An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso

Area of Science:

• Computational biology
• Biophysics
• Numerical analysis

Background:

• The bidomain model is crucial for understanding cardiac electrical activity.
• Simulating the heart's electrophysiology involves complex, coupled partial differential equations (PDEs) and ordinary differential equations (ODEs).
• Integrating torso electrical fields necessitates a third PDE, increasing computational complexity and demanding high spatiotemporal resolution.

Purpose of the Study:

• To present a novel numerical method for solving the coupled bidomain and torso electrical field equations.
• To address the challenges of complexity and strict resolution requirements in cardiac electrophysiology simulations.
• To develop a computationally efficient and accurate simulation technique.

Main Methods:

• The proposed method employs operator splitting techniques.
• A fully coupled discretization approach is used for the three PDEs.
• The numerical method is designed to handle the intricate system of equations governing cardiac electrical activity.

Main Results:

• Numerical experiments demonstrate the method's effectiveness for simulation cases.
• The algorithm achieves second-order accuracy in both space and time for fine discretizations.
• The approach provides a viable solution for complex cardiac electrophysiology modeling.

Conclusions:

• The developed numerical method offers an accurate and efficient approach to simulating cardiac electrical activity.
• This method can be applied to various applications requiring coupled bidomain and torso models.
• The findings contribute to advancing computational cardiology and understanding heart function.