Nonlinear viscoelastic behaviour of canine arterial walls

The nonlinear viscoelastic behaviour of arterial walls subjected to large deformation is studied theoretically and experimentally. It is assumed that the arterial walls are thick-walled cylindrical vessels composed of an incompressible, curvilinearly orthotropic and viscoelastic material. The radial displacement of vessel walls is simplified by superimposing a small time-dependent deformation due to pulse pressure on a large time-independent deformation. The radial and circumferential stresses are expressed as functions of the histories of strains in each direction. The functions are written in terms of a series of multiple integrals involving eight stress-relaxation functions. To determine these functions, experiments of stress relaxation were performed with common carotid and femoral arteries excised from mongrel dogs. For a strain imposition within 1-100 s, stress relaxation is expressed by a power-law function of time. On the basis of the theoretical equations, the vessel diameter and wall stresses are calculated as a function of time by assuming that a sinusoidal intraluminal pressure varying between 80 and 120 mm Hg is applied in the lumen. The creep phenomena are shown to be due to the viscoelasticity of the arterial walls. i.e. the deformation increases with elapsed time during pressure fluctuations.