A two-variable model robust to pacemaker behaviour for the dynamics of the cardiac action potential

Ionic models with two state variables are routinely used in patient specific electro-physiology simulations due to the small number of parameters to be constrained and their computational tractability. Among these models, the Mitchell and Schaeffer (MS) action potential model is often used in ventricle electro-physiology due to its ability to reproduce the shape of the action potential and its restitution properties. However, for some choices of parameters characterising this ionic model, unwanted pacemaker behaviour is present. The absence of any a priori criterion to exclude unstable parameter combinations affects parameter fitting algorithms, as unphysiological solutions can only be discarded a posteriori. In this paper we propose an adaptation of the MS model that does not exhibit pacemaker behaviour for any combination of the parameters. The robustness to pacemaker behaviour makes this model suitable for inverse problem applications.