Internal inconsistencies in models of electrical stimulation in neural tissue

Calculating the membrane potential of a neurite under extracellular electrical stimulation is important in the design of some recent stimulation strategies for neuroprosthetic devices including retinal implants, cochlear implants, deep brain stimulation. A common approach, widely used in the electrical stimulation literature uses a volume conductor model to calculate the electrical potential in the tissue and then extracts the voltage or current density on the surface of a neuron, which is used as input to the cable equation to calculate the neuron's response. However this approach ignores the effect of the neuron itself as well as surrounding neurons on the extracellular potential. Here we highlight that this leads to an internal inconsistency in the overall model because the result depends on whether the voltage or current density is used to calculate the neural response. The magnitude of this discrepancy is calculated for the example of a point source electrode in a homogeneous medium and is shown to be up to several hundred percent under some stimulus conditions. The inconsistency can be resolved by ensuring that the voltage is related to the current density by the transimpedance of the neurite. Deriving a volume conductor model that satisfies this relationship requires further work.