Magnetic stimulation of the nervous system: Induced electric field in unbounded, semi-infinite, spherical, and cylindrical media

Abstract

Knowledge of the electric field that is induced in the brain or the limbs is of importance in magnetic stimulation of the nervous system. Here, an analytical model based on the reciprocity theorem is used to compare the induced electric field in unbounded, semi-infinite, spherical, and cylinder-like volume conductors. Typical stimulation coil arrangements are considered, including the double coil and various orientations of the single coil. The results can be used to determine when the influence of the boundaries is negligible enough to allow the use of more simplified geometries.

Neuroendocrine and Behavioral Effects of Repetitive Transcranial Magnetic Stimulation in a Psychopathological Animal Model Are Suggestive of Antidepressant-like Effects

“…The map consisted of a fourth degree interpolating polynomial which takes the grayscale values (0-255) of the MRI images as the argument and returns the corresponding conductivity value at that point in space. The five known data points between which we interpolated were taken from the literature (Cerri et al 1995;Ravazzani et al 1996), where values ranged from 0.01 A/Vm (bone) to 1.6 A/Vm (cerebrospinal fluid). In between were skin, gray matter, and white matter.…”

“…In between were skin, gray matter, and white matter. A 3D network consisting of cubic cells was then fitted to the brain, which for the order of magnitude of the electromagnetic parameters appropriate for rTMS can be considered to be purely resistive (Cerri et al 1995;Ravazzani et al 1996). The number of meshes was 100 in the x and y directions and 85 in the z direction since the vertical edge of the reconstructed solid was shorter.…”

Transcranial Magnetic Stimulation for Investigating Causal Brain-behavioral Relationships and their Time Course

“…As a result, the only regions directly accessible to TMS are limited to the cortical mantle, although different shaped coils are being developed to reach deeper regions such as the basal ganglia 69 . TMS also has a spatial resolution of approximately 0.5 -1 cm 47,[70][71][72] . Thus, the method cannot be used to investigate the functional contributions from fine-grained spatial structures such as cortical columns.…”

FDTD-based Transcranial Magnetic Stimulation model applied to specific neurodegenerative disorders

“…Here we consider the modeling of a circular coil by 12 magnetic dipoles, as shown in Figure 1a). This model has a satisfactory degree of accuracy for coils to within approximately 60-80 mm, depending on several spatial parameters [8]. In this case, the parameters employed are listed in Table 1.…”

“…This requires an accurate computation of the induced electrical field within the brain as well as the dielectric properties of the brain tissues [7]. Early studies in this area were mostly based on spherical models [8], whereas the most recent ones employ a high-resolution model of human head and numerical methods such as the finite element method (FEM) [9,10].…”