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Ganesan P, Cherry EM, Huang DT, Pertsov AM, Ghoraani B. Atrial fibrillation source area probability mapping using electrogram patterns of multipole catheters. Biomed Eng Online 2020; 19:27. [PMID: 32370754 PMCID: PMC7201756 DOI: 10.1186/s12938-020-00769-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Accepted: 04/15/2020] [Indexed: 01/14/2023] Open
Abstract
BACKGROUND Catheter ablation therapy involving isolation of pulmonary veins (PVs) from the left atrium is performed to terminate atrial fibrillation (AF). Unfortunately, standalone PV isolation procedure has shown to be a suboptimal success with AF continuation or recurrence. One reason, especially in patients with persistent or high-burden paroxysmal AF, is known to be due to the formation of repeating-pattern AF sources with a meandering core inside the atria. However, there is a need for accurate mapping and localization of these sources during catheter ablation. METHODS A novel AF source area probability (ASAP) mapping algorithm was developed and evaluated in 2D and 3D atrial simulated tissues with various arrhythmia scenarios and a retrospective study with three cases of clinical human AF. The ASAP mapping analyzes the electrograms collected from a multipole diagnostic catheter that is commonly used during catheter ablation procedure to intelligently sample the atria and delineate the trajectory path of a meandering repeating-pattern AF source. ASAP starts by placing the diagnostic catheter at an arbitrary location in the atria. It analyzes the recorded bipolar electrograms to build an ASAP map over the atrium anatomy and suggests an optimal location for the subsequent catheter location. ASAP then determines from the constructed ASAP map if an AF source has been delineated. If so, the catheter navigation is stopped and the algorithm provides the area of the AF source. Otherwise, the catheter is navigated to the suggested location, and the process is continued until an AF-source area is delineated. RESULTS ASAP delineated the AF source in over 95% of the simulated human AF cases within less than eight catheter placements regardless of the initial catheter placement. The success of ASAP in the clinical AF was confirmed by the ablation outcomes and the electrogram patterns at the delineated area. CONCLUSION Our analysis indicates the potential of the ASAP mapping to provide accurate information about the area of the meandering repeating-pattern AF sources as AF ablation targets for effective AF termination. Our algorithm could improve the success of AF catheter ablation therapy by locating and subsequently targeting patient-specific and repeating-pattern AF sources inside the atria.
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Affiliation(s)
- Prasanth Ganesan
- Department of Computer and Electrical Engineering, Florida Atlantic University, Boca Raton, FL, USA
| | - Elizabeth M Cherry
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
| | - David T Huang
- Department of Cardiology, University of Rochester Medical Center, Rochester, NY, USA
| | - Arkady M Pertsov
- Department of Pharmacology, SUNY Upstate Medical Center, Syracuse, NY, USA
| | - Behnaz Ghoraani
- Department of Computer and Electrical Engineering, Florida Atlantic University, Boca Raton, FL, USA.
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Li X, Roney CH, Handa BS, Chowdhury RA, Niederer SA, Peters NS, Ng FS. Standardised Framework for Quantitative Analysis of Fibrillation Dynamics. Sci Rep 2019; 9:16671. [PMID: 31723154 PMCID: PMC6853901 DOI: 10.1038/s41598-019-52976-y] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2019] [Accepted: 10/23/2019] [Indexed: 12/21/2022] Open
Abstract
The analysis of complex mechanisms underlying ventricular fibrillation (VF) and atrial fibrillation (AF) requires sophisticated tools for studying spatio-temporal action potential (AP) propagation dynamics. However, fibrillation analysis tools are often custom-made or proprietary, and vary between research groups. With no optimal standardised framework for analysis, results from different studies have led to disparate findings. Given the technical gap, here we present a comprehensive framework and set of principles for quantifying properties of wavefront dynamics in phase-processed data recorded during myocardial fibrillation with potentiometric dyes. Phase transformation of the fibrillatory data is particularly useful for identifying self-perpetuating spiral waves or rotational drivers (RDs) rotating around a phase singularity (PS). RDs have been implicated in sustaining fibrillation, and thus accurate localisation and quantification of RDs is crucial for understanding specific fibrillatory mechanisms. In this work, we assess how variation of analysis parameters and thresholds in the tracking of PSs and quantification of RDs could result in different interpretations of the underlying fibrillation mechanism. These techniques have been described and applied to experimental AF and VF data, and AF simulations, and examples are provided from each of these data sets to demonstrate the range of fibrillatory behaviours and adaptability of these tools. The presented methodologies are available as an open source software and offer an off-the-shelf research toolkit for quantifying and analysing fibrillatory mechanisms.
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Affiliation(s)
- Xinyang Li
- National Heart and Lung Institute, Hammersmith Campus, Imperial College London, 72 Du Cane Rd, London, W120UQ, UK
| | - Caroline H Roney
- School of Biomedical Engineering & Imaging Sciences, King's College London, St. Thomas' Hospital, Westminster Bridge Road, London, UK
| | - Balvinder S Handa
- National Heart and Lung Institute, Hammersmith Campus, Imperial College London, 72 Du Cane Rd, London, W120UQ, UK
| | - Rasheda A Chowdhury
- National Heart and Lung Institute, Hammersmith Campus, Imperial College London, 72 Du Cane Rd, London, W120UQ, UK
| | - Steven A Niederer
- School of Biomedical Engineering & Imaging Sciences, King's College London, St. Thomas' Hospital, Westminster Bridge Road, London, UK
| | - Nicholas S Peters
- National Heart and Lung Institute, Hammersmith Campus, Imperial College London, 72 Du Cane Rd, London, W120UQ, UK
| | - Fu Siong Ng
- National Heart and Lung Institute, Hammersmith Campus, Imperial College London, 72 Du Cane Rd, London, W120UQ, UK.
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Roney CH, Pashaei A, Meo M, Dubois R, Boyle PM, Trayanova NA, Cochet H, Niederer SA, Vigmond EJ. Universal atrial coordinates applied to visualisation, registration and construction of patient specific meshes. Med Image Anal 2019; 55:65-75. [PMID: 31026761 PMCID: PMC6543067 DOI: 10.1016/j.media.2019.04.004] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 03/07/2019] [Accepted: 04/15/2019] [Indexed: 11/26/2022]
Abstract
We introduce a coordinate system for the atria based on anatomical landmarks. We construct the coordinates from solutions to Laplace’s equation. We demonstrate the mapping of both scalar and vector data between different atria. The coordinate system was used for registration and 2D visualisation of multimodal data. Patient specific meshes with atrial structures and fibre direction were constructed using just five landmark points.
Integrating spatial information about atrial physiology and anatomy in a single patient from multimodal datasets, as well as generalizing these data across patients, requires a common coordinate system. In the atria, this is challenging due to the complexity and variability of the anatomy. We aimed to develop and validate a Universal Atrial Coordinate (UAC) system for the following applications: combination and assessment of multimodal data; comparison of spatial data across patients; 2D visualization; and construction of patient specific geometries to test mechanistic hypotheses. Left and right atrial LGE-MRI data were segmented and meshed. Two coordinates were calculated for each atrium by solving Laplace’s equation, with boundary conditions assigned using five landmark points. The coordinate system was used to map spatial information between atrial meshes, including scalar fields measured using different mapping modalities, and atrial anatomic structures and fibre directions from a reference geometry. Average error in point transfer from a source mesh to a destination mesh and back again was less than 0.1 mm for the left atrium and 0.02 mm for the right atrium. Patient specific meshes were constructed using the coordinate system and phase singularity density maps from arrhythmia simulations were visualised in 2D. In conclusion, we have developed a universal atrial coordinate system allowing automatic registration of imaging and electroanatomic mapping data, 2D visualisation, and patient specific model creation.
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Affiliation(s)
- Caroline H Roney
- School of Biomedical Engineering and Imaging Sciences, King's College London, United Kingdom.
| | - Ali Pashaei
- Institute of Electrophysiology and Heart Modeling (IHU Liryc), Foundation Bordeaux University, Pessac-Bordeaux, France; IMB Bordeaux Institute of Mathematics, University of Bordeaux, 351 cours de la Libération, Talence 33405, France
| | - Marianna Meo
- Institute of Electrophysiology and Heart Modeling (IHU Liryc), Foundation Bordeaux University, Pessac-Bordeaux, France; University of Bordeaux, CRCTB, U1045, Bordeaux, France; INSERM, CRCTB, U1045, Bordeaux, France
| | - Rémi Dubois
- Institute of Electrophysiology and Heart Modeling (IHU Liryc), Foundation Bordeaux University, Pessac-Bordeaux, France; University of Bordeaux, CRCTB, U1045, Bordeaux, France; INSERM, CRCTB, U1045, Bordeaux, France
| | | | | | - Hubert Cochet
- Institute of Electrophysiology and Heart Modeling (IHU Liryc), Foundation Bordeaux University, Pessac-Bordeaux, France
| | - Steven A Niederer
- School of Biomedical Engineering and Imaging Sciences, King's College London, United Kingdom
| | - Edward J Vigmond
- Institute of Electrophysiology and Heart Modeling (IHU Liryc), Foundation Bordeaux University, Pessac-Bordeaux, France; IMB Bordeaux Institute of Mathematics, University of Bordeaux, 351 cours de la Libération, Talence 33405, France
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Roney CH, Whitaker J, Sim I, O'Neill L, Mukherjee RK, Razeghi O, Vigmond EJ, Wright M, O'Neill MD, Williams SE, Niederer SA. A technique for measuring anisotropy in atrial conduction to estimate conduction velocity and atrial fibre direction. Comput Biol Med 2019; 104:278-290. [PMID: 30415767 PMCID: PMC6506689 DOI: 10.1016/j.compbiomed.2018.10.019] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2018] [Revised: 10/17/2018] [Accepted: 10/17/2018] [Indexed: 01/04/2023]
Abstract
BACKGROUND Cardiac conduction properties exhibit large variability, and affect patient-specific arrhythmia mechanisms. However, it is challenging to clinically measure conduction velocity (CV), anisotropy and fibre direction. Our aim is to develop a technique to estimate conduction anisotropy and fibre direction from clinically available electrical recordings. METHODS We developed and validated automated algorithms for estimating cardiac CV anisotropy, from any distribution of recording locations on the atrial surface. The first algorithm is for elliptical wavefront fitting to a single activation map (method 1), which works well close to the pacing location, but decreases in accuracy further from the pacing location (due to spatial heterogeneity in the conductivity and fibre fields). As such, we developed a second methodology for measuring local conduction anisotropy, using data from two or three activation maps (method 2: ellipse fitting to wavefront propagation velocity vectors from multiple activation maps). RESULTS Ellipse fitting to CV vectors from two activation maps (method 2) leads to an improved estimation of longitudinal and transverse CV compared to method 1, but fibre direction estimation is still relatively poor. Using three activation maps with method 2 provides accurate estimation, with approximately 70% of atrial fibres estimated within 20∘. We applied the technique to clinical activation maps to demonstrate the presence of heterogeneous conduction anisotropy, and then tested the effects of this conduction anisotropy on predicted arrhythmia dynamics using computational simulation. CONCLUSIONS We have developed novel algorithms for calculating CV and measuring the direction dependency of atrial activation to estimate atrial fibre direction, without the need for specialised pacing protocols, using clinically available electrical recordings.
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Affiliation(s)
- Caroline H Roney
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom.
| | - John Whitaker
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Iain Sim
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Louisa O'Neill
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Rahul K Mukherjee
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Orod Razeghi
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Edward J Vigmond
- LIRYC Electrophysiology and Heart Modeling Institute, Campus Xavier Arnozan, Avenue du Haut Lévêque, 33600, Pessac, France; Univ. Bordeaux, IMB, UMR 5251, F-33400, Talence, France
| | - Matthew Wright
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Mark D O'Neill
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Steven E Williams
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
| | - Steven A Niederer
- School of Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom
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Roney CH, Ng FS, Debney MT, Eichhorn C, Nachiappan A, Chowdhury RA, Qureshi NA, Cantwell CD, Tweedy JH, Niederer SA, Peters NS, Vigmond EJ. Determinants of new wavefront locations in cholinergic atrial fibrillation. Europace 2018; 20:iii3-iii15. [PMID: 30476057 PMCID: PMC6251188 DOI: 10.1093/europace/euy235] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2018] [Accepted: 10/10/2018] [Indexed: 01/10/2023] Open
Abstract
AIMS Atrial fibrillation (AF) wavefront dynamics are complex and difficult to interpret, contributing to uncertainty about the mechanisms that maintain AF. We aimed to investigate the interplay between rotors, wavelets, and focal sources during fibrillation. METHODS AND RESULTS Arrhythmia wavefront dynamics were analysed for four optically mapped canine cholinergic AF preparations. A bilayer computer model was tuned to experimental preparations, and varied to have (i) fibrosis in both layers or the epicardium only, (ii) different spatial acetylcholine distributions, (iii) different intrinsic action potential duration between layers, and (iv) varied interlayer connectivity. Phase singularities (PSs) were identified and tracked over time to identify rotational drivers. New focal wavefronts were identified using phase contours. Phase singularity density and new wavefront locations were calculated during AF. There was a single dominant mechanism for sustaining AF in each of the preparations, either a rotational driver or repetitive new focal wavefronts. High-density PS sites existed preferentially around the pulmonary vein junctions. Three of the four preparations exhibited stable preferential sites of new wavefronts. Computational simulations predict that only a small number of connections are functionally important in sustaining AF, with new wavefront locations determined by the interplay between fibrosis distribution, acetylcholine concentration, and heterogeneity in repolarization within layers. CONCLUSION We were able to identify preferential sites of new wavefront initiation and rotational activity, in order to determine the mechanisms sustaining AF. Electrical measurements should be interpreted differently according to whether they are endocardial or epicardial recordings.
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Affiliation(s)
- Caroline H Roney
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
- LIRYC Electrophysiology and Heart Modeling Institute, Bordeaux Fondation, Avenue du Haut-Lévèque, Pessac, France
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Fu Siong Ng
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Michael T Debney
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Christian Eichhorn
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Arun Nachiappan
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Rasheda A Chowdhury
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Norman A Qureshi
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Chris D Cantwell
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Jennifer H Tweedy
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Steven A Niederer
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - Nicholas S Peters
- ElectroCardioMaths Programme, Imperial Centre for Cardiac Engineering, Imperial College London, London, UK
| | - Edward J Vigmond
- LIRYC Electrophysiology and Heart Modeling Institute, Bordeaux Fondation, Avenue du Haut-Lévèque, Pessac, France
- Univ. Bordeaux, IMB UMR 5251, F-33400 Talence, France
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Roney CH, Cantwell CD, Qureshi NA, Chowdhury RA, Dupont E, Lim PB, Vigmond EJ, Tweedy JH, Ng FS, Peters NS. Rotor Tracking Using Phase of Electrograms Recorded During Atrial Fibrillation. Ann Biomed Eng 2017; 45:910-923. [PMID: 27921187 PMCID: PMC5362653 DOI: 10.1007/s10439-016-1766-4] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Accepted: 11/08/2016] [Indexed: 11/25/2022]
Abstract
Extracellular electrograms recorded during atrial fibrillation (AF) are challenging to interpret due to the inherent beat-to-beat variability in amplitude and duration. Phase mapping represents these voltage signals in terms of relative position within the cycle, and has been widely applied to action potential and unipolar electrogram data of myocardial fibrillation. To date, however, it has not been applied to bipolar recordings, which are commonly acquired clinically. The purpose of this study is to present a novel algorithm for calculating phase from both unipolar and bipolar electrograms recorded during AF. A sequence of signal filters and processing steps are used to calculate phase from simulated, experimental, and clinical, unipolar and bipolar electrograms. The algorithm is validated against action potential phase using simulated data (trajectory centre error <0.8 mm); between experimental multi-electrode array unipolar and bipolar phase; and for wavefront identification in clinical atrial tachycardia. For clinical AF, similar rotational content (R 2 = 0.79) and propagation maps (median correlation 0.73) were measured using either unipolar or bipolar recordings. The algorithm is robust, uses standard signal processing techniques, and accurately quantifies AF wavefronts and sources. Identifying critical sources, such as rotors, in AF, may allow for more accurate targeting of ablation therapy and improved patient outcomes.
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Affiliation(s)
- Caroline H Roney
- Department of Bioengineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK
- IHU Liryc, Electrophysiology and Heart Modeling Institute, fondation Bordeaux Université, F-33600, Pessac-Bordeaux, France
| | - Chris D Cantwell
- Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.
| | - Norman A Qureshi
- National Heart and Lung Institute, Imperial College London, 4th floor Imperial Centre for Translational and Experimental Medicine, Hammersmith Campus, Du Cane Road, London, W12 0NN, UK
| | - Rasheda A Chowdhury
- National Heart and Lung Institute, Imperial College London, 4th floor Imperial Centre for Translational and Experimental Medicine, Hammersmith Campus, Du Cane Road, London, W12 0NN, UK
| | - Emmanuel Dupont
- National Heart and Lung Institute, Imperial College London, 4th floor Imperial Centre for Translational and Experimental Medicine, Hammersmith Campus, Du Cane Road, London, W12 0NN, UK
| | - Phang Boon Lim
- National Heart and Lung Institute, Imperial College London, 4th floor Imperial Centre for Translational and Experimental Medicine, Hammersmith Campus, Du Cane Road, London, W12 0NN, UK
| | - Edward J Vigmond
- IHU Liryc, Electrophysiology and Heart Modeling Institute, fondation Bordeaux Université, F-33600, Pessac-Bordeaux, France
| | - Jennifer H Tweedy
- Department of Bioengineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK
| | - Fu Siong Ng
- National Heart and Lung Institute, Imperial College London, 4th floor Imperial Centre for Translational and Experimental Medicine, Hammersmith Campus, Du Cane Road, London, W12 0NN, UK
| | - Nicholas S Peters
- National Heart and Lung Institute, Imperial College London, 4th floor Imperial Centre for Translational and Experimental Medicine, Hammersmith Campus, Du Cane Road, London, W12 0NN, UK
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Bayer JD, Roney CH, Pashaei A, Jaïs P, Vigmond EJ. Novel Radiofrequency Ablation Strategies for Terminating Atrial Fibrillation in the Left Atrium: A Simulation Study. Front Physiol 2016; 7:108. [PMID: 27148061 PMCID: PMC4828663 DOI: 10.3389/fphys.2016.00108] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Accepted: 03/07/2016] [Indexed: 12/19/2022] Open
Abstract
Pulmonary vein isolation (PVI) with radiofrequency ablation (RFA) is the cornerstone of atrial fibrillation (AF) therapy, but few strategies exist for when it fails. To guide RFA, phase singularity (PS) mapping locates reentrant electrical waves (rotors) that perpetuate AF. The goal of this study was to test existing and develop new RFA strategies for terminating rotors identified with PS mapping. It is unsafe to test experimental RFA strategies in patients, so they were evaluated in silico using a bilayer computer model of the human atria with persistent AF (pAF) electrical (ionic) and structural (fibrosis) remodeling. pAF was initiated by rapidly pacing the right (RSPV) and left (LSPV) superior pulmonary veins during sinus rhythm, and rotor dynamics quantified by PS analysis. Three RFA strategies were studied: (i) PVI, roof, and mitral lines; (ii) circles, perforated circles, lines, and crosses 0.5-1.5 cm in diameter/length administered near rotor locations/pathways identified by PS mapping; and (iii) 4-8 lines streamlining the sequence of electrical activation during sinus rhythm. As in pAF patients, 2 ± 1 rotors with cycle length 185 ± 4 ms and short PS duration 452 ± 401 ms perpetuated simulated pAF. Spatially, PS density had weak to moderate positive correlations with fibrosis density (RSPV: r = 0.38, p = 0.35, LSPV: r = 0.77, p = 0.02). RFA PVI, mitral, and roof lines failed to terminate pAF, but RFA perforated circles and lines 1.5 cm in diameter/length terminated meandering rotors from RSPV pacing when placed at locations with high PS density. Similarly, RFA circles, perforated circles, and crosses 1.5 cm in diameter/length terminated stationary rotors from LSPV pacing. The most effective strategy for terminating pAF was to streamline the sequence of activation during sinus rhythm with >4 RFA lines. These results demonstrate that co-localizing 1.5 cm RFA lesions with locations of high PS density is a promising strategy for terminating pAF rotors. For patients immune to PVI, roof, mitral, and PS guided RFA strategies, streamlining patient-specific activation sequences during sinus rhythm is a robust but challenging alternative.
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Affiliation(s)
- Jason D Bayer
- Electrophysiology and Heart Modeling Institute (LIRYC), Bordeaux University FoundationPessac, France; Cardiothoracic Research Center of Bordeaux (Inserm U 1045), University of BordeauxBordeaux, France
| | - Caroline H Roney
- Electrophysiology and Heart Modeling Institute (LIRYC), Bordeaux University FoundationPessac, France; Institute of Mathematics of Bordeaux (IMB), University of BordeauxTalence, France
| | - Ali Pashaei
- Electrophysiology and Heart Modeling Institute (LIRYC), Bordeaux University FoundationPessac, France; Institute of Mathematics of Bordeaux (IMB), University of BordeauxTalence, France
| | - Pierre Jaïs
- Electrophysiology and Heart Modeling Institute (LIRYC), Bordeaux University FoundationPessac, France; Cardiothoracic Research Center of Bordeaux (Inserm U 1045), University of BordeauxBordeaux, France; Haut-Lévêque Cardiology Hospital, University Hospital Center (CHU) of BordeauxPessac, France
| | - Edward J Vigmond
- Electrophysiology and Heart Modeling Institute (LIRYC), Bordeaux University FoundationPessac, France; Institute of Mathematics of Bordeaux (IMB), University of BordeauxTalence, France
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