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.
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机译:提出了一种新的数值方法来模拟动脉的主动响应。血流中的血管收缩剂和血管扩张剂通过内膜从管腔扩散到动脉壁,并导致平滑肌细胞(主要在介质中)收缩。我们将扩散过程与Yosibash和Priel中的机械模型相结合(Comput Methods Appl Mech Eng 237-240:51-66,2012)。基于对角隐式Runge-Kutta方法,研究了基于对角隐式Runge-Kutta方法的全耦合高阶时间积分方法的全耦合场问题的有限元计算,研究了其在线性和非线性加载路径下的收敛行为.由于血压是周期性的、高度非线性的外部负荷路径,因此必须调整步长估计,以尽量减少步长抑制。本文以实例实例为例,说明了所提出的时间自适应方案的优势。
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