Inverse localization of earliest cardiac activation sites from activation maps based on the viscous Eikonal equation

Abstract

In this study we propose a novel method for identifying the locations of earliest activation in the human left ventricle from activation maps measured at the epicardial surface. Electrical activation is modeled based on the viscous Eikonal equation. The sites of earliest activation are identified by solving a minimization problem. Arbitrary initial locations are assumed, which are then modified based on a shape derivative based perturbation field until a minimal mismatch between the computed and the given activation maps on the epicardial surface is achieved. The proposed method is tested in two numerical benchmarks, a generic 2D unit-square benchmark, and an anatomically accurate MRI-derived 3D human left ventricle benchmark to demonstrate potential utility in a clinical context. For unperturbed input data, our localization method is able to accurately reconstruct the earliest activation sites in both benchmarks with deviations of only a fraction of the used spatial discretization size. Further, with the quality of the input data reduced by spatial undersampling and addition of noise, we demonstrate that an accurate identification of the sites of earliest activation is still feasible.

Physics-Informed Neural Networks for Cardiac Activation Mapping

“…This can result in unrealistic interpolations with artificially high conduction velocities. The strategies that do include the physics assume either a constant conduction velocity field [7] or a fixed amount of activation sources [8]. Additionally, there are no recommendations on the best strategy to acquire new measurements toward reducing the procedure time and improving its accuracy.…”

An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

“…Proof The claims follow from a similar argumentation as in the proof of Proposition 2 in [15] using Garding's inequality and the weak maximum principle.…”

“…It is stated there that the model involving |∇T | 2 M is better for wavefront propagation and collision. In the earlier work [15] we have used |∇T | 2 M and solved the inverse shape problem of identifying the centers of the activation regions (spherical subdomains ω i ) from epicardial data z. An alternative approach for describing the wavefront propagation is based on the use of a function ϕ which at time t describes the level set of points for which ϕ(t, x) = 0 gives the position of the wavefront at that times, see [14].…”

“…In the second numerical example we perform the joint reconstruction of the activation sites and the activation instants. The activation sites are reconstructed by means of an adapted version of the shape gradient method introduced in [15] together with a projected gradient method for the reconstruction of the activation instants. The numerical examples illustrate the feasibility of the approach and are carried out on the 2D unit square with artificial data.…”

“…Biol. 79, 2033-2068, 2019. We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.…”