Abstract
Functional connectivity is of central importance in understanding brain function. For this purpose, multiple time series of electric cortical activity can be used for assessing the properties of a network: the strength, directionality, and spectral characteristics (i.e., which oscillations are preferentially transmitted) of the connections. The partial directed coherence (PDC) of Baccala and Sameshima (2001) is a widely used method for this problem. The three aims of this study are: (1) To show that the PDC can misrepresent the frequency response under plausible realistic conditions, thus defeating the main purpose for which the measure was developed; (2) To provide a solution to this problem, namely the “isolated effective coherence” (iCoh), which consists of estimating the partial coherence under a multivariate autoregressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest; and (3) To show that adequate iCoh estimators can be obtained from non-invasively computed cortical signals based on exact low resolution electromagnetic tomography (eLORETA) applied to scalp EEG recordings. To illustrate the severity of the problem with the PDC, and the solution achieved by the iCoh, three examples are given, based on: (1) Simulated time series with known dynamics; (2) Simulated cortical sources with known dynamics, used for generating EEG recordings, which are then used for estimating (with eLORETA) the source signals for the final connectivity assessment; and (3) EEG recordings in rats. Lastly, real human recordings are analyzed, where the iCoh between six cortical regions of interest are calculated and compared under eyes open and closed conditions, using 61-channel EEG recordings from 109 subjects. During eyes closed, the posterior cingulate sends alpha activity to all other regions. During eyes open, the anterior cingulate sends theta-alpha activity to other frontal regions.
Highlights
The type of problem that we are interested in can best be understood with an informal hypothetical example.Consider time series of local electric potential differences measured at five sites on the cortex
The three aims of this study are: (1) To show that the partial directed coherence (PDC) can misrepresent the frequency response under plausible realistic conditions, defeating the main purpose for which the measure was developed; (2) To provide a solution to this problem, namely the “isolated effective coherence”, which consists of estimating the partial coherence under a multivariate autoregressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest; and (3) To show that adequate iCoh estimators can be obtained from non-invasively computed cortical signals based on exact low resolution electromagnetic tomography applied to scalp EEG recordings
SIMULATED EEG The simulated EEG time series for 19 scalp electrodes, using as generators the five cortical locations described in the materials section (Figure 2), with time dynamics from the previous example, were analyzed with exact low resolution electromagnetic tomography (eLORETA)
Summary
The type of problem that we are interested in can best be understood with an informal hypothetical example. Consider time series of local electric potential differences measured at five sites (i.e., nodes) on the cortex (electrocorticogram, ECoG). Before connecting the five nodes, each one in isolation has its distinct activity. Node 1 oscillates at 28 Hz, node 2 at 16 Hz, and nodes 3, 4, and 5 at 23 Hz. In the construction step, some causal direct and directional connections with measurable time lags are established: node 1 sends to node 2; and node 2 sends identically to nodes 3, 4, and 5.
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