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

Abstract

The study presents the development of an alternative noise current term and novel voltage dependent current noise algorithm for conductance based stochastic auditory nerve fibre (ANF) models. ANFs are known to have significant variance in threshold stimulus which affects temporal characteristics such as latency. This variance is primarily caused by the stochastic behaviour or microscopic fluctuations of the node of Ranvier's voltage dependent sodium channels of which the intensity is a function of membrane voltage. Though easy to implement and low in computational cost, existing current noise models have two deficiencies: it is independent of membrane voltage and it is unable to inherently determine the noise intensity required to produce in vivo measured discharge probability functions. The proposed algorithm overcomes these deficiencies whilst maintaining its low computational cost and ease of implementation compared to other conductance and Markovian based stochastic models. The algorithm is applied to a Hodgkin-Huxley based compartmental cat ANF model and validated via comparison of the threshold probability and latency distributions to measured cat ANF data. Simulation results show the algorithm's adherence to in vivo stochastic fibre characteristics such as an exponential relationship between the membrane noise and transmembrane voltage, a negative linear relationship between the log of the relative spread of the discharge probability and the log of the fibre diameter and a decrease in latency with an increase in stimulus intensity.

Analysis of a purely conductance-based stochastic nerve fibre model as applied to compound models of populations of human auditory nerve fibres used in cochlear implant simulations

“…the auditory nerve properties through neural modelling (Badenhorst et al 2016;Bruce et al 1999b;Hanekom and Hanekom 2016;Macherey et al 2007;Rattay et al 2001a;Rattay et al 2001b;Smit et al 2010;van Gendt et al 2016), ii.…”

“…This threshold variance has been shown to be primarily caused by the stochastic behaviour or microscopic fluctuations of the node of Ranvier's voltage dependent sodium channels (Hales et al 2004;Rubinstein 1995;Sigworth 1980) of which the intensity is a function of the membrane voltage (Verveen and Derksen 1968). A number of methods are followed to model the threshold variability in phenomenological (Bruce et al 1999a;1999b;Macherey et al 2007), in conductance-based (Badenhorst et al 2016;Dangerfield et al 2010;Huang et al 2013;Imennov and Rubinstein 2009;O'Brien 2016;Rattay et al 2001b;Rubinstein 1995) and most recently in hybrid biophysical-phenomenological based (van Gendt et al 2016;van Gendt et al 2017) stochastic models. The majority of purely conductance-based stochastic models are applied on a single node of Ranvier due to their high computational cost compared to phenomenological and hybrid models which are easily applied to full length fibres.…”

“…(Intra-user comparison, for the purpose of this study, is defined as comparing the predictions of a user's deterministic model with the same user's stochastic model as opposed to comparing it to other users' predictions (inter-user comparison)) Therefore, of the three types of purely conductance-based stochastic models identified and reviewed by , a current noise method is used in this study due to it having the lowest computational cost for this initial investigation. The particular current noise method used is the voltage dependent current noise term and algorithm presented in Badenhorst et al (2016) which has been shown to adhere to the measured stochastic fibre characteristics of a negative linear log(Relative Spread) vs log(diameter) distribution and the exponential distribution of the standard deviation of membrane noise (Vrms) versus transmembrane voltage (Vmem) (Verveen 1962;Verveen and Derksen 1968). Relative spread (RS) is defined as the standard deviation (σ) of the discharge probability function (DPF), also referred to as the threshold region width or spread, divided by the 50% discharge probability stimulus intensity (μ) of the DPF, a.k.a.…”

“…the stochastic threshold (Rubinstein 1995;Verveen 1962). By keeping the stochastic model purely conductance-based, the origin of the stochasticity remains an inherent part of the ANF model through the membrane voltage (Verveen and Derksen 1968) and through the nodal surface area (via fibre diameter and nodal length), which accounts for the effect of the number of sodium channels per node on the noise magnitude (Badenhorst et al 2016;Rubinstein 1995).…”

“…This article presents the application of a purely conductance-based stochastic nerve fibre model (Badenhorst et al 2016) to a human ANF in a VC model of a semi-generic head and user-specific cochlea for four users. Section 2 provides the methodology in terms of the ANF morphology, VC modelling used, a brief overview of the stochastic conductance-based computational ANF model, creation of fibre population models and the validation criteria and procedures.…”