A finite-element model of tracheal collapse

The trachea has been approximated by an appropriate finite-element model. The three-dimensional equilibrium problems set by the tracheal deformation under various stresses have been solved using a convenient augmented Lagrangian functional. The dimensions were obtained from human tracheae. Mechanical constants for the anatomic components were calculated from the stress-strain relationships. The compressive narrowing is essentially due to the invagination of the posterior membrane in the tracheal lumen for transmural pressures down to -7 kPa. A surface of contact between the membranous wall and the lateral walls appears when the transmural pressure equals -6 kPa. The transmural pressure-area relationship is sigmoidal with a compliance equal to 0.08 kPa^-1 for a transmural pressure of -2 kPa. The tracheal collapse is greater when the material constants of the membranous wall decrease or when the tracheal segment is subjected to a longitudinal tension. A slight flexion of the trachea induces an asymmetric deformation.