Optimal geometry toward uniform current density electrodes

Electrodes are commonly used to inject current into the human body in various biomedical applications such as functional electrical stimulation, defibrillation, electrosurgery, RF ablation, impedance imaging, and so on. When a highly conducting electrode makes direct contact with biological tissues, the induced current density has strong singularity along the periphery of the electrode, which may cause painful sensation or burn. Especially in impedance imaging methods such as the magnetic resonance electrical impedance tomography, we should avoid such singularity since more uniform current density underneath a current-injection electrode is desirable. In this paper, we study an optimal geometry of a recessed electrode to produce a well-distributed current density on the contact area under the electrode. We investigate the geometry of the electrode surface to minimize the edge singularity and produce nearly uniform current density on the contact area. We propose a mathematical framework for the uniform current density electrode and its optimal geometry. The theoretical results are supported by numerical simulations.