Assessing direct paths of intracortical causal information flow of oscillatory activity with the isolated effective coherence (iCoh)

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.

Keywords: LORETA; alpha oscillation connectivity; causal intracortical connectivity; isolated effective coherence; resting state electriphysiological connectivity.

Figure 1

Direct causal directed connections between nodes, corresponding to the toy example defined by the multivariate autoregressive model in Equation 13.

Figure 2

Schematic representation of the anatomical locations of five cortical point sources used for generating EEG.

Figure 3

Estimated connectivity properties for the network in Figure 1. Isolated effective coherence (iCoh) shown in RED, and the generalized partial directed coherence (gPDC) shown in BLUE. Overlap of both curves is shown in BLACK. Vertical axis: 0 to 1. Frequency axis: 1 to 127 Hz. Columns are senders, rows are receivers. Coherence peak in column 1 occurs at 28 Hz. Coherence peak for iCoh in column 2 occurs at 16 Hz. Coherence peak for gPDC in column 2, row 1 occurs at 1 Hz; and Coherence peak for gPDC in column 2, rows 3, 4, and 5 occur at 23 Hz.

Figure 4

Estimated connectivity properties for simulated EEG signals (see Figure 2). Isolated effective coherence (iCoh) shown in RED, and the generalized partial directed coherence (gPDC) shown in BLUE. Vertical axis: 0 to 1. Frequency axis: 1 to 127 Hz. Columns are senders, rows are receivers. Coherence peak in column 1 occurs at 28 Hz. Coherence peak for iCoh in column 2 occurs at 16 Hz. Coherence peak for gPDC in column 2, row 1 occurs at 1 Hz; and Coherence peak for gPDC in column 2, rows 3, 4, and 5 occur at 23 Hz.

Figure 5

Estimated connectivity properties for rat EEG recordings from 15 skull electrodes. Isolated effective coherence (iCoh) shown in RED, and the generalized partial directed coherence (gPDC) shown in BLUE. Vertical axis: 0 to 1. Frequency axis: 7.8 to 250 Hz. Columns are senders, rows are receivers.

Figure 6

Comparison of electric neuronal activity (eLORETA) between eyes open and closed conditions. A Log-F-ratio statistic with correction for multiple testing was used, with corrected p = 0.05 at LogF = 0.91. Eyes open is characterized by significantly stronger activity in frontal cortical regions oscillating at 3 Hz (A) and in the beta band 23–28 Hz (C). Eyes closed is characterized by significantly stronger activity in occipital cortical regions oscillating at 10 Hz (B).

Figure 7

t-Statistics comparing eyes open minus eyes closed iCoh for 109 subjects, in six regions of interest: anterior cingulate, posterior cingulate, left and right inferior parietal, and left and right dorsolateral pre-frontal cortices. Frequency axis: 1 to 30 Hz. Corrected p = 0.05 was at t-threshold = 4.3, with vertical axis: −7 to +7. Blue color denotes eyes closed significantly larger, red color denotes eyes open significantly larger. The three numbers indicate the frequencies (Hz) for the significant results: start, end, and the most significant oscillation indicated with a superscript “^*.” Columns are senders (prefix “s”), rows are receivers (prefix “r”).

Figure 8

Summary of the main statistically significant results comparing the network properties between eyes open and closed conditions. During eyes closed, the posterior cingulate significantly sends mostly alpha oscillations to all other regions. During eyes open, the anterior cingulate significantly sends mostly theta-alpha oscillations to the dorsolateral pre-frontal cortices. PCC, posterior cingulate cortex; ACC, anterior cingulate cortex; LIPL, RIPL, left and right inferior parietal lobule; LDLPFC, RDLPFC, left and right dorsolateral pre-frontal cortex.