Neural rate equations for bursting dynamics derived from conductance-based equations

Robinson, P. A.; Wu, Huiying; Kim, J.W.

doi:10.1016/j.jtbi.2007.10.020

Cited by 25 publications

(33 citation statements)

References 25 publications

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“…We base this work upon the well-documented mean-field theory of Robinson and co-workers [40,39,7,37]. Rather than modeling individual neurons, we consider averaging properties over local groups of neurons.…”

Section: Methodsmentioning

confidence: 99%

“…However, the model is generalizable to spatially varying states [11]. The model of reference [37] includes feedback delayed in time as a simple model of a thalamocortical loop. For the purposes of simplifying the analysis, we do not consider this here, and confine ourselves to intra-cortical interactions only.…”

Section: Methodsmentioning

confidence: 99%

“…Table 1 gives a list of standard parameters chosen for this modelling. Values for the mean-field cortical modelling have been chosen drawing from references [38,39,37,11,45,46], with smaller rates being used for α B and β B to model the long timescale GABA B inhibitory post-synaptic potentials [32,34]. Values for the STDP have been chosen with reference to [1] and [11].…”

Section: Interpretation In Fourier Domainmentioning

confidence: 99%

“…Neural behaviour is modelled in terms of average firing rates and axonal flux rates of populations of neurons, rather than in terms of the behaviours of individual neurons [51,30,9,19,40,4,46,7,37,52]. This approach is particularly suited to the modelling of large-scale measures of brain activity, such as the electroencephalogram (EEG), which involve the sampling of many neurons.…”

Section: Introductionmentioning

confidence: 99%

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Numerical modelling of plasticity induced by transcranial magnetic stimulation

et al. 2013

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We use neural field theory and spike-timing dependent plasticity to make a simple but biophysically reasonable model of long-term plasticity changes in the cortex due to transcranial magnetic stimulation (TMS). We show how common TMS protocols can be captured and studied within existing neural field theory. Specifically, we look at repetitive TMS protocols such as theta burst stimulation and paired-pulse protocols. Continuous repetitive protocols result mostly in depression, but intermittent repetitive protocols in potentiation. A paired pulse protocol results in depression at short (<∼ 10 ms) and long (>∼ 100 ms) interstimulus intervals, but potentiation for mid-range intervals. The model is sensitive to the choice of neural populations that are driven by the TMS pulses, and to the parameters that describe plasticity, which may aid interpretation of the high variability in existing experimental results. Driving excitatory populations results in greater plasticity changes than driving inhibitory populations. Modelling also shows the merit in optimizing a TMS protocol based on an individual's electroencephalogram. Moreover, the model can be used to make predictions about protocols that may lead to improvements in repetitive TMS outcomes.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Interpretation In Fourier Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical modelling of plasticity induced by transcranial magnetic stimulation

et al. 2013

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“…Other possible explanations could include individual cortical neurons being slaves to an oscillation elsewhere in the brain, or a hybrid of collective and individual neuron modes. For example, Robinson et al have modelled the bursting of neocortical neurons using a model based on two coupled oscillators [17]. One oscillator describes the spiking dynamics of a neuron; the second generates a slow modulation from biophysical conductance-based equations.…”

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confidence: 99%

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia

et al. 2009

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We study the dynamics of the transition between the low-and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that the trajectory of a typical transition takes an approximately exponential form, equivalent to the response of a resistor-capacitor circuit to a step-change in input. The time constant for the transition is negatively correlated with the membrane potential of the lowfiring state, and values are broadly equivalent to neural time constants measured elsewhere. Overall, the results do not strongly support the hypothesis of a bistability in cortical neurons; rather, they suggest the cortical manifestation of the oscillation is a result of a step-change in input to the cortical neurons. Since there is evidence from previous work that a phase transition exists, we speculate that the step-change may be a result of a bistability within other brain areas, such as the thalamus, or a bistability among only a small subset of cortical neurons, or as a result of more complicated brain dynamics.

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