Column-based model of electric field excitation of cerebral cortex

Abstract

A model to explain the orientation selectivity of the neurophysiologic effects of electric-field transients applied to cerebral cortex is proposed and supported with neuroimaging evidence. Although it is well known that transcranial magnetic stimulation (TMS) excites cerebral cortex in an orientation-selective manner, a neurophysiologically compelling explanation of this phenomenon has been lacking. It is generally presumed that TMS-induced excitation is mediated by horizontal fibers in the cortical surfaces nearest to the stimulating coil, i.e., at the gyral crowns. No evidence exists, however, that horizontal fibers are orientation selective either anatomically or physiologically. We used positron emission tomography to demonstrate that TMS-induced cortical activation is selectively sulcal. This observation allows the well-established columnar organization of cerebral cortex to be invoked to explain the observed orientation selectivity. In addition, Rushton's cosine principle can used to model stimulation efficacy for an electrical field applied at any cortical site at any intensity and in any orientation.

Figure 1

Experimental preparation. The subject is immobilized in the PET scanner with a thermoplastic mask. The stimulating coil (A) is held by a NeuroMate robot (C) customized in‐house for this purpose. A second coil (B) was used to deliver sham stimulation, an auditory control. The rate of stimulation used (3 Hz) required a water‐cooled coil with waterlines (D).

Figure 2

Measurement of the distance from the stimulation point at the scalp to the detected response is illustrated for Subject 1246. The T1‐weighted MRI is shown in grey‐scale. The TMS‐induced PET activation response is shown in color overlay; note that it lies on the sulcal surface, and does not include the gyral crown. The scalp surface model was constructed from the tissue‐air interface of the MRI. The TMS coil is to scale. The shaded half‐dome is a calibrated 3D model of the E field created by the TMS coil. The distance to the center‐of‐mass of the TMS‐induced activation was measured with the depth probe function (yellow line) of the TMS Planning Tool software (RIC, UTHSCSA).

Figure 3

M1 responses to voluntary finger tapping (left column) and to TMS (right column) are shown for each of the seven subjects in whom an M1 blood‐flow response was observed in per‐subject PET images. In each instance the response is visualized in the parasagittal plane at the center‐of‐mass of the M1 response (cross‐hair). In every subject and for both stimuli, responses were on the sulcal surface of the central sulcus (BA4). There was no evidence of a response being present on the gyral crown during TMS stimulation or finger movement. This supports a column‐based model of E field interaction with cortex. Overlays were created using the TMS Planning Tool.

Figure 4

A scatter plot of the depths from the scalp surface for the M1 response to voluntary index finger movement (x‐axis) and TMS‐induced FDI activation (y‐axis) is shown. The depths of the responses were highly correlated (r = 0.93; P < 0.002). This indicates that the depth of the TMS‐induced activation was a function of the actual depth of the M1 cortex, as BA4 is known to extend a varying distance upward from the BA 3 border in the depths of the sulcal pit.

Figure 5

The locations of M1 responses to voluntary finger movement (squares) and to TMS‐induced finger movement (triangles) in standardized coordinates for each of seven subjects are illustrated. Per‐subject locations are open symbols; average locations are solid symbols. Location of activation did not differ significantly in any axis between the two types of M1 activation. Responses are plotted using the BrainMap Search and View software (online at http://www.brainmapdbj.org).

Figure 6

PET Responders. The M1 response to voluntary finger tapping (left group) and the M1 response to TMS (right group) are shown in group‐mean SPIs formed from the seven subjects in whom a significant M1 response to TMS was observed with per‐subject PET image analysis. For both conditions, Z‐score rose with averaging: to 5.7 (from 4.2) for voluntary movement, and to 5.0 (from 4.3) for TMS. The center‐of‐mass of the responses in the two images are very similar (Table III). In both SPIs, the response lies deep in the central sulcus, not on the gyral crown, supporting a column‐based model of E field effects on cortex.

Figure 7

PET Non‐responders. The M1 response to voluntary finger tapping (left) and the absence of an M1 response to TMS (right) are shown in group‐mean SPIs formed from four subjects in whom a significant M1was not observed with per‐subject PET image analysis. Although the response to hand movement rose with averaging to a Z‐score of 4.0 (average of per‐subject Z‐scores = 3.4), no response to TMS was observed even with averaging. As TMS did produce corticospinal track excitation (as evidenced by TMS‐induced muscle contractions), we infer that the EMG was induced via direct axonal depolarization rather than via cortical excitation.

Figure 8

The cortical column cosine (C³) model. The linear, scalp‐parallel E field (bold arrows) induced by a B‐shaped coil is illustrated. In this study, the average value of the E field applied at the scalp was 300 V/m. The average depth of M1 excitation by TMS was 31 mm. (A centimeter ruler is shown at right). The E field diminishes exponentially with distance from the scalp. The C³ model posits that activation is induced only by the column‐aligned component of E. The absolute E field vector (E_abs) is decomposed into two components: a column‐aligned component that is effective (E_eff) and column‐normal component that is ineffective. Otherwise stated, E_eff is the product of E_abs and the cosine of the angle between the column and the E vector (θ). Whereas the E_abs is greatest at the gyrus, the E_eff is least and activation fails to occur (A). In the sulcal depth (C), E_abs is least, but E_eff is greatest and cortical excitation threshold is achieved. On the shoulder of the gyrus (B), E_abs can be greater than in the sulcus (C), but E_eff may still fall below threshold. The bending angle (Φ) of the pyramidal cell axon as it exits cortex and enters the corticospinal tract is illustrated.