Data-driven phase-isostable reduction for optimal nonfeedback stabilization of cardiac alternans

Phase-isostable reduction is an emerging model reduction strategy that can be used to accurately replicate nonlinear behaviors in systems for which standard phase reduction techniques fail. In this work, we derive relationships between the cycle-to-cycle variance of the reduced isostable coordinates for systems subject to both additive white noise and periodic stimulation. Using this information, we propose a data-driven technique for inferring nonlinear terms of the phase-isostable coordinate reduction framework. We apply the proposed model inference strategy to the biologically motivated problem of eliminating cardiac alternans, an arrhythmia that is widely considered to be a precursor to more deadly cardiac arrhythmias. Using this strategy, by simply measuring a series of action potential durations in response to periodic stimulation, we are able to identify energy-optimal, nonfeedback control inputs to stabilize a period-1, alternans-free solution.