Sequential estimation of nonstationary oscillator states and stimulus responses

Neural oscillations have been linked to multiple behaviors and neuropsychiatric disorders. The individual contributions to behavior from both oscillations and non-oscillatory activity are still unclear, complicating efforts to link neurophysiology to cognition, hindering the discovery of novel biomarkers, and preventing the development of effective therapeutics. To overcome these hurdles, it will be critical to investigate the biological origins of neural oscillations by characterizing the dynamic properties of different brain regions. The dynamical regime for a population of neurons generating oscillations in neural recordings can be discovered by stimulating the population and recording its subsequent response to stimulation. There are different dynamical regimes that can produce population-level neural oscillations. For certain dynamical regimes, like that of a nonlinear oscillator, the phase response curve (PRC) can help differentiate the dynamic state of the population. The PRC can be measured by stimulating the population across different phases of its oscillatory state. However, neural dynamics are non-stationary, so neural oscillations will vary in frequency and amplitude across a recording and the PRC can change over time. This non-stationarity could bias a PRC estimated from an electrophysiological experiment, preventing accurate characterization of a neural populations dynamics. This necessitates tools that can operate online to trigger stimulation and update PRC estimates. To that end, we develop online methods for tracking non-stationary oscillations and recovering PRCs corrupted by estimation errors. We validate the performance of our non-stationary oscillation estimator compared to both a known ground truth model and an alternative phase estimation approach. We demonstrate that a PRC can be recovered online underdifferent random error conditions in silico and that a similar amplitude response curve (ARC) can be estimated from physiologic data using online methods compared to offline approaches.