Elucidating the mechanisms and loci of neuronal excitation by transcranial magnetic stimulation using a finite element model of a cortical sulcus

Abstract

Objective: This work aims to elucidate by what physical mechanisms and where stimulation occurs in the brain during transcranial magnetic stimulation (TMS), taking into account cortical geometry and tissue heterogeneity.

Methods: An idealized computer model of TMS was developed, comprising a stimulation coil, a cortical sulcus, and surrounding tissues. The distribution of the induced electric field was computed, and estimates of the relevant parameters were generated to predict the locus and type of neurons stimulated during TMS, assuming three different stimulation mechanisms.

Results: Tissue heterogeneity strongly affects the spatial distribution of the induced electric field and hence which stimulation mechanism is dominant and where it acts. Stimulation of neurons may occur in the gyrus, in the lip of the gyrus, and in the walls of the sulcus. The stimulated cells can be either pyramidal cells having medium to large caliber axons, or intracortical fibers of medium caliber.

Conclusions: The results highlight the influence of cortical folding on the action of magnetic and electric fields on cortical tissue.

Significance: Tissue geometry and heterogeneity in electrical conductivity both must be taken into account to predict accurately stimulation loci and mechanism in TMS.

Fig.1

Overall geometry of the volume conductor and stimulation coil showing a rectangular box (ROI) centered under the coil; Inset 1) Volume conductor viewed from above; Inset 2) Geometry of the sulcus. There are 5 surfaces (S1-S5), parallel to each other and 1 mm apart, over which the stimulation mechanisms were evaluated. Surfaces S1 and S4 represent the boundaries of the cortex.

Fig. 2

Projections of the electric field along the axon's axis, for different cells in the cortex. The projection of the electric field along a pyramidal axon is the component of E⃗ perpendicular to the cortical surface, E_n. The projection of the electric field along the axon of a horizontal cell is the component of E⃗ tangent to the cortical surface, E_t, since horizontal cells are oriented tangentially to the cortical surface.

Fig. 3

Fit of E_z along z. The data sets for each subdomain (CSF, cortex and WM) are fitted separately to calculate the electric field derivative, ∂E_z / ∂z, analytically.

Fig. 4

Comparison of the perpendicular projections of the different stimulation mechanisms in the heterogeneous model (left column) and in the equivalent homogeneous model (right column). “Perpendicular component of E” denotes − λE_n. Each stimulation mechanism is displayed over the same surface and for the same space constant (1 mm). For ease of comparison, the same scale is used for each horizontal pair of figures. The stimulation coil is positioned above and centered on the visualized volume (ROI, cf Fig. 1) and induces an electric field parallel to the P-A direction (+ x to − x).

Fig. 5

Effect of tissue heterogeneity on the gradient of the electric field: Comparison between the heterogeneous and the homogeneous models. The gradient is inspected along a line r1 perpendicular to the cortex (cf. inset) assuming a space constant of λ = 2 mm. The curved geometry of the cortex results in an increased gradient that may lead to stimulation of large pyramidal axons near the GM-WM interface.

Fig. 6

Comparison of the tangential projections of the stimulation mechanisms in the heterogeneous model (left column) and in the equivalent homogeneous model (right column). “Tangential component of E” denotes − λE_t. Each stimulation mechanism is displayed over the same surface and for the same space constant (1 mm). For ease of comparison, the same scale is used for each horizontal pair of graphics. The stimulation coil is positioned above and centered on the visualized volume (ROI, cf. Fig. 1) and induces an electric field parallel to the P-A direction (+ x to − x).