The electrodes may be connected together into several different kinds of bipolar and monopolar montages. In bipolar montages all electrodes are connected together in chains, with the second input to one channel becoming the first input to the next channel. The most common use of a bipolar montage is to record the electrooculogram. In this case horizontal eye movements are recorded by means of two electrodes placed at the external canthus of the left and right eyes, and blinks and vertical eye movements are recorded by means of two electrodes placed below and above the right eye, with a bipolar montage. In a monopolar montage, also called a common reference method, one electrode is active and the other one (or two electrodes linked together) acts as a reference electrode. Typical arrangements for the reference electrode(s) are the linked ears and the linked mastoids configurations. The reference lead must be as electrically neutral as possible with regard to brain activity, while it nevertheless records the basic activity underlying the various physiological functions of the body in spite of any possible external noise (electromagnetic waves). What is actually recorded is the difference that exists between the potential of the active site and that of the reference site. The most commonly used reference leads are the left or right ear (or ear lobe), or the linked or balanced ears (or ear lobes), the left or right mastoid, or the linked or balanced mastoids, the tip of the nose, the chest, and the balanced non-cephalic sternovertebral lead [see Tyner et al. (1983), p. 166, for a buildup scheme of this reference lead]. None of these is totally free of problems or is the best in an absolute sense. What is, however, important is the distance of these sites from the active electrode. Neighboring sites will cancel out electrical activation sites similar to the two electrodes. Conversely, distant sites will tend to capture more artifacts from many different sources. When using linked references, such as the two ear lobes (i.e., the so-called A1 and A2) or mastoids
(i. e., the so-called Ml and M2), it is advisable to use a balanced strategy to remove possible variations in impedance between the two linked reference sites. This allows a so-called balanced linked reference to be obtained. The balancing may be achieved in several different ways. For example, the same weighting (intensity) may be assigned to the two combined signals by connecting together two low-value (e.g., 5000 Q) resistances (R1 and R2), which are coupled in series to the electrode connectors. Alternatively, it is possible to use two variable resistances in series and to change their value as a function of possible variations in impedance during recording. Both procedures offer advantages and disadvantages.
The most important reason for making a careful choice of reference is the strong influence it has on the surface topographic distribution of the bioelectric signal (that
Voltage SCD SCD
1.23 to +1.23 ¡1V "128 to +128 pV/m2 -512 to +512 fjV/m2
1.23 to +1.23 ¡1V "128 to +128 pV/m2 -512 to +512 fjV/m2
FIGURE 2 Examples of spline or isoline maps viewed from the back. The maps have been computed at P1 peak latency (120 msec) on a difference wave form obtained by subtracting ERPs to gratings relevant in location but irrelevant in spatial frequency, from ERPs to gratings relevant in both features and presented in the right visual field. Left: Changes in voltage (microvolts) isolines and, as a consequence, in scalp topography with "offline" rereferencing (linked Fpl-2) with respect to referencing during "online" ERP recording (linked ears). Note that unlike the latter, the linked Fpl-2 reference determines a decrease in positivity at occipitotemporal sites, and an increase in negativity at right temporoparietal sites. Middle: Regardless of the reference, the computation of the Laplacian operator provides the same scalp current density (SCD) (in |V/m2) spline map. Here a larger neat positive focus, centered on Ol, O2, and POz mesial-occipital scalp sites, and a smaller one, focused at the posterior-temporal (T5) site, can be observed. (For electrode locations over the posterior scalp maps, see the electrode montage insert at the bottom.) Right: Examples of misleading representations of SCD maps. Top: A too large scale has been chosen, and too few isolines have been drawn in the map to represent the currents' topography over the scalp. In this way, not much topographic information is provided. Bottom: Unlike above, here a too small scale has been chosen, and too many isolines have been drawn in the map to represent the current source topography over the scalp, providing an overload of information to the observer. It follows that an extra effort is needed to figure out the topographic information.
is, on its geographic distribution over the scalp). As we have seen, the reference must be electrically "silent" (or neutral), but unfortunately there are no absolutely silent points in a living biological system. Consequently, because the recorded signal is the result of computing the difference between the signal recorded at the active electrode and that recorded at the earthed reference, the topographic distribution of the EEG signal on the scalp will vary as the reference value varies. This is of more than trivial importance. The topography of the biolectric signal from the same individual taken as the active agent in the same psy-chomotor task will be found to vary as the reference varies (see Fig. 2). This raises considerable problems as regards the identification of the cerebral areas activated during the performance of the task. To get around them several reference-free signal transformation solutions have been developed. The first of these consists of using the so-called average reference, which, as its name suggests, is based on taking the average value of all the active electrodes as reference (for a detailed treatment of the advantages and disadvantages of this method see Appendix E in the present volume). An alternative to this consists of using a method that enhances the local sources (i.e., radial currents, that is, currents perpendicular to the head), which minimizes the voltage gradients (or currents tangential to the head) due to spurious correlations among the various electrodes. This is done by transforming the scalp voltage values into scalp current density (SCD) by means of a Laplacian analysis. It involves solving the Laplace equation or second derivative of the interpolated voltage area. By acting as a spatial filter, this method eliminates the distant sources contribution (or remote potential fields). In this way it is possible to obtain a reference-free topographic representation of brain activation. So no matter what reference is used during the recording, SCD mapping provides a unique topographical solution (see Fig. 2). This procedure entails using a large number of electrodes because it is based on computing the difference between one specific electrode and many others that surround it. For a recording that takes in the entire head surface, a minimum of 32 electrodes is thus required (for further details on this method, see later, the section on "ERP Topographic Mapping").
To prevent charge accumulation during EEG recordings, participants have to be connected to charge dispersion devices by means of a ground lead linked to the security plant of the building where the lab is located, or, much better, to a small pit dug in the earth and constructed in accordance with the relevant norms. Grounded active leads, (e.g., Fz) located on the scalp are commonly used.
The bioelectric signals detected by the electrodes are conveyed separately to electronic amplifying devices—one channel for each electrode site. The amplifiers are made up of a series of resistors and capacitors that have the function of filtering and amplifying the signal. Biological potentials actually have only tiny voltages— millionths of a volt—which must be stepped up to the level of several tens of volts in order to be recorded. The purpose of the amplifiers is to supply energy to tiny potential differences so that they are multiplied tens of thousands of times. For instance, with a gain of 40 the signal is magnified 40,000 times. Unlike the EEG, the EOG is given a lower amplification. Because the EOG signals are actually generated by the electrophysiological signals of the eye muscles developed during eye movement, they have a relatively high amplitude and do not require much amplification.
To distinguish physiological potentials from potential differences with reference to the ground, amplifiers amplify the poten tial difference between their input terminals (i.e., electrodes) and are relatively insensitive to a potential between these terminals and the ground. For this reason they are known as differential or balanced amplifiers. The voltage with respect to ground common to two electrodes is called an in-phase or common mode signal. The potential difference between the electrodes is called the antiphase or differential signal. The specific property of a balanced amplifier is to record and amplify the antiphase signals while eliminating the inphase signals. This property is referred to as the high common mode rejection ratio.
"Online" Analog Filters
The electric circuits in the amplifier are equipped with filters. The main components of a filter usually consist of a resistor and a capacitor (R-C circuit). This circuit allows selective elimination of electric frequencies causing disturbance, or in any case that are extraneous to the brain's bioelectric activity, such as those due to muscle movement or to the alternating current circulating in the electrical equipment. Or else, depending on the aim of the research, filters allow the elimination of recorded physiological signals above or below a specified frequency, called the turnover or cutoff frequency (fc). Highpass, low-pass, or band-pass filters can commonly be found on commercially available amplifiers. For any of these filters, several frequency settings can be made. With high-pass filters, the setting regulator shows the cutoff frequency above which higher frequencies are passed, and lower frequencies are attenuated. For this reason they are also called low-frequency, or "L.F. cut," filters. Conversely, for low-pass filters the cutoff frequency setting indicates the frequency above which higher frequencies are attenuated, while lower frequencies are allowed to pass. For this reason they are called high-frequency, or "H.F. cut," filters. The band-pass filters delimit a "window" of frequencies accepted by the amplifier within two upper and lower extremes. For example, a band-pass filter suitable for recording evoked potentials could be 0.01-100 Hz for EOG and 0.1-100 Hz for EEG. However, with studies aimed at investigating cognitive processes, which develop more slowly than sensory processes (for instance, longer latency linguistic processes), a band of 0.01-100 Hz for EEG filtering is certainly more suitable. Notch filters to exclude the line frequency range (60 Hz for the United States and 50 Hz for most overseas countries) are not recommended in that they may significantly distort the recorded signal (Picton et al., 2000).
Common settings for high-pass filters indicate, rather than a cutoff frequency, how long it takes for a signal to return to the base line following an exponential curve. This is a curve that approaches its final value at a decreasing rate, with a slope of attenuation that is also called the rolloff. This is characterized by the time— usually measured in seconds—within which the signal amplitude falls to 37% of its initial value before the filter action takes place. This value, which is independent of the magnitude of the initial step, is called the time constant (TC). For these filters, then, the cutoff frequency has to be estimated through the following expression:
fc= 1/2^Tc, where TC is the time constant and 1/2^ is a constant equal to ~0.159, obtained by dividing 1 by the double of ^ = 3.14. Thus, fc = 0.159/TC may also be found. For example, with TC = 3 sec, fc = 0.053 Hz; with TC = 10 sec, fc = 0.0159 Hz. Clearly, in those rare cases in which fc, rather than TC, is known, the latter may be obtained by simple transposition of the above-mentioned expression: namely, TC= 1/2^/fc. For instance with fc = 0.053, TC = 0.159/0.053 = 3 sec. Much care has to be taken over these inversions in order to communicate accurately the characteristics of filters used during experimental recordings. Indeed, some risks are run, not only of communicating incorrect values of TC because of inconsistency in filter nomenclatures among amplifier manufacturers, but also of obtaining misleading data regarding signals of interest. For instance, when studies are carried out aimed at investigating late latency slow processes of the brain, these processes could be cut off by a misleading setting of the turnover frequency.
Different definitions are, in fact, reported for fc by different manufacturers, and confusion may arise. Mostly, fc is defined as the half-power frequency, that is, the frequency at which the "output power-to-input power ratio" (i.e., also called gain or sensitivity) is 0.5. The fc setting, by allowing a gain in power of 0.5, actually determines a gain in amplitude of 0.707, the latter simply being the square root of 0.5 (i.e., power = ampli-tude2). In other words, this means that the sensitivity amounts to 70.7% of its maximum value. Indeed, this is the definition of fc that is implicitly contained in the expression used above to compute TC. Because amplifier gain was often traditionally expressed in decibels (dB)—the logarithmic expression of frequency—this reduction in gain is the same as a "3-dB down" of the maximum value.
For some manufacturers, however, fc indicates the half-amplitude frequency, which is different from the half-power, because it actually marks the frequency at which a 50% decrease in sensitivity occurs. In decibels, this entails a further halving of the power with respect to 3 dB, that is, a "6-dB down." Obviously, at this point, when, unknown to the experimenter, in setting up a filter, the half-power is confused with the half-amplitude, for example, at fc = 0.053, the late-latency components—such as P300—might be partly washed out because of too fast a TC. With half-amplitude-regulated amplifiers, in order to record ERPs with, for instance, a TC = 3 sec, the fc value should be lower, namely, 0.031.
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