Biomedical Engineering Reference
In-Depth Information
Many of the methods that have been developed to study the dynamics of corti-
cal networks have been based on the idea that oscillatory activity plays a role in
organizing the activity of neuronal assemblies in large-scale neural networks
[100-103]. A functional task engaging such a network is expected to be accompa-
nied by rapidly changing interrelationships and interactions between the oscilla-
tions generated in the various components of the network. To measure these
interactions, investigators have studied temporal fluctuations in coherence [104,
105], brain electrical source analysis coherences [106], and oscillatory synchrony
[107, 108]. Recently, attention has also focused on the directionality of interactions
between brain regions. For this purpose various approaches have been adopted,
such as calculations of evoked potential covariances [109], the imaginary part of
coherency [110], adaptive phase estimation [111], and methods based on Granger
causality [112-120].
14.4.1 Analysis of Causality in Cortical Networks
According to Granger causality, an observed time series
x
l
(
t
) causes another series
x
k
(
t
) if knowledge of
x
l
(
t
)'s past significantly improves prediction of
x
k
(
t
). Methods
based on this concept, extended to multichannel data, may be designed to determine
the sources and targets for interactions among brain regions [121, 122], allowing
one to study the dynamic architecture of brain networks participating in cognitive
tasks. An important problem to be solved by multivariate causality analysis is
whether causal interactions are direct or indirect (mediated by another site or by
several sites). Granger causality itself does not answer the question. Thus, the direct-
ness of interactions may be inferred by related methods: combining directed transfer
function (DTF) [119] with phase spectrum and cross-correlogram analyses [123],
using partial direct coherence [112, 113, 120], or using a direct directed transfer
function (dDTF) [124, 125].
dDTF makes use of partial coherence (which reveals the directness of interac-
tions) [126, 127] and DTF (which reveals directionality of interactions), and has
been widely used in investigations of activity flow in amnesic and Alzheimer's
patients [128], in patients with spinal cord injuries [129], in investigations of the
source of seizure onset in epileptic neural networks [130-132], in studies of
wake-sleep transitions [133-135], in working memory [136], and during encoding
and retrieval [137], as well as in animal behaviors [138]. DTF and related methods
have also been employed to investigate causal influences in fMRI data [139-141]
and have been used in a brain-computer interface [142]. However, DTF and dDTF
are not designed to analyze very short data epochs, as needed to track the dynamics
of cognitive processes. This particular limitation may be overcome when multiple
trials of a particular cognitive task are available for analysis [143], in which case a
modification of DTF, the short-time directed transfer function (SDTF), may be used
[117, 144-147].
To combine the benefits of directionality, directness, and short-time window-
ing, Korzeniewska et al. [148] introduced a new estimator, the short-time direct
directed transfer function (SdDTF). This function evaluates the directions, intensi-
ties, and spectral contents of direct causal interactions between signals and is also
adapted for examining short-time epochs. These properties of SdDTF are expected
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