Micromechanical model of lung parenchyma hyperelasticity

Abstract

Mechanics plays a key role in respiratory physiology, as lung tissue cyclically deforms to bring air in and out the lung, a life-long process necessary for respiration. The study of regional mechanisms of deformation in lung parenchyma has received great attention to date due to its clinical relevance, as local overstretching and stress concentration in lung tissue is currently associated to pathological conditions such as lung injury during mechanical ventilation therapy. This mechanical approach to lung physiology has motivated the development of constitutive models to better understand the relation between stress and deformation in the lung. While material models proposed to date have been key in the development of whole-lung simulations, either they do not directly relate microstructural properties of alveolar tissue with coarse-scale behavior, or they require a high computational effort when based on real alveolar geometries. Furthermore, most models proposed to date have not been thoroughly validated for anisotropic deformation states, which are commonly found in normal lungs in-vivo. In this work, we develop a novel micromechanical model of lung parenchyma hyperelasticity using the framework of finite-deformation homogenization. To this end, we consider a tetrakaidecahedron unit cell with incompressible Neo-Hookean structural elements that account for the alveolar wall tissue responsible for the elastic response, and derive expressions for its effective coarse-scale behavior that directly depend on the alveolar wall elasticity, reference porosity, and two other geometrical coefficients. To validate the proposed model, we simulate the non-linear elastic response of twelve representative volume elements (RVEs) of lung parenchyma with micrometric dimensions, whose geometry is obtained from micrometric computed-tomography reconstructions of murine lungs. We show that the proposed micromechanical model accurately captures the RVEs response not only for isotropic volumetric expansion, but also for three other anisotropic loading conditions for different levels of tissue porosity, while displaying superior computational efficiency and stability in estimating coarse-scale response when compared to direct numerical simulations of RVEs. Further, we find that the most influential microstructural parameters on the response of the micromechanical model are the reference porosity and the alveolar wall elasticity. We also show that the model can reproduce uniaxial experimental tests on lung tissue samples, and estimate the Poisson ratio to be 0.22. We envision that our model will enable predictive and efficient whole-organ simulations useful to study the normal and diseased lung.