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Zhao J, Kennelly J, Nalar A, Kulathilaka A, Sharma R, Bai J, Li N, Fedorov VV. Chamber-specific wall thickness features in human atrial fibrillation. Interface Focus 2023; 13:20230044. [PMID: 38106912 PMCID: PMC10722209 DOI: 10.1098/rsfs.2023.0044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2023] [Accepted: 11/15/2023] [Indexed: 12/19/2023] Open
Abstract
Persistent atrial fibrillation (AF) is not effectively treated due to a lack of adequate tools for identifying patient-specific AF substrates. Recent studies revealed that in 30-50% of patients, persistent AF is maintained by localized drivers not only in the left atrium (LA) but also in the right atrium (RA). The chamber-specific atrial wall thickness (AWT) features underlying AF remain elusive, though the important role of AWT in AF is widely acknowledged. We aimed to provide direct evidence of the existence of distinguished RA and LA AWT features underlying AF drivers by analysing functionally and structurally mapped human hearts ex vivo. Coronary-perfused intact human atria (n = 7, 47 ± 14 y.o.; two female) were mapped using panoramic near-infrared optical mapping during pacing-induced AF. Then the hearts were imaged at approximately 170 µm3 resolution by 9.4 T gadolinium-enhanced MRI. The heart was segmented, and 3D AWT throughout atrial chambers was estimated and analysed. Optical mapping identified six localized RA re-entrant drivers in four hearts and four LA drivers in three hearts. All RA AF drivers were anchored to the pectinate muscle junctions with the crista terminalis or atrial walls. The four LA AF drivers were in the posterior LA. RA (n = 4) with AF drivers were thicker with greater AWT variation than RA (n = 3) without drivers (5.4 ± 2.6 mm versus 5.0 ± 2.4 mm, T-test p < 0.05; F-test p < 0.05). Furthermore, AWT in RA driver regions was thicker and varied more than in RA non-driver regions (5.1 ± 2.5 mm versus 4.4 ± 2.2 mm, T-test p < 0.05; F-test p < 0.05). On the other hand, LA (n = 3) with drivers was thinner than the LA (n = 4) without drivers. In particular, LA driver regions were thinner than the rest of LA regions (3.4 ± 1.0 mm versus 4.2 ± 1.0 mm, T-test p < 0.05). This study demonstrates chamber-specific AWT features of AF drivers. In RA, driver regions are thicker and have more variable AWT than non-driver regions. By contrast, LA drivers are thinner than non-drivers. Robust evaluation of patient-specific AWT features should be considered for chamber-specific targeted ablation.
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Affiliation(s)
- Jichao Zhao
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - James Kennelly
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Aaqel Nalar
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Anuradha Kulathilaka
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Roshan Sharma
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Jieyun Bai
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Ning Li
- Department of Physiology and Cell Biology, Bob and Corrine Frick Center for Heart Failure and Arrhythmia, The Ohio State University Wexner Medical Center, Columbus, OH, USA
| | - Vadim V Fedorov
- Department of Physiology and Cell Biology, Bob and Corrine Frick Center for Heart Failure and Arrhythmia, The Ohio State University Wexner Medical Center, Columbus, OH, USA
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2
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Loppini A, Barone A, Gizzi A, Cherubini C, Fenton FH, Filippi S. Thermal effects on cardiac alternans onset and development: A spatiotemporal correlation analysis. Phys Rev E 2021; 103:L040201. [PMID: 34005953 PMCID: PMC8202768 DOI: 10.1103/physreve.103.l040201] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 03/09/2021] [Indexed: 01/08/2023]
Abstract
Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)PREHBM2470-004510.1103/PhysRevE.100.020201] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.
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Affiliation(s)
- Alessandro Loppini
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Alessandro Barone
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
| | - Christian Cherubini
- Department of Science and Technology for Humans and the Environment and ICRA, Campus Bio-Medico University of Rome, 00128 Rome, Italy and International Center for Relativistic Astrophysics Network-ICRANet, 65122 Pescara, Italy
| | - Flavio H. Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia, USA
| | - Simonetta Filippi
- Department of Engineering and ICRA, Campus Bio-Medico University of Rome, 00128 Rome, Italy and International Center for Relativistic Astrophysics Network-ICRANet, 65122 Pescara, Italy
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3
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Loppini A, Gizzi A, Cherubini C, Cherry EM, Fenton FH, Filippi S. Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue. Phys Rev E 2019; 100:020201. [PMID: 31574686 DOI: 10.1103/physreve.100.020201] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Indexed: 06/10/2023]
Abstract
Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20 cm during one-to-one responses and it decreases to a specific value of about 3 cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1 cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.
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Affiliation(s)
- Alessandro Loppini
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
| | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
| | - Christian Cherubini
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
- ICRANet, Piazza delle Repubblica 10, I-65122 Pescara, Italy
| | - Elizabeth M Cherry
- School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332, USA
| | - Simonetta Filippi
- Department of Engineering, Campus Bio-Medico University of Rome, Via A. del Portillo 21, I-00128 Rome, Italy
- ICRANet, Piazza delle Repubblica 10, I-65122 Pescara, Italy
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4
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Gurevich DR, Grigoriev RO. Robust approach for rotor mapping in cardiac tissue. CHAOS (WOODBURY, N.Y.) 2019; 29:053101. [PMID: 31154775 PMCID: PMC6499622 DOI: 10.1063/1.5086936] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2018] [Accepted: 04/10/2019] [Indexed: 06/09/2023]
Abstract
The motion of and interaction between phase singularities that lie at the centers of spiral waves capture many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their position is thus quite important, even if the data are noisy and sparse, as in electrophysiology studies of cardiac arrhythmias, for instance. A recently proposed global topological approach [Marcotte and Grigoriev, Chaos 27, 093936 (2017)] promises to meaningfully improve the quality of the reconstruction compared with traditional, local approaches. Indeed, we found that this approach is capable of handling noise levels exceeding the range of the signal with minimal loss of accuracy. Moreover, it also works successfully with data sampled on sparse grids with spacing comparable to the mean separation between the phase singularities for complex patterns featuring multiple interacting spiral waves.
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Affiliation(s)
- Daniel R Gurevich
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Roman O Grigoriev
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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5
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Dierckx H, Panfilov AV, Verschelde H, Biktashev VN, Biktasheva IV. Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves. Phys Rev E 2019; 99:022217. [PMID: 30934367 DOI: 10.1103/physreve.99.022217] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/09/2023]
Abstract
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.
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Affiliation(s)
- Hans Dierckx
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - A V Panfilov
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
- Laboratory of Computational Biology and Medicine, Ural Federal University, Ekaterinburg 620075, Russia
| | - H Verschelde
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - I V Biktasheva
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
- Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom
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6
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Rossi S, Gaeta S, Griffith BE, Henriquez CS. Muscle Thickness and Curvature Influence Atrial Conduction Velocities. Front Physiol 2018; 9:1344. [PMID: 30420809 PMCID: PMC6215968 DOI: 10.3389/fphys.2018.01344] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Accepted: 09/06/2018] [Indexed: 12/04/2022] Open
Abstract
Electroanatomical mapping is currently used to provide clinicians with information about the electrophysiological state of the heart and to guide interventions like ablation. These maps can be used to identify ectopic triggers of an arrhythmia such as atrial fibrillation (AF) or changes in the conduction velocity (CV) that have been associated with poor cell to cell coupling or fibrosis. Unfortunately, many factors are known to affect CV, including membrane excitability, pacing rate, wavefront curvature, and bath loading, making interpretation challenging. In this work, we show how endocardial conduction velocities are also affected by the geometrical factors of muscle thickness and wall curvature. Using an idealized three-dimensional strand, we show that transverse conductivities and boundary conditions can slow down or speed up signal propagation, depending on the curvature of the muscle tissue. In fact, a planar wavefront that is parallel to a straight line normal to the mid-surface does not remain normal to the mid-surface in a curved domain. We further demonstrate that the conclusions drawn from the idealized test case can be used to explain spatial changes in conduction velocities in a patient-specific reconstruction of the left atrial posterior wall. The simulations suggest that the widespread assumption of treating atrial muscle as a two-dimensional manifold for electrophysiological simulations will not accurately represent the endocardial conduction velocities in regions of the heart thicker than 0.5 mm with significant wall curvature.
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Affiliation(s)
- Simone Rossi
- Cardiovascular Modeling and Simulation Laboratory, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, NC, United States
| | - Stephen Gaeta
- Clinical Cardiac Electrophysiology/Cardiology Division, Duke University Medical Center, Durham, NC, United States
| | - Boyce E. Griffith
- Cardiovascular Modeling and Simulation Laboratory, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, NC, United States
- Departments of Mathematics, Applied Physical Sciences, and Biomedical Engineering, University of North Carolina, Chapel Hill, NC, United States
- McAllister Heart Institute, University of North Carolina, Chapel Hill, NC, United States
| | - Craig S. Henriquez
- Department of Biomedical Engineering, Pratt School of Engineering, Duke University, Durham, NC, United States
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7
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Roy A, Varela M, Aslanidi O. Image-Based Computational Evaluation of the Effects of Atrial Wall Thickness and Fibrosis on Re-entrant Drivers for Atrial Fibrillation. Front Physiol 2018; 9:1352. [PMID: 30349483 PMCID: PMC6187302 DOI: 10.3389/fphys.2018.01352] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2018] [Accepted: 09/06/2018] [Indexed: 12/19/2022] Open
Abstract
Introduction: Catheter ablation (CA) is a common treatment for atrial fibrillation (AF), but the knowledge of optimal ablation sites, and hence clinical outcomes, are suboptimal. Increasing evidence suggest that ablation strategies based on patient-specific substrates information, such as distributions of fibrosis and atrial wall thickness (AWT), may be used to improve therapy. We hypothesized that competing influences of large AWT gradients and fibrotic patches on conductive properties of atrial tissue can determine locations of re-entrant drivers (RDs) sustaining AF. Methods: Two sets of models were used: (1) a simple model of 3D atrial tissue slab with a step change in AWT and a synthetic fibrosis patch, and (2) 3D models based on patient-specific right atrial (RA) and left atrial (LA) geometries. The latter were obtained from four healthy volunteers and two AF patients, respectively, using magnetic resonance imaging (MRI). A synthetic fibrotic patch was added in the RA and fibrosis distributions in the LA were obtained from gadolinium-enhanced MRI of the same patients. In all models, 3D geometry was combined with the Fenton-Karma atrial cell model to simulate RDs. Results: In the slab, RDs drifted toward, and then along the AWT step. However, with additional fibrosis, the RDs were localized in regions between the step and fibrosis. In the RA, RDs drifted toward and anchored to a large AWT gradient between the crista terminalis (CT) region and the surrounding atrial wall. Without such a gradient, RDs drifted toward the superior vena cava (SVC) or the tricuspid valve (TSV). With additional fibrosis, RDs initiated away from the CT anchored to the fibrotic patch, whereas RDs initiated close to the CT region remained localized between the two structures. In the LA, AWT was more uniform and RDs drifted toward the pulmonary veins (PVs). However, with additional fibrotic patches, RDs either anchored to them or multiplied. Conclusion: In the RA, RD locations are determined by both fibrosis and AWT gradients at the CT region. In the LA, they are determined by fibrosis due to the absence of large AWT gradients. These results elucidate mechanisms behind the stabilization of RDs sustaining AF and can help guide ablation therapy.
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Affiliation(s)
| | | | - Oleg Aslanidi
- Department of Biomedical Engineering, School of Biomedical Engineering & Imaging Sciences, King’s College London, King’s Health Partners, St Thomas’ Hospital, London, United Kingdom
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8
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Loewe A, Dössel O. Commentary: Virtual In-Silico Modeling Guided Catheter Ablation Predicts Effective Linear Ablation Lesion Set for Longstanding Persistent Atrial Fibrillation: Multicenter Prospective Randomized Study. Front Physiol 2018; 8:1113. [PMID: 29313849 PMCID: PMC5744431 DOI: 10.3389/fphys.2017.01113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2017] [Accepted: 12/15/2017] [Indexed: 11/13/2022] Open
Affiliation(s)
- Axel Loewe
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Olaf Dössel
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
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9
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Dierckx H, Biktasheva IV, Verschelde H, Panfilov AV, Biktashev VN. Filament Tension and Phase Locking of Meandering Scroll Waves. PHYSICAL REVIEW LETTERS 2017; 119:258101. [PMID: 29303350 DOI: 10.1103/physrevlett.119.258101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2017] [Indexed: 06/07/2023]
Abstract
Meandering spiral waves are often observed in excitable media such as the Belousov-Zhabotinsky reaction and cardiac tissue. We derive a theory for drift dynamics of meandering rotors in general reaction-diffusion systems and apply it to two types of external disturbances: an external field and curvature-induced drift in three dimensions. We find two distinct regimes: with small filament curvature, meandering scroll waves exhibit filament tension, whose sign determines the stability and drift direction. In the regimes of strong external fields or meandering motion close to resonance, however, phase locking of the meander pattern is predicted and observed.
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Affiliation(s)
- Hans Dierckx
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - I V Biktasheva
- Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - H Verschelde
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - A V Panfilov
- Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
| | - V N Biktashev
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
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10
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Gizzi A, Loppini A, Ruiz-Baier R, Ippolito A, Camassa A, La Camera A, Emmi E, Di Perna L, Garofalo V, Cherubini C, Filippi S. Nonlinear diffusion and thermo-electric coupling in a two-variable model of cardiac action potential. CHAOS (WOODBURY, N.Y.) 2017; 27:093919. [PMID: 28964112 DOI: 10.1063/1.4999610] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
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Affiliation(s)
- A Gizzi
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - A Loppini
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - R Ruiz-Baier
- Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG Oxford, United Kingdom
| | - A Ippolito
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - A Camassa
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - A La Camera
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - E Emmi
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - L Di Perna
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - V Garofalo
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - C Cherubini
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
| | - S Filippi
- Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy
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Song JS, Wi J, Lee HJ, Hwang M, Lim B, Kim TH, Uhm J, Joung B, Lee M, Seo JW, Pak HN. Role of atrial wall thickness in wave-dynamics of atrial fibrillation. PLoS One 2017; 12:e0182174. [PMID: 28827810 PMCID: PMC5565105 DOI: 10.1371/journal.pone.0182174] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Accepted: 07/13/2017] [Indexed: 01/13/2023] Open
Abstract
Background/Aims Atrial anatomy and thickness may affect the electrical wave-dynamics of atrial fibrillation (AF). We explored the relationship between left atrial (LA) wall thickness (LAWT) or LA geometry and AF wave-dynamics. Methods We included 15 patients with persistent AF (age, 62.3 ± 11.9 years) who underwent AF catheter ablation. We measured the LAWT, LA endocardial curvature, and SD-curvature (surface bumpiness) from preprocedural computed tomography images. We compared those anatomical characteristics with electrophysiologic parameters such as dominant frequency (DF), Shannon entropy (ShEn), or complex fractionated atrial electrogram (CFAE)-cycle length (CL), calculated from intracardiac bipolar electrograms (300–500 points, 5 s), acquired during ablation procedures. Results 1. LAWT (excluding fat) varied widely among patients, locations, and types of AF. LAWT was inversely correlated with LA volume (r = -0.565, p = 0.028) and positively correlated with SD-curvature (r = 0.272, p < 0.001). 2. LAWT was positively correlated with ShEn (r = 0.233, p < 0.001) and negatively correlated with CFAE-CL (r = -0.107, p = 0.038). 3. In the multivariate linear regression analyses for AF wave-dynamics parameters, DF (β = -0.29 [95% CI -0.44–-0.14], p < 0.001), ShEn (β = 0.19 [95% CI 0.12–0.25], p < 0.001), and CFAE-CL (β = 7.49 [95% CI 0.65–14.34], p = 0.032) were independently associated with LAWT. Conclusion Regional LAWT is associated with LA structural features, and has significant correlations with the wave-dynamics parameters associated with electrical wavebreaks or rotors in patients with persistent AF.
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Affiliation(s)
- Jun-Seop Song
- Yonsei University Health System, Seoul, Republic of Korea
| | - Jin Wi
- Yonsei University Health System, Seoul, Republic of Korea
| | - Hye-Jeong Lee
- Yonsei University Health System, Seoul, Republic of Korea
| | - Minki Hwang
- Yonsei University Health System, Seoul, Republic of Korea
| | - Byounghyun Lim
- Yonsei University Health System, Seoul, Republic of Korea
| | - Tae-Hoon Kim
- Yonsei University Health System, Seoul, Republic of Korea
| | - Jae‐Sun Uhm
- Yonsei University Health System, Seoul, Republic of Korea
| | - Boyoung Joung
- Yonsei University Health System, Seoul, Republic of Korea
| | | | - Jeong-Wook Seo
- Department of Pathology, Seoul National University College of Medicine, Seoul, Republic of Korea
| | - Hui-Nam Pak
- Yonsei University Health System, Seoul, Republic of Korea
- * E-mail:
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12
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BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology. PLoS One 2017; 12:e0172292. [PMID: 28467407 PMCID: PMC5415003 DOI: 10.1371/journal.pone.0172292] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2016] [Accepted: 02/02/2017] [Indexed: 01/16/2023] Open
Abstract
The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.
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13
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Abstract
We consider reaction-diffusion equations on a thin curved surface and obtain a set of effective reaction-diffusion (R-D) equations to O(ε^{2}), where ε is the surface thickness. We observe that the R-D systems on these curved surfaces can have space-dependent reaction kinetics. Further, we use linear stability analysis to study the Schnakenberg model on spherical and cylindrical geometries. The dependence of the steady state on the thickness is determined for both cases, and we find that a change in the thickness can stabilize the unstable modes, and vice versa. The combined effect of thickness and curvature can play an important role in the rearrangement of spatial patterns on thin curved surfaces.
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Affiliation(s)
- Sankaran Nampoothiri
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016, India
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14
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Ziepke A, Martens S, Engel H. Wave propagation in spatially modulated tubes. J Chem Phys 2016; 145:094108. [DOI: 10.1063/1.4962173] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- A. Ziepke
- Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, Technische Universität Berlin, 10623 Berlin, Germany
| | - S. Martens
- Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, Technische Universität Berlin, 10623 Berlin, Germany
| | - H. Engel
- Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, Technische Universität Berlin, 10623 Berlin, Germany
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15
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Marcotte CD, Grigoriev RO. Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation. CHAOS (WOODBURY, N.Y.) 2016; 26:093107. [PMID: 27781465 DOI: 10.1063/1.4962644] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.
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Affiliation(s)
| | - Roman O Grigoriev
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
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16
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Martens S. Note: From reaction-diffusion systems to confined Brownian motion. J Chem Phys 2016; 145:016101. [PMID: 27394126 DOI: 10.1063/1.4955492] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S Martens
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
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17
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Azhand A, Buchholz R, Totz JF, Engel H. A novel technique to initiate and investigate scroll waves in thin layers of the photosensitive Belousov-Zhabotinsky reaction. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:61. [PMID: 27329535 DOI: 10.1140/epje/i2016-16061-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Revised: 06/07/2016] [Accepted: 06/08/2016] [Indexed: 06/06/2023]
Abstract
While free scroll rings are non-stationary objects that either grow or contract with time, spatial confinement can have a large impact on their evolution reaching from significant lifetime extension (J.F. Totz, H. Engel, O. Steinbock, New J. Phys. 17, 093043 (2015)) up to formation of stable stationary and breathing pacemakers (A. Azhand, J.F. Totz, H. Engel, EPL 108, 10004 (2014)). Here, we explore the parameter range in which the interaction between an axis-symmetric scroll ring and a confining planar no-flux boundary can be studied experimentally in transparent gel layers supporting chemical wave propagation in the photosensitive variant of the Belousov-Zhabotinsky medium. Based on full three-dimensional simulations of the underlying modified complete Oregonator model for experimentally realistic parameters, we determine the conditions for successful initiation of scroll rings in a phase diagram spanned by the layer thickness and the applied light intensity. Furthermore, we discuss whether the illumination-induced excitability gradient due to Lambert-Beer's law as well as a possible inclination of the filament plane with respect to the no-flux boundary can destabilize the scroll ring.
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Affiliation(s)
- Arash Azhand
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623, Berlin, Germany.
| | - Rico Buchholz
- Theoretische Physik V, Universität Bayreuth, Univeristätsstrasse 30, D-95440, Bayreuth, Germany
| | - Jan F Totz
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623, Berlin, Germany
| | - Harald Engel
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623, Berlin, Germany
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Drift of Scroll Wave Filaments in an Anisotropic Model of the Left Ventricle of the Human Heart. BIOMED RESEARCH INTERNATIONAL 2015; 2015:389830. [PMID: 26539486 PMCID: PMC4619794 DOI: 10.1155/2015/389830] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Accepted: 02/12/2015] [Indexed: 11/17/2022]
Abstract
Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias.
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Ke H, Zhang Z, Steinbock O. Scroll wave drift along steps, troughs, and corners. CHAOS (WOODBURY, N.Y.) 2015; 25:064303. [PMID: 26117114 DOI: 10.1063/1.4921718] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Three-dimensional excitable systems can create nonlinear scroll waves that rotate around one-dimensional phase singularities. Recent theoretical work predicts that these filaments drift along step-like height variations. Here, we test this prediction using experiments with thin layers of the Belousov-Zhabotinsky reaction. We observe that over short distances scroll waves are attracted towards the step and then rapidly commence a steady drift along the step line. The translating filaments always reside on the shallow side of the step near the edge. Accordingly, filaments in the deep domain initially collide with and shorten at the step wall. The drift speeds obey the predicted proportional dependence on the logarithm of the height ratio and the direction depends on the vortex chirality. We also observe drift along the perimeter of rectangular plateaus and find that the filaments perform sharp turns at the corners. In addition, we investigate rectangular troughs for which vortices of equal chirality can drift in different directions. The latter two effects are reproduced in numerical simulations with the Barkley model. The simulations show that narrow troughs instigate scroll wave encounters that induce repulsive interaction and symmetry breaking. Similar phenomena could exist in the geometrically complicated ventricles of the human heart where reentrant vortex waves cause tachycardia and fibrillation.
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Affiliation(s)
- Hua Ke
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Zhihui Zhang
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Oliver Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
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