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Pravdin SF, Nezlobinsky TV, Panfilov AV, Dierckx H. High-frequency pacing of scroll waves in a three-dimensional slab model of cardiac tissue. Phys Rev E 2021; 103:042420. [PMID: 34005903 DOI: 10.1103/physreve.103.042420] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Accepted: 04/08/2021] [Indexed: 11/07/2022]
Abstract
Vortices in excitable media underlie dangerous cardiac arrhythmias. One way to eliminate them is by stimulating the excitable medium with a period smaller than the period of the vortex. So far, this phenomenon has been studied mostly for two-dimensional vortices known as spiral waves. Here we present a first study of this phenomenon for three-dimensional vortices, or scroll waves, in a slab. We consider two main types of scroll waves dynamics: with positive filament tension and with negative filament tension and show that such elimination is possible for some values of the period in all cases. However, in the case of negative filament tension for relatively long stimulation periods, three-dimensional instabilities occur and make elimination impossible. We derive equations of motion for the drift of paced filaments and identify a bifurcation parameter that determines whether the filaments orient themselves perpendicular to the impeding wave train or not.
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Affiliation(s)
- Sergei F Pravdin
- Krasovskii Institute of Mathematics and Mechanics, 620108 Ekaterinburg, Russia.,Ural Federal University, HPC Department, 620002 Ekaterinburg, Russia
| | - Timur V Nezlobinsky
- Krasovskii Institute of Mathematics and Mechanics, 620108 Ekaterinburg, Russia.,Ural Federal University, Biomed Laboratory, 620002 Ekaterinburg, Russia.,Ghent University, 9000 Ghent, Belgium
| | - Alexander V Panfilov
- Ural Federal University, Biomed Laboratory, 620002 Ekaterinburg, Russia.,Ghent University, 9000 Ghent, Belgium.,World-Class Research Center "Digital biodesign and personalized healthcare", I.M. Sechenov First Moscow State Medical University, 119146 Moscow, Russia
| | - Hans Dierckx
- KU Leuven Campus Kortrijk-Kulak, Department of Mathematics, Etienne Sabbelaan 53 bus 7657, 8500 Kortrijk, Belgium
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2
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Neuber JU, Varghese F, Pakhomov AG, Zemlin CW. Using Nanosecond Shocks for Cardiac Defibrillation. Bioelectricity 2019; 1:240-246. [PMID: 32685917 DOI: 10.1089/bioe.2019.0030] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
The purpose of this review article is to summarize our current understanding of the efficacy and safety of cardiac defibrillation with nanosecond shocks. Experiments in isolated hearts, using optical mapping of the electrical activity, have demonstrated that nanosecond shocks can defibrillate with lower energies than conventional millisecond shocks. Single defibrillation strength nanosecond shocks do not cause obvious damage, but repeated stimulation leads to deterioration of the hearts. In isolated myocytes, nanosecond pulses can also stimulate at lower energies than at longer pulses and cause less electroporation (propidium uptake). The mechanism is likely electroporation of the plasma membrane. Repeated stimulation leads to distorted calcium gradients.
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Affiliation(s)
- Johanna U Neuber
- Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk, Virginia.,Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia
| | - Frency Varghese
- Department of Medicine, University of Massachusetts Medical School, Worcester, Massachusetts
| | - Andrei G Pakhomov
- Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk, Virginia
| | - Christian W Zemlin
- Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk, Virginia.,Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia
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Otani NF, Wheeler K, Krinsky V, Luther S. Termination of Scroll Waves by Surface Impacts. PHYSICAL REVIEW LETTERS 2019; 123:068102. [PMID: 31491191 PMCID: PMC7381943 DOI: 10.1103/physrevlett.123.068102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2019] [Indexed: 06/10/2023]
Abstract
Three-dimensional scroll waves direct cell movement and gene expression, and induce chaos in the brain and heart. We found an approach to terminate multiple three-dimensional scrolls. A pulse of a properly configured electric field detaches scroll filaments from the surface. They shrink due to filament tension and disappear. Since wave emission from small heterogeneities is not used, this approach requires a much lower electric field. It is not sensitive to the details of the excitable medium. It may affect future studies of low-energy chaos termination in the heart.
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Affiliation(s)
- Niels F. Otani
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - Kayleigh Wheeler
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - Valentin Krinsky
- CNRS, INPHYNI, 1361, route des Lucioles, 06560 Valbonne France
- Max Planck Institute for Dynamics and Self-Organization, Research Group of Biomedical Physics, Am Fassberg, 17, 37077, Göttingen, Germany
| | - Stefan Luther
- Max Planck Institute for Dynamics and Self-Organization, Research Group of Biomedical Physics, Am Fassberg, 17, 37077, Göttingen, Germany
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Lim H, Cun W, Wang Y, Gray RA, Glimm J. The role of conductivity discontinuities in design of cardiac defibrillation. CHAOS (WOODBURY, N.Y.) 2018; 28:013106. [PMID: 29390616 DOI: 10.1063/1.5019367] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Fibrillation is an erratic electrical state of the heart, of rapid twitching rather than organized contractions. Ventricular fibrillation is fatal if not treated promptly. The standard treatment, defibrillation, is a strong electrical shock to reinitialize the electrical dynamics and allow a normal heart beat. Both the normal and the fibrillatory electrical dynamics of the heart are organized into moving wave fronts of changing electrical signals, especially in the transmembrane voltage, which is the potential difference between the cardiac cellular interior and the intracellular region of the heart. In a normal heart beat, the wave front motion is from bottom to top and is accompanied by the release of Ca ions to induce contractions and pump the blood. In a fibrillatory state, these wave fronts are organized into rotating scroll waves, with a centerline known as a filament. Treatment requires altering the electrical state of the heart through an externally applied electrical shock, in a manner that precludes the existence of the filaments and scroll waves. Detailed mechanisms for the success of this treatment are partially understood, and involve local shock-induced changes in the transmembrane potential, known as virtual electrode alterations. These transmembrane alterations are located at boundaries of the cardiac tissue, including blood vessels and the heart chamber wall, where discontinuities in electrical conductivity occur. The primary focus of this paper is the defibrillation shock and the subsequent electrical phenomena it induces. Six partially overlapping causal factors for defibrillation success are identified from the literature. We present evidence in favor of five of these and against one of them. A major conclusion is that a dynamically growing wave front starting at the heart surface appears to play a primary role during defibrillation by critically reducing the volume available to sustain the dynamic motion of scroll waves; in contrast, virtual electrodes occurring at the boundaries of small, isolated blood vessels only cause minor effects. As a consequence, we suggest that the size of the heart (specifically, the surface to volume ratio) is an important defibrillation variable.
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Affiliation(s)
- Hyunkyung Lim
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
| | - Wenjing Cun
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
| | - Yue Wang
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
| | - Richard A Gray
- Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland 20993-0002, USA
| | - James Glimm
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA
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Hornung D, Biktashev VN, Otani NF, Shajahan TK, Baig T, Berg S, Han S, Krinsky VI, Luther S. Mechanisms of vortices termination in the cardiac muscle. ROYAL SOCIETY OPEN SCIENCE 2017; 4:170024. [PMID: 28405398 PMCID: PMC5383855 DOI: 10.1098/rsos.170024] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2017] [Accepted: 02/14/2017] [Indexed: 06/07/2023]
Abstract
We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.
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Affiliation(s)
- D. Hornung
- Max Planck Institute DS, BMPG, Gottingen, Germany
| | | | - N. F. Otani
- Rochester Institute of Technology, Rochester, NY, USA
| | - T. K. Shajahan
- National Institute of Technology Karnataka, Bangalore, India
| | - T. Baig
- Max Planck Institute DS, BMPG, Gottingen, Germany
- Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen
| | - S. Berg
- Max Planck Institute DS, BMPG, Gottingen, Germany
- Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen
| | - S. Han
- Rochester Institute of Technology, Rochester, NY, USA
| | - V. I. Krinsky
- Max Planck Institute DS, BMPG, Gottingen, Germany
- INLN, CNRS, Valbonne, France
| | - S. Luther
- Max Planck Institute DS, BMPG, Gottingen, Germany
- Institute for Nonlinear Dynamics, Georg-August-Universität Göttingen, Am Faßberg 17, 37077 Göttingen
- Department of Pharmacology, University Medical Centre Göttingen, Robert-Koch-Str. 40, 37075 Göttingen, Germany
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Filament Dynamics during Simulated Ventricular Fibrillation in a High-Resolution Rabbit Heart. BIOMED RESEARCH INTERNATIONAL 2015; 2015:720575. [PMID: 26587544 PMCID: PMC4637469 DOI: 10.1155/2015/720575] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2014] [Accepted: 02/06/2015] [Indexed: 11/30/2022]
Abstract
The mechanisms underlying ventricular fibrillation (VF) are not well understood. The electrical activity on the heart surface during VF has been recorded extensively in the experimental setting and in some cases clinically; however, corresponding transmural activation patterns are prohibitively difficult to measure. In this paper, we use a high-resolution biventricular heart model to study three-dimensional electrical activity during fibrillation, focusing on the driving sources of VF: “filaments,” the organising centres of unstable reentrant scroll waves. We show, for the first time, specific 3D filament dynamics during simulated VF in a whole heart geometry that includes fine-scale anatomical structures. Our results suggest that transmural activity is much more complex than what would be expected from surface observations alone. We present examples of complex intramural activity, including filament breakup and reattachment, anchoring to the thin right ventricular apex; rapid transitions among various filament shapes; and filament lengths much greater than wall thickness. We also present evidence for anatomy playing a major role in VF development and coronary vessels and trabeculae influencing filament dynamics. Overall, our results indicate that intramural activity during simulated VF is extraordinarily complex and suggest that further investigation of 3D filaments is necessary to fully comprehend recorded surface patterns.
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Kuklik P, Sanders P, Szumowski L, Żebrowski JJ. Attraction and repulsion of spiral waves by inhomogeneity of conduction anisotropy--a model of spiral wave interaction with electrical remodeling of heart tissue. J Biol Phys 2013; 39:67-80. [PMID: 23860834 PMCID: PMC3532668 DOI: 10.1007/s10867-012-9286-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2012] [Accepted: 09/05/2012] [Indexed: 11/28/2022] Open
Abstract
Various forms of heart disease are associated with remodeling of the heart muscle, which results in a perturbation of cell-to-cell electrical coupling. These perturbations may alter the trajectory of spiral wave drift in the heart muscle. We investigate the effect of spatially extended inhomogeneity of transverse cell coupling on the spiral wave trajectory using a simple active media model. The spiral wave was either attracted or repelled from the center of inhomogeneity as a function of cell excitability and gradient of the cell coupling. High levels of excitability resulted in an attraction of the wave to the center of inhomogeneity, whereas low levels resulted in an escape and termination of the spiral wave. The spiral wave drift velocity was related to the gradient of the coupling and the initial position of the wave. In a diseased heart, a region of altered transverse coupling corresponds with local gap junction remodeling that may be responsible for stabilization-destabilization of spiral waves and hence reflect potentially important targets in the treatment of heart arrhythmias.
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Affiliation(s)
- Pawel Kuklik
- Centre for Heart Rhythm Disorders, Royal Adelaide Hospital, University of Adelaide, Adelaide, Australia.
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Kuklik P, Wong CX, Brooks AG, Zebrowski JJ, Sanders P. Role of spiral wave pinning in inhomogeneous active media in the termination of atrial fibrillation by electrical cardioversion. Comput Biol Med 2010; 40:363-72. [PMID: 20167311 DOI: 10.1016/j.compbiomed.2010.02.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2009] [Revised: 12/28/2009] [Accepted: 02/01/2010] [Indexed: 11/24/2022]
Abstract
Atrial fibrillation is the most common type of arrhythmia to affect humans. One of the treatment modalities for atrial fibrillation is an electrical cardioversion. Electrical cardioversion can result in one of three outcomes: an immediate termination of arrhythmic activity, a delayed termination or unsuccessful termination. The mechanism of delayed termination is unknown. Here we present a model of an atrial fibrillation as a coexistence of several spiral waves pinned to the inhomogeneities in active media. We show that in inhomogeneous system delayed termination can be explained as the unpinning of a spiral wave from inhomogeneities and its termination after collision with the edge of the system.
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Affiliation(s)
- Pawel Kuklik
- Cardiovascular Research Centre, Department of Cardiology, Royal Adelaide Hospital, University of Adelaide, Adelaide, SA 5000, Australia.
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Fleidervish IA, Goldberg Y, Ovsyshcher IE. Bolus injection of acetylcholine terminates atrial fibrillation in rats. Eur J Pharmacol 2007; 579:326-9. [PMID: 18078927 DOI: 10.1016/j.ejphar.2007.11.010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2007] [Revised: 10/24/2007] [Accepted: 11/03/2007] [Indexed: 11/27/2022]
Abstract
It is well established that a tonic increase in the availability of the atrial muscarinic K(+) channels, either by enhanced vagal tone or by steady infusion of a low-dose of cholinergic or adenosine receptor agonists, promotes the genesis of atrial fibrillation. Here, we aimed to test the hypothesis that bolus administration of a muscarinic receptor agonist would destabilize and terminate atrial arrhythmia by uniformly and transiently activating K(+) channels throughout the atria, and that if the agonist was rapidly hydrolysable, it would dissipate before the more tonic, pro-arrhythmic effects could take hold. The episodes of untreated atrial fibrillation, induced in anesthetized rats by programmed electrical stimulation via trans-esophageal bipolar catheter, lasted on average 8.6+/-2.2 min (n=32). Intravenous injection of a model hydrolysable muscarinic agonist, acetylcholine (0.2 mg/kg body weight), converted atrial fibrillation into sinus rhythm within 8.4+/-1.9 s (n=10, P<0.05). The termination of an atrial fibrillation episode was always accompanied by transient bradycardia; the sinus rhythm gradually accelerated and reached pre-atrial fibrillation values within 10-20 s of injection. In conclusion, our evidence indicates that bolus administration of rapidly hydrolysable muscarinic agonist could be an effective way to pharmacologically terminate atrial fibrillation and restore sinus rhythm.
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Affiliation(s)
- Ilya A Fleidervish
- Koret School of Veterinary Medicine, The Hebrew University of Jerusalem, Rehovot, Israel.
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