Variational Iteration Method for solving Electrocardiography inverse problem

Abstract

In this paper, the variational iteration method is proposed as a solution to an inverse problem in electrocardiography. The aim is to obtain approximate solutions to the model with the lowest error rate. This is crucial in determining the patient's heart activity and facilitating rapid medical intervention. The main challenges in accurately computing clinically relevant maps of cardiac depolarization stem from the ill-posed nature of the continuous problem and the presence of noise in the data. To tackle these difficulties, we have developed regularizing iterative algorithms based on domain decomposition techniques. These algorithms reformulate the inverse problem into several cases, depending on the solution area. This formulation has enabled us to establish a new stopping criterion that is more responsive and accurately reflects the behavior of the error on the non-accessible part of the boundary. The numerical results obtained through the variational iteration method demonstrate that the proposed approach effectively captures the error behavior on the non-accessible boundary. An additional advantage of these approaches is their ability to reduce execution time through their parallelized versions. Thus, we have successfully demonstrated the effectiveness of these methods in terms of quality (accuracy of approximation) and quantitative aspects (computation cost).