PSO with Tikhonov Regularization for the Inverse Problem in Electrocardiography

Abstract

AbstractIn this paper we present a nearest neighbor particle swarm optimization (PSO) algorithm applied to the numerical analysis of the inverse problem in electrocardiography. A two-step algorithm is proposed based on the application of the modified PSO algorithm with the Tikhonov regularization method to calculate the potential distribution in the heart. The PSO improvements include the use of the neighborhood particles as a strategy to balance exploration and exploitation in order to prevent premature convergences and produce a better local search. In the literature the inverse problem in electrocardiography is solved using the minimum energy norm in a Tikhonov regularization scheme. Although this approach solves the system, the solution may not have a meaning in the physical sense. Comparing to the classical reconstruction, the two-step PSO algorithm improves the accuracy of the solution with respect to the original distribution. Finally, to validate our results, we create a distribution over the heart by using a model of electrical activity (Bidomain model) coupled with a volume conductor model for the torso. Then, using our method, we make the reconstruction of the potential distribution.KeywordsDirect and inverse problemsParticle swarm optimization (PSO)Bio-inspired algorithmFinite elementElectrocardiographyBidomain