Pérez Elver A, Rojas-Solórzano Luis R, Finol Ender
Department of Energy Conversion and Transport. Universidad Simón Bolívar. Caracas, Venezuela.
Department. of Mechanical Engineering. Nazarbayev University. Astana, Rep. of Kazakhstan.
Chem Eng Trans. 2016 Apr;49:73-78. doi: 10.3303/CET1649013.
Abdominal aortic aneurysm (AAA) is a dilation of the abdominal aorta (above 50 % of its original diameter), which can cause death upon rupturing. It usually grows asymptomatically leading to late clinical intervention. The medical criteria to indicate surgery are based on measuring the diameter and growth rate, but in many cases aneurysms fail at uncharacterized critical values. In search of a more efficient technique in predicting AAA failure, there is consensus on the importance of studying its geometric characteristics and estimation of the wall stress, but no fully successful correlation has been found between the two yet. This work examines the relationship between a parameterized geometry (18 input variables and 10 dependent indices) and 1 output variable: the maximum wall stress. Design of Experiments (DOE) techniques are used to generate 183 geometric configurations, for which Finite Element Analyses are performed using ANSYS™ state-of-the-art solver with a hyperelastic, isotropic and homogeneous arterial model for the wall, considering systolic internal pressure (steady state) and the restriction of longitudinal movement at the blood vessel end-sections. Due to the large number of independent parameters to consider, a preliminary Parameters Correlation analysis was performed to determine if a correlation between all input parameters and the maximum stress existed. The correlations between input parameters and the output variable were determined using the Spearman Rank correlation. Correlations with the maximum wall stress for: maximum diameter (ρ = 0.46), wall thickness (ρ = 0.35), d parameter (ρ = 0.21) and tortuosity (ρ = 0.55) were found. The response surface function between geometry and maximum wall stress was estimated by three models: Universal Kriging geostatistical regression (18 parameters), multiple linear regression (4 parameters) and multiple exponential regression (4 parameters). The models accounted for the stress variance by 99 %, 61 % and 66 %, respectively, with average percentage errors of 0.12 %, 16 % and 17 %, respectively. The solution spaces obtained from this study might provide physicians with a better estimation of the AAA rupture potential and thus, facilitate safer and anticipated treatments of the condition.
腹主动脉瘤（AAA）是腹主动脉的扩张（超过其原始直径的50%），破裂时可导致死亡。它通常无症状地生长，导致临床干预较晚。指示手术的医学标准基于测量直径和生长速率，但在许多情况下，动脉瘤在未明确的临界值时破裂。为了寻找更有效的预测AAA破裂的技术，人们一致认为研究其几何特征和壁应力估计很重要，但尚未发现两者之间有完全成功的相关性。这项工作研究了参数化几何形状（18个输入变量和10个相关指标）与1个输出变量：最大壁应力之间的关系。实验设计（DOE）技术用于生成183种几何构型，使用ANSYS™ 最先进的求解器对其进行有限元分析，采用超弹性、各向同性和均匀的动脉壁模型，考虑收缩期内压（稳态）以及血管端部纵向运动的限制。由于要考虑大量独立参数，因此进行了初步的参数相关性分析，以确定所有输入参数与最大应力之间是否存在相关性。使用斯皮尔曼等级相关性确定输入参数与输出变量之间的相关性。发现与最大壁应力的相关性如下：最大直径（ρ = 0.46）、壁厚（ρ = 0.35）、d参数（ρ = 0.21）和迂曲度（ρ = 0.55）。通过三种模型估计几何形状与最大壁应力之间的响应面函数：通用克里金地质统计回归（18个参数）、多元线性回归（4个参数）和多元指数回归（4个参数）。这些模型分别解释了99%、61%和66%的应力方差，平均百分比误差分别为0.12%、16%和17%。本研究获得的解空间可能为医生提供更好的AAA破裂可能性估计，从而促进对该疾病更安全和预期的治疗。
