Stimulus-dependent onset latency of inhibitory recurrent activity

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.

Characterizing Deep Brain Stimulation effects in computationally efficient neural network models

BACKGROUND

Recent studies on the medical treatment of Parkinson's disease (PD) led to the introduction of the so called Deep Brain Stimulation (DBS) technique. This particular therapy allows to contrast actively the pathological activity of various Deep Brain structures, responsible for the well known PD symptoms. This technique, frequently joined to dopaminergic drugs administration, replaces the surgical interventions implemented to contrast the activity of specific brain nuclei, called Basal Ganglia (BG). This clinical protocol gave the possibility to analyse and inspect signals measured from the electrodes implanted into the deep brain regions. The analysis of these signals led to the possibility to study the PD as a specific case of dynamical synchronization in biological neural networks, with the advantage to apply the theoretical analysis developed in such scientific field to find efficient treatments to face with this important disease. Experimental results in fact show that the PD neurological diseases are characterized by a pathological signal synchronization in BG. Parkinsonian tremor, for example, is ascribed to be caused by neuron populations of the Thalamic and Striatal structures that undergo an abnormal synchronization. On the contrary, in normal conditions, the activity of the same neuron populations do not appear to be correlated and synchronized.

RESULTS

To study in details the effect of the stimulation signal on a pathological neural medium, efficient models of these neural structures were built, which are able to show, without any external input, the intrinsic properties of a pathological neural tissue, mimicking the BG synchronized dynamics.We start considering a model already introduced in the literature to investigate the effects of electrical stimulation on pathologically synchronized clusters of neurons. This model used Morris Lecar type neurons. This neuron model, although having a high level of biological plausibility, requires a large computational effort to simulate large scale networks. For this reason we considered a reduced order model, the Izhikevich one, which is computationally much lighter. The comparison between neural lattices built using both neuron models provided comparable results, both without traditional stimulation and in presence of all the stimulation protocols. This was a first result toward the study and simulation of the large scale neural networks involved in pathological dynamics.Using the reduced order model an inspection on the activity of two neural lattices was also carried out at the aim to analyze how the stimulation in one area could affect the dynamics in another area, like the usual medical treatment protocols require.The study of population dynamics that was carried out allowed us to investigate, through simulations, the positive effects of the stimulation signals in terms of desynchronization of the neural dynamics.

CONCLUSIONS

The results obtained constitute a significant added value to the analysis of synchronization and desynchronization effects due to neural stimulation. This work gives the opportunity to more efficiently study the effect of stimulation in large scale yet computationally efficient neural networks. Results were compared both with the other mathematical models, using Morris Lecar and Izhikevich neurons, and with simulated Local Field Potentials (LFP).

Cumulative and after-effects of short and weak coordinated reset stimulation: a modeling study

We show that the dynamical multistability of a network of bursting subthalamic neurons, caused by synaptic plasticity has a strong impact on the stimulus-response properties when exposed to weak and short desynchronizing stimuli. Intriguingly, such stimuli can reliably shift the network from a stable state with pathological synchrony and connectivity to a stable desynchronized state with down-regulated connectivity. However, unlike in the case of stronger coordinated reset stimulation, after termination of weaker stimulation the network may undergo a transient rebound of synchrony. When the coordinated reset stimulation is even weaker and/or shorter, so that a single stimulation epoch is not effective, the network dynamics and connectivity can still be reshaped in a cumulative manner by repetitive stimulation delivery.

Winner-take-all selection in a neural system with delayed feedback

We consider the effects of temporal delay in a neural feedback system with excitation and inhibition. The topology of our model system reflects the anatomy of the avian isthmic circuitry, a feedback structure found in all classes of vertebrates. We show that the system is capable of performing a 'winner-take-all' selection rule for certain combinations of excitatory and inhibitory feedback. In particular, we show that when the time delays are sufficiently large a system with local inhibition and global excitation can function as a 'winner-take-all' network and exhibit oscillatory dynamics. We demonstrate how the origin of the oscillations can be attributed to the finite delays through a linear stability analysis.

Therapeutic modulation of synaptic connectivity with desynchronizing brain stimulation

In a modeling study, we show that synaptic connectivity can effectively be reshaped by an appropriate modulation of neuronal dynamics. To this end, we incorporate synaptic plasticity with symmetric spike-timing characteristics into a population of bursting neurons, which are interacting via chemical synapses. Under spontaneous conditions, qualitatively different stable dynamical states may coexist. We observe states characterized either by pathological synchrony or by uncorrelated activity. Suitably designed stimulation protocols enable to shift the neuronal population from one dynamical state to another. Due to low-frequency periodic pulse train stimulation, the population learns pathologically strong interactions, as known from the kindling phenomenon. In contrast, desynchronizing stimulation, e.g., multi-site coordinated reset stimulation, enables the network to unlearn pathologically strong synaptic interactions, so that a powerful long-term anti-kindling is achieved. We demonstrate that anti-kindling can be achieved even with weak and/or short desynchronizing stimuli, which are not able to cause a complete desynchronization in the course of the stimulation. Our results show that desynchronizing stimulation may serve as a novel curative approach for the therapy of neurological diseases connected with pathological cerebral synchrony.

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.

Desynchronization in networks of globally coupled neurons with dendritic dynamics

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.

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.

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.