NeuroImage 120 (2015) 25–35

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On the importance of electrode parameters for shaping electric field patterns generated by tDCS Guilherme B. Saturnino a,b, André Antunes b, Axel Thielscher a,b,c,⁎ a b c

Danish Research Center for Magnetic Resonance, Copenhagen University Hospital Hvidovre, Denmark Max Planck Institute for Biological Cybernetics, Tübingen, Germany Biomedical Engineering Section, Technical University of Denmark, Kgs. Lyngby, Denmark

a r t i c l e

i n f o

Article history: Received 5 March 2015 Accepted 24 June 2015 Available online 2 July 2015 Keywords: Transcranial direct current stimulation Field calculations Finite element method Electrode modeling Spatial targeting

a b s t r a c t Transcranial direct current stimulation (tDCS) uses electrode pads placed on the head to deliver weak direct current to the brain and modulate neuronal excitability. The effects depend on the intensity and spatial distribution of the electric field. This in turn depends on the geometry and electric properties of the head tissues and electrode pads. Previous numerical studies focused on providing a reasonable level of detail of the head anatomy, often using simplified electrode models. Here, we explore via finite element method (FEM) simulations based on a high-resolution head model how detailed electrode modeling influences the calculated electric field in the brain. We take into account electrode shape, size, connector position and conductivities of different electrode materials (including saline solutions and electrode gels). These factors are systematically characterized to demonstrate their impact on the field distribution in the brain. The goals are to assess the effect of simplified electrode models; and to develop practical rules-of-thumb to achieve a stronger stimulation of the targeted brain regions underneath the electrode pads. We show that for standard rectangular electrode pads, lower saline and gel conductivities result in more homogeneous fields in the region of interest (ROI). Placing the connector at the center of the electrode pad or farthest from the second electrode substantially increases the field strength in the ROI. Our results highlight the importance of detailed electrode modeling and of having an adequate selection of electrode pads/gels in experiments. We also advise for a more detailed reporting of the electrode montages when conducting tDCS experiments, as different configurations significantly affect the results. © 2015 Elsevier Inc. All rights reserved.

Introduction Transcranial direct current stimulation (tDCS) is a non-invasive neuromodulation technique which is widely used in basic and clinical neuroscience research. It is based on passing weak currents through the brain by means of electrode pads attached to the head. Experiments in animal models and slice preparations suggest that the currents result in a systematic shift of the firing thresholds of cortical neurons (Bikson et al., 2004; Bindman et al., 1962). These effects remain stable for some time after stimulation offset, rendering tDCS an interesting method to modulate cortical plasticity both in healthy subjects (Nitsche and Paulus, 2000, 2001) and disease populations such as stroke patients (Raffin and Siebner, 2014; Stagg and Johansen-Berg, 2013). Most commonly, two large electrode pads (acting as anode and cathode) with areas of several tens of cm2 are used for feeding in currents of 1–2 mA into the underlying head and brain (Nitsche and Paulus, 2000). The simplicity of the setup makes it an attractive method for usage in clinical settings. However, it gives only limited control over ⁎ Corresponding author at: Danish Research Center for Magnetic Resonance Copenhagen University Hospital Hvidovre, DK-2650 Hvidovre, Denmark. E-mail address: [email protected] (A. Thielscher).

http://dx.doi.org/10.1016/j.neuroimage.2015.06.067 1053-8119/© 2015 Elsevier Inc. All rights reserved.

the resulting current distribution in the brain. In fact, poor spatial targeting is likely a major cause of the high variability of the stimulation outcome observed in tDCS (Raffin and Siebner, 2014). The latter severely hampers further developments of tDCS towards a standard method in clinical applications. Field calculations based on FEM and anatomically accurate models of the human head have provided important insights into the current distribution caused by tDCS in the brain and its dependence on anatomical factors. This includes testing the impact of the composition of the skull (including the effect of skull defects; Datta et al., 2010), the subdural fat layer of the skin (Truong et al., 2013), the layer of cerebrospinal fluid (CSF) (Opitz et al., 2015) as well as the gyrification pattern (Miranda et al., 2013; Neuling et al., 2012; Sadleir et al., 2010) on the field distribution in cortical gray matter. In a recent study, we could demonstrate that roughly 50% of the variance in the field in brain gray matter (GM) is explained by a small number of anatomical factors (Opitz et al., 2015), namely the thicknesses of the CSF layer and the skull, the gyral depth and the distances of the targeted gray matter regions to the electrodes. The influence of the properties of the electrode pads on the field distribution was tested in a further range of studies. The impact of the electrode area and the distance between the electrodes was assessed

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using in part simplified spherical head models (Datta et al., 2008; Faria et al., 2011; Miranda et al., 2006). It was demonstrated that the currents are strongest underneath the electrode borders, in particular underneath the ones closer to the other electrode (Miranda et al., 2006; Miranda et al., 2013; Wagner et al., 2007). Based on these observations, it was suggested that the strongest stimulation might not only occur in the brain regions directly underneath the electrodes, but also in the areas in-between them (Miranda et al., 2013; Opitz et al., 2015; Sadleir et al., 2010). The electrode models used to derive these results incorporated several simplifications or specific assumptions. For example, the upper surface of the electrodes was often set to a constant electric potential (equivalent to a well-conducting metal surface distributing the currents) or a constant current density (Miranda et al., 2006; Miranda et al., 2013; Neuling et al., 2012; Opitz et al., 2015; Sadleir et al., 2010; Wagner et al., 2007; see Kronberg and Bikson, 2012 for an exception). In practice, however, rubber pads with much lower conductivity are usually employed and the currents are fed into the pads by means of a small connector. As the ohmic resistance of the rubber hampers the current flow within the pads, it cannot be longer assumed that they form isopotential surfaces as it is the case for metal electrodes. Rather, the electric potential in the pads will depend on the distance to the connector. This also causes an inhomogeneous potential distribution at the electrode–electrolyte interface and will affect the pattern of current flow in the gel or sponge. Considering the area of typical tDCS electrodes, it opens the question of how well the simulation results obtained so far actually apply to the experiments performed in practice. In this paper we test the impact on the electric field of several electrode properties, including conductivities of the rubber and sponge (or gel) layers, connector position, electrode shape and size. A realistic head model is used to simulate the electric field in the brain. Given the large parameter space, we first explore the impact of these factors via specific examples. We then focus on “standard” electrodes of 35 cm2 and systematically characterize the dependence of the field on key properties of the electrodes. As a final step, we characterize to which extent the electrode properties also influence the field created by more focal multi-electrode arrangements. Methods Head modeling The simulations were based on an existing head model of a healthy volunteer (26 years, female, right handed). T1- and T2-weighted magnetic resonance images (MRI) were collected on a 3 T TIM Trio scanner (Siemens Healthcare, Erlangen, Germany) equipped with a 12-channel head coil at the MPI for Biological Cybernetics (Tübingen, Germany). Details on the MRI parameters, segmentation and volume meshing procedures can be found in Opitz et al. (2015). A modified version of SimNIBS (Simulation of Non-Invasive Brain Stimulation; Windhoff et al., 2013) was used to create a tetrahedral head mesh containing eight tissue types. Surface reconstructions of brain gray and white matter were obtained using FreeSurfer (Dale et al., 1999). The surfaces of the skin, spongy bone, compact bone, cerebro-spinal fluid (CSF; which corresponds to the inner skull boundary), the vitreous bodies of the eyes and the surrounding eye regions were created in a semi-automatic way; initial volume segmentations were obtained using FSL tools (Functional MRI of the brain Software Library; Jenkinson et al., 2012), followed by cleaning and surface reconstruction steps. The mesh resolution near the electrodes was enhanced to ensure a good mesh quality when modeling the electrodes. The average triangle area of the corresponding part of the skin surface was set to 0.88 mm2 (±0.21 mm2 SD) and it was ensured that the inner angles of the triangles did not fall below 18°. The average triangle area was further decreased to 0.22 mm2 (±0.03 mm2 SD) for one series of simulations that targeted small circular electrodes (4 × 1 ring arrangement; Datta et al., 2009; for details see below). The final mesh contained around 500,000 nodes and 3,000,000 tetrahedra

(Fig. 1A). In one simulation, a head model of a second individual (27 years, male, right handed) was used for control. The parameters of the MR protocols and the procedures for constructing the head model were identical to those of the first model. The study was approved by the local ethics committee of the Medical Faculty of the University of Tübingen and collection of the MR data was done after receiving written informed consent. Simulations The anode was placed above the hand knob region (Yousry et al., 1997) of the left primary motor cortex and the cathode above the right supraorbital region (see next section on the technical details), as often used in tDCS experiments to modulate motor plasticity. The conductivities of brain white matter (WM), gray matter and of CSF were set to 0.126 S/m, 0.275 S/m and 1.654 S/m (Thielscher et al., 2011). Values of 0.025 S/m and 0.008 S/m were used for the spongy and compact bone of the skull (Dannhauer et al., 2011; Miranda et al., 2013). Conductivities of 0.50 S/m and 0.25 S/m were applied for the eye balls and the surrounding eye region (Gabriel et al., 1996). Unless indicated otherwise, a value of 0.465 S/m was taken as conductivity of the skin (Thielscher et al., 2011). The electrode conductivities were varied throughout the study and are stated in the corresponding parts of the Results section. All tissues were treated as isotropic. The anisotropy of WM has been shown to affect the current flow pattern in particular in deeper brain areas (Wagner et al., 2014). When trying to get the best estimate of the current flow for a specific person, it should be considered to take WM anisotropy into account. Still, the general effects of changes in the electrode properties on the current flow are hardly affected by the type of WM conductivity. ! As described in Opitz et al. (2015), the electric field E was calculated ! by numerically solving E ¼ −∇φ (φ is the electric potential). The electric potential φ was computed using an electrostatic formulation with Dirichlet boundary conditions at the electrode connectors set to fixed potential values. The open-source finite element solver GetDP which implements the Galerkin method based on tetrahedral first order elements (Dular et al., 1998) was used. The residuals for the conjugate ! gradient solver were required to be b10−9. E was determined by taking ! the numerical gradient of the electric potential. The current density J ! ! was determined via Ohm's law J ¼ σ E . The potential difference and the field values were scaled such that a current of 1 mA was passing through the electrodes. As the electric field is discontinuous at surface ! boundaries, E was read out in the middle of the gray matter sheet rather than, e.g. at the GM surface. Electrode modeling The electrodes were modeled in three steps using custom-developed software. 1) The nodes of the skin surface were shifted in an iterative process to align them with the electrode shape while still ensuring a good mesh quality. 2) The part of the skin surface that then resembled the electrode surface was copied and shifted along a direction normal to the skin surface. For more realistic models that distinguished between several layers of material (such as gel or sponge and rubber), this process was repeated to create the necessary number of surface layers. For simplicity, these “multi-layer models of the electrode and gel or sponges” are referred to as electrode models in the following. 3) The volumes between the surface layers were filled with tetrahedra. Electrode details such as connector regions and holes in the electrodes were created in similar ways. In the first part of the study, six increasingly complex electrodes were modeled (depicted in Fig. 1B and named types A, B, C, etc.). The electrode shape was always set to a rectangular patch of 7 cm × 5 cm (35 cm2), as often used in tDCS.

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Fig. 1. A) Example showing two electrodes (anode above the left primary sensorimotor region in gray, cathode on the right supraorbital region in blue) attached to the head mesh. Eight tissue types are modeled: White matter (white), gray matter (gray), CSF (light blue), compact bone (green), spongy bone (yellow), vitreous bodies of the eyes (blue), surrounding eye regions (purple) and skin. In the right image, the red patch on the gray anode surface depicts a connector position at the posterior electrode edge. B) Overview of the simulated variants of rectangular 7 × 5 cm2 electrodes.

• Electrodes of type A consist of a single layer and have their whole upper surface set to the same electric potential (the isopotential areas of the electrodes are depicted in blue). This setup is equivalent to an electrode with a high conductivity layer on top to distribute the currents. • Electrodes of type B also consist of a single layer but only a small part of their upper surface has the same potential. This mimics a stimulation current that is fed into the electrode with a small connector. The connector region was modeled as a strip of 1.6 cm × 0.5 cm (see red patch in the right part of Fig. 1A). • Electrodes of type C take this further by also modeling a layer of rubber (gray layer in the electrode) on top of an underlying gel layer (white layer). These electrodes are a good approximation for rubber pads that are attached to the skin by means of electrode gel. For types A–C, the thicknesses of the gel (white) and rubber (gray) layers were set to 2.5 mm and 1.0 mm. • The two remaining electrode types D and E are aimed at modeling rubber electrodes inside a sponge pocket soaked in a conductive solution. Electrodes of type D have 3 layers (sponge–rubber–sponge) with thicknesses of 2.5, 1.0 and 2.5 mm. Type E is an example of more realistic models of the same kind of electrodes where the rubber pad is fully enclosed within a sponge pocket. Different ratios of the surface areas of the sponge and rubber pads were tested. The sponge, as a whole, has a thickness of 6 mm. The rubber electrode is centered inside the sponge and has a thickness of 1 mm.

In the second part of the study, different electrode shapes were tested. In addition to rectangular 7 × 5 cm2 electrode pads, a large (10 × 10 cm2) cathode was modeled, as Nitsche et al. (2007) suggested that neural activity might be less affected underneath large “return”

electrodes. In addition, a ring electrode (outer and inner diameters: 5 cm and 2.5 cm) as tested in Sehm et al. (2013) was modeled. In all cases, electrodes with a rubber layer of 1 mm and a gel layer of 2.5 mm were used. Choice of parameter ranges The third part of the study focused on a systematic characterization of the field changes caused by variations of four key properties of the anode placed above left M1, namely gel (or sponge) conductivity, rubber conductivity, connector position and ratio between the sponge and rubber areas. The electrode sizes, shapes and positions were kept constant for that purpose, using rectangular patches of 7 cm × 5 cm (35 cm2) for both electrodes. Also all remaining parameters of the cathode above the right supraorbital region were kept constant. It was modeled as a type C electrode (Fig. 1B) with a rubber layer with 1 S/m and 1 mm thickness and a gel layer with 4 S/m and 2.5 mm thickness. No connector was modeled, but the potential was set to the whole surface (similar to the type A electrodes; Fig. 1B). The same parameters were used for the anode baseline case. Thus, the baseline electrode configuration used in this paper resembles those characterized in prior simulation studies so far. When characterizing the effect of varying gel (or sponge) conductivities, type C electrodes were modeled (Fig. 1B) with a connector positioned at the posterior edge of the anode (see the right part of Fig. 1A). The parameter range explored for the gel conductivity was selected according to the values reported in literature so far. For sponges soaked with saline solutions, conductivities of 1–2 S/m are usually applied. The conductivities for electrode gels vary in the range of 1.5 S/m to 8 S/m (Minhas et al., 2010; Tallgren et al., 2005). For example, “Spectra 360” and “Signa Gel” (both from Parker Laboratories Inc., NJ, USA) are reported

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to have conductivities of around 1.5 S/m and 4 S/m (Minhas et al., 2010). Since the concentration of Cl− is more than two times higher for “Ten20” (D.O. Weaver and Co, CO, USA) than for “Signa Gel” (Tallgren et al., 2005), we estimate its conductivity to be around 8 S/m. In the simulations, gel conductivities of 1 S/m, 4 S/m and 8 S/m were tested to cover this range. To test the impact of the conductivity of the rubber pads on the electric field, a type C electrode was used for the anode, with the connector positioned at the posterior edge. The conductivities of the pads themselves vary strongly, depending on the used materials. The electrodes simulated in Miranda et al. (2006) consisted of a metal mesh held over a 10 mm thick sponge by means of a rubber frame (Amrex-zetron Inc., CA, USA; parts no. 2A-103 & 2A-105). This corresponds to a highly conductive layer placed above the sponge. However, nickel or carbonloaded silicone rubber electrodes originally designed for transcutaneous electrical nerve stimulation (TENS) are usually adopted for tDCS. These electrodes normally have low conductivities to improve the homogeneity of the current flow underneath their surface (Keller and Kuhn, 2008; Nolan, 1991). In the simulations, rubber layer conductivities of 0.1 S/m, 10 S/m and 100 S/m were tested, to cover the range from poorly to well conductive. In a further set of simulations, the effects of the position of the connector on the field in the brain were assessed by placing connectors at the center of the anode and at the posterior, anterior, medial and lateral edges. In addition, rubber pads embedded in a sponge pocket (type E in Fig. 1B) were tested, varying the ratio of the areas of the pad and sponge between 1.21, 2.25 and 4 — corresponding to ratios of 1.1, 1.5 and 2 between their edge lengths. A final set of simulations was aimed at testing to which extent the electrode properties influence the electric fields generated by more focal multi-electrode arrangements. A “4 × 1 ring” electrode arrangement (Datta et al., 2009) was tested, with the central anode positioned above the hand region of the primary sensorimotor area. All electrodes were modeled as circles with diameters of either 1.2 cm (Kuo et al., 2013) or 2.0 cm. They consisted of a gel layer of 2.5 mm thickness and the upper surface of the layer was set to fixed potentials to mimic “Ag/AgCl Disc” electrodes as tested in Minhas et al. (2010). The current for the central electrode was 1 mA and the sum of the currents of the peripheral cathodes was -1mA. The distance between the centers of the central and the peripheral electrodes was 3.5 cm. For both electrode diameters, the gel conductivity was varied between 0.1 S/m and 8 S/m. The lower limit is below the range of commercial electrode gels, but was included to explore the effects of low conductivity regimes. Data analysis The differences in the field distributions created by the various configurations were quantified using four indices. 1) |E| in skin ROI: As high electric field strengths (or current densities) fed into the skin increase the risk of burns, the field strength peaks that occurred in the vicinity of the anode were compared across configurations. To do so, the 80% and 90% percentiles of the electric field strength |E| were extracted in a spherical region-of-interest (ROI) of the skin surrounding the anode (radius of 5.0 cm around the center of the anode; shown on the right side of Fig. 4). 2) |E| in GM ROI: In order to test the strength of the stimulation in the GM region directly underneath the anode, the 80% and 90% percentiles of |E| were assessed within a spherical ROI of brain gray matter (radius of 4.5 cm; see the right side of Fig. 4). 3) Fraction of GM ROI exceeding threshold: The field strength in the GM ROI was compared to the overall field strength in the brain to measure the focality of stimulation. First, the 80% and 90% percentiles of the field magnitude were determined for overall GM. Then, it was assessed to which part these percentiles were exceeded in the GM ROI (calculated as volume fraction). The higher these values, the more the stimulation was focused towards the brain region

underneath the anode. They range from 0% (the highest field values consistently occur outside the ROI) to 100% (the highest field values occur in the ROI). 4) Jaccard index: This index was used to assess the similarity between the field distributions of the tested configurations versus that of the baseline configuration. For each individual configuration, the GM regions that experienced a field strength higher than the 80% (or 90%) percentile were determined. Then, the Jaccard index J(A, B) = |A ∩ B|/|A ∪ B| was used to assess the spatial overlap of these parts (indexed as A) compared to the corresponding parts in the baseline configuration (indexed as B). The values of J range from 0 (no overlap) to 1 (perfect overlap).

Results The study was organized in four parts. First, the complexity of the model of a “standard” rectangular electrode pad was successively increased and the impact on the field distribution in the brain was characterized. Then, the influence of different electrode geometries and sizes was explored based on examples derived from previous tDCS experiments. The focus was on demonstrating the interaction between electrode geometry (or size) and connector position (i.e., the way the current is fed into the electrode surface). In the third part of the study, a standard electrode pad was employed to systematically explore the dependence of the generated field on gel (or sponge) conductivity, rubber conductivity and connector position. This allowed deriving best and worst case scenarios for focusing the field in the brain region underneath the electrode (which is the intuitive goal when placing an electrode above a certain brain area). Finally, the impact of the gel conductivity on the field caused by a “4 × 1 ring” electrode arrangement was tested. Varying the complexity of the electrode model Both electrodes were modeled as patches of 7 × 5 cm2 with a conductivity of 1 S/m for the gel layer and (when used) 0.1 S/m for the rubber layer. In all cases, the cathode on the right supraorbital region was modeled as a single gel layer with the complete upper surface set to a constant potential. In the baseline case (left part of Figs. 2F & A) the same model was used for the anode. In accordance with prior findings, most of the current enters the skin along the electrode edges (known as “edge effect”; Miranda et al., 2006), and the electric field is stronger along the medial and anterior edges compared to the posterior and lateral electrode edges (left part of Fig. 2F). As a result, the field is strongest in the brain regions between the electrodes but is lower directly underneath them (Fig. 2A). Feeding in the currents using a connector at the posterior edge of the anode resulted in differences in the field distribution both in the skin and brain (right part of Figs. 2F & B). High field strength can be observed in the skin region around the connector, while the edge effect is diminished (right part of Fig. 2F). The resulting change of the electric field pattern in the brain exceeds one third of the maximal field strength (Fig. 2B). As a main effect, the field strength in the brain region underneath the electrode increased. Adding a low conductive rubber layer on top of the gel did not change this pattern (Fig. 2C). The addition of a second gel (or sponge) layer on the top of the electrode to coarsely mimic the effects of a sponge pocket diminished the observed effect (Fig. 2D). Visual inspection of the current flow in the electrode model revealed that the second layer increased the net conductivity of the electrode pad in the horizontal direction, resulting in more horizontal current flow in the electrode towards the electrode/skin interface at the anterior edge of the electrode. This effect was further increased when reducing the size of the rubber pad (Fig. 2E) as parts of the lowconductive rubber were replaced by better conducting sponge and the connector position moved towards the center of the electrode pad.

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the conductivities to 4 S/m and 0.1 S/m for the gel and rubber layers (see Discussion for a motivation of this particular choice). The positions were varied from the anterior (anode) and medial (cathode) edges to the posterior and lateral edges, thereby minimizing and maximizing, respectively, the distances between the connectors. This changed the field in large parts of the brain, with a variation of up to 1/3 of the maximal field strength. The second example (Fig. 3B) explored the field distribution when using a large (10 × 10 cm2) cathode and changing the connector position (conductivities of 1 S/m and 0.1 S/m were used for the gel and rubber layers). This was motivated by the suggested usage of large “return” electrodes to minimize the effects of the current flow on neural activity underneath that electrode (Nitsche et al., 2007). It can be seen that the large electrode area amplified the impact which the choice of the connector position had on the field distribution (with changes of up to 2/3 of the maximal field strength compared to the simplified situation in which the complete surface is set to a constant potential). The last example in Fig. 3C shows the field created by a ring electrode (outer and inner diameters: 5 cm and 2.5 cm; conductivities of 4.0 S/m and 0.1 S/m for gel and rubber layers; Sehm et al., 2013). The field strength in the primary somatosensory cortex seemed to be selectively increased when the connector was placed at the posterior edge of the electrode. In that case, the hole in the center disturbed the horizontal current flow within the electrode towards the anterior edge, as could be seen when comparing the results to those of normal circular electrodes without hole (Fig. S3). The three examples further stress the importance of an accurate modeling of the electrode properties. Systematic variation of gel conductivity, rubber conductivity and connector position

Fig. 2. Impact of increasingly complex electrode models. A) |E| in brain gray matter generated when the anode has only a gel layer and the electric potential is assigned to the complete surface. B) Effects of explicitly modeling the connector at the posterior edge of the electrode. C) Electrode model with gel and rubber layers and a connector at the posterior edge. D) Three layer electrode model (sponge–rubber–sponge) to coarsely mimic the geometry of a rubber pad inside a sponge pocket. E) Similar to D), but with the rubber pad fully enclosed within the sponge pocket. Left side: area of the rubber pad reduced to ~70% (ratio of 1.44) of the overall electrode area; right side: area of the rubber pad reduced to 25% (ratio of 4) of the overall electrode area. F) Electric field distribution on the skin surface, exemplarily shown for electrodes of types A and B. Note: The images in B) to E) show the differences Δ|E| between the fields created by the electrode models compared to the baseline model in A). That is, yellow to red colors indicate regions in which the field is stronger compared to the baseline model, blue colors indicate the opposite behavior. The original field distributions for B) to E) are shown in Supplementary Fig. S1.

To summarize, the electrode model had substantial influence on the estimated field distribution in the brain. Characterizing the field created by different electrode shapes In the previous paragraph, the cathode was modeled as a single layer electrode with its complete surface set to a constant potential. In practice, however, the properties of both electrodes will deviate from this model so that the particular choice of the connector positions can have a clear-cut influence on the field distribution, as can be seen in Fig. 3A. In the example, the electrode areas were set to 7 × 5 cm2 and

The conductivity of gel and rubber as well as the connector position were systematically varied while keeping the other parameters constant. The aim was to better understand how the field distribution depended on the choice of these key parameters. The field distribution was characterized by means of four indices, as described in the “Data analysis” part of the Methods section. Shortly, the measure “|E| in skin ROI” assesses the peak field strength in the skin region underneath the anode. The index “|E| in GM ROI” tests the same in the gray matter region underneath the anode. The “Fraction of GM ROI exceeding threshold” compares the field strength in the GM ROI to the strength achieved in the overall brain gray matter. The higher the given value, the more the field is focused in the GM ROI. The Jaccard index is used to assess the similarity of the field with that of the baseline case. Note that the strengths of the observed effects depend on the choice for all parameters, rather than exclusively on the varied parameter. Whether or not a change of one parameter leads to marked changes of the field distribution also depends on the choices made for the other parameters. However, the general direction of the effects (e.g., increase vs. decrease of focality or peak field strength achieved in the targeted brain region) is likely stable. For that reason, we took a two step approach. First, the effects of the different parameters were systematically varied, with the main interest being the direction of the effects rather than their strengths. Then, best and worst cases for targeting the sensorimotor area underneath the anode were derived based on these results. The goal of this second step was to demonstrate how strong the effects can get for combined variations of the studied parameters. The baseline configuration used gel and rubber conductivities of 4 S/m and 1 S/m, with the electric potential set to the complete surfaces of both electrodes. Fig. 4 depicts the results for variation of the gel conductivity (rubber conductivity of 1 S/m, connector at the posterior edge of the anode). Low gel conductivities lead to higher field strength in the brain region underneath the anode (Figs. 4B & D), while higher gel conductivities increased the edge effect and caused a field more similar to the baseline case (Fig. 4C). The peak field strength in the skin was highest for low

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Fig. 3. Impact of different electrode shapes. The middle and right images show differences Δ|E| to the baseline models on the left. The original field distributions can be found in Supplementary Fig. S2. A) Example for changing the positions of the connectors on both electrodes. The left image shows the field strength |E| when the connectors are put close together (on the anterior edge for the anode and the medial edge for the cathode). The right image shows the difference Δ|E| to the left results when a large distance between the connectors is used (on the posterior edge for the anode and the lateral edge for the cathode). B) Example for changing the connector position on a large (10 × 10 cm2) cathode. The left picture shows the resulting field when the electric potentials are set to the complete surfaces of both electrodes. The center and right images depict the differences Δ|E| to the left results when a connector is modeled at the medial or lateral edge of the cathode. C) Example for changing the connector position on a ring electrode (5 cm outer diameter, 2.5 cm inner diameter). The left picture shows the electric field strength when the electric potentials are set to the complete surfaces of both electrodes. The center and right images depict the differences Δ|E| to the left results when a connector is modeled at the anterior or posterior edge of the anode.

gel conductivities (Fig. 4A). In that case, the horizontal current flow within the electrode was reduced, leading to a strong flow through the gel/skin interface directly underneath the connector. This pattern of findings was qualitatively similar for both thresholds (80% and 90% percentiles). Varying the rubber conductivity (Table 1A) revealed a similar pattern (gel conductivity of 4 S/m, connector at the posterior edge of the anode). Low rubber conductivities helped to focus the field in the brain region underneath the electrode while higher conductivities made it more similar to the baseline case (only the results for the 90% percentiles are reported; using the 80% percentiles as thresholds resulted in qualitatively similar findings). The field distribution also experienced a systematic dependence on the connector position (Table 1B), with lateral and posterior positions maximizing the field underneath the electrodes and center and anterior positions making it more similar to the baseline case (rubber and gel conductivities of 1 S/m and 4 S/m as in the baseline case). The medial

connector position resulted in high field strength in the skin that was caused by increased shunting of the currents in the skin layer (as the position of current injection was very close to the cathode in that case). Changing the area of the rubber pad within a sponge pocket had little effect on the fields created by the anode (Table 1C). The rubber conductivity was set to 0.1 S/m, the sponge conductivity was set to 1 S/m and the connector was in the center of the rubber pad. In all cases, the field in the brain region underneath the electrode was slightly higher than for the baseline case, but the field pattern was similar to that of the baseline (as indicated by the high Jaccard index). This pattern of findings was likely driven by the choice of the connector position in the center (see the previous section). Based on the above pattern of findings, we derived best and worst case scenarios for targeting the brain region underneath the electrode (Fig. 4E). Using low conductivities both for rubber (0.1 S/m) and gel (1 S/m) in combination with a connector position at the posterior edge helped to focus the field towards the GM ROI. In the converse,

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Fig. 4. Effects of varying the gel/sponge conductivity on the electric field in the skin and brain. A) 80% and 90% percentiles of the field strength |E| in the skin ROI underneath the anode (the ROI is indicated in red in the inset). The highest values are reached for low gel conductivities. In this case, much of the current is concentrated below the connector (see also Fig. 2F). B) 80% and 90% percentiles of the field strength in the gray matter ROI. The strongest stimulation of the GM ROI is achieved for low gel conductivities. C) Jaccard index of similarity of |E| in the gray matter ROI relative to the baseline case. The field distribution is similar to the baseline case only for high gel conductivities. D) Fraction of the gray matter ROI in which the field strength exceeded the 80% (or 90%) percentile of the field in overall gray matter. Low gel conductivities help to focus the field more towards the GM ROI. E) Best and worst case scenarios for obtaining a strong field in the gray matter region underneath the electrode (see corresponding Results section for the electrode parameters). F) Same best and worst case scenarios, but for a head model of a different person. The field in the region underneath the electrode shows a similar dependence on the electrode parameters. The maps on the right show the differences Δ|E| between both scenarios, with red colors indicating stronger field strengths for the best case scenario.

high conductivities (1 S/m for rubber, 8 S/m for gel) and a connector position at the medial electrode edge effectively prevented a strong stimulation of the GM ROI. Variation of these three factors in combination resulted in a change in the electric field that reached up to 2/3 of the peak field strength and was strongest in the region underneath the anode (right part of Fig. 4E). Comparison with a multi-electrode montage As expected, the 4 × 1 montage delivered a more focal field distribution in cortical gray matter (Fig. 5A). The strongest field occurred within the indicated GM ROI for all tested cases: The used measure of focality

(“fraction of the GM ROI exceeding the 90% percentile threshold”; see Fig. 4D for the results of the standard montage) was consistently at 100% and is therefore not shown as a separate subfigure. The spatial stimulation pattern in GM was hardly influenced by the variation of the gel conductivity or the electrode diameter (consistently high Jaccard indices as shown in Fig. 5E). However, the peak field strength in GM decreased with increasing electrode diameter (Fig. 5D). As the minimal distance between the electrode edges got smaller when the electrode diameter increased, more current was shunted within the skin layer in that case. As visible in Fig. 5D, the peak field in GM also depended slightly on the gel conductivity for the electrodes with d = 2.0 cm. For the peripheral electrodes, higher gel conductivities favored the current

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G.B. Saturnino et al. / NeuroImage 120 (2015) 25–35

Table 1 Impact of electrode parameters on the field distribution. The table lists the results for the 90% percentile of |E| (see “Data analysis” part of the Methods section for details on the reported parameters). Peak values are highlighted in bold. A) Results when selectively varying the rubber conductivity. The connector was placed at the posterior edge of the anode. For low rubber conductivities, the field in the region underneath the anode is increased (see the 2nd & 4th columns). For high conductivities, the field is most similar to that of the baseline case (high Jaccard index — 3rd column). B) Impact of connector position (conductivities identical to baseline case). The field is most similar to that of the baseline case when the connector is placed in the center or at the anterior edge of the anode. It is strongest within the GM ROI for the lateral and posterior connector positions. C) Variation of the rubber area relative to the overall electrode area. The rubber area has little impact on the field distribution for the tested configuration. Varied parameter

|E| in skin ROI [V/m]

Baseline

|E| in GM ROI [V/m]

Jaccard index

Fraction of GMROI exceeding threshold

1.18

0.170

1.00

0.21

A) Conductivity of rubber [S/m]

0.1 10 100

1.21 1.16 1.17

0.181 0.176 0.171

0.67 0.80 0.96

0.26 0.24 0.21

B) Connector position

Anterior Lateral Posterior Medial Center

1.29 1.29 1.20 1.60 1.15

0.172 0.184 0.180 0.176 0.177

0.79 0.59 0.69 0.66 0.85

0.22 0.26 0.26 0.21 0.24

C) Pocket electrode: Ratio: Area of rubber/area of sponge

1.21 2.25 4.0

1.15 1.15 1.15

0.180 0.180 0.180

0.78 0.79 0.79

0.25 0.25 0.25

flow at the electrode edges close to the center electrode and by that increased the amount of shunting in the skin layer. Generally, the 4 × 1 montage resulted in much higher peak field strengths in the skin compared to the standard montage (Figs. 5B and 4A) and the electrode radius had a clear impact on the peak field. Low gel conductivities led to a more homogeneous distribution of the field in the skin region underneath the center electrode. This effect was mainly visible for the small electrodes (upper row of Fig. 5F). As a consequence, larger parts of the skin ROI experienced high field strength at low gel conductivities (falling slope in Fig. 5B that depicts the 90%ile of |E| in the skin ROI). At the same time, the edge effect was decreased for low conductivities so that the very high field strengths at the electrode rim were lowered (resulting in a rising slope in Fig. 5C that depicts the 99%ile). Robustness of results The final set of simulations aimed at testing the robustness of the results. First, simulations were run for a low and high mesh resolution in the region of the anode (Fig. 6A). The conductivities were 0.1 S/m and 8 S/m for the rubber and gel layers and the connector was placed at the posterior edge of the anode (no dedicated connector was modeled for the cathode). The results were consistent across both simulations (Table 2), demonstrating that the mesh resolution used in this study was sufficient to derive accurate results. The values used for the tissue conductivities are uncertain to some extent and the conductivity assumed here for the skin (σskin = 0.465 S/m) is higher than the one used in some other studies (Opitz et al., 2015; Truong et al., 2013). For that reason, the effects of lowering the skin conductivity to 50% and 25% of its original value were also tested (Fig. 6B; Table 2). Conductivities of 1 S/m and 4 S/m were used for rubber and gel and the connector was at the posterior edge of the anode (no connector was modeled for the cathode). The field strength in the brain increased with decreasing skin conductivity, as less current was shunted within the skin layer before entering the skull. Importantly, the spatial pattern of the field distribution in the brain hardly changed (as visible in Fig. 6B and also indicated by the high correlation coefficients in Table 2).

Fig. 5. Electric field created by a more focal electrode montage consisting of one central anode and four surrounding cathodes. Note that the diameters of the skin and GM ROIs around the center electrode were reduced to 4.0 cm and 3.4 cm for the analysis of this arrangement. A) Electrode arrangement and exemplary field distribution (gel conductivity 0.1 S/m, electrode diameters 1.2 cm). B) 90% percentiles of the field strength |E| in the skin ROI (indicated in red on the head surface in the inset) underneath the anode. The squares and circles indicate the results for electrode diameters of 1.2 cm and 2 cm. C) Same as B, but for the 99% percentile. D) 90% percentiles of the field strength in the gray matter ROI (indicated in red on the brain in the inset). E) Jaccard index of similarity of |E| in the gray matter ROI relative to the results for gel conductivities of 0.1 S/m. F) Electric field strength in the skin region around the center electrode shown for the two simulated electrode diameters and for very low and high conductivities.

While the electric field distribution also depends on the individual anatomy, the general pattern of findings and the strengths of the effects reported here can be expected to hold robustly, at least for healthy individuals. As example, Fig. 4F shows the best and worst case scenarios for another individual, resulting in a similar dependence of the electric field underneath the anode on the electrode parameters as seen in Fig. 4E.

G.B. Saturnino et al. / NeuroImage 120 (2015) 25–35

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Fig. 6. A) Example demonstrating the consistency of results for different mesh resolutions. The high resolution mesh had around 1,200,000 triangles in the skin surface, while the low resolution mesh had ~30,000 triangles in this surface (the meshes used in the main part of the study were selectively refined in the skin region underneath the anode, resulting in ~43,000 triangles). B) Example showing the stability of the results for different skin conductivities.

Discussion Electrode pads of several tens of cm2 are commonly used in tDCS for feeding in the currents. The intuitive rationale behind this choice is the wish to homogenously distribute the current flow through the electrolyte–skin interface across a large area. Prior modeling studies have already demonstrated that this aim is difficult to achieve and that the currents might be strongest at the electrode edges. However, the electrodes modeled in those studies were often simplified versions of the electrodes used in practice. Here, we demonstrate that electrode properties such as the conductivities of the rubber and the electrolyte gel (or sponge) and the connector position have a clear-cut impact on the field distribution created in the brain. As a rough rule of thumb, high conductivities favor the horizontal current flow within the electrodes, causing the edge effect described in earlier modeling studies. For low conductivities, the connector position (relative to the position of the other electrode) plays an important role: placing the connector away from the other electrode (posterior and lateral connector positions for the anode in our case) strengthens the electric field in the brain region underneath the electrode. The hole in ring electrodes increases this effect as it disturbs the horizontal current flow. As a result, a clear impact of the connector position was observed for comparatively high gel conductivities of 4 S/m. This effect gets also more pronounced with increasing electrode area, as seen for the 10 × 10 cm2 return electrodes.

Our results suggest that the field strength is generally increased in the skin region close to the connector. This effect varies with connector position and is strongest when the connector is placed closer to the other electrode (medial connector position for the anode in our case). This also maximizes the amount of current that is shunted through the skin layer and does not enter the brain. Stating what is a “high” or “low” value for the gel and rubber conductivity is difficult, as there is an additional dependence on factors such as the area, type and thickness of the electrode. When varying these conductivities, we observed a clear-cut difference to the baseline case for the lowest tested conductivities (1 S/m for gel, 0.1 S/m for rubber), as also used in the best case scenario (Fig. 4E). It is worth noting that only one electrode was varied in these tests. When changing the connector positions on both electrodes (Fig. 3A), substantial effects on the electric field were already observed for relatively high gel conductivities of 4 S/m. This indicates that the impact of particular combinations of electrode pads and gels should be tested in simulations. Our results indicate that the electrode properties may also play a role when using smaller electrodes in a multi-electrode setup (Dmochowski et al., 2011). The spatial stimulation pattern in the brain is hardly affected when changing gel conductivity or electrode diameter. However, the achieved peak field strengths in GM depend on these factors, as they influence the amount of current that is shunted within the skin layer. Both factors also affect the field distribution in the skin regions underneath the electrodes. Larger electrode diameters can substantially decrease

Table 2 Robustness of the results when varying the mesh resolution or the skin conductivity.

Mean (±SD) |E| in overall GM [V/m] Mean (±SD) |E| in GM ROI [V/m] Correlation (overall GM) Correlation (GM ROI)

Low mesh resolution

High mesh resolution

Normal skin conductivity

Skin conductivity reduced to 50%

Skin conductivity reduced to 25%

0.083 ± 0.030 0.099 ± 0.027 – –

0.083 ± 0.030 0.099 ± 0.027 0.993 0.991

0.10 ± 0.04 0.13 ± 0.03 – –

0.13 ± 0.05 0.18 ± 0.05 0.993 0.996

0.16 ± 0.07 0.22 ± 0.06 0.976 0.982

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the peak field strengths. Decreasing the gel conductivity to enforce a more homogeneous field distribution and – in turn – decreasing the peak field strengths underneath the electrode edges seems to be less effective as clear-cut effects were only seen for very low conductivities of b0.5 S/m. Implication for results of prior modeling studies Prior computational work has helped to shed light on the range of peak electric field strength that tDCS causes in brain gray matter (Datta et al., 2009; Miranda et al., 2013). It has further revealed a range of anatomical factors that can influence the current distribution in the brain, such as the gyrification pattern, skull composition or thickness of CSF (Datta et al., 2010; Miranda et al., 2013; Neuling et al., 2012; Opitz et al., 2015; Sadleir et al., 2010). These studies remain valuable sources to understand the biophysics underlying tDCS. However, simulation results demonstrating that the strongest stimulation likely occurs in the brain areas between the electrodes rather than underneath them have to be interpreted with care (Miranda et al., 2006; Miranda et al., 2013; Opitz et al., 2015; Wagner et al., 2007). They only hold for specific assumptions regarding the electrode properties. Our results show that strong “edge effects” underneath the electrode edges are obtained when setting the complete electrode surface to a common electric potential, as done in many modeling studies so far. These models do not properly approximate many of the electrodes used in practice which normally consist of low conductive rubber pads. This highlights the need for a more careful modeling of the electrodes in future computational tDCS studies. Implication for practical tDCS experiments The main conclusion to be drawn from our results is that all electrode properties such as their size, the thickness of the layers and the conductivities of the materials should be carefully selected and also documented when reporting the results. This includes the position of the cable connector which is not always centered, but often at one of the sides of the rubber pads. Up to now, these details are usually not reported to the full extent, or are even unknown to the user as the information is not conveyed by the manufacturers. This can cause systematic differences between tDCS studies and render the replication of results more difficult. During the last years, sponge electrodes have been increasingly replaced by rubber pads which are attached to the skin using electrode gel or paste. This allows for an easier and more stable positioning of the electrodes and prevents changes in the course of the experiment due to drying sponges. However, often gels originally designed for EEG are used which have a rather high conductivity. Our results suggest that low gel conductivities in the range of 1 S/m seem to be favorable for tDCS. Appropriate gels in combination with a careful selection of the connector position open up the possibility to focus the stimulation more to brain positions underneath electrodes. This helps to align the stimulated brain areas better with the chosen target areas. Importantly, matching the stimulation pattern to the neuroscientific or medical aims might also help to decrease the interindividual variability of the stimulation effects. It seems worth to adjust the electrode diameters to the distance between the electrodes when using multi-electrode setups (Dmochowski et al., 2011). The goal would be to find the best compromise between minimizing the amount of current that is shunted in the skin and does not enter the brain versus limiting the peak field strength that occurs in the skin layer underneath the center electrode. Obviously, simulation studies can be useful in this task. These could further be employed to explore more refined electrode designs such as conically recessed electrodes in combination with low conductive gels in order to ensure more homogeneous current strengths at the gel–skin interface (Gilad et al.,

2007). It might also be valuable to explore the usage of a center electrode that is larger than the remaining electrodes. Limitations of the study The results reported here are based on calculations performed with a single head model of a healthy individual. We are confident that the main findings hold robustly and can be generalized as they are driven by the different conductivity ratios of the electrode materials and the biological tissues rather than by specific individual anatomical features. It can thus be expected that similar effects will occur as long as the conductivities correspond roughly to those tested here. This is also supported by the control calculations in which the skin conductivity was varied (Fig. 6B; Table 2) and in which another head model was used to replicate the worst and best case scenarios derived from the systematic variations of the electrode parameters (Figs. 4E & F). While varying many of the electrode properties, the height of the gel and rubber layers was kept fixed in this study. Their variation would have added to the complexity of the results while not revealing much additional information. The general pattern of field changes when varying the layer thickness is roughly predictable from our results. For example, doubling the thickness of the rubber layer roughly corresponds to doubling its conductivity, as it will allow for a stronger horizontal current flow within the electrode. In the future, more detailed results should rather be selectively determined for the specific electrode parameters that are used in individual studies. Putative effects at the electrode–electrolyte or electrolyte–skin interfaces that will increase the resistance for the current flow across these interfaces were not modeled here (Neuman, 2015). However, given that the results were robust to changes of the skin conductivity, we are confident that the pattern of findings as presented here holds in general. This also holds for the differences observed for the field strengths in the skin layer for normal electrode pads versus the circular electrodes in a 4 × 1 arrangement. The differences are expected as the same overall current of 1 mA has to pass through a much smaller area of electrode–skin interface. The peak values, however, should be taken with some care as details such as inhomogeneities in the skin layer were not taken into account (Keller and Kuhn, 2008). In practice, several factors can cause spatial inhomogeneity in the conductivity profile of the electrodes. This comprises, e.g. spatial variations in the pressure by the rubber band that is used to hold the electrode in place, variations in the thickness of the electrode paste, or the drying out of the sponge corners. While these will potentially have an impact on the current distribution, it will vary from experiment to experiment and are therefore difficult to take into account in the modeling process. In any case, minimizing them as much as possible by careful experimental procedures is likely the most effective way to deal with them. Finally, it should be pointed out that this simulation study focused on assessing the distribution of the electric field strength in cortical gray matter as an outcome measure rather than making direct predictions of the physiological stimulation effects. It is still not well understood how the physiological effects are linked to the externally caused electric field. Based on work in rodents and in brain slice preparations, it is thought that the physiological effects are dependent on the direction of the current flow (or electric field vector) relative to the gray matter sheet (Bikson et al., 2004; Bindman et al., 1962). In the future, the work presented here could be extended to test how the electrode configuration and parameters affect the homogeneity of the field direction in a cortical target region. Large parts of the field are oriented parallel rather than perpendicular to the cortical sheet and it is suggested that these parallel currents are also effective in modulating neural activity (Kabakov et al., 2012; Rahman et al., 2013). However, it is currently not feasible to make clear assumptions on the type (facilitatory vs. inhibitory) of the physiological effects caused by this kind of current flow, as it might also depend on the local orientation of the neural

G.B. Saturnino et al. / NeuroImage 120 (2015) 25–35

pathways in the stimulated gray matter volume. This makes it challenging to take this kind of current flow systematically into account in simulation-based optimization approaches. Conclusion Detailed modeling of the electrode pads used in tDCS studies demonstrates the importance of electrode properties on the electric field distribution in the brain. The spatial pattern of current flow reported in many modeling studies so far only holds for some of the electrode types used in experiments. Our results encourage careful modeling of electrodes in computational studies and highlight the importance of an informed selection and detailed reporting of the electrode properties in experimental tDCS studies. It might be worth noting that quite sophisticated designs exist for defibrillation electrodes that employ gradually decreasing conductivities towards the electrode edges in order to enforce a more homogeneous current distribution through the gel–skin interface (Garcia et al., 1998; Papazov et al., 2002). Exploring this kind of design in the future also for tDCS could be valuable, in particular when the goal is to achieve a distributed current flow by means of large electrode pads. Acknowledgments This work was supported by a project grant sponsored by Lundbeckfonden (PI: Axel Thielscher; Grant Nr. R118-A11308), a Grant of Excellence “ContAct” sponsored by Lundbeckfonden (PI: Hartwig Siebner; Grant Nr. R59 A5399), an Interdisciplinary Synergy Grant “Basics” sponsored by NovoNordisk fonden (recipients: Hartwig Siebner, Axel Thielscher & Lars K Hansen, Grant Nr. 11413), a project grant sponsored by the German Federal Ministry for Economic Affairs and Energy (PI: Axel Thielscher; Grant Nr. KF2881001KJ1) and a Science Without Borders Scholarship from the Brazilian Ministry of Science and Technology (grant no. 1423-31-2) (Recipient: Guilherme B Saturnino). Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.neuroimage.2015.06.067. References Bikson, M., Inoue, M., Akiyama, H., Deans, J.K., Fox, J.E., Miyakawa, H., Jefferys, J.G.R., 2004. Effects of uniform extracellular DC electric fields on excitability in rat hippocampal slices in vitro. J. Physiol. Lond. 557, 175–190. Bindman, L.J., Lippold, O.C.J., Redfearn, J.W., 1962. Long-lasting changes in level of electrical activity of cerebral cortex produced by polarizing currents. Nature 196, 584–585. Dale, A.M., Fischl, B., Sereno, M.I., 1999. Cortical surface-based analysis — I. Segmentation and surface reconstruction. NeuroImage 9, 179–194. Dannhauer, M., Lanfer, B., Wolters, C.H., Knösche, T.R., 2011. Modeling of the human skull in EEG source analysis. Hum. Brain Mapp. 32, 1383–1399. Datta, A., Elwassif, M., Battaglia, F., Bikson, M., 2008. Transcranial current stimulation focality using disc and ring electrode configurations: FEM analysis. J. Neural Eng. 5, 163–174. Datta, A., Bansal, V., Diaz, J., Patel, J., Reato, D., Bikson, M., 2009. Gyri-precise head model of transcranial direct current stimulation: improved spatial focality using a ring electrode versus conventional rectangular pad. Brain Stimul. 2, 201–207 (207 e201). Datta, A., Bikson, M., Fregni, F., 2010. Transcranial direct current stimulation in patients with skull defects and skull plates: high-resolution computational FEM study of factors altering cortical current flow. NeuroImage 52, 1268–1278. Dmochowski, J., Datta, A., Bikson, M., Su, Y., Parra, L., 2011. Optimized multi-electrode stimulation increases focality and intensity at target. J. Neural Eng. 8, 046011. Dular, P., Geuzaine, C., Henrotte, F., Legros, W., 1998. A general environment for the treatment of discrete problems and its application to the finite element method. IEEE Trans. Magn. 34, 3395–3398. Faria, P., Hallett, M., Miranda, P.C., 2011. A finite element analysis of the effect of electrode area and inter-electrode distance on the spatial distribution of the current density in tDCS. J. Neural Eng. 8.

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