Stress, deformation, and atelectasis of the lung

The lung parenchyma as a tissue has a rather unusual stress-strain relationship. A theoretical derivation of this relationship is presented which connects the surface tension and the tissue elastic stress in the alveolar septa with the alveolar geometry. The mathematical expression contains a few meaningful physical constants which can be determined by in vitro and in vivo experiments. With this stress-strain relationship, the general equations of lung mechanics are formulated, and solutions to some simpler problems are presented. First, the equilibrium of a lung subjected to a uniform inflation pressure (definition: alveolar air pressure - intrapleural pressure - pleural tension X mean curvature of pleura) is analyzed, and the stability of the equilibrium states with respect to small perturbations is examined. Second, an exact solution for a lung in a chest under the influence of gravity is presented; the solution is "exact," of course, for only a particular lung, but it can serve as a standard to check numerical procedures being developed in many laboratories. Finally, three types of possible atelectasis-planar, axial, and focal-are analyzed. The planar type can exist in a normally inflated lung, provided the layers of alveoli are forced to collapse toward a plane by some external agent. But axial atelectasis (alveoli collapse into a cylinder) can occur only if the dimension (at which the elastic tension in the alveolar septa vanishes). Similarly, focal atelectasis can occur only if the entire lung is smaller than the resting volume.