Mathematical Modeling of the First Inflation of Degassed Lungs

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Abstract
The pressure–volume (P-V) relationship of degassed lungs during the first inflation is different from that in consecutive inflations. We developed a mathematical model of the P-V curve of the first inflation by assuming that (1) central airways are open leading to many subtrees of n generations that are initially closed; (2) an airway opens when inflation pressure reaches the opening threshold pressure of that segment; and (3) the opening threshold pressures do not depend on airway generation. In this model, airway opening occurs in cascades or avalanches. To test the model which contains only two parameters, n and a pressure, Plow, at which at least one subtree completely opens, we measured the first inflation P-V curves of 15 excised and degassed rabbit lungs. By fitting these data, we found that n=17±5, Plow=23 ± 4 cmH2O, and that there is a wide distribution of threshold pressures for airways with diameters 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8710+e

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