Studying the magnetic stimulation of nervous tissues: A calculation framework to investigate stimulation areas

The electromagnetic stimulation of nervous tissue has represented an alternative to electrical stimulation since the 1980s. The growing number of potential applications has led to an increasing interest in the development of modeling tools that can help the design of novel electromagnetic stimulators. In this context, the aim of this paper is to provide a versatile calculation framework to investigate the properties of the electric field generated by a plurality of miniature coils, arranged in cuff configuration. Furthermore, the capability of the miniature coils to elicit a neuronal response in specific portions of the (peripheral) nerve will be investigated. Starting from Jefimenko's equations, a model was implemented in MATLAB. It calculates the electromagnetic field induced by coils, with arbitrary shape and spatial orientation, and the activating function around the coils through simple numerical integration. By studying the activating functions, it is possible to determine where the neurons can be excited. The model was validated by comparison with FEM simulations. A dimensional analysis was conducted to compare in terms of shape and depth of the stimulation volumes different coil geometries, regardless of design parameters such as current, number of turns and coil sizes.The dimensionless groups identified according to Buckingham's theorem provide a direct estimate of the stimulation depth reached within the nerve.The calculation tools developed in this paper can be used in the design of coils to quickly compare different geometries and spatial distribution of coils in order to identify the optimal configurations for the specific application addressed by the designer.