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The variational multiscale formulation for the fully-implicit log-morphology equation as a tensor-based blood damage

Stefan Haßler1, Lutz Pauli1, Marek Behr1

  • 1Chair for Computational Analysis of Technical Systems (CATS), Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University, Aachen, 52056, Germany.

International Journal for Numerical Methods in Biomedical Engineering
|September 8, 2019
PubMed
Summary

A new variational multiscale (VMS) finite element method improves blood damage modeling. This log-morph equation approach enhances numerical stability for simulations, outperforming previous methods in complex device applications.

Keywords:
computational hemodynamicsfinite element methodlog-morphology formulationvariational multiscale formulationventricular assist device

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Area of Science:

  • Computational Fluid Dynamics
  • Biomedical Engineering
  • Finite Element Analysis

Background:

  • Accurate modeling of blood damage is crucial for designing medical devices.
  • Existing blood damage models face numerical challenges, including unphysical negative eigenvalues.
  • Viscoelastic, tensor-based models require robust numerical stabilization techniques.

Purpose of the Study:

  • To derive a variational multiscale (VMS) finite element formulation for a viscoelastic, tensor-based blood damage model.
  • To introduce a logarithmic shape tensor description for numerical stabilization.
  • To evaluate the performance of the proposed VMS stabilization against existing methods.

Main Methods:

  • Development of a variational multiscale (VMS) finite element formulation.
  • Implementation of a logarithmic shape tensor for stabilizing the tensor equation.
  • Numerical treatment of VMS stabilization terms for the log-morph equation.
  • Comparison with Galerkin/least squares (GLS) and Streamline Upwind Petrov-Galerkin (SUPG) stabilization.

Main Results:

  • The log-morph equation with VMS stabilization demonstrated significantly improved numerical behavior compared to GLS-stabilized untransformed morphology simulations.
  • The VMS stabilization showed clear advantages over SUPG stabilization in simulations.
  • Successful application of the VMS method to a centrifugal ventricular assist device (VAD).

Conclusions:

  • The proposed VMS finite element formulation with logarithmic shape tensor stabilization offers a robust and accurate approach for blood damage modeling.
  • This method enhances numerical stability, preventing unphysical results.
  • The VMS approach shows significant potential for improving the design and performance of blood-contacting medical devices like VADs.