Modeling extracellular electrical neural stimulation: from basic understanding to MEA-based applications

Extracellular electrical stimulation of neural networks has been widely used empirically for decades with individual electrodes. Since recently, microtechnology provides advanced systems with high-density microelectrode arrays (MEAs). Taking the most of these devices for fundamental goals or developing neural prosthesis requires a good knowledge of the mechanisms underlying electrical stimulation. Here, we review modeling approaches used to determine (1) the electric potential field created by a stimulation and (2) the response of an excitable cell to an applied field. Computation of the potential field requires solving the Poisson equation. While this can be performed analytically in simple electrode-neuron configurations, numerical models are required for realistic geometries. In these models, special care must be taken to model the potential drop at the electrode/tissue interface using appropriate boundary conditions. The neural response to the field can then be calculated using compartmentalized cell models, by solving a cable equation, the source term of which (called activating function) is proportional to the second derivative of the extracellular field along the neural arborization. Analytical and numerical solutions to this equation are first presented. Then, we discuss the use of approximated solutions to intuitively predict the neuronal response: Either the "activating function" or the "mirror estimate", depending on the pulse duration and the cell space constant. Finally, we address the design of optimal electrode configurations allowing the selective activation of neurons near each stimulation site. This can be achieved using either multipolar configurations, or the "ground surface" configuration, which can be easily integrated in high-density MEAs. Overall, models highlighting the mechanisms of electrical microstimulation and improving stimulating devices should help understanding the influence of extracellular fields on neural elements and developing optimized neural prostheses for rehabilitation.