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.
Keywords: Electro physiology; Inverse problems; Nonlinear elliptic PDEs; Shape optimization.