Accuracy of electrocardiographic imaging using the method of fundamental solutions

Abstract

Solving the inverse problem of electrocardiology via the Method of Fundamental Solutions has been proposed previously. The advantage of this approach is that it is a meshless method, so it is far easier to implement numerically than many other approaches. However, determining the heart surface potential distribution is still an ill-posed problem and thus requires some form of Tikhonov regularisation to obtain the required distributions. In this study, several methods for determining an "optimal" regularisation parameter are compared in the context of solving the inverse problem of electrocardiology via the Method of Fundamental Solutions. It is found that the Robust Generalised Cross-Validation method most often yields epicardial potential distributions with the least relative error when compared to the input distribution. The study also compares the inverse solutions obtained with the Method of Fundamental Solutions with those obtained in a previous study using the boundary element method. It is found that choosing the best solution methodology and regularisation parameter determination method depends on the particular scenario being considered.

Generalization and Regularization for Inverse Cardiac Estimators

“…To our best knowledge, few out-of-sample implementations ensuring the generalization when using regularization techniques can be found in the ECGI literature. The Generalized Cross Validation Method proposed and used in [45], [46] used a criterion on the change of behavior of an L-curve. A recent study was devoted to analyze with detail the impact of signal processing techniques on the reconstructions of single-site pacing data on a torso-tank experimental setup [47], which mostly used elbow detection on the L-curve.…”

Multiobjective Optimization Approach to Localization of Ectopic Beats by Single Dipole: Case Study

“…The attempts of several research groups were summarized recently in [2]. Because the inverse problem is ill-posed its solution requires some form of regularization, selection of which is one of the specific tasks of the problem [3]. Clinical applicability of ECGI reconstruction of activation as well as the repolarization phase of the heartbeat cycle was studied and demonstrated also in [4].…”

Solution of direct and inverse conduction heat transfer problems using the method of fundamental solutions and differential evolution

“…The numerical implementation of the EC 37,9 MFS only depends on the locations of boundary nodes and source points and has no requirements of the mesh generation and the numerical quadrature (Qu et al, 2019). Because of simple mathematical expressions and high accuracy, the MFS has become the popular approach used widely in many applications such as potential, Helmholtz and diffusion problems (Golberg and Chen, 1998), linear diffusion-reaction equations (Balakrishnan and Ramachandran, 2000), the evaluation of effectiveness factors for a first order reaction in complex catalyst geometries in trickle bed reactors (Palmisano et al, 2003), applications of the MFS to inverse problems (Karageorghis et al, 2011), the sound-soft interior acoustic scatterer (Marin et al, 2017), the high frequency acoustic problem (Li et al, 2018), solution of an inverse problem of electrocardiology to determine the heart surface potential distribution (Johnston, 2018), solution of twodimensional nonlinear elastic problems by using the MFS associated with the asymptotic numerical method (Askour et al, 2018), the solution of a steady-state nonlinear heat conduction problem in two dimensions considering the association between the homotopy analysis method and the MFS (Chang et al, 2019), analysis of three-dimensional interior acoustic fields (Qu et al, 2019), numerical solution of non-Newtonian fluid flow and heat transfer problems in ducts with sharp corners (Grabski, 2019), etc applications.…”