MODELING AND NUMERICAL-ANALYSIS OF STRESSES AND STRAINS IN THE HUMAN LUNG INCLUDING TISSUE-GAS INTERACTION

A complete mechanical model of lungs, valid for the analysis of stress es in tissues, which considers mechanical couplings between the tissue deformation and the air flow, is presented. The concept of a continuo us description of the lung is adopted, with its volume assumed to be f illed with a nonlinearly elastic, highly deformable solid - parenchyma , which is a thin-walled porous tissue structure on the micro-scale. C entral airways are modelled as a discrete system of conduits immersed in the parenchyma. For the flow in peripheral airways and alveoli, a m odel of filtration in a three-dimensional two-phase porous medium (gas -tissue skeleton) is assumed. A new approach to pseudoelastic nonlinea r constitutive modelling of parenchyma aiming at computational applica tions is presented. A fundamental set of nonlinear differential equati ons for the quasi-static coupled problem is derived and frictionless c ontact boundary conditions are included. A finite element formulation of the problem with an implicit time integration scheme is presented. The results of numerical examples obtained using the algorithm agree q ualitatively with experimental data.