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Abstract

Introduction Transcranial weak current stimulation (tCS) are a range of brain stimulation methods in which current is applied to the brain through surface electrodes mounted on the scalp, with the goal of promoting cortical excitability in a certain brain region. However, electric fields are governed by the Laplace equation, which result in physical constraints on how the electric field will be distributed in the tissue and to which extent its distribution can be controlled by manipulation of the external electrode configuration and applied current strengths. Methods In order to assess the inherent limits on tCS focality, we set up various constrained optimization problems to find electrode positions and current combinations which maximize either the field strength at a selected target or stimulation focality, while keeping the injected current within safe limits. Simulations were performed in both simple 3-layered spherical models as well as realistic head models, generated by the SimNIBS package (www.simnibs.org). Results The human head can be approximated as a piecewise-constant conductor, with constant conductivity in each tissue and boundaries between tissues. In such a conductor, it can be shown that due to the inherent properties of the Laplace equation, the maximal electrical field in any of the constant conductivity domains must be in its boundaries. This means that focal stimulation of deep cortical targets is not feasible under normal circumstances. Also, for limited amounts of current, our optimization results show that there is a natural trade-off between field focality and intensity at a target in tCS. That is, if we optimize the stimulation so that it is maximally focal, intensity at the target is lost, and vice versa. Conclusion While optimization procedures can substantially improve tCS targeting in terms of focality, the electric fields produced by those techniques are inherently subject to physical constraints, which fundamentally limit the focality and selectivity of stimulation, in particular for deeper targets.