Laplace Interpolation Research Articles

Electrocardiographic Change in V1, V5 and V6 Leads in Patients with Pulmonary Hypertension who are Receiving Effective Treatment

Body surface potential mapping (BSPM) provides additional electrophysiological information that can be useful for the detection of cardiac diseases. Moreover, BSPMs are currently utilized in electrocardiographic imaging (ECGI) systems within clinical practice. Missing information due to noisy recordings, poor electrode contact is inevitable. In this study, we present an interpolation method that combines Laplacian minimization and principal component analysis (PCA) techniques for interpolating this missing information.The dataset used consisted of 117 lead BSPMs recorded from 744 subjects (a training set of 384 subjects, and a test set of 360). This dataset is a mixture of normal, old myocardial infarction, and left ventricular hypertrophy subjects. The missing data was simulated by ignoring data recorded from 7 regions: the first region represents three rows of five electrodes on the anterior torso surface (high potential gradient region), and the other six regions were realistic patterns that have been drawn from clinical data and represent the most likely regions of broken electrodes. Three interpolation methods including PCA based interpolation, Laplacian interpolation, and hybrid Laplacian-PCA interpolation methods were used to interpolate the missing data from the remaining electrodes. In the simulated region of missing data, the calculated potentials from each interpolation method were compared with the measured potentials using relative error (RE) and correlation coefficient (CC) over time.In the hybrid Laplacian-PCA interpolation method, the missing data are firstly interpolated using Laplacian interpolation, then the resulting BSPM of 117 potentials was multiplied by the (117 × 117) coefficient matrix calculated using the training set to get the principal components. Out of 117 principal components (PCs), the first 15 PCs were utilized for the second stage of interpolation. The best performance of interpolation was the reason for choosing the first 15 PCs.The differences in the median of relative error (RE) between Laplacian and Hybrid method ranged from 0.01 to 0.35 (p < 0.001), while the differences in the median of correlation between them ranged from 0.0006 to 0.034 (p < 0.001). PCA-interpolation method performed badly especially in some scenarios where the number of missing electrodes was up to 12 or higher causing a high region of missing data. The figures of median of RE for PCA-method were between 0.05 and 0.6 lower than that for Hybrid method (p < 0.001). However, the median of correlation was between 0.0002 and 0.26 lower than the figure for the Hybrid method (p < 0.001).Comparison between the three methods of interpolation (Laplacian, PCA, Hybrid) in reconstructing missing data in BSPM showed that the Hybrid method was always better than the other methods in all scenarios; whether the number of missed electrodes is high or low, and irrespective of the location of these missed electrodes.

The specific His-bundle pacing features in electrocardiogram

Body surface potential mapping (BSPM) provides additional electrophysiological information that can be useful for the detection of cardiac diseases. Moreover, BSPMs are currently utilized in electrocardiographic imaging (ECGI) systems within clinical practice. Missing information due to noisy recordings, poor electrode contact is inevitable. In this study, we present an interpolation method that combines Laplacian minimization and principal component analysis (PCA) techniques for interpolating this missing information.The dataset used consisted of 117 lead BSPMs recorded from 744 subjects (a training set of 384 subjects, and a test set of 360). This dataset is a mixture of normal, old myocardial infarction, and left ventricular hypertrophy subjects. The missing data was simulated by ignoring data recorded from 7 regions: the first region represents three rows of five electrodes on the anterior torso surface (high potential gradient region), and the other six regions were realistic patterns that have been drawn from clinical data and represent the most likely regions of broken electrodes. Three interpolation methods including PCA based interpolation, Laplacian interpolation, and hybrid Laplacian-PCA interpolation methods were used to interpolate the missing data from the remaining electrodes. In the simulated region of missing data, the calculated potentials from each interpolation method were compared with the measured potentials using relative error (RE) and correlation coefficient (CC) over time.In the hybrid Laplacian-PCA interpolation method, the missing data are firstly interpolated using Laplacian interpolation, then the resulting BSPM of 117 potentials was multiplied by the (117 × 117) coefficient matrix calculated using the training set to get the principal components. Out of 117 principal components (PCs), the first 15 PCs were utilized for the second stage of interpolation. The best performance of interpolation was the reason for choosing the first 15 PCs.The differences in the median of relative error (RE) between Laplacian and Hybrid method ranged from 0.01 to 0.35 (p < 0.001), while the differences in the median of correlation between them ranged from 0.0006 to 0.034 (p < 0.001). PCA-interpolation method performed badly especially in some scenarios where the number of missing electrodes was up to 12 or higher causing a high region of missing data. The figures of median of RE for PCA-method were between 0.05 and 0.6 lower than that for Hybrid method (p < 0.001). However, the median of correlation was between 0.0002 and 0.26 lower than the figure for the Hybrid method (p < 0.001).Comparison between the three methods of interpolation (Laplacian, PCA, Hybrid) in reconstructing missing data in BSPM showed that the Hybrid method was always better than the other methods in all scenarios; whether the number of missed electrodes is high or low, and irrespective of the location of these missed electrodes.

Sick sinus syndrome in a patient with hypertrophic cardiomyopathy

Body surface potential mapping (BSPM) provides additional electrophysiological information that can be useful for the detection of cardiac diseases. Moreover, BSPMs are currently utilized in electrocardiographic imaging (ECGI) systems within clinical practice. Missing information due to noisy recordings, poor electrode contact is inevitable. In this study, we present an interpolation method that combines Laplacian minimization and principal component analysis (PCA) techniques for interpolating this missing information.The dataset used consisted of 117 lead BSPMs recorded from 744 subjects (a training set of 384 subjects, and a test set of 360). This dataset is a mixture of normal, old myocardial infarction, and left ventricular hypertrophy subjects. The missing data was simulated by ignoring data recorded from 7 regions: the first region represents three rows of five electrodes on the anterior torso surface (high potential gradient region), and the other six regions were realistic patterns that have been drawn from clinical data and represent the most likely regions of broken electrodes. Three interpolation methods including PCA based interpolation, Laplacian interpolation, and hybrid Laplacian-PCA interpolation methods were used to interpolate the missing data from the remaining electrodes. In the simulated region of missing data, the calculated potentials from each interpolation method were compared with the measured potentials using relative error (RE) and correlation coefficient (CC) over time.In the hybrid Laplacian-PCA interpolation method, the missing data are firstly interpolated using Laplacian interpolation, then the resulting BSPM of 117 potentials was multiplied by the (117 × 117) coefficient matrix calculated using the training set to get the principal components. Out of 117 principal components (PCs), the first 15 PCs were utilized for the second stage of interpolation. The best performance of interpolation was the reason for choosing the first 15 PCs.The differences in the median of relative error (RE) between Laplacian and Hybrid method ranged from 0.01 to 0.35 (p < 0.001), while the differences in the median of correlation between them ranged from 0.0006 to 0.034 (p < 0.001). PCA-interpolation method performed badly especially in some scenarios where the number of missing electrodes was up to 12 or higher causing a high region of missing data. The figures of median of RE for PCA-method were between 0.05 and 0.6 lower than that for Hybrid method (p < 0.001). However, the median of correlation was between 0.0002 and 0.26 lower than the figure for the Hybrid method (p < 0.001).Comparison between the three methods of interpolation (Laplacian, PCA, Hybrid) in reconstructing missing data in BSPM showed that the Hybrid method was always better than the other methods in all scenarios; whether the number of missed electrodes is high or low, and irrespective of the location of these missed electrodes.

Geometrically Non-linear Analysis of Elastic Structures by Petrov-Galerkin Natural Element Method

This paper is concerned with the geometrically non-linear analysis of elastic structures using the natural element method, particularly a Petrov-Galerkin Natural Element Method (PG-NEM). The geometrically non-linear problem is linearized and formulated by the Taylor series expansion and the Total Lagrangian (TL) method. The Voronoi polygon-based Laplace Interpolation (LI) functions are used to approximate the displacement increments, while the Delaunay triangle-supported Constant-Strain (CS) basis functions are adopted for the expansion of the virtual displacement. The iterative computation is performed by the Newton-Raphson method, and a set of Delaunay triangles serves as a background cell for the traditional Gauss integration rule-based numerical integration. The proposed PG-NEM is illustrated through the numerical experiments, and its numerical accuracy is compared with MSC/Marc, CS-FEM and BG-NEM.

Quantum Yang-Mills theory: An overview of a program

We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\mathbb{Z}/2\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. Finally, the continuum limit of our ansatz as the lattice regulator is removed is then described. This paper is intended as an abstract for an ongoing programme: there are still many open problems.

Stress recovery techniques for natural element method in 2-D solid mechanics

This paper is concerned with the stress recovery for the natural element method in which the problem domain is discretized with Delaunay triangles and the structural behavior is approximated with Laplace interpolation functions. Basically, the global and local patch recovery techniques based on the L2-projection method are adopted. For the local patch recovery, the local element patches are defined by the supports of each Laplace interpolation function. For the comparison purpose, the local stress recovery is also performed using Lagrange-type basis functions that are used for 3- and 6-node triangular elements. The stresses that are recovered by the present global and local recovery techniques are compared each other and compared with the available analytic solution, in terms of their spatial distributions and the convergence rates. As well, the dependence of the recovered stress field on the type of test basis functions that are used forbnov-Galerkin (BG) and Petrov-Galerkin (PG) natural element methods is also investigated.

Bayer Demosaicking With Polynomial Interpolation.

Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g., mobile phones, tablet, and so on). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking. Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper, we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over the existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB ΔE*, and FSIM), and visual performance.

Polarized radiative transfer in two-dimensional scattering medium with complex geometries by natural element method

The natural element method (NEM) is extended to solve the polarized radiative transfer problem in a two-dimensional scattering medium with complex geometries, in which the angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by the Galerkin weighted residuals approach. The Laplace interpolation scheme is adopted to obtain the shape functions used in the Galerkin weighted residuals approach. The NEM solution to the vector radiative transfer in a square enclosure filled with a Mie scattering medium is first examined to validate our program. We then study the polarized radiative transfer in two kinds of geometries filled with scattering medium which is equivalent to a suspension of latex spheres in water. Three sizes of spheres are considered. The results for non-dimensional polarized radiative flux along the boundaries and the angular distributions of the Stokes vector at specific positions are presented and discussed. For the complex geometry bounded by the square and circular object, numerical solutions are presented for the cases both with Lambertian (diffuse) reflection and with Fresnel reflection. Some interesting phenomenon are found and analyzed.

Computation of 2-D mixed-mode stress intensity factors by Petrov-Galerkin natural element method

The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.

Calculation of stress intensity factors in 2‐D linear fracture mechanics by Petrov–Galerkin natural element method

SUMMARYThis paper is concerned with the numerical calculation of stress intensity factors in two‐dimensional linear fracture problems by Petrov–Galerkin natural element method, for which the Voronoi polygon‐based Laplace interpolation functions and constant strain finite element basis functions are taken for the trial and test functions, respectively. A local element patch recovery technique is employed to obtain more accurate smoothed strain and stress fields, and the stress intensity factors of edge and angled center cracks are calculated by both the J‐integral and interaction integral methods. The influence of the grid density, integral domain size, and weighting function type on the numerical accuracy is investigated through the numerical experiments. In addition, the present method is compared with the hybrid crack elements in combination with extended FEM and the scaled boundary FEM. It is confirmed that Petrov–Galerkin natural element method provides the numerical accuracy similar to these recent direct methods. Also, it is found that the accuracy of the J‐integral is affected by the grid density but not by the integral domain size. In the case of the interaction integral, the numerical accuracy is influenced by both the type of weighting function and the integral domain size. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Natural element approximation of Reissner–Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures

A rotation-free mixed natural element approximation of Reissner–Mindlin plate for the locking-free numerical analysis of plate-like thin elastic structures is presented, motivated by the rotation-free approximation for plate- and shell-like elastic structures and the high smoothness of Laplace interpolation functions used in natural element method. The mid-surface deflection and the rotation of shear are directly approximated using Laplace interpolation functions, while the Voronoi polygon-wise constant curvatures and bending moments are indirectly computed by area-averaging the boundary integrals of deflection derivatives and rotation of shear. The present approximation of the deflection and rotation of shear of discretized Reissner–Mindlin plate bending problem is formulated according to the modified mixed Hu-Washizu principle. Through the numerical results, it is verified that the rotation-free mixed natural element approximation of only the deflection and rotation of shear successfully prevents shear locking in the numerical analysis of plate-like thin elastic structures.

Illumination correction of retinal images using Laplace interpolation

Retinal images are frequently corrupted by unwanted variations in intensity that occur due to general imperfections in the image acquisition process. This inhomogeneous illumination across the retina can limit the useful information accessible within the acquired image. Specifically, this can lead to serious difficulties when performing image processing tasks requiring quantitative analysis of features present on the retina. Given that the spatial frequency content of the shading profile often overlaps with that of retinal features, retrospectively correcting for inhomogeneous illumination while maintaining the radiometric fidelity of the real data can be challenging. This paper describes a simple method for obtaining an estimate of the illumination profile in retinal images, with the particular goal of minimizing its influence upon features of interest. This is achieved by making use of Laplace interpolation and a multiplicative image formation model.

An eikonal-diffusion solver and its application to the interpolation and the simulation of reentrant cardiac activations

AbstractElectrical propagation of the cardiac impulse in the myocardium can be described by the eikonal-diffusion equation. This equation governs the field of activation times in a domain where conduction properties are specified. This approach has been applied to knowledge-based interpolation of sparse measurements of activation times and to the creation of initial conditions for detailed ionic models of cardiac propagation. This paper presents the mathematical basis, matrix formulation, and compact Matlab implementation of an iterative finite-element solver (triangular meshes) for the eikonal-diffusion equation extended to reentrant activations, which automatically identifies the period of reentry and computes the resulting isochrones. An iterative algorithm is designed to perform Laplacian interpolation of reentrant activation maps to be used as initial estimate for the eikonal-diffusion solver. The performance of the algorithm is analyzed in test-case geometries (ventricular slice and simplified atrial surface model).

개별요소법을 이용한 삼각망 생성기법 개발

수치해석을 수행할 경우 좀 더 정확한 수치모의를 위하여 해석영역의 특성에 따라 적절하게 요소를 배치하는 것이 필요하다. 본 연구에서 사용한 개별요소법(DEM)은 입자의 마찰력 및 항력을 제외한 반발력과 인장력만을 적용하였다. 초기 쿼드트리(Quad-tree)형식으로 충진된 입자들을 DEM을 이용하여 재배치할 경우 입자의 형상이 원형이기 때문에 입자사이에 존재하는 빈 공간을 최소화 할 수 있다. 결국 입자 중심점의 배치가 정삼각형에 가깝게 되는 특징을 보여준다. 이 재배치된 입자를 대상으로 Delaunay 삼각기법을 이용하여 삼각망을 구성하고, Laplace 보간을 수행하여 격자 품질을 향상시켰다. Laplace 보간 전 후의 형상비(Aspect Ratio: AR)를 비교한 결과 DEM을 이용하여 작성한 격자의 품질도 우수하지만, Laplace보간을 수행한 이후 보다 높은 품질의 격자가 생성되는 것을 확인하였다. 본 연구에서 개발한 기법은 기존의 삼각격자망 생성기법에 비해 다소 계산시간이 오래 걸리는 단점이 있지만, 복잡한 형상과 정확한 지형의 재현을 필요로 하는 파랑 해석용 유한요소 격자망 작성 및 다양한 수치모의 분야에서 그 적용 가능성이 매우 높다고 사료된다. When the numerical analysis is carried out, it is necessary to set proper elements as a feature of analysis domains for more accurate simulations. In this study, Distinct Element Method(DEM) is applied, only considering repulsive force and tensile force except for frictional force and resisting force of particle. When the filled particles with initial Quad-tree type is relocated by DEM, a blank space existing among the particles can be minimized because the shape of particle is circular. Finally, it is the effective feature that the centroidal disposion of the particles is similar to an equilateral triangle. Triangular mesh are formed by using the Delaunay triangular technique on these relocated particles, the quality of triangular mesh is more improved by carrying out Laplace interpolations. The compared result of Aspect Ratio before and after the Laplace interpolation is shown that although the quality of triangular mesh made by DEM is good, the later triangular mesh are higher quality than the formers. In this study, although the developed technique takes a longer calculational time than the previous technique to generate triangular mesh, it is considered that the applicable possibility is very high in the generation of finite element mesh about wave analysis and various numerical simulation to need a complex or reappearance of exact topography.

Three-phase compressible flow in porous media: Total Differential Compatible interpolation of relative permeabilities

We describe the construction of Total Differential (TD) three-phase data for the implementation of the exact global pressure formulation for the modeling of three-phase compressible flow in porous media. This global formulation is preferred since it reduces the coupling between the pressure and saturation equations, compared to phase or weighted formulations. It simplifies the numerical analysis of the problem and boosts its computational efficiency. However, this global pressure approach exists only for three-phase data (relative permeabilities, capillary pressures) which satisfy a TD condition. Such TD three-phase data are determined by the choice of a global capillary pressure function and a global mobility function, which take both saturations and global pressure level as argument. Boundary conditions for global capillary pressure and global mobility are given such that the corresponding three-phase data are consistent with a given set of three two-phase data. The numerical construction of global capillary pressure and global mobility functions by C1 and C0 finite element is then performed using bi-Laplacian and Laplacian interpolation. Examples of the corresponding TD three-phase data are given for a compressible and an incompressible case.

Robust and Scalable Transmission of Arbitrary 3D Models over Wireless Networks

We describe transmission of 3D objects represented by texture and mesh over unreliable networks, extending our earlier work for regular mesh structure to arbitrary meshes and considering linear versus cubic interpolation. Our approach to arbitrary meshes considers stripification of the mesh and distributing nearby vertices into different packets, combined with a strategy that does not need texture or mesh packets to be retransmitted. Only the valence (connectivity) packets need to be retransmitted; however, storage of valence information requires only 10% space compared to vertices and even less compared to photorealistic texture. Thus, less than 5% of the packets may need to be retransmitted in the worst case to allow our algorithm to successfully reconstruct an acceptable object under severe packet loss. Even though packet loss during transmission has received limited research attention in the past, this topic is important for improving quality under lossy conditions created by shadowing and interference. Results showing the implementation of the proposed approach using linear, cubic, and Laplacian interpolation are described, and the mesh reconstruction strategy is compared with other methods.

An adaptive color plane interpolation method based on edge detection

In this letter, an adaptive interpolation algorithm based on edge detection is proposed. With this algorithm, all the missing green values can be reconstructed in Bayer pattern image by using edge detection interpolation method. Reconstructed images composed of green pixels are classified according to the high frequency components in image, and the threshold T needed for all kinds of green images in the edge detection is determined through experiments. The edge detection is carried out based on the one Dimensional (1D) gradient operator. If the gradient value is greater than T, this pixel is located on the edge; otherwise the pixel is in the smooth area of the image. Finally, the simple bilinear interpolation is used for the smooth area while the Laplacian interpolation with the second-order correction term is adopted to reconstruct the other red/blue values on the edge. This algorithm resolves effectively the conflicts between reconstructing high quality color image and reducing computational complexity, and thus largely enhances the processing speed for the reconstructed color image.

A study on the performance of natural neighbour‐based Galerkin methods

AbstractIn this paper we address the problem of improving natural element simulations in terms of computational cost. Several problems are discussed, that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour‐based interpolation algorithms. In particular, we review the so‐called pseudo‐NEM, a moving least squares‐like approximation scheme that employs natural neighbours, and compare it with traditional Sibson and Laplace interpolation schemes in terms of both accuracy and computational cost. Some examples in linear Elasticity and visco‐plasticity are analysed in order to test the proposed schemes in engineering problems. Copyright © 2007 John Wiley &amp; Sons, Ltd.

2-D frictionless dynamic contact analysis of large deformable bodies by Petrov–Galerkin natural element method

This paper presents a Petrov–Galerkin natural element method for the nonlinear analysis of 2-D dynamic contact problems without friction. The frictionless dynamic contact problem is formulated according to the linearized total Lagrangian method incorporated with the linearized penalty method. The displacement increment is approximated with Laplace interpolation functions defined with the help of Voronoi polygons, while the admissible virtual displacement is expanded with constant strain functions which are supported on Delaunay triangles. The spatial numerical integration is carried out by applying the conventional Gauss quadrature rule to Delaunay triangles and the temporal time integration is performed by the implicit Newmark method. The validity of the proposed method is examined through the illustrating numerical experiments.

Epicardial potential distribution reconstruction from recordings of intravenous and transthoracic mapping catheters: A feasibility study

Catheter-based epicardial mapping is possible with two access methods: transthoracic pericardial access and transvenous access. Transthoracic pericardial access is based on the introduction of the catheters into the pericardial space using a percutaneous subxiphoid puncture and may at times require lengthy sequential mapping procedures. From the transthoracic pericardial approach major regions of the epicardium may also be inaccessible. Transvenous access uses the multielectrode (4–20 electrodes) catheters placed in the coronary veins thus increases the speed of the mapping procedure, however, leaves most of the epicardium inaccessible to direct measurement. The aim of this present study is to demonstrate that the reconstruction of the high-resolution maps using sparse measurements from different sites on the epicardium and on the multielectrode catheters is possible with a reasonably high accuracy in terms of locating the origin of the ventricular arrhythmia. In this study we investigated strategies for the reconstruction of epicardial potential distribution from recordings of intravenous and transthoracic epicardial mapping catheters, alone and in combination. For this purpose, we first examined the problem of best number of epicardial measurement sites (or best sampling resolution) using transthoracic mapping catheters and secondly studied the feasibility of the combined usage of both mapping approaches. In the prediction of the surrogate measurements at inaccessible sites from the measurements localized to the cardiac veins and sparse epicardial sites we evaluated two prediction methods: the Laplacian interpolation and statistical estimation, to overcome the sparsity of the measurements. We performed 14 dog experiments with various interventions to create a high-resolution epicardial potential map database. This database included a total of 592 beats which were recorded using a sock array placed on the ventricles of dog hearts. We found that 2 cm sampling resolution is quite feasible, which means that the time for the mapping procedure may be reduced considerably. Predictions from the combination of 21 intravenous catheter leads and 30 transthoracic catheter leads were better than when only 21 or 30 leads were used. The results of this study encourage further investigation and provide adequate evidence that an epicardial mapping approach based on the combined usage of transvenous and transthoracic pericardial access methods for the mapping of the outer surface of the heart is feasible and can provide adequate accuracy for clinical applications.