An eikonal model with re-excitability for fast simulations in cardiac electrophysiology

Precision cardiology based on cardiac digital twins relies on accurate yet computationally efficient simulations of cardiac electrophysiology and arrhythmias. Detailed biophysical models, such as the monodomain equation, are computationally demanding and therefore have limited applicability in clinical settings. It is thus desirable to develop reduced models that preserve the main physiological features of arrhythmic propagation while enabling faster computation. The standard eikonal model, an approximation of the monodomain model, effectively predicts the arrival times of the electrical wavefronts, but cannot reproduce the complex re-entrant dynamics characteristic of many cardiac arrhythmias. In this work, we extend the eikonal model to include tissue re-excitability, allowing it to capture re-entries occurring during cardiac arrhythmias. Re-excitability properties are inferred from the cable equation. The proposed formulation also incorporates tissue anisotropy and structural heterogeneities, such as scar and border zones. This structure separates the anatomical substrate for propagation from local restitution properties, which determine tissue recovery after excitation. When compared to the monodomain equation, our model reproduces anisotropic conduction and action potential duration with qualitative accuracy in cases involving macro re-entries. Its computational efficiency and limited preprocessing requirements make it suitable for potential real-time applications and integration within clinical digital twin frameworks. KEY POINTS: Re-entry is a key mechanism sustaining cardiac arrhythmias, but detailed computer models can be too slow for patient-specific clinical use. The eikonal model is fast, but normally describes only one activation wave and cannot reproduce repeated tissue excitation. We extend the eikonal model by adding tissue recovery, restitution properties and anisotropic conduction. The formulation separates local propagation, shaped by anatomy and conduction properties, from local tissue recovery, which can reflect cellular physiology. This fast approach reproduces major features of atrial and ventricular macro-re-entry and can support rapid screening of possible re-entry circuits.