Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, Beijing, China.
Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, Beijing, China.
Comput Methods Programs Biomed. 2024 Dec;257:108457. doi: 10.1016/j.cmpb.2024.108457. Epub 2024 Oct 10.
Incorporating tissue support in fluid-structure interaction analysis of cardiovascular flows is crucial for accurately representing physiological constraints, achieving realistic vessel wall motion, and minimizing artificial oscillations. The generalized Robin boundary condition, which models tissue support with a spring-damper-type force, uses elastic and damping parameters to represent the viscoelastic behavior of perivascular tissues. Using spatially distributed parameters for tissue support, rather than uniform ones, is more realistic and aligns with the varying properties of vessel walls. However, considering the spatial distribution of both can increase the complexity of preprocessing and numerical implementation. In this work, we develop an effective property method for efficient modeling of non-uniform tissue support and quantifying the contribution of tissue support to the mechanical behaviors of vessel walls.
Based on the theory of linear viscoelasticity, we derive the mathematical formulas for the effective property method, integrating the parameters of generalized Robin boundary condition into vessel wall properties. The pulse wave velocity incorporating the influence of tissue support is also analyzed. Furthermore, we modify the coupled momentum method, originally formulated for elastic problems, to account for the viscoelastic properties of the vessel wall.
The method is verified with three-dimensional fluid-structure interaction simulations, achieving a maximum relative error of less than 2.2% for flow rate and less than 0.7% for pressure. This method shows that tissue support parameters can be integrated into vessel wall properties, resulting in increased apparent wall stiffness and viscosity, and further changing pressure, flow rate, and wave propagation.
In this study, we develop an effective property method for quantitatively assessing the impact of tissue support and for efficiently modeling non-uniform tissue support. Moreover, this method offers further insights into clinically measured pulse wave velocity, demonstrating that it reflects the combined influence of both vessel wall properties and tissue support.
在心血管流动的流固耦合分析中纳入组织支撑对于准确表示生理约束、实现真实的血管壁运动以及最小化人为振荡至关重要。广义 Robin 边界条件使用弹簧阻尼型力来模拟组织支撑，使用弹性和阻尼参数来表示血管周围组织的粘弹性行为。使用空间分布的组织支撑参数而不是均匀参数更符合实际情况，并且与血管壁的变化特性一致。然而，考虑到组织支撑的空间分布会增加预处理和数值实现的复杂性。在这项工作中，我们开发了一种有效的属性方法，用于高效地建模非均匀组织支撑，并量化组织支撑对血管壁力学行为的贡献。
基于线性粘弹性理论，我们推导出有效属性方法的数学公式，将广义 Robin 边界条件的参数整合到血管壁特性中。还分析了包含组织支撑影响的脉搏波速度。此外，我们修改了最初为弹性问题制定的耦合动量方法，以考虑血管壁的粘弹性特性。
该方法通过三维流固耦合模拟进行验证，流量的最大相对误差小于 2.2%，压力的最大相对误差小于 0.7%。该方法表明，组织支撑参数可以整合到血管壁特性中，导致表观壁刚度和粘度增加，进一步改变压力、流量和波传播。
在这项研究中，我们开发了一种有效的属性方法，用于定量评估组织支撑的影响，并高效地建模非均匀组织支撑。此外，该方法进一步深入了解临床测量的脉搏波速度，表明它反映了血管壁特性和组织支撑的综合影响。
