Optimal use of EEG recordings to target active brain areas with transcranial electrical stimulation

Abstract

To demonstrate causal relationships between brain and behavior, investigators would like to guide brain stimulation using measurements of neural activity. Particularly promising in this context are electroencephalography (EEG) and transcranial electrical stimulation (TES), as they are linked by a reciprocity principle which, despite being known for decades, has not led to a formalism for relating EEG recordings to optimal stimulation parameters. Here we derive a closed-form expression for the TES configuration that optimally stimulates (i.e., targets) the sources of recorded EEG, without making assumptions about source location or distribution. We also derive a duality between TES targeting and EEG source localization, and demonstrate that in cases where source localization fails, so does the proposed targeting. Numerical simulations with multiple head models confirm these theoretical predictions and quantify the achieved stimulation in terms of focality and intensity. We show that constraining the stimulation currents automatically selects optimal montages that involve only a few (4-7) electrodes, with only incremental loss in performance when targeting focal activations. The proposed technique allows brain scientists and clinicians to rationally target the sources of observed EEG and thus overcomes a major obstacle to the realization of individualized or closed-loop brain stimulation.

Keywords: Closed-loop stimulation; EEG; Reciprocity; Source localization; Transcranial direct current stimulation; Transcranial electrical stimulation.

Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Figures

Fig. 1

Reciprocal stimulation produces an electric field focused on the site of neural activation. (A) Focal neural activation of the right frontocentral cortex produces a radially-symmetric pattern of electric potentials on the scalp. Inset: BEM head model employed to simulate EEG activations and electric fields during TES. (B) By patterning the stimulation currents according to the observed scalp activity (i.e., I ∝ V ), “naive” reciprocity generates a diffuse electric field that is strong at the site of activation but also over expansive regions of cortex. (C) Applying TES in proportion to the spatially decorrelated EEG (i.e., I=c(RRT)−1V) yields focal stimulation at the neural activation. Note that the injected reciprocal currents are both positive (“anodal”) and negative (“cathodal”) over the scalp regions marked by positive EEG potentials.

Fig. 2

Localization of EEG is equivalent to targeting in TES. (A) Bilateral activation of the superior parietal lobule. (B) The observed EEG pattern, simulated here for a high signal-to-noise ratio (SNR) of 100, shows a radially-symmetric topography focused over centroparietal electrodes. (C) The TES montage that targets the source of this EEG is composed of a center anode and surrounding cathodes, producing an electric field (D) concentrated at the source of the parietal activation. Moreover, this electric field is perfectly correlated with the minimum-norm estimate (E) of the EEG source distribution. (F) An increase in the noise level (SNR=1) leads to a distorted EEG topography, which then results in a reciprocal TES montage (G) that erroneously utilizes lateral frontal electrodes. The resulting electric field (H) is no longer focused on the site of neural activation. Correspondingly, the estimate of the EEG source (I) is also mismatched with the actual neural activation.

Fig. 3

Constraining the L1 norm of reciprocal TES montages produces intense electric fields at the target. (A) Activation of primary visual cortex and the associated EEG pattern. (B) Unconstrained reciprocity distributed the applied current over approximately 8 electrodes. This led to a concentration of the electric field at the occipital target (focality of 3.3 cm), with a peak electric field intensity of 0.18 V/m. (C) By constraining the L1-norm of the reciprocal TES solution with c = 1010, the applied currents were contained to 5 electrodes, yielding to a three-fold increase in the intensity of the stimulation at the activated region (0.53 V/m), while only sacrificing 4 mm in focality (3.7 cm). (D) Comparing unconstrained and L1-constrained reciprocity across all cortical sources showed that L1-constrained reciprocity achieves an average increase in field intensity of 163%, while only sacrificing 4% in focality (error bars represent standard deviations across 15,002 sources).

Fig. 4

Quantifying the focality-intensity tradeoff in L1 constrained reciprocity. L1 constrained reciprocal TES at increasing values of parameter c was performed on the EEG generated by activation of the (A) superior temporal gyrus (STG), (B) the dorsolateral prefrontal cortex (DLPFC), (C) superior parietal lobule (SPL) and (D) visual area V5 (also known as the middle temporal visual area). Increasing c led to higher intensity and reduced focality at the activation. However, the focality-intensity increased gradually at low values of c, suggesting that intensity can be significantly increased (2 or 3×) while only sacrificing a small amount of focality (1 or 2 cm). A good tradeoff between intensity and focality was found here to be c = 1010 or c = 1011. Increasing c also led to a reduction in the number of electrodes recruited by the optimal montage (denoted by color of markers), which was approximately 4–7 at c = 1010.

Fig. 5

The performance of reciprocal stimulation as a function of target location. (A) The focality of L1-constrained reciprocal TES, as measured by the radius bounding half of the total electric field, shown as a function of the location of neural activation. Focality ranged from 1.9 to 6.5 cm, exhibiting optimal values over dorsolateral prefrontal, temporoparietal, and lateral occipital cortices. (B) Same as A but now for the intensity of the electric field at the target. Intensity ranged from 0.0002 to 0.50 V/m, exhibiting discrete hotspots over lateral prefrontal, middle temporal, and occipital cortex. (C) The error between target location and the peak of the electric field was less than 1 cm along the dorsal surface, while exceeding 5 cm on ventral cortex. The three measures were all significantly correlated (|r| > 0.56, p=0 to numerical precision, N=74382), with locations receiving focal stimulation stimulated with high intensity and low targeting error.

Fig. 6

Reciprocal TES accounts for varying source orientation. (A) A source in the left motor cortex was activated with both radial and tangential source orientations. (B) Radial activation led to a monopolar EEG pattern over central electrodes. (C) The reciprocal TES montage for this scalp pattern consisted of two dominant anodes and one dominant cathode. (D) The resulting electric field was marked by a strong radial component (0.064 V/m) and a significantly weaker (E) tangential component (0.0003 V/m) at the intended source location (white circle). Note that the peak of the tangential field is no longer over the target, as the source is radially oriented. (F) Activation of a tangential source at the same target location resulted in a dipolar pattern of scalp potentials. (G) The TES montage targeting this EEG pattern consisted of a single dominant anode and cathode. (H) This montage produced a weak radial electric field component (0.004 V/m) relative to the (I) tangential direction of the electric field (0.13 V/m). Thus, for both cases, reciprocal TES produced an electric field whose dominant direction matched the orientation of the activated source. Note that projections of the electric field in the radial or tangential direction may be positive or negative.

Fig. 7

Reciprocal TES with distributed source activations. (A) Activation of distinct regions along the ventral visual stream (from middle out): primary visual cortex (V1), V2, V4, and the inferior temporal cortex (ITC). (B) The resulting EEG pattern showed focal positivity over the bilateral temporal and medial occipital electrodes. (C) Reciprocal TES on this EEG pattern led to a montage with stimulation electrodes positioned at both occipital and temporal sites. (D) The resulting electric field had pronounced intensity at both occipital and inferior temporal targets. However, the strength of the field was dampened at the inferior temporal sources (0.066 V/m) relative to that at the occipital sources (>0.12 V/m), presumably reflecting the difficulty in targeting ventral regions with TES.