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Spatial and temporal processing of intracardiac electrograms provides relevant information to support the arrhythmia ablation during electrophysiological studies. Current cardiac navigation systems (CNS) and electrocardiographic imaging (ECGI) build detailed 3-D electroanatomical maps (EAM), which represent the spatial anatomical distribution of bioelectrical features, such as activation time or voltage.
We present a principled methodology for spectral analysis of both EAM geometry and bioelectrical feature in CNS or ECGI, including their spectral representation, cutoff frequency, or spatial sampling rate (SSR).
Existing manifold harmonic techniques for spectral mesh analysis are adapted to account for a fourth dimension, corresponding to the EAM bioelectrical feature. Appropriate scaling is required to address different magnitudes and units.
With our approach, simulated and real EAM showed strong SSR dependence on both the arrhythmia mechanism and the cardiac anatomical shape. For instance, high frequencies increased significantly the SSR because of the "early-meets-late" in flutter EAM, compared with the sinus rhythm. Besides, higher frequency components were obtained for the left atrium (more complex anatomy) than for the right atrium in sinus rhythm.
The proposed manifold harmonics methodology opens the field toward new signal processing tools for principled EAM spatiofeature analysis in CNS and ECGI, and to an improved knowledge on arrhythmia mechanisms.
The most common sustained cardiac arrhythmias in humans are atrial tachyarrhythmias, mainly atrial fibrillation. Areas of complex fractionated atrial electrograms and high dominant frequency have been proposed as critical regions for maintaining atrial fibrillation; however, there is a paucity of data on the relationship between the characteristics of electrograms and the propagation pattern underlying them. In this study, a realistic 3D computer model of the human atria has been developed to investigate this relationship. The model includes a realistic geometry with fiber orientation, anisotropic conductivity and electrophysiological heterogeneity. We simulated different tachyarrhythmic episodes applying both transient and continuous ectopic activity. Electrograms and their dominant frequency and organization index values were calculated over the entire atrial surface. Our simulations show electrograms with simple potentials, with little or no cycle length variations, narrow frequency peaks and high organization index values during stable and regular activity as the observed in atrial flutter, atrial tachycardia (except in areas of conduction block) and in areas closer to ectopic activity during focal atrial fibrillation. By contrast, cycle length variations and polymorphic electrograms with single, double and fragmented potentials were observed in areas of irregular and unstable activity during atrial fibrillation episodes. Our results also show: 1) electrograms with potentials without negative deflection related to spiral or curved wavefronts that pass over the recording point and move away, 2) potentials with a much greater proportion of positive deflection than negative in areas of wave collisions, 3) double potentials related with wave fragmentations or blocking lines and 4) fragmented electrograms associated with pivot points. Our model is the first human atrial model with realistic fiber orientation used to investigate the relationship between different atrial arrhythmic propagation patterns and the electrograms observed at more than 43000 points on the atrial surface.
The Laplace-Beltrami operator for graphs has been been widely used in many machine learning issues, such as spectral clustering and transductive inference. Functions on the nodes of a graph with vanishing Laplacian are called harmonic functions. In differen-tial geometry, the Laplace-de Rham operator generalizes the Laplace-Beltrami operator. It is a differential operator on the exterior al-gebra of a differentiable manifold, and it is equivalent to the Laplace-Beltrami operator when acting on a scalar function. In this pa-per, we develop a discrete analogue of the Laplace-de Rham operator, which naturally generalizes the discrete Laplace-Beltrami op-erator. The discrete Laplace-de Rham op-erator can then be used to define harmonic functions on arbitrary paths in a graph, in particular, functions on edges. Conse-quently, we build discrete regularization us-ing the discrete Laplace-de Rham operator, and validate it on real-world web categoriza-tion tasks.
Catheter ablation of atrial fibrillation (AF) focuses on pulmonary vein (PV) ablation with or without additional atrial substrate modification. These procedures require significant fluoroscopy exposure. A new 3D non-fluoroscopic navigation system (CARTO(®) 3 System, Biosense Webster, CA, USA) that allows precise location visualization of diagnostic and ablation catheters was evaluated for its impact on fluoroscopic exposure during AF ablation procedures.
Two groups of patients were treated by our centres for drug refractory AF. One group was treated using the new CARTO(®) 3 system to guide catheter ablation (Group A, 117 patients). The other group was treated using the CARTO(®) XP system (Biosense Webster) 3 months previously (Group B, 123 patients). For both groups, circumferential PV ostia ablation was performed; PV isolation was validated using a circular catheter placed at each ostium. There was no difference in any clinical characteristics (age, sex, AF type, left atrium diameter and volume, and heart disease) among the two study groups. The mean number of PVs identified and isolated per patient was similar in both groups, as were the mean procedural duration and radiofrequency time. However, mean fluoroscopic time was significantly reduced in Group A (15.9±12.3 min) as compared with Group B (26±15.1 min) (P < 0.001).
This multicentre observational study demonstrates a significant reduction of fluoroscopy exposure using a new 3D non-fluoroscopic mapping system to guide AF catheter ablation.
The use of antiarrhythmic drugs is common to treat heart rhythm disorders. Computational modeling and simulation are promising tools that could be used to investigate the effects of specific drugs on cardiac electrophysiology. In this paper, we study the multiscale effects of dofetilide, a drug that blocks IKr, from cellular to organ level paying special attention to its effect on heart structures, in particular the specialized cardiac conduction system (CCS). We include a model of the CCS in a patient-specific anatomical ventricular model and study the drug effects in simulations with and without a CCS. Results confirmed the expected effects of dofetilide at cellular level, increasing the action potential duration, and at organ level, prolonging the QT segment. Notable differences are shown between models with and without the CCS on action potential duration distributions. These techniques show the importance of heart heterogeneity and the global effects of the interaction of drugs with cardiac structures.
Dominant frequency analysis (DFA) and organization analysis (OA) of cardiac electrograms (EGMs) aims to establish clinical targets for cardiac arrhythmia ablation. However, these previous spectral descriptions of the EGM have often discarded relevant information in the spectrum, such as the harmonic structure or the spectral envelope. We propose a fully automated algorithm for estimating the spectral features in EGM recordings. This approach, called Fourier OA (FOA), accounts jointly for the organization and periodicity in the EGM, in terms of the fundamental frequency instead of dominant frequency. In order to compare the performance of FOA and DFA-OA approaches, we analyzed simulated EGM, obtained in a computer model, as well as two databases of implantable defibrillator-stored EGM. FOA parameters improved the organization measurements with respect to OA, and averaged cycle length and regularity indexes were more accurate when related to the fundamental (instead of dominant) frequency, as estimated by the algorithm (p < 0.05 comparing f(0) estimated by DFA and by FOA). FOA yields a more detailed and robust spectral description of EGM compared to DFA and OA parameters.
In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/image generation - display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - curve, surface, solid, and object representations;J.6[Com- puter Applications]: Computer-Aided Engineering - computeraided design General Terms: Algorithms, Graphics. 1
Electrical and anatomical maps (EAM) are built by cardiac navigation systems (CNS) and by Electrocardiographic Imaging systems for supporting arrhythmia ablation during electrophysiological procedures. Manifold Harmonics Analysis (MHA) has been proposed for analyzing the spectral properties of EAM of voltages and times in CNS by using a representation of the EAM supported by the anatomical mesh. MHA decomposes the EAM in a set of basis functions and coefficients which allow to conveniently reconstruct the EAM. In this work, we addressed the effect of normalization of the mesh spatial coordinates and the bioelectrical feature on the EAM decomposition for identifying regions with strong variation on the feature. For this purpose, a simulated EAM with three foci in a ventricular and in an atrial tachycardia was used. These foci were located at different distances amongst themselves, and different voltages were also considered. Our experiments show that it is possible to identify the foci origin by considering the first 3–5 projections only when normalization was considered, both for atrial and ventricular EAM. In this case, better quality in the EAM reconstruction was also obtained when using less basis functions. Hence, we conclude that normalization can help to identify regions with strong feature variation in the first stages of the EAM reconstruction.
Post-infarct ventricular tachycardia is associated with channels of surviving myocardium within scar characterized by fractionated and low-amplitude signals usually occurring late during sinus rhythm. Conventional automated algorithms for 3-dimensional electro-anatomic mapping cannot differentiate the delayed local signal of conduction within the scar from the initial far-field signal generated by surrounding healthy tissue. Ripple mapping displays every deflection of an electrogram, thereby providing fully informative activation sequences. We prospectively used CARTO-based ripple maps to identify conducting channels as a target for ablation.
Methods and results:
High-density bipolar left ventricular endocardial electrograms were collected using CARTO3v4 in sinus rhythm or ventricular pacing and reviewed for ripple mapping conducting channel identification. Fifteen consecutive patients (median age 68 years, left ventricular ejection fraction 30%) were studied (6 month preprocedural implantable cardioverter defibrillator therapies: median 19 ATP events [Q1-Q3=4-93] and 1 shock [Q1-Q3=0-3]). Scar (<1.5 mV) occupied a median 29% of the total surface area (median 540 points collected within scar). A median of 2 ripple mapping conducting channels were seen within each scar (length 60 mm; initial component 0.44 mV; delayed component 0.20 mV; conduction 55 cm/s). Ablation was performed along all identified ripple mapping conducting channels (median 18 lesions) and any presumed interconnected late-activating sites (median 6 lesions; Q1-Q3=2-12). The diastolic isthmus in ventricular tachycardia was mapped in 3 patients and colocated within the ripple mapping conducting channels identified. Ventricular tachycardia was noninducible in 85% of patients post ablation, and 71% remain free of ventricular tachycardia recurrence at 6-month median follow-up.
Ripple mapping can be used to identify conduction channels within scar to guide functional substrate ablation.
Rhythmia(TM) is a new technology capable of rapid and high-resolution mapping. However, its potential advantage over existing technologies in mapping complex scar-related atrial tachycardias (AT) has not been yet evaluated.
To examine its utility for mapping scar-related AT in patients who had failed previous ablation procedure(s).
This multicenter study included 20 patients with recurrent AT within 2 years after a previous ablation procedure (1.8±0.7 per patient). In all cases, the AT could not be adequately mapped during the index procedure due to scar with fractionated electrograms precluding accurate time annotation, frequent change in the tachycardia in response to pacing, and/or degeneration into atrial fibrillation (AF). These patients underwent repeat mapping and ablation procedure with Rhythmia(TM).
From a total of 28 inducible ATs, 24 were successfully mapped. Eighteen ATs (75%) terminated during radiofrequency ablation and 4 (16.6%) with catheter pressure or entrainment from the site of origin or isthmus. Two ATs that were mapped to the interatrial septum slowed but did not terminate with ablation. In 21/24 ATs the mechanism was macroreentry, while in 3/24 the mechanism was focal. Interestingly, in 5 patients with previously failed ablation of an allegedly "focal" tachycardia, high-resolution mapping demonstrated macroreentrant arrhythmia. The mean mapping time was 28.6±17 minutes and the mean radiofrequency ablation time to arrhythmia termination was 3.2±2.6 minutes. During a mean follow-up of 7.5±3.1 months, 15 (75%) of 20 patients were free of AT recurrences.
The Rhythmia(TM) mapping system may be advantageous for mapping complex scar-related AT.
In this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh‐free. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications. In particular, we use the eigenstructure of the discrete operator for filtering and shape segmentation. Point‐based surface deformation is another application that can be easily carried out from the proposed discretization method.
Cardiac excitation is determined by interactions between the source of electric activation (membrane depolarization) and the load that cardiac tissue presents. This relationship is altered in pathology by remodeling processes that often create a substrate favoring the development of cardiac arrhythmias. Most studies of arrhythmia mechanisms and arrhythmogenic substrates have been conducted in animal models, which may differ in important ways from the human pathologies they are designed to represent. Electrocardiographic imaging is a noninvasive method for mapping the electric activity of the heart in humans in real-world conditions. This review summarizes results from electrocardiographic imaging studies of arrhythmogenic substrates associated with human clinical arrhythmias. Examples include heart failure, myocardial infarction scar, atrial fibrillation, and abnormal ventricular repolarization.
Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early work in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis of mesh geometry based on a combinatorial Laplacian aids our understanding of the low-pass filtering approach to mesh smoothing. Over the past 15 years, the list of applications in the area of geometry processing which utilize the eigenstructures of a variety of mesh operators in different manners have been growing steadily. Many works presented so far draw parallels from developments in fields such as graph theory, computer vision, machine learning, graph drawing, numerical linear algebra, and high-performance computing. This paper aims to provide a comprehensive survey on the spectral approach, focusing on its power and versatility in solving geometry processing problems and attempting to bridge the gap between relevant research in computer graphics and other fields. Necessary theoretical background is provided. Existing works covered are classified according to different criteria: the operators or eigenstructures employed, application domains, or the dimensionality of the spectral embeddings used. Despite much empirical success, there still remain many open questions pertaining to the spectral approach. These are discussed as we conclude the survey and provide our perspective on possible future research.
We present an explicit method to compute a generalization of the Fourier Transform on a mesh. It is well known that the eigenfunctions of the Laplace Beltrami operator (Manifold Harmonics) define a function basis allowing for such a transform. However, computing even just a few eigenvectors is out of reach for meshes with more than a few thousand vertices, and storing these eigenvectors is prohibitive for large meshes. To overcome these limitations, we propose a band-by-band spectrum computation algorithm and an out-of-core implementation that can compute thousands of eigenvectors for meshes with up to a million vertices. We also propose a limited-memory filtering algorithm, that does not need to store the eigenvectors. Using this latter algorithm, specific frequency bands can be filtered, without needing to compute the entire spectrum. Finally, we demonstrate some applications of our method to interactive convolution geometry filtering. These technical achievements are supported by a solid yet simple theoretic framework based on Discrete Exterior Calculus (DEC). In particular, the issues of symmetry and discretization of the operator are considered with great care.
Representations are at the heart of artificial intelligence (AI). This book is devoted to the problem of representation discovery: how can an intelligent system construct representations from its experience? Representation discovery re-parameterizes the state space - prior to the application of information retrieval, machine learning, or optimization techniques - facilitating later inference processes by constructing new task-specific bases adapted to the state space geometry. This book presents a general approach to representation discovery using the framework of harmonic analysis, in particular Fourier and wavelet analysis. Biometric compression methods, the compact disc, the computerized axial tomography (CAT) scanner in medicine, JPEG compression, and spectral analysis of time-series data are among the many applications of classical Fourier and wavelet analysis. A central goal of this book is to show that these analytical tools can be generalized from their usual setting in (infinite-dimensional) Euclidean spaces to discrete (finite-dimensional) spaces typically studied in many subfields of AI. Generalizing harmonic analysis to discrete spaces poses many challenges: a discrete representation of the space must be adaptively acquired; basis functions are not pre-defined, but rather must be constructed. Algorithms for efficiently computing and representing bases require dealing with the curse of dimensionality. However, the benefits can outweigh the costs, since the extracted basis functions outperform parametric bases as they often reflect the irregular shape of a particular state space. Case studies from computer graphics, information retrieval, machine learning, and state space planning are used to illustrate the benefits of the proposed framework, and the challenges that remain to be addressed. Representation discovery is an actively developing field, and the author hopes this book will encourage other researchers to explore this exciting area of research. Table of Contents: Overview / Vector Spaces / Fourier Bases on Graphs / Multiscale Bases on Graphs / Scaling to Large Spaces / Case Study: State-Space Planning / Case Study: Computer Graphics / Case Study: Natural Language / Future Directions
This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed Finite-Element/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators.
Advances in electroanatomic mapping systems,
B J Cross
Spectral analysis of electroanatomical maps for spatial bandwidth estimation as support to ablation,