Introduction: The stress and deformation in an artery are determined from an axisymmetric analysis of thick-walled cylinder with a time-dependent internal pressure. The purpose is to understand how different constitutive, loading, and geometric conditions affect the stress and deformation state within the artery.
Materials and methods: The equilibrium, compatibility, and constitutive equations are applied at N discretized points in the arterial wall, in an efficient scheme using Mathcad software on a desktop computer. The constitutive equations are a modification to a standard linear solid, so that one of the linear elements is nonlinear, and so that the 3-D response is anisotropic and dissipates energy only under deviatoric (shearing) stress states. Solution at each successive time increment requires inversion of a 6N by 6N matrix.
Results: The model reproduces experimental stress relaxation data with a correlation coefficient of 0.985 and can reproduce quasi-static stress strain data with equal accuracy. Features such as conditioning of the tissue are understood in terms of the time-dependent properties of the tissue.
Conclusion: The program can produce transient and steady-state responses that closely mimic tissue response. The analysis allows for quick and stable determination of the stress and strain states for a variety of loading conditions.