Neural stimulation with magnetic fields: analysis of induced electric fields

Spatial distributions of the derivative of the electric field induced in a planar semi-infinite tissue model by various current-carrying coils and their utility in neural stimulation are evaluated. Analytical expressions are obtained for the electric field and its spatial derivatives produced by an infinitely short current element. Fields and their derivatives for an arbitrarily shaped coil are then obtained by numerical summation of contributions from all the elements forming the coil. The simplicity of the solution and a very short computation time make this method particularly attractive for gaining a physical insight into the spatial behavior of the stimulating parameter and for the optimization of coils. Such analysis is useful as the first step before undertaking a more complex numerical analysis of a model more closely representing the tissue geometry and heterogeneity.