Hyperelastic modeling of swelling in fibrous soft tissue with application to tracheal angioedema

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.