Following topical anesthesia of the nasal mucosa with lidocaine, the balloon was passed transnasally into the stomach and then gradually withdrawn until a negative deflection of Pes was recorded during inflation. The balloon was then withdrawn to 5, 10, or 15 cm above the gastroesophageal junction, where at each level, a series of pressure and volume readings were recorded. The level of the balloon within the esophagus was chosen at random. The volume of air in the balloon was 0.5 mL and was checked frequently during the course of the experiment.

The study was performed in seated and supine positions. In each posture and each esophageal level, the subject generated the P-V curves by watching the tracing on the oscilloscope. To monitor the tracings in supine position, the subject watched the oscilloscopic tracing reflected from a mirror mounted above his head. The occlusion test was used to validate the esophageal balloon technique as a means of measuring pleural pressure [21] . After 5 minutes of quiet breathing in either posture, the subject performed 3 inspiratory vital capacity (VC) maneuvers (to maintain consistent volume history) while watching the oscilloscope. Upon reaching the peak of the third VC maneuver, the lung was deflated to residual volume (RV) in a stepwise manner, keeping the glottis open at all times. After reaching RV, the direction was reversed, with the lungs inflating to TLC in a similar stepwise manner. Subjects held their breath for 1 - 2 seconds at each of 10 - 15 steps in each limb of the P-V curve. We found that, on average, this number of steps was within the tolerance range of breath-holding for our subjects. Measurements of Pes were not made during periods of esophageal contractions.

Physiologic variables were expressed as mean ± SD. Differences amongst variables at different body positions and esophageal levels were computed by analysis of variance.

Figure 1 shows inflation and deflation curves obtained in sitting and supine positions with the balloon placed at 3 different esophageal levels in subject no. 1. In 5 of 6 curves, the exponential curves fit the raw data well. The highest portions of the curves above the points of inflection shifted to the right in the supine posture with the balloon at 5 and 10 cm above the cardia. Moreover, the effect of moving the balloon to a more cephalad position in the esophagus resulted in a shift of both the deflation and inflation curves to the right, indicating an increase in elastic recoil. As can be seen in Table 2 , this finding was, in most instances, reflected in both postures by an increase in the Ptp at TLC with the balloon placed more cephalad. The exception was at 10 cm in the supine position, a finding likely related to gravitational pressure from the heart.

Values are expressed as mean (SD). †p < 0.05, ††p < 0.01, differences amongst variables within each group according to balloon levels, analysis of variance. *p < 0.05, **p < 0.01, differences amongst K₁ between deflation and inflation curves at corresponding esophageal levels, analysis of variance. Abbreviations: V: lung volume in liters; P_L: maximum Pst(L) in cm H₂O; Vd: volume at the point of deflection; V_o: constant representing theoretical minimum or maximum volume; K_o: constant describing the ratio of the volume at the half inflation pressure; h: to the volume difference from V_o to V_o at zero transpulmonary pressure; K₁: constant describing the elastic property of the lung (i.e., convexity of the curve); r²: correspondence of recorded data points with respect to the theoretically computed P-V points based on the twin-exponential fit.

Table 2 lists the physical and regression constants of the inflation and deflation portions of the P-V curve in the 10 subjects, seated and supine. Variables relevant to the derived exponential P-V curves have been separated according to those obtained at ≥51% TLC and those derived at <50% TLC. Note that during deflation, V_o, the derived maximal theoretical volume, was within 8% of the actual TLC at Vd ≥ 51% TLC at all esophageal levels in both postures, whereas the minimal theoretical value was 21% - 23% of TLC at Vd < 50% TLC. Of greatest interest, the shape constant K₁, defining curvilinearity, during deflation at volumes ≥ 51% TLC in most instances exceeded values during inflation at corresponding esophageal levels in both postures, reflecting the greater downward concavity in this region. Differences in K₁ between deflation and inflation were less apparent at volumes < 51% TLC in supine posture, again a likely consequence of dependent airway closure. Most mean values of K₁ at volumes ≥ 51% TLC tended to be lower than those at <51% TLC at all esophageal levels in both positions, consistent with the increased curvilinearity (with opposite concavity) of the lower portion of the P-V curve. The exceptions were during deflation at the 15 cm level in seated posture and at the 5 cm level in supine position, where K₁ was greater than their corresponding seated and supine values, respectively, indicating a “straightening” of the curve in these conditions. At the 15 cm level, regional lung volume remains closer to maximal inflation with an increase in Pst(L). By contrast, at the 5 cm level, the difference in curvilinearity can be accounted for by gravitational effects of the heart and “closing volume” which displaces Ptp more to the left (i.e., less positive value) for a unit volume change below FRC [3] [10] . In both postures at the 5 cm esophageal level, the mean K₁ during deflation was greater than during inflation at both above and below 50% TLC (p < 0.05), reflecting the more acute pressure changes occurring during deflation.

The esophageal level also influenced K₁. At TLC ≥ 51%, in the supine posture, during both inflation and deflation, K₁ decreased in magnitude (by more than 50%) with the balloon moving from 5 cm to 15 cm above the cardia, indicating flattening of this portion of the curve with an increase in end-inspiratory Ptp in regions farther from the diaphragm, findings similar those reported by Milic-Emili et al. [3] This change was not apparent while seated or at volumes < 51% TLC, reflecting greater curvilinearity related to end-expiratory lung compression occurring in the supine position.

Transpulmonary pressure at half lung volume, h, was greatest at all esophageal levels during inflation in both postures at ≥51% TLC. It averaged 1.5 to 9 times the Ptp at corresponding esophageal levels in both postures at <51% TLC. These findings reflect the greater separation of the curves at high lung volumes and convergence of both curves at lower lung volumes due to closing volume.

The highest elastic recoil pressures were recorded at the 15 cm esophageal level in seated posture (p < 0.025), reflecting increasingly negative pleural pressures and alveolar expansion at a more cephalad esophageal level.

In nine of 10 patients, there were sufficient data points to construct inflation and deflation curves from peak to minimum lung volume. In a tenth subject, insufficient data points were available during inflation to construct complete P-V curves. In 5 subjects, data point fitting was difficult in the high-volume range because of a wide spread of Pst(L) points over a small volume range, particularly in the supine position. In 2 of these subjects, there was also difficulty in fitting data points in the lower limb of the curve. Five patients exhibited good overlap (that is, merging) of both inflation and deflation curves at their respective inflection points, and TLC was chosen to be between 50% and 60%. In 4 subjects, the overlaps were suboptimal above or below the inflection points in either the inflation or deflation curve.

In curves with acceptable data points, at all esophageal levels and in both body positions, the correspondence of recorded data points with respect to the theoretically computed P-V points based on the twin-exponential fit was excellent, with mean r² ranging between 96.9% and 99.7% ( Table 2 ).

We found statistically significant relations between h and specific elastance, predominantly in inflation curves at all lung volumes and lower esophageal levels, especially at the 10 cm level ( Table 3 ). Amongst deflation curves, the only correlative significance was found in seated posture at the 10 cm esophageal level (p < 0.03).

h, half-inflation pressure; Esp, L, specific elastance.

Supine position moved the P-V curve up and to the left at every balloon position, findings also reported by Milic-Emili et al. [3] ; mean values of Ptp (= Pm − Pes) were 2 - 3 cm H₂O lower than in seated posture. In some of our subjects, lung volumes were lower than 20% VC, and Ptp decreased disproportionately in the supine position, likely reflecting mediastinal effects and closing volume. Pleural pressure recordings can also be distorted at higher esophageal levels, likely due to traction on, or compression of, the esophagus by mediastinal structures, notably the trachea [3] .

The issue of pleural pressure (Ppl) measurement and its relation to regional lung mechanics and body posture bears an important influence on our findings. The indirect measurement of Ppl is based on the principle that when the regional static distribution of gas and the intrinsic static mechanical properties are known, the regional distribution of Ppl can be determined. Chest wall deformations during maximal muscle contractions, such as when performing TLC and RV maneuvers, can alter Ppl swings from those that are generated during quiet tidal breathing [7] . Such deformations are less likely to occur while seated, where lung weight influences regional differences in Ppl.

Our values of K₁ ( Table 2 ) are like those in previously described healthy young individuals (assuming a balloon level of 10 cm in a seated position); mean K₁ was 0.106 and 0.073 for deflation and inflation, respectively [11] [15] . The curve’s variables (of greatest importance being K₁, representing curvature) also correlate with changes in pulmonary elasticity with aging and smoking [5] [9] [11] - [14] [16] [25] - [28] .

We found a significant relationship of h to Esp, L that occurred most often during inflation curves in both postures. Eight of 12 associations were statistically significant, 3 of 6 at >50% VC and 5 of 6 at <50% VC. All but one exhibited a positive relationship; the only negative association occurred at the supine 5 cm esophageal level, most likely because of the distorting effects of closing volume and mediastinal factors [3] . The explanation for why the relationship is more robust during inflation is likely related to a more circular rib cage adopted during inflation, resulting in a more uniform distribution of pleural pressure than during deflation [1] [7] [29] [30] . The exception would be at regions close to the diaphragm where pleural pressure swings are greater in magnitude than corresponding mouth pressure swings, as shown by the “occlusion test” [2] [21] .

Because the magnitude of both elastance and compliance depends on lung volume while h is independent of lung volume [31] [16] , correction for Est, L was made by expressing elastic recoil as specific elastance, Esp, L = Est, L x lung volume [6] . Our findings indicate that the relationship found between h and Esp, L at any lung volume estimates its slope at that volume, at least during inflation at most esophageal levels.

We found our method of curve-fitting to be more practical than previously described techniques [9] [15] [23] [32] because of the simplicity of its equations and short computing time. There have been few attempts to define the P-V curve in its lower as well as upper portions in humans using either the exponential or sigmoidal method [4] [24] [26] [27] [33] . Colebatch et al. [4] used a single exponential function best fitted to static inflation-deflation pressure-volume data above FRC by an iterative least-squares analysis in 12 of 43 awake subjects (the other 31 subjects underwent deflation analysis only). Ferreira et al. [26] derived data only from sigmoidal inflation curves in anesthetized and paralyzed patients with idiopathic pulmonary fibrosis. Harris et al. [27] analyzed only sigmoidal inflation curves in 10 mechanically ventilated patients with acute respiratory distress syndrome. Paiva et al. [22] demonstrated that a single sigmoid mathematical model applied only to the expiratory limb of P-V curves allowed reporting of volumes and pressures by their actual values (rather than by visual fit) and would allow the fitting of the whole P-V curve. However, the model of Paiva et al. [22] was constructed based on P-V data obtained only above FRC, and while theoretical data under FRC obtained by sigmoid analysis were added to the curve, the authors conceded the difficulty of fitting data points under FRC. These problems were attributed to the quasi-static method of constructing the curves and measurements of Pes. Using the exponential technique, similar conclusions were reached by Kraemer et al. [19] , who studied the elastic behavior of lungs in healthy children at volumes above FRC, and by Collie et al. [23] in anesthetized sheep.

Our twin-exponential model incorporating inspiratory and expiratory limbs showed a close fit to experimentally obtained pressure-volume data over the entire range of lung volume, even at low lung volumes. This approach may be compared to other P-V curve models. Murphy and Engel [8] present a detailed comparison of different equations used to fit P-V data. While the exponential method of Salazar and Knowles [16] has been widely used to characterize the inflation and deflation limbs of normal and diseased lungs, data, including the low range of lung volumes, is poorly fitted by their equation [6] , particularly in conditions exhibiting alveolar de-recruitment and airway closure. To compensate for this poor fitting at low lung volumes, various polynomial equations have been employed to improve curve fits [9] [11] , but they incorporate increased numbers of parameters that provide little physiologic relevance [27] . While we used the modified Salazar and Knowles [16] exponential curve to describe the inflation and deflation limbs above and below their respective inflection points, its close fit to the experimentally recorded points attests to its adaptability in at least young, healthy individuals. Exponential model equations provide close approximations in high and low-pressure regions, and their parameters are influenced by the characteristics of the P-V curve [34] .

The novel aspect of our investigation is its application of the exponential approach in seated and supine postures using the esophageal balloon technique. We attempted to derive a greater degree of “realism” in our curves by combining a number of technical methods: a) the use of 2 separate exponential functions above and below FRC during both inflation and deflation, allowing increased concordance between actual data points and the exponential analysis; b) we measured Pes with the glottis open at each quasi-static step, rather than measuring the Ptp by having subjects relax against a closed valve, thus avoiding errors associated with compression and expansion of alveolar gas, upper airway, and cheeks [35] ; and c) our method of analysis also avoided the disadvantage of an inflection point related to airway closure which may lead to under or overestimation of K₁ and overestimation of Vmax [11] [23] .

The main limitation in this analysis is the use of identical mathematical functions (except for the reversal in signs) for the upper and lower portions of the inflation and deflation curves. This approach assumes that the curvilinearity of the upper and lower parts are mirror images of (symmetrical with respect to) each other. However, as shown by our data (K₁ in particular), they are not identical. Harris et al. [27] and Venegas et al. [24] used a simple sigmoidal equation that closely corresponded to the inflation and deflation limbs of experimental and diseased states and was symmetrical above and below the inflection point, which may not be the case in diseased lungs, or with postural change as was the case in this study. As Venegas et al. [24] state, it may be necessary to modify the sigmoidal equation to fit data sets that extend further onto both asymptotes. Paiva et al. [22] proposed a sigmoidal model that fits better than the exponential relationship described by Salazar and Knowles [16] but also assumed a lower asymptote of lung volume of zero, which may not be zero in diseased lungs.

Finally, this study was conducted in young, healthy (mostly male) adults and may not apply to infants and small children. In a study of curves in newborn mammals (and a review of the same in human infants), Saetta and Mortola [36] showed that the monoexponential fitting reflected only a small portion of the P-V curve, with the K value being higher than in adult mammals. This was explained by the airspace per unit of lung mass being smaller than in adults of corresponding species, that is, exhibiting a decreased compliance. Conversely, aging and/or disease induce collagen and elastin-related changes in mechanical properties, specifically the slope and hysteresis area enclosed by P-V curves in diseases such as emphysema and fibrosis [5] , in part related to percolation and lung tissue viscoelasticity [37] . Future studies in this area may consider expanding the age and sex distribution. The application of this twin exponential approach needs to be further investigated in older individuals and in disease states.

Our measurements were obtained by analog means with the use of pressure transducers, an oscilloscope, and a chart recorder, while curves were constructed by computer. Modern electronic devices, including analog to digital converters with appropriate anti-aliasing filters and solid-state pressure transducers, are likely to increase the efficiency of such measurements and computation. Time, however, was not an issue for the completion of this study. Instead, careful attention was paid to the recordings obtained and subsequent computations to minimize errors in precision.