Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks.

Area of Science:

• Computational Biology
• Cardiac Electrophysiology
• Numerical Algorithms

Background:

• Cardiac Purkinje fibers are crucial for coordinated heart contraction.
• Accurate electrophysiological modeling of the Purkinje network is essential for understanding cardiac function.
• Previous computational models faced limitations in efficiency and mathematical consistency.

Purpose of the Study:

• To develop and evaluate an efficient numerical algorithm for Purkinje network electrophysiology.
• To implement and compare CPU, hybrid CPU/GPU, and pure GPU versions of the algorithm.
• To improve the mathematical consistency of the model at network bifurcations.

Main Methods:

• Operator splitting numerical method.
• Three distinct hardware implementations: pure CPU, hybrid CPU/GPU, and pure GPU.
• Modification of the explicit gap junction term for enhanced mathematical consistency.
• Empirical convergence study against analytical solutions.
• Comparative efficiency analysis across varying network resolutions and membrane model complexities.

Main Results:

• All three implementations (CPU, hybrid, GPU) demonstrated equivalent convergence rates.
• The algorithm produced consistent results across different hardware platforms.
• Both hybrid and pure GPU implementations significantly outperformed the pure CPU implementation in efficiency.
• Performance gains of GPU implementations were dependent on Purkinje network size and membrane model complexity.

Conclusions:

• The developed numerical algorithm offers an efficient solution for in silico studies of cardiac Purkinje networks.
• The GPU-accelerated implementations provide substantial performance advantages over traditional CPU methods.
• The algorithm's improved mathematical consistency and cross-platform equivalence enhance its reliability for complex cardiac electrophysiology research.