Robust Shape Optimization for Artifical Blood Pumps: Hematological Design, Large-scale Transient Simulations, and Influence of Constitutive Models, Sensitivity Analysis

血液处理机械设备的分析和设计优化，特别是微型心脏辅助血泵，提出了一些独特的挑战。血液的微观结构特性影响着设计目标的选择，如最大限度地减少血液损伤和凝血，以及流动方程的选择，这应该考虑血液作为一个连续体的非牛顿性质。在血泵形状优化的背景下，我们提出了可以与血液损伤沿流动路径积累相关的目标函数的问题，以及本构模型(牛顿、广义牛顿和粘弹性)对最优形状的影响。整个优化工具链基于分析得出的灵敏度和伴随项，然后在适合优化过程的自动微分的帮助下进行灵敏度分析。预计用于检测本构模型中的缺陷的标准将被举例说明，例如，通过最佳形状对模型参数的极端敏感性。在本项目的这一阶段，要解决轴流血泵实际复杂几何形状中的样本形状优化问题。

Analysis and design optimization of blood-handling mechanical devices, and in particular, miniature heart-assist blood pumps, presents a number of unique challenges. The micro-structural properties of blood affect both the choice of the design objectives, such as minimizing blood damage and clotting, and the choice of flow equations, which should account for the non-Newtonian nature of blood as a continuum. We propose to address, in the context of shape optimization of blood pumps, the issue of objective functions which can be correlated with the accumulation of blood damage along flow pathlines, and the influence of constitutive model (Newtonian, generalized Newtonian, and viscoelastic) on the optimal shapes. The entire optimization tool chain, based on analytically-derived sensitivities and adjoints, will be then subjected to sensitivity analysis with the help of automatic differentiation suitably adapted to the optimization procedure. It is expected that criteria for detecting inadequacies in constitutive modeling will be exemplified, e.g., by extreme sensitivity of the optimal shapes to model parameters. A sample shape optimization problem in an actual complex geometry of an axial blood pump is to be solved during this phase of the project.