[2] Neuroanatomical connectivity is inherently difficult to define given the fact that at the microscopic scale of neurons, new synaptic connections or elimination of existing ones are formed dynamically and are largely dependent on the function executed, but may be considered as pathways extending over regions of the brain, which are in accordance with general anatomical knowledge.
Functional connectivity, may be defined as the temporal correlation (in terms of statistically significant dependence between distant brain regions) among the activity of different neural assemblies, whereas effective connectivity may be defined as the direct or indirect influence that one neural system exerts over another.
[7] Transfer entropy has been applied in neuroimaging studies to infer effective connectivity, particularly in dynamic systems like resting-state fMRI.
Vincent Calhoun and colleagues have employed TE to identify connectivity alterations in disorders like schizophrenia.
Nonlinear measures require long stationary segments of signals, are prone to systematic errors, and above all are very sensitive to noise.
[7][8][11] The comparison of nonlinear methods with linear correlation in the presence of noise reveals the poorer performance of non-linear estimators.
In fact it was demonstrated by means of surrogate data test,[12][13] and time series forecasting [14] that nonlinearity in EEG and LFP is the exception rather than the norm.
Consider the very common situation that the activity from a given source is measured at electrodes positioned at different distances, hence different delays between the recorded signals.
When a bivariate measure is applied, propagation is always obtained when there is a delay between channels.,[19] which results in a lot of spurious flows.
Granger causality principle can be expressed in terms of two-channel multivariate autoregressive model (MVAR).
By the transformation to the frequency domain we get: H(f) is a transfer matrix of the system, it contains information about the relationships between signals and their spectral characteristics.
Model order may be found by means of criteria developed in the framework of information theory,[22] e.g. AIC criterion.
First, the model is fitted to whole n-channel system, leading to the residual variance Vi,n(t) = var(Ei,n(t)) for signal xi.
The dDTFj→i has a nonzero value when both functions Fij(f) and Cij(f) are non-zero, in that case there exists a direct causal relation between channels j→i.
[29] The partial directed coherence (PDC) was defined by Baccala and Sameshima [30] in the following form: In the above equation Aij(f) is an element of A(f)—a Fourier transform of MVAR model coefficients A(t), where aj(f) is j-th column of A(f) and the asterisk denotes the transpose and complex conjugate operation.
Estimation of MVAR coefficients is based on calculation of the correlation matrix between channels Rij of k signals Xi from multivariate set,[22] separately for each trial.
The variance of the function value is obtained by repeated calculation of the results for a randomly selected (with repetitions) pool of the original data trials.
Specifically, DTF found multiple applications, the early ones involved: localization of epileptic foci,[41] estimation of EEG propagation in different sleep stages and wakefulness,[42] determination of transmission between brain structures of an animal during a behavioral test.
In the deep sleep the source is over corpus callosum, presumably it is connected with feeding the cortex from the sub-cortical structures.
[44][45] The results corresponded very well with the known phenomena of event related synchronization and desynchronization such as decrease of the activity in alpha and beta band and brief increase of activity in the gamma band during movement in the areas corresponding to primary motor cortex, beta rebound after movement and so-called surround effect.
In case of real movement the short burst of gamma propagation was observed from the electrode positioned over finger primary motor cortex .
[49] The results obtained by means of SDTF in experiments involving working memory were compatible with fMRI studies on the localization of the active sites and supplied the information concerning the temporal interaction between them.
Recent articles[52][53] highlight that previous claims[54] that DTF and PDC were insensitive to volume conduction were inaccurate.
Indeed, DTF results obtained for signals recorded from the scalp are in general affected by volume conduction.
Even though the effects of volume conduction might be minimal in specific recording situations,[55] appropriate preprocessing on channel data (such as source identification) should be performed before estimating DTF or PDC.
The existence of well defined sources of brain activity connected with particular experimental conditions are well established in fMRI experiments, by means of inverse solution methods and intracortical measurements.