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A deformable finite element derived finite difference method for cardiac activation problems.

Martin Buist1, Gregory Sands, Peter Hunter

  • 1Bioengineering Research Group, Department of Engineering Science, The University of Auckland, Auckland, New Zealand. m.buist@auckland.ac.nz

Annals of Biomedical Engineering
|May 22, 2003
PubMed
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A new finite difference (FD) technique solves cardiac activation problems on deforming geometries. This method uses a finite element (FE) mesh to generate an embedded FD mesh for accurate bidomain equation solutions.

Area of Science:

  • Computational biology
  • Biomedical engineering
  • Mathematical modeling

Background:

  • Cardiac activation simulation is crucial for understanding heart function and disease.
  • Existing methods face challenges with deforming geometries.
  • The bidomain model is a standard for simulating cardiac electrophysiology.

Purpose of the Study:

  • To introduce a novel finite element (FE)-derived finite difference (FD) technique.
  • To enable accurate solutions for cardiac activation problems on deforming geometries.
  • To provide an invariant solution in material space despite geometric changes.

Main Methods:

  • A high-resolution FD mesh is generated over an FE mesh defining the geometry.
  • Bidomain equations are transformed to an embedded, regular, and orthogonal FD mesh.

Related Experiment Videos

  • Solution points adapt to geometric deformation while maintaining material space invariance.

    • Main Results:

    • The presented technique accurately solves cardiac activation problems.
    • The method demonstrates robustness over deforming geometries.
    • Validation through a series of examples confirms the framework's accuracy.

    Conclusions:

    • The FE-derived FD technique offers a powerful new tool for cardiac electrophysiology simulations.
    • This approach enhances the ability to model dynamic cardiac behaviors.
    • The method is accurate and invariant to geometric deformations.