With renewed appreciation for the biophysics of EEG generation, we now realize that this assumption is true only in limited cases in which the spike or seizure voltage field is purely radial in its orientation.¹ Such fields are typically generated by the crowns of convexity cortex. However, many brain regions that are highly epileptogenic are not found on the cortical convexity. This includes the entire base of the brain, in particular orbitofrontal and basal temporal regions. These cortices produce EEG fields that are tangential to the head surface rather than radial. Similarly, epileptogenic foci in major fissures, such as Sylvian or interhemispheric, produce tangentially oriented EEG fields. Such sources are important to understand because little or no EEG potential is recorded directly above them; rather, the negative and positive EEG fields on the head are displaced on either side of their true location. In such a situation, considering the negative field maximum as the source location will result in false localization and even a false lateralization in certain situations (Figure 5-1).

Figure 5–1 Three cortical sources are noted by color overlay on the MRI—interhemispheric (blue), lateral convexity (green), and temporal base (red). Scalp voltage fields produced by depolarization of these sources (1, 2, and 3, respectively) are depicted surrounding the MRI. Isopotential lines denote field amplitude; speckled field is negative in polarity. An equivalent current dipole for each voltage field is shown adjacent to the cortical source. Note that the orientation of the dipole is orthogonal to the net orientation of the source cortex, and the position of the dipole is deep to the cortical surface.

EEG Fields from Cortical Sources

In the generation of any cortical EEG potential, be it epileptiform or normal, current sinks and sources are created on opposite ends of the palisaded pyramidal cells. By electromagnetic necessity, the extracellular space at one end of this cell layer is relatively negative, and the other end is relatively positive. This separation of charge creates a dipole. EEG potentials are characteristically dipolar in nature because of this generating mechanism. In epileptiform activity, the superficial laminae are often depolarized initially, leading to the prominence of negative potentials for epileptic spikes and seizure potentials. Of note, this is the opposite of normal sensory-evoked potentials, where depolarization of layer 4 results in passive hyperpolarization of the superficial laminae and a resultant surface-positive potential. Recurrent circuits within the cortex produce reverberating depolarization/hyperpolarization sequences. Thus many cortical potentials, including epileptic activity, exhibit recurrent cycling of negative and positive waveforms, such as in spike-wave complexes. All cortical EEG potentials have a dipolar field configuration; however, given limited spatial sampling of scalp electrodes, we may not record both sides of this dipole field. This is particularly true for radial sources near the vertex that have a positive field maximum at the bottom of the head. Conversely, for basal brain sources only the positive field maximum may be recordable from standard 10 to 20 electrode positions. However, for sources in the lateral aspect of the brain, both maxima are typically evident in traditional montages (see Figure 5-1).

A three-dimensional line drawn between the negative and positive field maximum of a spike potential on the head has the same orientation as that of the pyramidal cells generating the potential. The actual cortical source may be geometrically complex, but this line represents the net orientation of those cells. Because pyramidal cells are orthogonal to the cortical surface, the orientation of an EEG field is also orthogonal to the source cortex. Theoretically, the center of the cortical source must lie along this 3-D line. Its location is proportionally nearer the field maximum with greater amplitude. Thus, in most cases sources are located nearer the higher amplitude negative field maximum. However, when the voltage field is tangential, the source location is equidistant between field maxima. Simply by inspecting the spike/seizure voltage fields over the head, one can gain considerable information about the likely source of these fields. Such visual analysis is essentially a form of source modeling. This same spatial information regarding voltage fields is the basic data used by all source modeling mathematical algorithms.

The Dipole as a Model of Cortical Sources

The most common source modeling technique used for clinical applications is the single equivalent current dipole.² As noted earlier, cortical sources of EEG spikes or seizure rhythms produce voltage fields that are dipolar in nature. It makes sense, therefore, to use a model that is dipole based. However, the dipole used in modeling is a theoretical point source with a separation of charge, whereas the actual source of an EEG potential is a relatively large region of cortex that forms a dipole layer. Although the geometry of the actual dipole layer may be complex and comprised of several gyri and sulci, the voltage fields produced by this convoluted source will add or cancel one another in a linear way to produce a resultant simple dipolar field at the scalp. In fact, recent studies of simultaneous intracranial and scalp EEG have shown that a region of gyral cortex 10 or more square centimeters in area is necessary to produce an EEG potential that is distinguishable from the ongoing background rhythm.³ In fact, large and easily identified epileptiform potentials are often generated by cortical sources of 20 to 30 cm² in size, thus encompassing a substantial sublobar region. Even though more complex multipolar geometry such as quadrapoles and octopoles may be produced by these large convoluted sources at the cortex, the dipolar field component dominates at the scalp. Because a point source dipole model attempts to explain scalp EEG fields produced by a large cortical patch, these dipole solutions are usually deep to the actual generating cortex in order to project a field of equivalent area (Figure 5-2).

Figure 5–2 Major cortical sources and their equivalent dipoles for temporal lobe spikes/seizures are illustrated—lateral cortex (top left), tip cortex (bottom left), and base cortex (top right). To the right of each source is the scalp voltage field produced by the source. Note that a three-dimensional line connecting the negative (blue) and positive (red) field maximum defines the orientation of the field and that of the equivalent dipole. Lateral temporal cortex dipoles are horizontal and radial; temporal tip dipoles are horizontal and tangential; temporal base dipoles are vertical and tangential. Note, too, that dipoles are deep to the cortical sources.

Physical laws of electromagnetic field theory state that the voltage fields on the surface of a spherical volume conductor can be accurately predicted if the location, orientation, and strength of a dipole source within the conductor are known.^4,⁵ This is called the forward solution, and it is unique. However, what we attempt to do in clinical dipole modeling is the reverse. We measure the surface voltage field on the head and attempt to identify the source within this volume conductor. This is the “inverse solution,” and it is not unique because a number of different dipolar source configurations within the brain can produce the same surface field.⁶^–⁸ Therefore, we have to use certain assumptions to minimize the possibilities, and the principal one is that the source is a single current dipole. Various algorithms exist for identifying an equivalent dipole source.⁸^–¹¹ Most of these algorithms use an iterative-minimizing approach, whereby an estimate of source location is made. The forward solution is performed, and the difference between the forward solution and the actual measured field is characterized. Subsequent random movements of the dipole model attempt to minimize this difference. When the smallest difference is obtained, the putative dipolar source has been identified.

Dipole models display in three-dimensional terms the same information that a person can perceive by visually inspecting the voltage fields as explained earlier. In addition, these equivalent dipoles can be coregistered either with a head schematic or with an actual three-dimensional magnetic resonance imaging (MRI) to identify the putative source within the brain. With a head or brain schematic, it is possible to identify the most likely lobe or perhaps even sublobar area containing the source. It is very tempting to coregister these data with three-dimensional MRIs, as is commonly done with other functional imaging techniques. The problem with doing so is that sources or colored blobs that are placed on a real brain image take on a seductive pseudorealism that in reality must be verified. In the case of EEG dipole models, sources in the cortical convexity are accurately localized. This is because even simple spherical head models used by source-modeling algorithms work well in this most spherical part of the head and brain. However, when sources were near the base of the brain, such as in the temporal lobe, systematic dipole location errors occurred for known sources.^12,¹³ This error was typically in the vertical direction toward the vertex, and it could be as great as 2 or more centimeters in magnitude. A spherical head model was the reason for this error.¹³^–¹⁵ Such a model cannot be used to localize sources near nonspherical parts of the head, such as the base of the skull (Figure 5-3).