A model of non-uniform lung parenchyma distortion

A finite element model of mammalian lung parenchyma is used to study the effect of large non-uniform distortions on lung elastic behaviour. The non-uniform distortion is a uni-axial stretch from an initial state of uniform pressure expansion. For small distortions, the parenchymal properties are linearly isotropic and described by two elastic moduli. However, for large distortions, the parenchyma has anisotropic non-linear elastic properties described by five independent elastic moduli dependent on the degree of distortion; they are computed for a range of distortions and initial pressures. EzEz, the Young's modulus in the direction of stretch, increases significantly with distortion (εzεz) while ExEx, the Young's modulus in the plane perpendicular to the stretch, is approximately constant. The greater the initial pressure, the bigger the difference between the two moduli at larger distortion strains. The shear modulus GxzGxz is approximately independent of degree of distortion except at the highest initial pressure. The Poisson's ratio, νxzνxz is approximately constant with distortion strain for lower initial pressures, but increases significantly with εzεz at higher pressures. Model predictions of the relation between GxzGxz and initial uniform inflation pressure show a good correlation with reported experimental data for small distortion strains in a range of species. The model also exhibits similar behaviour to the experimentally measured uni-axial large deformations of a tri-axially pre-loaded block of parenchyma (Hoppin et al., 1975, Journal of Applied Physiology 39, 742–751).