BAYESIAN INFERENCE OF LATENT SPECTRAL AND TEMPORAL NETWORK ORGANIZATIONS FROM HIGH DIMENSIONAL NEURAL DATA

Abstract

The field of neuroscience has striven for more than a century to understand how the brain functionally coordinates billions of neurons to perform its many tasks. Recent advancements in neural data acquisition techniques such as multi-electrode arrays, two-photon calcium imaging, and high-speed light-sheet microscopy have significantly contributed to this endeavor's progression by facilitating concurrent observation of spiking activity in large neuronal populations. However, existing methods for network-level inference from these data have several shortcomings: including undermining the non-linear dynamics, ignoring non-stationary brain activity, and causing error propagation by performing inference in a multi-stage fashion. The goal of this dissertation is to close this gap by developing models and methods to directly infer the dynamic spectral and temporal network organizations in the brain, from these ensemble neural data.

In the first part of this dissertation, we introduce Bayesian methods to infer dynamic frequency-domain network organizations in neuronal ensembles from spiking observations, by integrating techniques such as point process modeling, state-space estimation, and multitaper spectral estimation. Firstly, we introduce a semi-stationary multitaper multivariate spectral analysis method tailored for neuronal spiking data and establish theoretical bounds on its performance. Building upon this estimator, we then introduce a framework to derive spectrotemporal Granger causal interactions in a population of neurons from spiking data. We demonstrate the validity of these methods through simulations, and applications on real data recorded from cortical neurons of rats during sleep, and human subjects undergoing anesthesia. Finally, we extend these methods to develop a precise frequency-domain inference method to characterize human heart rate variability from electrocardiogram data.

The second part introduces a methodology to directly estimate signal and noise correlation networks from two-photon calcium imaging observations. We explicitly model the observation noise, temporal blurring of spiking activities, and other underlying non-linearities in a Bayesian framework, and derive an efficient variational inference method. We demonstrate the validity of the resulting estimators through theoretical analysis and extensive simulations, all of which establish significant gains over existing methods. Applications of our method on real data recorded from the mouse primary auditory cortex reveal novel and distinct spatial patterns in the correlation networks. Finally, we use our methods to investigate how the correlation networks in the auditory cortex change under different stimulus conditions, and during perceptual learning.

In the third part, we investigate the respiratory network and the swimming-respiration coordination in larval zebrafish by applying several spectro-temporal analysis techniques, on whole-brain light-sheet microscopy imaging data. Firstly, using multitaper spectrotemporal analysis techniques, we categorize brain regions that are synchronized with the respiratory rhythm based on their distinct phases. Then, we demonstrate that zebrafish swimming is phase-locked to breathing. Next, through the analysis of neural activity and behavior under optogenetic stimulations and two-photon ablations, we identify the brain regions that are key for this swimming-respiration coordination. Finally, using the Izhikevich model for spiking neurons, we develop and simulate a circuit model that replicates this swimming-respiration coupling phenomenon, providing new insights into the possible underlying neural circuitry.