A minimally invasive neurostimulation method for controlling abnormal synchronisation in the neuronal activity

Evoked resonant neural activity long-term dynamics can be reproduced by a computational model with vesicle depletion

Subthalamic deep brain stimulation (DBS) robustly generates high-frequency oscillations known as evoked resonant neural activity (ERNA). Recently the importance of ERNA has been demonstrated through its ability to predict the optimal DBS contact in the subthalamic nucleus in patients with Parkinson's disease. However, the underlying mechanisms of ERNA are not well understood, and previous modelling efforts have not managed to reproduce the wealth of published data describing the dynamics of ERNA. Here, we aim to present a minimal model capable of reproducing the characteristics of the slow ERNA dynamics published to date. We make biophysically-motivated modifications to the Kuramoto model and fit its parameters to the slow dynamics of ERNA obtained from data. Our results demonstrate that it is possible to reproduce the slow dynamics of ERNA (over hundreds of seconds) with a single neuronal population, and, crucially, with vesicle depletion as one of the key mechanisms behind the ERNA frequency decay in our model. We further validate the proposed model against experimental data from Parkinson's disease patients, where it captures the variations in ERNA frequency and amplitude in response to variable stimulation frequency, amplitude, and to stimulation pulse bursting. We provide a series of predictions from the model that could be the subject of future studies for further validation.

A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidating how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP and by the lack of low-dimensional description that could provide analytical insights. Phase-difference-dependent plasticity (PDDP) rules approximate STDP in phase oscillator networks, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe part of the phase space for this very high-dimensional system. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multiharmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a family of low-dimensional descriptions based on the mean-field dynamics of each cluster and average coupling weights between and within clusters. Finally, we show that such a two-cluster mean-field model can be fitted to synthetic data to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step toward a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.

Coupled and Synchronization Models of Rhythmic Arm Movement in Planar Plane

Nonlinear dynamics have become a new perspective on model human movement variability; however, it is still a debate whether chaotic behavior is indeed possible to present during a rhythmic movement. This paper reports on the nonlinear dynamical behavior of coupled and synchronization models of a planar rhythmic arm movement. Two coupling schemes between a planar arm and an extended Duffing-Van der Pol (DVP) oscillator are investigated. Chaos tools, namely phase space, Poincare section, Lyapunov Exponent (LE), and heuristic approach are applied to observe the dynamical behavior of orbit solutions. For the synchronization, an orientation angle is modeled as a single well DVP oscillator implementing a Proportional Derivative (PD)-scheme. The extended DVP oscillator is used as a drive system, while the orientation angle of the planar arm is a response system. The results show that the coupled system exhibits very rich dynamical behavior where a variety of solutions from periodic, quasi-periodic, to chaotic orbits exist. An advanced coupling scheme is necessary to yield the route to chaos. By modeling the orientation angle as the single well DVP oscillator, which can synchronize with other dynamical systems, the synchronization can be achieved through the PD-scheme approach.

Dependence of Working Memory on Coordinated Activity Across Brain Areas

Neural signatures of working memory (WM) have been reported in numerous brain areas, suggesting a distributed neural substrate for memory maintenance. In the current manuscript we provide an updated review of the literature focusing on intracranial neurophysiological recordings during WM in primates. Such signatures of WM include changes in firing rate or local oscillatory power within an area, along with measures of coordinated activity between areas based on synchronization between oscillations. In comparing the ability of various neural signatures in any brain area to predict behavioral performance, we observe that synchrony between areas is more frequently and robustly correlated with WM performance than any of the within-area neural signatures. We further review the evidence for alteration of inter-areal synchrony in brain disorders, consistent with an important role for such synchrony during behavior. Additionally, results of causal studies indicate that manipulating synchrony across areas is especially effective at influencing WM task performance. Each of these lines of research supports the critical role of inter-areal synchrony in WM. Finally, we propose a framework for interactions between prefrontal and sensory areas during WM, incorporating a range of experimental findings and offering an explanation for the observed link between intra-areal measures and WM performance.

Role of modularity in self-organization dynamics in biological networks

Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting structure between different neurons, proteins, or species influences the functioning of their respective systems. It is well established that many biological networks are constructed in a highly hierarchical way with two main properties: short average paths that join two apparently distant nodes (neuronal, species, or protein patches) and a high proportion of nodes in modular aggregations. Although several hypotheses have been proposed so far, still little is known about the relation of the modules with the dynamical activity in such biological systems. Here we show that network modularity is a key ingredient for the formation of self-organizing patterns of functional activity, independently of the topological peculiarities of the structure of the modules. In particular, we propose a self-organizing mechanism which explains the formation of macroscopic spatial patterns, which are homogeneous within modules. This may explain how spontaneous order in biological networks follows their modular structural organization. We test our results on real-world networks to confirm the important role of modularity in creating macroscale patterns.

Natural rhythms of periodic temporal attention

That attention is a fundamentally rhythmic process has recently received abundant empirical evidence. The essence of temporal attention, however, is to flexibly focus in time. Whether this function is constrained by an underlying rhythmic neural mechanism is unknown. In six interrelated experiments, we behaviourally quantify the sampling capacities of periodic temporal attention during auditory or visual perception. We reveal the presence of limited attentional capacities, with an optimal sampling rate of ~1.4 Hz in audition and ~0.7 Hz in vision. Investigating the motor contribution to temporal attention, we show that it scales with motor rhythmic precision, maximal at ~1.7 Hz. Critically, motor modulation is beneficial to auditory but detrimental to visual temporal attention. These results are captured by a computational model of coupled oscillators, that reveals the underlying structural constraints governing the temporal alignment between motor and attention fluctuations.