Finite-element-based discretization and regularization strategies for 3-D inverse electrocardiography

Area of Science:

• Biomedical Engineering
• Computational Electrophysiology

Background:

• The inverse electrocardiographic problem is crucial for understanding cardiac electrical activity.
• Numerical approximations of this ill-posed problem using finite-element methods face challenges with discretization and regularization.

Purpose of the Study:

• To enhance numerical approximation strategies for the ill-posed inverse electrocardiographic problem.
• To introduce novel discretization techniques and regularizers for improved accuracy in computing epicardial potentials.

Main Methods:

• Proposed refinement guidelines for finite-element method discretization, necessitating hybrid elements (tetrahedra and prisms).
• Introduced a new family of variational regularizers, preserving the L(2) norm for consistent multiscale simulations.
• Validated techniques using a 3-D torso/heart model and empirical cardiac data.

Main Results:

• The proposed hybrid element technique and variational regularizers mitigate ill-conditioning.
• Discretization strategies significantly improve the accuracy of the inverse solution for epicardial potentials.
• Simulations demonstrated enhanced numerical quality and consistent regularization across different scales.

Conclusions:

• The developed strategies effectively address the ill-posed nature of the inverse electrocardiographic problem.
• Variational-formed regularizers offer an advantageous alternative to traditional methods, preserving the L(2) norm.
• The variational formulation shows potential for broader applications in bioelectric problems.