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.
Begis
D
D
Institut National de la Santé et de la Recherche Médicale, U.296, Faculté de Médecine, Créteil, France.
Delpuech
C
C
Le Tallec
P
P
Loth
L
L
Thiriet
M
M
Vidrascu
M
M
D004548:Elasticity; D006801:Humans; D008433:Mathematics; D008953:Models, Anatomic; D008954:Models, Biological; D012119:Respiration; D014132:Trachea / Q000502:physiology*