The results presented in this paper illustrate the effect that electrode area and inter-electrode distance may have on the current density distribution during tDCS. The results also apply to transcranial AC stimulation (tACS) inasmuch as the quasistatic approximation holds (Roth et al., 1991
For all montages, the injected current was adjusted so as to maintain the magnitude of the current density at the reference point in the brain constant. Since the current density is linearly proportional to the injected current, all current density plots in this paper can be scaled appropriately to obtain current density values for other current intensities. In future work, a physiological more meaningful alternative would be to adjust the current intensity so that the average current density in a predefined brain region is kept constant for all montages.
We found that when the area of one of the electrodes is reduced below the 25–35 cm2 often used in tDCS there is a significant decrease in the extent of the region where the magnitude of the current density reaches a significant fraction of its peak value, both in depth and on the brain surface ( and ). This is corroborated by the values of the half-power areas, A50, shown in , for inter-electrode distances greater than about 12 cm (30% D). The same figures also indicate that once the area of the smaller electrode is less than 12 cm2 then further reductions in electrode area lead to diminishing improvements in focality. This effect is due to the low conductivity of the skull.
The increase in focality in the brain achieved by smaller electrodes is accompanied by an increase in the current density in the scalp, even after adjusting the current intensity to obtain the reference current density value at the reference point. Under the edge of the electrode in contact with the scalp, the current density may be as high as 6 A/m2
for a 1 cm2
electrode compared to about 2 A/m2
for a 7 cm2
electrode and 1 A/m2
for a 35 cm2
electrode (). It is therefore essential to minimize electrode-scalp impedance using the usual EEG techniques of scalp preparation and impedance monitoring, when using small electrodes. In addition, adverse effects on the skin can be minimized by appropriate choices of electrode material and gel (Minhas, 2010
High current densities on the scalp may render tDCS intolerable or may make sham stimulation (Gandiga, 2006
) impracticable. Given that smaller electrodes produce more focal distribution at the cost of increasing current density on the scalp, in the manner shown in and , there should exist an optimal electrode size that maximizes focality and minimizes scalp current density, i.e., minimizes the product of A50
and the current density on the edges of the electrode. In our modeling study, for an inter-electrode distance of about 19 cm (50% D) and with the injected current adjusted as explained before, this product exhibits a broad minimum between 3.5 and 12 cm2
. Electrodes with sizes in this range may be useful in applications where a more focal stimulation is important. For example, a 3.5 cm2
electrode and a current intensity of 0.1 mA have been used to selectively modulate the cortical excitability of the representation of the abductor digiti minimi without affecting the first dorsal interosseus (Nitsche et al., 2007
The current intensities presented in confirm that smaller electrodes require less injected current to achieve a given current density on the brain under the electrode. However, the required current intensity is not proportional to electrode area, which implies that stimulus intensity does not scale as the ratio of the current intensity and the electrode area (Miranda et al., 2009
). Given the lack of a simple rule, how should the current intensity be set for different electrode areas? The current intensities in could be taken as initial estimates. However, these estimates could also be verified experimentally by quantifying a physiological aftereffect, such as the change in magnitude of the motor evoked potential.
The last 3 rows of show that when the area of the smaller electrode drops below 12 cm2
, and the area of the larger electrode is fixed at 35 cm2
, the current density distribution has a single half-power region located under the smaller electrode. Thus, a mixed electrode montage, using two electrodes with different areas, should help to increase the focality of cortical stimulation in the sense that it allows a decrease in the stimulated region under the smaller electrode as well as a significant reduction of the functional effects of the stimulation under the larger one, as suggested by Nitsche et al.
(Nitsche et al., 2007
The ratio of the maximal current densities under E1 and E2 increases from 1:1 in the standard montage (two 35 cm2
electrodes) to 1.9:1 when the area of E1 is reduced to 1 cm2
, independently of the current intensity. This is a modest increase considering that the ratio of electrode areas increased from 1:1 to 35:1. Slightly higher ratios can be obtained by increasing the area of the largest electrode but this may become difficult to handle. A more efficient way is to replace the larger electrode by n electrodes of the same size as the smaller one and which are all connected to the same terminal of the stimulator. Some calculations have already been performed with multiple return electrodes (Datta et al., 2009
; Faria et al., 2009
). Provided that the n electrodes are well separated on the scalp and approximately equidistant from E1, this should increase the current density ratio to about n:1.
Both electrode area and inter-electrode distance influence the position of the maximum of the current density magnitude in the brain. As the electrode area increases, the maximum shifts from under the center of the electrode towards the other electrode. Although the shift can be large, up to several centimeters, the difference between the magnitude of the current density under the center of the electrode and its maximum value remains small, in relative terms, when the electrodes are far apart (). When these electrodes are close together, i.e., when their centers are less than 8 cm (20% D) apart, the maximum can be located between the two electrodes (). Our results suggest that when using large electrodes, 25 to 35 cm2, the current density in the target region may be increased slightly by placing the electrode’s front edge (the edge closer to the other electrode) over the target region, instead of placing its center over the target region as is currently done.
The high conductivity of the scalp relative to that of the skull and the high conductivity of the CSF relative to those of the skull and the brain constrain a significant percentage of the injected current to flow tangentially in these tissues and never reach the brain. Even so, at least 35% of the injected current may reach the brain if the electrodes are 8 cm (20% D) apart and 60% or more for inter-electrode distances greater than 20 cm (50% D). The current shunted through the scalp and the CSF is unlikely to be harmful but if too much current is shunted through the scalp then stimulation may become less well tolerated.
The use of a spherical head model enabled us to investigate the effect of electrode size and inter-electrode distance on the current density distribution, independently of detailed anatomical information. Even though the more general features of this distribution, such as the non-linear variation of A50
with electrode area, are likely to remain valid when considering a more realistic head model, it is also clear that significant differences may arise. This is due to the heterogeneity of the brain tissues and the convoluted nature of the cortical sheet, which, in combination, have a complex effect on the current density distribution. Thus, the location of current density peaks in a realistic head model will be determined by the local cortical geometry as well as the size and the position of the electrodes on the scalp. Also, our model does not include the various openings that exist in the skull and which may affect the current density in the nearby cortex (Paulus, 2010
; Schutter and Hortensius, 2010
). In addition, the analysis of focality was based on the distribution of the magnitude of the current density, and does not take into account the relative orientation of the current density and the neuronal cells. Some information on this issue may be gathered from the plots of the radial and tangential components of the current density, such as those shown in and , if the orientation of the target cells in the brain is known. All these limitations should be addressed using more realistic, albeit more demanding, head models featuring accurate representations of the grey and white matter surfaces. Even so, knowledge of the predictions of the spherical head model will be important for a critical appreciation of the more complicated results obtained with a realistic head model.
Despite the above-mentioned limitations, the results presented in this paper indicate clearly that small electrodes can stimulate the cortical surface efficiently and focally. This suggest the implementation of a versatile multi-electrode system based on small electrodes that could be used to target different brain regions, simultaneously or sequentially, by choosing appropriate combinations of two or more electrodes (see, for example, Dmochowski, 2011
). Such a system could be based on the use of EEG electrodes and an EEG cap, to place the electrodes in standard positions, such as those defined in the 10/10 International System (Faria et al., 2009
). Each electrode could be used either to inject current or to record an EEG signal. Large tDCS electrodes could be simulated by linking together several neighboring electrodes. Electrode impedance could be easily monitored and the EEG gel could provide a uniform and stable electrical contact. Such a combined tDCS and EEG system could be used to monitor the effect of the stimulation on the brain’s activity during or immediately after tDCS.