New approach of controlling cardiac alternans

Abstract

The alternans of the cardiac action potential duration is a pathological rhythm. It is considered to be relating to the onset of ventricular fibrillation and sudden cardiac death. It is well known that, the predictive control is among the control methods that use the chaos to stabilize the unstable fixed point. Firstly, we show that alternans (or period-2 orbit) can be suppressed temporally by the predictive control of the periodic state of the system. Secondly, we determine an estimation of the size of a restricted attractions basin of the unstable equilibrium point representing the unstable regular rhythm stabilized by the control. This result allows the application of predictive control after one beat of alternans. In particular, using predictive control of periodic dynamics, we can delay the onset of bifurcations and direct a trajectory to a desired target stationary state. Examples of the numerical results showing the stabilization of the unstable normal rhythm are given.

Simplification of weakly nonlinear systems and analysis of cardiac activity using them

“…The existence of weak solutions to the underlying coupled electromechanical bidomain model is proved numerically. Chaos-based predictive control is studied in [17] to stabilize an unstable fixed point representing an unstable regular rhythm.…”

“…It is obvious that the qualitative properties of solutions to system (10) are related to the essential coefficients f (j) k , for which the indices satisfy (17). Such coefficients completely determine the invariable qualitative properties of the solutions to system (10), and, as a first approximation, they do not depend of nonessential coefficients, the indices of which do not satisfy the equality (17).…”