El problema inverso en electrocardiografía: estudio de la caracterización paramétrica de isquemias cardíacas

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The Inverse Problem of electrocardiography (IPE) can be summarized as the characterization of the electrical behavior of the heart using measurements obtained by electrodes that are not directly in contact with the cardiac surfaces. Many cardiac pathologies such as ischemia, infarction, ventricular tachycardia, arrhythmia can be detected by the determination of this electrical activity. From a mathematical point of view, the IPE is ill-posed due, in part, to smoothing and attenuation of the cardiac signal during its propagation in the medium between the heart muscle and the electrodes. To mitigate these difficulties, an extensive number of regularization techniques have been proposed in the literature, mostly of the Tikhonov type. However, most of these techniques consider each instant of time independently from the others, thus ignoring the temporal correlation among voltage measurements. The objective of this Thesis is to analyze the use of simple models to solve the IPE. Specifically, we analyze the IPE in terms of localizing cardiac ischemic regions from remote voltage measurements. The inverse procedure exploits the spatio-temporal correlations contained in the observed data, which is formulated as a parametric adjust of a mathematical model that minimizes the misfit between the simulated and the observed data. To this end, we incorporate a time-dependent monodomain model of the cardiac electric activity into the inversion scheme. The proposed method is based on the approach presented by Alvarez et al, were the mathematical model to obtain the real (forward) and the predicted (inverse) data are exactly the same, thus they are under the Inverse Crime scenario. The aim of this work is to extend this method avoiding the IC. For this purpose, we use the Luo-Rudy dynamic (LRd) model as a detailed computational model to simulate the electrical behavior of the cardiac cells, while for the inverse procedure we use the Two-Current (TC) phenomenological model proposed by Mitchell and Schaeffer. The inversion procedure also incorporates a semi-automatic stage to characterize the conduction properties of the cardiac tissue. The ischemic regions are modeled using standard level set techniques. Following an incremental approach, we test the proposed method using different geometries from a 2D cardiac tissue to a 3D realistic anatomical geometry of heart and torso. Numerical results show that the algorithm is capable of estimating the position, size and shape of cardiac ischemic regions from noisy voltage measurements. Our inverse procedure is benchmarked against zero-order Tikhonov regularization. On the other hand, this Thesis is a proof of principle demonstrating the possibility of using simple models in the IPE providing good solutions towards realistic situations.
Mención Internacional en el título de doctor
Proceso de señales, Ingeniería biomédica, Enfermedades cardiovasculares, Problema Inverso en Electrocardiografía (PIE).
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