A simple model considering spiking probability during extracellular axon stimulation.

The spiking probability of an electrically stimulated axon as a function of stimulus amplitude increases in a sigmoidal dependency from 0 to 1. However, most computer simulation studies for neuroprosthetic applications calculate thresholds for neural targets with a deterministic model and by reducing the sigmoid curve to a step function, they miss an important information about the control signal, namely how the spiking efficiency increases with stimulus intensity. Here, this spiking efficiency is taken into account in a compartment model of the Hodgkin Huxley type where a noise current is added in every compartment with an active membrane. A key parameter of the model is a common factor knoise which defines the ion current fluctuations across the cell membrane for every compartment by its maximum sodium ion conductance. In the standard model Gaussian signals are changed every 2.5 µs as a compromise of accuracy and computational costs. Additionally, a formula for other noise transmission times is presented and numerically tested. Spiking probability as a function of stimulus intensity can be approximated by the cumulative distribution function of the normal distribution with RS = σ/µ. Relative spread RS, introduced by Verveen, is a measure for the spread (normalized by the threshold intensity µ), that decreases inversely with axon diameter. Dynamic range, a related measure used in neuroprosthetic studies, defines the intensity range between 10% and 90% spiking probability. We show that (i) the dynamic range normalized by threshold is 2.56 times RS, (ii) RS increases with electrode-axon distance and (iii) we present knoise values for myelinated and unmyelinated axon models in agreement with recoded RS data. The presented method is applicable for other membrane models and can be extended to whole neurons that are described by multi-compartment models.

Impact of electrode position on the dynamic range of a human auditory nerve fiber.

Objective. Electrodes of a cochlear implant generate spikes in auditory nerve fibers (ANFs). While the insertion depth of each of the electrodes is linked to a frequency section of the acoustic signal, the amplitude of the stimulating pulses controls the loudness of the related frequency band. However, in comparison to acoustic stimulation the dynamic range (DR) of an electrically stimulated ANF is quite small.Approach. The DR of an electrically stimulated ANF is defined as the interval of stimulus amplitudes that causes firing probabilities between 10% and 90%. A compartment model that includes sodium ion current fluctuations as the stochastic key component for spiking was evaluated for different electrode placements and fiber diameters.Main results. The DR is reversely related to ANF diameter. An increased DR is expected to improve the quality of auditory perception for CI users. Electrodes are often placed as close to the center axis of the cochlea as possible. The analysis of the simulated auditory nerve firing showed that this placement is disadvantageous for the DR of a selected ANF.Significance. Five times larger DRs are expected for electrodes close to the terminal of the dendrite or at mid-dendritic placement as opposed to electrodes close to the modiolus.