Current Distribution in the Brain From Surface Electrodes

Rush, Stanley; Driscoll, Daniel A.

doi:10.1213/00000539-196811000-00016

Cited by 468 publications

(264 citation statements)

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“…Early validation efforts for simple spherical models used ex vivo recordings (Rush and Driscoll, 1968), surface recordings (Burger and Milaan, 1943) or in vivo recordings in simian (Hayes, 1950). Modern models have compared predictions to human scalp surface recordings (Bangera et al, 2010;Datta et al, 2013), but detailed models have not been validated with intracranial recordings in vivo.…”

Section: Introductionmentioning

confidence: 99%

Measurements and models of electric fields in the in vivo human brain during transcranial electric stimulation

et al. 2017

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Transcranial electric stimulation aims to stimulate the brain by applying weak electrical currents at the scalp. However, the magnitude and spatial distribution of electric fields in the human brain are unknown. We measured electric potentials intracranially in ten epilepsy patients and estimated electric fields across the entire brain by leveraging calibrated current-flow models. When stimulating at 2 mA, cortical electric fields reach 0.8 V/m, the lower limit of effectiveness in animal studies. When individual whole-head anatomy is considered, the predicted electric field magnitudes correlate with the recorded values in cortical (r = 0.86) and depth (r = 0.88) electrodes. Accurate models require adjustment of tissue conductivity values reported in the literature, but accuracy is not improved when incorporating white matter anisotropy or different skull compartments. This is the first study to validate and calibrate current-flow models with in vivo intracranial recordings in humans, providing a solid foundation to target stimulation and interpret clinical trials.

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Section: Introductionmentioning

confidence: 99%

Measurements and models of electric fields in the in vivo human brain during transcranial electric stimulation

et al. 2017

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“…near the sinuses), and varies in thickness around the head [47]. It is also well known that the skull conducts faster radially than tangentially, leading to a smearing effect on the recorded scalp EEG [48]. It has recently been shown, however, that geometrical modeling errors of the skull have a larger effect on electromagnetic source localization than the conductivity model assigned to the skull region(s) [49].…”

Section: Discussionmentioning

confidence: 99%

“…It has recently been shown, however, that geometrical modeling errors of the skull have a larger effect on electromagnetic source localization than the conductivity model assigned to the skull region(s) [49]. At present our implementation uses a simple single-shell skull with an isotropic conductivity of 0.0042 S/m (roughly 1/80 th that of the grey matter) [48]. Segmenting the skull into three compartments is difficult from T1-weighted MR images and additional sequences may be necessary.…”

Section: Discussionmentioning

confidence: 99%

A finite-element reciprocity solution for EEG forward modeling with realistic individual head models

et al. 2014

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We present a finite element modeling (FEM) implementation for solving the forward problem in electroencephalography (EEG). The solution is based on Helmholtz's principle of reciprocity which allows for dramatically reduced computational time when constructing the leadfield matrix. The approach was validated using a 4-shell spherical model and shown to perform comparably with two current state-of-the-art alternatives (OpenMEEG for boundary element modeling and SimBio for finite element modeling).We applied the method to real human brain MRI data and created a model with five tissue types: white matter, grey matter, cerebrospinal fluid, skull, and scalp. By calculating conductivity tensors from diffusion-weighted MR images, we also demonstrate one of the main benefits of FEM: the ability to include anisotropic conductivities within the head model. Root-mean square deviation between the standard leadfield and the leadfield including white-matter anisotropy showed that ignoring the directional conductivity of white matter fiber tracts leads to orientation-specific errors in the forward model. Realistic head models are necessary for precise source localization in individuals. Our approach is fast, accurate, open-source and freely available online.

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“…Furthermore, when the media is anisotropic, E (r) is not necessarily in the same direction as j (r), and ρ needs to be a rank-two tensor. However, at the scalp, equation (8) is an excellent approximation to EEG, as the ρ is approximately isotropic in the tangential direction (Rush and Driscoll, 1968;Wolters et al, 2006;Petrov, 2012). meaning comes from Gauss's Law, which in its differential form given by Maxwell is written as…”

Section: Physical Interpretation Of the Surface Laplacianmentioning

confidence: 99%

The surface Laplacian technique in EEG: Theory and methods

Carvalhaes¹,

Barros

2015

International Journal of Psychophysiology

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This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for EEG researchers unfamiliar with the technique. The popular methods of finite difference and splines are reviewed in detail. The former has the advantage of simplicity and low computational cost, but its estimates are prone to a variety of errors due to discretization. The latter eliminates all issues related to discretization and incorporates a regularization mechanism to reduce spatial noise, but at the cost of increasing mathematical and computational complexity. These and several others issues deserving further development are highlighted, some of which we address to the extent possible. Here we develop a set of discrete approximations for Laplacian estimates at peripheral electrodes and a possible solution to the problem of multiple-frame regularization. We also provide the mathematical details of finite difference approximations that are missing in the literature, and discuss the problem of computational performance, which is particularly important in the context of EEG splines where data sets can be very large. Along this line, the matrix representation of the surface Laplacian operator is carefully discussed and some figures are given illustrating the advantages of this approach. In the final remarks, we briefly sketch a possible way to incorporate finite-size electrodes into Laplacian estimates that could guide further developments.

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Current Distribution in the Brain From Surface Electrodes

Cited by 468 publications

References 0 publications

Measurements and models of electric fields in the in vivo human brain during transcranial electric stimulation

Measurements and models of electric fields in the in vivo human brain during transcranial electric stimulation

A finite-element reciprocity solution for EEG forward modeling with realistic individual head models

The surface Laplacian technique in EEG: Theory and methods

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