Neural Scales in SEEG: Biophysical Principles and Technological Advances

Acknowledgments

We thank John Seymour of UTHealth Houston Department of Neurosurgery, Salvadore Dural-Bernal of SUNY Downstate Health Sciences Center, and Takfarinas Medani of the University of Southern California Signal & Image Processing Institute for the use of their figures and discussions with them about the practicalities of micro cellular models and SEEG finite element modeling. Research reported in this publication was supported in part by the National Institute of Neurological Disorders and Stroke under R01NS128924 and by the National Institute of Biomedical Imaging and Bioengineering under R01EB026299, both of the National Institutes of Health. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Introduction

To highlight the challenges and interpretations of SEEG modeling, we begin the discussion of this chapter with Fig. 4.1 of a unilateral implantation. The left figure, Fig. 4.1A , is a standard coronal view of a single SEEG electrode with multiple contacts. The other two images are of the same electrode and several others with respect to a 3D rendering of the cortical surface. The cortical surface is tessellated with nearly 540,000 small triangles, comprising nearly 270,000 vertices. As we will discuss, each triangular vertex can be modeled as the surface point of an elemental cortical column that descends directly below the point for about 2 mm. Since the adult human cortical surface is approximately 240,000 square mm, each vertex nominally represents about a square mm of the pial surface. The challenges we discuss in this chapter center on the scales of the neural models that comprise these cortical columns, and, correspondingly, on the scales of the recordings possible with conventional SEEG electrodes. We also briefly examine the next generation of SEEG electrodes in prototype and design that may enhance our ability to differentiate multiple sources of neural activity.

Neuronal activity: From microscale to macroscale

The Single Cortical Column

To illustrate the scales discussed in this chapter, we begin with a detailed cortical column created in our labs for research and proposal purposes, shown in Fig. 4.2 . The cylindrical column model is 2 mm long and 0.2 mm in diameter, comprising over 12,000 cells spanning about 40 different cell types. For our purposes here, the types of cells are not important. The column spans the classic model of six layers of the cortex, with representative densities given in the figure. The top six cell types are displayed in the central figure, with each cell indicated by a point.

Each of these individual neurons creates “micro-current sources. ” These micro-current sources are synaptic and action potentials at neuronal membranes. The post-synaptic potentials could be excitatory (EPSPs), with inflow of Na + ions at the apical dendrites, or inhibitory (IPSPs) with an inflow of Cl-ions at the soma. Excitatory synapses predominate on dendrites while inhibitory synapses predominate on soma and basal dendrites. The potential difference between the synaptic area and the rest of the cell causes intracellular and extracellular currents. The synapse outside the cell now will equivalently be an “active sink” of negative polarity. The soma and basal dendrites can be assumed as a distributed “passive source” resulting in an extracellular potential of positive polarity. A similar mechanism follows for the IPSPs.

Using a detailed NEURON model of activation for these cellular sources, the final panel of Fig. 4.2 shows a raster plot of cellular activation for all of the cells. In Fig. 4.3 , we calculated the voltage signal that might be recorded at distances of 1–2 mm from this column, over the one second course of the activations shown by the raster plot in Fig. 4.2 . As the right-most panel in Fig. 4.3 shows, the measured voltage falls off rapidly in this logarithmic scale, for even just 2 mm from this cell population. Indeed, at even these short distances of a few mm, the exquisite details of the cortical model rapidly become the approximate simple model shown in Fig. 4.4 . The simplified cortical column now emphasizes the dominant sources and sinks within the column, with corresponding positive and negative charges. These in turn are more simply modeled as a single charge separation within the column, with current “pumped” from the negative charge to the positive charge, as indicated by the current dipole arrow, giving us the simple model of “primary current” within the cortical column.

The Neural Scales

Because of this rapid fall-off of potentials as a function of relatively small distances, we may break our cortical column model down into four recording scales, as summarized by Nunez :

1.

Micro-scale recordings : The micro recordings of the surface or transmembrane potentials correspond to the actions of the individual cells, such as we have modeled above. In this chapter, we generally assume that this level of recording is not available in human recording.
2.

Local field potentials or LFPs: More realistically for SEEG and related human invasive recordings, the “small-scale potentials” or “local field potentials (LFP)” are recorded by electrodes within the brain tissue. These small-scale fields reflect PSPs within 0.1–1 mm of the recording electrodes. This summed PSPs activity of few thousand neurons is referred to as LFPs. The tissue volumes are typically 0.001 to 1 cubic mm.
3.

Intermediate (meso) scale fields : The meso-scale potentials reflect summed neuronal PSPs activity of typically 1 to 20 cubic mm of tissue volume, representing distances about 2–5 mm from the cortical column.
4.

Macro-scale fields : At distances greater than about 5–8 mm from the column, we are essentially in the macro field. Nunez denotes this macro distance as roughly four times the height of the source, and our columnar sources are nominally 2 mm high.

For the non-invasive measurements made by scalp EEG and MEG, only the macro field model is useful due to the combination of CSF, skull, and scalp thickness. Indeed, even subdural electrocorticography (ECoG) mostly employs a macro model, except perhaps for sources directly in contact with a sensor at the pial surface of a gyrus. The SEEG electrode is therefore unusual in its ability to come close enough to a wide range of sources at many depths, such that we may consider additional LFP or meso scale models, in addition to the macro scale.

Dipoles, Quadrupoles, and Patches

By electromagnetic superposition, the total measured potential or magnetic field is simply the summation of the fields from all the individual sources. Because each source has a direction, then some sources will be parallel and directly sum together, while other sources will be in opposition and cancel each other. While the micro-scale represents the individual cells in a column, for SEEG purposes the more useful elemental model sums these tens of thousands of cells into a single cortical column, as was shown above in Fig. 4.4 . The classic cortical model aligns these cortical columns as perpendicular to the cortical surface, representing the columnar organization of the pyramidal cells in the gray matter. We caution this columnar organization is only an approximate model of the neocortex, since as noted by Nunez, many regions of cortex may not be as simply columnar in organization; nonetheless, we find the columnar model useful at many scales.

In Fig. 4.5 , we show an exemplar region of interest (ROI), the pars opercularis (left) of the Desikan-Killiany segmentation. The MRI is the widely available “Colin27” template model, and the pial surface has been segmented and labeled by Freesurfer, with rendering in the Brainstorm program. The ROI spans about 3000 square mm of cortex and is tessellated here with about 3000 vertices. Thus each triangular vertex nominally represents one square mm of surface of the cortex, and the cortical column extends down into the gray matter in the direction of the vertex normal, a direction readily calculated by any surface rendering software. We therefore find the cortical column model to be a readily achievable model in practice, simply modeling each triangle vertex as a cortical column.

At this scale of the cortical column, we may simply model the column as a current dipole, represented by a source and a sink, with the “primary current” being forcibly driven from the source (negative) to the sink (positive). We next address the question of how much current might we anticipate for a square mm of cortex, i.e., one of the vertices in Fig. 4.5 . From Okada, their experimental results suggest an upper limit of about 1 nA-m per square mm for many animals, with the human subjects measured close to 0.2 nA-m. We emphasize that this “Okada Constant” simply sets the plausible upper range of current, but this limit is nonetheless quite useful when we consider later “extended” regions of activity on the cortical surface. Given the nominal electrical length of the column to be about 2 mm, the model therefore suggests an upper limit of 0.5 microamps flowing up and down the column.

Rather than just a single cortical column, however, models of evoked responses and interictal spikes suggest several square cm of cortex are involved in the generation and observation of neural activity. For example, in Fig. 4.6 , we show a subregion of the pars opercularis of Fig. 4.5 , spanning about 500 square mm of cortex. In this “patch,” we now observe that individual cortical columns are nominally radially oriented to the sphere of the head, or tangentially oriented, and/or on opposing sides of the sulcal wall. If we assume that all cortical columns are uniformly active, then by electromagnetic superposition, we have a complicated combination of elemental sources that may constructively or destructively add to each other.