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.
Citation: Frederik Riis Mikkelsen. A model based rule for selecting spiking thresholds in neuron models[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 569-578. doi: 10.3934/mbe.2016008
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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.
References
|
[1]
|
Lect. Notes Phys., 368 (1990), p5.
|
|
[2]
|
J. Physiol., 213 (1971), 31-53.
|
|
[3]
|
Computational Neuroscience, MIT Press, Cambridge, MA, 2001.
|
|
[4]
|
J. Math. Biol., 67 (2012), 989-1017.
|
|
[5]
|
J. Math. Biol., 67 (2013), 239-259.
|
|
[6]
|
Biophys. J., 1 (1961), 445-466.
|
|
[7]
|
Int. J. Bifurcat. Chaos, 16 (2006), 887-910.
|
|
[8]
|
J. Physiol., 117 (1952), 500-544.
|
|
[9]
|
The MIT Press, 2007.
|
|
[10]
|
Biol. Cybern., 66 (1992), p381.
|
|
[11]
|
Biofizika, 18 (1973), p506.
|
|
[12]
|
Biol. Cybern., 67 (1992), 461-468.
|
|
[13]
|
Biophys. J., 35 (1981), 193-213.
|
|
[14]
|
Proc. IRE, 50 (1962), 2061-2070.
|
|
[15]
|
J. Phys. Soc. Jpn., 41 (1976), 1815-1816.
|
|
[16]
|
Phil. Trans. R Soc. Lond. A, 337 (1991), 275-289.
|
|
[17]
|
3rd edition, Texts in Applied Mathematics, 7, Springer, 2000.
|
|
[18]
|
PLoS Comput. Biol., 6 (2010), e1000850, 16 pp.
|
|
[19]
|
IEEE T. Bio. Med. Eng., 51 (2004), 1665-1672.
|
|
[20]
|
Phys. Rev. E, 90 (2014), 022701.
|
|
[21]
|
in Nonautonomous Dynamical Systems in the Life Sciences, Lecture Nones in Math., 2102, Springer, 2013, 89-132.
|
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