EXPONENTIAL DESCRIPTION OF THE STATIC PRESSURE-VOLUME CURVE OF NORMAL AND DISEASED LUNGS

Abstract

The practical value of a simple mathematical description of the static pressure-volume (PV) curve of the lungs above functional residual capacity was examined by fitting a monoexponential function of the form V = Vmax-Ac-KP (where Vmax is the volume extrapolated to infinite P, and A and K are constants) to PV curves obtained in 45 normal subjects and 39 patients with emphysema, intermediate .alpha.1-antitrypsin deficiency, fibrosing alveolitis or sarcoidosis. Quality of fit was assessed by calculation of the SE of the parameters, by the reduction of original variance (R2) and by the application of sign and runs tests. The runs test proved particularly useful for detecting minor deviations from a monoexponential function; the value of R2 was less discriminating and largely depended on the magnitude of experimental error. The exponential function described the expiratory pressure-volume data well in 42 of the 45 normal subjects and in all of the patients with lung disease. The shape of the pressure-volume curve was characterized by the parameter K. The other 2 parameters of the equation Vmax and A were combined as a ratio (Vmax-A)/Vmax (or VO/Vmax, where VO represents the volume extrapolated to 0 pressure and is equal to Vmax-A), which relates the position of the curve to the volume axis. The value of K was above the normal range in 10 of 12 patients with emphysema and in 4 of 13 subjects with asymptomatic intermediate .alpha.1-antitrypsin deficiency. Among 14 patients with decreased lung volumes due to fibrosis, K was less than normal in 2 and VO/Vmax was greater than normal in 3. In most cases, deviation from the exponential model was no greater than that introduced by experimental error. Compared to conventional indices of lung distensibility, such as chord compliance or transpulmonary pressure at standard volumes, the exponential description has the advantages of using data over a wide volume range and producing indices that are independent of sex and lung size. Any possible physiologic basis for the apparent exponential nature of lung deflation remains uncertain.