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，提出了许多独特的挑战。血液的微观结构特性既影响设计目标的选择，如尽量减少血液损伤和凝血，也影响流动方程的选择，这应该考虑到血液作为连续体的非牛顿性质。我们建议在血泵形状优化的背景下，解决与血流路径上血液损伤积累相关的目标函数问题，以及本构模型（牛顿模型、广义牛顿模型和粘弹性模型）对最佳形状的影响。整个优化工具链，基于解析导出的灵敏度和伴随，然后将在适应优化程序的自动微分的帮助下进行灵敏度分析。预计将举例说明检测本构建模不足的标准，例如，最佳形状对模型参数的极端敏感性。在此阶段的项目中，将解决一个实际复杂几何形状的轴向血泵样品形状优化问题。

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.