A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long-scale FSI problems are solved, confirming the importance of incorporating stress variations on small time-scales. In the homogenization approach, a periodic fine-scale problem, which is periodic with respect to the heart beat, has to be solved for each long-scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2-3 heart beats by simple time-stepping.

中文翻译：

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动脉粥样硬化斑块生长数值模拟中的时间均质化

用于动脉粥样硬化斑块生长数值模拟的时间均质化方法扩展到完全耦合的流固耦合 (FSI) 模拟。数值结果表明，与简单的启发式平均相比，两尺度方法产生了显着不同的结果，其中仅解决了平稳的长尺度 FSI 问题，证实了在小时间尺度上结合应力变化的重要性。在均质化方法中，必须为每个长尺度时间步长解决一个周期性的精细尺度问题，该问题相对于心跳是周期性的。即使没有确切的初始条件可用，也可以通过简单的时间步长在 2-3 次心跳内实现周期性。