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 eq uation with four parameters, V(P) = a + b{1 1 exp[-(P - c)/d]}(-1), has bee n demonstrated to fit inflation and deflation data obtained under a variety of conditions extremely well. In the present report, a differential equati on on V( P) is identified, thus relating the fourth parameter, d, to the di fference between the upper and the lower asymptotes of the volume, b, throu gh 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 nond imensional 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 i nitial volume (at 1) and a final volume (at 2). Six sets of P-V data availa ble 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.