A constitutive model for lung mechanics and injury applicable to static, dynamic, and shock loading

Abstract

A continuum model for lung parenchyma is constructed. The model describes the thermomechanical response over a range of loading rates—from static to dynamic to shock waves—and a range of stress states, including isotropic expansion, triaxial extension, simple shear, and plane wave compression. Nonlinear elasticity, viscoelasticity, and damage are included, with the latter associated with changes of biological function as well as mechanical stiffness. A Gram–Schmidt decomposition of the deformation gradient leads to strain attributes that enter the thermodynamic potentials as state variables. A free energy function is designed for loading at low to moderate rates and tensile pressures, whereby the tissue response, with surface tension, is preeminent. An internal energy function is designed for wave propagation analysis, including shock waves, whereby compressibility of the air inside the alveoli is addressed via a composite stiffness based on a closed-cell assumption. The model accurately represents the response to triaxial loading, pressure relaxation, and dynamic torsion with relatively few parameters. Longitudinal wave speeds are reasonable for ranges of internal airway pressure and transpulmonary pressure. Airway pressure strongly affects the response to plane wave compression. Criteria for local injury and damage progression depend on a normalized energy density and its gradient, where the latter is paramount for impact problems involving fast pressure rises. Results suggest that local damage associated with edema is induced at load intensities much lower than those that would cause significant stiffness changes due to rupture, major tearing, or local collapse.