Analytically Solvable Asymptotic Model of Atrial Excitability

We report a three-variable simplified model of excitation fronts in human atrial tissue. The model is derived by novel asymptotic techniques \new{from the biophysically realistic model of Courtemanche et al (1998) in extension of our previous similar models. An iterative analytical solution of the model is presented which is in excellent quantitative agreement with the realistic model. It opens new possibilities for analytical studies as well as for efficient numerical simulation of this and other cardiac models of similar structure

Multi-formalism Modelling of Cardiac Tissue

Many models of the cardiovascular system (e.g. cardiac electrical activity, autonomous nervous system, ...) have been proposed for the last decades. Research is now focusing on the integration of these different models, in order to study more complicated physiopathological states in clinical applications context. To get round the practical limitations of existing models, multi-formalism modelling appears as a way to ease the integration of these different models together. This paper presents an original methodology allowing to combine different types of description formalisms. This method has been applied to define a multi-formalism model of cardiac action potential propagation on a 2D grid of endocardial cells, combining cellular automata and a set of cells defined by the Beeler-Reuter model. Results, obtained under physiologic and ischemic conditions, highlight the improvements in term of computing compared with mono-formalism systems, while keeping the necessary explanatory strength for a practical clinical use