Effective desynchronization with bipolar double-pulse stimulation

Optimal phase-selective entrainment of electrochemical oscillators with different phase response curves

We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.

Data-driven control of oscillator networks with population-level measurement

Controlling complex networks of nonlinear limit-cycle oscillators is an important problem pertinent to various applications in engineering and natural sciences. While in recent years the control of oscillator populations with comprehensive biophysical models or simplified models, e.g., phase models, has seen notable advances, learning appropriate controls directly from data without prior model assumptions or pre-existing data remains a challenging and less developed area of research. In this paper, we address this problem by leveraging the network's current dynamics to iteratively learn an appropriate control online without constructing a global model of the system. We illustrate through a range of numerical simulations that the proposed technique can effectively regulate synchrony in various oscillator networks after a small number of trials using only one input and one noisy population-level output measurement. We provide a theoretical analysis of our approach, illustrate its robustness to system variations, and compare its performance with existing model-based and data-driven approaches.

Feedback control of collective dynamics in an oscillator population with time-dependent connectivity

We present a numerical study of pulsatile feedback-based control of synchrony level in a highly-interconnected oscillatory network. We focus on a nontrivial case when the system is close to the synchronization transition point and exhibits collective rhythm with strong amplitude modulation. We pay special attention to technical but essential steps like causal real-time extraction of the signal of interest from a noisy measurement and estimation of instantaneous phase and amplitude. The feedback loop's parameters are tuned automatically to suppress synchrony. Though the study is motivated by neuroscience, the results are relevant to controlling oscillatory activity in ensembles of various natures and, thus, to the rapidly developing field of network physiology.

Suppression and frequency control of repetitive spiking in the FitzHugh-Nagumo model

The FitzHugh-Nagumo equation is a simple model equation that exhibits spiking. The output signal of a neuron is represented in the spiking frequency or firing rate. We consider a few control methods for spiking from the viewpoint of nonlinear dynamics. The repetitive spiking can be suppressed in the FitzHugh-Nagumo model by the periodic sinusoidal force with high frequency. We study the transition to the suppressed state numerically and perform a linear stability analysis to understand the suppression of the spiking. Next, we study coupled FitzHugh-Nagumo equations. We find that the periodic forcing makes the system chaotic, and the desynchronization induced by chaos weakens the total output of spiking in a certain parameter range. Finally, we propose a method of feedback control for the spiking frequency. We can get the desired spiking and bursting frequency using this feedback control. The feedback control method is analyzed using a mapping for the input.

Controlling pallidal oscillations in real-time in Parkinson's disease using evoked interference deep brain stimulation (eiDBS): Proof of concept in the human

Approaches to control basal ganglia neural activity in real-time are needed to clarify the causal role of 13-35 Hz ("beta band") oscillatory dynamics in the manifestation of Parkinson's disease (PD) motor signs. Here, we show that resonant beta oscillations evoked by electrical pulses with precise amplitude and timing can be used to predictably suppress or amplify spontaneous beta band activity in the internal segment of the globus pallidus (GPi) in the human. Using this approach, referred to as closed-loop evoked interference deep brain stimulation (eiDBS), we could suppress or amplify frequency-specific (16-22 Hz) neural activity in a PD patient. Our results highlight the utility of eiDBS to characterize the role of oscillatory dynamics in PD and other brain conditions, and to develop personalized neuromodulation systems.

Optimizing charge-balanced pulse stimulation for desynchronization

Collective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it is undesirable, which calls for control techniques. In this paper, we focus on pulsatile control, with the goal to either increase or decrease the level of synchrony. We quantify this level by the entropy of the phase distribution. Motivated by possible applications in neuroscience, we consider pulses of a realistic shape. Exploiting the noisy Kuramoto-Winfree model, we search for the optimal pulse profile and the optimal stimulation phase. For this purpose, we derive an expression for the change of the phase distribution entropy due to the stimulus. We relate this change to the properties of individual units characterized by generally different natural frequencies and phase response curves and the population's state. We verify the general result by analyzing a two-frequency population model and demonstrating a good agreement of the theory and numerical simulations.

Real-time suppression and amplification of frequency-specific neural activity using stimulation evoked oscillations

BACKGROUND

Approaches to predictably control neural oscillations are needed to understand their causal role in brain function in healthy or diseased states and to advance the development of neuromodulation therapies.

OBJECTIVE

We present a closed-loop neural control and optimization framework to actively suppress or amplify low-frequency neural oscillations observed in local field potentials in real-time by using electrical stimulation. The rationale behind this control approach and our working hypothesis is that neural oscillatory activity evoked by electrical pulses can suppress or amplify spontaneous oscillations via destructive or constructive interference when the pulses are continuously delivered with appropriate amplitudes and at precise phases of the modulated oscillations in a closed-loop scheme.

METHODS

We tested our hypothesis in two nonhuman primates that exhibited a robust increase in low-frequency (8-30 Hz) oscillatory power in the subthalamic nucleus (STN) following administration of the neurotoxin 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). To test our neural control approach, we targeted 8-17 Hz oscillations and used electrode arrays and electrical stimulation waveforms similar to those used in humans chronically implanted with brain stimulation systems. Stimulation parameters that maximize the suppression or amplification of neural oscillations were predicted using mathematical models of the stimulation evoked oscillations.

RESULTS

Our neural control and optimization approach was capable of actively and robustly suppressing or amplifying oscillations in the targeted frequency band (8-17 Hz) in real-time in the studied subjects.

CONCLUSIONS

The results from this study support our hypothesis and suggest that the proposed neural control framework allows one to characterize in controlled experiments the functional role of frequency-specific neural oscillations by using electrodes and stimulation waveforms currently being employed in humans.

Controlling collective synchrony in oscillatory ensembles by precisely timed pulses

We present an efficient technique for control of synchrony in a globally coupled ensemble by pulsatile action. We assume that we can observe the collective oscillation and can stimulate all elements of the ensemble simultaneously. We pay special attention to the minimization of intervention into the system. The key idea is to stimulate only at the most sensitive phase. To find this phase, we implement an adaptive feedback control. Estimating the instantaneous phase of the collective mode on the fly, we achieve efficient suppression using a few pulses per oscillatory cycle. We discuss the possible relevance of the results for neuroscience, namely, for the development of advanced algorithms for deep brain stimulation, a medical technique used to treat Parkinson's disease.

Fast phase randomization via two-folds

A two-fold is a singular point on the discontinuity surface of a piecewise-smooth vector field, at which the vector field is tangent to the discontinuity surface on both sides. If an orbit passes through an invisible two-fold (also known as a Teixeira singularity) before settling to regular periodic motion, then the phase of that motion cannot be determined from initial conditions, and, in the presence of small noise, the asymptotic phase of a large number of sample solutions is highly random. In this paper, we show how the probability distribution of the asymptotic phase depends on the global nonlinear dynamics. We also show how the phase of a smooth oscillator can be randomized by applying a simple discontinuous control law that generates an invisible two-fold. We propose that such a control law can be used to desynchronize a collection of oscillators, and that this manner of phase randomization is fast compared with existing methods (which use fixed points as phase singularities), because there is no slowing of the dynamics near a two-fold.

A Multichannel Recording System with Optical Stimulation for Closed-Loop Optogenetic Experiments

Selective perturbation of the activity of specific cell types in the brain tissue is essential in understanding the function of neuronal circuits involved in cognition and behavior and might also provide therapeutic neuromodulation strategies. Such selective neuronal addressing can be achieved through the optical activation of light-sensitive proteins called opsins that are expressed in specific cell populations through genetic methods-hence the name "optogenetics." In optogenetic experiments, the electrical activity of the targeted cell populations is optically triggered and monitored using arrays of microelectrodes. In closed-loop studies, the optical stimulation parameters are adjusted based on the recorded activity, ideally in real time. Here we describe the basic tools and the protocols allowing closed-loop optogenic experiments in vivo.

Designing a deep brain stimulator to suppress pathological neuronal synchrony

Some of neuropathologies are believed to be related to abnormal synchronization of neurons. In the line of therapy, designing effective deep brain stimulators to suppress the pathological synchrony among neuronal ensembles is a challenge of high clinical relevance. The stimulation should be able to disrupt the synchrony in the presence of latencies due to imperfect knowledge about parameters of a neuronal ensemble and stimulation impacts on the ensemble. We propose an adaptive desynchronizing deep brain stimulator capable of dealing with these uncertainties. We analyze the collective behavior of the stimulated neuronal ensemble and show that, using the designed stimulator, the resulting asynchronous state is stable. Simulation results reveal the efficiency of the proposed technique.

Closed-loop optical neural stimulation based on a 32-channel low-noise recording system with online spike sorting

OBJECTIVE

Closed-loop operation of neuro-electronic systems is desirable for both scientific and clinical (neuroprosthesis) applications. Integrating optical stimulation with recording capability further enhances the selectivity of neural stimulation. We have developed a system enabling the local delivery of optical stimuli and the simultaneous electrical measuring of the neural activities in a closed-loop approach.

APPROACH

The signal analysis is performed online through the implementation of a template matching algorithm. The system performance is demonstrated with the recorded data and in awake rats.

MAIN RESULTS

Specifically, the neural activities are simultaneously recorded, detected, classified online (through spike sorting) from 32 channels, and used to trigger a light emitting diode light source using generated TTL signals.

SIGNIFICANCE

A total processing time of 8 ms is achieved, suitable for optogenetic studies of brain mechanisms online.

DESYNCHRONIZATION OF TWO COUPLED LIMIT-CYCLE OSCILLATORS USING AN ASTROCYTE-INSPIRED CONTROLLER

Astrocytes have potential to break synchrony between neurons. Authors' recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an efficient controller, parameters of controller are tuned through an optimization algorithm. The proposed bio-inspired controller takes advantages of three important properties: (1) the controller desynchronizes the oscillators without any undesirable effects (e.g. stopping, annihilating or starting divergent oscillations); (2) it consumes little effort to preserve the desirable desynchronized state; and (3) the controller is robust with respect to parameters' variations. Simulation results reveal the ability of the proposed controller.

Desynchronizing the abnormally synchronized neural activity in the subthalamic nucleus: a modeling study

A mathematical model of a target area for deep brain stimulation was used to investigate the effects of electrical stimulation on pathologically synchronized clusters of neurons. In total, three newly developed stimulation techniques based on multisite coordinated reset and delayed feedback were tested and compared with a high-frequency stimulation method that is currently used as a standard stimulation protocol for deep brain stimulation. By modeling both excitatory and inhibitory actions of the electrical stimulation, we revealed the desynchronization impacts of the novel stimulation techniques. This contrasts with standard high-frequency stimulation, which failed to desynchronize the target population and whose inhibitory effects blocked all neuronal activity. We also explored the demand-controlled character of the proposed methods, and demonstrated that the amount of stimulation current required was considerably smaller than that for high-frequency stimulation. These novel stimulation methods appear to be superior to standard high-frequency stimulation techniques, and we propose the methods now be used for deep brain stimulation.

Phase synchronization of oxygenation waves in the frontal areas of children with attention-deficit hyperactivity disorder detected by optical diffusion spectroscopy correlates with medication

The beneficial effects of pharmacotherapy on children with attention-deficit hyperactivity disorder (ADHD) are well documented. We use near-infrared spectroscopy (NIRS) methodology to determine reorganization of brain neurovascular properties following the medication treatment. Twenty-six children with ADHD (ages six through 12) participated in a modified laboratory school protocol to monitor treatment response with lisdexamfetamine dimesylate (LDX; Vyvanse®, Shire US Inc.). All children refrained from taking medication for at least two weeks (washout period). To detect neurovascular reorganization, we measured changes in synchronization of oxy (HbO2) and deoxy (HHb) hemoglobin waves between the two frontal lobes. Participants without medication displayed average baseline HbO2 phase difference at about -7-deg. and HHb differences at about 240-deg.. This phase synchronization index changed after pharmacological intervention. Medication induced an average phase changes of HbO2 after first medication to 280-deg. and after medication optimization to 242-deg.. Instead first medication changed of the average HHb phase difference at 186-deg. and then after medication optimization to 120-deg. In agreement with findings of White et al., and Varela et al., we associated the phase synchronization differences of brain hemodynamics in children with ADHD with lobe specific hemodynamic reorganization of HbO2- and HHB oscillations following medication status.

MULTISITE COORDINATED DELAYED FEEDBACK FOR AN EFFECTIVE DESYNCHRONIZATION OF NEURONAL NETWORKS

We present a novel, particularly robust technique for effective desynchronization of neuronal populations in the presence of noise. For this, delayed feedback signals are administered in a spatially coordinated way via at least two stimulation sites using different delays for each stimulation site, respectively. For medical applications different variants of this approach are developed. These techniques are numerically tested in a physiologically realistic model. We propose our methods as novel, particularly mild and effective stimulation protocols for the therapy of patients suffering from Parkinson's disease, essential tremor or epilepsy.

Synchronization in a chaotic neural network with time delay depending on the spatial distance between neurons

The synchronization is investigated in a two-dimensional Hindmarsh-Rose neuronal network by introducing a global coupling scheme with time delay, where the length of time delay is proportional to the spatial distance between neurons. We find that the time delay always disturbs synchronization of the neuronal network. When both the coupling strength and length of time delay per unit distance (i.e., enlargement factor) are large enough, the time delay induces the abnormal membrane potential oscillations in neurons. Specifically, the abnormal membrane potential oscillations for the symmetrically placed neurons form an antiphase, so that the large coupling strength and enlargement factor lead to the desynchronization of the neuronal network. The complete and intermittently complete synchronization of the neuronal network are observed for the right choice of parameters. The physical mechanism underlying these phenomena is analyzed.

Time-delayed feedback in neurosystems

The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. A time delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic synchronization of instantaneously coupled neurons under the influence of white noise can be deliberately controlled by local time-delayed feedback. By appropriate choice of the delay time, synchronization can be either enhanced or suppressed. In delay-coupled neurons, antiphase oscillations can be induced for sufficiently large delay and coupling strength. The additional application of time-delayed self-feedback leads to complex scenarios of synchronized in-phase or antiphase oscillations, bursting patterns or amplitude death.

Modeling the current distribution across the depth electrode-brain interface in deep brain stimulation

The mismatch between the extensive clinical use of deep brain stimulation (DBS), which is being used to treat an increasing number of neurological disorders, and the lack of understanding of the underlying mechanisms is confounded by the difficulty of measuring the spread of electric current in the brain in vivo. In this article we present a brief review of the recent computational models that simulate the electric current and field distribution in 3D space and, consequently, make estimations of the brain volume being modulated by therapeutic DBS. Such structural modeling work can be categorized into three main approaches: target-specific modeling, models of instrumentation and modeling the electrode-brain interface. Comments are made for each of these approaches with emphasis on our electrode-brain interface modeling, since the stimulating current must travel across the electrode-brain interface in order to reach the surrounding brain tissue and modulate the pathological neural activity. For future modeling work, a combined approach needs to be taken to reveal the underlying mechanisms, and both structural and dynamic models need to be clinically validated to make reliable predictions about the therapeutic effect of DBS in order to assist clinical practice.

Multistability in the Kuramoto model with synaptic plasticity

We present a simplified phase model for neuronal dynamics with spike timing-dependent plasticity (STDP). For asymmetric, experimentally observed STDP we find multistability: a coexistence of a fully synchronized, a fully desynchronized, and a variety of cluster states in a wide enough range of the parameter space. We show that multistability can occur only for asymmetric STDP, and we study how the coexistence of synchronization and desynchronization and clustering depends on the distribution of the eigenfrequencies. We test the efficacy of the proposed method on the Kuramoto model which is, de facto, one of the sample models for a description of the phase dynamics in neuronal ensembles.

Control of neuronal synchrony by nonlinear delayed feedback

We present nonlinear delayed feedback stimulation as a technique for effective desynchronization. This method is intriguingly robust with respect to system and stimulation parameter variations. We demonstrate its broad applicability by applying it to different generic oscillator networks as well as to a population of bursting neurons. Nonlinear delayed feedback specifically counteracts abnormal interactions and, thus, restores the natural frequencies of the individual oscillatory units. Nevertheless, nonlinear delayed feedback enables to strongly detune the macroscopic frequency of the collective oscillation. We propose nonlinear delayed feedback stimulation for the therapy of neurological diseases characterized by abnormal synchrony.

Extreme sensitivity to detuning for globally coupled phase oscillators

We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N = 2, appears at isolated parameter values for N = 3 and N = 4, and can appear robustly for open sets of parameter values for N > or = 5 oscillators.

Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study

In detailed simulations we present a coordinated delayed feedback stimulation as a particularly robust and mild technique for desynchronization. We feed back the measured and band-pass filtered local filed potential via several or multiple sites with different delays, respectively. This yields a resounding desynchronization in a naturally demand-controlled way. Our novel approach is superior to previously developed techniques: It is robust against variations of system parameters, e.g., the mean firing rate. It does not require time-consuming calibration. It also prevents intermittent resynchronization typically caused by all methods employing repetitive administration of shocks. We suggest our novel technique to be used for deep brain stimulation in patients suffering from neurological diseases with pathological synchronization, such as Parkinsonian tremor, essential tremor or epilepsy.

Phase chaos in coupled oscillators

A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos is a common property of networks of oscillators of very different natures, such as phase oscillators, limit-cycle oscillators, and chaotic oscillators, e.g., Rössler systems.

Desynchronization of coupled electrochemical oscillators with pulse stimulations

Various stimulation desynchronization techniques are explored in a laboratory experiment on electrochemical oscillators, a system that exhibits transient dynamics, heterogeneities, and inherent noise. Stimulation with a short, single pulse applied at a vulnerable phase can effectively desynchronize a cluster. A double pulse method, that can be applied at any phase, can be improved either by adding an extra weak pulse between the original two pulses or by adding noise to the first pulse.

Effective desynchronization by nonlinear delayed feedback

We show that nonlinear delayed feedback opens up novel means for the control of synchronization. In particular, we propose a demand-controlled method for powerful desynchronization, which does not require any time-consuming calibration. Our technique distinguishes itself by its robustness against variations of system parameters, even in strongly coupled ensembles of oscillators. We suggest our method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization.

Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms

We suggest a method for suppression of synchrony in a globally coupled oscillator network, based on the time-delayed feedback via the mean field. Having in mind possible applications for suppression of pathological rhythms in neural ensembles, we present numerical results for different models of coupled bursting neurons. A theory is developed based on the consideration of the synchronization transition as a Hopf bifurcation.

Mechanism of desynchronization in the finite-dimensional Kuramoto model

We study how a decrease of the coupling strength causes a desynchronization in the Kuramoto model of N globally coupled phase oscillators. We show that, if the natural frequencies are distributed uniformly or close to that, the synchronized state can robustly split into any number of phase clusters with different average frequencies, even culminating in complete desynchronization. In the simplest case of N=3 phase oscillators, the course of the splitting is controlled by a Cherry flow. The general N-dimensional desynchronization mechanism is numerically illustrated for N=5.

Delayed feedback as a means of control of noise-induced motion

Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.

High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) or the internal segment of the globus pallidus (GPi) has recently been recognized as an important form of intervention for alleviating motor symptoms associated with Parkinson's disease, but the mechanism underlying its effectiveness remains unknown. Using a computational model, this paper considers the hypothesis that DBS works by replacing pathologically rhythmic basal ganglia output with tonic, high frequency firing. In our simulations of parkinsonian conditions, rhythmic inhibition from GPi to the thalamus compromises the ability of thalamocortical relay (TC) cells to respond to depolarizing inputs, such as sensorimotor signals. High frequency stimulation of STN regularizes GPi firing, and this restores TC responsiveness, despite the increased frequency and amplitude of GPi inhibition to thalamus that result. We provide a mathematical phase plane analysis of the mechanisms that determine TC relay capabilities in normal, parkinsonian, and DBS states in a reduced model. This analysis highlights the differences in deinactivation of the low-threshold calcium T -current that we observe in TC cells in these different conditions. Alternative scenarios involving convergence of thalamic signals in the cortex are also discussed, and predictions associated with these results, including the occurrence of rhythmic rebound bursts in certain TC cells in parkinsonian states and their drastic reduction by DBS, are stated. These results demonstrate how DBS could work by increasing firing rates of target cells, rather than shutting them down.

Controlling synchronization in an ensemble of globally coupled oscillators

We propose a technique to control coherent collective oscillations in ensembles of globally coupled units (self-sustained oscillators or maps). We demonstrate numerically and theoretically that a time delayed feedback in the mean field can, depending on the parameters, enhance or suppress the self-synchronization in the population. We discuss possible applications of the technique.