Approaches for Control of Cardiac Electrical Dynamics

This project is a component of a larger effort is to develop the foundations of modeling, synthesis and development of verified medical device software and systems from verified closed-loop models of the device and organ(s). This research spans both implantable medical devices such as cardiac pacemakers and physiological control systems such as drug infusion pumps which have multiple networked medical systems. Here we focus on alternans, a beat-to-beat alternation (period-2 dynamics) in cellular action potential shape and duration that leads to alternans in the T-wave of the ECG and often precedes more dangerous arrhythmias like ventricular fibrillation. Because alternans is a pathway to fibrillation, methods to control alternans are an important area of study. Many methods proposed for controlling alternans have been tested using models that include only one mechanism for alternans. Our goal is to understand how the alternans mechanism affects the ability to suppress alternans. In this project, we use a discrete-time model of cardiac electrical dynamics by Qu et al. to test the effectiveness of two types of control methods for alternans driven by each of two mechanisms: voltage instabilities and calcium instabilities. The first type of control includes methods that alter the timing of applied stimuli, either by keeping the time interval between action potential durations constant or through proportional-feedback perturbations to timing. The second type applies proportional feedback directly to a state variable either as that state's deviation from an approximation of the fixed point or as the difference in that state's preceding values. We found that most methods were successful in eliminating mild to moderate but not severe alternans. For control applied to a state variable, only the state variable representing action potential duration was effective, even when period-2 dynamics arose via calcium, and feedback proportional to the difference in previous action potential durations allowed smaller gain values to be used. In the future, we aim to perform controllability analysis aimed at understanding our results in more detail, to broaden our results to spatially extended systems, and to apply these types of control schemes to real-world settings involving cardiac tissue.