An inverse Eikonal method for identifying ventricular activation sequences from epicardial activation maps

Thomas Grandits, Karli Gillette, Aurel Neic, Jason Bayer, Edward Vigmond, Thomas Pock, Gernot Plank*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A key mechanism controlling cardiac function is the electrical activation sequence of the heart's main pumping chambers termed the ventricles. As such, personalization of the ventricular activation sequences is of pivotal importance for the clinical utility of computational models of cardiac electrophysiology. However, a direct observation of the activation sequence throughout the ventricular volume is virtually impossible. In this study, we report on a novel method for identification of activation sequences from activation maps measured at the outer surface of the heart termed the epicardium. Conceptually, the method attempts to identify the key factors governing the ventricular activation sequence – the timing of earliest activation sites (EAS) and the velocity tensor field within the ventricular walls – from sparse and noisy activation maps sampled from the epicardial surface and fits an Eikonal model to the observations. Regularization methods are first investigated to overcome the severe ill-posedness of the inverse problem in a simplified 2D example. These methods are then employed in an anatomically accurate biventricular model with two realistic activation models of varying complexity – a simplified trifascicular model (3F) and a topologically realistic model of the His-Purkinje system (HPS). Using epicardial activation maps at full resolution, we first demonstrate that reconstructing the volumetric activation sequence is, in principle, feasible under the assumption of known location of EAS and later evaluate robustness of the method against noise and reduced spatial resolution of observations. Our results suggest that the FIMIN algorithm is able to robustly recover the full 3D activation sequence using epicardial activation maps at a spatial resolution achievable with current mapping systems and in the presence of noise. Comparing the accuracy achieved in the reconstructed activation maps with clinical data uncertainties suggests that the FIMIN method may be suitable for the patient-specific parameterization of activation models.

Original languageEnglish
Article number109700
JournalJournal of Computational Physics
Publication statusPublished - 15 Oct 2020


  • Fast iterative method
  • Fast marching
  • His-Purkinje system
  • Inverse Eikonal
  • Minimization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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