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Tyree TJ, Murphy P, Rappel WJ. Annihilation dynamics during spiral defect chaos revealed by particle models. CHAOS (WOODBURY, N.Y.) 2024; 34:053131. [PMID: 38787314 PMCID: PMC11141445 DOI: 10.1063/5.0203319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Accepted: 04/30/2024] [Indexed: 05/25/2024]
Abstract
Pair-annihilation events are ubiquitous in a variety of spatially extended systems and are often studied using computationally expensive simulations. Here, we develop an approach in which we simulate the pair-annihilation of spiral wave tips in cardiac models using a computationally efficient particle model. Spiral wave tips are represented as particles with dynamics governed by diffusive behavior and short-ranged attraction. The parameters for diffusion and attraction are obtained by comparing particle motion to the trajectories of spiral wave tips in cardiac models during spiral defect chaos. The particle model reproduces the annihilation rates of the cardiac models and can determine the statistics of spiral wave dynamics, including its mean termination time. We show that increasing the attraction coefficient sharply decreases the mean termination time, making it a possible target for pharmaceutical intervention.
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Affiliation(s)
- Timothy J. Tyree
- Department of Physics, University of California San Diego, San Diego, California 92093, USA
| | - Patrick Murphy
- Department of Mathematics and Statistics, San Jose State University, San Jose, California 95192, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California San Diego, San Diego, California 92093, USA
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Rappel WJ, Baykaner T, Zaman J, Ganesan P, Rogers AJ, Narayan SM. Spatially Conserved Spiral Wave Activity During Human Atrial Fibrillation. Circ Arrhythm Electrophysiol 2024; 17:e012041. [PMID: 38348685 PMCID: PMC10950516 DOI: 10.1161/circep.123.012041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 01/17/2024] [Indexed: 03/21/2024]
Abstract
BACKGROUND Atrial fibrillation is the most common cardiac arrhythmia in the world and increases the risk for stroke and morbidity. During atrial fibrillation, the electric activation fronts are no longer coherently propagating through the tissue and, instead, show rotational activity, consistent with spiral wave activation, focal activity, collision, or partial versions of these spatial patterns. An unexplained phenomenon is that although simulations of cardiac models abundantly demonstrate spiral waves, clinical recordings often show only intermittent spiral wave activity. METHODS In silico data were generated using simulations in which spiral waves were continuously created and annihilated and in simulations in which a spiral wave was intermittently trapped at a heterogeneity. Clinically, spatio-temporal activation maps were constructed using 60 s recordings from a 64 electrode catheter within the atrium of N=34 patients (n=24 persistent atrial fibrillation). The location of clockwise and counterclockwise rotating spiral waves was quantified and all intervals during which these spiral waves were present were determined. For each interval, the angle of rotation as a function of time was computed and used to determine whether the spiral wave returned in step or changed phase at the start of each interval. RESULTS In both simulations, spiral waves did not come back in phase and were out of step." In contrast, spiral waves returned in step in the majority (68%; P=0.05) of patients. Thus, the intermittently observed rotational activity in these patients is due to a temporally and spatially conserved spiral wave and not due to ones that are newly created at the onset of each interval. CONCLUSIONS Intermittency of spiral wave activity represents conserved spiral wave activity of long, but interrupted duration or transient spiral activity, in the majority of patients. This finding could have important ramifications for identifying clinically important forms of atrial fibrillation and in guiding treatment.
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Affiliation(s)
| | - Tina Baykaner
- Department of Medicine, Stanford University, Palo Alto
| | - Junaid Zaman
- Department of Cardiovascular Medicine, University of Southern California, Los Angeles, CA
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Tyree TJ, Murphy P, Rappel WJ. Annihilation dynamics during spiral defect chaos revealed by particle models. ARXIV 2024:arXiv:2402.10308v1. [PMID: 38410644 PMCID: PMC10896354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 02/28/2024]
Abstract
Pair-annihilation events are ubiquitous in a variety of spatially extended systems and are often studied using computationally expensive simulations. Here we develop an approach in which we simulate the pair-annihilation of spiral wave tips in cardiac models using a computationally efficient particle model. Spiral wave tips are represented as particles with dynamics governed by diffusive behavior and short-ranged attraction. The parameters for diffusion and attraction are obtained by comparing particle motion to the trajectories of spiral wave tips in cardiac models during spiral defect chaos. The particle model reproduces the annihilation rates of the cardiac models and can determine the statistics of spiral wave dynamics, including its mean termination time. We show that increasing the attraction coefficient sharply decreases the mean termination time, making it a possible target for pharmaceutical intervention. Many physical systems exhibit annihilation events during which pairs of objects collide and are removed from the system. These events occur in a number of soft-matter and active-matter systems that exhibit spatiotemporal patterning. For example, topological defects in nematic liquid crystals can develop motile topological defects that annihilate when they meet 1,2. Pair-wise annihilation of defects or singularities also plays a role in a number of biological systems. In bacterial biofilms, for instance, imperfect cell alignment results in point-like defects that carry half-integer topological charge and can annihilate in pairs. These topological defects explain the formation of layers and have been proposed as a model for the buckling of biofilms in colonies of nematically ordered cells3,4.
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Affiliation(s)
- Timothy J Tyree
- Department of Physics, University of California, San Diego, CA
| | - Patrick Murphy
- Department of Mathematics and Statistics, San Jose State University, San Jose, CA
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Maciunas K, Snipas M, Kraujalis T, Kraujalienė L, Panfilov AV. The role of the Cx43/Cx45 gap junction voltage gating on wave propagation and arrhythmogenic activity in cardiac tissue. Sci Rep 2023; 13:14863. [PMID: 37684404 PMCID: PMC10491658 DOI: 10.1038/s41598-023-41796-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2023] [Accepted: 08/31/2023] [Indexed: 09/10/2023] Open
Abstract
Gap junctions (GJs) formed of connexin (Cx) protein are the main conduits of electrical signals in the heart. Studies indicate that the transitional zone of the atrioventricular (AV) node contains heterotypic Cx43/Cx45 GJ channels which are highly sensitive to transjunctional voltage (Vj). To investigate the putative role of Vj gating of Cx43/Cx45 channels, we performed electrophysiological recordings in cell cultures and developed a novel mathematical/computational model which, for the first time, combines GJ channel Vj gating with a model of membrane excitability to simulate a spread of electrical pulses in 2D. Our simulation and electrophysiological data show that Vj transients during the spread of cardiac excitation can significantly affect the junctional conductance (gj) of Cx43/Cx45 GJs in a direction- and frequency-dependent manner. Subsequent simulation data indicate that such pulse-rate-dependent regulation of gj may have a physiological role in delaying impulse propagation through the AV node. We have also considered the putative role of the Cx43/Cx45 channel gating during pathological impulse propagation. Our simulation data show that Vj gating-induced changes in gj can cause the drift and subsequent termination of spiral waves of excitation. As a result, the development of fibrillation-like processes was significantly reduced in 2D clusters, which contained Vj-sensitive Cx43/Cx45 channels.
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Affiliation(s)
- Kestutis Maciunas
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
| | - Mindaugas Snipas
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania.
- Department of Mathematical Modelling, Kaunas University of Technology, Kaunas, Lithuania.
| | - Tadas Kraujalis
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
- Department of Applied Informatics, Kaunas University of Technology, Kaunas, Lithuania
| | - Lina Kraujalienė
- Institute of Cardiology, Lithuanian University of Health Sciences, Kaunas, Lithuania
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent, Belgium
- Department of Cardiology, Leiden University Medical Center, Leiden, The Netherlands
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Aron M, Lilienkamp T, Luther S, Parlitz U. Optimising low-energy defibrillation in 2D cardiac tissue with a genetic algorithm. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:1172454. [PMID: 37555132 PMCID: PMC10406519 DOI: 10.3389/fnetp.2023.1172454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Accepted: 06/28/2023] [Indexed: 08/10/2023]
Abstract
Sequences of low-energy electrical pulses can effectively terminate ventricular fibrillation (VF) and avoid the side effects of conventional high-energy electrical defibrillation shocks, including tissue damage, traumatic pain, and worsening of prognosis. However, the systematic optimisation of sequences of low-energy pulses remains a major challenge. Using 2D simulations of homogeneous cardiac tissue and a genetic algorithm, we demonstrate the optimisation of sequences with non-uniform pulse energies and time intervals between consecutive pulses for efficient VF termination. We further identify model-dependent reductions of total pacing energy ranging from ∼4% to ∼80% compared to reference adaptive-deceleration pacing (ADP) protocols of equal success rate (100%).
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Affiliation(s)
- Marcel Aron
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
| | - Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Computational Physics for Life Science, Nuremberg Institute of Technology Georg Simon Ohm, Nuremberg, Germany
| | - Stefan Luther
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Göttingen, Germany
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany
- German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
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Abstract
The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.
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Affiliation(s)
- Wouter-Jan Rappel
- Department of Physics, University of California San Diego, La Jolla, CA 92037
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Steyer J, Lilienkamp T, Luther S, Parlitz U. The role of pulse timing in cardiac defibrillation. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:1007585. [PMID: 36926106 PMCID: PMC10013017 DOI: 10.3389/fnetp.2022.1007585] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2022] [Accepted: 10/28/2022] [Indexed: 01/05/2023]
Abstract
Life-threatening cardiac arrhythmias require immediate defibrillation. For state-of-the-art shock treatments, a high field strength is required to achieve a sufficient success rate for terminating the complex spiral wave (rotor) dynamics underlying cardiac fibrillation. However, such high energy shocks have many adverse side effects due to the large electric currents applied. In this study, we show, using 2D simulations based on the Fenton-Karma model, that also pulses of relatively low energy may terminate the chaotic activity if applied at the right moment in time. In our simplified model for defibrillation, complex spiral waves are terminated by local perturbations corresponding to conductance heterogeneities acting as virtual electrodes in the presence of an external electric field. We demonstrate that time series of the success rate for low energy shocks exhibit pronounced peaks which correspond to short intervals in time during which perturbations aiming at terminating the chaotic fibrillation state are (much) more successful. Thus, the low energy shock regime, although yielding very low temporal average success rates, exhibits moments in time for which success rates are significantly higher than the average value shown in dose-response curves. This feature might be exploited in future defibrillation protocols for achieving high termination success rates with low or medium pulse energies.
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Affiliation(s)
- Joshua Steyer
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.,Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany.,Institute of Biomedical Engineering, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Thomas Lilienkamp
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.,Faculty for Applied Mathematics, Physics, and General Science, Computational Physics for Life Science, Nuremberg Institute of Technology Georg Simon Ohm, Nürnberg, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.,Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany.,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany.,Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Göttingen, Germany
| | - Ulrich Parlitz
- Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.,Institute for the Dynamics of Complex Systems, Georg-August-Universität Göttingen, Göttingen, Germany.,German Center for Cardiovascular Research (DZHK), Partner Site Göttingen, Göttingen, Germany
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