  Our goal is to model and measure functional and effective (directional)
connectivity in multichannel brain physiological signals (e.g.,
electroencephalograms, local field potentials). The difficulties from analyzing
these data mainly come from two aspects: first, there are major statistical and
computational challenges for modeling and analyzing high dimensional
multichannel brain signals; second, there is no set of universally-agreed
measures for characterizing connectivity. To model multichannel brain signals,
our approach 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). Then we employ some measures of connectivity but put an emphasis on
partial directed coherence (PDC) which can capture the directional connectivity
between channels. PDC is a frequency-specific measure that explains the extent
to which the present oscillatory activity in a sender channel influences the
future oscillatory activity in a specific receiver channel relative to all
possible receivers in the network. The proposed modeling approach provided key
insights into potential functional relationships among simultaneously recorded
sites during performance of 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.
