MATHEMATICAL-MODELING OF THE FIRST INFLATION OF DEGASSED LUNGS

The pressure-volume (P-V) relationship of degassed lungs during the fi rst inflation is different from that in consecutive inflations. We dev eloped a mathematical model of the P-V curve of the first inflation by assuming that (1) central airways are open leading to many subtrees o f n generations that are initially closed, (2) an airway opens when in flation pressure reaches the opening threshold pressure of that segmen t; and (3) the opening threshold pressures do not depend on airway gen eration. In this model, airway opening occurs in cascades or avalanche s. To test the model which contains only two parameters, n and a press ure, P-low at which at least one subtree completely opens, we measured the first inflation P-V curves of 15 excised and degassed rabbit lung s. By fitting these data, we found that n=17+/-5, P-low=23+/-4 cmH(2)O , and that there is a wide distribution of threshold pressures for air ways with diameters <2 mm. Analysis of the P-V curve in a lung which w as lavaged with a liquid of constant surface tension and in which airw ays are presumably open demonstrated that the distribution of threshol d pressures is narrow, and hence no avalanches occur during inflation. We conclude that in normal lungs the first inflation is dominated by avalanche behavior of airway opening providing information on the glob al distribution of threshold pressures and the average site of airway closure. (C) 1998 Biomedical Engineering Society.