Parametric study of the Noble’s action potential model for cardiac Purkinje fibers

The effect of parameter variation on repolarization processes in the Noble model (Hodjkin–Huxley type) for action potential (AP) generation in Purkinje cells is studied using a combination of computer simulation and nonlinear dynamic system theory including Hopf bifurcation analysis. Both the original Noble model and a simplified Noble model are used in this study. It is shown that these models have similar qualitative dynamic behavior in the presence of parameter variations. In particular, it is demonstrated that both normal and abnormal modes of cell performance can be obtained by varying the potassium and anion conductances. The abnormal mode (cardiac arrest) may play a significant role in disorganizing the electrical activities in the heart muscles. The existence of Hopf bifurcation with respect to variations in the anion conductance and fixed values of potassium conductances is studied in detail. The regions corresponding to spontaneous AP excitation, and various types of cardiac arrest in the ion-conductance parameter space of both full and simplified Noble models with and without external stimuli are mapped out using computer simulation.