Physiology driven adaptivity for the numerical solution of the bidomain equations

Area of Science:

• Computational electrophysiology
• Biomedical engineering
• Numerical analysis

Background:

• Previous work established a stable, semi-implicit numerical scheme for bidomain equations.
• The existing scheme permitted timestep selection based on accuracy, not stability.
• Bidomain equations are crucial for modeling cardiac electrical activity.

Purpose of the Study:

• To modify the existing numerical scheme for adaptive time and space solutions.
• To improve computational efficiency and reduce memory requirements for bidomain simulations.
• To enhance the accuracy and speed of cardiac electrophysiology modeling.

Main Methods:

• Developed an adaptive algorithm integrated with a stable, semi-implicit numerical scheme.
• Spatial mesh size determined by transmembrane and extracellular potential gradients.
• Timestep determined by fast sodium current and calcium release current values.

Main Results:

• Achieved a computational efficiency increase of approximately 250-fold for 2D simulations.
• Significantly reduced computational memory requirements compared to previous methods.
• Demonstrated potential for even greater speedup in 3D simulations.

Conclusions:

• The adaptive numerical scheme significantly enhances computational efficiency for bidomain equation solving.
• This method offers a more efficient approach to modeling cardiac electrical propagation.
• Further improvements in computational performance are expected for three-dimensional models.