Can transcranial electric stimulation with multiple electrodes reach deep targets?

Abstract

To reach a deep target in the brain with transcranial electric stimulation (TES), currents have to pass also through the cortical surface. Thus, it is generally thought that TES cannot achieve focal deep brain stimulation. Recent efforts with interfering waveforms and pulsed stimulation have argued that one can achieve deeper or more intense stimulation in the brain. Here we argue that conventional transcranial stimulation with multiple current sources is just as effective as these new approaches. The conventional multi-electrode approach can be numerically optimized to maximize intensity or focality at a desired target location. Using such optimal electrode configurations we find in a detailed and realistic head model that deep targets may in fact be strongly stimulated, with cerebro-spinal fluid guiding currents deep into the brain.

Keywords: Intersectional short pulse stimulation; Noninvasive deep brain stimulation; Optimized transcranial electric stimulation; Temporal interferential stimulation.

Fig. B.4.

Focality for interferential and conventional transcranial electrical stimulation. Same simulations as shown in Fig. 2 except here spatial extent of stimulation is evaluated for each location. Color indicates the size of the volume stimulated at 50% (or more) of the intensity found at each location (again, showing the cubic root of the volume to indicate the length scale in centimeter).

Fig. 1.

Examples of targeted stimulation using multiple electrodes. (A) Electrode locations and currents are optimized to achieve focal stimulation at a superficial target location (black circle). Total current is limited to 2 mA. Optimal locations are shown on the left with color indicating current magnitude through each electrode. Gray electrodes indicate possible locations considered by the algorithm, but which draw no current for this target. Resulting spatial distribution of electric field magnitudes in the brain is shown on the right. (B) Optimization here attempts maximally intense stimulation at a target location in the brain, again using 2 mA. The optimal solution only includes two small electrodes. (C) Here a total of 6 mA is used to target the same location as in (B), but current through each electrode is constrained to a maximum of 1 mA. Maximally intense stimulation is achieved by spreading the currents among 12 electrodes (6 anodes and 6 cathodes). This “high-definition” TES montage is equivalent to the “inter-sectional pulsed stimulation” protocol of [7]; but using optimal electrode locations. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 2.

Modulation depth for interferential and conventional transcranial electrical stimulation. Stimulation is applied through two pairs of electrodes as shown on the left. (A) Waveform of interferential stimulation (light blue) along with the envelope for interferential (red) and conventional stimulation (black). Here we used 20 Hz as carrier frequency and 1 Hz as modulation frequency for better visualization. Waveforms were computed with values from the electric fields generated by each electrode pair (a and b in the equations of D) at the frontal brain location marked with a black circle in panel B. (B) In this configuration current flows between electrodes Fp1 and P7 on the left, and between Fp2 and P8 on the right, such that current flows predominantly in the posterior/anterior direction. (C) Here electrodes are closer together (with electrode pairs FT7/P7 and FT8/P8) generating more focal but also weaker stimulation. In panels B & C the first two rows show axial view of field modulation depth across the head (including skull and scalp). The third row indicates histograms across the entire brain. The four columns show the modulation depth of the electric field (M™, Eq. (E.1)) in three different directions (n): posterior/anterior (P/A), radial direction pointing to the MNI origin, i.e. anterior commissure (Radial), and the direction with the maximal modulation depth (Max). The last column is the modulation for the field magnitude (Mag.), or more specifically, the square-root of power modulation ($\sqrt{M_{\left|\right|\tilde{\mathbf{s}}|{|}^2}}$, Eq. (E.5)). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3.

Distribution of achieved focality and intensity across the brain. (A) For each location a separate optimal electrode montage is found with the goal of achieving focal stimulation. The optimal montage is evaluated for the resulting size of the stimulated volume. Color indicates the size of the volume stimulated at 50% (or more) of the intensity at the target (we show the cubic root of the volume to indicate the length scale in centimeter). (B) Electrode montage is optimized, for each target location, to achieve maximal intensity with 2 mA. False color indicates the maximal value achieved at that location. (C) Same as B, but now injecting a total of 6 mA while constraining the current in each electrode to no more than 1 mA. Targeting was performed using a detailed 0.5 mm resolution current-flow model (as shown in Fig. 1), but target locations were surveyed only on a 2 mm grid. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)