Optimal mechano-electric stabilization of cardiac alternans

Alternation of normal action potential morphology in the myocardium is a condition with a beat-to-beat oscillation in the length of the electric wave which is linked through electromechanical coupling to the cardiac muscle contraction, and is believed to be the first manifestation of the onset of life threatening ventricular arrhythmias and sudden cardiac death. In this work, the effects of electrical and mechanical stimuli are utilized in alternans annihilation problem. Electrical stimuli that alter the action-potential morphology are represented by a pacer located at the domain´s boundary, while mechanical stimuli are distributed within the spatial domain and affect the action potential by altering intracellular calcium kinetics. Alternation of action potential is described by the small amplitude of alternans parabolic partial differential equation (PDE). Spatially uniform unstable steady-state of the alternans amplitude PDE is stabilized by optimal control methods through boundary and spatially distributed actuation. Mixed boundary and spatially distributed actuation is manipulated by a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control structure and in a compensator design with a Luenberger-type observer, and it achieves exponential stabilization in a finite size tissue cable length. The proposed control problem formulation and the performance and robustness of the closed-loop system under the proposed linear controller are evaluated through simulations.