Linking Microscopic Spatial Patterns of Tissue Destruction in Emphysema to Macroscopic Decline in Stiffness Using a 3D Computational Model

Pulmonary emphysema is a connective tissue disease characterized by the progressive destruction of alveolar walls leading to airspace enlargement and decreased elastic recoil of the lung. However, the relationship between microscopic tissue structure and decline in stiffness of the lung is not well understood. In this study, we developed a 3D computational model of lung tissue in which a pre-strained cuboidal block of tissue was represented by a tessellation of space filling polyhedra, with each polyhedral unit-cell representing an alveolus. Destruction of alveolar walls was mimicked by eliminating faces that separate two polyhedral either randomly or in a spatially correlated manner, in which the highest force bearing walls were removed at each step. Simulations were carried out to establish a link between the geometries that emerged and the rate of decline in bulk modulus of the tissue block. The spatially correlated process set up by the force-based destruction lead to a significantly faster rate of decline in bulk modulus accompanied by highly heterogeneous structures than the random destruction pattern. Using the Karhunen-Loève transformation, an estimator of the change in bulk modulus from the first four moments of airspace cell volumes was setup. Simulations were then obtained for tissue destruction with different idealized alveolar geometry, levels of pre-strain, linear and nonlinear elasticity assumptions for alveolar walls and also mixed destruction patterns where both random and force-based destruction occurs simultaneously. In all these cases, the change in bulk modulus from cell volumes was accurately estimated. We conclude that microscopic structural changes in emphysema and the associated decline in tissue stiffness are linked by the spatial pattern of the destruction process.Author Summary: Current standards for characterizing microscopic structural changes in emphysema are based on estimating the amount of tissue loss using stereological techniques. However, several previous studies reported that, in emphysema, there is a lack of correlation between stereological indices of tissue structure and increases in lung compliance, which is the inverse of tissue stiffness. In this study, we developed a novel three-dimensional computational model to show that the amount of tissue loss is not the sole determinant of increased lung compliance in emphysema. A key component that needs to be considered is the pattern of tissue destruction, which we demonstrate has a significant effect on the rate of decline in stiffness. Our findings also indicate that the heterogeneity observed at the microscopic scale in emphysema is a signature of the spatial history of the destruction process. These results highlight the importance of characterizing the heterogeneity of lung tissue structure in order to be able to relate microscopic structural changes to macroscopic functional measures such as lung compliance.