Estimation of Spontaneous Transient Dynamics based on Peri-event Data

Spontaneously occurring transient events are ubiquitous in complex systems like the brain. This can be observed during sleep, where network mechanisms give rise to a variety of patterns in the electrophysiological activity recorded in multiple structures: for example cortical slow waves, thalamic spindles and hippocampal sharp wave-ripples (SPW-Rs). Understanding the emergence and dynamics of such transient phenomena is a key step to understand their functional role. Investigating brain dynamics related to events typically relies on a two-step procedure: 1) events are detected as repetitive patterns of neural activities via thresholding of a detection signal based on classical filtering (e.g. [1]) or template matching approaches (e.g. [2]), and 2) peri-event traces are gathered as multi-trial panel data for further analysis of peri-event dynamics. However, this approach is problematic because the statistics of the collected peri-event data are biased by the detection procedure, thereby misrepresenting the properties of the true dynamical system. We thus develop a mathematical model of the whole event-triggered analysis procedure that takes into account the effect of detection on dynamic inference (Figure 1A). Within the framework of dynamical systems and ergodic theory [3], we treat time-varying peri-event dynamics as consecutive snapshots of the state space trajectories, whose time-varying dynamics can be modeled by Gaussian linear autoregressive models. We show that the detection procedure induces selection bias in the embedding space (Figure 1B) and analyze the nature of such bias using Structural Causal Models [4]. We then develop a bias correction procedure - DeSnap - whose ability to properly estimate the model parameters (auto-regressive coefficients) based on debiased peri-event statistics (mean and covariance), is demonstrated on simulated dynamical systems (Figure 1C, D). We also show that the de-biased power spectrograms of hippocampal SPW-Rs are able to categorize SPW-R events defined in ten frequency bands into two groups that are consistent with experimental findings. Overall, these results suggest that the event analysis framework we proposed, as well as the DeSnap algorithm, has a better potential to characterize system dynamics underlying transient events