Computational Modeling and Visualization of Ischemic Effects on an Advanced Purkinje Network

1. Introduction

The heart’s electrical system relies on precise timing and coordination. Central to this system is the Purkinje network—a branching system of specialized fibers that rapidly conduct impulses through the ventricles. Myocardial ischemia, which restricts blood supply, can impair this network, disrupting normal impulse propagation and leading to arrhythmias such as ventricular tachycardia or fibrillation.^1,5

Figure 1. A: Three-dimensional visualization of the Purkinje network containing 500 cells randomly distributed within a cubic spatial domain.

Cell positions reflect spatial dispersion approximating Purkinje fiber branching within the ventricular myocardium. Figure 1B: Histogram illustrating the distribution of conduction velocities assigned to the Purkinje cells. The variability in conduction speed reflects physiological heterogeneity, with values ranging from 0.3 to 2.0 m/s. Figure 1C: Visualization of ischemia severity gradients applied across two ischemic zones in the Purkinje network. One region demonstrates a linear severity decline, while the other applies an exponential decay gradient, simulating different ischemic injury patterns. Figure 1D: Heatmap representation of the network adjacency matrix showing binary connections between Purkinje cells. The randomized connectivity results in heterogeneous local coupling densities while maintaining overall network integrity. Figure 1E: Histogram depicting the distribution of refractory periods assigned to individual Purkinje cells, ranging between 150 and 350 milliseconds, consistent with experimentally observed values. Figure 1F: Two-dimensional XY projection of the 3D network, providing an alternative view of spatial clustering, network density, and ischemic region overlap for enhanced visual interpretation.

Computational modeling offers a powerful, non-invasive approach to investigate these mechanisms. While existing Purkinje fiber models have provided important insights,^1–3 many lack integration of spatial anatomy, cellular heterogeneity, and detailed ischemic effects. To address these gaps, we developed a comprehensive computational framework simulating and visualizing ischemia-induced electrophysiological disturbances in a 3D Purkinje network.

2. Methods

3. Results

Simulations with 500 Purkinje cells and two ischemic zones (one linear, one exponential) revealed the following patterns:

Three-dimensional network views displayed an interconnected, random spatial distribution, reflecting a plausible biological layout. Conduction velocities displayed a heterogeneous histogram, in line with experimental observations of Purkinje fiber variability.² Ischemia severity accurately reflected the defined severity gradients—higher at the core, fading toward the periphery. The connectivity matrix heatmap demonstrated random but dense cell interconnections. Refractory periods varied widely, which is critical for modeling re-entrant conditions. Two-dimensional XY projections helped analyze spatial density and clustering (Figure 1).

4. Discussion

This modeling approach effectively captures how ischemia alters key electrophysiological parameters, such as conduction velocity and refractory period, while enabling direct visual correlation between spatial structure and functional disruption. Notably, areas with high ischemia severity often align with slowed conduction or shortened refractoriness—both recognized as precursors to arrhythmia.^5–7 While the current model uses randomized cell properties and connectivity, it is designed for future extensibility. Planned enhancements include integrating anatomically accurate branching patterns based on imaging data,⁴ implementing detailed electrophysiological models like Hodgkin-Huxley or Rudy-Li,^1,2 simulating action potential propagation with dynamic feedback, and exploring pharmacological interventions to assess therapeutic effects.^3,7

Limitations of this model include its current focus on static representation of ischemia and cell properties. Dynamic simulations of impulse propagation, feedback mechanisms, and the temporal evolution of ischemic injury are not yet integrated. The cell model is simplified, and detailed ion channel kinetics are not considered.

5. Conclusion

We have developed a computational framework that models and visualizes how ischemia affects the Purkinje network. It integrates cell-level variability, customizable ischemic regions, and rich visual outputs, all within a Python-based ecosystem. The model provides a clear, visual, and quantitative understanding of how ischemic damage disrupts electrical conduction and may contribute to arrhythmia. With future enhancements, it holds strong potential for in silico exploration of cardiac pathology and intervention design.