Computational analysis of the impact of aortic bifurcation geometry to AAA haemodynamics

IF 0.5 4区 数学 Q4 MATHEMATICS, APPLIED Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-11-01 DOI:10.1515/rnam-2022-0026
D. Tikhvinskii, Lema R. Merzhoeva, A. Chupakhin, A. Karpenko, D. Parshin
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Abstract

Abstract Abdominal aortic aneurysm is a widespread disease of cardiovascular system. Predicting a moment of its rupture is an important task for modern vascular surgery. At the same time, little attention is paid to the comorbidities, which are often the causes of severe postoperative complications or even death. This work is devoted to a numerical study of the haemodynamics of the model geometry for possible localizations of abdominal aortic aneurysm: on the aortic trunk or on its bifurcation. Both rigid and FSI numerical simulations are considered and compared with the model aortic configuration without aneurysm. It is shown that in the case of localization of the aneurysm on the bifurcation, the pressure in aorta increases upstream. Moreover, only in the case of a special geometry,when the radii of the iliac arteries are equal (r1 = r2), and the angle between them is 60 degrees, there is a linear relationship between the pressure in the aorta above the aneurysm and the size of the aneurysm itself: the slope of the straight line is in the interval a ∈ (0.003; 0.857), and the coefficient of determination is R2 ⩾ 0.75. The area bounded by the curve of the ‘pressure–velocity’ diagram for the values of velocity and pressure upstream in the presence of an aneurysm decreases compared to a healthy case (a vessel without an aneurysm). The simulation results in the rigid and FSI formulations agree qualitatively with each other. The obtained results provide a better understanding of the relationship between the geometrical parameters of the aneurysm and the changing of haemodynamics in the aortic bifurcation and its effect on the cardiovascular system upstream of the aneurysm.
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主动脉分叉几何形状对AAA血流动力学影响的计算分析
摘要腹主动脉瘤是一种广泛存在的心血管系统疾病。预测其破裂时刻是现代血管外科的一项重要任务。同时,很少关注合并症,这些合并症往往是导致严重术后并发症甚至死亡的原因。这项工作致力于对腹主动脉瘤可能定位的模型几何结构的血液动力学进行数值研究:在主动脉干或其分叉处。考虑了刚性和FSI数值模拟,并与没有动脉瘤的模型主动脉结构进行了比较。结果表明,在动脉瘤位于分叉处的情况下,主动脉上游的压力增加。此外,只有在特殊几何形状的情况下,当髂动脉的半径相等(r1=r2),并且它们之间的角度为60度时,动脉瘤上方主动脉中的压力与动脉瘤本身的大小之间存在线性关系:直线的斜率在区间a∈(0.003;0.857)内,确定系数为r2⩾0.75。与健康病例(没有动脉瘤的血管)相比,存在动脉瘤的情况下,上游速度和压力值的“压力-速度”图曲线所限定的面积减少。刚性公式和FSI公式的模拟结果在质量上相互一致。所获得的结果更好地理解了动脉瘤的几何参数与主动脉分叉处血流动力学变化之间的关系及其对动脉瘤上游心血管系统的影响。
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来源期刊
CiteScore
1.40
自引率
16.70%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest. Topics: -numerical analysis- numerical linear algebra- finite element methods for PDEs- iterative methods- Monte-Carlo methods- mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.
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