A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations

The coordinated reset of neural subpopulations is introduced as an effectively desynchronizing stimulation technique. For this, short sequences of high-frequency pulse trains are administered at different sites in a coordinated way. Desynchronization is easily maintained by performing a coordinated reset with demand-controlled timing or by periodically administering resetting high-frequency pulse trains of demand-controlled length. Unlike previously developed methods, this novel approach is robust against variations of model parameters and does not require time-consuming calibration. The novel technique is suggested to be used for demand-controlled deep brain stimulation in patients suffering from Parkinson's disease or essential tremor. It might even be applicable to diseases with intermittently emerging synchronized neural oscillations like epilepsy.     

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.     

Unlearning tinnitus-related cerebral synchrony with acoustic coordinated reset stimulation: theoretical concept and modelling

Tinnitus is a deafferentation-induced phantom phenomenon characterized by abnormal cerebral synchrony and connectivity. Computationally, we show that desynchronizing acoustic coordinated reset (CR) stimulation can effectively counteract both up-regulated synchrony and connectivity. CR stimulation has initially been developed for the application to electrical deep brain stimulation. We here adapt this approach to non-invasive, acoustic CR stimulation. For this, we use the tonotopic organization of the central auditory system and replace electrical stimulation bursts applied to different brain sites by acoustically delivered tones of different pitch. Based on our simulations, we propose non-invasive acoustic CR stimulation as a possible novel therapy for tinnitus.     

Therapeutic rewiring by means of desynchronizing brain stimulation

We study possible anti-kindling effects of the standard high-frequency deep brain stimulation (HFDBS) and of a desynchronizing multisite coordinated reset stimulation (MCRS) theoretically in a mathematical model of the subthalamic nucleus (STN). The latter is an effective target for deep brain stimulation (DBS) in patients suffering from Parkinson's disease (PD). Depending on the structures being activated, electrical pulses may have excitatory and/or inhibitory impact. According to our simulation results MCRS may achieve robust long-term anti-kindling (i.e., curative) effects, irrespectively, of the ratio between excitatory and inhibitory impact. This means, that during MCRS the STN unlearns its pathologic synaptic connections and reestablishes a physiological level of connectivity. In contrast, HFDBS has anti-kindling effects only if its impact is predominantly excitatory. Our results are relevant for selecting appropriate locations for DBS electrodes. In fact, even with HFDBS we may expect anti-kindling effects, provided the target is properly chosen.     

神经元网络动力学的统计物理方法

本文回顾了利用统计物理的方法研究神经元网络动力学的数学降维描述.以一个全兴奋性的“整合-发放”神经元网络为出发点,导出了描写神经元群体活动的概率分布函数的(2+1)-维对流-扩散方程.在没有引入任何新参数的情况下,讨论了如何利用moment closure scheme得到(1+1)-维的动力学方程.我们将此方程的预测...     

Coarse-grained event tree analysis for quantifying Hodgkin-Huxley neuronal network dynamics

We present an event tree analysis of studying the dynamics of the Hodgkin-Huxley (HH) neuronal networks. Our study relies on a coarse-grained projection to event trees and to the event chains that comprise these trees by using a statistical collection of spatial-temporal sequences of relevant physiological observables (such as sequences of spiking multiple neurons). This projection can retain information about network dynamics that covers multiple features, swiftly and robustly. We demonstrate that for even small differences in inputs, some dynamical regimes of HH networks contain sufficiently higher order statistics as reflected in event chains within the event tree analysis. Therefore, this analysis is effective in discriminating small differences in inputs. Moreover, we use event trees to analyze the results computed from an efficient library-based numerical method proposed in our previous work, where a pre-computed high resolution data library of typical neuronal trajectories during the interval of an action potential (spike) allows us to avoid resolving the spikes in detail. In this way, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable statistical accuracy in terms of average firing rate and power spectra of voltage traces. Our numerical simulation results show that the library method is efficient in the sense that the results generated by using this numerical method with much larger time steps contain sufficiently high order statistical structure of firing events that are similar to the ones obtained using a regular HH solver. We use our event tree analysis to demonstrate these statistical similarities.     

Pseudo-Lyapunov exponents and predictability of Hodgkin-Huxley neuronal network dynamics

We present a numerical analysis of the dynamics of all-to-all coupled Hodgkin-Huxley (HH) neuronal networks with Poisson spike inputs. It is important to point out that, since the dynamical vector of the system contains discontinuous variables, we propose a so-called pseudo-Lyapunov exponent adapted from the classical definition using only continuous dynamical variables, and apply it in our numerical investigation. The numerical results of the largest Lyapunov exponent using this new definition are consistent with the dynamical regimes of the network. Three typical dynamical regimes—asynchronous, chaotic and synchronous, are found as the synaptic coupling strength increases from weak to strong. We use the pseudo-Lyapunov exponent and the power spectrum analysis of voltage traces to characterize the types of the network behavior. In the nonchaotic (asynchronous or synchronous) dynamical regimes, i.e., the weak or strong coupling limits, the pseudo-Lyapunov exponent is negative and there is a good numerical convergence of the solution in the trajectory-wise sense by using our numerical methods. Consequently, in these regimes the evolution of neuronal networks is reliable. For the chaotic dynamical regime with an intermediate strong coupling, the pseudo-Lyapunov exponent is positive, and there is no numerical convergence of the solution and only statistical quantifications of the numerical results are reliable. Finally, we present numerical evidence that the value of pseudo-Lyapunov exponent coincides with that of the standard Lyapunov exponent for systems we have been able to examine.     

Long-term anti-kindling effects of desynchronizing brain stimulation: a theoretical study

In a modeling study we show that desynchronization stimulation may have powerful anti-kindling effects. For this, we incorporate spike-timing-dependent plasticity into a generic network of coupled phase oscillators, which serves as a model network of synaptically interacting neurons. Two states may coexist under spontaneous conditions: a state of uncorrelated firing and a state of pathological synchrony. Appropriate stimulation protocols make the network learn or unlearn the pathological synaptic interactions, respectively. Low-frequency periodic pulse train stimulation causes a kindling. Permanent high-frequency stimulation, used as golden standard for deep brain stimulation in medically refractory movement disorders, basically freezes the synaptic weights. In contrast, desynchronization stimulation, e.g., by means of a multi-site coordinated reset, has powerful long-term anti-kindling effects and enables the network to unlearn pathologically strong synaptic interactions. We propose desynchronization stimulation for the therapy of movement disorders and epilepsies.     

Behavior-related neuronal reactions and dynamics of neuronal activity

Functionally, behavior-related discharges of associative neurons are an efferent flow of pulses continuously generated over the course of each behavioral act of an animal. However, predominant research approaches are based on the "stimulus - reaction" principle. Analysis of the dynamics of unit activity in monkeys during performance of a multi-step behavioral complex showed that differences related to different behavioral acts consist in composition changes in the active neurons (or their recombination) rather than in a number of responsive cells or involvement of action-specific neurons. Each combination of active neurons ensures the distribution of efferent signals characteristic of the given combination. These findings suggest the addressing coding of the efferent neuronal signals.     

Evaluation of neuronal coupling dynamics

Temporary correlated activity of neuron assemblies is believed to play a substantial role for the brain's pattern recognition ability. To study the underlying principles of such mechanisms, a method is proposed for the characterization of the interneuronal and stimulus-response coupling changes of two periodically driven and simultaneously recorded units. The coupling measure is derived from the cross correlation function by calculating the actual correlation contributions without performing the subsequent time-average (which would give the cross correlation function). Examples are given for simultaneously recorded spike trains from visual cortical units, but the method can be applied equally well to evoked potentials or intracellular recordings.     

Stochastic models of neuronal dynamics

Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs.We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker-Planck equation. The solution of this equation is the temporal evolution of a probability density over state-space, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a neuron. Measurements can be modelled by taking expectations over this density, e.g. mean membrane potential, firing rate or energy consumption per neuron. The key motivation behind our approach is that ERPs represent an average response over many neurons. This means it is sufficient to model the probability density over neurons, because this implicitly models their average state. Although the dynamics of each neuron can be highly stochastic, the dynamics of the density is not. This means we can use Bayesian inference and estimation tools that have already been established for deterministic systems. The potential importance of modelling density dynamics (as opposed to more conventional neural mass models) is that they include interactions among the moments of neuronal states (e.g. the mean depolarization may depend on the variance of synaptic currents through nonlinear mechanisms).Here, we formulate a population model, based on biologically informed model-neurons with spike-rate adaptation and synaptic dynamics. Neuronal sub-populations are coupled to form an observation model, with the aim of estimating and making inferences about coupling among sub-populations using real data. We approximate the time-dependent solution of the system using a bi-orthogonal set and first-order perturbation expansion. For didactic purposes, the model is developed first in the context of deterministic input, and then extended to include stochastic effects. The approach is demonstrated using synthetic data, where model parameters are identified using a Bayesian estimation scheme we have described previously.     

Modeling the contribution of lamina 5 neuronal and network dynamics to low frequency EEG phenomena

The Electroencephalogram (EEG) is an important clinical and research tool in neurophysiology. With the advent of recording techniques, new evidence is emerging on the neuronal populations and wiring in the neocortex. A main challenge is to relate the EEG generation mechanisms to the underlying circuitry of the neocortex. In this paper, we look at the principal intrinsic properties of neocortical cells in layer 5 and their network behavior in simplified simulation models to explain the emergence of several important EEG phenomena such as the alpha rhythms, slow-wave sleep oscillations, and a form of cortical seizure. The models also predict the ability of layer 5 cells to produce a resonance-like neuronal recruitment known as the augmenting response. While previous models point to deeper brain structures, such as the thalamus, as the origin of many EEG rhythms (spindles), the current model suggests that the cortical circuitry itself has intrinsic oscillatory dynamics which could account for a wide variety of EEG phenomena.Electronic Supplementary Material Supplementary material is available for this article at Sensorimotor Control Project- MIT Harvard NeuroEngineering Research Collaborative.     

Magnetic stimulation of one-dimensional neuronal cultures

Transcranial magnetic stimulation is a remarkable tool for neuroscience research, with a multitude of diagnostic and therapeutic applications. Surprisingly, application of the same magnetic stimulation directly to neurons that are dissected from the brain and grown in vitro was not reported to activate them to date. Here we report that central nervous system neurons patterned on large enough one-dimensional rings can be magnetically stimulated in vitro. In contrast, two-dimensional cultures with comparable size do not respond to excitation. This happens because the one-dimensional pattern enforces an ordering of the axons along the ring, which is designed to follow the lines of the magnetically induced electric field. A small group of sensitive (i.e., initiating) neurons respond even when the network is disconnected, and are presumed to excite the entire network when it is connected. This implies that morphological and electrophysiological properties of single neurons are crucial for magnetic stimulation. We conjecture that the existence of a select group of neurons with higher sensitivity may occur in the brain in vivo as well, with consequences for transcranial magnetic stimulation.     

A neuronal network for the logic of Limax learning

We construct a neuronal network to model the logic of associative conditioning as revealed in experimental results using the terrestrial mollusk Limax maximus. We show, in particular, how blocking to a previously conditioned stimulus in the presence of the unconditional stimulus, can emerge as a dynamical property of the network. We also propose experiments to test the new model. Action Editor: G. Bard Ermentrout     

Ion concentration dynamics as a mechanism for neuronal bursting

We describe a simple conductance-based model neuron that includes intra- and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems.     

Modulation of a neuronal network by electrical high frequency stimulation in striatal slices of the rat in vitro

The effects of the GABA(A) receptor antagonist bicuculline, the D2-like receptor antagonist sulpiride and the D1-like receptor antagonist SCH-23390 on the electrical high frequency stimulation (HFS)-evoked gamma-aminobutyric acid (GABA) and dopamine (DA) release were measured from slices of the rat striatum by means of HPLC method with electrochemical detection. HFS with 130Hz stimulated veratridine-activated GABAergic neurons resulting in an increased GABA outflow while DA outflow decreased. In the presence of the GABA(A) receptor antagonist bicuculline extracellular GABA and DA outflow were enhanced. When the competitive dopamine D2-like receptor antagonist S-(-)-sulpiride was added to incubation medium, the HFS-evoked stimulatory effect on GABA outflow declined to values found after veratridine (1microM) without HFS. After co-incubation of sulpiride and the competitive D1-like receptor antagonist R-(+)-SCH-23390, the effect of sulpiride on HFS plus veratridine-evoked GABA outflow was completely reversed. Neither sulpiride nor SCH-23390 had any influence on the effect of HFS on veratridine-induced DA outflow. No effect of HFS on glutamate outflow was observed in all experiments. These results led us to suggest that in our model HFS primarily affects GABAergic neurons. These neurons are embedded in a neuronal network with a GABA-dopamine circuit, and thus, HFS interacts with a neuronal network, not only with one neurotransmitter system or one neuron population.     

Bi-level optimization programming for the shipper-carrier network problem

The paper presents a bi-level modeling approach that captures hierarchical relationships between shippers and carriers in maritime freight transportation networks. Ocean carriers, land carriers and port terminal operators provide transportation services at different parts of the multimodal network. Port terminal operators are regarded as a special type of carrier due to their behavior. The carriers determine service charges and delivery routes (port services) through competition and interactions among themselves. Shippers are users of the transportation services. Shippers choose a sequence of carriers, based on the carriers’ pricing and routing decisions. These relationships are captured in a bi-level model where carriers are the leaders and shippers are the followers. The paper focuses on the behavior of shippers having the transportation service information with spatial price equilibrium. A numerical example is used to demonstrate the validity of the developed model.