Optimization of coil design for neuronal excitation by magnetic stimulation

A theoretical basis for optimizing a magnetic coil for neural stimulation is presented. The coil length, upper outer radius, lower outer radius, wire size and position are optimized to produce the largest transfer of charge across a neural membrane. Charge transfer is shown to be proportional to the maximum current passed through the coil and dependent on the spatial derivative of the electric field induced in the conducting medium. Although no single coil is found to be optimal, discriminant analysis applied to a population of coils indicates that charge transfer is maximized for conically shaped coils (larger base near the conducting region)