Accessibility of cortical regions to focal TES: Dependence on spatial position, safety, and practical constraints

Abstract

Transcranial electric stimulation (TES) can modulate intrinsic neural activity in the brain by injecting weak currents through electrodes attached to the scalp. TES has been widely used as a neuroscience tool to investigate how behavioural and physiological variables of brain function are modulated by electric stimulation of specific brain regions. For an unambiguous interpretation of TES experiments, it is important that the electric fields can be steered towards one or several brain regions-of-interest. However, the conductive proprieties of the human head impose inherent physical limitations on how focal the electric fields in the brain produced by multi-electrode TES can be. As a rule of thumb, it is not feasible to selectively target deep brain areas with TES, although focusing the field in some specific deeper locations might be possible due to favourable conductive properties in the surrounding tissue. In the present study, we first propose a computationally efficient method for the automatic determination of electrode placements and stimulation intensities to optimally affect a given target position. We provide a computationally efficient and robust implementation of the optimization procedure that is able to adhere to safety constraints, while explicitly controlling both the number of active electrodes and the angular deviation of the field in the target area relative to the desired field direction. Leveraging the high computational efficiency of our method, we systematically assess the achievable focality of multi-electrode TES for all cortex positions, thereby investigating the dependence on the chosen constraints. Our results provide comprehensive insight into the limitations regarding the achievable TES dose and focality that are imposed by the biophysical constraints and the safety considerations of TES. version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 2012; Ruffini et al., 2014;Wagner et al., 2015;Guler et al., 2016a). These methods share the same basic approach to employ grids of fixed electrode positions, but they differ, among others, in the way the optimization problems are set-up and how they account for the constraints set by the safety limits for TES and for other practical aspects such as a limited number of available stimulation channels. For example, in © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 6 where vector − = [ 1 1 ⋯ 1 ] 1 −1 and the matrix −1 −1 is the ( − 1) ( − 1) identity matrix. Applying and its pseudo inverse † to Eq. 5, we obtain © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 7

Individual Targeting Increases Control Over Inter-Individual Variability in Simulated Transcranial Electric Fields

“…In sum, the a priori estimation and the post-hoc evaluation of individual tES-induced target current densities are highly recommended in order to evaluate effects of individual anatomy on the behavioral or neurophysiological efficacy of tES. Recent studies showed that the stimulation intensity and focality that can be achieved by targeting is strongly dependent on the respective location of the stimulation target within the cortex of one standard FEM head model [36], [66]. Critically, the present results further indicate that, in addition, inter-individual variability (i.e.…”

“…We conclude that -in intermediate depth of the simulated parietal target in the present experiment -targets with tangential orientations would be stimulated with a relatively higher current density, compared to radial targets, across individual participants. Nevertheless, the same conclusion does not necessarily hold for other stimulation targets in deeper [64], [65], or more superficial cortical areas, or other regions of the brain, other than parietal cortex [66].…”

Deep Cerebellar Transcranial Direct Current Stimulation of the Dentate Nucleus to Facilitate Standing Balance in Chronic Stroke Survivors—A Pilot Study

“…Convex optimization is not only applicable for least-square regression problem shown above but also for linear programming where the objective is to maximize the electric field, → E, at the targeted nodes of the brain region based on a vector of weights, W ∈ R 3m , i.e.,Î = arg max I W T LI . The 'beamforming' problem in array signal processing [46,50] based on the minimization of the total energy stored in an electric field constrained to a target electric field, → E, at a volume is equivalent to the least-square problem (can be shown using Lagrange multipliers) [49].…”

Optimizing the Electric Field Strength in Multiple Targets for Multichannel Transcranial Electric Stimulation

“…We set up an optimization problem to minimize the field outside the target region, while keeping the mean field strength in the target region at a desired value , in line with [9]:…”

“…Here, P1.1 calculates the total field energy, P1.2 controls the field strength in the target, P1.3 enforces Kirchhoff's law, P1.4 limits the total current injected, and P1.5 limits the current injected through each electrode. Please see [9] for more details. In the following, we only consider the field energy in GM for optimization (P1.1).…”