A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation.

Area of Science:

• Computational biology
• Biophysics
• Cardiovascular research

Background:

• The monodomain model is crucial for in-silico cardiology, simulating cardiac excitation propagation.
• Operator splitting, often using semi-implicit methods, is common but can be computationally intensive.
• Explicit methods offer lower memory footprint and higher scalability but face conditional stability limitations.

Purpose of the Study:

• To introduce a fully explicit numerical method for the decoupled monodomain model.
• To overcome the conditional stability issues inherent in explicit methods.
• To enhance computational efficiency and scalability in cardiac electrophysiology simulations.

Main Methods:

• Development of a dual adaptive explicit method for solving both reaction and diffusion terms.
• Application of adaptive time integration to both decoupled terms.
• Simulation of cardiac propagation under physiological and pathophysiological conditions using numerical examples.

Main Results:

• The proposed dual adaptive explicit method demonstrates preserved accuracy.
• Significant improvements in computational efficiency were observed compared to standard operator splitting methods.
• The method effectively overcomes conditional stability limitations of explicit approaches.

Conclusions:

• The dual adaptive explicit method provides an accurate and computationally efficient alternative for monodomain model simulations.
• This approach offers enhanced scalability, making it suitable for complex in-silico cardiology applications.
• The findings contribute to advancing numerical techniques in cardiac modeling.