**1. Introduction**

The EEG is a neuroimaging device that reflects the electrophysiological activity of the cerebrum that is generated by the synchronistic firing of nerve cells [1, 2]. Because the EEG reflects dynamic neurocognitive processes according to millisecond variations, the statistical properties of neural activation and processes fluctuate according to time, depth, and orientation of the neural generators. Measurement

of the electrical activity reflected by the EEG is best conceptualized as a nonlinear stochastic process that is inherently spatio-temporally dependent [1, 2].

Extracellular currents are derived from excitatory and inhibitory postsynaptic potentials allow for dipole moment per unit volume approximations [1, 3]. The dipole moment per unit volume approximations allow for the derivation of weighted estimations of current source density according to neural generators across and between local tissues and the orthogonal orientation of nerve cells within the neocortical layers [1].

While measurements of extracellular currents can be measured using divergent mathematical algorithms (i.e., phase shift, phase lock, coherence, and lagged coherence), the interaction between neurons that generate excitatory and inhibitory postsynaptic potentials must be evaluated according to time, frequency, and the location of the neural generators [4, 5]. Utilization of the Fast Fourier Transformation (FFT) allows for the derivation of EEG frequency bands from the raw signal according to time. FFT analyses elucidate phase angle and phase differences from the EEG frequency domains. When the phase angle is stable or constant, this indicates that coherence = 1.0 whereas coherence = 0 when there are phase differences due to moment to moment variations in the phase angle. Thus, coherence elucidates communication between distal and contiguous neuroanatomical regions and therefore, across and between functional networks via coupled neural oscillators [4, 5].

Mathematical modeling of current sources can be reflected as *P* (*r*′, *t*) when the estimation is derived according to dipole moment per unit volumetric approximations [1]. This algorithmic model asserts that *r*′ is the estimated location of the neural source according to volume where t indicates time. Limitations of source localization methods are attributable to the inverse problem and assumptions related to the head volume conduction model [1–6]. The head volume conduction model is significantly flawed because there are multiple layers of biological material that the electrical current must surpass before it can be reflected on the scalp [1, 7]. Furthermore, because of the anisotropic conductivity of the brain, which is attributable to the inhomogeneous conductivity of the cerebrospinal fluid, dura and cerebral tissue, there are an infinite number of solutions to the inverse solution [1, 8–10].
