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Cravings that precede loss of control (LOC) over food consumption present an opportunity for intervention in patients with the binge eating disorder (BED). In this pilot study, we used responsive deep brain stimulation (DBS) to record nucleus accumbens (NAc) electrophysiology during food cravings preceding LOC eating in two patients with BED and severe obesity (trial registration no. NCT03868670). Increased NAc low-frequency oscillations, prominent during food cravings, were used to guide DBS delivery. Over 6 months, we observed improved self-control of food intake and weight loss. These findings provide early support for restoring inhibitory control with electrophysiologically-guided NAc DBS. Further work with increased sample sizes is required to determine the scalability of this approach.

Deep brain stimulation (DBS) is a neurosurgical procedure that allows targeted circuit-based neuromodulation. DBS is a standard of care in Parkinson disease, essential tremor and dystonia, and is also under active investigation for other conditions linked to pathological circuitry, including major depressive disorder and Alzheimer disease. Modern DBS systems, borrowed from the cardiac field, consist of an intracranial electrode, an extension wire and a pulse generator, and have evolved slowly over the past two decades. Advances in engineering and imaging along with an improved understanding of brain disorders are poised to reshape how DBS is viewed and delivered to patients. Breakthroughs in electrode and battery designs, stimulation paradigms, closed-loop and on-demand stimulation, and sensing technologies are expected to enhance the efficacy and tolerability of DBS. In this Review, we provide a comprehensive overview of the technical development of DBS, from its origins to its future. Understanding the evolution of DBS technology helps put the currently available systems in perspective and allows us to predict the next major technological advances and hurdles in the field.

We computationally study whether it is possible to stimulate a neuronal population in such a way that its mean firing rate increases without an increase of the population's net synchronization. For this, we use coordinated reset (CR) stimulation, which has previously been developed to desynchronize populations of oscillatory neurons. Intriguingly, delivered to a population of predominantly silent FitzHugh–Nagumo or Hindmarsh–Rose neurons at sufficient stimulation amplitudes, CR robustly causes a multi-frequency activation: different Arnold tongues such as 1 : 1 or n : mentrained neuronal clusters emerge, which consist of phase-shifted sub clusters. Owing to the clustering pattern the neurons' timing is well balanced, so that in total there is no synchronization. Our findings may contribute to the development of novel and safe stimulation treatments that specifically counteract cerebral hypo-activity without promoting pathological synchronization or inducing epileptic seizures.

A model of two coupled phase oscillators is studied, where both oscillators are subject to random forces but only one oscillator is repetitively stimulated with a pulsatile stimulus. A pulse causes a reset, which is transmitted to the other oscillator via the coupling. The transmission time of the cross-trial (CT) averaged responses, i.e. the difference in time between the maxima of the CT averaged responses of both oscillators differs from the time difference between the maxima of the oscillators' resets. In fact, the transmission time of the CT averaged responses directly corresponds to the phase difference in the stable synchronized state with integer multiples of the oscillators' mean period added to it. With CT averaged responses it is impossible to reliably estimate the time elapsing, owing to the stimulus' action being transmitted between the two oscillators.

Based on our stochastic approach to phase resetting of an ensemble of oscillators, in this article we investigate two stimulation mechanisms which exhibit qualitatively different dynamical behaviour as compared with the stimulation mechanism analysed in a previous study. Both the ‘old’ as well as one of the ‘new’ stimulation mechanisms give rise to a characteristic desynchronization behaviour: A stimulus of a given (non-vanishing) intensity administered at a critical initial ensemble phase for a critical duration Tcrit annihilates the ensemble's synchronized oscillation. When the stimulation duration exceeds Tcrit a transition from type 1 resetting to type 0 resetting occurs. The second ‘new’ stimulation mechanism does not cause a desynchronization which is connected with a phase singularity. Correspondingly this mechanism only leads to type 1 resetting. In contrast to the stimulation mechanism analysed in a previous study, both ‘new’ stimulation mechanisms cause burst splitting. According to our results, in this case peak or onset detection algorithms are not able to reveal a correct estimate of the ensemble phase. Thus, whenever stimulation induced burst splitting occurs, phase-resetting curves determined by means of peak or onset detection may be nothing but artifacts. Therefore it is necessary to understand burst splitting in order to develop reliable phase detection algorithms, which are e.g. based on detecting bursts' centers of mass. Our results are important for experimentalists: Burst splitting is, for instance, well-known from tremor resetting experiments. Thus, it often turned out to be at least rather difficult to derive reliable phase-resetting curves from experimental data.

We present a stochastic approach to phase-resetting of an ensemble of oscillators. In order to describe stimulation-induced dynamical phenomena we develop a stochastic model which consists of an ensemble of phase oscillators interacting via random forces. Every single oscillator is submitted to a phase stimulus. The ensemble's dynamics is determined by a Fokker-Planck equation. The stationary states are calculated explicitly, whereas the transients are analysed numerically. If the stimulus of a given (non-vanishing) intensity is administered at a critical initial cluster phase for a critical duration Tcrit the ensemble's synchronized oscillation is annihilated. A transition from type 1 resetting to type 0 resetting occurs when the stimulation duration exceeds Tcrit. Stimulation causes a shift of the mean frequency of every single oscillator. This frequency shift is explicitly calculated by deriving the mean first passage time. The model shows that there is a subcritical intensity which is connected with an enhanced vulnerability to stimulation. The desynchronized states, the so-called black holes, are typically associated with a double peak in the ensemble's phase distribution. This is important for analysing experimental data because simple peak-detection algorithms are not able to extract the underlying dynamics.

We theoretically investigate pattern formation during simple visual hallucinations caused by epileptic activity. To this end we analyze the activator-inhibitor model of Ermentrout and Cowan [1]. In contrast to these authors we focus on a different disease mechanism: According to experimental findings (cf. [2]) we decrease the influence of the inhibitor on the activator. This causes spontaneous pattern formation due to a bifurcation. The model parameters determine whether one or two or four modes become unstable. By means of the center manifold theorem, in all cases the order parameter equation is derived, the stability of the solution is proofed, and the bifurcating activity pattern is calculated explicitely in lowest order. Taking into account terms up to third order in all cases the order parameter equation has a potential. For the two-modes and the four-modes instability this potential causes a winner-takes all dynamics. We integrate the order parameter equation numerically and plot the visual hallucinations which result from the bifurcating cortical activity. The theoretically derived hallucinations correspond to clinically observed visual hallucinations (cf. [3, 4]), which are, for instance, well-known from petit mal epilepsy [5].

We present a phenomenological model to an experiment, where a person is systematically confronted with a delayed effect of her or his reaction to a time-periodic external signal. The model equations are derived from purely macroscopic considerations. Applying methods developed in the realm of synergetics we can analyze the first instability in the person's behaviour semi-analytically. A careful numerical study is devoted to the higher order instabilities and a comparison between experiment and the results obtained from our model is performed in detail.

From a theoretical point of view we investigate cortical activity patterns causing dynamic visual hallucinations. For this reason we analyze an oscillatory instability of the dynamics ofthe activator-inhibitor model of Ermentrout and Cowan.Such an oscillatory instability occurs as a result of several disease mechanisms.We explicitly derive the order parameter equation. By means of the averaging theorem, we obtain the averaged order parameter equation.The latter enables us to determine stable and unstable bifurcating cortical activity patterns analytically in lowest order.Depending on model parameters as well as on initial conditions two types of cortical activity patterns occur: travelling waves and ’blinking rolls‘, i.e.standing waves oscillating with the same frequency and with a phase shift of π/2. In contrast to cortical activitypatterns caused by non-oscillatory instabilitiesanalyzed by Ermentrout and Cowan and by the author the travelling waves and the blinking rolls lead to a variety of dynamic visual hallucinations which are discussed indetail.

We analyze two nonlinearly phase coupled oscillators with eigenfrequencies ω1and ω2, where n\gw1=m\gw2+\gp, with integernandm. For \gh=0 there are up to four stable synchronized states which differ from each other only by the difference of the oscillators\rs phases. The number of different synchronized states depends on the coupling constants. If \gh does not vanish phase shifts and frequency shifts may occur givig rise to stable synchronized states which also differ from each other due to the frequencies. By means of the center manifold theorem we calculate these shifts explicitely. Different coupling constants are investigated: symmetrical, homogenously asymmetrical and arbitrary coupling constants. Our results point out the decisive influence of the symmetry of the coupling constants upon the frequency and phase shifts. Moreover the local stability of the unperturbed synchronized state (i.e. for \gh=0) determines the magnitude of the frequency and phase shifts.

We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.

We investigate the synchronization behaviour of three different networks of nonlinearly coupled oscillators. Each network consists of several clusters of oscillators, and the clusters themselves consist of any number of oscillators. In each cluster the eigenfrequencies scatter around the cluster frequency (mean frequency). The coupling strength varies in each cluster, too. We analyze the synchronized states by means of the center manifold theorem. This enables us to calculate these states explicitly, and to prove their stability. Moreover we are able to determine frequency shifts caused by different coupling mechanisms. In a number of cases we calculate the synchronisation threshold explicitely. Numerical simulations illustrate our analytical results. In one of the three networks we have additionally analyzed a single cluster consisting of infinitely many oscillators, that is an oscillatory field. Again, the center manifold theorem enabled us to calculate the synchronized state explicitly and to prove its stability. Our results concerning the oscillatory field are in contradiction to Ermentrout’s analysis [6].

The coordinated reset of neural sub-populations 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, i.e. separated by suitable fixed delays. Desynchronization is effectively 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. I suggest the novel technique to be used for demand-controlled deep brain stimulation in patients suffering from Parkinson's disease or essential tremor. Furthermore, the novel stimulation method might even be applicable to diseases with intermittently emerging synchronized neural oscillations like epilepsy.

We apply a quantitative method for the identification of asymmetric relations between weakly interacting self-sustained oscillators to the study of rhythmic neural electrical activity. We begin by testing the method on biophysically motivated neural oscillator models considering first two diffusively coupled Hindmarsh-Rose oscillators, and then two ensembles of globally coupled neurons interacting through their mean fields. Next, we consider the more complex case of interactions among several oscillatory units. The method is further applied to the analysis of the control of externally vs internally paced movements in humans. A pilot study in one healthy subject reveals that asymmetry of interactions between different brain areas may strongly change with the transition from external to internal pacing, while the degree of synchronization hardly changes. Furthermore, our preliminary results highlight the important role of the secondary auditory cortex in internal rhythm generation.

The basic principles of a stochastic approach to phase resetting in populations of interacting phase oscillators are presented in this article. This theory explains how synchronization and desynchronization processes are caused by a pulsatile stimulus. It is a central goal of this approach to establish a theoretical basis for the design of efficient and intelligent new deep brain stimulation techniques. Accordingly, the theory is used to design a new deep brain stimulation technique with feedback control in patients suffering from Parkinson's disease or essential tremor.