Noninvasive epi-endocardial electrocardiographic imaging of ventricular septal pacing

Noninvasive epi-endocardial ElectroCardioGraphic Imaging (ECGI) allows reconstruction of electrograms and high-resolution visualization of various isoparametric maps based on multichannel ECG recordings and tomography. We aimed to verify the ECGI accuracy during septal ventricular pacing in patients with pre-implanted pacemakers using the new ECGI algorithm.Methods. Ten patients underwent epi-endocardial ECGI mapping (Amycard 01C EP Lab, Amycard LLC, Russia - EP Solutions SA, Switzerland). The iterative Equal Single Layer algorithm (ESL-iterative) and a new Fast Route algorithm in combination with the vector approach (FRA-V) were used to reconstruct isopotential and correlation similarity maps. Geodesic distance between noninvasively reconstructed early activation zone and RV reference pacing sites were measured to evaluate the ECGI accuracy.Results. The mean (SD) geodesic distance between noninvasively identified sites and reference pacing sites was 22 (15) mm for the ESL-iterative and 12 (7) for FRA-V algorithms, median (25-75% IQR) - 23 (8-29) mm and 10 (8-14) mm, respectively. The accuracy of ECGI mapping based on the FRA-V algorithm was significantly better than ESL-iterative algorithm (p=0,01). A detailed visual analysis of correlation similarity and isopotential maps showed significantly more accurate localization of early activation zones using the new FRA-V algorithm.Conclusions. Our study showed the feasibility and accuracy of a novel epi-endocardial ECGI mapping approach to identify early activation zones during septal ventricular pacing using the new FRA-V algorithm. The FRA-V algorithm is significantly better for epi-endocardial ECGI mapping and shows a significant advantage of this technique compared to other non-invasive methods of topical diagnostics. Moreover, simultaneous beat-to-beat mapping of entire ventricular septum allows using this technique for pre-ablation evaluation of unstable and polymorphic ventricular arrhythmia exit sites.

Noninvasive epi-endocardial electrocardiographic imaging of ventricular septal pacing

Noninvasive epi-endocardial ElectroCardioGraphic Imaging (ECGI) allows reconstruction of electrograms and high-resolution visualization of various isoparametric maps based on multichannel ECG recordings and tomography. This study shows results of ECGI accuracy verification based on septal ventricular pacing in patients with pre-implanted pacemakers using new algorithm for solving the inverse problem of electrocardiography.Methods. 10 patients in this study underwent epi-endocardial ECGI mapping (Amycard 01C EP Lab, Amycard LLC, Russia - EP Solutions SA, Switzerland). An iterative Equal Single Layer algorithm (ESL-iterative) and new Fast Route algorithm in combination with vector approach (FRA-V) were used to reconstruct isopotential and correlation similarity maps. Geodesic distance between noninvasively reconstructed early activate zone and RV reference pacing site were measured to evaluate ECGI accuracy.Results. The mean (SD) geodesic distance between noninvasively reconstructed and reference pacing site was 22 (15) mm for ESL-iterative and 12 (7) for FRA-V algorithm, median (25-75% IQR) - 23 (8-29) mm and 10 (8-14) mm respectively. Accuracy of ECGI mapping based on FRA-V algorithm was significantly better than ESL-iterative algorithm (p=0,01). Detailed visual analysis of correlation similarity and isopotential maps showed significantly more accurate localization of early activation zones using new FRA-V algorithm.Conclusions. These results showed a possibility of novel epi-endocardial ECGI mapping to detect early activation zone during septal ventricular pacing with sufficient accuracy (median 10 mm) using new FRA-V algorithm. Therefore, FRA-V algorithm is significantly better for epi-endocardial ECGI mapping and shows a significant advantage of this technique compared to other non-invasive methods of topical diagnostics. Moreover, simultaneous beat-to-beat mapping of entire ventricular septum allows using of this technique for preoperative topical diagnosis of complex unstable and polymorphic ventricular arrhythmias.

Surface Curve Design by Orthogonal Projection of Space Curves Onto Free-Form Surfaces

A novel technique for designing curves on surfaces is presented. The design specifications for this technique derive from other works on curvature continuous surface fairing. Briefly stated, the technique must provide a computationally efficient method for the design of surface curves that is applicable to a very general class of surface formulations. It must also provide means to define a smooth natural map relating two or more surface curves. The resulting technique is formulated as a geometric construction that maps a space curve onto a surface curve. It is designed to be coordinate independent and provides isoparametric maps for multiple surface curves. Generality of the formulation is attained by solving a tensorial differential equation formulated in terms of local differential properties of the surfaces. For an implicit surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This technique has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations.

Quadratic isoparametric systems in ℝn+mp

The notions of isoparametric maps and submanifolds in semi-Riemannian spaces are the generalizations of such notions in Riemannian spaces. The generalizations are different according to the purposes. We take the definitions as in the Riemannian case. Quadratic isoparametric maps and submanifolds are interesting examples which can be studied in detail. In this paper we study what we call quadratic isoparametric systems. In fact we give a classification of such systems of codimension 2. We use three different methods to show that quadratic isoparametric submanifolds of codimension 2 are homogeneous. The classification of quadratic isoparametric systems is done algebraically. By this we have changed the geometric problem of classifying quadratic submanifolds of codimension 2 into the algebraic problem of classifying quadratic isoparametric systems of codimension 2. The classification of such systems with arbitrary codimension is still open.