A model based rule for selecting spiking thresholds in neuron models

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 o...

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Main Author: Frederik Riis Mikkelsen
Format: Article
Language:English
Published: AIMS Press 2015-12-01
Series:Mathematical Biosciences and Engineering
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2016008
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author Frederik Riis Mikkelsen
author_facet Frederik Riis Mikkelsen
author_sort Frederik Riis Mikkelsen
collection DOAJ
description 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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spelling doaj-art-5118fe328e7c479895384e66f18842842025-01-24T02:35:23ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-12-0113356957810.3934/mbe.2016008A model based rule for selecting spiking thresholds in neuron modelsFrederik Riis Mikkelsen0Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, 2100Determining 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.https://www.aimspress.com/article/doi/10.3934/mbe.2016008spikinghodgkin-huxleyneuron modellingexcitabilitythreshold selection.dynamical systems
spellingShingle Frederik Riis Mikkelsen
A model based rule for selecting spiking thresholds in neuron models
Mathematical Biosciences and Engineering
spiking
hodgkin-huxley
neuron modelling
excitability
threshold selection.
dynamical systems
title A model based rule for selecting spiking thresholds in neuron models
title_full A model based rule for selecting spiking thresholds in neuron models
title_fullStr A model based rule for selecting spiking thresholds in neuron models
title_full_unstemmed A model based rule for selecting spiking thresholds in neuron models
title_short A model based rule for selecting spiking thresholds in neuron models
title_sort model based rule for selecting spiking thresholds in neuron models
topic spiking
hodgkin-huxley
neuron modelling
excitability
threshold selection.
dynamical systems
url https://www.aimspress.com/article/doi/10.3934/mbe.2016008
work_keys_str_mv AT frederikriismikkelsen amodelbasedruleforselectingspikingthresholdsinneuronmodels
AT frederikriismikkelsen modelbasedruleforselectingspikingthresholdsinneuronmodels