*5.1.1. Mathematical algorithms to estimate cortical connectivity*

*Functional cortical connectivity* may be estimated by calculating the correlation coefficient between signals of different regions, the covariance or the coherence of two or several signals. The disadvantage of these algorithms is the inability to determine the direction of data exchange between cortical and subcortical areas.

*Effective cortical connectivity* is estimated with the direct transfer function (DTF), based on Granger causality. Named after Clive Granger, econometrician awarded the Nobel Memorial Prize in Economic Sciences in 2003, the Granger linear systems causality states that for two time series (such as two EEG channels) with a unidirectional data exchange from the Y series to the X series, the modifications from the Y series will be found after a certain amount of time in the X series, or that analyzing Y series data can better predict X series modifications. By evaluating effective connectivity through DTF, we may analyze several time series/ EEG channels. This algorithm was developed by Polish mathematicians Kaminski and Blinowska in 1991 [90].

BSMART is a cortical connectivity analysis software package that can run on the MATLAB program.

Cortical connectivity can also be evaluated through imagistic methods (such as MRI) or electrophysiological methods (EEG).

High-density electroencephalography (64–256 electrodes) can provide information on intercortical connectivity, and is based on EEG signal analysis of different cortical regions. It has the advantage of being usable bedside, and data analysis can be performed more quickly than in the case of imagistic methods [91, 92].
