Inverse Problem of Electrocardiography: Estimating the Location of Cardiac Ischemia in a 3D Realistic Geometry

Abstract

The inverse problem in cardiology (IPC) has been formulated in different ways in order to non invasively obtain valuable informations about the heart condition. Most of the formulations solve the IPC under a quasistatic assumption neglecting the dynamic behavior of the electrical wave propagation in the heart. In this work we take into account this dynamic behavior by constraining the cost function with the monodomain model. We use an iterative algorithm combined with a level set formulation allowing us to localize an ischemic region in the heart. The method has been presented by Alvarez et al in [1] and [4], in which the authors developed a method for localize ischemic regions using a simple phenomenological model in a 2D cardiac tissue. In this work, we analyze the performance of this method in different 3D geometries. The inverse procedure exploits the spatiotemporal 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. We start by testing this method on two concentric spheres and then analyze the performance in a 3D real anatomical geometry. Both for analytical and real life geometries, numerical results show that using this algorithm we are capable of identifying the position and, in most of the cases, approximate the size of the ischemic regions.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

“…Combining (5.12) and (5.13) we get 15) in the weak * topology of C 0 (Ω). On account of (3.5), we deduce also 16) in the weak * topology of C 0 (Ω).…”

“…Indeed, even for the linear counterpart of the inverse problem, it has been shown in [22] and [27] that infinitely many measurements are needed to detect uniquely the unknown inclusions, and that the continuous dependence of the inclusion from the data is logarithmic [20]. Moreover, despite the inverse problem of ischemia identification from measurements of surface potentials has been tackled in an optimization framework for numerical purposes [32,30,1,15], a detailed mathematical analysis of this problem has never been performed. To our knowledge, no theoretical investigation of inverse problems related with ischemia detection involving the monodomain and/or the bidomain model has been carried out.…”

<b>Inverse problem for porosity estimation during solidification of TNT

“…However, in this paper, the analytical solution (Zhang et al, 2009) solves the solidification process in a semi-infinite domain, considering a Stefan model, while the numerical solution solves the solidification process in a finite domain, considering the effective heat capacity approach. In this sense, the inverse crime is not present in this study, because the analytical solution is used to simulate experimental data and the numerical solution solves the inverse procedure (Chávez, Alonzo-Atienza, & Álvarez, 2013). However, different levels of random noise were also introduced in the analytical solution (Zhang et al, 2009) …”

Model-Based Feature Augmentation for Cardiac Ablation Target Learning From Images

“…As in [40], we modelled every myocardium volume element (tetrahedron) as a spatially fixed but time varying current dipole. We define the equivalent current density j eq as:…”