Micro-Poro-Mechanical Modeling of the Lung Parenchyma: Theoretical Modeling and Parameters Identification

Microporo-mechanical approaches can be employed to simulate the behavior of porous media, such as lung parenchyma, with respect to their microscopic morphological and mechanical features. In this work, we propose a general micromechanical framework to describe the behavior of a porous hyperelastic material in large strains, including surface tension, and adapt its parameters to reproduce lung parenchyma behavior. We illustrate the method on a two-dimensional (2D) periodic microstructure. The modeling framework is adaptable to any microstructure and any combination of stress, strain, and pressure loadings. The identification of the model parameters in the context of lung parenchyma, based on existing experimental morphological and pressure-volume data, is performed sequentially. Twelve parameters related to morphology, alveolar wall constitutive behavior, and surface tension are calibrated to reproduce pressure-volume curves in various conditions, for a porosity in the unloaded state set to φ_f0=63%. The calibrated alveolar diameter is D_alv=54 μm. The identifiability of the Neo-Hookean and Ogden-Ciarlet-Geymonat hyperelastic potential parameters is studied; their values are β₁=88.6 Pa, β₂=11.0 Pa, β₃=628 Pa, and α=3.41. The hysteretic response of lung to pressure is reproduced thanks to the formulation of a surface-dependent surface tension. This work paves the way for a better understanding of the relationship between microscopic features and the macroscopic response of lung, in healthy and pathological conditions. Further experimental investigations could help confirm the ranges of parameters obtained in this study.