Functional Connectivity and Aging: Comodulation and Coherence Differences

ABSTRACT

Introduction. Misconceptions about coherence and comodulation has hindered their simultaneous use in assessing electroencephalography (EEG). Coherence refers to phase synchrony, whereas comodulation refers to magnitude synchrony. Child and adult EEG data were analyzed for age functions to demonstrate coherence and comodulation differences.

Method. Eyes closed resting EEG was analyzed for 101 children and adults between ages of 5 and 35 years (34 female, 67 male; M age = 17.5 years). Spectral analysis focused on site-centered connectivity of 10 frequency bands. Site-centered connectivity refers to averaged coherence or comodulation associated with a site, an estimate of its network traffic.

Results. Site-centered coherence and comodulation increased with age for frequencies below 30 Hz in most sites. Age-related changes in anterior connectivity occurred for adults but not for children. The strongest age function was found for alpha comodulation at electrode site T5. Differences in coherence and comodulation results are also reported.

Conclusion. Functional connectivity increases steadily with age. Anterior EEG connectivity increased during adulthood but not during childhood. This finding parallels previous research on anterior callosal myelination and suggests that EEG connectivity measures may in part reflect myelination patterns. A model that associates coherence and comodulation with feedforward and feedback activity of the brain is proposed. A Periodicity Table for creating new and potentially relevant psychophysiological coefficients was described.

KEYWORDS:

• Age
• coherence
• comodulation
• EEG
• entropy
• maturation
• periodicity table

M.B. Sterman contributed to the development of this work intellectually and financially.

Notes

Note. Significant correlations are in bold. t(99) > 4.055, p < .0001. SMR = sensorimotor range.

Note. Significant correlations are in bold. t(99) > 4.055, p < .0001. SMR = sensorimotor range.

Note. Significant correlations are in bold. p < .0001. SMR = sensorimotor range.

Note. Significant correlations are in bold. p < .0001. SMR = sensorimotor range.

Note. Significant correlations are in bold. p < .001. SMR = sensorimotor range.

Note. Local activity (column 1): Amplitude is voltage per unit time. Magnitude is a linear summation of burst incidence, duration, and intensity or amplitude. Autophase is “phase slippage” or mean phase difference of a given frequency from one epoch to the next. One formulation is Arctan [(Σ cos_t sin_t+1 − Σ cos_t+1 sin_t)²/(Σ cos_t sin_t+1 + Σ cos_t+1 sin_t)²] where t is current sample. Biamplitude is a ratio of spectral activity of one frequency to another, such as theta/beta power ratios (Lubar, Swartwood, Swartwood, & O'Donnell, 1995; Monastra et al., 2005). Biphase (or phase bicoherence) is mean phase difference between frequencies and it is monitored during anesthesia and neonatally (Shils, Litt, Skolnick, & Stecker, 1996; Witte et al., 2004). Spectral entropy is number of possible arrangements inherent in a signal, logarithmically-compressed (Shannon, 1948). Nunes (2004) likened spectral entropy to freedom: “conscious cortex is free to move among a huge number of available microstates” as long as the same macrostate is produced. Disorderly (high freedom) EEG is associated with mental effort and wakefulness while orderly EEG occur with sleep, isoelectricity, and non-responsiveness. Spectral entropy is monitored during anesthesia (Lipping, Ferenets, Mortier, & Struys, 2007): As entropy decreases, fewer magnitude combinations are available and level of consciousness decreases. Increasing cortical microstate arrangeability has neurotherapeutic implication (e.g., Martin, 2006). Phase entropy is phase freedom or independence (Breakspear, 2002).

Stability of activity (column 2): Autocorrelation is the auto-correlogram peak for a signal for all possible time lags. One formulation is Σ (z_t∗ z_t+1)/n where z refers to z-score of voltages and t to current sample and n total number of samples. Automodulation is magnitude consistency of a given frequency across time. One formulation is Σ (z_t∗ z_t+1)/n where z refers to z-score of magnitudes and t the current sample and n total number of samples. Autoherence is phase consistency of a given frequency across time. Bimodulation is magnitude consistency between frequencies (see Figure 10). One formulation is time-displaced bimodulation is Σ (z_a∗ z^b+t)/n where z refers to z-score of magnitude of two frequencies a and b, t equals time moments removed from signal a, and n number of samples. Trimodulation is magnitude consistency among three frequencies, i.e., mean normalized round-robin cross-product. Triherence (or tricoherence) is phase consistency among frequencies (Chandran, 1994).

Network state or connectivity (column 3): Reversals refer to temporal density of voltage polarity reversals in a signal. Unity is magnitude asymmetry subtracted from one with valence ignored, 1−|A−B|/(A + B). Sites attain unity (+ 1) when no difference in mean magnitude exists and there is disunity as differences increase. Unity may be especially useful in homologue assessment (Kaiser, 2007a; Figure 4). A more common magnitude asymmetry index is difference between sites compared to its sum, (A−B)/(A + B) (Strobos, 1960). Phase lag (phase asymmetry) is mean phase difference between sites. Cross-biamplitude compares spectral activity at a given frequency to activity in another frequency at another site (Schack et al., 2001). Frontal theta activity may be compared to simultaneous posterior alpha activity, or at different times (lags). Cross-biphase is mean phase difference between sites for different frequencies. Joint entropy is a measure of mutual information of two signals in terms of spectral magnitude or power, which is valuable to artifact detection (Jung et al., 2000; Makeig, Jung, Ghahremani, Bell, & Sejnowski, 1996). Autocorrelation of joint entropy (entropy modulation) over time provides a stability index. The spectral correlation coefficient (SCC) of Lexicor Medical Technology, Inc. estimates similarity of spectral constituents between signals by correlating sub-range spectral values, a rough estimate of joint entropy. In physics SCC refers to magnitude consistency (Eberly & Kujawski, 1968; Won, Kimb, & Mina, 2004). Joint phase entropy is a measure of mutual phase information (Barnett & Phoenix, 1991). Autocorrelation of joint phase entropy over time provides a stability index (phase entropy modulation).

Network stability (column 4): Reversal variability is standard deviation of reversal density per epoch. Comodulation is magnitude consistency between sites at a given frequency. One formulation is Σ (z_a∗ z_b)/n where z is normalized magnitude for signals a and b and n is number of evenly spaced samples. Coherence is phase consistency between sites at a given frequency. Cross-bimodulation is magnitude consistency of a given frequency at one site compared to another frequency at another site (see Figure 10). Cross-bicoherence is phase consistency of a given frequency at one site compared to another frequency at another site (Saltzberg, Burton, Birch, Fletcher, & Michaels, 1986).

System state (column 5): Peak amplitude is site of highest voltage. Rogue site estimates a topographic pattern of magnitude independence. Whichever site is least like all others in auto-normalized magnitude is termed rogue and percent of time spent rogue is computed (Kaiser, 2004). Rogue phase (or rogue site by phase) estimates a topographic pattern of phase independence. Each site is compared to all others on Autophase (or homologue phase, or mean cross-phase) and percent time spent rogue is determined. Site biamplitude is mean ratio of spectral activity at a given frequency compared to mean spectral activity for all other sites at another frequency. Site biphase is mean phase difference for a given frequency at a site compared to all other sites for another frequency. Rogue frequency estimates independence across topography and spectrum, using maximum percent time spent rogue for auto-normalized magnitudes at any frequency. Rogue frequency-phase estimates independence across topography and spectrum using autophase (or homologue) phase.

System stability (column 6): Peak autocorrelation is site of highest autocorrelation for any time lag. Site comodulation is mean comodulation of all electrode partners (19 pairings minus 1 auto-comparison), an estimate of network traffic or common activity at each site. Site coherence is mean coherence of all electrode partners, a phase-based estimate of network traffic. Site bimodulation is spectral activity at a given frequency correlated with mean spectral activity for all other sites at another frequency. Site bicoherence is bicoherence of a given frequency at one site compared to mean spectral activity of remaining sites (i.e., mean cospectrum, quaspectrum).

Global comodulation is a single number to summarize comodulation of 171 site-pairings for a frequency range, an estimate of total network activity. Global coherence is a phase-based estimate of total network activity, a summary of all site-pair coherences.