Abstract:We show that synchronization processes can effectively be controlled with nonlinear delayed feedback. We demonstrate that nonlinear delayed feedback can have a twofold impact on the collective dynamics of large ensembles of coupled oscillators: synchronizing and, mostly, desynchronizing effects. By means of a model equation for the mean field, we explore the existence and stability of the feedback-induced desynchronized states, their multistability and dynamical properties. We propose nonlinear delayed feedbac… Show more
“…Moreover, the desynchronization regions occupy larger domains of the parameter space and increase in size for larger values of the stimulation intensity K . The favorable desynchronizing effect of NDF at large stimulation intensities has been revealed for several other models and stimulation setups 50, 54, 56, 76, 78 . We therefore investigate the behavior of the order parameter of the stimulated STN neurons while the parameter of the stimulation intensity K increases.Figure 7Impact of the pulsatile NDF stimulation (7) on the neuronal ensemble (1)-(3).…”
Computationally it was shown that desynchronizing delayed feedback stimulation methods are effective closed-loop techniques for the control of synchronization in ensembles of interacting oscillators. We here computationally design stimulation signals for electrical stimulation of neuronal tissue that preserve the desynchronizing delayed feedback characteristics and comply with mandatory charge deposit-related safety requirements. For this, the amplitude of the high-frequency (HF) train of biphasic charge-balanced pulses used by the standard HF deep brain stimulation (DBS) is modulated by the smooth feedback signals. In this way we combine the desynchronizing delayed feedback approach with the HF DBS technique. We show that such a pulsatile delayed feedback stimulation can effectively and robustly desynchronize a network of model neurons comprising subthalamic nucleus and globus pallidus external and suggest this approach for desynchronizing closed-loop DBS. Intriguingly, an interphase gap introduced between the recharging phases of the charge-balanced biphasic pulses can significantly improve the stimulation-induced desynchronization and reduce the amount of the administered stimulation. In view of the recent experimental and clinical studies indicating a superiority of the closed-loop DBS to open-loop HF DBS, our results may contribute to a further development of effective stimulation methods for the treatment of neurological disorders characterized by abnormal neuronal synchronization.
“…Moreover, the desynchronization regions occupy larger domains of the parameter space and increase in size for larger values of the stimulation intensity K . The favorable desynchronizing effect of NDF at large stimulation intensities has been revealed for several other models and stimulation setups 50, 54, 56, 76, 78 . We therefore investigate the behavior of the order parameter of the stimulated STN neurons while the parameter of the stimulation intensity K increases.Figure 7Impact of the pulsatile NDF stimulation (7) on the neuronal ensemble (1)-(3).…”
Computationally it was shown that desynchronizing delayed feedback stimulation methods are effective closed-loop techniques for the control of synchronization in ensembles of interacting oscillators. We here computationally design stimulation signals for electrical stimulation of neuronal tissue that preserve the desynchronizing delayed feedback characteristics and comply with mandatory charge deposit-related safety requirements. For this, the amplitude of the high-frequency (HF) train of biphasic charge-balanced pulses used by the standard HF deep brain stimulation (DBS) is modulated by the smooth feedback signals. In this way we combine the desynchronizing delayed feedback approach with the HF DBS technique. We show that such a pulsatile delayed feedback stimulation can effectively and robustly desynchronize a network of model neurons comprising subthalamic nucleus and globus pallidus external and suggest this approach for desynchronizing closed-loop DBS. Intriguingly, an interphase gap introduced between the recharging phases of the charge-balanced biphasic pulses can significantly improve the stimulation-induced desynchronization and reduce the amount of the administered stimulation. In view of the recent experimental and clinical studies indicating a superiority of the closed-loop DBS to open-loop HF DBS, our results may contribute to a further development of effective stimulation methods for the treatment of neurological disorders characterized by abnormal neuronal synchronization.
“…Clinical studies have reported a reduction in the level of beta-band activity following the application of DBS [8], [4], leading to the LFP's being suggested as a biomarker for use in the design of closed-loop DBS [9]. Whilst computational investigations of "mild" stimulation methods, such as coordinated reset and mean field feedback, suggest a return to physiological network activity [12], [13], [14], closed-loop high frequency DBS relies on the same underlying mechanisms of action as openloop DBS. It is likely that closed-loop high frequency DBS would be more immediately suitable for implementation than alternative closed-loop methods, due to the similarity of the signal generation circuitry to current open-loop technology.…”
Section: Discussionmentioning
confidence: 99%
“…The first uses high-frequency DBS waveforms as currently used in open-loop configuration, but applies closed-loop control to vary the stimulation parameters [10]. The second, termed "mild stimulation", attempts to desynchronise pathological oscillatory networks in an on-demand fashion [11], [12], [13], [14]. At present, the only implanted stimulation hardware for closed-loop DBS that has been proposed for clinical use is designed to deliver high-frequency DBS [15].…”
“…Till now, several methods such as desynchronization with pulsatile stimulation protocols (Tass 1999(Tass , 2001a(Tass ,b, 2002(Tass , 2003, time delayed feedback (Rosenblum and Pikovsky 2004a;Popovych et al 2005), and proportional-integro-differential feedback (Pyragas et al 2007) have been presented in theoretical and numerical studies. For its effectiveness and robustness, time delayed feedback for desynchronization in ensembles of globally coupled oscillators has been extensively studied (Rosenblum and Pikovsky 2004a,b;Popovych et al 2005Popovych et al , 2006Popovych et al , 2008Hauptmann et al 2005;Rosenblum et al 2006). However, it may bring undesirable instability and requires careful parameter tuning.…”
We propose an approach for desynchronization in an ensemble of globally coupled neural oscillators. The impact of washout filter aided mean field feedback on population synchronization process is investigated. By blocking the Hopf bifurcation of the mean field, the controller desynchronizes the ensemble. The technique is generally demand-controlled. It is robust and can be easily implemented practically. We suggest it for effective deep brain stimulation in neurological diseases characterized by pathological synchronization.
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