A micromechanical model of lung tissue rheology

The rheological properties of lung tissue are complex and nonlinear and contribute significantly to both the elastic and dissipative mechanical properties of the lung. Nevertheless, there remain large gaps in our understanding of precisely how the bulk rheological behavior of lung tissue is linked to the properties of its constituents and their interactions. In this paper a model is developed that attempts to provide such a link. The model consists of a sheet of randomly aligned fibers whose orientations are constantly changing due to thermal motion. When the sheet is suddenly stretched uniaxially, the fibers align themselves preferentially in the direction of strain. However, as a result of the continual thermal motion of the fibers, there is a net transfer of momentum between the fibers and the rest of the tissue. This produces a restoring force in the tissue sheet. The thermal motion also makes the fibers gradually revert back to a random orientation, so that the strain-generated stress within the tissue decays asymptotically to zero. It is shown that the behavior of this model closely approximates quasilinear viscoelasticity, in which the static stress-strain behavior is separable from the dynamic stress relaxation behavior.