Heart arrhythmia is a pathological condition where the sequence of electrical impulses
in the heart deviates from the normal rhythm. It is often associated with specific
channelopathies in cardiac tissue, yet how precisely the changes in ionic channels
affect the electrical activity of cardiac cells is still an open question. Even though
sodium channel mutations that underlie cardiac syndromes like the Long-Q-T and the
Brugada-syndrome are known to affect a number of channel parameters simultaneously,
previous studies have predominantly focused on the persistent late component of the
sodium current as the causal explanation for an increased risk of heart arrhythmias
in these cardiac syndromes. A systematic analysis of the impact of other important
sodium channel parameters is currently lacking. Here, we investigate the reduced ten-Tusscher-model
for single human epicardium ventricle cells and use mathematical bifurcation analysis
to predict the dependence of the cardiac action potential on sodium channel activation
and inactivation time-constants and voltage dependence. We show that, specifically,
shifts of the voltage dependence of activation and inactivation curve can lead to
drastic changes in the action potential dynamics, inducing oscillations of the membrane
potential as well as bistability. Our results not only demonstrate a new way to induce
multiple co-existing states of excitability (biexcitability) but also emphasize the
critical role of the voltage dependence of sodium channel activation and inactivation
curves for the induction of heart-arrhythmias.
