A two-variable model of cardiac action potential with controlled pacemaker activity and ionic current interpretation

Since the introduction of the historical Fitzhugh-Nagumo model (1961) with its two state-variables used to describe the excitability phenomena of cell membranes and action potential generation, more complex models have been proposed to better capture the physiology of cardiac cells. However in some model-based signal or image processing applications, two-state-variable models are still useful and there is a need to improve both their qualitative behaviors (shape of action potential, pacemaker activity) and the interpretation of their parameters. Several models have then been derived from the Fitzhugh-Nagumo model, e.g. the van Capelle-Durrer (1980) or Aliev-Panfllov (1996) models, or from simplifications of more complex ionic models, like the Mitchell-Schaeffer model (2003). In this paper, we introduce a two state-variable model of cardiac action potentials from which the above mentioned models can be derived for particular values of its parameters. Like the Mitchell-Schaeffer model, it has an ionic current interpretation relevant for inverse problems and it improves that model, being capable of pacemaker activity as we show using the phase plane representation and a bifurcation analysis.