Greater (more positive) expiratory pressures were developed at higher VL, while greater (more negative) inspiratory pressures were developed at lower VL. In women Pe increased with volume from 39 to 61 cmH2O and Pi decreased with volume from 66 to 28 cmH2O. In men, Pe increased with volume from 63 to 97 cmH2O and P1 decreased with volume from 97 to 39 cmH2O. These trends occur primarily for two reasons. First, respiratory muscles work both with and against respiratory tissue elastance to produce pressure. Expiratory efforts are aided by tissue elastance (lung recoil effects) at high VL and inhibited at low VL. Inspiratory efforts are inhibited by tissue elastance at high VL and aided at low VL. Second, respiratory muscles exert greater tension when they are stretched to greater lengths. Expiratory muscles are stretched when the lung is inflated, while inspiratory muscles are stretched when the lung is deflated. Both of these factors describe the general trend of the data.
The volume dependence of Pi was much more pronounced than the volume dependence of Pe in both women and men. This can be seen as a higher slope of the inspiratory equation compared to the expiratory equation in Figure 1. This may reflect a combination of strength differences between diaphragm (largely responsible for inhalation) and abdominal muscles (largely responsible for exhalation) recruitment of intercoastal muscle (largely responsible for posture maintenance), and different mechanical advantages of each type of muscle as the lung volume varies.
The Laplace equation may be relevant here. This equation states that enclosed pressure is proportional to the product of wall tension and wall thickness and inversely proportional to the radius of curvature. The Laplace equation for a sphere differs from that of a cylinder by a factor of two. Pressure in a sphere (P =
) is twice that of a cylinder (P = ), all other things being equal.
The diaphragm is positioned under the lungs and curves upward in a somewhat spherical shape. As it contracts, it becomes flatter, meaning that its radius of curvature increases. Lung volume increases as the diaphragm contracts. If the Laplace equation can be applied to the respiratory system, then it would show that inspiratory pressure should decrease as radius, and thus lung volume, increases (Pi ∝ , as long as wall tension and thickness remain steady).
The abdominal muscles are arranged differently, more like wrapping around a cylinder. The abdominal muscles flatten at smaller lung volumes instead of larger lung volumes, and the Laplace equation indicates that higher pressures should be developed at larger lung volumes (P ∝ V).
Both effects have been observed. Inspiratory pressures increase as lung volume decreases and expiratory pressure increases as lung volume increases. There is roughly a factor of two between the dependence of pressures upon lung volumes for inspiration and expiration. This could well be related to the difference in the Laplace equation for a sphere and a cylinder.
The pressure-volume data obtained in this study are of the same general magnitudes as those previously reported [1, 2, 6]. Rahn et al.  studied Pi in 11 men and Pe in 12 men using similar methods. The highest pressures from three efforts at each of six starting volumes were recorded. Measurements were read from a mercury manometer connected to the subjects' noses. Pressure-volume data closely match the results of the present study. Craig  produced pressure-volume diagrams from 10 men using methods similar to the present study. Pressures were taken from a mercury manometer connected to the subjects' mouths. These data also closely match the results of the present study. Cook et al.  studied 17 males and 9 females using two techniques. One technique was a conventional occlusion maneuver. The other technique involved subjects breathing into or out of large, fixed volumes. The compressibility of the air in differently sized containers provided for various ultimate lung volumes. The volumes were calculated from Boyle's Law using peak pressures that could be sustained for 1–2 seconds. Five volumes were used. It was concluded that the results of the occlusion method and the compression method were the same. In women, the compression-method Pi values were similar to those of the present study at high volumes, but slightly higher at lower volumes. The Pe values were similar at low volumes, but much higher at higher lung volumes. In men, the compression-method Pi values agree well with those of the present study. However, the Pe values are much higher than those of the present study at the higher volumes. Cook et al.  suggested that their Pe values might have been higher than the Rahn et al. values because of the use of mouth pressure measurements rather than nose pressure measurements. It was also hypothesized that these Pe values exceeded Craig's values due to better mouthpiece sealing.
As the results of this study are more in agreement with work of Rahn et al.  and Craig , it is more likely that there is another reason for the discrepancy. Aside from muscle strength alone, Pe and Pi are highly effort dependent. Subjects may limit their maximum pressures due to factors such as pain in the ear or general discomfort. During some maximum pressure maneuvers, researchers have observed changes in hemodynamics leading to loss of consciousness . It is possible that the subjects of the Cook et al.  study were more highly motivated. It is also possible that these subjects were of above average strength.
Numerous authors have collected maximal pressures at a single VL. Most recently, Wilson et al.  measured maximal Pe and Pi in 87 women and 48 men using partial occlusion and Bourdon gauges. The women were found to have Pe = 93 ± 17 cmH2O and Pi = 73 ± 22 cmH2O and the men were found to have Pe = 148 ± 34 cmH2O and Pi = 106 ± 31 cmH2O. It could be expected that the Pi and Pe values from a single volume study would exceed the values from a multiple volume study because more efforts are made at the optimal VL in the single volume study, while muscle fatigue can be a factor in the multiple volume study.
Judging from inspiration values, this does not appear to be the case. In the present study, women were found to have Pi = 66 ± 32 cmH2O at VL = 12%VC and men were found to have Pi = 97 ± 46 cmH2O at VL = 14%VC. These values are virtually identical to the Wilson et al.  data. On the other hand, women in this study were found to have Pe = 61 ± 39 cmH2O at VL = 84%VC and men were found to have Pe 97 ± 42 cmH2O at VL = 81%VC. These values are considerably smaller than the Wilson et al. data. The Pe values of the single volume study fall in between the maximum Pe values of the present study and the maximum Pe values of the Cook et al.  study.
Satisfactorily describing maximum lung pressures with mathematical expressions can be helpful for respiratory mechanical modeling . It is not likely that maximal pressures would be developed in young, healthy adults during quiet breathing. During exercise, and especially during expiratory flow limitation, however, maximum pressures may well be developed. For example, modeling the effects of respiratory masks during hard work could use these equations to calculate respiratory work rate. These equation forms are good because pressures and lung volumes both appear as relative rather than absolute values. That way, both men's and women's pressures could be determined with the same equations despite large differences in absolute pressures developed. Respiratory models for those conditions could well use the equations developed here.
Although we have no data to support the notion, it is possible, if their respiratory mechanics changed proportionally, that maximum pressures developed by patients with respiratory impairments could be described by the same equations as developed here. That is because these equations are in relative pressure and volume form. One would expect that Pmax could be much lower in diseased patients, but P/Pmax could be scaled the same. If this were so, then equations developed here could have more universal value.