Key result
Adding temporal delay to the Aliev-Panfilov model induces sustained oscillations analogous to cardiac arrhythmias.
Why the study?
The classical Aliev-Panfilov mathematical representation of cardiac excitation required extension to account for physiologically motivated temporal delays representing latency in cellular signaling and tissue-level propagation.
Mathematical modeling using an extended Aliev-Panfilov model demonstrates that small temporal delays in cellular signaling and tissue propagation can destabilize cardiac excitation and induce sustained oscillations analogous to cardiac arrhythmias.
Delay-extended Aliev-Panfilov model is mathematically well-posed; leaves open experimental validation before any arrhythmia modeling applications.
The Aliev-Panfilov model is a widely adopted mathematical representation of cardiac excitation, renowned for capturing the essential restitution properties of cardiac tissue. In this study, we extend the classical model by incorporating a physiologically motivated temporal delay to account for latency in cellular signaling and tissue-level propagation. We begin by establishing the well-posedness of the delay model, proving the existence, uniqueness, and boundedness of its solutions. A detailed equilibrium analysis is conducted to determine conditions for the existence and stability of steady states, revealing how time delay alters the system's dynamical behavior. To assess global stability, we construct suitable Lyapunov functions, while local stability of the non-delayed system is examined using the Routh--Hurwitz criterion. The delay-augmented model is further analyzed through its characteristic equation, leading to a bifurcation study that identifies Hopf bifurcations ``marking the emergence of sustained oscillations'' as the delay parameter crosses critical thresholds. Our results demonstrate that even small delays can destabilize the system, potentially inducing abnormal rhythmic patterns analogous to cardiac arrhythmias. This work underscores the significant role of temporal delay in cardiac dynamics and provides a rigorous mathematical framework for understanding delay-induced excitability changes in cardiac tissue.
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Das et al. (2026) studied Cardiac excitation and arrhythmias. Delay-augmented Aliev-Panfilov mathematical model vs. Classical non-delayed Aliev-Panfilov model was evaluated on Dynamical stability and emergence of Hopf bifurcations. Incorporating temporal delay into the Aliev-Panfilov cardiac excitation model induces Hopf bifurcations and sustained oscillations analogous to cardiac arrhythmias.
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