Delay differential equation-based models of cardiac tissue: Efficient implementation and effects on spiral-wave...

Area of Science:

• Computational Biology
• Cardiac Electrophysiology
• Mathematical Modeling

Background:

• Delay differential equations (DDEs) are increasingly used to model cardiac electrophysiology, capturing complex dynamics like alternans, instabilities, and chaos.
• These models are crucial for understanding cellular and tissue-level mechanisms underlying cardiac arrhythmias.
• However, DDEs introduce significant computational challenges, particularly memory demands for storing variable histories in simulations.

Purpose of the Study:

• To develop novel numerical methods for solving DDEs in cardiac tissue simulations, reducing memory requirements.
• To analyze the impact of DDEs on spiral wave dynamics and wave propagation in two-dimensional cardiac tissue.
• To investigate how incorporating delays in gating variables affects cardiac tissue behavior.

Main Methods:

• Developed new numerical techniques to optimize history size dynamically based on action potential time scales, mitigating memory usage in DDE simulations.
• Implemented these optimized methods to simulate wave propagation in 2D cardiac tissue models incorporating DDEs.
• Utilized a canine myocyte model to study spiral wave dynamics under DDE influence.

Main Results:

• The proposed methods reduced memory usage by up to 95% in cardiac tissue simulations compared to standard algorithms.
• For the first time, DDEs were analyzed for their effects on spiral wave dynamics in 2D cardiac tissue.
• Introducing delays in calcium current gating variables using DDEs was shown to induce spiral wave breakup.

Conclusions:

• Optimized numerical methods significantly improve the computational efficiency of DDE-based cardiac electrophysiology models.
• DDEs, particularly when modeling delays in ionic currents, can be a key factor in inducing complex dynamics like spiral wave breakup in cardiac tissue.
• These findings advance the understanding of cardiac arrhythmias and computational approaches for their simulation.