J Appl Physiol. 1998 Jan;84(1):389-95. doi: 10.1152/jappl.1918.104.22.1689.
A comprehensive equation for the pulmonary pressure-volume curve
Jose G Venegas, R Scott Harris, Brett A Simon.
Quantification of pulmonary pressure-volume (P-V) curves is often limited to calculation of specific compliance at a given pressure or the recoil pressure (P) at a given volume (V). These parameters can be substantially different depending on the arbitrary pressure or volume used in the comparison and may lead to erroneous conclusions. We evaluated a sigmoidal equation of the form, V = a + b[1 - e-(P-c)/d]-1, for its ability to characterize lung and respiratory system P-V curves obtained under a variety of conditions including normal and hypocapnic pneumoconstricted dog lungs (n = 9), oleic acid-induced acute respiratory distress syndrome (n = 2), and mechanically ventilated patients with acute respiratory distress syndrome (n = 10). In this equation, a corresponds to the V of a lower asymptote, b to the V difference between upper and lower asymptotes, c to the P at the true inflection point of the curve, and d to a width parameter proportional to the P range within which most of the V change occurs. The equation fitted equally well inflation and deflation limbs of P-V curves with a mean goodness-of-fit coefficient (R2) of 0.997 +/- 0.02 (SD). When the data from all analyzed P-V curves were normalized by the best-fit parameters and plotted as (V-a)/b vs. (P-c)/d, they collapsed into a single and tight relationship (R2 = 0.997). These results demonstrate that this sigmoidal equation can fit with excellent precision inflation and deflation P-V curves of normal lungs and of lungs with alveolar derecruitment and/or a region of gas trapping while yielding robust and physiologically useful parameters.
Asthma is a common disease affecting an increasing number of children throughout the world. In asthma, pulmonary airways narrow in response to contraction of surrounding smooth muscle. The precise nature of functional changes during an acute asthma attack is unclear. The tree structure of the pulmonary airways has been linked to complex behaviour in sudden airway narrowing and avalanche-like reopening. Here we present experimental evidence that bronchoconstriction leads to patchiness in lung ventilation, as well as a computational model that provides interpretation of the experimental data. Using positron emission tomography, we observe that bronchoconstricted asthmatics develop regions of poorly ventilated lung. Using the computational model we show that, even for uniform smooth muscle activation of a symmetric bronchial tree, the presence of minimal heterogeneity breaks the symmetry and leads to large clusters of poorly ventilated lung units. These clusters are generated by interaction of short- and long-range feedback mechanisms, which lead to catastrophic shifts similar to those linked to self-organized patchiness in nature. This work might have implications for the treatment of asthma, and might provide a model for studying diseases of other distributed organs.