Bifurcation analysis of a certain Hodgkin-Huxley model depending on multiple bifurcation parameters

Abstract

In this paper, we study the dynamics of a certain Hodgkin-Huxley model describing the action potential (AP) of a cardiac muscle cell for a better understanding of the occurrence of a special type of cardiac arrhythmia, the so-called early afterdepolarisations (EADs). EADs are pathological voltage oscillations during the repolarisation or plateau phase of cardiac APs. They are considered as potential precursors to cardiac arrhythmia and are often associated with deficiencies in potassium currents or enhancements in the calcium or sodium currents, e.g., induced by ion channel diseases, drugs or stress. Our study is focused on the enhancement in the calcium current to identify regions, where EADs related to enhanced calcium current appear. To this aim, we study the dynamics of the model using bifurcation theory and numerical bifurcation analysis. Furthermore, we investigate the interaction of the potassium and calcium current. It turns out that a suitable increasing of the potassium current adjusted the EADs related to an enhanced calcium current. Thus, one can use our result to balance the EADs in the sense that an enhancement in the potassium currents may compensate the effect of enhanced calcium currents.