Simplified analytical solutions for magnetic stimulation of neurons

Karu P. Esselle*, Maria A. Stuchly

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Strong pulses of magnetic field are used to stimulate peripheral nerves and motor neurons in the cerebral cortex. Such stimulation is used in neurology for numerous diagnostic purposes. The electric field induced in tissue along the neuron and its spatial derivative are the parameters determining neural response. Another important parameter influencing the efficiency of stimulation is the inductance of a coil producing the magnetic field, as it defines the current time derivative for a given pulse generator. For arbitrarily located coils of arbitrary shapes, a semi-analytical solution is presented to calculate spatial distributions of the electric field and its spatial derivatives in a semi-infinite tissue model. Analytical solutions are given for coils composed of linear segments parallel or perpendicular to the air-tissue interface. Expressions for inductance of coils having suitable geometries for neural stimulation are derived. Coils can be optimized for stimulation of nerves at given orientation and distance from the air-tissue interface. In the optimization, coil dimensions and shape are considered as they affect both the induced field and inductance. A quadruple coil consisting of triangular sections appears to offer some advantages over other shapes for stimulation of shallow nerves. For deep nerves spaced quadruple square and three-dimensional coils are preferred.

Original languageEnglish
Pages (from-to)162-178
Number of pages17
JournalApplied Computational Electromagnetics Society Journal
Issue number2
Publication statusPublished - Dec 1992
Externally publishedYes


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