Objective. Transcranial magnetic stimulation (TMS) coil design involves a tradeoff among multiple parameters, including magnetic flux density (B), inductance (L), induced electric (E) field, focality, penetration depth, coil heating, etc. Magnetic materials with high permeability have been suggested to enhance coil efficiency. However, the introduction of magnetic core invariably increases coil inductance compared to its air-core counterpart, which in turn weakens theEfield. Our lab previously reported a rodent-specific TMS coil with silicon steel magnetic core, achieving 2 mm focality. This study aims to better understand the tradeoffs amongB,L,andEin the presence of magnetic core.Approach. The magnetic core initially operates within the linear range, transitioning to the nonlinear range when it begins to saturate at high current levels and reverts to the linear range as coil current approaches zero; both linear and nonlinear analyses were performed. Linear analysis assumes a weak current condition when magnetic core is not saturated; a monophasic TMS circuit was employed for this purpose. Nonlinear analysis assumes a strong current condition with varying degrees of core saturation.Main results. Results reveal that, the secondaryEfield generated by the silicon steel core substantially changed the dynamics during TMS pulse. Linear and nonlinear analyses revealed that higher inductance coils produced stronger peakEfields and longerEfield waveforms. On a macroscopic scale, the effects of these two factors on neuronal activation could be conceptually explained through a one-time-constant linear membrane model. Four coils with differentB,L,andEcharacteristics were designed and constructed. BothEfield mapping and experiments on awake rats confirmed that inductance could be much higher than previously anticipated, provided that magnetic material possesses a high saturation threshold.Significance. Our results highlight the novel potentials of magnetic core in TMS coil designs, especially for small animals.
Keywords: boundary element fast multipole method; coil inductance; magnetic core; motor threshold; transcranial magnetic stimulation.
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