An efficient technique for the numerical solution of the bidomain equations

Area of Science:

• Computational science
• Biomedical engineering
• Applied mathematics

Background:

• Numerical solutions to the bidomain equations present a substantial computational challenge in cardiac electrophysiology.
• Existing semi-implicit numerical schemes offer stability but can be computationally expensive.

Purpose of the Study:

• To develop a novel, computationally efficient numerical scheme for solving the bidomain equations.
• To extend a previously established stable numerical method for bidomain equation solutions.

Main Methods:

• A new numerical scheme was developed, leveraging the selective updating of ionic current components.
• The fast sodium current is computed on a fine spatial mesh, while other ionic currents are calculated on a coarser mesh and interpolated.
• This approach was applied to compute transmembrane and extracellular potentials.

Main Results:

• The developed scheme achieves computational efficiency exceeding two orders of magnitude compared to standard numerical techniques.
• The selective updating strategy introduces minimal error in the computed transmembrane and extracellular potentials.
• Significant computational speed-up was demonstrated for bidomain equation simulations.

Conclusions:

• The proposed numerical scheme offers a highly efficient method for solving the bidomain equations.
• This advancement can accelerate computational modeling in cardiac electrophysiology.
• The technique provides a substantial improvement in computational performance without compromising solution accuracy.