Coherence
Coherence and Phase synchrony are common mathematical methods for quantifying frequency and phase dependent correlations of brain activity measured by two or more brain sensors. Functional connectivity does not determine the specific direction of information flow in the brain. It just shows that these regions have similar signal content and therefor are most likely connected. Neurons communicate with other neurons by releasing one of over 50 different types of neurotransmitters in the brain, some of which are excitatory (stimulate the brain) and some are inhibitory (calm the brain) [9]
Voltage-gated ion channels generate action potentials and periodic spiking membrane potentials which produces oscillatory activity and facilitates synchronous activity in neighboring neurons [34, 35]. Coherent neuronal communications are based on neurotransmission dynamics dictated by major neurotransmitters like the amino acids glutamate and GABA. Other important neurotransmitters include acetylcholine, dopamine, adrenaline, histamine, serotonin and melatonin [24, 44, 48]. These action potentials activate a neighboring population of neurons which in turn may affect other populations of neurons at a distance creating a network of connectivity. Coherence across a network is when these populations of neurons are active at the same time or in a time-related fashion with other populations, not a relationship of activity between individual neurons.
Synchronized activity of a significantly large population of neurons can give rise to large electric field oscillations with a concomitant magnetic field. EEG measure the return or volume currents outside of the neuron (secondary currents Coherence is a mathematical technique that quantifies the frequency and amplitude of the synchronicity of neuronal patterns of oscillating brain activity. This technique quantifies the neuronal patterns of synchronicity measured between spatially separated scalp electrodes (Electroencephalogram) or coils (Magnetoencephalogram) [14]. Coherence is an estimate of the consistency of relative amplitude and phase between signals detected in coils or electrodes within a set frequency band. In sensor space if signals are in phase then their amplitudes will add, if they are out of phase the signals will subtract possibly reducing the coherence value. The method for quantifying the oscillations is to first apply a time-frequency decomposition technique such as the Fast Fourier transform (FFT), on a contiguous or slightly overlapping sequence of short data segments. This generates a sequence of amplitude/phase components for each narrow frequency bin (i.e. 2–4 Hz) of the FFT that spans the frequency (i.e. 1–100 Hz) content of the data. After transformation to a time frequency representation, the strength of network interactions can be estimated by calculation of coherence, which measures the synchrony between signals from different electrodes or coils at each FFT frequency bin. Coherence is a linear math method in the frequency domain for calculating neuronal networks. The result is a symmetrical matrix that provides no information on directionality. Coherence is the most common measure used to determine if different areas of the brain are generating signals that are significantly correlated (coherent) or not significantly correlated (not coherent). If the signals measured by two electrodes or coils are identical then they have a coherence value of 1; depending on how dissimilar they are the coherent value will approach 0.
Coherence in Source Space Specific to the local brain region that is active and indicated by colored pixels
Typically EEG Coherence in sensor space has been widely used in studying epileptiform activity to determine seizure onset zones. Brazier in 1972 [6] was the first to use coherence to detect the influence of one brain region over another during epileptic seizure. Later Gotman in 1981 [18] made the method more reliable by including more frequencies and validating the use of this method to detect inter hemispheric interactions. In the present day, Song et al. has shown that EEG coherence can be used to characterize a pattern of strong coherence centered on temporal lobe structures in several patients with epilepsy [43].
Ozerdem et al. [39] found patients with a Bipolar disorder showed bilaterally diminished long-distance gamma coherence between frontal and temporal as well as between frontal and temporo-parietal regions compared with healthy controls. In patients with Alzheimer’s the most common finding is a decrease in the alpha and beta band coherences between distant structures during resting state [1, 36]. Coherence does provide a global estimate of all important regions of network activity regardless of source amplitudes. Because of the need to minimize bias by increasing the number of data segments in calculations, coherence is not well suited for quantifying rapid temporal changes in synchronized activity. Rather it is best when used for long time series of data to identify sources of brain network activity that persist for long durations. Coherence analysis supplies information on the degree of synchrony of brain activity at different locations for each frequency, independent of power.
