冠状动脉旁路移植术中参数化最优流控制的降阶方法，面向患者特异性数据同化
Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation
AI总结：
本研究针对冠状动脉旁路移植术参数化最优流控制问题，利用未知控制变量解决边界条件量化挑战，并通过POD-Galerkin降阶方法投影至低维解流形，构建高效可靠的计算环境以实现患者特异性生理数据匹配。
摘要：
冠状动脉旁路移植术（CABG）是一种用于规避冠状动脉疾病（CAD）中部分或完全血流阻塞的侵入性手术。在本研究中，我们将数值最优流控制模型应用于从真实手术病例的临床图像重建的CABG患者特异性几何结构中，并采用参数化设置。这些应用的目标是将已知生理数据与通过调整某些参数产生的不同场景对应的数值血流动力学相匹配。此类应用是实现患者特异性血管几何结构中患者特异性生理数据最佳匹配的初步步骤。据报道，此类问题中出现的两个关键挑战是：（i）缺乏对尽可能匹配已知数据所需的有意义边界条件的稳健量化；（ii）高计算成本。在本研究中，我们利用最优流控制问题中的未知控制变量来解决第一个挑战。此外，为应对第二个挑战，我们通过proper orthogonal decomposition (POD)--Galerkin将问题投影到低维解流形上，为这类参数化问题提出了一个时间高效且可靠的计算环境。
英文摘要：
Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease (CAD). In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step towards matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are, $\left( i \right)$. lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and $\left( ii \right)$. high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition (POD)--Galerkin.
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