  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 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 novel method for the automatic
calculation 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.
