Comparative electrothermal analysis of single and small-electrode grid configurations for HD-inspired peripheral...

High-density (HD)-inspired peripheral transcutaneous neurostimulation systems employing clusters of small-area electrode arrays may improve spatial controllability during electrical stimulation of superficial limb tissues, as used in TENS/NMES/FES-like wearable applications. However, the electrothermal consequences of small electrodes can affect usability due to complexities in safety considerations. Therefore it is of critical interest to understand the effects of these systems, and to determine how subdivision topology shapes localized current concentration and thermal accumulation under fixed electrode geometry conditions.

This study investigates how high-density clusters of small-area electrodes influences current-density distribution and electrothermal behavior. This project is part of a larger study to design and optimize these high-density neurostimulation arrays to improve spatial scaling.

A coupled electrical-thermal finite-element model was developed in COMSOL Multiphysics 6.3 to compare conventional single-electrode configurations with a systematic series of HD-inspired small-electrode grid configurations ranging from 1 to 16 electrodes (grid1 through grid16). The individual electrode radius and inter-electrode spacing were held constant while the number of active electrodes was varied. Current-density distribution, temperature change, and thermal transient effects were evaluated using current-controlled pulsed stimulation with varying current amplitudes, pulse widths, and frequencies.

Electrothermal effects did not increase linearly with the number of active electrodes. Three distinct electrothermal regimes were identified based on stimulation-side behavior: an extreme concentration regime ( $N=1$ -4), a transition regime ( $N=5$ -8), and a regime in which stimulation-side load falls below a fixed return-electrode background contribution ( $N\ge 9$ , crossover $N^{*}=8$ -9), where $N$ is the number of active electrodes in a grid. The $N=9$ regime showed the closest stimulation-side electrothermal behavior to the single-electrode reference among all configurations tested ( $\Delta T=1.340$ °C vs. 1.370 °C, or a difference of 0.030 °C). The stimulation-side $\Delta T$ declined with electrode count across this full range ( $\Delta T\approx 9.69\times N^{-0.91}$ , $R^2=0.999$ ). A dedicated area-matched control series, in which electrode radius was increased to hold total active area constant showed a decline in stimulation-side current density and a temperature rise with electrode count. A complementary, exploratory comparison holding electrode count fixed while varying the total active area also showed decline in both quantities. Together, these results indicate that electrode count and total active area each contribute to the observed electrothermal decline. However, causal effects were not isolated from one another. As expected from established current-concentration effects of small electrodes, the sparse grid1 configuration produced the highest superficial current density and temperature rise among the investigated configurations ( $\Delta T=10.18$ °C, or 7.43 $\times$ reference-electrode baseline). A discretized parameter-space analysis (128 sampled current amplitude/pulse-width/frequency combinations) showed that the $\Delta T\ge 8$ °C region occupied by each configuration declined continuously with electrode count. Specifically, from 72 combinations for grid1 (4.50 $\times$ single) to 4 combinations for grid16 (0.25 $\times$ single). Therefore, electrode grid configurations with higher electrode counts distribute the current across a progressively larger area, and thus reduced per-electrode current density.

Under the idealized modeling conditions investigated here, electrothermal behavior was jointly determined by electrode count and total active electrode area. These two variables are intrinsically coupled in the fixed-radius grid1-grid16 design where both contribute to a reduction in stimulation-side electrothermal load. These findings represent comparative, geometry-specific modeling trends rather than validated thermal safety predictions. The present study provides a comparative computational framework for evaluating HD-inspired electrode subdivision strategies in compact peripheral transcutaneous neurostimulation design, where electrode count and total active area jointly determine the resulting current-distribution topology and associated localized thermal accumulation.