This paper reports on the derivation and implementation of a shape optimization procedure for the minimization of hemolysis induction in blood flows through biomedical devices.Despite the significant progress in relevant experimental studies, the ever-growing advances in computational science have made computational fluid dynamics an indispensable tool for the design of biomedical devices. However, even the latter can lead to a restrictive cost when the model requires an extensive number of computational elements or when the simulation needs to be overly repeated. This work aims at the formulation of a continuous adjoint complement to a power-law hemolysis prediction model dedicated to efficiently identifying the shape sensitivity to hemolysis. The proposed approach can accompany any gradient-based optimization method at the cost of approximately one additional flow solution per shape update. The approach is verified against analytical solutions of a benchmark problem and computed sensitivity derivatives are validated by a finite differences study on a generic 2D stenosed geometry. The included application addresses a 3D ducted geometry which features typical characteristics of blood-carrying devices. An optimized shape, leading to a potential improvement up to 22%, is identified. It is shown that the improvement persists for different hemolysis-evaluation parameters.

In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape derivatives in this context cannot be directly used as a shape update in gradient-based optimization strategies. Instead, an auxiliary problem has to be solved to obtain a gradient from the sensitivity. While several choices for these auxiliary problems were investigated mathematically, the complexity of the concepts behind their derivation has often prevented their application in engineering. This work aims at an explanation of several approaches to compute shape updates from an engineering perspective. We introduce the corresponding auxiliary problems in a formal way and compare the choices by means of numerical examples. To this end, a test case and exemplary applications from computational fluid dynamics are considered.

The contribution is devoted to combined shape- and mesh-update strategies for parameter-free (CAD-free) shape optimization methods. Three different strategies to translate the shape sensitivities computed by adjoint shape optimization procedures into simultaneous updates of both the shape and the discretized domain are employed in combination with a mesh-morphing strategy. Considered methods involve a linear Steklov–Poincaré (Hilbert space) approach, a recently suggested highly non-linear p-Laplace (Banach space) method, and a hybrid variant which updates the shape in Hilbert space. The methods are scrutinized for optimizing the power loss of a two-dimensional bent duct flow using an unstructured, locally refined grid that initially displays favorable grid properties. Optimization results are compared with respect to the optimization convergence, the computational effort, and the preservation of the mesh quality during the optimization sequence. Results indicate that all methods reach, approximately, the same converged optimal solution, which reduces the objective function by about 18% for this classical benchmark example. However, as regards the preservation of the mesh quality, more advanced Banach space methods are advantageous in comparison to Hilbert space methods even when the shape update is performed in Hilbert space to save costs. In specific, while the computational cost of the Banach space method and the hybrid method is about 3.5 and 2.5 times the cost of the pure Hilbert space method, respectively, the grid quality metrics are 2 times and 1.7 times improved for the Banach space and hybrid method, respectively.

This paper reports on the derivation and implementation of a shape optimization procedure for the minimization of hemolysis induction in biomedical devices. Hemolysis is a blood damaging phenomenon that may occur in mechanical blood-processing applications where large velocity gradients are found. An increased level of damaged blood can lead to deterioration of the immune system and quality of life. It is, thus, important to minimize flow-induced hemolysis by improving the design of next-generation biomedical machinery. Emphasis is given to the formulation of a continuous adjoint complement to a power-law hemolysis prediction model dedicated to efficiently identifying the shape sensitivity to hemolysis. The computational approach is verified against the analytical solutions of a benchmark problem, and computed sensitivity derivatives are validated by a finite differences study on a generic 2D stenosed geometry. The application included addresses a 3D ducted geometry which features typical characteristics of biomedical devices. An optimized shape, leading to a potential improvement in hemolysis induction up to 22%, is identified. It is shown, that the improvement persists for different, literature-reported hemolysis-evaluation parameters.

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