Firing responses of bursting neurons with delayed feedback

Abstract

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.

Generalized seizures in a neural field model with bursting dynamics

“…Here we have shown how both network effects and cellular bursting mechanisms are involved in the stereotyped oscillations seen in absence seizures. This broadly agrees with experimental studies on network oscillations coordinating cellular firing activity, while the neurons feed back and enhance the network activity (Wu et al 2011;Steriade and Deschenes 1984;Steriade et al 1993a;Steriade and Contreras 1995). Furthermore, this leads us to argue that bursting dynamics in the reticular nucleus is sufficient for S-W seizures to be observed in the EEG.…”

“…8d where there is a sharp spike followed by a wave that descends to a low φ e value before rising again which reaches a temporary plateau then begins to rapidly form a sharp spike again which reproduces results found previously by Roberts and Robinson (2008). We have previously studied the dynamics of a generic neuronal model driven by delayed feedback from bursting thalamic neurons (Wu et al 2011). Bursting behavior showed response patterns that were dependent on the intrinsic bursting frequency of thalamic neurons and the resonant frequency of the loop delay, thus implying an interplay between cellular and network effects.…”

“…Bursting behavior showed response patterns that were dependent on the intrinsic bursting frequency of thalamic neurons and the resonant frequency of the loop delay, thus implying an interplay between cellular and network effects. Here, we explore parameter changes on the neural field model with bursting dynamics incorporated in a form suitable for mean-field modeling Wu et al 2011;Zhao et al 2015).…”

“…Here, we analyze the corticothalamic dynamics of this extended neural field model to reproduce absence seizures studied under the original neural field model Breakspear et al 2006) while analyzing how bursting dynamics in the reticular nucleus affects such seizures, which links to a previous study of the interplay between network and bursting dynamics (Wu et al 2011). This will also aid in elucidating the heterogeneous nature of S-W discharges and propose hypotheses on their mechanisms.…”

NFTsim: Theory and Simulation of Multiscale Neural Field Dynamics

“…For example, single neuron models abound in neuroscience, and can include a large number of biophysical effects with relatively few approximations. Many such models have also been used to study networks of interconnected neurons with varying degrees of idealization, thereby revealing a huge number of insights [9–11]. However, several key problems arise as network size grows: (i) the computational resources required become prohibitive, meaning that simulations can often only be carried out in physiologically unrealistic scenarios, typically with idealized neurons, which may be quantitatively and/or qualitatively inappropriate for the real brain; (ii) it is increasingly difficult to measure and assign biophysical parameters to the individual neurons—e.g., individual connectivities, synaptic strengths, or morphological features, so large groups of neurons are typically assigned identical parameters, thereby partly removing the specificity of such simulations; (iii) analysis and interpretation of results, such as large collections of timeseries of individual soma voltages, becomes increasingly difficult and demanding on storage and postprocessing; (iv) emergence of collective network-level phenomena can be difficult to recognize; (v) the scales of these simulations are well suited to relate to single-neuron measurements, and microscopic pieces of brain tissue, but are distant from those of noninvasive imaging modalities such as functional magnetic resonance imaging (fMRI), electroencephalography (EEG), and magnetoencephalography (MEG) [12–14], which detect signals that result from the aggregate activity of large numbers of neurons; and (vi), inputs from other parts of the brain are neglected, meaning that such models tend to represent isolated pieces of neural tissue.…”