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

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When impaired—particularly by ischemia—it can trigger life-threatening arrhythmias. In this study, we present an advanced computational model of the Purkinje network that integrates cell-level heterogeneity, spatial organization, and localized ischemic zones with customizable severity gradients. Developed in Python using open-source libraries (NumPy, matplotlib, pandas, seaborn), the model generates rich visualizations of network structure, conduction velocities, ischemia severity, and electrophysiological parameters. Simulations demonstrate how ischemia alters conduction and refractoriness in a spatially dependent manner, providing insights into arrhythmogenic risk. This modeling framework can advance understanding of cardiac conduction under pathological conditions and support therapeutic development." } { "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": "1", "item": { "@id": "https://f1000research.com/", "name": "Home" } }, { "@type": "ListItem", "position": "2", "item": { "@id": "https://f1000research.com/browse/articles", "name": "Browse" } }, { "@type": "ListItem", "position": "3", "item": { "@id": "https://f1000research.com/articles/14-940", "name": "Computational Modeling and Visualization of Ischemic Effects on an..." } } ] } Home Browse Computational Modeling and Visualization of Ischemic Effects on an... ALL Metrics - Views Downloads Get PDF Get XML Cite How to cite this article Khan L, khan M, Rzayev N et al. Computational Modeling and Visualization of Ischemic Effects on an Advanced Purkinje Network [version 1; peer review: awaiting peer review] . F1000Research 2025, 14 :940 ( https://doi.org/10.12688/f1000research.168245.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. Close Copy Citation Details Export Export Citation Sciwheel EndNote Ref. Manager Bibtex ProCite Sente EXPORT Select a format first Track Share ▬ ✚ Software Tool Article Computational Modeling and Visualization of Ischemic Effects on an Advanced Purkinje Network [version 1; peer review: awaiting peer review] Laiba Khan https://orcid.org/0009-0005-4845-3900 1 , Maham khan https://orcid.org/0009-0002-2994-143X 1 , Nijat Rzayev https://orcid.org/0009-0006-0570-6928 1 , Mahmood Ahmad https://orcid.org/0000-0001-9107-3704 1 , Joanne Lac https://orcid.org/0009-0004-3533-434X 2 Laiba Khan https://orcid.org/0009-0005-4845-3900 1 , Maham khan https://orcid.org/0009-0002-2994-143X 1 , [...] Nijat Rzayev https://orcid.org/0009-0006-0570-6928 1 , Mahmood Ahmad https://orcid.org/0000-0001-9107-3704 1 , Joanne Lac https://orcid.org/0009-0004-3533-434X 2 PUBLISHED 18 Sep 2025 Author details Author details 1 Royal Free Hospital, London, England, UK 2 University College London, London, England, UK Laiba Khan Roles: Methodology, Validation, Visualization, Writing – Review & Editing Maham khan Roles: Writing – Review & Editing Nijat Rzayev Roles: Writing – Review & Editing Mahmood Ahmad Roles: Writing – Review & Editing Joanne Lac Roles: Funding Acquisition, Supervision, Validation, Visualization OPEN PEER REVIEW REVIEWER STATUS AWAITING PEER REVIEW This article is included in the Bioinformatics gateway. This article is included in the University College London collection. Abstract The cardiac Purkinje network plays a vital role in the heart’s electrical conduction system, ensuring efficient and synchronized ventricular contraction. When impaired—particularly by ischemia—it can trigger life-threatening arrhythmias. In this study, we present an advanced computational model of the Purkinje network that integrates cell-level heterogeneity, spatial organization, and localized ischemic zones with customizable severity gradients. Developed in Python using open-source libraries (NumPy, matplotlib, pandas, seaborn), the model generates rich visualizations of network structure, conduction velocities, ischemia severity, and electrophysiological parameters. Simulations demonstrate how ischemia alters conduction and refractoriness in a spatially dependent manner, providing insights into arrhythmogenic risk. This modeling framework can advance understanding of cardiac conduction under pathological conditions and support therapeutic development. READ ALL READ LESS Keywords cardiac purkunje Corresponding Author(s) Joanne Lac ( [email protected] ) Close Corresponding author: Joanne Lac Competing interests: No competing interests were disclosed. Grant information: The author(s) declared that no grants were involved in supporting this work. Copyright: © 2025 Khan L et al . This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite: Khan L, khan M, Rzayev N et al. Computational Modeling and Visualization of Ischemic Effects on an Advanced Purkinje Network [version 1; peer review: awaiting peer review] . F1000Research 2025, 14 :940 ( https://doi.org/10.12688/f1000research.168245.1 ) First published: 18 Sep 2025, 14 :940 ( https://doi.org/10.12688/f1000research.168245.1 ) Latest published: 18 Sep 2025, 14 :940 ( https://doi.org/10.12688/f1000research.168245.1 ) 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 2.1 Purkinje network model We implemented the AdvancedPurkinjeNetwork class in Python to simulate a network of n_cells Purkinje cells. Each cell includes spatial coordinates (x, y, z), assigned randomly within a bounded 3D volume to simulate biological dispersion. Cells are categorized as bundle_branch, fascicle, or purkinje to reflect histological diversity. A boolean pacemaker flag allows some cells to exhibit spontaneous firing. Key electrophysiological parameters include conduction velocity, refractory period, and ATP level. To simulate pathology, each cell carries an is_ischemic flag and a continuous ischemia_severity score (0.0–1.0). Network connectivity is represented by a binary adjacency matrix, which, while currently randomized, is designed for future integration of anatomical branching data. 4 2.2 Simulating ischemia We developed an algorithm to define ischemic regions by specifying a center, radius, and severity. The Euclidean distance from each cell to the ischemic core determines individual severity, applied via linear or exponential gradients. Linear gradients model gradual decline, while exponential gradients simulate more abrupt severity transitions, consistent with ischemic tissue decay. 5 – 7 2.3 Visualization and simulation The ComprehensivePurkinjeSimulator class generates detailed visualizations to illustrate how ischemia impacts the Purkinje network. It includes 3D spatial plots of the cell layout, conduction velocity histograms, ischemia severity maps, and heatmaps of network connectivity. Additionally, it visualizes refractory period distributions and 2D projections of the cell positions. These individual components are integrated using the create_advanced_visualizations() function, which compiles them into a cohesive, publication-quality figure. This comprehensive visualization approach enhances interpretation of both structural organization and functional alterations within the network. 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. 4.1 Limitations This model currently focuses 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. 4.2 Future work Future work will focus on implementing dynamic action potential propagation, developing anatomically informed connectivity models, and integrating biophysically detailed Purkinje cell models. We also aim to simulate pharmacological interventions and validate model predictions using experimental data from in vitro or in vivo studies. 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. Software availability - Source code available from: https://github.com/laibakhan122/Purkinje-Ischemia-Model - Archived software available from: https://doi.org/10.5281/zenodo.16945221 - License: Apache-2.0 License References 1. Noble D: A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action potential. J. Physiol. 1962; 160 (2): 317–352. PubMed Abstract | Publisher Full Text | Free Full Text 2. Li P, Rudy Y: A model of canine Purkinje cell electrophysiology and Ca2+ cycling. Circ. Res. 2011; 109 (1): 71–79. PubMed Abstract | Publisher Full Text | Free Full Text 3. Mohr M, Chambard JM, Ballet V, et al. : Accurate in silico simulation of the rabbit Purkinje fiber electrophysiological assay to facilitate early pharmaceutical cardiosafety assessment: Dream or reality? J. Pharmacol. Toxicol. Methods. 2022; 115 : 107172. Publisher Full Text 4. Melange P, Vigmond EJ, Rinaldi C: Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks. White Rose Research Online. 2017; 33 . Publisher Full Text Reference Source 5. Rayanova NA, Trayanova MB: Modeling cardiac ischemia. Prog. Biophys. Mol. Biol. 2011; 107 (1): 21–31. PubMed Abstract | Publisher Full Text | Free Full Text 6. Seemann G: Cardiac ischemia—insights from computational models. Curr. Cardiol. Rep. 2018; 20 (1): 1–8. Publisher Full Text 7. Corda A, Pagani S, Vergara C: Acute ischaemia and gap junction modulation modify propagation patterns across Purkinje-myocardial junctions. Front. Physiol. 2025; 16 : 1540400. PubMed Abstract | Publisher Full Text | Free Full Text Comments on this article Comments (0) Version 1 VERSION 1 PUBLISHED 18 Sep 2025 ADD YOUR COMMENT Comment Author details Author details 1 Royal Free Hospital, London, England, UK 2 University College London, London, England, UK Laiba Khan Roles: Methodology, Validation, Visualization, Writing – Review & Editing Maham khan Roles: Writing – Review & Editing Nijat Rzayev Roles: Writing – Review & Editing Mahmood Ahmad Roles: Writing – Review & Editing Joanne Lac Roles: Funding Acquisition, Supervision, Validation, Visualization Competing interests No competing interests were disclosed. Grant information The author(s) declared that no grants were involved in supporting this work. Article Versions (1) version 1 Published: 18 Sep 2025, 14:940 https://doi.org/10.12688/f1000research.168245.1 Copyright © 2025 Khan L et al . This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Download Export To Sciwheel Bibtex EndNote ProCite Ref. Manager (RIS) Sente metrics Views Downloads F1000Research - - PubMed Central info_outline Data from PMC are received and updated monthly. - - Citations open_in_new 0 open_in_new 0 open_in_new SEE MORE DETAILS CITE how to cite this article Khan L, khan M, Rzayev N et al. Computational Modeling and Visualization of Ischemic Effects on an Advanced Purkinje Network [version 1; peer review: awaiting peer review] . 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