Modeling current-distance effects on microstimulation sensitivity

Direct brain stimulation is used to provide artificial sensory percepts after injury to natural sensory pathways. The threshold current for neuronal activation strongly increases with neuron distance from the stimulating electrode. We hypothesized that this current-distance relationship could make perceptual thresholds susceptible to substantial variability if percepts are based on integrating the activity within very small ( $< 50$ neuron) populations, as has been shown to be the case in recent work on natural sensory encoding. To test this hypothesis, we used a computational model to study current-distance effects on perceptual thresholds. We assumed population spike count was the decision variable that a downstream observer used for stimulus detection and discrimination. We derived exact decision probabilities for an ideal observer integrating the stimulus-evoked activity within any size neuronal population. A bootstrap procedure, in which neuron distances to the stimulating electrode were randomly shuffled, was used to estimate the coefficient of variation (CV) of detection and discrimination thresholds as a function of population size. As hypothesized, the dispersion of thresholds was inversely related to the population size. For 20-neuron populations previously shown to be sufficient for natural sensory encoding, the current-distance effects on detection and discrimination thresholds were substantial, with a CV of 20% and 10% respectively. The results aid interpretation of experimental studies of stimulation sensitivity, where electrode instability could produce high perceptual threshold variance in susceptible sparse encoding populations.