Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

Abstract

Effective desynchronization can be exploited as a tool for probing the functional significance of synchronized neural activity underlying perceptual and cognitive processes or as a mild treatment for neurological disorders like Parkinson's disease. In this article we show that pulse-based desynchronization techniques, originally developed for networks of globally coupled oscillators (Kuramoto model), can be adapted to networks of coupled neurons with dendritic dynamics. Compared to the Kuramoto model, the dendritic dynamics significantly alters the response of the neuron to the stimulation. Under medium stimulation amplitude a bistability of the response of a single neuron is observed. When stimulated at some initial phases, the neuron displays only modulations of its firing, whereas at other initial phases it stops oscillating entirely. Significant alterations in the duration of stimulation-induced transients are also observed. These transients endure after the end of the stimulation and cause maximal desynchronization to occur not during the stimulation, but with some delay after the stimulation has been turned off. To account for this delayed desynchronization effect, we have designed a new calibration procedure for finding the stimulation parameters that result in optimal desynchronization. We have also developed a new desynchronization technique by low frequency entrainment. The stimulation techniques originally developed for the Kuramoto model, when using the new calibration procedure, can also be applied to networks with dendritic dynamics. However, the mechanism by which desynchronization is achieved is substantially different than for the network of Kuramoto oscillators. In particular, the addition of dendritic dynamics significantly changes the timing of the stimulation required to obtain desynchronization. We propose desynchronization stimulation for experimental analysis of synchronized neural processes and for the therapy of movement disorders.

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

“…However, they do cite papers related to Parkinson's disease where the Kuramoto model is specifically mentioned. Interestingly, in brain activity studies, the Kuramoto model is playing a quite important role in the study of desynchronisation in the context of pulse based desynchronisation techniques for the treatment of Parkinson's disease [103,122,123]. However, such investigations give no insight about the nature of the initiation of the synchronisation in either epilepsy or Parkinson's disease.…”

“…The utility of the generalisation is acknowledged by Velazquez et al [124], who suggest its application to earlier work on desynchronisation [122]. It is explicitly exploited by Lin and Lin [125] and Ghosh et al [126], who used the generalisation to study neuronal synchronisation in the brain.…”

A review of models used for understanding epileptic seizures

“…A number of authors have examined the utility of the Cumin-Unsworth generalization for the modelling of neuronal activity. The utility of the generalization is acknowledged in Velazquez et al (2007), who suggest its application to earlier work on desynchronization (Majtanik et al, 2006). It is explicitly exploited in Lin and Lin (2009);Ghosh et al (2009), where the generalization is used to study neuronal synchronization in the brain.…”

“…However, they do cite papers related to Parkinson's disease where the Kuramoto model is specifically mentioned. Interestingly, in brain activity studies, the Kuramoto model is playing a quite important role in the study of desynchronization in the context of pulse-based desynchronization techniques for the treatment of Parkinson's disease (Dolan et al, 2005;Majtanik et al, 2006;Moazami-Goudarzi et al, 2008). However, it should be mentioned that such investigations give no insight about the nature of the initiation of the synchronization in either epilepsy or Parkinson's disease.…”

Signal transmission in two-way coupled neural system: system size effect

“…Up to now, nonlinear dynamics of neurons has been studied both experimentally and theoretically as a main topic in neuroscience [21][22][23][24]. Moreover, since neural input is derived from a large number of other neurons, randomlike behavior may occur which might be highly correlated among a piece of neurons [25].…”