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J Appl Physiol 91: 201-210, 2001;
8750-7587/01 $5.00
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Vol. 91, Issue 1, 201-210, July 2001

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

Uichiro Narusawa

Department of Mechanical, Industrial, and Manufacturing Engineering, Northeastern University, Boston, Massachusetts 02115

A pulmonary pressure-volume (P-V) curve represented by a sigmoidal model equation with four parameters, V(P) = a + b{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, alpha , with its order of magnitude of 10-4 to 10-5 (in ml-1 · cmH2O-1). When the model equation is normalized using a nondimensional volume, &Vmacr; (-1 < &Vmacr; < 1), and a nondimensional pressure, &Pmacr; (=(p/c) - 1), the resulting &Pmacr;-&Vmacr; curve depends on a single nondimensional parameter, Lambda  = alpha bc. A nondimensional work of expansion/compression, &Wmacr;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 (Lambda  defining the shape of the sigmoidal curve and &Wmacr;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.

pulmonary pressure-volume curve; sigmoidal equation; lung compliance; acute respiratory distress syndrome; lung recoil


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