General characteristics of the sigmoidal model equation representing quasi-static pulmonary P-V curves

A pulmonary pressure-volume (P-V) curve represented by a sigmoidal model equation with four parameters, V(P) = a + b{1 1 exp[-(P - c)/d]}(-1), has been demonstrated to fit inflation and deflation data obtained under a variety of conditions extremely well. In the present report, a differential equation on V( P) is identified, thus relating the fourth parameter, d, to the difference between the upper and the lower asymptotes of the volume, b, through a proportionality constant, a, with its order of magnitude of 10(-4) to 10(-5) (in ml(-1).cmH(2)O(-1)). When the model equation is normalized using a nondimensional volume, (V) over bar (-1 < <(V)over bar> < 1), and a nondimensional pressure, <(P)over bar> (=(p/c)(-1)), the resulting (P) over bar-(V) over bar curve depends on a single nondimensional parameter, Lambda = alpha bc. A nondimensional work of expansion/compression, (W) over bar (1-2), is also obtained along the quasi-static sigmoidal P-V curve between an initial volume (at 1) and a final volume (at 2). Six sets of P-V data available in the literature are used to show the changes that occur in these two parameters (L defining the shape of the sigmoidal curve and (W) over bar (1-2) accounting for the range of clinical data) with different conditions of the total respiratory system. The clinical usefulness of these parameters requires further study.