Quantitative Analysis of Evoked Haptic Sensations by Transcutaneous Electrical Nerve Stimulation for Electrode Array Size Optimization

Haptic feedback is critical for enabling dexterous manipulation in prosthetic users. The electrode array technique is often used in transcutaneous electrical nerve stimulation to improve stimulation efficacy and spatial resolution. However, the effect of the array geometric parameters-specifically electrode diameter and spacing-on haptic sensations has never been investigated and remains an open question. Six integrated and reusable 2× 8 electrode arrays with varying diameters and spacings were designed and fabricated using the 3D print technique, targeting the median and ulnar nerve bundles along the medial side of the upper arm. Successive 3-second stimulations containing charge-balanced biphasic square-wave pulses at 150 Hz were delivered to all 120 pairwise electrode combinations. For each 3-second stimulation, the regions of elicited sensations were recorded on a digital hand map. Metrics including the active electrode pair count, sensation coverage ratio, Jaccard similarity, activated centroid distribution and sensation pattern clusters were analyzed. The results indicate that minimizing electrode diameter (10 mm vs. 14 mm) and spacing (15 mm vs. 18 mm) enhances activation probability (active pairs increased by 44.1% and 31.5%, respectively), sensation coverage (coverage ratio increased by 55.4% and 20.7%, respectively) and spatial dispersion. Meanwhile, a wider inter-electrode spacing (18 mm vs. 15 mm) facilitates the generation of a richer diversity of sensation patterns (clusters increased by 74.4%). These findings confirm that electrode geometry is a critical design variable for sensation induction and demonstrate that sensory recruitment can be modulated from focal to widespread by optimizing electrode array dimensions. These outcomes provide guidelines to customize array sizes for specific haptic feedback patterns during prosthetic interactions, potentially improving user embodiment and closed-loop control.