Event-Related Potentials of the Cerebral Cortex

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Chapter 7 (pp. 169-190) in: Robert P. Vertes and Robert W. Stackman Jr. (eds.), Electrophysiological Recording Techniques, Neuromethods, vol. 54, DOI 10.1007/978-1-60327-202-5_7, © Springer Science+Business Media, LLC 2011

Steven L. Bressler

Center for Complex Systems & Brain Sciences Florida Atlantic University 777 Glades Road Boca Raton, FL 33431, USA [email protected]; Tel: (561)297-2322; Fax: (561)297-3634

Introduction

It has long been known that electrical activity can be recorded from the living brains of humans (Berger, 1929) and other mammals (Caton, 1875). From the earliest days of recording this activity, researchers have sought to understand its relation to brain function and to use it to monitor and assess brain state. Continuous records of brain activity, examined without regard to particular points in time, are often useful for determining brain state. However, more detailed knowledge of brain function depends on temporal registration of the activity to specific events, either in the external environment or self- generated. The Event-Related Potential (ERP) is a temporal signature of brain electrical activity that occurs in relation to a sensory or motor event (Coles and Rugg, 1997; Bressler, 2002; Bressler and Ding, 2006). The Event-Related Field (ERF) is the magnetic correlate of this activity1. ERPs and ERFs have an advantage over indices of brain function that monitor blood flow or metabolism in that their time course more closely follows the activity of neuronal populations in the brain.

According to one point of view, the ERP refers only to a transient waveform that results from averaging multiple brain electrical potential time series, all precisely time-locked to an external event. There are many examples, however, of event-related electrophysiological phenomena that are temporally related to an external event but not precisely time-locked to it, and do not require averaging to be observed (Freeman, 1975). Therefore, the perspective taken in this chapter is a broader one, in which any brain electrical potential waveform that reliably occurs in relation to a sensory or motor event qualifies as an ERP. Thus, oscillatory phenomena that reliably occur in the brain either before or after an event are considered to be ERPs, even if the timing is imprecise, whereas oscillatory phenomena that arise spontaneously without relation to an event are not.

ERPs provide a window onto the dynamics of neuronal population activity in the brain in relation to sensory, motor, and cognitive processes. Neuronal population activity results from the cooperative interactions of individual neurons. The fraction of any single neuron’s total activity that represents its involvement in cooperative interaction may be exceedingly small, yet it is the cooperative activity of populations that carries influences between different parts of the brain. Population activity originates at the local neuronal circuit level, but becomes coordinated across widely distributed brain systems. Thus, the ERP derives from cooperative interactions in local neuronal populations, and is modulated by long-range interactions between neuronal populations transmitted over axonal pathways.

Generation of Electromagnetic Activity in the Cerebral Cortex

Electromagnetic activity is generated by neurons throughout the brain, both in their axons and dendrites (Freeman, 1975; Basar, 1980; Pantev et al., 1994). The dendritic activity of

1 General considerations regarding the ERP throughout this article also apply to the ERF, except where noted.

1 neurons in the cerebral cortex is responsible for the macroscopic electrical and magnetic activity observed with extracranial sensors (Murakami and Okada, 2006). The cortical pyramidal cell is an important class of excitatory neuron that is critically involved in the generation of cortical electrical field potentials and the corresponding magnetic fields.

The dendrites of pyramidal cells, like most other neurons, are specialized to receive excitation and inhibition at chemical synapses where postsynaptic ion channels are gated by ionotropic receptors. At these synapses, the release of neurotransmitter from the presynaptic axon terminal causes the ion channels to open, and electromotive forces (EMFs) cause current to flow through the channels. As a result, current circulates in closed loops across the cell membrane and through the intracellular and extracellular spaces. The excitatory postsynaptic potential is a depolarization of the dendritic transmembrane potential due to a net inward flow of positive current across the postsynaptic membrane. Dendritic excitatory synapses create loop currents consisting of net positive charge that flows inward across the postsynaptic dendritic membrane, passes through the intracellular compartment, flows outward across passive membrane with a strength that decreases with distance from the sites of influx, and finally completes the loop through the extracellular space (Figure 1). The dendritic inhibitory postsynaptic potential is a hyperpolarization of the dendritic transmembrane potential at inhibitory synapses due to a net outward flow of positive current across the postsynaptic membrane. Loop currents are also created by inhibitory synapses, but the flow of current is in the opposite direction to that created by excitatory synapses (Freeman, 1975; Speckmann, 1997). When both excitatory and inhibitory synapses are active, the net balance of all active synapses determines the direction of flow of loop currents.

[Figure 1 near here]

Loop currents cause pyramidal cells to generate trains of pulses (action potentials). They do so by establishing a gradient of transmembrane potential that continuously varies in time and space along the pyramidal cell dendrites as a function of current strength. The sum of currents contributed by all the active synapses on the dendritic tree produces a resultant transmembrane potential at the cell body and the initial segment of the axon. When this resultant potential exceeds the firing threshold, the initial segment responds by generating a pulse train that actively propagates along the axon, diverges into the axonal branches, and, by causing the release of neurotransmitter at the branch terminals, leads to the excitation or inhibition of other neurons. Thus, the loop currents generated by a pyramidal cell determine its effect on other neurons.

Loop currents generated by neighboring pyramidal cells summate in the extracellular space when they flow in the same direction, and cancel otherwise. The passage of extracellular current across the resistance in this space is manifested as the extracellular electrical field of potential, or field potential (Speckmann, 1997). The extracellular components of the net loop currents generated by a population of active neighboring pyramidal cells give rise to the population mean field potential (Freeman, 2000). The population mean field potential of pyramidal cells can be recorded by an electrode of appropriate size and position in the extracellular space of the cortical tissue (the Local

2 Field Potential, or LFP), on the cortical surface (the electrocorticogram), or even at the scalp surface (electroencephalogram). The ability to detect the cortical field potential at a distance from the cortical tissue depends on it being an open field (see below), and summating over large populations of pyramidal cells. The intracellular components of the same closed-loop currents giving rise to the field potential are primarily responsible for the closely related magnetic field recorded extracranially as the magnetoencephalogram (Okada et al., 1997; Hamalainen and Hari, 2002).

The magnitude of the LFP recorded by an extracellular microelectrode at any instant in time depends on multiple factors, including the number of nearby synchronously active pyramidal cells, the strength and directions of their currents, their morphology and alignment, and the position of the electrode in the field. In general, for any population of neurons to generate a strong field potential, it is not sufficient that the neurons actively generate strong extracellular currents. The morphology and alignment of those neurons must also promote the summation of the currents in the extracellular space. For example, the field potential generated by a population of neurons in which the orientations of the dendrites are uniformly distributed in all directions is zero, on average, due to cancellation of extracellular currents, even if the individual dendrites are all maximally excited. On the other hand, parallel alignment of the dendrites, as with the pyramidal cells, promotes extracellular current summation if the same portion of each dendrite, e.g. the distal end, is excited. However, cancellation may still occur if the location of the excitation is randomly distributed along the dendrites.

The cortical pyramidal cells have a single long apical dendrite aligned in parallel across the population, and perpendicular to the cortical surface. The population typically receives concurrent excitation or inhibition at the same dendritic locale, e.g. distal or proximal end, and thus tends to generate extracellular currents that maximally summate and augment the field potential. They are densely interconnected with each other and with neighboring neuron types, both excitatory and inhibitory, to form local neuronal circuits that are complex but similarly organized throughout the cortex. Pyramidal cells are also targets for synaptic inputs from other cortical and subcortical areas, and likewise send long, myelinated axons to those areas.

The pyramidal cell population is called a dipole generator because the field it generates is a distributed dipole field, meaning that the summated loop currents which emerge from one end (pole) of the cells are detected by an extracellular electrode there as a current source, and the currents which enter into the other end (pole) are detected by an extracellular electrode there as a current sink (Freeman, 1975). An important property of the dipolar source-sink population geometry is that it generates a field which is open, meaning that the currents spread in the volume of the brain and can be detected at a distance from the generating population (Lopes da Silva and Van Rotterdam, 1982). Thus, a local population of synchronously active pyramidal cells can generate an open dipole field that is recordable either locally or at a distance from the population (Figure 2). A superficial cortical sink may be recorded as a negative potential (and a superficial source as a positive potential) by an electrode in the superficial cortical layers, at the cortical surface, or at the scalp. Synchronously active dipole fields of multiple local

3 populations tend to summate and thus be detectable at a greater distance than those of the individual local populations alone, unless cancellation occurs due to surface folding (Gloor, 1985).

[Figure 2 near here]

The question of what causes field potentials to change over time is central to understanding the relation of ERPs to brain function. Although the determinants of temporal variation of the field potential are diverse, and their effects are not well understood, some basic aspects of pyramidal cell population activity that bring about temporal variation of its generated field potential may be identified (Elul, 1972). One important consideration is that the number of single neuron generators contributing to the population activity, and the magnitudes of the currents that they generate, may change over time. Another crucial aspect is that neuronal synchrony, the tendency for the unitary generators in the population to be similarly active, may also change over time. Factors such as inputs from other populations and intrinsic changes in the excitability of the population can affect both the total magnitude of currents generated by the neurons of the population and their degree of synchrony. These factors thus influence the time course of the population field potential and ultimately determine the dynamics of ERP generation in relation to brain function.

Measurement of the Cortical ERP

The cerebral cortex is uniquely positioned to make the principle contribution to brain activity recorded extracranially, and is also a common target of intracranial recording, because cortical population activity is thought to be fundamentally related to cognitive processes (Fuster, 2003). Depending on the size of the recording and reference electrodes, and the location within or outside the head, recorded cortical field potentials integrate neural activity over a range of spatial scales. The nature, size and location of both the indicator and reference electrodes are important for determining the spatial scale of integration of the field potential that is represented by a recorded voltage trace, as well as the recorded voltage range.

Microelectrodes placed directly within the cortex record field potentials, integrated on a submillimeter scale, that are predominantly generated by local neuronal populations. In order to truly localize the field potential to a restricted population, two closely spaced electrodes are inserted into the same cortical region and the potential difference between the two is recorded as the LFP. Although the amplitude range can vary considerably, intracortical field potentials are generally no larger than 1500 microvolts in peak-to-peak amplitude.

Electrodes placed on the surface of the brain integrate over a larger submillimeter to millimeter scale. Since the cerebral cortex makes up most of the brain’s surface, and the non-cortical surfaces are difficult to access, the intracranial brain surface field potential is almost always recorded from the cortex as the electrocorticogram (ECoG). The ECoG recording may be bipolar, i.e. the difference in field potential activity recorded from two

4 nearby cortical surface electrodes, or monopolar, i.e. from one cortical surface electrode with respect to a distant neutral reference electrode. ECoG amplitudes are normally in the range of several hundred microvolts.

Integrating over an even greater spatial extent, the extracranial electroencephalogram (EEG) is recorded from the surface of the head, again either bipolarly or monopolarly. Scalp-recorded EEGs are greatly attenuated due to the high resistivity of the skull and scalp, and peak-to-peak amplitudes usually lie between 10 and 50 microvolts in the adult human. Finally, the magnetoencephalogram (MEG) records the magnetic field with sensors located just outside the head. MEG records from a third-order gradiometer are commonly less than 1-2 picoTesla in peak-to-peak amplitude. Both the EEG and MEG integrate over a centimeter spatial scale.

Measurement of ERPs at the cortical surface or scalp involves the detection of summated dipole fields of extracellular currents generated by cortical pyramidal cell populations that have become synchronously active as a result of a sensory or motor event. Measurement of the ERF involves detection of magnetic fields generated by intradendritic current flow of cortical pyramidal cell populations (Okada et al., 1997). The generator populations that are detected by the ERP and ERF generally overlap, but are not identical because of differences between the two measures in sensitivity to generator orientation and depth. The time-varying ERP or ERF waveform is commonly treated as a signal to be detected in the presence of noise. The following discussion deals explicitly with the ERP, but similar considerations also apply to the ERF.

Noise refers to any contribution to the potential difference (voltage) recorded from two electrodes that is not from the signal source. Common sources of noise in brain electrical recordings include: (1) potentials from the brain (cephalic noise); (2) potentials from the head muscles and skin, eyes, and tongue (extracephalic cranial noise); (3) potentials from parts of the body other than the head, such as the heart (extracranial physiological noise); (4) random microscopic fluctuations at the electrodes (thermal noise); (5) noise from movement of the person or animal (movement artifact); (6) fluctuations introduced by electronic recording components (electronic noise); (7) radiated contamination from other electrical equipment (environmental noise); and even (8) fluctuations due to imprecision in the discrete digitization of the continuously varying voltage from the electrode for storage in a digital computer (quantization noise).

The ability to detect the ERP waveform signal in the presence of noise depends on the relative strengths of signal and noise, as measured by the ratio of signal power (magnitude squared) to noise power. If this signal-to-noise ratio is large then the signal may be observable in the digitized time series of just a single voltage trace. If it is small, however, some procedure is required for signal detection. A simple and effective signal detection technique is to average over an ensemble of realizations (also called trials) of the voltage time series. This is a reasonable procedure if each individual time series realization is registered to a common time marker representing the occurrence of an event.

5 The cortical sensory evoked potential is an example of a signal that is commonly detected by ensemble averaging (Figure 3). Repeated stimuli, e.g. flashes of light or brief tones, are presented to a subject while voltages are recorded from arrays of monopolar or bipolar electrodes placed within or near the corresponding region of sensory, e.g. visual or auditory, cortex. The voltage records are digitized and broken into time segments corresponding to successive stimulus presentations, called trials. The resulting time series segments from the individual trials are collected, temporally registered with respect to the time of each stimulus, and averaged separately for each electrode.

[Figure 3 near here]

When using ensemble averaging to detect the transient cortical sensory evoked potential, it is generally assumed that a dipole generator population of pyramidal cells in the sensory cortex responds to each stimulus in a characteristic manner by generating a reproducible waveform signal. This waveform may not be detectable in the single-trial time series if the signal-to-noise ratio is too small. It is further assumed that the signal occurs with a fixed amplitude and latency with respect to the stimulus. The noise, on the other hand, is deemed to be temporally unrelated to the stimulus.

These premises embody the standard model of the ERP, which is discussed below. The standard model predicts that ensemble averaging of single-trial time series maintains the magnitude of the stimulus-evoked signal while decreasing the magnitude of the noise by destructive waveform cancellation. The signal-to-noise ratio increases in proportion to the square root of the number of trials averaged. If the assumptions of the standard model hold, or are not too severely violated, ensemble averaging is a simple method for ERP estimation.

Varieties of the Cortical ERP

The cortical ERP is an electrical signal generated by neuronal populations in relation to a behaviorally significant event. The corresponding event-related magnetic field (ERF) has many of the same dynamic and functional properties as the ERP. Two general classes of ERP are distinguished by whether the relevant event is continuous or discrete.

In the case of continuous events, such as when sensory stimuli are presented rapidly and repetitively, the steady-state ERP takes the form of a continuous periodic response, and is analyzed in long epochs. The steady-state ERP shows the same repetition frequency as the stimulus, within limits, and preferred frequencies at which the steady-state response is maximal have been suggested to represent the natural resonant frequencies of oscillating neuronal populations in the sensory cortices (Herrmann, 2001). Steady-state visual evoked potentials have proven useful in the assessment of cognitive function (Silberstein et al., 1995, Müller et al., 2006). The study of steady-state ERPs depends on a variant of frequency analysis (see below). Field potentials recorded during periodically modulated sensory stimulation are narrow-band filtered around the frequency of the driving periodicity to derive the steady-state (periodic) ERP. Variations in the amplitude and

6 phase of the steady-state ERP are interpreted in terms of driving frequency, spatial location, and behavioral state.

In the case of discrete events, the associated transient ERP is analyzed in short epochs time-locked to the event. Transient ERPs have engendered a great deal of interest because of their potential for revealing the dynamics of cognitive processing by the brain. They may occur with either relatively fixed or variable latency (or phase) in relation to the repeated event. If the latency is variable, then ensemble averaging is destructive since components of opposite polarity on successive trials tend to be cancelled, and hence may not reveal the ERP. Non-phase-locked ERPs are referred to as “induced” when they reliably occur following a stimulus, and “spontaneous” when they reliably arise in the period prior to a stimulus or motor response. This type of ERP may be effectively analyzed by averaging the frequency content of single-trial time series, rather than averaging the time series themselves.

Non-phase-locked transient event-related phenomena are detected as frequency-specific changes in the ERP time series. These phenomena may consist either of an event-related increase or decrease of power in a particular frequency range, typically the alpha (8-13 Hz) or beta (14-30 Hz) bands. Because the level of ERP power is typically considered to reflect the degree of synchrony within local neuronal populations, a power increase is called event-related synchronization and a power decrease is called event-related desynchronization (Pfurtscheller and Lopes da Silva, 1999).

Phase-locked transient ERPs show temporal variation on a sub-second time scale that is conducive to measurement of the rapidly changing dynamics of cognition (Rugg and Coles, 1997). For this reason, a long lasting effort in the study of ERPs has been to identify components that span brief periods of time in the ERP before or after a measurable event. The ERP waveform consists of a series of positive and negative wave- like components that are identified by their time of occurrence and polarity. Thus, for example, the P300 component occurs as a positive wave which peaks at or near 300 ms after a stimulus event. Components sometimes are also designated simply according to their serial order, so that the P300 component might also be called the P3 component, meaning the third positive wave following the stimulus. Other components are named based on event properties. The Contingent Negative Variation (CNV), for example, is a slow negative wave that appears in the interval between two stimuli after a contingency of the second stimulus on the first has been established.

ERP components are also categorized as relating to sensory, motor, or higher-order cognitive processes of the brain. Sensory ERPs may be recorded by electrodes placed in sensory brain structures, on the surface of sensory cortices, or on the overlying scalp. They are typically extracted from noise by ensemble averaging with respect to an external stimulus in one of the sensory modalities. The early poststimulus components are directly related to stimulus-evoked sensory processing, and because their characteristics depend on the physical properties of the stimulus they are called exogenous. Olfactory ERPs are usually large with respect to the background, and thus do

7 not requiring averaging to be observed. They are also oscillatory, and thus do not have readily identified components (Freeman, 1975).

In the auditory and somatosensory modalities, early components generated by sensory relay nuclei in the brain stem are revealed in extracranial recordings by the ensemble averaging of large numbers of trials. Since these early components are considered obligatory, they have clinical value as a test of the integrity of the subcortical sensory pathways. In the visual modality, the brain stem nuclei apparently generate closed potential fields, and thus the earliest components observable from the scalp are generated within the cortex (Coles and Rugg, 1997). In animal studies, sensory nerve stimulation produces a positive-negative wave complex at the cortical surface. The positive deflection may arise from a dipole field with a superficial source generated by depolarization of layer 4 neurons in primary cortex, and the negative deflection from a superficial-sink dipole generated by depolarization in the superficial layers (Schroeder et al., 1998). The latencies of early sensory cortical components are of great interest to researchers who study cortical information processing (Nowak and Bullier, 1998; Ledberg et al., 2007).

Motor ERPs are extracted from noise by ensemble averaging with respect to a movement-related event rather than a sensory stimulus. Since the characteristics of motor ERP components do not depend on external stimulus properties, but rather on a subject’s internal state, they are called endogenous. The most well-known motor component is the Readiness Potential (RP), a slow, ramp-like negative potential shift that begins as early as 1.5 sec before the production of voluntary limb movements. The RP magnitude grows larger in recordings over the sensorimotor cortex contralateral to the movement, as compared to the ipsilateral side, as the time of the movement approaches. Together with the observation that the RP has a somatotopic organization in the contralateral sensorimotor cortex, this finding indicates that the RP component is related to preparation for limb movement. The RP (also designated N1) is terminated by a positive-negative (P1-N2) complex prior to muscle contraction, which is then followed by a late positive (P2) component. The P1 deflection is often absent unless the movement is brisk and forceful.

Cognitive ERP components are related to cognitive, rather than sensory or motor, processes of the brain. They can provide valuable information about the spatial organization of large-scale cortical network activity underlying a cognitive function, as well as the temporal organization on a sub-second time scale (Bressler and Kelso, 2001; Bressler, 2002). By definition, cognitive ERP components are considered to be endogenous. The aforementioned Contingent Negative Variation (CNV) is an endogenous cognitive ERP component that occurs in the interval between two stimuli (S1 and S2), presented in any sensory modality, for which a contingency has been established by their prior pairing. Most often, the subject is required to execute a motor response to the S2. The CNV arises as a ramp-like, negative-going wave that peaks shortly after S2. It appears maximally in the EEG over frontal and central regions, and can be as large as 20 microvolts. When the S1-to-S2 duration is sufficiently long, the CNV resolves into early and late subcomponents, the early one related to the sensory processing of S1, and

8 the late one associated with anticipation of S2 and motor preparation. The late subcomponent is thought to be generated by the prefrontal cortex (Rosahl and Knight, 1995) in relation to that structure’s role in mediating cross-temporal contingencies (Fuster, 1985).

Whereas the late CNV occurs prior to a stimulus, reflecting anticipation and preparation, other cognitive effects appear following a stimulus. The Mismatch Negativity (MMN) is an early poststimulus ERP component that may reflect the maintenance of sensory working memory (Näätänen, 2008). It is thought to be elicited by stimuli having physical properties that deviate from prior (standard) stimuli registered in sensory memory. Occurring between 80 and 200 ms after presentation of deviant stimuli, thus overlapping the N1 and P2 components, the MMN is revealed by computing the difference wave between averaged ERPs evoked by deviant and standard stimuli. The MMN is subserved by a large-scale network that includes the dorsolateral prefrontal cortex in addition to sensory cortical areas (Alain et al., 1998). The question of whether the MMN is automatic, or whether it may be affected by attention has been controversial. Modulation of the early post-stimulus ERP components has been reported in relation to spatial or non-spatial attention in the auditory, visual, and somatosensory modalities (Mangun and Hillyard, 1997).

The P3 component appears as a positive deflection between 300 and 900 ms poststimulus that is related to the cognitive context of the stimulus (Sutton et al., 1965). Context is usually established by presenting a subject with a series of events of one class interspersed with rarer (oddball) events of a second class to which the subject must respond. Two P3 components are distinguished (Squires et al., 1975): an earlier, frontal P3a component and a later, parietal P3b component. The P3a is elicited by unexpected novel stimuli. The amplitude of the P3b depends on the relative event probability, and the latency reflects the degree of difficulty in categorizing the stimulus. A widely distributed cortical network underlying the P3b is thought to be involved in the categorization of stimuli as significant events, with network strength reflecting the degree of “consonance” resulting from comparison of stimulus attributes with a maintained “expectation” (Kok, 2001).

Finally, an ERP component related to semantic memory is the negative-going N400. It occurs between 200 and 500 ms after presentation of a potentially meaningful information-bearing stimulus when that stimulus is incongruent with the prevailing semantic context established by previous stimuli. The amplitude of the N400 is directly related to the degree of semantic deviance of the word from its sentence context, and is attenuated by prior priming with semantically related words. The N400 amplitude is reduced as a function of associative, semantic, and repetition priming within or across sensory modalities (Kutas and Federmeier, 2000). Variation of its scalp-recorded topographic distribution with task and stimulus type suggests that the N400 reflects the construction of meaning by cross-modal interactions in a large-scale cortical network. This view is supported by intracranial evidence that the N400 arises from similar waves of activity in multiple brain areas, particularly in the temporal and prefrontal cortices, during the retrieval of information from semantic memory.

Models of the Cortical ERP

The traditional approach to the analysis of transient ERPs is to consider the ERP as a characteristic waveform that occurs in relation to a behaviorally significant discrete event, and to consider the recorded single-trial field potential as composed of activity that is both associated (“ERP signal’) and not associated (“noise”) with the event. Thus, averaging single-trial field potential time series, in temporal registration with the event, is commonly employed to extract the ERP from the non-event-related noise. Justification for this analytic procedure is provided by a standard model, entailing three important assumptions (Dawson, 1954). Firstly, although the amplitude and latency of a component may be affected by a host of different conditions, once the conditions are fixed the component itself is considered to be an entirely reproducible signal whose waveform does not vary from one trial to the next. Secondly, the component is considered to be unitary in form, meaning that it is not composed of more basic waveforms. Thirdly, the signal is considered to be completely independent of any ongoing neural processes, which if they exist are simply treated as additive uncorrelated noise.

Despite the fact that this standard model has proven to be remarkably robust, evidence suggests that each of these three assumptions requires modification (Truccolo et al., 2002, 2003). First to be considered are findings of variability in both component amplitude and latency across trials, even under controlled conditions. Trial-to-trial variability of component amplitude does not seriously affect signal detection by ensemble averaging as long as the polarity remains constant: the averaged component retains the latency and shape of the single-trial signal despite variations in amplitude. Ensemble averaging is also robust to latency variability, providing that the signal waveform does not contain polarity reversals: the averaged component degrades smoothly as the degree of latency variability increases.

Changes in component polarity over trials, or latency variability of a component containing polarity reversals, may result in destructive cancellation of the signal during the ensemble averaging process. This possibility is particularly relevant in the case of high-frequency oscillatory field potential responses of the brain to sensory stimulation (Tallon-Baudry et al., 1996). These oscillatory components are said to be induced rather than evoked because the oscillatory waves within the component have variable latency (or phase), although the onset times of the component itself may be relatively constant with respect to the stimulus event. The high-frequency oscillatory waveform of these induced signals guarantees that polarity reversals will destructively cancel with even a small degree of trial-to-trial latency variability. Therefore, the standard model cannot be assumed to hold in the case of induced high-frequency oscillations, and methods other than ensemble averaging are required for signal detection.

Other studies have brought into question the second assumption from the standard model that ERPs represent fundamental, indecomposable waveforms. Some investigators have argued that evoked oscillations are fundamental to brain function, and that ERPs arise from the summation of evoked oscillations of different frequencies (Karakaş et al., 2000).

10 Others have suggested instead that evoked Gaussian potentials are fundamental basis functions that combine to form ERP components (Melkonian et al., 2001).

Both the second and third assumptions of the standard model are violated by evidence indicating that ongoing activity at the time of a stimulus may contribute to the poststimulus ERP (Makeig et al., 2004). It is generally agreed that the EEG and MEG contain ongoing oscillatory activity at specific frequencies, and that the phases of ongoing oscillations at the time of the stimulus are random from trial to trial. If the stimulus acted to reset the phase of these oscillations to the same value on each trial, summation of poststimulus phase-aligned waves would result when the trials were averaged. To distinguish phase resetting models from the standard model requires techniques that allow comparison of prestimulus and poststimulus activity on a single- trial basis.

In summary, a wealth of knowledge about ERPs has been obtained from the ensemble averaging of single-trial time series, under assumptions of the standard model of ERP generation. Nonetheless, substantial evidence indicates that this model is not completely adequate, and that exclusive reliance on ensemble averaging may obscure important issues relating to the genesis and functional relevance of ERPs. To provide a more detailed understanding of ERP component structure than is available by ensemble averaging, additional methods are required that derive information from the entire ensemble of single-trial time series. Frequency domain analysis is a class of methods that quantifies oscillatory activity in the trial ensemble in terms of its frequency, amplitude, and phase. It may be advantageous for addressing issues such as the occurrence of induced oscillations and the phase reorganization of ongoing oscillations. These considerations emphasize the need for the more sophisticated forms of ERP analysis reviewed in the next section.

Analysis of the Cortical ERP

A general problem in the investigation of ERPs is that field potential recordings, whether LFP, ECoG, or EEG, most often contain a combination of potentials, in unknown proportions, from multiple sources. (The same problem applies to the ERF.) Thus, in addition to the ERP, which is derived from specific neuronal populations associated with a behavioral event, the field potential typically also contains potentials derived from the more general field activity of larger populations. Thus, a primary task of all ERP studies is to extract invariant features of the event-related activity from a set of field potential recordings. This section deals with different methodologies by which this is accomplished.

11 Time Domain Analysis

The most common form of ERP analysis is performed in the time domain by measurement of the amplitudes and latencies of components identified in the waveform averaged over an ensemble of single-trial time series. This approach necessarily involves a loss of information about the distributional properties of the ensemble of single trials. Various alternative time domain techniques have been devised for analysis of the entire ensemble of single-trial time series rather than the single-ensemble average.

One general class of time domain analysis operates by application of a weighting function, or filter, directly to the single-trial time samples. The filter is applied either to the entire time series of each trial, or to segments of it. One such weighting function, called the Minimum Mean Square Error filter (or “Wiener” filter), is designed to selectively enhance the ERP signal while suppressing the noise (Gevins, 1987). Of course, to implement such a filter requires knowledge of the signal, which may be problematic. A related technique is matched filtering, in which the average ERP is used as a template that is “matched” by correlation with the single-trial time series. Matched filtering has been used to improve the average ERP by recreating it from “latency- corrected” trials (Woody, 1967), as well as to correlate the distributions of single-trial latency and amplitude values with behavioral or other parameters (Liang et al., 2002; Truccolo et al., 2002, 2003). Another weighting function is the band-pass filter, which is used to extract ERP components on the basis of their frequency characteristics. This approach is related to frequency domain analysis, which is described below. Similar to band-pass filtering are single-trial filtering techniques based on wavelet transforms (Browne and Cutmore, 2000). Time domain filtering techniques have been used in a variety of applications to investigate ERP function and composition.

Statistical feature extraction represents another approach to understanding the ERP from the analysis of ensembles of single-trial time series data. Principal Components Analysis (PCA) is one such method that has been used to extract overlapping (principal) ERP components based on the inherent variability structure of the data set (Donchin and Heffley, 1979; Dien et al., 2005). This variability occurs over time in the trial, over the ensemble of trials, over simultaneously sampled locations, and over different experimental conditions. The method involves computing the eigenvalues and eigenvectors of the covariance matrix of the original time series data, with the principal components being derived from the eigenvectors that are located along the directions of maximal data variance. Thus, the principal components reflect the intrinsic morphology of the single-trial waveforms, rather than a predetermined set of basis functions as in most filtering techniques. However, due to the orthogonality of the components that comes from the eigenvector decomposition, a potential problem with the PCA procedure is the misallocation of variance between the components (Wood and McCarthy, 1984). Various proposals have been made for overcoming this and other problems with the application of PCA to ERPs (Kayser and Tenke, 2005). A related approach that avoids the imposed component orthogonality constraint of PCA is Independent Component Analysis (ICA) (Stone, 2002).

12 Frequency Domain Analysis

A second general class of analysis operates in the frequency domain by converting a series of amplitude values over time into a series of amplitude values over frequency through application of the Discrete Fourier Transform. Frequency domain analysis, or spectral analysis, provides greater insight into the organization and function of ERPs than is available from time domain techniques alone. It can distinguish a time period during which the ERP consists of oscillatory activity at particular frequencies, i.e. is narrow- band, from that in which the activity is distributed over a wide range of frequencies, i.e. is broad-band. Since use of frequency domain analysis assumes that the time series is stationary, additional procedures are required to analyze transient ERPs, which are inherently nonstationary.

Combined time-frequency analysis is performed using a short time window that is moved over a longer time period of interest, e.g. the delay period in a working memory task. Time-frequenc analysis seeks to provide an adequate representation of the temporal evolution of frequency components in the ERP. A number of time-frequency analysis methods have been advanced, including multitaper (Mitra and Pesaran, 1999), wavelet or Hilbert transform (Bruns, 2004), and parametric modeling techniques (Franaszczuk et al., 1985; Lopes da Silva and Mars, 1987; Ding et al., 2000; Cui et al., 2008).

Spatial Analysis

The neural processes underlying ERP generation are extended in space within the brain. Spatial analysis is therefore an important tool for understanding the relations between ERPs recorded at different spatial locations within or outside the brain (Lehmann, 1987). When simultaneous recordings are obtained with a sufficiently dense grid of electrodes on the brain or at the scalp, a basic form of spatial analysis, called topographic mapping, may be performed. The topographic distribution is an important feature of ERP components that complements other features such as latency, amplitude, polarity, and frequency content. Components that may otherwise be difficult to disambiguate, may, in some cases, be easily distinguished by their topographic distributions. In fact, topographic patterning of the ERP may be fundamentally related to brain state at spatial scales from microscopic to macroscopic (Freeman, 2003). Beyond simple topographic mapping, spatial analysis of the ERP takes the form of spatial spectral analysis (Freeman et al., 2000), spatiotemporal PCA analysis (Fuchs et al., 2000), and inverse transformation to obtain estimates of cortical sources (Darvas et al., 2004).

Interdependency Analysis

The ERP may be defined not only by its timing, frequency content, and spatial distribution, but also by higher-order features. Interdependency measures attempt to characterize the similarity structure of the waveform morphology of ERPs recorded at different spatial locations. Interdependency analysis is performed in either the temporal or frequency domain. In either case, stationarity considerations dictate that when applied to ERPs the analysis be performed in short time windows. A relatively simple tool for

13 interdependency analysis in the time domain is the cross-correlation function, which measures linear relations between different time series. Nonlinear relations are characterized by measures based on the concept of mutual information (Mars and Lopes da Silva, 1987).

A useful technique for interdependency analysis in the frequency domain is parametric spectral estimation (Franaszczuk et al., 1985; Ding et al., 2000; Cui et al., 2008). This method, which allows spectral interdependency quantities such as multiple coherence and ordinary coherence to be computed from autoregressive model parameters, has proven advantageous in the investigation of oscillatory network interdependencies when applied to simultaneously recorded ERPs from a distributed set of recording sites in the brain. The multiple coherence assesses the interdependency of each recording site with the group of all the other sites, whereas the ordinary coherence gauges the interdependency between two specific sites. Time-frequency analysis allows measurement of event-related interdependency between ERPs recorded at different cortical sites. ERP interdependency in different frequency ranges has been identified as a neural correlate of basic sensory and motor processes, as well as higher cognitive processes such as perception and recall of semantic entities (Bressler and Kelso, 2001; Varela et al., 2001).

Another approach to interdependency analysis derives from the concept of causal influence. Wiener (1956) proposed that, for two simultaneously measured time series, one series may be considered causal to the other if knowledge of the first allows better prediction of the second. This concept was adopted and formalized by Granger (1969) in the context of autoregressive models of stochastic processes. Specifically, if the variance of the prediction error for the second process at a given time is reduced by including past measurements from the first in the second’s autoregressive model, then the first process is considered to have a Granger causal influence on the second process.

[Figure 4 near here]

Causal influences may be characterized in the time domain, or in the frequency domain using a spectral decomposition for Granger causality derived by Geweke (1982). The Geweke spectral measure is useful for revealing important aspects of event-related oscillatory network dynamics (Brovelli et al., 2004; Figure 4). The possibility that the measured Granger causality from one process to a second is actually the result of common driving from a third process cannot be excluded when that third process is not recorded. However, when a third process is recorded, the technique of conditional Granger causality analysis can be used to unequivocally determine whether that third process is responsible for Granger causality between the first two (Chen et al., 2006).

Discussion

The cortical ERP reflects the coordinated behavior of large numbers of neurons in relation to a meaningful externally or internally generated event. It is an important neural signal that provide a window onto the dynamics of sensory, motor, and cognitive processing in the brain, and its usefulness can be heightened by careful applications of

14 the analytic techniques described above. Single neurons are coordinated in the operations of neuronal populations, whose dynamics may effectively be studied at the mesoscopic and macroscopic levels of organization by ERP analysis. ERP analysis is thus an indispensable complement to single-cell neurophysiology and whole-head neuroimaging techniques.

In animal recording, ERPs allow access to the dynamics of neuronal population activity that cannot be achieved with unit recording techniques. In human recording, ERPs allow access to changes in brain activity on the order of milliseconds that cannot be achieved with hemodynamic-based neuroimaging techniques. Other recording methodologies with temporal resolution comparable to the ERP, such as voltage-sensitive optical imaging and direct magnetic resonance imaging of neuronal magnetic fields, are currently under development. However, even if these other modes of recording should eventually supplant the ERP, the same types of functional consideration and analytic technique discussed in this article will nevertheless apply to them as well.

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Figure 1. Schematic membrane potential recordings (MP1, MP2, MP3) from intracellular microelectrodes (ME1, ME2, ME3) in superficial and deeper parts of a cortical pyramidal neuron, and simultaneous field potential recordings (FP1, FP2, FP3) from extracellular electrodes (E1, E2, E3), following apical dendrite depolarization resulting from afferent fiber stimulation. Loop currents are indicated by dashed lines [Modified from Speckmann, 1997].

Figure 2. Left: Dipolar electrical field resulting from depolarization of the apical dendrites of a single cortical pyramidal neuron. Isopotential surfaces are represented by dashed lines, and extracellular field currents by solid lines. Right: Electrical field created in the surrounding volume by a synchronously active sheet of pyramidal cell dipole generators resulting from depolarization of their apical dendrites. Isopotential surfaces are represented by solid lines [Modified from Gloor, 1985].

Figure 3. A visual event-related potential derived by averaging an ensemble of single-trial LFPs recorded from the posterior parietal cortex of a macaque monkey. The LFPs were recorded from a chronically implanted bipolar transcortical electrode consisting of 51-µm-diameter platinum wires with 2.5-mm tip separation [Modified from Bressler, 2002].

Figure 4. Interdependency analysis of the sensorimotor cortex of the right hemisphere of a macaque monkey Network interactions during a maintained manual postural position are shown by graphs of ordinary coherence (left) and Granger causality (right) based on oscillatory LFPs in the beta frequency range [Modified from Brovelli et al., 2004].