Firing pattern of bursting neurons under sinusoidal drive in mean-field modeling

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

doi:10.1016/j.jtbi.2009.03.022

Cited by 3 publications

(6 citation statements)

References 31 publications

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“…The model is compact, but retains the two key features of (i) multiscale mean-field modeling of the brain (e.g., corticothalamic neural populations, see Robinson et al 2003b) and (ii) conductance-based single neuron modeling (e.g., multiple ion channels, see Wilson 1999a, b) Similar model approaches, but not having a delay-loop structure, have been studied to reproduce key features of neural firing patterns recently (Robinson et al 2007;Wu et al 2009). In order to isolate the key effects of the delay loop, we make a minimal modification to this compact model, as seen in Fig.…”

Section: Theorymentioning

confidence: 99%

“…The activity of the population s is simulated by employing a prototype mean-field model (Wu et al 2009). In the previous study, a set of neural rate equations was derived from a conductance-based model (Robinson et al 2007) and incorporated into a mean-field model (Robinson 2005;Robinson et al 1997Robinson et al , 2002Robinson et al , 2003a.…”

Section: Theorymentioning

confidence: 99%

“…When the transmembrane potential reaches the firing threshold, the neurons start firing, and such firing leads to a generation of new pulse fields. With modulations of the firing threshold, the previous model generates bursting in a complex manner (Robinson et al 2007;Wu et al 2009). …”

Section: Theorymentioning

confidence: 99%

“…We thus consider only two special cases for our analysis. First, the case of ν sx = 0 (i.e., no feedback loop) was already studied and it was shown that the model can show limit cycles that depend on the baseline voltage V 0 (Wu et al 2009). For the given V 0 = 15.24 mV, the dominant response frequencies f B are f B 0 = 3.8 Hz and its hormonics.…”

Section: Linear Stability Analysis Of the Modelmentioning

confidence: 99%

“…In contrast, continuum or mean-field models describe the net behavior of populations of neurons, which enables large scale activities to be modeled (Lopes da Silva et al 1974;Nunez 1974;Wright and Liley 1996;Robinson et al 1997;Robinson 2005;Deco et al 2008). In particular, neural rate equations for bursting neurons were derived from a conductance-based model (Robinson et al 2007) and used to develop a prototype mean-field bursting model (Wu et al 2009). The model is capable of producing regular bursting at a population level.…”

Section: Introductionmentioning

confidence: 99%

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Firing responses of bursting neurons with delayed feedback

Robinson

Kim

2010

J Comput Neurosci

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Thalamic neurons, which play important roles in the genesis of rhythmic activities of the brain, show various bursting behaviors, particularly modulated by complex thalamocortical feedback via cortical neurons. As a first step to explore this complex neural system and focus on the effects of the feedback on the bursting behavior, a simple loop structure delayed in time and scaled by a coupling strength is added to a recent mean-field model of bursting neurons. Depending on the coupling strength and delay time, the modeled neurons show two distinct response patterns: one entrained to the unperturbed bursting frequency of the neurons and one entrained to the resonant frequency of the loop structure. Transitions between these two patterns are explored in the model's parameter space via extensive numerical simulations. It is found that at a fixed loop delay, there is a critical coupling strength at which the dominant response frequency switches from the unperturbed bursting frequency to the loop-induced one. Furthermore, alternating occurrence of these two response frequencies is observed when the delay varies at fixed coupling strength. The results demonstrate that bursting is coupled with feedback to yield new dynamics, which will provide insights into such effects in more complex neural systems.

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Section: Theorymentioning

confidence: 99%