Two-dimensional Chebyshev pseudospectral modelling of cardiac propagation

Area of Science:

• Computational biology
• Biophysics
• Cardiac electrophysiology

Background:

• Cardiac tissue modeling is crucial for understanding action potential propagation.
• Traditional finite difference methods often require extensive computational resources for accurate simulations.
• Existing methods face limitations with realistic cardiac tissue dimensions.

Purpose of the Study:

• To introduce a Chebyshev pseudospectral method for cardiac tissue modeling.
• To demonstrate the efficiency and accuracy of this new numerical approach.
• To overcome the computational limitations of finite difference methods.

Main Methods:

• Solving the nonlinear partial differential equation for the monodomain model.
• Utilizing Chebyshev polynomial expansions for transmembrane potential.
• Enforcing the equation at Gauss-Lobatto grid points.
• Employing the fast Fourier transform for spatial derivatives and an explicit technique for time advancement.

Main Results:

• The Chebyshev pseudospectral method achieved a sixteenfold reduction in required nodes.
• The new method maintained solution accuracy comparable to traditional methods.
• Simulations using the pseudospectral approach required approximately twelve times less CPU time and memory.

Conclusions:

• The Chebyshev pseudospectral method offers a significant computational advantage for cardiac tissue modeling.
• This technique enables more feasible and efficient simulations of cardiac electrophysiology.
• The reduced computational cost facilitates studies on action potential propagation with realistic parameters.