Controlling synchrony by precisely timed pulses: A possible approach to deep brain stimulation

We present a model study of the synchrony level control in a highly interconnected network, e.g., in a neuronal ensemble. The proposed technique exploits delayed or non-delayed feedback and efficiently suppresses collective activity by pulsatile action. We assume that we can monitor the collective oscillation, e.g., the local field potential and that stimulation affects at least a large part of ensemble elements. We pay special attention to the minimization of intervention in the system. The key idea is to stimulate only at the most sensitive phase. To find this phase, we implement an adaptive feedback control. Estimating the instantaneous phase and amplitude of the collective mode on the fly, we achieve efficient suppression using a few pulses per oscillatory cycle. Another essential feature of the algorithm is the gradual reduction of the stimulation strength. Thus, the desired state is maintained by a very weak action. Next, we exploit the delayed values to implement a bandpass filter required to extract the rhythm of interest from its mixture with noise and other rhythms. We discuss the possible relevance of the results for neuroscience, namely, for developing advanced algorithms for deep brain stimulation.