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Paul L. Nunez and Ramesh Srinivasan (2007), Scholarpedia, 2(2):1348. doi:10.4249/scholarpedia.1348 revision #91219 [link to/cite this article]
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Curator: Ramesh Srinivasan

Figure 1: A geodesic net with 128 electrodes making scalp contact with a salinated sponge material is shown (Courtesy Electrical Geodesics, Inc). This is one of several kinds of EEG recording methods. Reproduced from Nunez (2002).

The electroencephalogram (EEG) is a record of the oscillations of brain electric potentials recorded from perhaps 20 to 256 electrodes attached to the human scalp as indicated in Figure 1.

The recorded signals are transmitted to an EEG system composed of amplifiers, filters, and paper chart or computer monitor. The first human EEG recordings were accomplished by the German psychiatrist Hans Berger in 1924. Berger’s subjects (typically his children) revealed robust changes when the eyes were closed and when the subjects performed mental arithmetic. The scientific community was at first quite skeptical that these scalp signals originated in brain tissue but by 1934 their brain origins had been established.


A Window on the Mind

The EEG provides a convenient window on the mind, revealing synaptic action that is moderately to strongly correlated with brain state. A few EEG channels and corresponding amplitude spectra are shown in Figure 2 in a subject awake and relaxed with eyes closed. Most EEG signals originate in the brain’s outer layer (the cerebral cortex), believed largely responsible for our individual thoughts, emotions and behavior. Cortical synaptic action generates electrical signals that change in the 10 to 100 millisecond range. EEG and MEG (magnetoencephalography) are the only widely available technologies with sufficient temporal resolution to follow these fast dynamic changes. On the other hand, EEG and MEG spatial resolutions are poor relative to modern brain structural imaging methods like computer tomography (CT), positron emitted tomography (PET) and magnetic resonance imaging (MRI). Each scalp electrode (or MEG coil) records electrical activity at very large scales, recording electric potentials (or magnetic fields) generated in tissue containing something like 10 million to one billion neurons in the cortical layer.

Figure 2: (Upper) Alpha rhythm recorded from a healthy relaxed subject (age 25) with closed eyes using an electrode on the neck as reference. Four seconds of data are shown from four scalp locations (left frontal-channel 30; right frontal-channel 26; left posterior-channel 108; right posterior-channel 100). The amplitude is given in microvolts. This EEG was recorded at the Brain Sciences Institute in Melbourne. (Lower) The corresponding amplitude spectra based on the full five minute record reveals dominant activity in the alpha (8-13 Hz) band. Reproduced from Nunez and Srinivasan (2006).

Electrodes are placed inside the skull to study non-human mammals or human epilepsy patients. Such intracranial recordings provide measures of cortical dynamics at several small scales depending on electrode size. By contrast, scalp recorded EEG dynamics is exclusively large scale and nearly independent of electrode size because of the severe space averaging between brain current sources and scalp electrodes. The technical and ethical limitations of human intracranial recording force emphasis on scalp recordings. Luckily, these large-scale estimates provide important measures of brain dysfunction for clinical work and cognition or behavior for basic scientific studies.

EEG monitors the state of consciousness of patients in clinical work or experimental subjects in basic research. Oscillations of scalp voltage tell a very limited but important part of the story of brain functioning. For example, states of deep sleep are associated with slower EEG oscillations of larger amplitude. Various signal analysis methods allow for robust identifications of distinct sleep stages, depth of anesthesia, epileptic seizures and connections to detailed cognitive events.

Human spontaneous EEG occurs in the absence of specific sensory stimuli, but may be easily altered by such stimuli. Averaged evoked potentials (EPs) are associated with sensory stimuli like repeated light flashes, auditory tones, finger pressure or mild electric shocks; they are recorded by time averaging to remove (mostly) effects of spontaneous EEG. Event-related potentials (ERPs) are recorded in the same way as EPs, but occur at longer latencies from the stimuli and are more associated with endogenous brain state. With transient EPs or ERPs the stimuli consist of repeated short pulses. The number of pulses required to produce an average evoked potential may be anything between about ten and several thousand, depending on application. The scalp response to each input pulse is averaged over the individual pulses. The EP or ERP in any experiment consists of a waveform containing a series of characteristic components, typically occurring less than 500 milliseconds after presentation of the stimulus. The amplitude, latency from the stimulus, and covariance (in the case of multiple electrode sites) of each component may be studied, in connection with a cognitive task (ERP) or with no task (EP). Steady state visually evoked potentials (SSVEPs) use a continuous sinusoidally modulated flickering light, typically superimposed in front of a TV monitor displaying a cognitive task. The brain response in a narrow frequency band containing the stimulus frequency is measured. Magnitude, phase and coherence (in the case of multiple electrode sites) may be related to different parts of the cognitive task.

Recording Methods

Human EEG is recorded using electrodes with diameters typically in the 0.4 to 1.0 cm range, held in place on the scalp with special pastes, caps or nets as in the example of Figure 1. EEG recording procedures are noninvasive, safe and painless. Experimental subjects recruited for research are often the same students or scientists conducting the research. In standard clinical practice, 19 recording electrodes are placed uniformly over the scalp (the International 10-20 System). In addition, one or two reference electrodes (often placed on ear lobes) and a ground electrode (often placed on the nose to provide amplifiers with reference voltages) are required. In referential recordings, potentials between each recording electrode and a fixed reference are measured over time. The distinction between "recording" and "reference" electrodes is mostly artificial since both electrode categories involve potential differences between body sites, allowing closed current loops through tissue and EEG machine. Bipolar recordings measure potential differences between adjacent scalp electrodes. When such bipolar electrodes are placed close together (say 1 or 2 centimeters), potential differences are estimates of tangential electric fields (or current densities) in the scalp between the electrodes. Electrode placements and the different ways of combining electrode pairs to measure potential differences on the head constitute the electrode montage.

Most research and some clinical laboratories use many more electrodes to obtain detailed information about brain sources. However, additional electrodes may add minimal useful information unless supplemented by computer algorithms to reduce raw EEG data to manageable form; often 64 to 131 recording electrodes or more are used in research. Any single electrode may be chosen as the reference and potentials at other locations recorded with respect to this reference. In EEG practice, inappropriate reference choices have often led to erroneous interpretations of brain source locations and measures of dynamic behavior. When large numbers of electrodes are employed, potential at each location may be measured with respect to the average of all potentials (the common average reference), which often provides a good estimate of potential at infinity. The common average reference is not appropriate when electrode coverage is sparse (perhaps less than 64 electrodes).

The resulting multi-channel data are submitted to algorithms that estimate potentials on the brain surface by accounting for distortions caused by intervening tissue and the physical separation of electrodes from brain. The combined use of high electrode density and computer algorithms providing such "inward continuation estimates" to the brain surface is called high resolution EEG. Another approach using computer methods is dipole localization. This method can estimate the location of source regions in the brain depths in a few specialized applications where EEG is mainly generated in only one or two isolated source regions.

Figure 3: A cortical column with micro current sources generating the mesoscopic "dipole sources" (dipole moment per unit volume). These intermediate scale sources and the volume conductor properties determine the scalp potential as indicated by Eq. (2). The vector \(r\) locates the cortical columns and the vector \(w\) locates the micro current sources within the column.

Meso-scale Brain Sources

The sources of scalp potentials are best described as micro-current sources at cell membranes. Relationships between such very small-scale sources and macroscopic potentials at the scalp are made easier by employing an intermediate (mesoscopic) descriptive scale. This approach makes use of the columnar structure of neocortex, believed to contain the dominant sources of spontaneous scalp potentials. The mesoscopic source strength of a volume of tissue is defined by its electric dipole moment per unit volume \[\tag{1} P(r, t) = \frac{1}{W} \iiint_W ws(r, w, t) dW(w) \ .\]

The integration is over a small (mm scale) volume \(W\) of tissue where \(s(r, w, t)\) is the local volume source current (\(\mu\)A/mm3) near membrane surfaces inside a tissue volume with vector location \(r\ ,\) and \(w\) is the vector location of sources within \(dW(w)\) as indicated in Figure 3. The current dipole moment per unit volume \(P(r, t)\) in a conductive medium is analogous to charge polarization in a dielectric (insulator). Mesoscopic tissue volumes satisfy the condition of electroneutrality at EEG frequencies. That is, current consists of movement of positive and negative ions in opposite directions, but the total charge in any mesoscopic tissue volume is essentially zero. Cortical morphology is characterized by its columnar structure with pyramidal cell axons aligned normal to the local cortical surface. Because of this layered structure, the volume elements \(dW(w)\) may be viewed as cortical columns with height \(\approx\) 2-5 mm. For purposes of describing scalp potentials, the choice of basic cortical column diameter is somewhat arbitrary. Anything between the cortical minicolumn (\(\approx\) 0.03 mm) and macrocolumn scales (\(\approx\) 1 mm) may be used to describe scalp potentials.

The micro-sources \(s(r, w, t)\) are generally of mixed sign due to local inhibitory and excitatory synapses. In addition to these active sources, the \(s(r, w, t)\) include passive membrane (return) current required for current conservation. Dipole moment per unit volume \(P(r, t)\) has units of current density (\(\mu\)A/mm2). For the idealized case of sources of one sign confined to a superficial cortical layer and sources of opposite sign confined to a deep layer, \(P(r, t)\) is roughly the diffuse current density across the column, corresponding to superficial inhibitory synapses and deep excitatory synapses. More generally, column source strength \(P(r, t)\) is reduced when excitatory and inhibitory synapses overlap substantially along column axes.

Human neocortical sources may be viewed as forming large dipole sheets (or layers) of perhaps 1500 to 3000 cm2 over which the function \(P(r, t)\) varies continuously with cortical location \(r\ ,\) measured in and out of cortical folds. In special cases, this dipole layer might consist of only a few discrete regions where \(P(r, t)\) is large, for example, in the subclass of epilepsies that originate at an epileptic focus (typically involving 10 to 20 cm2 of cortical surface). More generally, \(P(r, t)\) is distributed over the entire folded surface. The question of whether \(P(r, t)\) is distributed or localized in particular brain states is often controversial. The averaging of evoked potentials over trials substantially alters the nature of this issue since time averaging strongly biases evoked potentials towards (trial to trial) time stationary sources, for example sources confined to primary sensory cortex. A convenient conceptual framework pictures \(P(r, t)\) as composed of some combination of global field and neural network activity.

Computational Methods

Spectral analysis

Voltage traces of EEG signals recorded from each electrode pair oscillate with mixtures of component waveforms. Each component may be defined in terms of three parameters, its amplitude (\(A_{nm}\)), frequency (\(f_{nm}\)), and phase (\(\phi_{nm}\)), where the subscript \(n\) denotes the frequency component and the subscript \(m\) indicates the electrode pair. One may express any physical waveform by a Fourier series, a sum of components with different frequencies, amplitudes and phases. The EEG voltage \(V_m(t)\) recorded from any electrode pair \(m\) is then expressed generally as a sum over frequency components \[ V_m(t) = \sum_{n=1}^N A_{nm}\sin(2\pi f_{nm}t-\phi_{nm}) \ .\] EEG frequency ranges are categorized as delta (1 to 4 Hz), theta (4 to 8 Hz), alpha (8 to 13 Hz) and beta (greater than 13 Hz). Very high frequencies (typically 30 to 40 Hz) are referred to as gamma activity. These distinctive labels correspond roughly to frequency bands that often dominate particular human brain states. For example, delta activity with frequencies lower than about 1 or 2 Hz is dominant during deep sleep and in many coma and anesthesia states. Alpha, often mixed with low amplitude delta, theta and beta is typically predominant in awake-resting states and in alpha coma. Different combinations of these rhythms may be associated with behavioral or cognitive state, brain location, or by other criteria.

Human EEG exhibits many disparate waveforms, especially in the experience of clinical electroencephalographers (neurologists with this specialized training). Many EEGs have known clinical significance and many do not. Electroencephalographers sometimes prefer picturesque descriptions to Fourier analysis and characterize the "zoo" of EEG waveforms with labels like paradoxical alpha, spike and wave, delta focus, sharp transient, sleep spindle, non-specific dysrhythmia, and so forth. To the mathematically or theoretically minded, many of these waveforms appear typical of nonlinear systems.

Cortical EEG (ECoG) typically consists of complex waveforms, composed of rhythms with different frequencies, locations and spatial extent. This normal ECoG differentiation between cortical areas tends to be eliminated by anesthesia, suggesting a transition from more locally to more globally dominated brain dynamics of the mesosource field \(P(r, t)\ .\) Highly localized cortical rhythms are not recorded on the scalp; for example, cortical beta rhythms are often strongly attenuated between cortex and scalp because they are more localized than the globally coherent alpha band activity. Other parts of the alpha band appear to be generated in more local patches, perhaps indicating network activity. EEG during sleep, coma, and anesthesia typically exhibit large scalp amplitudes, implying widely distributed synchronous cortical source activity.

Covariance and coherence

EEG dynamic behavior depends on both time and scalp location; one may picture this dynamics as neural network activity embedded in large scale fields, analogous to social networks embedded in a culture. Multi-channel recordings suggest many different measures of brain dynamic behavior because amplitude, phase and frequency vary over time and scalp location. Two important measures of functional relations between pairs of signals are covariance (used in EP) and coherence (used in EEG and SSVEP). The (normalized) covariance of two signals is a correlation coefficient expressed as a function of time delay for characteristic waveforms recorded at the two locations. The coherence of a signal pair is also a correlation coefficient (squared); it measures the phase consistency between pairs of signals in each frequency band.

An EEG record involving \(J\) recording electrodes will generally provide \(J(J-1)/2\) covariance estimates for each time delay or coherence estimates for each frequency band. The (generally complicated) covariance or coherence picture may be called the covariance or coherence structure of EEG, providing information about local versus global dynamic behavior that varies with brain state. Coherence provides one important measure of functional interactions between oscillating brain sub-systems. EEG coherence is a somewhat different measure than EEG synchrony, which refers to sources oscillating roughly in phase so that their individual contributions to EEG add by superposition. Thus, desynchronization is often associated with amplitude reduction. Sources that are synchronous (small phase differences) over substantial periods will also tend to be coherent. But, the converse need not be true; coherent sources may remain approximately 180 degrees out of phase so their individual contributions to EEG tend to cancel.

Volume conduction. Forward and inverse problems

Scalp potential may be expressed as a volume integral of dipole moment per unit volume over the entire brain provided \(P(r, t)\) is defined generally rather than in columnar terms. For the important case of dominant cortical sources, scalp potential may be approximated by the following integral over the cortical volume \(\Theta\) \[\tag{2} V_S(r, t) = \iiint_\Theta G(r, r')\cdot P(r', t)d\Theta(r') \ .\]

If the volume element \(d\Theta(r')\) is defined in terms of cortical columns (Figure 3), the volume integral may be reduced to an integral over the folded cortical surface. Equation (2) indicates that the time-dependence of scalp potential is the weighted sum of all dipole time variations in the brain, although deep dipole volumes typically make negligible contributions. The vector Green's function \(G(r, r')\) contains all geometric and conductive information about the head volume conductor and weights the integral accordingly. Thus, each scalar component of the Green’s function is essentially an inverse electrical distance between each source component and scalp location. For the idealized case of sources in an infinite medium of constant conductivity, the electrical distance equals the geometric distance. The Green’s function accounts for the tissue’s finite spatial extent and its inhomogeneity and anisotropy.

The forward problem in EEG consists of choosing a head model to provide \(G(r, r')\) and carrying out the integral in Eq (2) for some assumed source distribution. The inverse problem consists of using the recorded scalp potential distribution \(V_S(r, t)\) plus some constraints (usually assumptions) on \(P(r, t)\) to find the best fit source distribution \(P(r, t)\ .\) Since the inverse problem has no unique solution, any inverse solution depends critically on the chosen constraints, for example, only one or two isolated sources, distributed sources confined to cortex, or spatial and temporal smoothness criteria.

High resolution EEG uses the experimental scalp potential \(V_S(r, t)\) to predict the potential on the dura surface (the unfolded membrane surrounding the cerebral cortex) \(V_D(r, t)\ .\) This may be accomplished using a head model Green’s function \(G(r, r')\) or by estimating the surface Laplacian with either spherical or 3D splines. These two approaches typically provide very similar dura potentials \(V_D(r, t)\ ;\) the estimates of dura potential distribution are unique subject to head model, electrode density, and noise issues.

The most common head models consist of three or four concentric spherical shells, representing brain, cerebrospinal fluid, skull and scalp tissue with different electrical conductivities \(\sigma\ .\) More complicated numerical methods are also be used to estimate \(G(r, r')\ ,\) sometime employing MRI to determine tissue boundaries. The accuracy of both analytic and numerical methods is, however, severely limited by incomplete knowledge of conductivity (generally tensors reflecting anisotropic tissue properties; see Volume Conduction.)

Figure 4: The EEG (a), spline Laplacian (b), and MEG (c) sensitivity distributions for a fixed electrode location (yellow circle at right inset figure) and magnetic coil position (green line at right inset figure) are shown. The cortical surface was constructed from the MRI of one subject. Simulated dipole sources \(P(r, t)\) (100,000 in one hemisphere) were assumed normal to the local cortical surface. Scalp surface potentials, scalp Laplacians, and surface normal magnetic fields due to each dipole were calculated at the electrode and coil locations shown in the inset using the appropriate Green’s function (one for each measure) based on a confocal 3-ellipsoid head model. The three Green’s functions were normalized with respect to their maximum values so that the relative sensitivity of the three measured could be compared.

The estimated sensitivity distributions of EEG, spline Laplacian, and MEG are shown in Figure 4. In (a) the potential at one EEG electrode (yellow circle in inset figure) due to 100,000 cortical sources \(P(r, t)\) is calculated from Eq (2) using a Green’s function \(G(r, r')\) based on three confocal ellipsoids representing brain, skull, and scalp tissue. The sources are assumed normal to the local (folded) cortical surface determined from the MRI of a human subject. The EEG is most sensitive to gyral sources under the electrode, but this electrode is also sensitive to large source regions occupying relatively remote gyral crowns and much less sensitive to sources in cortical folds. In (b) the spline Laplacian is shown to be most sensitive to gyral sources under the electrode; sensitivity falls off rapidly at moderate and large distances. In (c) the MEG is shown to be most sensitive to sources in cortical folds that tend to be tangent to MEG coils. Maximum MEG sensitivity occurs in folds that are roughly 4 cm from the coil in directions tangent to the surface. Regions in blue provide contributions to MEG of opposite sign to those of yellow/orange, reflecting dipoles on opposite sides of folds that tend to produce cancelling magnetic fields at the coil.

Dynamic behavior of sources

EEG waveforms recorded on the scalp are due to a linear superposition of contributions from billions of micro-current sources or, expressed another way, by thousands to millions of columnar sources \(P(r, t)\) located in cerebral cortex, as indicted by Eq (2). However, the underlying physiological bases for the dynamic behavior of the sources themselves are mostly unknown. The 10 Hz range oscillations of alpha rhythm, the 1 Hz range oscillations of deep sleep and other waveforms in the EEG "zoo" must be based on characteristic time delays produced at smaller scales. Such delays can be developed in neural networks that cover a wide range of spatial scales. Locally generated activity in small networks and more globally generated activity involving spatially extensive networks up to the global scale of the entire cerebral cortex may be reasonably assumed. The local network category includes thalamocortical feedback networks that could oscillate in specific frequency ranges (local resonances). Other possible mechanisms occur at intermediate scales between local and global involving widespread cortical locations. Preferred frequencies generated at intermediate scales may be termed regional resonances. At the global scale, the generation of resonant frequencies (global resonances) due to standing waves of synaptic action has been proposed.

Delays in local networks are believed due mainly to rise and decay times of postsynaptic potentials. By contrast, global delays occur as a result of propagation of action potentials at finite speeds along axons connecting distant cortical regions (cortico-cortical fibers). Delays in regional networks may involve both local and global mechanisms. A working conjecture is that local, regional and global resonant phenomena all potentially contribute to source dynamics. However, the relative contributions of networks with different sizes may be quite different in different brain states. The cortical EEG (ECoG) may change from rhythms depending strongly on location to rhythms that look similar over widespread cortical locations. Another example is desynchronization (amplitude reduction) of alpha rhythms that occurs with eye opening and certain mental tasks.

A number of mathematical theories have been developed since the early 1970's to explain the physiologically bases for source dynamics, that is, the underlying reasons for specific time dependent behaviors of the source function \(P(r, t)\ .\) Some common EEG properties for which plausible quantitative explanations have emerged naturally from mathematical theories include the following observed relations: frequency ranges, amplitude versus frequency, spatial versus temporal frequency, maturation of alpha rhythm, alpha frequency-brain size correlation, frequency versus cortico-cortical propagation speed, frequency versus scalp propagation speed, frequency dependence on neurotransmitter action, resonant interactions between networks, and mechanisms for cross-scale interactions between hierarchical networks. Because the brain is so complex, such theories must involve many approximations to genuine physiology and anatomy. As a result, verification or falsification of specific theories for the physiological bases for EEG is difficult. However, such mathematical theories can profoundly influence our general conceptual framework of brain processes and suggest new studies to test these ideas.


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See Also

Cortex, Desynchronization, Event-Related Brain Dynamics, Fast Oscillations, Intracellular Recording, Magnetoencephalography, Source Localization, Synchronization, Thalamocortical Oscillations, Volume Conduction

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