UC Irvine

The hippocampus is critical to memory consolidation. To study the underlying neuronal mechanisms of hippocampus in sequential memory, we consider an experiment recording multi-trial local field potentials (LFPs) from hippocampal region CA1 of rats that performed a complex sequence of memory tasks in different experimental conditions. Our work aims at (1.) modeling and measuring functional and effective (directional) connectivity in multi-channel LFP data; (2.) quantifying and differentiating connectivity in rat’s hippocampus at condition-level in order to study heterogeneous hippocampal functions. Our work addresses multiple statistical and computational challenges for modeling and analyzing multi-channel LFPs since the parameter space is usually high dimensional. Also, our contribution allows to measure the effective connectivity between channels in frequency domain with inferring directionality. Thirdly, we successfully incorporate within-conditions connectivity similarity with between-conditions connectivity heterogeneity in modeling and provide a natural way to conduct trial- and condition-level inference on effective connectivity.

To model multi-channel LFPs, we propose two approaches. The first one is to fit a vector autoregressive (VAR) model with potentially high lag order so that complex lead-lag temporal dynamics between the channels can be captured. Estimates of the VAR model will be obtained by our proposed hybrid LASSLE (LASSO+LSE) method which combines regularization (to control for sparsity) and least squares estimation (to improve bias and mean-squared error). One of the novelties of our approach is the use of a frequency-specific measure, partial directed coherence (PDC), to characterize effective connectivity. More specifically, PDC allows us to infer directionality and explain the extent to which the present oscillatory activity at certain frequency in a sender channel influences the future oscillatory activity in a specific receiver channel relative to all possible receivers in the brain network.

The second approach is using a Bayesian hierarchical vector autoregressive (BH-VAR) model to characterize brain connectivity and make inference on the difference of connectivity across experimental conditions. Within-conditions connectivity similarity and between-conditions connectivity heterogeneity are accounted by the priors on trial-specific models. In addition to the fully Bayesian framework, we also propose an alternative two-stage computation approach which still allows straightforward uncertainty quantification of between-trial conditions via MCMC posterior sampling, but provides a fast approximate procedure for the estimation of trial-specific VAR parameters.

Our proposed approaches provided key insights into both trial- and condition-level hippocampal connectivity among simultaneously recorded sites during performance of rats in a complex memory task. Specifically, this novel method was successful in quantifying patterns of effective connectivity across electrode locations, and in capturing how these patterns varied across trial epochs and trial types.