An algorithmic scheme for the automated calculation of fiber orientations in arterial walls
An algorithmic scheme for the automated calculation of fiber orientations in arterial walls
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DOI：
10.1007/s00466-016-1321-z
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发表时间：
2016-11-01
影响因子：
4.1
通讯作者：
Schroder, Joerg
中科院分区：
文献类型：
--
作者：
Fausten, Simon;Balzani, Daniel;Schroder, Joerg
我们提出了一个算法方案的数值计算的纤维方向在动脉壁。该手术背后的基本假设是，纤维方向主要由主拉伸应力方向决定，由于应力的重新分布，导致动脉内的负荷转移得到改善。这反映了软组织不断适应其力学环境以优化其承载能力的生物学动机。这里提出的算法方案提高了Hariton等人（Biomech Model Mechanobiol 6（3）：163-175，2007）中给出的一般程序的效率，该程序包括基于在特定加载情况下的主拉伸应力重复地识别有利的纤维取向，然后用修改的有利纤维取向重新计算该加载情况的应力。由于该方法仍然依赖于一个高精度的应力近似的有限元公式，这是不直接获得特别是不可压缩和高度各向异性材料，此外，修改后的模型引入。该模型不仅根据局部主应力，而且根据在单个有限元上计算的主应力的体积平均值来定义有利的纤维取向。因此，不完美的应力近似的影响可以被削弱，导致稳定的收敛的重取向过程和更合理的纤维取向与更少的数值噪声。针对不同的有限元公式和不同的有利纤维取向模型研究了所提出的纤维重取向方案的性能，Hariton等人（Biomech Model Mechanobiol 6（3）：163-175，2007）和Cyron和Humphrey（Math Mech Solids 1-17，2014）。此外，它还可用于计算患者特定动脉几何结构中的纤维方向。
We propose an algorithmic scheme for the numerical calculation of fiber orientations in arterial walls. The basic assumption behind the procedure is that the fiber orientations are mainly governed by the principal tensile stress directions resulting in an improved load transfer within the artery as a consequence of the redistribution of stresses. This reflects the biological motivation that soft tissues continuously adapt to their mechanical environment in order to optimize their load-bearing capacities. The algorithmic scheme proposed here enhances efficiency of the general procedure given in Hariton et al. (Biomech Model Mechanobiol 6(3):163-175, 2007), which consists of repeatedly identifying a favored fiber orientation based on the principal tensile stresses under a certain loading scenario, and then re-calculating the stresses for that loading scenario with the modified favored fiber orientation. Since the method still depends on a highly accurate stress approximation of the finite element formulation, which is not straightforward to obtain in particular for incompressible and highly anisotropic materials, furthermore, a modified model is introduced. This model defines the favored fiber orientation not only in terms of the local principal stresses, but in terms of the volume averages of the principal stresses computed over individual finite elements. Thereby, the influence of imperfect stress approximations can be weakened leading to a stabilized convergence of the reorientation procedure and a more reasonable fiber orientation with less numerical noise. The performance of the proposed fiber reorientation scheme is investigated with respect to different finite element formulations and different favored fiber orientation models, Hariton et al. (Biomech Model Mechanobiol 6(3):163-175, 2007) and Cyron and Humphrey (Math Mech Solids 1-17, 2014). In addition, it is applied to calculate the fiber orientation in a patient-specific arterial geometry.