A Numerical Implementation to Predict Residual Strains from the Homogeneous Stress Hypothesis with Application to Abdominal Aortic Aneurysms
A Numerical Implementation to Predict Residual Strains from the Homogeneous Stress Hypothesis with Application to Abdominal Aortic Aneurysms
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DOI：
10.1007/s10439-013-0749-y
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发表时间：
2013-07-01
影响因子：
3.8
通讯作者：
Vlachovsky, Robert
中科院分区：
文献类型：
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作者：
Polzer, Stanislav;Bursa, Jiri;Vlachovsky, Robert
腹主动脉瘤（AAA）的壁应力分析是一种很有前途的方法，以确定AAA的高风险破裂。然而，忽略患者特定有限元分析模型的无载荷配置中的残余应变（RS）是严重的限制，其强烈影响计算的壁应力。尽管已经提出了几种包括RS的方法，但它们不能直接应用于患者特定的AAA模拟。通过体积组织生长预测AAA壁中的RS，旨在满足平均动脉压负荷下的均匀应力假设。组织生长在壁厚上线性插值，动脉瘤组织由各向同性本构方程描述。总的变形是乘法分裂成弹性和增长的贡献，和交错的计划是用来解决现场变量。该算法在圆柱形动脉模型上进行定性验证，然后应用于患者特定AAA（n = 5）。诱导的RS状态是完全三维的，并且与实验观察定性一致，即，从无负荷的墙壁上切下的墙壁条显示出通常在实验室实验中看到的应力释放变形。与无RS模拟相比，该算法将跨壁的von Mises应力梯度降低了十倍。考虑RS导致壁应力均匀化，除了降低峰值壁应力（PWS）外，在某些情况下还改变了其位置。本研究表明，均匀应力假设可以有效地用于预测RS在无负荷配置的血管壁。所提出的算法导致RS的快速和鲁棒的预测，这是完全能够为患者特定的AAA破裂风险评估。忽略RS会导致严重高估PWS的非现实壁应力值。
Wall stress analysis of abdominal aortic aneurysm (AAA) is a promising method of identifying AAAs at high risk of rupture. However, neglecting residual strains (RS) in the load-free configuration of patient-specific finite element analysis models is a sever limitation that strongly affects the computed wall stresses. Although several methods for including RS have been proposed, they cannot be directly applied to patient-specific AAA simulations. RS in the AAA wall are predicted through volumetric tissue growth that aims at satisfying the homogeneous stress hypothesis at mean arterial pressure load. Tissue growth is interpolated linearly across the wall thickness and aneurysm tissues are described by isotropic constitutive formulations. The total deformation is multiplicatively split into elastic and growth contributions, and a staggered schema is used to solve the field variables. The algorithm is validated qualitatively at a cylindrical artery model and then applied to patient-specific AAAs (n = 5). The induced RS state is fully three-dimensional and in qualitative agreement with experimental observations, i.e., wall strips that were excised from the load-free wall showed stress-releasing-deformations that are typically seen in laboratory experiments. Compared to RS-free simulations, the proposed algorithm reduced the von Mises stress gradient across the wall by a tenfold. Accounting for RS leads to homogenized wall stresses, which apart from reducing the peak wall stress (PWS) also shifted its location in some cases. The present study demonstrated that the homogeneous stress hypothesis can be effectively used to predict RS in the load-free configuration of the vascular wall. The proposed algorithm leads to a fast and robust prediction of RS, which is fully capable for a patient-specific AAA rupture risk assessment. Neglecting RS leads to non-realistic wall stress values that severely overestimate the PWS.