Yamada H, Hasegawa Y
Department of Biological Functions and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, Kitakyushu, Japan.
Comput Methods Biomech Biomed Engin. 2007 Feb;10(1):53-61. doi: 10.1080/10255840601086531.
We extended a method of estimating the stress acting on an axisymmetric abdominal aortic aneurysm (AAA) under a load in vivo (Elger, D. F., Blackketter, D. M., Budwig, R. S., Johansen, K. H. (1996) The influence of shape on the stresses in model abdominal aortic aneurysms, Journal of Biomechanical Engineering, 118, pp. 326-32.) to bilaterally-symmetric AAAs, which are symmetric about the sagittal plane. Stresses were calculated along the anterior and posterior median lines of the AAA wall. Of the two force equilibrium equations, the Laplace equation held in this study. The longitudinal equilibrium was extended to hold by approximating the meridional tension and the directional cosine of the wall surface as constants along the circumference. The estimated stresses were compared with the results of a finite element analysis. Comparisons showed that the maximal principal stress, usually the circumferential stress or sometimes the meridional stress depending on location, sufficiently represented the wall stress. The proposed method provides a reasonable index for evaluating the rupture risk using the peak value of the maximal principal stress and its location without using the stress-free geometry and constitutive equation.
我们将一种在体内负荷下估算作用于轴对称腹主动脉瘤（AAA）应力的方法（埃尔格，D.F.，布莱克凯特，D.M.，布德维格，R.S.，约翰森，K.H.（1996年）形状对模型腹主动脉瘤应力的影响，《生物力学工程杂志》，118卷，第326 - 32页）扩展到关于矢状面对称的双侧对称AAA。沿着AAA壁的前后中线计算应力。在两个力平衡方程中，本研究采用拉普拉斯方程。通过将子午向张力和壁面方向余弦沿圆周近似为常数，扩展纵向平衡使其成立。将估算的应力与有限元分析结果进行比较。比较表明，最大主应力，通常是周向应力，有时根据位置是子午向应力，充分代表了壁应力。所提出的方法提供了一个合理的指标，用于利用最大主应力的峰值及其位置评估破裂风险，而无需使用无应力几何形状和本构方程。
