Mathematical Modeling of the First Inflation of Degassed Lungs

Authors: Suki B.¹; Andrade Jr. J.S.²; Coughlin M.F.¹; Stamenovi cacute D.¹; Stanley H.E.³; Sujeer M.¹; Zapperi S.³

Source: Annals of Biomedical Engineering, Volume 26, Number 4, July 1998 , pp. 608-617(10)

Publisher: Springer

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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

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,

and a pressure, P_{\text{low}}, 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

=17±5, P_{\text{low}}=23 \pm 4 \text{cmH}_{\text{2}}\text{O}, and that there is a wide distribution of threshold pressures for airways with diameters <2 mm. Analysis of the P--V

curve in a lung which was lavaged with a liquid of constant surface tension and in which airways are presumably open demonstrated that the distribution of threshold 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 global distribution of threshold pressures and the average site of airway closure. © 1998 Biomedical Engineering Society. PAC98: 8745Hw, 8710+e

Keywords: Pressure–volume relation; Airways; Alveoli; Avalanches; Surface tension; Modeling; Inflation; Lung; Lung: mechanics

Document Type: Research article

DOI: http://dx.doi.org/10.1114/1.126

Affiliations: 1: Department of Biomedical Engineering, Boston University, Boston, MA 2: Departamento de F inodot ´sica, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil ´sica, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil "> 3: Center for Polymer Studies, Department of Physics, Boston University, Boston, MA

Publication date: 1998-07-01

Mathematical Modeling of the First Inflation of Degassed Lungs

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