Design of the eccentric curved symmetrical array for enhanced focalized transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a rapidly advancing neuromodulation technology whose efficacy depends directly on the spatial distribution of induced electric fields (E-fields). Traditional planar TMS coils with large diameters can increase stimulation intensity but at the cost of reduced focalization. To address this trade-off, we propose an eccentric curved symmetric array (ECS array), which integrates inner planar coils with smaller radii and outer curved coils with larger radii. Together, they form an eccentric symmetric structure. Depending on the bending direction of the outer coils, the ECS array can be classified as upward bending (U-ECS) or downward bending. Finite element analysis of the ECS array demonstrates a bounded, highly focused E-field distribution on the target plane 2 cm below the coil. Compared with the conventional figure-of-eight coil, the optimized U-ECS array enhances stimulation intensity by 63.29% and reduces the focusing area by 12.33%. To validate these findings, we built an ECS prototype with a dedicated TMS stimulation circuit and measured the induced E-fields. The experimental results closely matched simulations, confirming that the ECS array can deliver stronger and more focused stimulation fields. This design provides a promising strategy for non-invasive neural modulation, with potential applications in therapeutic interventions and cognitive neuroscience.