Eulerian Formulation of the Tensor-Based Morphology Equations for Strain-Based Blood Damage Modeling

TL;DR

This work formulates a full-order Eulerian tensor-based morphology model for strain-based hemolysis in blood-contacting devices, deriving an Eulerian evolution equation that remains analytically equivalent to the classic Lagrangian Arora model while enabling domain-wide evaluation. To address numerical challenges, a tank-treading logarithmic model (TTLM) reduces rotational dynamics and adopts a robust, reduced two-parameter deformation description with a logarithmic transform to keep eigenvalues positive. A dedicated equilibrium-steady orientation algorithm, combined with spectral projections, yields stable 3D orientation in practice, and the model is implemented in an in-house finite element framework with one-way coupling to flow. Numerical results across simple shear, rotating shear, a square stirrer, and a 3D pump demonstrate that TTLM reproduces the full-order model with high fidelity while offering substantial computational efficiency, outperforming simplified Eulerian formulations. The approach provides a workable, physics-informed tool for RBC deformation and hemolysis prediction in realistic device geometries, with potential for design optimization and further validation with experimental data.

Abstract

The development of blood-handling medical devices, such as ventricular assist devices, requires the analysis of their biocompatibility. Among other aspects, this includes hemolysis, i.e., red blood cell damage. For this purpose, computational fluid dynamics (CFD) methods are employed to predict blood flow in prototypes. The most basic hemolysis models directly estimate red blood cell damage from fluid stress in the resulting flow field. More advanced models explicitly resolve cell deformation. On the downside, these models are typically written in a Lagrangian formulation, i.e., they require pathline tracking. We present a new Eulerian description of cell deformation, enabling the evaluation of the solution across the whole domain. The resulting hemolysis model can be applied to any converged CFD simulation due to one-way coupling with the fluid velocity field. We discuss the efficient numerical treatment of the model equations in a stabilized finite element context. We verify the model by comparison to the original Lagrangian formulation in selected benchmark flows. Two more complex test cases demonstrate the method's capabilities in real-world applications. The results highlight the advantages over previous hemolysis models. In conclusion, the model holds great potential for the design process of future generations of medical devices.

Figures (11)

• Figure 1: Ellipsoidal cell representation in Arora morphology model
• Figure 2: Strain terms in full-order Eulerian formulation
• Figure 3: Determining equilibrium orientation in 2D and 3D
• Figure 4: Comparison of morphology models under simple shear.
• Figure 5: Comparison of morphology models under short exposure times $\tau = x / U$.