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Angioedema, the rapid swelling of under-skin tissue, is typically triggered by complex biochemical processes that disrupt an original steady state filtration of liquid through the tissue. Swelling stabilizes once a new steady state is achieved in which the tissue has significantly increased liquid content. These processes are controlled by events at the molecular to the cellular length scale. For describing consequences at organ level length scales it is useful to invoke consolidated continuum mechanics treatments within a generalized hyperelastic framework. We describe the challenges associated with such modeling and demonstrate their use in the context of tracheal angioedema. The trachea is modeled as a two layered cylindrical tube. The inner layer and outer layer represent the soft mucosal tissue and the stiffer cartilaginous tissue respectively. Axially oriented fibers contribute anisotropy to the inner layer, and the swelling is largely confined to this layer. A boundary value problem is formulated; existence and uniqueness is verified. Numerical solutions track airway constriction as a function of mucosal swelling.

Angioedema is a tissue-swelling pathology due to rapid change in soft tissue fluid content. Its occurrence in the trachea is predominantly localized to the soft mucous tissue that forms the innermost tracheal layer. The biomechanical consequences, such as airway constriction, are dependent upon the ensuing mechanical interactions between all of the various tissues that comprise the tracheal tube. We model the stress interactions by treating the trachea organ as a three-tissue system consisting of swellable mucous in conjunction with nonswelling cartilage and nonswelling trachealis musculature. Hyperelastic constitutive modeling is used by generalizing the standard anisotropic, incompressible soft tissue framework to incorporate the swelling effect. Finite element stress analysis then proceeds with swelling of the mucous layer providing the driving factor for the mechanical analysis. The amount of airway constriction is governed by the mechanical interaction between the three predominant tissue types. The detailed stress analysis indicates the presence of stress concentrations near the various tissue junctions. Because of the tissue's nonlinear mechanical behavior, this can lead to material stiffness fluctuations as a function of location on the trachea. Patient specific modeling is presented. The role of the modeling in the interpretation of diagnostic procedures and the assessment of therapies is discussed. [ABSTRACT FROM AUTHOR]