Uniformization method for solving cardiac electrophysiology models based on the Markov-chain formulation.

Area of Science:

• Computational biology
• Biophysics
• Numerical analysis

Background:

• Cardiac electrophysiology models often use continuous-time Markov chains (MCs) to represent subcellular structures like ion channels.
• MCs can lead to stiff ordinary differential equations, limiting time steps in traditional numerical methods.
• Existing methods like Euler explicit and Rush-Larsen (RL) struggle with the computational demands of these stiff models.

Purpose of the Study:

• To evaluate the efficacy of the uniformization method for solving myocyte models of cardiac electrophysiology.
• To compare the stability and computational performance of uniformization-enhanced methods against traditional numerical techniques.
• To demonstrate the benefits of uniformization for handling stiff ordinary differential equations arising from MC-based models.

Main Methods:

• Application of the uniformization method to enhance first-order numerical solvers (Euler explicit, RL).
• Implementation and testing on various cardiac electrophysiology models incorporating MCs.
• Comparative analysis of time step stability and computational speed.

Main Results:

• Uniformization substantially increases the stability of Euler explicit and RL methods.
• Significant increases in achievable time steps were observed for cardiac electrophysiology models.
• Computational performance improved by up to 150 times compared to standard Euler and RL methods.

Conclusions:

• The uniformization method offers a powerful approach to overcome numerical limitations in cardiac electrophysiology modeling.
• This technique enables more efficient and stable simulations of complex cellular processes.
• Uniformization presents a significant advancement for computational efficiency in biophysical modeling.