A model based rule for selecting spiking thresholds in neuron models

Frederik Riis  Mikkelsen

doi:10.3934/mbe.2016008

Article Contents

2016, Volume 13, Issue 3: 569-578. Doi: 10.3934/mbe.2016008

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A model based rule for selecting spiking thresholds in neuron models

Frederik Riis Mikkelsen^1,

1.
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, 2100

Received: February 2015

Revised: November 2015

Published: December 2015

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Abstract

Determining excitability thresholds in neuronal models is of high interest due to its applicability in separating spiking from non-spiking phases of neuronal membrane potential processes. However, excitability thresholds are known to depend on various auxiliary variables, including any conductance or gating variables. Such dependences pose as a double-edged sword; they are natural consequences of the complexity of the model, but proves difficult to apply in practice, since gating variables are rarely measured.
In this paper a technique for finding excitability thresholds, based on the local behaviour of the flow in dynamical systems, is presented. The technique incorporates the dynamics of the auxiliary variables, yet only produces thresholds for the membrane potential. The method is applied to several classical neuron models and the threshold's dependence upon external parameters is studied, along with a general evaluation of the technique.

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Mathematics Subject Classification: Primary: 37C10, 65L05; Secondary: 92C20.

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