Simulating the temporal change of the active response of arteries by finite elements with high-order time-integrators

A new numerical method to model the active response of arteries is proposed. Vasoconstrictors and vasodilators in the bloodstream diffuse from the lumen into the arterial wall through the intima and cause the smooth muscle cells, mostly in the media, to contract. We combine the diffusion process with the mechanical model in Yosibash and Priel (Comput Methods Appl Mech Eng 237–240:51–66, 2012). Finite element computations of the fully coupled field problem using time-adaptive, high-order time-integration methods based on diagonally-implicit Runge–Kutta methods are investigated with respect to their convergence behavior for linear and non-linear loading paths. Since the blood pressure is periodic, highly non-linear external loading path, the step-size estimation has to be adapted to minimize step-size rejections. An example of an artery analysis that illustrates the advantage of the proposed time-adaptive scheme is provided.