A time domain finite element model of extracellular neural stimulation predicts that non-rectangular stimulus waveforms may offer safety benefits

Abstract

Efforts to understand and model the process of extracellular neural electric stimulation have been driven by the desire to intelligently design neural prostheses in order to minimize tissue damage and to maximize the success for stimulating targeted neural structures. Tissue damage and electrode corrosion have been associated with high charge density, which is the integral of the current density passing through the electrode surface over the duration of the stimulus. Importantly, the current density distribution on the surface of stimulating electrodes can be extremely nonuniform, especially when high voltages or frequencies cause a decrease in the electrode-electrolyte impedance. Large current densities are found locally in regions of high curvature, such as the edge of a disk electrode or the tip of a conical electrode. We use a time domain finite element model of a platinum disk electrode and a simplified retinal ganglion cell to explore the potential for Gaussian and sinusoidal voltage-controlled stimulus waveforms to reduce the nonuniformity of the current densities on the electrode surface while maintaining stimulation efficacy. We model an overpotential-dependent electrode-electrolyte interfacial impedance consistent with the platinum-saline interface. An excitable cell membrane is incorporated using the Fohlmeister-Coleman-Miller model of a retinal ganglion cell. Both the electrode-electrolyte interface and the cell membrane were incorporated into the finite element model using a thin layer approximation. All simulations were performed in the COMSOL Multiphysics modeling environment. Rectangular stimulus waveforms were compared to waveforms of Gaussian and sinusoidal shapes. The results suggest that Gaussian and Sinusoidal waveforms may significantly decrease the nonuniformity of the current density distribution while retaining stimulation efficacy.