High-order finite element methods for cardiac monodomain simulations

Area of Science:

• Computational biology
• Biophysics
• Numerical analysis

Background:

• Accurate cardiac electrophysiology modeling is crucial for understanding heart function and disease.
• Simulations face computational challenges due to steep action potential gradients requiring fine spatial scales.
• High-order interpolation methods offer theoretical advantages for improving simulation convergence.

Purpose of the Study:

• To compare the convergence of linear Lagrange, cubic Hermite, and serendipity interpolation methods for cardiac monodomain equation simulations.
• To introduce and validate the cell Thiele modulus as a superior metric for assessing numerical convergence.
• To establish convergence criteria for clinically relevant cardiac activation patterns in patient-specific models.

Main Methods:

• Finite element simulations of the cardiac monodomain equation.
• Comparative analysis of linear Lagrange, cubic Hermite, and cubic Hermite-style serendipity interpolation.
• Development and application of the cell Thiele modulus for convergence assessment.

Main Results:

• High-order methods (Hermite, serendipity) achieved converged solutions with fewer degrees of freedom and longer elements than linear methods.
• The cell Thiele modulus proved more effective than element size alone for determining convergence.
• Established convergence criteria using the cell Thiele modulus for accurate activation patterns.

Conclusions:

• High-order interpolation methods enhance the efficiency and accuracy of cardiac electrophysiology simulations.
• The cell Thiele modulus provides a robust metric for ensuring numerical convergence in cardiac modeling.
• This work facilitates more reliable patient-specific cardiac modeling for clinical applications.