HingePlace: Harnessing the neural thresholding behavior to optimize Transcranial Electrical Stimulation

TL;DR

This work addresses off-target stimulation and inter-subject variability in transcranial electrical stimulation by unifying major electrode-placement approaches and introducing HingePlace, a convex, threshold-aware montage design. By employing a symmetrized hinge loss that leverages neural thresholding, HingePlace directly targets focal neural responses rather than solely minimizing off-target fields. Theoretical results show equivalence between CDM and LCMV-E, unifying four major classes of electrode placements, while HingePlace breaks the zero-off-target constraint to exploit biology. Empirical validation across MRI head models and a biophysically realistic sea-of-neurons model demonstrates that HingePlace achieves substantially more focal neural activation (up to ~60% improvement in some cases) compared with traditional montages, suggesting meaningful gains for clinical efficacy and personalized stimulation.

Abstract

Transcranial Electrical Stimulation (tES) is a neuromodulation technique that utilizes electrodes on the scalp to stimulate target brain regions. tES has shown promise in treating many neurological conditions, such as stroke rehabilitation and chronic pain. Several electrode placement algorithms have been proposed to optimize tES-based therapies by designing multi-electrode montages that create focal neural responses. We first extend a well-known unification result by Fernandez-Corazza et al. to unify all major traditional electrode placement algorithms. We utilize this unification result to identify a common restriction among traditional electrode placement algorithms: they do not harness the thresholding behavior of neural response. Consequently, these algorithms only partially harness the properties of neural response to optimize tES, particularly increasing the focality of neural response. We propose a new electrode placement algorithm, HingePlace, that utilizes a symmetrized hinge loss to harness the thresholding behavior of neural response. We extensively compare the HingePlace algorithm with traditional electrode placement algorithms in two simulation platforms. Across both platforms, we find that HingePlace-designed montages consistently generate more focal neural responses -- by as much as 60% -- than the electrode montages designed by traditional electrode placement algorithms.

Figures (18)

• Figure 1: A representation of the HingePlace algorithm utilizing the hinge loss (top-left) to allow sub-threshold electric field amplitudes in off-target regions (shown in the top-middle) to reduce off-target stimulation volume (represented by the smaller stimulated region depicted in top-right). In contrast, traditional electrode placement algorithms utilize the $l_2$ loss (bottom-left) that minimizes the electric field amplitude in the off-target regions (shown in the bottom-middle), which counter-intuitively leads to a larger off-target stimulation volume than the HingePlace algorithm (represented by the larger stimulated region depicted in the bottom-right).
• Figure 2: A visualization of the $l_2$ (square) loss and the HingePlace loss with different values of $p$ as a function of electric field amplitude at a single voxel in the off-target region.
• Figure 3: a and b present a sagittal and horizontal view of the realistic MRI head model discussed in Sec. \ref{['sec:results:mri']}. The electrodes are shown in blue, and the brain is represented using the salmon color. c shows the five different target locations used in the simulation studies described in Sec. \ref{['sec:results:mri']}. MC denotes a target location in the motor cortex, and the MNI coordinates of target locations $1$, $2$, $3$, and $4$ are provided in Appendix D. d provides a schematic of the sea of neurons model discussed in Sec. \ref{['sec:results:sea-of-neurons']}. The electrode locations are denoted by blue points. e provides a 2-D representation of the electrode locations shown in d. f is a zoomed-in version of d to show the neuron morphology.
• Figure 4: A representative plot of the electric field along the radial-in direction and the corresponding region where the radial-in electric field intensity above $0.8\text{Vm}^{-1}$ generated by electrode montages designed using the HingePlace and LCMV-E algorithms in Sec. \ref{['sec:results:mri:MC']}. The target location was the motor cortex and the values of $I_{safe}$ and $I_{tot}^{mul}$ were $4.5$mA and $2$, respectively. We observe that LCMV-E produces the least off-target electric field, but has a larger volume above the stimulation threshold compared to HingePlace. Additional representative plots are provided in Appendix E.
• Figure 5: a-c plot the relative decrease in the stimulated volume between the HingePlace and LCMV-E montages for the simulation study described in Sec. \ref{['sec:results:mri:MC']}. a, b, and c correspond to different values of $I_{tot}^{mul}$, namely, $2$, $4$, and $8$, respectively. Similarly, d, e, and f plot the relative decrease in stimulated volume between HingePlace and LCMV-E montages for the studies described in Sec. \ref{['sec:results:mri:larger-focus']}, Sec. \ref{['sec:results:mri:multi-site']}, and Sec. \ref{['sec:results:mri:diff-targets']}, respectively.

Theorems & Definitions (15)

• Theorem 1
• proof
• Lemma 1
• proof
• Claim 1
• proof : Proof
• Claim 2
• proof : Proof
• Lemma 2
• proof