Analysis of neural excitability and oscillations
Methods in neuronal modeling
Oscillatory and bursting properties of neurons
The handbook of brain theory and neural networks
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The stability of induced pacemaker activity in a virtual human ventricular cell is analysed by numerical simulations and continuation algorithms, with the conductance of the time independent inward rectifying potassium current (IK1) as the bifurcation parameter. Autorhythmicity is induced within a narrow range of this conductance, where periodic oscillations and bursting behaviour are observed. The frequency of the oscillations approaches zero as the parameter moves towards the bifurcation point, suggesting a homoclinic bifurcation. Intracellular sodium ([Na+]i) and calcium ([Ca2+]i) concentration dynamics can influence the location of the bifurcation point and the stability of the periodic states. These two concentrations function as slow variables, pushing the fast membrane voltage system into and out of the periodic region, producing bursting behaviour. Moreover, suppressing IK1 will prolong action potential duration and may introduce risks of developing stable periodic intermittency and arrhythmia. A genetically engineered pacemaker may appear an attractive idea, but simple analysis suggests inherent problems.