  Objective: Numerical modeling of electric fields induced by transcranial
alternating current stimulation (tACS) is currently a part of the standard
procedure to predict and understand neural response. Quasi-static approximation
for electric field calculations is generally applied to reduce the
computational cost. Here, we aimed to analyze and quantify the validity of the
approximation over a broad frequency range. Approach: We performed
electromagnetic modeling studies using an anatomical head models and considered
approximations assuming either a purely ohmic medium (i.e., static formulation)
or a lossy dielectric medium (quasi-static formulation). The results were
compared with the solution of Maxwell's equations in the cases of harmonic and
pulsed signals. Finally, we analyzed the effect of electrode positioning on
these errors. Main Results: Our findings demonstrate that the quasi-static
approximation is valid and produces a relative error below 1% up to 1.43 MHz.
The largest error is introduced in the static case, where the error is over 1%
across the entire considered spectrum and as high as 20% in the brain at 10 Hz.
We also highlight the special importance of considering the capacitive effect
of tissues for pulsed waveforms, which prevents signal distortion induced by
the purely ohmic approximation. At the neuron level, the results point a
difference of sense electric field as high as 22% at focusing point, impacting
pyramidal cells firing times. Significance: Quasi-static approximation remains
valid in the frequency range currently used for tACS. However, neglecting
permittivity (static formulation) introduces significant error for both
harmonic and non-harmonic signals. It points out that reliable low frequency
dielectric data are needed for accurate tCS numerical modeling.
