Biomedical Engineering Reference
In-Depth Information
lacking in TFR analysis (Sect.
3.2.2
). Connectivity measures can be classifi ed into
two categories: (1)
functional
connectivity, which indicates symmetrical correla-
tions in activity between brain regions, and (2)
effective
connectivity, which repre-
sents asymmetric causal dependencies in activity between brain regions (Bullmore
and Sporns
2009
).
In this section, we will outline some commonly used spectral connectivity mea-
sures for multitrial multichannel data, which can be derived from the coeffi cients of
the vector autoregressive (VAR) model.
1
The accurate estimation of VAR coeffi -
cients requires that each time series be covariance stationary, i.e., its mean and vari-
ance remain unchanged over time. However, ECoG signals are usually highly
nonstationary, exhibiting dramatic and transient fl uctuations (see examples in
Fig.
3.1b
). Several methods have been proposed to improve stationarity [more detail
in (Delorme et al.
2011
)]. In this chapter, we will demonstrate connectivity mea-
sures by implementing a sliding-window method. The concept is to segment the
signals into suffi ciently small windows, then measure connectivity within each
window, where the signal is
locally
stationary.
A detailed tutorial of VAR-based connectivity measures can be found in the
Source Information Flow Toolbox (SIFT) handbook (
http://sccn.ucsd.edu/wiki/
2011
) together with other libraries, such as EEGLAB (Delorme and Makeig
2004
),
Granger causal connectivity analysis (GCCA) (Seth
2010
), and Brain-System for
Multivariate AutoRegressive Timeseries (BSMART) (Cui et al.
2008
).
Preprocessing Before Connectivity Measures
For multitrial data, the standard preprocessing steps for achieving local stationarity
are (1) detrending, (2) temporal normalization, and (3) ensemble normalization
(Ding et al.
2000
). Detrending, which is the subtraction of the best-fi tting line from
each time series, removes the linear drift in the data. Temporal normalization, which
is the subtraction of the mean of each time series and division by the standard devia-
tion, ensures that all variables have equal weights across the trial. These processes
should be performed on each trial for each channel. Ensemble normalization, which
is the pointwise subtraction of the ensemble mean and division by the ensemble
standard deviation, targets rich task-relevant information that cannot be inferred
from the event-related potential (ERP) (Ding et al.
2000
; Bressler and Seth
2011
).
1
A parametric model used to capture the linear interdependencies among multiple time series. A
VAR model describes a set of variables over the sample period as a linear function of their past
evolution, i.e., the variables of sample
t
as a linear combination of the variables of samples [
t
− 1,
t
− 2 ,…,
t
−
p
], where
p
is referred to as the
model order
. The VAR coeffi cients, after being trans-
formed into the frequency domain via Z transformation, can be used to compute spectral connec-
tivity measures.
