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首页> 外文期刊>International Journal for Numerical Methods in Fluids >On optimization, control and shape design of an arterial bypass
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On optimization, control and shape design of an arterial bypass

机译：关于动脉旁路的优化，控制和形状设计

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Multi-level geometrical approaches in the study of aorto-coronaric bypass anastomoses configurations are discussed. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the incoming branch of the bypass (the toe) into the coronary. At this level, two possible options are available in shape design: one implements local boundary variations in computational domain, the other, based on the theory of small perturbations, makes use of a linearized design in a reference domain. At a coarser level, reduced basis methodologies based on parametrized partial differential equations are developed to provide (a) a sensitivity analysis for geometrical quantities of interest in bypass configurations and (b) rapid and reliable prediction of integral functional outputs. The aim is (i) to provide design indications for arterial surgery in the perspective of future development for prosthetic bypasses, (ii) to develop multi-level numerical methods for optimization and shape design by optimal control, and (iii) to provide an input-output relationship led by models with lower complexity and computational costs. We have numerically investigated a reduced model based on Stokes equations and a vorticity cost functional (to be minimized) in the down-field zone of bypass: a Taylor like patch has been found. A feedback procedure with Navier-Stokes fluid model is proposed based on the analysis of wall shear stress-related indexes.
机译：讨论了在主动脉冠状旁路旁路吻合构型研究中的多层次几何方法。为了优化旁路（脚趾）进入冠状动脉的进入分支的形状，应用了基于伴随公式的最优控制理论。在此级别上，形状设计有两种可能的选择：一种在计算域中实现局部边界变化，另一种基于小扰动理论在参考域中使用线性化设计。在较粗糙的级别上，开发了基于参数化偏微分方程的简化基础方法，以提供（a）对旁路配置中感兴趣的几何量进行灵敏度分析，以及（b）快速可靠地预测整体功能输出。目的是（i）从假体旁路的未来发展角度为动脉外科手术提供设计指标;（ii）通过优化控制开发用于优化和形状设计的多级数值方法，以及（iii）提供输入信息-输出关系由具有较低复杂度和计算成本的模型主导。我们对基于斯托克斯方程的简化模型进行了数值研究，并在旁路的低场区域中研究了涡度成本函数（有待最小化）：找到了一个类似Taylor的贴片。在分析墙体剪应力相关指标的基础上，提出了基于Navier-Stokes流体模型的反馈程序。

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