SIMPLIFIED ANALYTICAL SOLUTIONS FOR MAGNETIC SIMULATION OF NEURONS

Abstract

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 spaces quadruple square and three-dimensional coils are preferred. Analyses described are useful in evaluating various options, gaining an insight into the physical phenomena involved, and as the first step before undertaking a numerical analysis of models more closely representing the tissue electrical and geometrical complexities. [Vol. 7, No. 2, pp. 162-178 (1992), Special Issue on Bioelectromagnetic Computations]