tube from a low-impedance bag in which the gas was maintained at BTPS by a thermostated water bath. Box pressure (Pbox) and the pressure drop across the pneumotachograph were measured with MP45 ±2-hPa Validyne transducers (Validyne, Northridge, CA) and Pao with a DP15 ±50-hPa Validyne transducer. All transducers were matched within 1% of amplitude and 2° of phase up to 30 Hz. Pao was calibrated by using a slanted fluid manometer and by the integral method that uses a 1-liter syringe. Pbox was calibrated in terms of Vpl with a small reciprocating pump at frequency of ~2 Hz.

Protocol. The subjects supported their cheeks firmly with their palms during the measurements. After Pbox had steadied, the forced oscillation data were collected for 33 s. Then, the oscillations were stopped, the shutter was closed and the subject was asked to pant for 5 s against the occlusion to measure TGV by the usual approach (6). The flow signal was sampled without interruption during the whole sequence so that any difference between the mean lung volume during the forced oscillation measurements and the volume when the shutter was closed could be computed and corrected for. Five to six such measurements were made at 2- to 3-min intervals, the rebreathing bag being thoroughly washed with fresh air between successive measurements.

Data analysis. Because the mechanical time constant of the plethysmograph was kept relatively short (3 s) to minimize the drift of Pbox and avoid saturating the analog-to-digital converter, Vpl was first corrected for it. This was done by adding to Vpl its integral divided by the time constant (16). Then, forced oscillation signals were high-pass filtered at 2 Hz to eliminate the main breathing components. The Fourier coefficients of the signals were computed at the 10 frequencies of interest and combined to obtain the in-phase and out-of-phase components of Zrs and Vpl/. Both were corrected for the 2.1-ms time constant of the pneumotachograph. Vpl/ was also corrected for the gas compression in the loudspeaker enclosure (0.8 liter); gas compression in the rebreathing bag appeared negligible and was not corrected for. The loss of flow through the extrathoracic airway walls (cheeks, mouth floor, pharynx) was corrected for by dividing both Zrs and Vpl/ by 1  Zrs/Zuaw, where Zuaw is the impedance of upper airway walls. Zuaw was measured separately in all subjects during Valsalva maneuvers according to Michaelson et al. (13) by using the same equipment as above to record Pao and . Finally, forced oscillation TGV (TGV_os) was computed from the values of Xrs and Xpl according to Eq. 6.

	RESULTS

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An example of the raw reactance data is shown in Fig. 1. The main results are summarized in Table 1. TGV_os derived from the forced oscillation data obtained over the entire frequency range was highly correlated with TGV_st but was 11.8% larger (4.28 ± 0.80 liters compared with 3.83 ± 0.73 liter, P < 0.001). The differences were much less when the data at the lowest frequencies were discarded, and they averaged +2.4% (P < 0.05) and 1.6% (not significant) within the 6- to 29- and 9- to 29-Hz frequency ranges, respectively. Discarding the highest frequencies did not improve the agreement. It is also in the 6- to 29- and 9- to 29-Hz ranges that the SD of the differences was the lowest. The 95% "limits of agreement" [mean ± tSD of differences, with t = 1.99 for 76 degrees of freedom (3)] were +0.79 to 0.61 liter for 6-29 Hz and +0.70 to 0.82 liter for 9-29 Hz. Variance analysis showed that the differences varied significantly among subjects (P < 0.001 within all frequency ranges). Mean individual data at 6-29 Hz are presented in Table 2: differences ranged from 0.33 to +0.65 liter and were significantly different from 0 in 7 of 15 subjects. In terms of the unsigned relative differences (100 · |TGV_os  TGV_st|/TGV_st), the 95% limits (mean ± 1.67 SD) were 17.3 and 18.7% for 6-29 and 9-29 Hz, respectively (Table 1). The relationship between TGV_os at 6-29 Hz and TGV_st, and the relationship between their difference and their mean, are shown in Fig. 2. Whatever the frequency range, there was no significant correlation between the differences and the means (Table 1).

View larger version (13K): [in this window] [in a new window]   Fig. 1.   Respiratory (Xrs) and plethysmographic (Xpl) reactance data as a function of frequency ( f ). Values are means ± SD (when larger than symbol) of 30 one-second data blocks from a single measurement in a representative subject.

View larger version (17K): [in this window] [in a new window]   Fig. 2.   Forced oscillation thoracic gas volume (TGVos) computed from 6- to 29-Hz data and standard TGV (TGVst; n = 77 measurements). Top: relationship between 2 estimates; line of identity (dashed line) and regression line (solid line) are shown. Bottom: relationship between differences and mean of 2 estimates; mean of differences and 95% limits of agreement are shown.

As noted in MATERIALS AND METHODS, the above-mentioned data were obtained after Zrs and Vpl/ were corrected for the flow lost through upper airway walls. Omitting that correction did not appreciably change the results. For instance, within the 6- to 29-Hz frequency range, uncorrected TGV_os was 4.02 ± 0.61 liters (2.5% larger than with the correction), and the differences to TGV_st averaged 0.19 ± 0.37 liter (95% limits of agreement: +0.92 to 0.54 liter).

	DISCUSSION

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Differences between estimates of a biological quantity by using two methods include the systematic and random errors of both methods, as well as biological variability when the measurements are not simultaneous (3). In this study, a number of potential sources of differences were absent or minimized: the two methods were based on the measurements of the same variables with the use of the same transducers so that static calibration errors would similarly affect TGV_os and TGV_st. The measurements were made in close succession in subjects in the same posture, and any change in lung volume was measured and corrected for. On the other hand, the frequency ranges of the two measurements differed considerably, which, although the frequency responses of the transducers and of the plethysmograph appeared satisfactory, could be responsible for some instrumental differences. The measurement of TGV by the method of DuBois et al. (6), taken as a reference in this study, involves substantial and easily measurable Pao and Vpl variations; moreover, our linear regression method with drift correction ensures a highly accurate determination of the slope of the Vpl-Pao relationship (20). The physiological or pathological factors that may bias TGV_st have been extensively studied in the past (1, 2, 4, 5, 10, 25, 26). Bohadana et al. (4) observed in healthy subjects that total lung capacities derived from TGV_st decreased by ~200 ml from low (0.5-Hz) to medium (2.2-Hz) panting frequencies. Computer simulation eliminated intrathoracic and extrathoracic airway wall compliance as potential factors but suggested as a remote possibility a combination of mechanical inhomogeneity and pleural pressure nonuniformity. Abdominal gas compression could be responsible for some over- or underestimation of TGV, depending on the relative phase of abdominal pressure and PA changes (5, 10). The error, however, should not exceed 150 ml at normal lung volumes (1). On the basis of the above considerations, we expect the contribution of errors in TGV_st to the observed differences not to exceed ±0.2 liter. Assuming the random errors in TGV_os associated with the experimental noise to be on the same order of magnitude, one would expect most of the differences between the two estimates to be within ±0.4 liter. Actually, the differences were outside that range in 20 of 77 measurements (6-29 Hz). In addition, differences between the mean TGV_os and the mean TGV_st (which should be little affected by random errors) were above +0.4 liter in 3 of 15 subjects (Table 2). This suggests the presence of some systematic cause of error in TGV_os in some subjects. Below we examine the factors that could be responsible for the discrepancies.

A crucial assumption in the computation of TGV_os is that Xaw increases linearly with frequency (Eq. 3). This will only be the case if Iaw is constant and if the effects of other potential determinants of Xaw (airway wall elasticity, mechanical inhomogeneity) are negligible.

The fluid inertance of a tube depends not only on its geometry and gas density but also on the velocity profile of the gas: the fluid inertance is 33% lower when the velocity profile is blunt than when it is parabolic (14). Because the velocity profile tends to get blunter when the frequency increases (8), one may expect some decrease in Iaw with increasing frequency. To assess this factor, we measured the inertance of 20-cm-long rigid tubes with internal diameters similar to those of the large airways (1.23-1.90 cm). We observed a regular decrease in inertance amounting to 6-9% from 5 to 30 Hz. We did some computer simulation to evaluate the influence of such a decrease on the estimation of TGV. The model included an airway characterized by Raw and Iaw, alveolar gas elasticity (TGV/K), and tissues with their resistance (Rti), compliance (Cti), and inertance (Iti). Iaw was made to decrease linearly by 10% from 4 to 29 Hz. Zrs and Vpl/ were computed at the usual frequencies and analyzed in the usual manner. The relative error in TGV_os was independent of Raw and TGV, depended little on Iti, but decreased with increasing Rti and increased with increasing Iaw and Cti. For reasonable values of Rti (1 hPa · s · l¹), Cti (0.04 l/hPa), and Iaw (0.015 hPa · s² · l¹ at 4 Hz) (19), TGV_os was overestimated by 3.2, 7.8, and 19.8% within the 4- to 29-, 6- to 29-, and 9- to 29-Hz frequency ranges, respectively. These figures are inconsistent with our observations (Table 1), particularly with the fact that TGV_os tended to decrease when the lower end of the frequency range was increased. It suggests that the frequency dependence of Iaw in the airways is less than what we observed in tubes, probably because the velocity profile is already rather blunt in the large airways during spontaneous breathing (8, 9).

Mechanical inhomogeneity of the respiratory system may be responsible for amplitude and phase differences between local PA values. In that situation, instantaneous Vpl, as measured by plethysmography, is proportional to the local PA values weighted by the local TGV values [Vpl = ( PA_i · TGV_i)/(K )], where index i designates any parallel lung compartment (15). This will compromise the validity of Eqs. 2-6 and the linear increase in the apparent Xaw with frequency. Some computer simulation was made to evaluate the corresponding error in TGV_os. The model included two compartments in parallel, each with its Zaw, TGV, and lung tissue compliance (CL,ti); it also included a common airway and a common chest wall, but they were seen to influence the error negligibly. Starting from the homogeneous situation (Raw = 2 hPa · s · l¹, Iaw = 0.01 hPa · s² · l¹, TGV = 2 liters, CL,ti = 0.05 l/hPa in both compartments), increasing one of the Raw values by a factor of two decreased TGV_os by 3.8-5.2%, depending on the frequency range; the error reached 18-19% when the ratio of local Raw was raised to five. On the other hand, changing the distribution of TGV between the compartments (1 and 3 liters, respectively) and changing one of the CL,ti values by a factor of 5 had very little or no effect. It therefore appears that substantial mechanical inhomogeneity of airway resistance may lead to an underestimation of TGV_os.

Another potential cause of error is airway wall elasticity. Its consequence is that some of the flow oscillation entering the airway is shunted to the intrathoracic space so that the flow in the peripheral airway is less than in the central airways. The shunt is negligible as long as airway wall impedance is large compared with that of the peripheral lung but may become important at high frequencies in the presence of peripheral airway obstruction (12). We analyzed that situation with a model including a central airway with a resistance (Rc = 1 hPa · s · l¹) and an inertance (Ic = 0.015 hPa · s² · l¹), a resistive peripheral airway (Rp), CL,ti (0.1 l/hPa), TGV (4 liters), and a resistive (Rw = 1 hPa · s · l¹), compliant (Cw = 0.1 l/hPa), and inertive (Iw = 0.002 hPa · s² · l¹) chest wall. Airway wall properties were modeled as a compliance (elastic bridge; Cb), shunting Rp and CL,ti (23). With a Cb of 0.003 l/hPa, as suggested from dead-space volume changes over the vital capacity range (24) and a low value of Rp (0.2 hPa · s · l¹), as expected in normal subjects, the error in TGV_os was <1 ml; raising Rp to 1 hPa · s · l¹ TGV_os was underestimated by 2.2, 3.2, and 8.2% within the 4- to 29-, 6- to 29-, and 9- to 29-Hz frequency ranges, respectively; the corresponding figures were 13, 26.5, and 48%, respectively, when Rp was raised to 2 hPa · s · l¹. From these computer simulations, we conclude that the method should provide reasonably accurate results for moderate degrees of mechanical inhomogeneities and airway wall shunting but not in the case of severe abnormalities; these factors are, therefore, unlikely to be responsible for the differences seen in some of our subjects.

Finally, it is postulated in Eq. 1 that Vpl is only related to PA variations. Other potential factors during breathing are the changes in gas temperature and PH₂O in the airways and the variations in the respiratory exchange ratio during the respiratory cycle (7). These factors are minimized by having the subject rebreathe in a circuit in which the gas is maintained at BTPS (7, 11). This is what we attempted to do in this study. However, we observed that the low-frequency respiratory component of Vpl during breathing was not always perfectly in phase with , but included a small component in phase with volume. This suggested that the gas conditioning was not perfect and that the above factors had not been completely eliminated. We measured by linear regression of Vpl vs. volume the amplitude of that component (G, dimensionless) and found it to range from 0.013 to +0.027: a negative value of G indicates that the inspired gas is too hot and cools down in the airways, and a positive value indicates that it warms up or increases its PH₂O. The relationship between TGV_os  TGV_st at 6-29 Hz and G is shown in Fig. 3. The differences were loosely but significantly correlated with G (r = 0.441, P < 0.001); a higher correlation (r = 0.561) was seen within the 4- to 29-Hz frequency range. These observations are consistent with the expected effect on TGV_os of a small thermal component in the Vpl- relationship. Computer simulation taking into account a time constant of 80 ms (18) for the change in gas condition shows that a negative value of G is associated with a frequency-dependent overestimation of TGV_os: with G = 0.01 and for reasonable values of tissue properties (Rti = 1 hPa · s · l¹, CL,ti = 0.04 l/hPa, Iti = 0.002 hPa · s² · l¹), TGV_os would be overestimated by 0.08 and 0.05 liter at 4-29 Hz and 6-29 Hz, respectively. The effect depends very much on the thermal time constant and may become much larger if the latter is shorter. Imperfect gas conditioning may therefore explain some of the variance in the differences. It is not clear whether it is also responsible for the overestimation of TGV_os at 4-29 Hz (11.7%); indeed, on the basis of the positive mean value of G (0.0034 ± 0.0093), TGV_os should rather be slightly underestimated on average. We have no other explanation to offer, however, for that finding.

View larger version (10K): [in this window] [in a new window]   Fig. 3.   Relationship between differences of TGVos and TGVst and slope (G; dimensionless) of relationship between plethysmographic measurement of body volume changes (Vpl) and airway flow () during breathing. Significant correlation (r = 0.44) suggests that a thermal factor is responsible for some of variance of TGVos  TGVst.

To summarize our results, this study showed a close relationship but not a perfect agreement between the values of TGV derived from forced oscillation measurements and those obtained with the usual panting maneuvers in normal subjects. The results depended slightly on the frequency range over which the data were analyzed, which may, in part, be related to imperfect gas conditioning to BTPS. Even with the optimal frequency range, differences >10% were seen in ~30% of the measurements; 95% limits of agreement were about ±0.7 liter (disregarding the small systematic bias) or 17%. These values are obviously too large for applications requiring a very accurate measurement of TGV. They are not so large, however, compared with the 95% confidence interval of predicted functional residual capacity or total lung capacity in adults (1.96 residual SD above 1 liter) (21). The method could, therefore, have some usefulness in situations in which, for some reason, the method of DuBois et al. (6) cannot be used and in which severe mechanical inhomogeneity and airway wall shunting are not expected.