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Wolff–Parkinson–White syndrome is a disease where an arrhythmia is caused by the ventricles being electrically excited by an additional accessory pathway that links the atria to the ventricles. The spread of the activation wave from this pathway to the ventricles is modeled using a simplified model of Hodgkin–Huxley sodium channel kinetics, in a two ion-channel model. The model is investigated both analytically (using an asymptotic analysis) and numerically, and both methods are shown to give the same result. It is found that for a given width of the accessory pathway, there is a critical sodium channel density needed for the activation wave to spread from the pathway to the tissue. This result provides an explanation for the success of class-I anti-arrhythmic drugs in treating Wolff–Parkinson–White syndrome.

Original publication




Journal article


International Journal of Bifurcation and Chaos


World Scientific Pub Co Pte Lt

Publication Date





3827 - 3834