Peribronchial Stress Analysis Utilizing Concentric Cylindrical Shells of Parenchyma

Abstract

The mechanical dependence of bronchial volume on parenchymal properties and on intrabronchial and pleural pressures was investigated utilizing finite elasticity theory. Treating the lung parenchyma as a compressible continuum, and using a simple strain-energy-density function fitted to pressure-volume curves of saline-filled lungs, we analyzed nonhomogeneous large deformations of the fluid-filled excised dog lobe by numerical procedures. For the purpose of obtaining peribronchial stress distributions, the lung was represented by a hollow very thick-walled cylinder corresponding to an axial bronchus with surrounding parenchyma. Finite elements consisted of concentric cylindrical shells. In general, we found that the theoretical results corresponded well to published stress and strain data for bronchial collapse. Peribronchial radial and circumferential stresses were found to be concentrated at the bronchial wall, but dissipated rapidly within 1–2 bronchial radii away from the wall. We conclude that the magnitude of regional lung recoil around bronchi during collapse can be reasonably well estimated by a theoretical analysis based on total lung pressure-volume relationships.