Objective: 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).
Methods: Numerical methods were used to calculate the current density distribution in a standard spherical head model as well as in a homogeneous cylindrical conductor.
Results: 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.
Conclusions: 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.
Significance: 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.