A new approach to the intracardiac inverse problem using Laplacian distance kernel

Abstract

BackgroundThe inverse problem in electrophysiology consists of the accurate estimation of the intracardiac electrical sources from a reduced set of electrodes at short distances and from outside the heart. This estimation can provide an image with relevant knowledge on arrhythmia mechanisms for the clinical practice. Methods based on truncated singular value decomposition (TSVD) and regularized least squares require a matrix inversion, which limits their resolution due to the unavoidable low-pass filter effect of the Tikhonov regularization techniques.MethodsWe propose to use, for the first time, a Mercer’s kernel given by the Laplacian of the distance in the quasielectrostatic field equations, hence providing a Support Vector Regression (SVR) formulation by following the principles of the Dual Signal Model (DSM) principles for creating kernel algorithms.ResultsSimulations in one- and two-dimensional models show the performance of our Laplacian distance kernel technique versus several conventional methods. Firstly, the one-dimensional model is adjusted for yielding recorded electrograms, similar to the ones that are usually observed in electrophysiological studies, and suitable strategy is designed for the free-parameter search. Secondly, simulations both in one- and two-dimensional models show larger noise sensitivity in the estimated transfer matrix than in the observation measurements, and DSM−SVR is shown to be more robust to noisy transfer matrix than TSVD.ConclusionThese results suggest that our proposed DSM−SVR with Laplacian distance kernel can be an efficient alternative to improve the resolution in current and emerging intracardiac imaging systems.

Electrocardiographic Imaging for Atrial Fibrillation: A Perspective From Computer Models and Animal Experiments to Clinical Value

“…Moreover, cardiac signals are usually low-pass filtered during their pre-processing, to improve SNR. It has also been pointed out that the basic equations of the inverse problem could be much more sensitive to noise in the geometrical conductivity relationship (captured by the matrix) than to noise in the recorded signals (Caulier-Cisterna et al, 2018). To the best of our knowledge, this has not been evaluated in detailed simulations or in real data, but it would be consistent with the ill-posed nature of the inverse problem.…”

Generalization and Regularization for Inverse Cardiac Estimators

“…2) TSVD: has also been proposed [30], [31] aiming to overcome the ill-posing character of signal models like the one in (6). To do this, TSVD uses a better defined transfer matrix than H, denoted by H k .…”

Stable Identification of Sources Located on Interface of Nonhomogeneous Media

“…The Cauchy problem is important and applicable to various fields, e.g., inverse electrocardiography, inverse electroencephalography, and electrical capacitance tomography [16,18,21,36]. To investigate the Cauchy problem, we considered the following linear, injective, and compact operator K :…”

“…The latter problem involves determining the source that yields the measurement on the boundary of the region [12][13][14]. The inverse source problem appears in different applications, such as inverse electroencephalography, inverse electrocardiography and inverse geophysics (see, e.g., [15][16][17][18][19][20][21][22][23]), where the problems are modeled using differential equations. Numerical solutions to differential equations are crucial in mathematics and engineering because they appear in many applications, such as population growth, diffusion processes, electromagnetic problems, and elasticity problems.…”