A Graphical-Based Mathematical Model for Simulating Excitability in a Single Cardiac Cell

Excitability is a phenomenon seen in different kinds of systems, e.g., biological systems. Cardiac cells and neurons are well-known examples of excitable biological systems. Excitability as a crucial property should be involved in mathematical models of cardiac cells, along with the other biological properties. Excitability of mathematical cardiac-cell models is usually investigated in the phase plane (or the phase space) which is not applicable with simple mathematical analysis. Besides, the possible roles of each model parameter in the excitability property cannot be investigated explicitly and independently using phase plane analysis. In this paper, we present a new graphical-based method for designing excitability of a single cardiac cell. Each parameter in the presented approach not only has electrophysiological interpretation but also its role in regulating excitability is evident and can be analysed explicitly. Our approach is simpler and more tractable by mathematical analysis than the phase plane method. Another advantage of our approach is that the other important feature of the cardiac cell action potential, i.e., plateau morphology, can be designed and regulated separately from the excitability property. To evaluate our presented approach, we applied it for simulating excitability in well-known complex electrophysiological models of ventricular and atrial cells. Results show that our model can simulate excitability and time evolution of the plateau phase simultaneously.