Model predictive control of the cardiac amplitude of alternans PDE

Sudden cardiac death resulting from ventricular arrhythmia is one of the leading causes of mortality in the United States. The beat-to-beat oscillations in the action potential duration (APD) of paced cardiac cells, defined as cardiac alternans, has been identified as a potential precursor to ventricular arrhythmia. Therefore, the annihilation of these alternans is a promising antiarrhythmic strategy. In this work, the small amplitude of alternans partial differential equation (PDE) for a one dimensional cable of cardiac cells is stabilized through model predictive control (MPC). In our proposed control strategy, both boundary and spatially distributed actuators are utilized in suppressing the alternans along the cable. The low-order MPC formulation is developed for the finite-dimensional, discrete state space representation of the PDE. Furthermore, input and state constraints are addressed explicitly in the MPC formulation. The input constraints may arise due to actuator limitations, while state constraints are naturally present in cardiac systems. By satisfying these constraints, we can ensure that the controller action will not induce conduction block in the cardiac cells. Simulation results are presented to demonstrate the successful annihilation of alternans using the proposed control algorithm.