Suppressing cardiac alternans: analysis and control of a border-collision bifurcation in a cardiac conduction model

This paper describes the utility of dynamic bifurcation control for suppressing a pathological period-2 rhythm (cardiac alternans) in an atrioventricular modal conduction model. A commonly held view has linked alternans rhythms in this model to period-doubling bifurcations. Our analysis shows that the alternans rhythm is actually associated with a period-1 to period-2 border-collision bifurcation. In the control design, we employ a dynamic feedback control incorporating washout filter to suppress the cardiac alternans. Important features of the dynamic control law include equilibrium preservation even in the presence of model uncertainty, and automatic targeting of the orbits to be controlled. An independent experiment of suppressing cardiac alternans in a piece of dissected rabbit heart demonstrates the viability and utility of the proposed bifurcation control approach. Controlling nonlinear cardiac dynamics may have important clinical implications since arrhythmias in the heart such as fibrillation and ectopic foci are life threatening. The controller designs described here can lead to the development of future smart clinical pacemakers.