  Background: Computer models for simulating cardiac electrophysiology are
valuable tools for research and clinical applications. Traditional
reaction-diffusion (RD) models used for these purposes are computationally
expensive. While eikonal models offer a faster alternative, they are not
well-suited to study cardiac arrhythmias driven by reentrant activity. The
present work extends the diffusion-reaction eikonal alternant model (DREAM),
incorporating conduction velocity (CV) restitution for simulating complex
cardiac arrhythmias.
  Methods: The DREAM modifies the fast iterative method to model cyclical
behavior, dynamic boundary conditions, and frequency-dependent anisotropic CV.
Additionally, the model alternates with an approximated RD model, using a
detailed ionic model for the reaction term and a triple-Gaussian to approximate
the diffusion term. The DREAM and monodomain models were compared, simulating
reentries in 2D manifolds with different resolutions.
  Results: The DREAM produced similar results across all resolutions, while
experiments with the monodomain model failed at lower resolutions. CV
restitution curves obtained using the DREAM closely approximated those produced
by the monodomain simulations. Reentry in 2D slabs yielded similar results in
vulnerable window and mean reentry duration for low CV in both models. In the
left atrium, most inducing points identified by the DREAM were also present in
the high-resolution monodomain model. DREAM's reentry simulations on meshes
with an average edge length of 1600$\mu$m were 40x faster than monodomain
simulations at 200$\mu$m.
  Conclusion: This work establishes the mathematical foundation for using the
accelerated DREAM simulation method for cardiac electrophysiology. Cardiac
research applications are enabled by a publicly available implementation in the
openCARP simulator.
