A stochastic model of the electrically stimulated auditory nerve: single-pulse response

Abstract

Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.

Development of a voltage-dependent current noise algorithm for conductance-based stochastic modelling of auditory nerve fibres

“…Considering first the unmyelinated pre-somatic region and soma of the human ANF, it has been noted before that an increase in diameter or surface area of an unmyelinated, active node will cause the node to become less stochastic or "noisy" as the significance of a single sodium channel decreases compared to the total ionic conductance (Bruce et al 1999b;Rubinstein 1995). Both the proposed current noise term in Eq.…”

“…Nodal and compartmental lengths were kept unchanged and constant. Rattay et al (2001b) A bi-phasic, cathodic first stimulation with a 100 μs pulse width using a single monopolar point electrode in an infinite homogeneous medium (ρ e = 0.3 kΩ•cm) was applied at a model temperature of 38°C (Bruce et al 1999b;Rubinstein 1995;Shepherd and Javel 1997). The electrode was positioned 99 μm above node 2 of the straight ANF with d axon = 1.81 μm and d dend = 1.02 μm to obtain a deterministic threshold of 60 dB (re 1 µA) which is within the range of stochastic thresholds measured by Shepherd and Javel (1997).…”

“…The modelled ESNRs are used to improve our understanding of the auditory nerve properties, the percepts produced by the CI and the wide variance in performance among CI users. An improved understanding in turn allows for improved stimulation strategies and CI designs so as to ultimately improve the sound perception of the CI user (Bruce et al 1999b;Frijns et al 2001;Frijns et al 1995;Macherey et al 2007;Rattay 1989;Rattay et al 2001a;Rattay et al 2001b).…”

“…The intensity of these microscopic fluctuations, also referred to as membrane noise, in turn has been shown to be a function of membrane voltage (Verveen and Derksen 1968). Numerous approaches are followed to account for the threshold variability in both conductance based (Dangerfield et al 2012;Goldwyn and SheaBrown 2011;Huang et al 2013;Rattay et al 2001b;Rubinstein 1995) and phenomenological (Bruce et al 1999a;1999b;Macherey et al 2007) stochastic models. The present study focusses on conductance based models and in particular the Hodgkin-Huxley (HH) model since only these models provide biophysically meaningful results (Izhikevich 2004) as required in the study and modelling of CIs (Rattay et al 2001b).…”

“…This inverse proportionality results in the fibre's discharge probability becoming more deterministic as A increases and subsequently RS decreases such that log(RS) vs log(A) has a negative linear relationship (Rubinstein 1995;Verveen 1962). The decrease in RS as a result of the increase in the DPF gradient can also be viewed from the perspective that as the fibre diameter increases, and consequently the number of channels on a Ranvier node, the voltage fluctuation caused by a single channel becomes less significant when compared to the total ionic conductance and thus the fibre becomes less stochastic or less "noisy" (Bruce et al 1999b;Rubinstein 1995). On a macro ANF scale, this results in the ANF becoming less stochastic or more deterministic (increased DPF gradient) as the diameter increases as found by Verveen (1962).…”