1
|
Erhardt J, Ludwig S, Brock J, Hörning M. Native mechano-regulative matrix properties stabilize alternans dynamics and reduce spiral wave stabilization in cardiac tissue. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1443156. [PMID: 39381499 PMCID: PMC11458432 DOI: 10.3389/fnetp.2024.1443156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/03/2024] [Accepted: 09/09/2024] [Indexed: 10/10/2024]
Abstract
The stability of wave conduction in the heart is strongly related to the proper interplay between the electrophysiological activation and mechanical contraction of myocytes and extracellular matrix (ECM) properties. In this study, we statistically compare bioengineered cardiac tissues cultured on soft hydrogels ( E ≃ 12 kPa) and rigid glass substrates by focusing on the critical threshold of alternans, network-physiological tissue properties, and the formation of stable spiral waves that manifest after wave breakups. For the classification of wave dynamics, we use an improved signal oversampling technique and introduce simple probability maps to identify and visualize spatially concordant and discordant alternans as V- and X-shaped probability distributions. We found that cardiac tissues cultured on ECM-mimicking soft hydrogels show a lower variability of the calcium transient durations among cells in the tissue. This lowers the likelihood of forming stable spiral waves because of the larger dynamical range that tissues can be stably entrained with to form alternans and larger spatial spiral tip movement that increases the chance of self-termination on the tissue boundary. Conclusively, we show that a dysfunction in the excitation-contraction coupling dynamics facilitates life-threatening arrhythmic states such as spiral waves and, thus, highlights the importance of the network-physiological interplay between contractile myocytes and the ECM.
Collapse
Affiliation(s)
| | | | | | - Marcel Hörning
- Institute of Biomaterials and Biomolecular Systems, University of Stuttgart, Stuttgart, Germany
| |
Collapse
|
2
|
Iwamiya S, Ihara K, Nitta G, Sasano T. Atrial Fibrillation and Underlying Structural and Electrophysiological Heterogeneity. Int J Mol Sci 2024; 25:10193. [PMID: 39337682 PMCID: PMC11432636 DOI: 10.3390/ijms251810193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2024] [Revised: 09/16/2024] [Accepted: 09/19/2024] [Indexed: 09/30/2024] Open
Abstract
As atrial fibrillation (AF) progresses from initial paroxysmal episodes to the persistent phase, maintaining sinus rhythm for an extended period through pharmacotherapy and catheter ablation becomes difficult. A major cause of the deteriorated treatment outcome is the atrial structural and electrophysiological heterogeneity, which AF itself can exacerbate. This heterogeneity exists or manifests in various dimensions, including anatomically segmental structural features, the distribution of histological fibrosis and the autonomic nervous system, sarcolemmal ion channels, and electrophysiological properties. All these types of heterogeneity are closely related to the development of AF. Recognizing the heterogeneity provides a valuable approach to comprehending the underlying mechanisms in the complex excitatory patterns of AF and the determining factors that govern the seemingly chaotic propagation. Furthermore, substrate modification based on heterogeneity is a potential therapeutic strategy. This review aims to consolidate the current knowledge on structural and electrophysiological atrial heterogeneity and its relation to the pathogenesis of AF, drawing insights from clinical studies, animal and cell experiments, molecular basis, and computer-based approaches, to advance our understanding of the pathophysiology and management of AF.
Collapse
Affiliation(s)
- Satoshi Iwamiya
- Department of Cardiovascular Medicine, Tokyo Medical and Dental University (TMDU), 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8510, Japan
| | - Kensuke Ihara
- Department of Cardiovascular Medicine, Tokyo Medical and Dental University (TMDU), 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8510, Japan
| | - Giichi Nitta
- Department of Cardiovascular Medicine, Tokyo Medical and Dental University (TMDU), 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8510, Japan
| | - Tetsuo Sasano
- Department of Cardiovascular Medicine, Tokyo Medical and Dental University (TMDU), 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8510, Japan
| |
Collapse
|
3
|
Baranwal T, Lebert J, Christoph J. Dreaming of electrical waves: Generative modeling of cardiac excitation waves using diffusion models. APL MACHINE LEARNING 2024; 2:036113. [PMID: 39364376 PMCID: PMC11446137 DOI: 10.1063/5.0194391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/26/2023] [Accepted: 08/19/2024] [Indexed: 10/05/2024]
Abstract
Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias, such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which describe reaction-diffusion dynamics in excitable media. More recently, data-driven generative modeling has emerged as an alternative to generate spatio-temporal patterns in physical and biological systems. Here, we explore denoising diffusion probabilistic models for the generative modeling of electrical wave patterns in cardiac tissue. We trained diffusion models with simulated electrical wave patterns to be able to generate such wave patterns in unconditional and conditional generation tasks. For instance, we explored the diffusion-based (i) parameter-specific generation, (ii) evolution, and (iii) inpainting of spiral wave dynamics, including reconstructing three-dimensional scroll wave dynamics from superficial two-dimensional measurements. Furthermore, we generated arbitrarily shaped bi-ventricular geometries and simultaneously initiated scroll wave patterns inside these geometries using diffusion. We characterized and compared the diffusion-generated solutions to solutions obtained with corresponding biophysical models and found that diffusion models learn to replicate spiral and scroll wave dynamics so well that they could be used for data-driven modeling of excitation waves in cardiac tissue. For instance, an ensemble of diffusion-generated spiral wave dynamics exhibits similar self-termination statistics as the corresponding ensemble simulated with a biophysical model. However, we also found that diffusion models produce artifacts if training data are lacking, e.g., during self-termination, and "hallucinate" wave patterns when insufficiently constrained.
Collapse
Affiliation(s)
| | - Jan Lebert
- Cardiovascular Research Institute, University of California, San Francisco, San Francisco, California 94158, USA
| | - Jan Christoph
- Author to whom correspondence should be addressed: . URL: http://cardiacvision.ucsf.edu
| |
Collapse
|
4
|
Kiseleva DG, Dzhabrailov VD, Aitova AA, Turchaninova EA, Tsvelaya VA, Kazakova MA, Plyusnina TY, Markin AM. Arrhythmogenic Potential of Myocardial Edema: The Interstitial Osmolality Induces Spiral Waves and Multiple Excitation Wavelets. Biomedicines 2024; 12:1770. [PMID: 39200234 PMCID: PMC11351629 DOI: 10.3390/biomedicines12081770] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2024] [Revised: 08/01/2024] [Accepted: 08/03/2024] [Indexed: 09/02/2024] Open
Abstract
Myocardial edema is a common symptom of pathological processes in the heart, causing aggravation of cardiovascular diseases and leading to irreversible myocardial remodeling. Patient-based studies show that myocardial edema is associated with arrhythmias. Currently, there are no studies that have examined how edema may influence changes in calcium dynamics in the functional syncytium. We performed optical mapping of calcium dynamics on a monolayer of neonatal rat cardiomyocytes with Fluo-4. The osmolality of the solutions was adjusted using the NaCl content. The initial Tyrode solution contained 140 mM NaCl (1T) and the hypoosmotic solutions contained 105 (0.75T) and 70 mM NaCl (0.5T). This study demonstrated a sharp decrease in the calcium wave propagation speed with a decrease in the solution osmolality. The successive decrease in osmolality also showed a transition from a normal wavefront to spiral wave and multiple wavelets of excitation with wave break. Our study demonstrated that, in a cellular model, hypoosmolality and, as a consequence, myocardial edema, could potentially lead to fatal ventricular arrhythmias, which to our knowledge has not been studied before. At 0.75T spiral waves appeared, whereas multiple wavelets of excitation occurred in 0.5T, which had not been recorded previously in a two-dimensional monolayer under conditions of cell edema without changes in the pacing protocol.
Collapse
Affiliation(s)
- Diana G. Kiseleva
- Laboratory of Cellular and Molecular Pathology of Cardiovascular System, Petrovsky National Research Centre of Surgery, 119991 Moscow, Russia;
- Department of Biophysics, Faculty of Biology, Lomonosov Moscow State University, 119991 Moscow, Russia;
| | - Vitalii D. Dzhabrailov
- ITMO University, 191002 Saint-Petersburg, Russia; (V.D.D.); (V.A.T.)
- Moscow Center for Advanced Studies, Kulakova Str. 20, 123592 Moscow, Russia
| | - Aleria A. Aitova
- Moscow Center for Advanced Studies, Kulakova Str. 20, 123592 Moscow, Russia
- M.F. Vladimirsky Moscow Regional Clinical Research Institute, 129110 Moscow, Russia
| | - Elena A. Turchaninova
- ITMO University, 191002 Saint-Petersburg, Russia; (V.D.D.); (V.A.T.)
- Moscow Center for Advanced Studies, Kulakova Str. 20, 123592 Moscow, Russia
| | - Valeriya A. Tsvelaya
- ITMO University, 191002 Saint-Petersburg, Russia; (V.D.D.); (V.A.T.)
- Moscow Center for Advanced Studies, Kulakova Str. 20, 123592 Moscow, Russia
| | - Maria A. Kazakova
- Department of Biophysics, Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia;
| | - Tatiana Yu. Plyusnina
- Department of Biophysics, Faculty of Biology, Lomonosov Moscow State University, 119991 Moscow, Russia;
| | - Alexander M. Markin
- Laboratory of Cellular and Molecular Pathology of Cardiovascular System, Petrovsky National Research Centre of Surgery, 119991 Moscow, Russia;
- Medical Institute, Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University), 117198 Moscow, Russia
| |
Collapse
|
5
|
Zhang Y, Zhang Z, Qu Z. Curvature-mediated source and sink effects on the genesis of premature ventricular complexes in long QT syndrome. Am J Physiol Heart Circ Physiol 2024; 326:H1350-H1365. [PMID: 38551483 PMCID: PMC11380949 DOI: 10.1152/ajpheart.00004.2024] [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: 01/02/2024] [Revised: 03/13/2024] [Accepted: 03/25/2024] [Indexed: 05/08/2024]
Abstract
Premature ventricular complexes (PVCs) are spontaneous excitations occurring in the ventricles of the heart that are associated with ventricular arrhythmias and sudden cardiac death. Under long QT conditions, PVCs can be mediated by repolarization gradient (RG) and early afterdepolarizations (EADs), yet the effects of heterogeneities or geometry of the RG or EAD regions on PVC genesis remain incompletely understood. In this study, we use computer simulation to systematically investigate the effects of the curvature of the RG border region on PVC genesis under long QT conditions. We show that PVCs can be either promoted or suppressed by negative or positive RG border curvature depending on the source and sink conditions. When the origin of oscillation is in the source region and the source is too strong, a positive RG border curvature can promote PVCs by causing the source area to oscillate. When the origin of oscillation is in the sink region, a negative RG border curvature can promote PVCs by causing the sink area to oscillate. Furthermore, EAD-mediated PVCs are also promoted by negative border curvature. We also investigate the effects of wavefront curvature and show that PVCs are promoted by convex but suppressed by concave wavefronts; however, the effect of wavefront curvature is much smaller than that of RG border curvature. In conclusion, besides the increase of RG and occurrence of EADs caused by QT prolongation, the geometry of the RG border plays important roles in PVC genesis, which can greatly increase the risk of arrhythmias in cardiac diseases.NEW & NOTEWORTHY The effects of the curvature or geometry of the repolarization gradient region and wavefront curvature on the genesis of premature ventricular complexes are systematically investigated using computer modeling and simulation. Premature ventricular complexes can be promoted by either positive or negative curvature of the gradient region depending on the source and sink conditions. The underlying mechanisms of the curvature effects are revealed, which provides mechanistic insights into arrhythmogenesis in cardiac diseases.
Collapse
Affiliation(s)
- Yuhao Zhang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, People's Republic of China
| | - Zhaoyang Zhang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, People's Republic of China
| | - Zhilin Qu
- Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, California, United States
| |
Collapse
|
6
|
Hussaini S, Lädke SL, Schröder-Schetelig J, Venkatesan V, Quiñonez Uribe RA, Richter C, Majumder R, Luther S. Dissolution of spiral wave's core using cardiac optogenetics. PLoS Comput Biol 2023; 19:e1011660. [PMID: 38060618 PMCID: PMC10729946 DOI: 10.1371/journal.pcbi.1011660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Revised: 12/19/2023] [Accepted: 11/04/2023] [Indexed: 12/20/2023] Open
Abstract
Rotating spiral waves in the heart are associated with life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation. These arrhythmias are treated by a process called defibrillation, which forces electrical resynchronization of the heart tissue by delivering a single global high-voltage shock directly to the heart. This method leads to immediate termination of spiral waves. However, this may not be the only mechanism underlying successful defibrillation, as certain scenarios have also been reported, where the arrhythmia terminated slowly, over a finite period of time. Here, we investigate the slow termination dynamics of an arrhythmia in optogenetically modified murine cardiac tissue both in silico and ex vivo during global illumination at low light intensities. Optical imaging of an intact mouse heart during a ventricular arrhythmia shows slow termination of the arrhythmia, which is due to action potential prolongation observed during the last rotation of the wave. Our numerical studies show that when the core of a spiral is illuminated, it begins to expand, pushing the spiral arm towards the inexcitable boundary of the domain, leading to termination of the spiral wave. We believe that these fundamental findings lead to a better understanding of arrhythmia dynamics during slow termination, which in turn has implications for the improvement and development of new cardiac defibrillation techniques.
Collapse
Affiliation(s)
- Sayedeh Hussaini
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Germany
| | - Sarah L. Lädke
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Johannes Schröder-Schetelig
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Germany
| | - Vishalini Venkatesan
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
| | - Raúl A. Quiñonez Uribe
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Germany
| | - Claudia Richter
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Germany
- WG Cardiovascular Optogenetics, Lab Animal Science Unit, Leibniz Institute for Primate research, Göttingen, Germany
| | - Rupamanjari Majumder
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Germany
| | - Stefan Luther
- Research Group Biomedical Physics, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- Institute of Pharmacology and Toxicology, University Medical Center Göttingen, Germany
- DZHK (German Center for Cardiovascular Research), Partner Site Göttingen, Germany
- Institute for the Dynamics of Complex Systems, Göttingen University, Germany
| |
Collapse
|
7
|
Zhang Z, Zhang Y, Qu Z. Bistable spiral wave dynamics in electrically excitable media. Phys Rev E 2023; 108:064405. [PMID: 38243532 PMCID: PMC11338078 DOI: 10.1103/physreve.108.064405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 11/13/2023] [Indexed: 01/21/2024]
Abstract
We show that a positive feedback loop between sodium current inactivation and wave-front ramp-up speed causes a saddle-node bifurcation to result in bistable planar and spiral waves in electrically excitable media, in which both slow and fast waves are triggered by different stimulation protocols. Moreover, the two types of spiral wave conduction may interact to give rise to more complex spiral wave dynamics. The transitions between different spiral wave behaviors via saddle-node bifurcation can be a candidate mechanism for transitions widely seen in cardiac arrhythmias and neural diseases.
Collapse
Affiliation(s)
- Zhaoyang Zhang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, China
| | - Yuhao Zhang
- Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo, Zhejiang 315211, China
| | - Zhilin Qu
- Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
| |
Collapse
|
8
|
Song E. Impact of noise on the instability of spiral waves in stochastic 2D mathematical models of human atrial fibrillation. J Biol Phys 2023; 49:521-533. [PMID: 37792115 PMCID: PMC10651617 DOI: 10.1007/s10867-023-09644-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Accepted: 09/08/2023] [Indexed: 10/05/2023] Open
Abstract
Sustained spiral waves, also known as rotors, are pivotal mechanisms in persistent atrial fibrillation (AF). Stochasticity is inevitable in nonlinear biological systems such as the heart; however, it is unclear how noise affects the instability of spiral waves in human AF. This study presents a stochastic two-dimensional mathematical model of human AF and explores how Gaussian white noise affects the instability of spiral waves. In homogeneous tissue models, Gaussian white noise may lead to spiral-wave meandering and wavefront break-up. As the noise intensity increases, the spatial dispersion of phase singularity (PS) points increases. This finding indicates the potential AF-protective effects of cardiac system stochasticity by destabilizing the rotors. By contrast, Gaussian white noise is unlikely to affect the spiral-wave instability in the presence of localized scar or fibrosis regions. The PS points are located at the boundary or inside the scar/fibrosis regions. Localized scar or fibrosis may play a pivotal role in stabilizing spiral waves regardless of the presence of noise. This study suggests that fibrosis and scars are essential for stabilizing the rotors in stochastic mathematical models of AF. Further patient-derived realistic modeling studies are required to confirm the role of scar/fibrosis in AF pathophysiology.
Collapse
Affiliation(s)
- Euijun Song
- Yonsei University College of Medicine, Seoul, Republic of Korea.
- , Gyeonggi, Republic of Korea.
| |
Collapse
|
9
|
Abstract
Cardiac alternans arises from dynamical instabilities in the electrical and calcium cycling systems of the heart, and often precedes ventricular arrhythmias and sudden cardiac death. In this review, we integrate clinical observations with theory and experiment to paint a holistic portrait of cardiac alternans: the underlying mechanisms, arrhythmic manifestations and electrocardiographic signatures. We first summarize the cellular and tissue mechanisms of alternans that have been demonstrated both theoretically and experimentally, including 3 voltage-driven and 2 calcium-driven alternans mechanisms. Based on experimental and simulation results, we describe their relevance to mechanisms of arrhythmogenesis under different disease conditions, and their link to electrocardiographic characteristics of alternans observed in patients. Our major conclusion is that alternans is not only a predictor, but also a causal mechanism of potentially lethal ventricular and atrial arrhythmias across the full spectrum of arrhythmia mechanisms that culminate in functional reentry, although less important for anatomic reentry and focal arrhythmias.
Collapse
Affiliation(s)
- Zhilin Qu
- Departments of Medicine (Cardiology), Physiology, and Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA
| | - James N. Weiss
- Departments of Medicine (Cardiology), Physiology, and Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA
| |
Collapse
|
10
|
He YJ, Xia YX, Mei JT, Zhou K, Jiang C, Pan JT, Zheng D, Zheng B, Zhang H. Topological charge-density-vector method of identifying filaments of scroll waves. Phys Rev E 2023; 107:014217. [PMID: 36797968 DOI: 10.1103/physreve.107.014217] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Scroll waves have been found in a variety of three-dimensional excitable media, including physical, chemical, and biological origins. Scroll waves in cardiac tissue are of particular significance as they underlie ventricular fibrillation that can cause sudden death. The behavior of a scroll wave is characterized by a line of phase singularity at its organizing center, known as a filament. A thorough investigation into the filament dynamics is the key to further exploration of the general theory of scroll waves in excitable media and the mechanisms of ventricular fibrillation. In this paper, we propose a method to identify filaments of scroll waves in excitable media. From the definition of the topological charge of filaments, we obtain the discrete expression of the topological charge-density vector, which is useful in calculating the topological charge vectors at each grid in the space directly. The set of starting points of these topological charge vectors represents a set of phase singularities, thereby forming a line of phase singularity, that is, a filament of a scroll wave.
Collapse
Affiliation(s)
- Yin-Jie He
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Yuan-Xun Xia
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Jin-Tao Mei
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Kuangshi Zhou
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Chenyang Jiang
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Dafang Zheng
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Bo Zheng
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
- School of Physics and Astronomy, Yunnan University, Kunming 650091, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics, School of Physics, Zhejiang University, Hangzhou 310058, China
| |
Collapse
|
11
|
Pravdin SF, Patrakeev MA, Panfilov AV. Meander pattern of spiral wave and the spatial distribution of its cycle length. Phys Rev E 2023; 107:014215. [PMID: 36797919 DOI: 10.1103/physreve.107.014215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 01/06/2023] [Indexed: 01/27/2023]
Abstract
One of the most interesting dynamics of rotating spiral waves in an excitable medium is meandering. The tip of a meandering spiral wave moves along a complex trajectory, which often takes the shape of an epitrochoid or hypotrochoid with inward or outward petals. The cycle lengths (CLs) of a meandering spiral wave are not constant; rather, they depend on the meandering dynamics. In this paper, we show that the CLs take two mean values, outside T^{out} and inside T^{in} the meandering trajectory with a ratio of T^{in}/T^{out}=(n+1)/n for the inward and (n-1)/n for the outward petals, where n is the number of petals in the tip trajectory. We illustrate this using four models of excitable media and prove this result. These formulas are shown to be suitable for a meandering spiral wave in an anatomical model of the heart. We also show that the effective periods of overdrive pacing of meandering spiral waves depend on the electrode location relative to the tip trajectory. Overall, our approach can be used to study the meandering pattern from the CL data; it should work for any type of dynamics that produces complex tip trajectories of the spiral wave, for example, for a drift due to heterogeneity.
Collapse
Affiliation(s)
- Sergei F Pravdin
- Krasovskii Institute of Mathematics and Mechanics, 620108 Ekaterinburg, Russia and Ural Federal University, High-Performance Computing Department, 620002 Ekaterinburg, Russia
| | - Mikhail A Patrakeev
- Krasovskii Institute of Mathematics and Mechanics, 620108 Ekaterinburg, Russia and Ural Federal University, Mathematical Analysis Department, 620002 Ekaterinburg, Russia
| | - Alexander V Panfilov
- Ural Federal University, Research Laboratory "Mathematical Modeling in Physiology and Medicine Based on Supercomputers", 620002 Ekaterinburg, Russia and World-Class Research Center "Digital biodesign and personalized healthcare", Sechenov University, 119146 Moscow, Russia
| |
Collapse
|
12
|
Oknińska M, Mączewski M, Mackiewicz U. Ventricular arrhythmias in acute myocardial ischaemia-Focus on the ageing and sex. Ageing Res Rev 2022; 81:101722. [PMID: 36038114 DOI: 10.1016/j.arr.2022.101722] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 08/17/2022] [Accepted: 08/20/2022] [Indexed: 01/31/2023]
Abstract
Annually, approximately 17 million people die from cardiovascular diseases worldwide, half of them suddenly. The most common direct cause of sudden cardiac death is ventricular arrhythmia triggered by an acute coronary syndrome (ACS). The study summarizes the knowledge of the mechanisms of arrhythmia onset during ACS in humans and in animal models and factors that may influence the susceptibility to life-threatening arrhythmias during ACS with particular focus on the age and sex. The real impact of age and sex on the arrhythmic susceptibility within the setting of acute ischaemia is masked by the fact that ACSs result from coronary artery disease appearing with age much earlier among men than among women. However, results of researches show that in ageing process changes with potential pro-arrhythmic significance, such as increased fibrosis, cardiomyocyte hypertrophy, decrease number of gap junction channels, disturbances of the intracellular Ca2+ signalling or changes in electrophysiological parameters, occur independently of the development of cardiovascular diseases and are more severe in male individuals. A review of the literature also indicates a marked paucity of research in this area in female and elderly individuals. Greater awareness of sex differences in the aging process could help in the development of personalized prevention methods targeting potential pro-arrhythmic factors in patients of both sexes to reduce mortality during the acute phase of myocardial infarction. This is especially important in an era of aging populations in which women will predominate due to their longer lifespan.
Collapse
Affiliation(s)
- Marta Oknińska
- Department of Clinical Physiology, Centre of Postgraduate Medical Education, Marymoncka 99/103, 01-813 Warsaw, Poland
| | - Michał Mączewski
- Department of Clinical Physiology, Centre of Postgraduate Medical Education, Marymoncka 99/103, 01-813 Warsaw, Poland
| | - Urszula Mackiewicz
- Department of Clinical Physiology, Centre of Postgraduate Medical Education, Marymoncka 99/103, 01-813 Warsaw, Poland.
| |
Collapse
|
13
|
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.
Collapse
Affiliation(s)
- Wouter-Jan Rappel
- Department of Physics, University of California San Diego, La Jolla, CA 92037
| |
Collapse
|
14
|
Feng X, Yin X, Wen J, Wu H, Gao X. Removal of spiral turbulence by virtual electrodes through the use of a circularly polarized electric field. CHAOS (WOODBURY, N.Y.) 2022; 32:093145. [PMID: 36182381 DOI: 10.1063/5.0102031] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
Heart disease is the leading cause of death and is often accompanied by cardiac fibrillation. Defibrillation using the virtual electrode effects is a promising alternative compared to using the high-voltage electric shock in the clinic. Our earlier works [S. L. Murphy, K. D. Kochanek, J. Xu, and E. Arias, NCHS Data Brief 427 (2021); R. A. Gray, A. M. Pertsov, and J. Jalife, Nature 392, 75-78 (1998); F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, Nature 392, 78-82 (1998); M. Santini, C. Pandozi, G. Altamura, G. Gentilucci, M. Villani, M. C. Scianaro, A. Castro, F. Ammirati, and B. Magris, J. Interv. Card. Electrophysiol. 3, 45-51 (1999).] prove that, compared with other external electric fields, a low voltage circularly polarized electric field is more efficient in turning non-excitable defects in cardiac tissue into virtual electrodes. It, therefore, needs lower voltage to stimulate the excitation waves and causes less harm to reset the spiral turbulence of cardiac excitation for defibrillation. In this paper, we investigate the virtual electrode effect of multiple defects by the circularly polarized electric field for the removal of spiral turbulence. Considering different shapes, sizes, and distributions of multiple defects, we reveal the phase locking of stimulated excitations around multiple virtual electrodes. Furthermore, the circularly polarized electric field parameters are optimized to remove the spiral turbulence.
Collapse
Affiliation(s)
- Xia Feng
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - XunLi Yin
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - JunQing Wen
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - Hua Wu
- Faculty of Science, Xi'an Shiyou University, Xi'an 710065, China
| | - Xiang Gao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| |
Collapse
|
15
|
Influence of a circular obstacle on the dynamics of stable spiral waves with straining. Sci Rep 2022; 12:14479. [PMID: 36008513 PMCID: PMC9411171 DOI: 10.1038/s41598-022-18602-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2022] [Accepted: 08/16/2022] [Indexed: 11/09/2022] Open
Abstract
The current study envisages to investigate numerically, probably for the first time, the combined effect of a circular obstacle and medium motion on the dynamics of a stable rotating spiral wave. A recently reconstructed spatially fourth and temporally second order accurate, implicit, unconditionally stable high order compact scheme has been employed to carry out simulations of the Oregonator model of excitable media. Apart from studying the effect of the stoichiometric parameter, we provide detailed comparison between the dynamics of spiral waves with and without the circular obstacles in the presence of straining effect. In the process, we also inspect the dynamics of rigidly rotating spiral waves without straining effect in presence of the circular obstacle. The presence of the obstacle was seen to trigger transition to non-periodic motion for a much lower strain rate.
Collapse
|
16
|
Li QH, Xia YX, Xu SX, Song Z, Pan JT, Panfilov AV, Zhang H. Control of spiral waves in optogenetically modified cardiac tissue by periodic optical stimulation. Phys Rev E 2022; 105:044210. [PMID: 35590553 DOI: 10.1103/physreve.105.044210] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 03/30/2022] [Indexed: 06/15/2023]
Abstract
Resonant drift of nonlinear spiral waves occurs in various types of excitable media under periodic stimulation. Recently a novel methodology of optogenetics has emerged, which allows to affect excitability of cardiac cells and tissues by optical stimuli. In this paper we study if resonant drift of spiral waves in the heart can be induced by a homogeneous weak periodic optical stimulation of cardiac tissue. We use a two-variable and a detailed model of cardiac tissue and add description of depolarizing and hyperpolarizing optogenetic ionic currents. We show that weak periodic optical stimulation at a frequency equal to the natural rotation frequency of the spiral wave induces resonant drift for both depolarizing and hyperpolarizing optogenetic currents. We quantify these effects and study how the speed of the drift and its direction depend on the initial conditions. We also derive analytical formulas based on the response function theory which correctly predict the drift velocity and its trajectory. We conclude that optogenetic methodology can be used for control of spiral waves in cardiac tissue and discuss its possible applications.
Collapse
Affiliation(s)
- Qi-Hao Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
- Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518066, China
| | - Yuan-Xun Xia
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Shu-Xiao Xu
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Zhen Song
- Department of Mathematics and Theories, Peng Cheng Laboratory, Shenzhen 518066, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620002, Russia
- World-Class Research Center "Digital biodesign and personalized healthcare," Sechenov University, Moscow 119146, Russia
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| |
Collapse
|
17
|
Tsumoto K, Kurata Y. Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations. Biomolecules 2022; 12:459. [PMID: 35327651 PMCID: PMC8946197 DOI: 10.3390/biom12030459] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 03/09/2022] [Accepted: 03/14/2022] [Indexed: 12/23/2022] Open
Abstract
The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.
Collapse
Affiliation(s)
| | - Yasutaka Kurata
- Department of Physiology II, Kanazawa Medical University, Uchinada 920-0293, Japan;
| |
Collapse
|
18
|
Sutanto H. Individual Contributions of Cardiac Ion Channels on Atrial Repolarization and Reentrant Waves: A Multiscale In-Silico Study. J Cardiovasc Dev Dis 2022; 9:jcdd9010028. [PMID: 35050238 PMCID: PMC8779488 DOI: 10.3390/jcdd9010028] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Revised: 12/28/2021] [Accepted: 01/13/2022] [Indexed: 02/01/2023] Open
Abstract
The excitation, contraction, and relaxation of an atrial cardiomyocyte are maintained by the activation and inactivation of numerous cardiac ion channels. Their collaborative efforts cause time-dependent changes of membrane potential, generating an action potential (AP), which is a surrogate marker of atrial arrhythmias. Recently, computational models of atrial electrophysiology emerged as a modality to investigate arrhythmia mechanisms and to predict the outcome of antiarrhythmic therapies. However, the individual contribution of atrial ion channels on atrial action potential and reentrant arrhythmia is not yet fully understood. Thus, in this multiscale in-silico study, perturbations of individual atrial ionic currents (INa, Ito, ICaL, IKur, IKr, IKs, IK1, INCX and INaK) in two in-silico models of human atrial cardiomyocyte (i.e., Courtemanche-1998 and Grandi-2011) were performed at both cellular and tissue levels. The results show that the inhibition of ICaL and INCX resulted in AP shortening, while the inhibition of IKur, IKr, IKs, IK1 and INaK prolonged AP duration (APD). Particularly, in-silico perturbations (inhibition and upregulation) of IKr and IKs only minorly affected atrial repolarization in the Grandi model. In contrast, in the Courtemanche model, the inhibition of IKr and IKs significantly prolonged APD and vice versa. Additionally, a 50% reduction of Ito density abbreviated APD in the Courtemanche model, while the same perturbation prolonged APD in the Grandi model. Similarly, a strong model dependence was also observed at tissue scale, with an observable IK1-mediated reentry stabilizing effect in the Courtemanche model but not in the Grandi atrial model. Moreover, the Grandi model was highly sensitive to a change on intracellular Ca2+ concentration, promoting a repolarization failure in ICaL upregulation above 150% and facilitating reentrant spiral waves stabilization by ICaL inhibition. Finally, by incorporating the previously published atrial fibrillation (AF)-associated ionic remodeling in the Courtemanche atrial model, in-silico modeling revealed the antiarrhythmic effect of IKr inhibition in both acute and chronic settings. Overall, our multiscale computational study highlights the strong model-dependent effects of ionic perturbations which could affect the model’s accuracy, interpretability, and prediction. This observation also suggests the need for a careful selection of in-silico models of atrial electrophysiology to achieve specific research aims.
Collapse
Affiliation(s)
- Henry Sutanto
- Department of Physiology and Pharmacology, State University of New York (SUNY) Downstate Health Sciences University, Brooklyn, NY 11203, USA;
- Department of Cardiology, CARIM School for Cardiovascular Diseases, Maastricht University, 6229 ER Maastricht, The Netherlands
| |
Collapse
|
19
|
Li QH, Van Nieuwenhuyse E, Xia YX, Pan JT, Duytschaever M, Knecht S, Vandersickel N, Zhou C, Panfilov AV, Zhang H. Finding type and location of the source of cardiac arrhythmias from the averaged flow velocity field using the determinant-trace method. Phys Rev E 2021; 104:064401. [PMID: 35030872 DOI: 10.1103/physreve.104.064401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 11/05/2021] [Indexed: 06/14/2023]
Abstract
Life threatening cardiac arrhythmias result from abnormal propagation of nonlinear electrical excitation waves in the heart. Finding the locations of the sources of these waves remains a challenging problem. This is mainly due to the low spatial resolution of electrode recordings of these waves. Also, these recordings are subjected to noise. In this paper, we develop a different approach: the AFV-DT method based on an averaged flow velocity (AFV) technique adopted from the analysis of optical flows and the determinant-trace (DT) method used for vector field analysis of dynamical systems. This method can find the location and determine all important types of sources found in excitable media such as focal activity, spiral waves, and waves rotating around obstacles. We test this method on in silico data of various wave excitation patterns obtained using the Luo-Rudy model for cardiac tissue. We show that the method works well for data with low spatial resolutions (up to 8×8) and is stable against noise. Finally, we apply it to two clinical cases and show that it can correctly identify the arrhythmia type and location. We discuss further steps on the development and improvement of this approach.
Collapse
Affiliation(s)
- Qi-Hao Li
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | | | - Yuan-Xun Xia
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | | | | | - Nele Vandersickel
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
| | - Changsong Zhou
- Department of Physics, Zhejiang University, Hangzhou 310027, China
- Department of Physics, Centre for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Research Centre, HKBU Institute of Research and Continuing Education, Shenzhen 518057, China
- Beijing Computational Science Research Center, Beijing 100084, China
| | - Alexander V Panfilov
- Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620002, Russia
- World-Class Research Center "Digital biodesign and personalized healthcare," Sechenov University, Moscow 119146, Russia
| | - Hong Zhang
- Department of Physics, Zhejiang University, Hangzhou 310027, China
| |
Collapse
|
20
|
He YJ, Li QH, Zhou K, Jiang R, Jiang C, Pan JT, Zheng D, Zheng B, Zhang H. Topological charge-density method of identifying phase singularities in cardiac fibrillation. Phys Rev E 2021; 104:014213. [PMID: 34412332 DOI: 10.1103/physreve.104.014213] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 06/28/2021] [Indexed: 11/07/2022]
Abstract
Spiral waves represent the key motifs of typical self-sustained dynamical patterns in excitable systems such as cardiac tissue. The motion of phase singularities (PSs) that lies at the center of spiral waves captures many qualitative and, in some cases, quantitative features of their complex dynamics. Recent clinical studies suggested that ablating the tissue at PS locations may cure atrial fibrillation. Here, we propose a different method to determine the location of PSs. Starting from the definition of the topological charge of spiral waves, we obtain the expression of the topological charge density in a discrete case. With this expression, we can calculate the topological charge at each grid in the space directly, so as to accurately identify the position of PSs.
Collapse
Affiliation(s)
- Yin-Jie He
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Qi-Hao Li
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Kuangshi Zhou
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Ruhong Jiang
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Chenyang Jiang
- Department of Cardiology, Sir Run Run Shaw Hospital, School of Medicine, Zhejiang University, Hangzhou 310016, China
| | - Jun-Ting Pan
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Dafang Zheng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Bo Zheng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China.,School of Physics and Astronomy, Yunnan University, Kunming 650091, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| |
Collapse
|
21
|
Pagani S, Manzoni A. Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e3450. [PMID: 33599106 PMCID: PMC8244126 DOI: 10.1002/cnm.3450] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Revised: 02/05/2021] [Accepted: 02/07/2021] [Indexed: 06/12/2023]
Abstract
We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.
Collapse
Affiliation(s)
- Stefano Pagani
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
| | - Andrea Manzoni
- MOX, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
| |
Collapse
|
22
|
Landaw J, Yuan X, Chen PS, Qu Z. The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue. Am J Physiol Heart Circ Physiol 2021; 320:H826-H837. [PMID: 33385322 PMCID: PMC8082802 DOI: 10.1152/ajpheart.00608.2020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Revised: 12/22/2020] [Accepted: 12/22/2020] [Indexed: 11/22/2022]
Abstract
Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup. In this study, we carried out computer simulations of two-dimensional homogeneous tissues using five ventricular action potential models. We show that the transient outward potassium current (Ito), although it is not required, plays a key role in promoting spiral wave breakup in all five models. As the maximum conductance of Ito increases, it first promotes spiral wave breakup and then stabilizes the spiral waves. In the absence of Ito, speeding up the L-type calcium kinetics can prevent spiral wave breakup, however, with the same speedup kinetics, spiral wave breakup can be promoted by increasing Ito. Increasing Ito promotes single-cell dynamical instabilities, including action potential duration alternans and chaos, and increasing Ito further suppresses these action potential dynamics. These cellular properties agree with the observation that increasing Ito first promotes spiral wave breakup and then stabilizes spiral waves in tissue. Implications of our observations to spiral wave dynamics in the real hearts and action potential model improvements are discussed.NEW & NOTEWORTHY Spiral wave breakup manifesting as multiple wavelets is a mechanism of ventricular fibrillation. It has been known that spiral wave breakup in cardiac tissue can be caused by a steeply sloped action potential duration restitution curve, a property mainly determined by the recovery of L-type calcium current. Here, we show that the transient outward potassium current (Ito) is another current that plays a key role in spiral wave breakup, that is, spiral waves can be stable for low and high maximum Ito conductance but breakup occurs for intermediate maximum Ito conductance. Since Ito is present in normal hearts of many species and required for Brugada syndrome, it may play an important role in the spiral wave stability and arrhythmogenesis under both normal condition and Brugada syndrome.
Collapse
Affiliation(s)
- Julian Landaw
- Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, California
- Department of Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, California
| | - Xiaoping Yuan
- Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, California
- Information Engineering School, Hangzhou Dianzi University, Hangzhou, People's Republic of China
| | | | - Zhilin Qu
- Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, California
- Department of Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, California
| |
Collapse
|
23
|
Tomii N, Yamazaki M, Ashihara T, Nakazawa K, Shibata N, Honjo H, Sakuma I. Spatial phase discontinuity at the center of moving cardiac spiral waves. Comput Biol Med 2021; 130:104217. [PMID: 33516959 DOI: 10.1016/j.compbiomed.2021.104217] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Revised: 01/10/2021] [Accepted: 01/10/2021] [Indexed: 11/30/2022]
Abstract
BACKGROUND Precise analysis of cardiac spiral wave (SW) dynamics is essential for effective arrhythmia treatment. Although the phase singularity (PS) point in the spatial phase map has been used to determine the cardiac SW center for decades, quantitative detection algorithms that assume PS as a point fail to trace complex and rapid PS dynamics. Through a detailed analysis of numerical simulations, we examined our hypothesis that a boundary of spatial phase discontinuity induced by a focal conduction block exists around the moving SW center in the phase map. METHOD In a numerical simulation model of a 2D cardiac sheet, three different types of SWs (short wavelength; long wavelength; and low excitability) were induced by regulating ion channels. Discontinuities of all boundaries among adjacent cells at each instance were evaluated by calculating the phase bipolarity (PB). The total amount of phase transition (PTA) in each cell during the study period was evaluated. RESULTS Pivoting, drifting, and shifting SWs were observed in the short-wavelength, low-excitability, and long-wavelength models, respectively. For both the drifting and shifting cases, long high-PB edges were observed on the SW trajectories. In all cases, the conduction block (CB) was observed at the same boundaries. These were also identical to the boundaries in the PTA maps. CONCLUSIONS The analysis of the simulations revealed that the conduction block at the center of a moving SW induces discontinuous boundaries in spatial phase maps that represent a more appropriate model of the SW center than the PS point.
Collapse
Affiliation(s)
- Naoki Tomii
- Faculty of Medicine, The University of Tokyo, 7 -3-1 Hongo, Bunkyo-ku, Tokyo, 113-8655, Japan.
| | - Masatoshi Yamazaki
- School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
| | - Takashi Ashihara
- Shiga University of Medical Science, Setatsukinowa-cho, Otsu-city, Shiga, 520-2192, Japan
| | - Kazuo Nakazawa
- Morinomiya University of Medical Sciences, 1-26-16 Minami-Kohoku, Suminoe-ku, Osaka City, 559-8611, Japan
| | - Nitaro Shibata
- Shinjuku Mitsui Building Clinic, 2-1-1 Nishi-Shinjuku, Shinjuku-ku, Tokyo, 163-0404, Japan
| | - Haruo Honjo
- Research Institute of Environmental Medicine, Nagoya University, Furo-cho Chikusa-ku, Nagoya City, Aichi, 464-8601, Japan
| | - Ichiro Sakuma
- School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
| |
Collapse
|
24
|
Electrophysiological Effects of Extracellular Vesicles Secreted by Cardiosphere-Derived Cells: Unraveling the Antiarrhythmic Properties of Cell Therapies. Processes (Basel) 2020. [DOI: 10.3390/pr8080924] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Although cell-based therapies show potential antiarrhythmic effects that could be mediated by their paracrine action, the mechanisms and the extent of these effects were not deeply explored. We investigated the antiarrhythmic mechanisms of extracellular vesicles secreted by cardiosphere-derived cell extracellular vesicles (CDC-EVs) on the electrophysiological properties and gene expression profile of HL1 cardiomyocytes. HL-1 cultures were primed with CDC-EVs or serum-free medium alone for 48 h, followed by optical mapping and gene expression analysis. In optical mapping recordings, CDC-EVs reduced the activation complexity of the cardiomyocytes by 40%, increased rotor meandering, and reduced rotor curvature, as well as induced an 80% increase in conduction velocity. HL-1 cells primed with CDC-EVs presented higher expression of SCN5A, CACNA1C, and GJA1, coding for proteins involved in INa, ICaL, and Cx43, respectively. Our results suggest that CDC-EVs reduce activation complexity by increasing conduction velocity and modifying rotor dynamics, which could be driven by an increase in expression of SCN5A and CACNA1C genes, respectively. Our results provide new insights into the antiarrhythmic mechanisms of cell therapies, which should be further validated using other models.
Collapse
|
25
|
Zimik S, Pandit R, Majumder R. Anisotropic shortening in the wavelength of electrical waves promotes onset of electrical turbulence in cardiac tissue: An in silico study. PLoS One 2020; 15:e0230214. [PMID: 32168323 PMCID: PMC7069633 DOI: 10.1371/journal.pone.0230214] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2019] [Accepted: 02/24/2020] [Indexed: 12/03/2022] Open
Abstract
Several pathological conditions introduce spatial variations in the electrical properties of cardiac tissue. These variations occur as localized or distributed gradients in ion-channel functionality over extended tissue media. Electrical waves, propagating through such affected tissue, demonstrate distortions, depending on the nature of the ionic gradient in the diseased substrate. If the degree of distortion is large, reentrant activity may develop, in the form of rotating spiral (2d) and scroll (3d) waves of electrical activity. These reentrant waves are associated with the occurrence of lethal cardiac rhythm disorders, known as arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), which are believed to be common precursors of sudden cardiac arrest. By using state-of-the-art mathematical models for generic, and ionically-realistic (human) cardiac tissue, we study the detrimental effects of these ionic gradients on electrical wave propagation. We propose a possible mechanism for the development of instabilities in reentrant wave patterns, in the presence of ionic gradients in cardiac tissue, which may explain how one type of arrhythmia (VT) can degenerate into another (VF). Our proposed mechanism entails anisotropic reduction in the wavelength of the excitation waves because of anisotropic variation in its electrical properties, in particular the action potential duration (APD). We find that the variation in the APD, which we induce by varying ion-channel conductances, imposes a spatial variation in the spiral- or scroll-wave frequency ω. Such gradients in ω induce anisotropic shortening of wavelength of the spiral or scroll arms and eventually leads to instabilitites.
Collapse
Affiliation(s)
- Soling Zimik
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
| | - Rupamanjari Majumder
- Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
- * E-mail:
| |
Collapse
|
26
|
Lombardo DM, Rappel WJ. Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities. Phys Rev E 2019; 99:062409. [PMID: 31330597 PMCID: PMC7296979 DOI: 10.1103/physreve.99.062409] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Indexed: 11/07/2022]
Abstract
Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation, where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.
Collapse
|
27
|
Abstract
Spatially extended excitable systems can exhibit spiral defect chaos (SDC) during which spiral waves continuously form and disappear. To address how this dynamical state terminates using simulations can be computationally challenging, especially for large systems. To circumvent this limitation, we treat the number of spiral waves as a stochastic population with a corresponding birth-death equation and use techniques from statistical physics to determine the mean episode duration of SDC. Motivated by cardiac fibrillation, during which the heart's electrical activity becomes disorganized and shows fragmenting spiral waves, we use generic models of cardiac electrophysiology. We show that the duration can be computed in minimal computational time and that it depends exponentially on domain size. Therefore, the approach can result in efficient and accurate predictions of mean episode duration which may be extended to more complex geometries and models.
Collapse
Affiliation(s)
- David Vidmar
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
| |
Collapse
|
28
|
Wang W, Zhang S, Ni H, Garratt CJ, Boyett MR, Hancox JC, Zhang H. Mechanistic insight into spontaneous transition from cellular alternans to arrhythmia-A simulation study. PLoS Comput Biol 2018; 14:e1006594. [PMID: 30500818 PMCID: PMC6291170 DOI: 10.1371/journal.pcbi.1006594] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Revised: 12/12/2018] [Accepted: 10/23/2018] [Indexed: 02/01/2023] Open
Abstract
Cardiac electrical alternans (CEA), manifested as T-wave alternans in ECG, is a clinical biomarker for predicting cardiac arrhythmias and sudden death. However, the mechanism underlying the spontaneous transition from CEA to arrhythmias remains incompletely elucidated. In this study, multiscale rabbit ventricular models were used to study the transition and a potential role of INa in perpetuating such a transition. It was shown CEA evolved into either concordant or discordant action potential (AP) conduction alternans in a homogeneous one-dimensional tissue model, depending on tissue AP duration and conduction velocity (CV) restitution properties. Discordant alternans was able to cause conduction failure in the model, which was promoted by impaired sodium channel with either a reduced or increased channel current. In a two-dimensional homogeneous tissue model, a combined effect of rate- and curvature-dependent CV broke-up alternating wavefronts at localised points, facilitating a spontaneous transition from CEA to re-entry. Tissue inhomogeneity or anisotropy further promoted break-up of re-entry, leading to multiple wavelets. Similar observations have also been seen in human atrial cellular and tissue models. In conclusion, our results identify a mechanism by which CEA spontaneously evolves into re-entry without a requirement for premature ventricular complexes or pre-existing tissue heterogeneities, and demonstrated the important pro-arrhythmic role of impaired sodium channel activity. These findings are model-independent and have potential human relevance.
Collapse
Affiliation(s)
- Wei Wang
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Shanzhuo Zhang
- School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China
| | - Haibo Ni
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Clifford J. Garratt
- Manchester Heart Centre, Manchester Royal Infirmary, Manchester, United Kingdom
| | - Mark R. Boyett
- Manchester Heart Centre, Manchester Royal Infirmary, Manchester, United Kingdom
| | - Jules C. Hancox
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom
- School of Physiology, Pharmacology and Neuroscience, and Cardiovascular Research Laboratories, School of Medical Sciences, University of Bristol, Bristol, United Kingdom
| | - Henggui Zhang
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom
- School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China
- Key Laboratory of Medical Electrophysiology of Ministry of Education and Medical Electrophysiological Key Laboratory of Sichuan Province, Institute of Cardiovascular Research, Southwest Medical University, Luzhou, Sichuan, China
- Space Institute of Southern China, Shenzhen, China
| |
Collapse
|
29
|
Hummel JP, Akar JG, Baher A, Webber CL. New skip parameter to facilitate recurrence quantification of signals comprised of multiple components. CHAOS (WOODBURY, N.Y.) 2018; 28:085718. [PMID: 30180597 DOI: 10.1063/1.5024845] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Accepted: 07/26/2018] [Indexed: 06/08/2023]
Abstract
Recurrence analyses are typically performed on discretized time series after applying proper embeddings, delays, and thresholds. In our study of atrial electrograms, we found limitations to this approach when sequential bipolar complexes were defined as the timings of the first two zero crosses following the initiation of each event. The reason for this is that each bipolar component consists of two points in odd-even pairings. Since recurrence analysis starts vectors on each sequential point, incorrect even-odd pairings occur for every other vector. To overcome this limitation, a new parameter SKIP is introduced such that recurrence vectors can skip 1 (or 2) points for signals with defined multiple components. To demonstrate the utility of parameter SKIP, we used the Courtemanche model to simulate the electrical activity in the human atrium on a square, two-dimensional plane with 800 × 800 nodes. Over this plane, a grid of 39 × 39 virtual unipoles was created. Neighboring unipoles formed 39 × 38 bipolar pairs, which were recorded as 1482 continuous and synchronous time series. At each unipolar site, the actual wavefront direction was determined by comparing the relative activation timings of the local intracellular potentials. Parameters were set such that the "tissue" exhibited both spiral waves (organized activity) and wave breakups (chaotic activity). For each bipolar complex in the continuous electrogram, discretized electrogram conformation was defined as the timing delays from the start of the complex to the first two zero-crosses. Long sequences of paired zero-cross timings were subjected to recurrence analysis using SKIP values of 0 (no skipping) and 1 (single skipping). Recurrence variables were computed and correlated with the absolute wavefront directions. The results showed that the introduction of the skipping window improved the correlations of some recurrence variables with absolute wavefront directions. This is critically important because such variables may be better markers for wavefront directions in human recordings when the absolute wavefront directions cannot be calculated directly.
Collapse
Affiliation(s)
- James P Hummel
- Division of Cardiovascular Medicine, University of Wisconsin School of Medicine and Public Health, Madison, Wisconsin 53726, USA
| | - Joseph G Akar
- Section of Cardiovascular Medicine, Department of Medicine, Yale University School of Medicine, New Haven, Connecticut 06510, USA
| | - Alex Baher
- Division of Cardiovascular Medicine, School of Medicine, University of Utah Health, Salt Lake City, Utah 84132, USA
| | - Charles L Webber
- Department of Cell and Molecular Physiology, Loyola University Chicago - Health Sciences Division, Maywood, Illinois 60153, USA
| |
Collapse
|
30
|
Aronis KN, Ashikaga H. Impact of number of co-existing rotors and inter-electrode distance on accuracy of rotor localization. J Electrocardiol 2017; 51:82-91. [PMID: 28988690 DOI: 10.1016/j.jelectrocard.2017.08.032] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2017] [Indexed: 12/01/2022]
Abstract
BACKGROUND Conflicting evidence exists on the efficacy of focal impulse and rotor modulation on atrial fibrillation ablation. A potential explanation is inaccurate rotor localization from multiple rotors coexistence and a relatively large (9-11mm) inter-electrode distance (IED) of the multi-electrode basket catheter. METHODS AND RESULTS We studied a numerical model of cardiac action potential to reproduce one through seven rotors in a two-dimensional lattice. We estimated rotor location using phase singularity, Shannon entropy and dominant frequency. We then spatially downsampled the time series to create IEDs of 2-30mm. The error of rotor localization was measured with reference to the dynamics of phase singularity at the original spatial resolution (IED=1mm). IED has a significant impact on the error using all the methods. When only one rotor is present, the error increases exponentially as a function of IED. At the clinical IED of 10mm, the error is 3.8mm (phase singularity), 3.7mm (dominant frequency), and 11.8mm (Shannon entropy). When there are more than one rotors, the error of rotor localization increases 10-fold. The error based on the phase singularity method at the clinical IED of 10mm ranges from 30.0mm (two rotors) to 96.1mm (five rotors). CONCLUSIONS The magnitude of error of rotor localization using a clinically available basket catheter, in the presence of multiple rotors might be high enough to impact the accuracy of targeting during AF ablation. Improvement of catheter design and development of high-density mapping catheters may improve clinical outcomes of FIRM-guided AF ablation.
Collapse
Affiliation(s)
- Konstantinos N Aronis
- Division of Cardiology, Johns Hopkins University School of Medicine, Baltimore, MD, United States
| | - Hiroshi Ashikaga
- Division of Cardiology, Johns Hopkins University School of Medicine, Baltimore, MD, United States; Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, United States.
| |
Collapse
|
31
|
Krogh-Madsen T, Christini DJ. Slow [Na +] i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model. CHAOS (WOODBURY, N.Y.) 2017; 27:093907. [PMID: 28964146 DOI: 10.1063/1.4999475] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Accumulation of intracellular Na+ is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na+ concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na+ concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na+]i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na+]i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na+]i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na+]i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na+]i may play complex roles in cellular and tissue-level cardiac dynamics.
Collapse
Affiliation(s)
- Trine Krogh-Madsen
- Greenberg Division of Cardiology, Weill Cornell Medicine, New York, New York 10065, USA; Institute for Computational Biomedicine, Weill Cornell Medicine, New York, New York 10065, USA; and Cardiovascular Research Institute, Weill Cornell Medicine, New York, New York 10065, USA
| | - David J Christini
- Greenberg Division of Cardiology, Weill Cornell Medicine, New York, New York 10065, USA; Institute for Computational Biomedicine, Weill Cornell Medicine, New York, New York 10065, USA; and Cardiovascular Research Institute, Weill Cornell Medicine, New York, New York 10065, USA
| |
Collapse
|
32
|
Lombardo DM, Rappel WJ. Systematic reduction of a detailed atrial myocyte model. CHAOS (WOODBURY, N.Y.) 2017; 27:093914. [PMID: 28964163 PMCID: PMC5570595 DOI: 10.1063/1.4999611] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Accepted: 05/01/2017] [Indexed: 05/02/2023]
Abstract
Cardiac arrhythmias are a major health concern and often involve poorly understood mechanisms. Mathematical modeling is able to provide insights into these mechanisms which might result in better treatment options. A key element of this modeling is a description of the electrophysiological properties of cardiac cells. A number of electrophysiological models have been developed, ranging from highly detailed and complex models, containing numerous parameters and variables, to simplified models in which variables and parameters no longer directly correspond to electrophysiological quantities. In this study, we present a systematic reduction of the complexity of the detailed model of Koivumaki et al. using the recently developed manifold boundary approximation method. We reduce the original model, containing 42 variables and 37 parameters, to a model with only 11 variables and 5 parameters and show that this reduced model can accurately reproduce the action potential shape and restitution curve of the original model. The reduced model contains only five currents and all variables and parameters can be directly linked to electrophysiological quantities. Due to its reduction in complexity, simulation times of our model are decreased more than three-fold. Furthermore, fitting the reduced model to clinical data is much more efficient, a potentially important step towards patient-specific modeling.
Collapse
Affiliation(s)
- Daniel M Lombardo
- Department of Physics, University of California, San Diego, California 92903, USA
| | - Wouter-Jan Rappel
- Department of Physics, University of California, San Diego, California 92903, USA
| |
Collapse
|
33
|
Hummel JP, Baher A, Buck B, Fanarjian M, Webber CL, Akar JG. A method for quantifying recurrent patterns of local wavefront direction during atrial fibrillation. Comput Biol Med 2017; 89:497-504. [PMID: 28889077 DOI: 10.1016/j.compbiomed.2017.08.027] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2017] [Revised: 08/24/2017] [Accepted: 08/25/2017] [Indexed: 10/18/2022]
Abstract
INTRODUCTION Spiral wave reentry is a potential mechanism of atrial fibrillation (AF), but is difficult to differentiate clinically from multiple wavelet breakup using standard bipolar recordings. We developed a new methodology using bipolar recordings to estimate the direction of local activation wavefronts during AF by calculating the electrogram conformation (Egm-C). We subsequently used recurrence quantification analysis (RQA) of Egm-C to differentiate regions of spiral wave reentry from wavelet breakup. METHODS A 2D computer simulation was created with regions containing a stable spiral wave and also regions of wavebreak. A grid of 40 × 40 unipolar electrodes was superimposed. At each site, the actual wavefront direction (WD) was determined by comparing relative activation timings of the local intracellular recordings, and the estimated wavefront direction (Egm-C) was determined from the morphology of the local bipolar electrogram. RQA of Egm-C was compared to RQA of actual WD in order to differentiate AF mechanisms. RESULTS RQA of actual WD and Egm-C both distinguished regions of spiral wave reentry from wavelet breakup with high correlation between the two methods (recurrence rate, r = 0.96; determinism, r = 0.61; line max, r = 0.95; entropy, r = 0.84; p < 0.001 for all). In areas of stable spiral wave reentry, the recurrence plots of both Egm-C and actual WD demonstrated stable, periodic dynamics, while regions of wavelet breakup demonstrated chaotic behavior largely devoid of repetitive activation patterns. CONCLUSION Calculation of Egm-C allows RQA to be performed on bipolar electrograms during AF and differentiates regions of spiral wave reentry from multiple wavelet breakup.
Collapse
Affiliation(s)
- James P Hummel
- Division of Cardiology, University of North Carolina, Chapel Hill, NC, USA.
| | - Alex Baher
- The Section of Cardiovascular Medicine, Department of Medicine, Yale University School of Medicine, New Haven, CT, USA
| | - Ben Buck
- Division of Cardiology, University of North Carolina, Chapel Hill, NC, USA
| | - Manuel Fanarjian
- Division of Cardiology, University of North Carolina, Chapel Hill, NC, USA
| | - Charles L Webber
- Department of Cell and Molecular Physiology, Loyola University Chicago - Health Sciences Division, Maywood, IL, USA
| | - Joseph G Akar
- The Section of Cardiovascular Medicine, Department of Medicine, Yale University School of Medicine, New Haven, CT, USA
| |
Collapse
|
34
|
Modeling Atrial Fibrillation using Human Embryonic Stem Cell-Derived Atrial Tissue. Sci Rep 2017; 7:5268. [PMID: 28706272 PMCID: PMC5509676 DOI: 10.1038/s41598-017-05652-y] [Citation(s) in RCA: 51] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2017] [Accepted: 06/01/2017] [Indexed: 12/31/2022] Open
Abstract
Since current experimental models of Atrial Fibrillation (AF) have significant limitations, we used human embryonic stem cells (hESCs) to generate an atrial-specific tissue model of AF for pharmacologic testing. We generated atrial-like cardiomyocytes (CMs) from hESCs which preferentially expressed atrial-specific genes, and had shorter action potential (AP) durations compared to ventricular-like CMs. We then generated confluent atrial-like CM sheets and interrogated them using optical mapping techniques. Atrial-like CM sheets (~1 cm in diameter) showed uniform AP propagation, and rapid re-entrant rotor patterns, as seen in AF could be induced. Anti-arrhythmic drugs were tested on single atrial-like CMs and cell sheets. Flecainide profoundly slowed upstroke velocity without affecting AP duration, leading to reduced conduction velocities (CVs), curvatures and cycle lengths of rotors, consistent with increased rotor organization and expansion. By contrast, consistent with block of rapid delayed rectifier K+ currents (Ikr) and AP prolongation in isolated atrial-like CMs, dofetilide prolonged APs and reduced cycle lengths of rotors in cell sheets without affecting CV. In conclusion, using our hESC-derived atrial CM preparations, we demonstrate that flecainide and dofetilide modulate reentrant arrhythmogenic rotor activation patterns in a manner that helps explain their efficacy in treating and preventing AF.
Collapse
|
35
|
Karagueuzian HS, Pezhouman A, Angelini M, Olcese R. Enhanced Late Na and Ca Currents as Effective Antiarrhythmic Drug Targets. Front Pharmacol 2017; 8:36. [PMID: 28220073 PMCID: PMC5292429 DOI: 10.3389/fphar.2017.00036] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2016] [Accepted: 01/18/2017] [Indexed: 11/30/2022] Open
Abstract
While recent advances clarified the molecular and cellular modes of action of antiarrhythmic drugs (AADs), their link to suppression of dynamical arrhythmia mechanisms remains only partially understood. The current classifications of AADs (Classes I, III, and IV) rely on blocking peak Na, K and L-type calcium currents (ICa,L), with Class II with dominant beta receptor blocking activity and Class V including drugs with diverse classes of actions. The discovery that the calcium and redox sensor, cardiac Ca/calmodulin-dependent protein kinase II (CaMKII) enhances both the late Na (INa-L) and the late ICa,L in patients at high risk of VT/VF provided a new and a rational AAD target. Pathological rise of either or both of INa-L and late ICa,L are demonstrated to promote cellular early afterdepolarizations (EADs) and EAD-mediated triggered activity that can initiate VT/VF in remodeled hearts. Selective inhibition of the INa-L without affecting their peak transients with the highly specific prototype drug, GS-967 suppresses these EAD-mediated VT/VFs. As in the case of INa-L, selective inhibition of the late ICa,L without affecting its peak with the prototype drug, roscovitine suppressed oxidative EAD-mediated VT/VF. These findings indicate that specific blockers of the late inward currents without affecting their peaks (gating modifiers), offer a new and effective AAD class action i.e., “Class VI.” The development of safe drugs with selective Class VI actions provides a rational and effective approach to treat VT/VF particularly in cardiac conditions associated with enhanced CaMKII activity such as heart failure.
Collapse
Affiliation(s)
- Hrayr S Karagueuzian
- Translational Arrhythmia Section, David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA; Cardiovascular Research Laboratory, Departments of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA
| | - Arash Pezhouman
- Translational Arrhythmia Section, David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA; Cardiovascular Research Laboratory, Departments of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA
| | - Marina Angelini
- Department of Anesthesiology and Perioperative Medicine, David Geffen School of Medicine, University of California, Los Angeles Los Angeles, CA, USA
| | - Riccardo Olcese
- Cardiovascular Research Laboratory, Departments of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA; Department of Anesthesiology and Perioperative Medicine, David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA; Department of Physiology, David Geffen School of Medicine, University of California, Los AngelesLos Angeles, CA, USA
| |
Collapse
|
36
|
Wu F, Wang C, Xu Y, Ma J. Model of electrical activity in cardiac tissue under electromagnetic induction. Sci Rep 2016; 6:28. [PMID: 28442705 PMCID: PMC5431370 DOI: 10.1038/s41598-016-0031-2] [Citation(s) in RCA: 109] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Accepted: 10/31/2016] [Indexed: 11/09/2022] Open
Abstract
Complex electrical activities in cardiac tissue can set up time-varying electromagnetic field. Magnetic flux is introduced into the Fitzhugh-Nagumo model to describe the effect of electromagnetic induction, and then memristor is used to realize the feedback of magnetic flux on the membrane potential in cardiac tissue. It is found that a spiral wave can be triggered and developed by setting specific initials in the media, that is to say, the media still support the survival of standing spiral waves under electromagnetic induction. Furthermore, electromagnetic radiation is considered on this model as external stimuli, it is found that spiral waves encounter breakup and turbulent electrical activities are observed, and it can give guidance to understand the occurrence of sudden heart disorder subjected to heavily electromagnetic radiation.
Collapse
Affiliation(s)
- Fuqiang Wu
- Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China
| | - Chunni Wang
- Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China
| | - Ying Xu
- Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China
| | - Jun Ma
- Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China.
| |
Collapse
|
37
|
Lee YS, Song JS, Hwang M, Lim B, Joung B, Pak HN. A New Efficient Method for Detecting Phase Singularity in Cardiac Fibrillation. PLoS One 2016; 11:e0167567. [PMID: 27907144 PMCID: PMC5131933 DOI: 10.1371/journal.pone.0167567] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Accepted: 11/16/2016] [Indexed: 12/31/2022] Open
Abstract
Background The point of phase singularity (PS) is considered to represent a spiral wave core or a rotor in cardiac fibrillation. Computational efficiency is important for detection of PS in clinical electrophysiology. We developed a novel algorithm for highly efficient and robust detection of PS. Methods In contrast to the conventional method, which calculates PS based on the line integral of the phase around a PS point equal to ±2π (the Iyer-Gray method), the proposed algorithm (the location-centric method) looks for the phase discontinuity point at which PS actually occurs. We tested the efficiency and robustness of these two methods in a two-dimensional mathematical model of atrial fibrillation (AF), with and without remodeling of ionic currents. Results 1. There was a significant association, in terms of the Hausdorff distance (3.30 ± 0.0 mm), between the PS points measured using the Iyer-Gray and location-centric methods, with almost identical PS trajectories generated by the two methods. 2. For the condition of electrical remodeling of AF (0.3 × ICaL), the PS points calculated by the two methods were satisfactorily co-localized (with the Hausdorff distance of 1.64 ± 0.09 mm). 3. The proposed location-centric method was substantially more efficient than the Iyer-Gray method, with a 28.6-fold and 28.2-fold shorter run times for the control and remodeling scenarios, respectively. Conclusion We propose a new location-centric method for calculating PS, which is robust and more efficient compared with the conventionally used method.
Collapse
Affiliation(s)
| | | | - Minki Hwang
- Yonsei University Health System, Seoul, Korea
| | | | | | - Hui-Nam Pak
- Yonsei University Health System, Seoul, Korea
- * E-mail:
| |
Collapse
|
38
|
Alonso S, Bär M, Echebarria B. Nonlinear physics of electrical wave propagation in the heart: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:096601. [PMID: 27517161 DOI: 10.1088/0034-4885/79/9/096601] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.
Collapse
Affiliation(s)
- Sergio Alonso
- Physikalisch-Technische Bundesanstalt, Abbestr. 2-12 10587, Berlin, Germany. Department of Physics, Universitat Politècnica de Catalunya, Av. Dr. Marañón 44, E-08028 Barcelona, Spain
| | | | | |
Collapse
|
39
|
Weiss JN, Qu Z, Shivkumar K. Ablating atrial fibrillation: A translational science perspective for clinicians. Heart Rhythm 2016; 13:1868-77. [PMID: 27241354 PMCID: PMC4996702 DOI: 10.1016/j.hrthm.2016.05.026] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/12/2016] [Indexed: 12/22/2022]
Abstract
Although considerable progress has been made in developing ablation approaches to cure atrial fibrillation (AF), outcomes are still suboptimal, especially for persistent and long-lasting persistent AF. In this topical review, we review the arrhythmia mechanisms, both reentrant and nonreentrant, that are potentially relevant to human AF at various stages/settings. We describe arrhythmia mapping techniques used to distinguish between the different mechanisms, with a particular focus on the detection of rotors. We discuss which arrhythmia mechanisms are likely to respond to ablation, and the challenges and prospects for improving upon current ablation strategies to achieve better outcomes.
Collapse
Affiliation(s)
| | - Zhilin Qu
- UCLA Cardiovascular Research Laboratory
| | - Kalyanam Shivkumar
- Cardiac Arrhythmia Center & Neurocardiology Research Center of Excellence, Departments of Medicine (Cardiology) and Physiology, David Geffen School of Medicine, University of California, Los Angeles, California
| |
Collapse
|
40
|
Seenivasan P, Easwaran S, Sridhar S, Sinha S. Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models. Front Physiol 2016; 6:390. [PMID: 26793114 PMCID: PMC4707587 DOI: 10.3389/fphys.2015.00390] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Accepted: 11/30/2015] [Indexed: 11/13/2022] Open
Abstract
Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.
Collapse
Affiliation(s)
- Pavithraa Seenivasan
- Theoretical Physics Group, The Institute of Mathematical Sciences Chennai, India
| | - Soumya Easwaran
- Theoretical Physics Group, The Institute of Mathematical Sciences Chennai, India
| | - Seshan Sridhar
- Theoretical Physics Group, The Institute of Mathematical SciencesChennai, India; Scimergent Analytics and Education Pvt Ltd.Chennai, India
| | - Sitabhra Sinha
- Theoretical Physics Group, The Institute of Mathematical Sciences Chennai, India
| |
Collapse
|
41
|
Connolly A, Trew ML, Smaill BH, Plank G, Bishop MJ. Local Gradients in Electrotonic Loading Modulate the Local Effective Refractory Period: Implications for Arrhythmogenesis in the Infarct Border Zone. IEEE Trans Biomed Eng 2015; 62:2251-2259. [PMID: 25872206 PMCID: PMC5395087 DOI: 10.1109/tbme.2015.2421296] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Ectopic electrical activity that originates in the peri-infarct region can give rise to potentially lethal re-entrant arrhythmias. The spatial variation in electrotonic loading that results from structural remodelling in the infarct border zone may increase the probability that focal activity will trigger electrical capture, but this has not previously been investigated systematically. This study uses in-silico experiments to examine the structural modulation of effective refractory period on ectopic beat capture. Informed by 3-D reconstructions of myocyte organization in the infarct border zone, a region of rapid tissue expansion is abstracted to an idealized representation. A novel metric is introduced that defines the local electrotonic loading as a function of passive tissue properties and boundary conditions. The effective refractory period correlates closely with local electrotonic loading, while the action potential duration, conduction, and upstroke velocity reduce in regions of increasing electrotonic load. In the presence of focal ectopic stimuli, spatial variation in effective refractory period can cause unidirectional conduction block providing a substrate for reentrant arrhythmias. Consequently, based on the observed results, a possible novel mechanism for arrhythmogenesis in the infarct border zone is proposed.
Collapse
Affiliation(s)
- Adam Connolly
- Department of Biomedical Engineering, Kings College London, London WC2R 2LS, U.K
| | - Mark L. Trew
- Auckland Bioengineering Institute, University of Auckland
| | | | - Gernot Plank
- Institute of Biophysics, Medical University of Graz
| | - Martin J. Bishop
- Department of Biomedical Engineering, Kings College London, London WC2R 2LS, U.K
| |
Collapse
|
42
|
Feng X, Gao X, Tang JM, Pan JT, Zhang H. Wave trains induced by circularly polarized electric fields in cardiac tissues. Sci Rep 2015; 5:13349. [PMID: 26302781 PMCID: PMC4548189 DOI: 10.1038/srep13349] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Accepted: 07/22/2015] [Indexed: 11/28/2022] Open
Abstract
Clinically, cardiac fibrillation caused by spiral and turbulent waves can be terminated by globally resetting electric activity in cardiac tissues with a single high-voltage electric shock, but it is usually associated with severe side effects. Presently, a promising alternative uses wave emission from heterogeneities induced by a sequence of low-voltage uniform electric field pulses. Nevertheless, this method can only emit waves locally near obstacles in turbulent waves and thereby requires multiple obstacles to globally synchronize myocardium and thus to terminate fibrillation. Here we propose a new approach using wave emission from heterogeneities induced by a low-voltage circularly polarized electric field (i.e., a rotating uniform electric field). We find that, this approach can generate circular wave trains near obstacles and they propagate outwardly. We study the characteristics of such circular wave trains and further find that, the higher-frequency circular wave trains can effectively suppress spiral turbulence.
Collapse
Affiliation(s)
- Xia Feng
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Xiang Gao
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China.,School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
| | - Juan-Mei Tang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jun-Ting Pan
- Institute of Physical Oceanography and Ocean College, Zhejiang University, Hangzhou 310058, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| |
Collapse
|
43
|
Ashikaga H, Aguilar-Rodríguez J, Gorsky S, Lusczek E, Marquitti FMD, Thompson B, Wu D, Garland J. Modelling the heart as a communication system. J R Soc Interface 2015; 12:20141201. [PMID: 25740854 PMCID: PMC4387519 DOI: 10.1098/rsif.2014.1201] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2014] [Accepted: 02/11/2015] [Indexed: 12/14/2022] Open
Abstract
Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in two-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.
Collapse
Affiliation(s)
- Hiroshi Ashikaga
- Division of Cardiology, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - José Aguilar-Rodríguez
- Institute of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland Swiss Institute of Bioinformatics, Lausanne, Switzerland
| | - Shai Gorsky
- Department of Economics, University of Utah, Salt Lake City, UT, USA
| | - Elizabeth Lusczek
- Department of Surgery, University of Minnesota, Minneapolis, MN, USA
| | | | | | - Degang Wu
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, HKSAR, China
| | - Joshua Garland
- Department of Computer Science, University of Colorado, Boulder, CO, USA
| |
Collapse
|
44
|
Ganesan AN, Kuklik P, Gharaviri A, Brooks A, Chapman D, Lau DH, Roberts-Thomson KC, Sanders P. Origin and characteristics of high Shannon entropy at the pivot of locally stable rotors: insights from computational simulation. PLoS One 2014; 9:e110662. [PMID: 25401331 PMCID: PMC4234245 DOI: 10.1371/journal.pone.0110662] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2014] [Accepted: 09/19/2014] [Indexed: 11/18/2022] Open
Abstract
Background Rotors are postulated to maintain cardiac fibrillation. Despite the importance of bipolar electrograms in clinical electrophysiology, few data exist on the properties of bipolar electrograms at rotor sites. The pivot of a spiral wave is characterized by relative uncertainty of wavefront propagation direction compared to the periphery. The bipolar electrograms used in electrophysiology recording encode information on both direction and timing of approaching wavefronts. Objective To test the hypothesis that bipolar electrograms from the pivot of rotors have higher Shannon entropy (ShEn) than electrograms recorded at the periphery due to the spatial dynamics of spiral waves. Methods and Results We studied spiral wave propagation in 2-dimensional sheets constructed using a simple cell automaton (FitzHugh-Nagumo), atrial (Courtemanche-Ramirez-Nattel) and ventricular (Luo-Rudy) myocyte cell models and in a geometric model spiral wave. In each system, bipolar electrogram recordings were simulated, and Shannon entropy maps constructed as a measure of electrogram information content. ShEn was consistently highest in the pivoting region associated with the phase singularity of the spiral wave. This property was consistently preserved across; (i) variation of model system (ii) alterations in bipolar electrode spacing, (iii) alternative bipolar electrode orientation (iv) bipolar electrogram filtering and (v) in the presence of rotor meander. Directional activation plots demonstrated that the origin of high ShEn at the pivot was the directional diversity of wavefront propagation observed in this location. Conclusions The pivot of the rotor is consistently associated with high Shannon entropy of bipolar electrograms despite differences in action potential model, bipolar electrode spacing, signal filtering and rotor meander. Maximum ShEn is co-located with the pivot for rotors observed in the bipolar electrogram recording mode, and may be an intrinsic property of spiral wave dynamic behaviour.
Collapse
Affiliation(s)
- Anand N. Ganesan
- Centre for Heart Rhythm Disorders (CHRD), South Australian Health and Medical Research Institute (SAHMRI), University of Adelaide and Royal Adelaide Hospital, Adelaide, Australia
- * E-mail:
| | - Pawel Kuklik
- Department of Physiology, Maastricht University Medical Center, Maastricht, The Netherlands
- Department of Cardiology, Electrophysiology, University Heart Center, Hamburg, Germany
| | - Ali Gharaviri
- Department of Physiology, Maastricht University Medical Center, Maastricht, The Netherlands
| | - Anthony Brooks
- Centre for Heart Rhythm Disorders (CHRD), South Australian Health and Medical Research Institute (SAHMRI), University of Adelaide and Royal Adelaide Hospital, Adelaide, Australia
| | - Darius Chapman
- Centre for Heart Rhythm Disorders (CHRD), South Australian Health and Medical Research Institute (SAHMRI), University of Adelaide and Royal Adelaide Hospital, Adelaide, Australia
| | - Dennis H. Lau
- Centre for Heart Rhythm Disorders (CHRD), South Australian Health and Medical Research Institute (SAHMRI), University of Adelaide and Royal Adelaide Hospital, Adelaide, Australia
| | - Kurt C. Roberts-Thomson
- Centre for Heart Rhythm Disorders (CHRD), South Australian Health and Medical Research Institute (SAHMRI), University of Adelaide and Royal Adelaide Hospital, Adelaide, Australia
| | - Prashanthan Sanders
- Centre for Heart Rhythm Disorders (CHRD), South Australian Health and Medical Research Institute (SAHMRI), University of Adelaide and Royal Adelaide Hospital, Adelaide, Australia
| |
Collapse
|
45
|
Qu Z, Weiss JN. Mechanisms of ventricular arrhythmias: from molecular fluctuations to electrical turbulence. Annu Rev Physiol 2014; 77:29-55. [PMID: 25340965 DOI: 10.1146/annurev-physiol-021014-071622] [Citation(s) in RCA: 75] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Ventricular arrhythmias have complex causes and mechanisms. Despite extensive investigation involving many clinical, experimental, and computational studies, effective biological therapeutics are still very limited. In this article, we review our current understanding of the mechanisms of ventricular arrhythmias by summarizing the state of knowledge spanning from the molecular scale to electrical wave behavior at the tissue and organ scales and how the complex nonlinear interactions integrate into the dynamics of arrhythmias in the heart. We discuss the challenges that we face in synthesizing these dynamics to develop safe and effective novel therapeutic approaches.
Collapse
Affiliation(s)
- Zhilin Qu
- Departments of 1Medicine (Cardiology) and
| | | |
Collapse
|
46
|
Abstract
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.
Collapse
Affiliation(s)
- Zhilin Qu
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Correspondence to: Zhilin Qu, PhD, Department of Medicine, Division of Cardiology, David Geffen School of Medicine at UCLA, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095, Tel: 310-794-6050, Fax: 310-206-9133,
| | - Gang Hu
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Alan Garfinkel
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Integrative Biology and Physiology, University of California, Los Angeles, California 90095, USA
| | - James N. Weiss
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
- Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
| |
Collapse
|
47
|
Nayak AR, Pandit R. Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation. Front Physiol 2014; 5:207. [PMID: 24959148 PMCID: PMC4050366 DOI: 10.3389/fphys.2014.00207] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2013] [Accepted: 05/14/2014] [Indexed: 11/20/2022] Open
Abstract
We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity θ and the wavelength λ of a plane wave; we show that PD leads to a periodic, spatial modulation of θ and a temporally periodic modulation of λ; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNP04 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNP04 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.
Collapse
Affiliation(s)
- Alok R. Nayak
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of ScienceBangalore, India
- Robert Bosch Centre for Cyber Physical Systems, Indian Institute of ScienceBangalore, India
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of ScienceBangalore, India
- Jawaharlal Nehru Centre for Advanced Scientific ResearchBangalore, India
| |
Collapse
|
48
|
Cai MC, Pan JT, Zhang H. Core solutions of rigidly rotating spiral waves in highly excitable media. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022920. [PMID: 25353558 DOI: 10.1103/physreve.89.022920] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 06/04/2023]
Abstract
Analytical spiral wave solutions for reaction-diffusion equations play an important role in studying spiral wave dynamics. In this paper, we focus on such analytical solutions in the case of highly excitable media. We present numerical evidence that, for rigidly rotating spiral waves in highly excitable media, the species values in the spiral core region do harmonic oscillations but not relaxation ones, and their amplitudes grow linearly with the distance from the rotation center. An analytical solution is proposed to describe such spiral wave dynamics, and the quantitative comparisons between the numerical results and the analytical solutions show that the proposed spiral core solution works well in highly excitable media.
Collapse
Affiliation(s)
- Mei-Chun Cai
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Jun-Ting Pan
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China and Institute of Physical Oceanography and Ocean College, Zhejiang University, Hangzhou 310058, China
| | - Hong Zhang
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China
| |
Collapse
|
49
|
Nayak AR, Shajahan TK, Panfilov AV, Pandit R. Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts. PLoS One 2013; 8:e72950. [PMID: 24023798 PMCID: PMC3762734 DOI: 10.1371/journal.pone.0072950] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2013] [Accepted: 07/15/2013] [Indexed: 11/18/2022] Open
Abstract
Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.
Collapse
Affiliation(s)
- Alok Ranjan Nayak
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
| | - T. K. Shajahan
- Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montreal, Canada
| | - A. V. Panfilov
- Department of Physics and Astronomy, Gent University, Gent, Belgium
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, India
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
- * E-mail:
| |
Collapse
|
50
|
Spector P. Principles of cardiac electric propagation and their implications for re-entrant arrhythmias. Circ Arrhythm Electrophysiol 2013; 6:655-61. [PMID: 23778249 DOI: 10.1161/circep.113.000311] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Affiliation(s)
- Peter Spector
- University of Vermont College of Medicine, Burlington, VT 05401, USA.
| |
Collapse
|