What does the ratio of injected current to electrode area tell us about current density in the brain during tDCS?

Abstract

To examine the relationship between the ratio of injected current to electrode area (I/A) and the current density at a fixed target point in the brain under the electrode during transcranial direct current stimulation (tDCS). Numerical methods were used to calculate the current density distribution in a standard spherical head model as well as in a homogeneous cylindrical conductor. The calculations using the cylindrical model showed that, for the same I/A ratio, the current density at a fixed depth under the electrode was lower for the smaller of the two electrodes. Using the spherical model, the current density at a fixed target point in the brain under the electrode was found to be a non-linear function of the I/A ratio. For smaller electrodes, more current than predicted by the I/A ratio was required to achieve a predetermined current density in the brain. A non-linear relationship exists between the injected current, the electrode area and the current density at a fixed target point in the brain, which can be described in terms of a montage-specific I-A curve. I-A curves calculated using realistic head models or obtained experimentally should be used when adjusting the current for different electrode sizes or when comparing the effect of different current-electrode area combinations.