Multi-coil arrays applied in transcranial magnetic stimulation (TMS) are proposed to accurately stimulate brain tissues and modulate neural activities by an induced electric field (EF). Composed of numerous independently driven coils, a multi-coil array has alternative energizing strategies to evoke EFs targeting at different cerebral regions. To improve the locating resolution and the stimulating focality, we need to fully understand the variation properties of induced EFs and the quantitative control method of the spatial arrangement of activating coils, both of which unfortunately are still unclear. In this paper, a comprehensive analysis of EF properties was performed based on multi-coil arrays. Four types of planar multi-coil arrays were used to study the relationship between the spatial distribution of EFs and the structure of stimuli coils. By changing coil-driven strategies in a basic 16-coil array, we find that an EF induced by compactly distributed coils decays faster than that induced by dispersedly distributed coils, but the former has an advantage over the latter in terms of the activated brain volume. Simulation results also indicate that the attenuation rate of an EF induced by the 36-coil dense array is 3 times and 1.5 times greater than those induced by the 9-coil array and the 16-coil array, respectively. The EF evoked by the 36-coil dispense array has the slowest decay rate. This result demonstrates that larger multi-coil arrays, compared to smaller ones, activate deeper brain tissues at the expense of decreased focality. A further study on activating a specific field of a prescribed shape and size was conducted based on EF variation. Accurate target location was achieved with a 64-coil array 18 mm in diameter. A comparison between the figure-8 coil, the planar array, and the cap-formed array was made and demonstrates an improvement of multi-coil configurations in the penetration depth and the focality. These findings suggest that there is a tradeoff between attenuation rate and focality in the application of multi-coil arrays. Coil-energizing strategies and array dimensions should be based on an adequate evaluation of these two important demands and the topological structure of target tissues.
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