Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson's Disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson's disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson's disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.Comment: 19 pages, 8 figure

Delayed feedback control in quantum transport

Feedback control in quantum transport has been predicted to give rise to several interesting effects, amongst them quantum state stabilisation and the realisation of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system be affected instantaneously after the measurement of electronic jumps through it. In this contribution I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state-stabilisation and Maxwell's-daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.Comment: 13 pages, 5 figure

It's all about timing : an electrophysiological examination of feedback-based learning with immediate and delayed feedback

Feedback regarding an individual's action can occur immediately or with a temporal delay. Processing of feedback that varies in its delivery time is proposed to engage different brain mechanisms. fMRI data implicate the striatum in the processing of immediate feedback, and the medial temporal lobe (MTL) in the processing of delayed feedback. The present study offers an electrophysiological examination of feedback processing in the context of timing, by studying the effects of feedback timing on the feedback-related negativity (FRN), a product of the midbrain dopamine system, and elucidating whether the N170 ERP component could capture MTL activation associated with the processing of delayed feedback. Participants completed a word-object paired association learning task; they received feedback 500 ms (immediate feedback condition) following a button press during the learning of two sets of 14 items, and at a delay of 6500 ms (delayed feedback condition) during the learning of the other two sets. The results indicated that while learning outcomes did not differ under the two timing conditions, Event Related Potential (ERPs) pointed to differential activation of the examined ERP components. FRN amplitude was found to be larger following the immediate feedback condition when compared with the delayed feedback condition, and sensitive to valence and learning only under the immediate feedback condition. Additionally, the amplitude of the N170 was found larger following the delayed feedback condition when compared with the immediate feedback condition. Taken together, the findings of the present study support the contention that the processing of delayed feedback involves a shift away from midbrain dopamine activation to the recruitment of the MTL

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 timescales of noise-induced motion by changing the time delay.Comment: 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d) were amended. The reason is numerical error found, that affected the quantitative estimates of correlation time, but did not affect the main messag

Delayed Feedback Control near Hopf Bifurcation

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The results are used to compare delayed versus undelayed feedback, as well as discrete versus distributed delays. Conditions are obtained for which delayed feedback with partial state information can yield stability where undelayed feedback is ineffective. Furthermore, it is shown that if the feedback is stabilizing (respectively, destabilizing), then a discrete delay is locally the most stabilizing (resp., destabilizing) one among delay distributions having the same mean. The result also holds globally if one considers delays that are symmetrically distributed about their mean

Bifurcation structure of cavity soliton dynamics in a VCSEL with saturable absorber and time-delayed feedback

We consider a wide-aperture surface-emitting laser with a saturable absorber section subjected to time-delayed feedback. We adopt the mean-field approach assuming a single longitudinal mode operation of the solitary VCSEL. We investigate cavity soliton dynamics under the effect of time- delayed feedback in a self-imaging configuration where diffraction in the external cavity is negligible. Using bifurcation analysis, direct numerical simulations and numerical path continuation methods, we identify the possible bifurcations and map them in a plane of feedback parameters. We show that for both the homogeneous and localized stationary lasing solutions in one spatial dimension the time-delayed feedback induces complex spatiotemporal dynamics, in particular a period doubling route to chaos, quasiperiodic oscillations and multistability of the stationary solutions

Spontaneous spiking in an autaptic Hodgkin-Huxley set up

The effect of intrinsic channel noise is investigated for the dynamic response of a neuronal cell with a delayed feedback loop. The loop is based on the so-called autapse phenomenon in which dendrites establish not only connections to neighboring cells but as well to its own axon. The biophysical modeling is achieved in terms of a stochastic Hodgkin-Huxley model containing such a built in delayed feedback. The fluctuations stem from intrinsic channel noise, being caused by the stochastic nature of the gating dynamics of ion channels. The influence of the delayed stimulus is systematically analyzed with respect to the coupling parameter and the delay time in terms of the interspike interval histograms and the average interspike interval. The delayed feedback manifests itself in the occurrence of bursting and a rich multimodal interspike interval distribution, exhibiting a delay-induced reduction of the spontaneous spiking activity at characteristic frequencies. Moreover, a specific frequency-locking mechanism is detected for the mean interspike interval.Comment: 8 pages, 10 figure