Modelling positive Granger Causality and negative phase lag between cortical areas

Matias F. S.; Gollo, L. L., Carelli, P.; Bressler, S.; Copelli, M.; Mirasso, C. R.
Neuroimage 99, 411-418 (2014)

Different measures of directional influence have been employed to
infer effective connectivity in the brain. When the connectivity between
two regions is such that one them (the sender) strongly influences
the other (the receiver), a positive phase lag is often expected.
The assumption is that the time difference implicit in the relative
phase reflects the transmission time of neuronal activity. However,
Brovelli et al. (2004) observed that, in monkeys engaged in processing
a cognitive task, a dominant directional influence from one area of sensorimotor
cortex to another may be accompanied by either a negative
or a positive time delay. Here we present a model of two brain regions,
coupled with a well-defined directional influence, that displays similar
features to those observed in the experimental data. This model is
inspired by the theoretical framework of Anticipated Synchronization
developed in the field of dynamical systems. Anticipated Synchronization
is a form of synchronization that occurs when a unidirectional
influence is transmitted from a sender to a receiver, but the receiver
leads the sender in time. This counterintuitive synchronization regime
can be a stable solution of two dynamical systems coupled in a masterslave
(sender-receiver) configuration when the slave receives a negative
delayed self-feedback. Despite efforts to understand the dynamics of
Anticipated Synchronization, experimental evidence for it in the brain
has been lacking. By reproducing experimental delay times and coherence
spectra, our results provide a theoretical basis for the underlying
mechanisms of the observed dynamics, and suggest that the primate
cortex could operate in a regime of Anticipated Synchronization as
part of normal neurocognitive function.

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