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978-3-8439-2810-6, Reihe Strömungsmechanik

Lutz Pauli
Stabilized Finite Element Methods for Computational Design of Blood-Handling Devices

194 Seiten, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen (2016), Softcover, A5

Zusammenfassung / Abstract

The development of reliable blood damage models is a key issue for the virtual design of ventricular assist devices (VADs). The mechanical hemolysis in VADs is an example for a microscale effect that can only be measured on the macroscale. Therefore, hemolysis is usually modeled as a bulk phenomenon and based on a simple power law, depending on scalar shear-stress and exposure time. In the commonly used stress-based model, the scalar shear stress depends solely on the precomputed Navier-Stokes equations. The stress-based model is only able to account for macroscale phenomena and therefore, it implicitly assumes that red blood cells (RBCs) deform instantaneously. A different approach is a simulation by means of a strain-based model. Here, the viscoelastic deformation of RBCs is computed by a tensorial evolution equation. The tensor results are used to estimate a distortion of RBCs in the flow field. With the distortion, an effective shear stress can be computed, which is acting on the RBC itself. As a consequence, microscale effects are considered in the simulation, even though the overall result is on the macroscale.

In this thesis, the flow field and hemolysis quantities in VADs are computed by stabilized space-time finite element methods. The stabilization theory is critically reviewed for a generic convection-diffusion-reaction equation and tailored to the individual problem statements. The impeller movement in VADs is incorporated by either a multiple reference frames method, or a moving mesh technique based on the ALE formulation and the shear-slip mesh update method. Turbulence is considered by large eddy simulation with the sigma-model or the variational multiscale model. Hemolysis is computed by an Eulerian or field-based approach. The Eulerian approach allows simple identification of critical regions in the pump, which is useful for computer-aided design optimization.

Comparisons of stress-based and strain-based hemolysis models in a benchmark blood pump show very significant differences. Stress peaks with short exposure time contribute to the overall hemolysis in the stress-based model, whereas regions with increased shear and long exposure time are responsible for damage in the strain-based model.

The developed numerical framework leads to very accurate numerical predictions and can be a valuable engineering tool for the design of new blood-handling devices or the optimization of existing ones.