An approximate solution to the periodic bidomain equations in one dimension

Area of Science:

• Biomedical Engineering
• Computational Biology
• Cardiac Electrophysiology

Background:

• The bidomain model is essential for simulating cardiac electrical propagation.
• Periodic intracellular junctions in cardiac tissue pose computational challenges.
• Accurate modeling of transmembrane potentials is critical for understanding arrhythmias.

Purpose of the Study:

• To develop a computationally tractable approximate solution for the periodic bidomain model.
• To simplify the analysis of potentials in cardiac tissue with periodic intracellular junctions.
• To provide a method applicable to higher spatial dimensions, including anisotropy and inhomogeneities.

Main Methods:

• Decomposition of the periodic bidomain problem into spectral domain components.
• Solving the single-fiber classical bidomain problem with averaged intracellular conductivity.
• Approximating the "junctional" potential due to discrete junctional locations.
• Comparison of approximate solutions with rigorous solutions for validation.

Main Results:

• An approximate solution for periodic bidomain potentials was successfully developed.
• The proposed method significantly reduces numerical effort compared to rigorous solutions.
• The approximation accurately captures the essential features of the junctional potential.
• The approach is validated by comparing approximate and rigorous solutions.

Conclusions:

• The proposed approximate solution offers a computationally efficient alternative for the periodic bidomain model.
• This method facilitates the study of transmembrane potential distribution in complex cardiac tissues.
• The approach is extendable to higher dimensions, incorporating tissue anisotropy and junctional inhomogeneities.