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Objective. High frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) suppresses excessive beta band (∼13–30 Hz) activity of the motor cortex in Parkinson’s disease (PD). While the mechanisms of action of STN DBS are not well-understood, strong evidence supports a role for cortical network modulating effects elicited by antidromic activation of cortical axons via the hyperdirect pathway. Approach. A spiking model of the thalamo-cortical microcircuit was developed to examine modulation of cortical network activity by antidromic STN DBS, mediated by direct activation of deep pyramidal neurons (PNs) and subsequent indirect activation of other thalamo-cortical structures. Main results. Increasing synaptic coupling strength from cortical granular to superficial layers, from inhibitory neurons to deep PNs, and from thalamus reticular to relay cells, along with thalamocortical connection strength, accompanied by reduced coupling from cortical superficial to granular layers, from thalamus relay cells to reticular neurons, and corticothalamic connection strength, led to increased beta activity and neural synchrony, as observed in PD. High frequency DBS desynchronized correlated neural activity, resulting in clusters of both excited and inhibited deep cortical PNs. The emergence of additional frequency components in the local field potential (LFP), and increased power at subharmonics of the DBS frequency as observed in patients with dyskinesia during DBS, occurred under different stimulus amplitudes and frequencies. While high-frequency (>100 Hz) DBS suppressed the LFP beta power, low-frequency (<40 Hz) DBS increased beta power when more than 10% of PNs were activated, but reduced the total beta power at lower levels of neural activation. Significance. The results suggest a potential mechanism for experimentally observed alterations in cortical neural activity during DBS via the propagation of DBS stimuli throughout the cortical network, modulated by short-term synaptic plasticity, and the emergence of resonance due to interaction of DBS with existing M1 rhythms by engaging feedforward-feedback loops.

Many neurons in the auditory system of the brain must encode amplitude variations of a periodic signal. These neurons under periodic stimulation display rich dynamical states including mode-locking and chaotic responses [1]. Periodic stimuli such as sinusoidal waves and amplitude modulated (AM) sounds can lead to various forms of n:m mode-locked states, similar to the mode-locking phenomenon in a LASER resonance cavity. Obtaining Arnold tongues provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. In this study we obtained the regions of existence of various mode-locked states on the frequency-amplitude plane, which are called Arnold tongues, for Izhikevich neurons (see Figure 1). This study is based on the model for neurons by Izhikevich (2003), which is a reduced model of a Hodgkin-Huxley neuron [2]. This model is much simpler in terms of the dimension of the coupled non-linear differential equations compared to other existing models, but excellent for generating the complex spiking patterns observed in real neurons [3]. Hence we can describe the construction of harmonic and sub-harmonic responses in the early processing stages of the auditory system, such as the auditory nerve and cochlear nucleus. ConclusionDifferent mode-locked regions that are shown in the Arnold tongues diagram are predictors of mode-locking of auditory system neurons to sound, which in turn predict the formation of harmonics and sub-harmonics of the sound in the brain.

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Solving phase equations for systems with high degrees of nonlinearities is cumbersome. However, in the case of two coupled canonical oscillators, that is, a reduced model of translated Wilson–Cowan neuronal dynamics, under slowly varying amplitude and rotating wave approximations, we suggested a convenient way to find their average relative phase evolution. This approach enabled us to find an explicit solution for the average relative phase of the two coupled canonical oscillators based on the original neuronal model parameters, and importantly, to find their phase-locking constraint. This methodology is straightforward to implement in any Wilson–Cowan-type coupled oscillators with applications in gradient frequency neural networks (GFNNs).