Delayed Feedback Control of Oscillations in a Spiking Neural
Network Model of Aberrant Brain Dynamics
Ioannis Vlachos and Arvind Kumar
Bernstein Center Freiburg, University of Freiburg, Hansastrasse 9a, Freiburg, Germany
Keywords: Closed-Loop Control, Oscillations, Desynchronization, DBS.
Abstract: Open-loop methods for deep-brain stimulation have been effective in controlling aberrant activity associated
with various neurological disorders such as Parkinson's disease. Recently, adaptive control strategies have
emerged, which promise to increase the efficacy of these existing stimulation methods. Here, we investigate
the effects of closed-loop control schemes in networks of spiking neurons that operate in a synchronous
irregular regime. In this regime the population activity is highly regular, despite the fact that individual
neurons fire stochastically. These oscillations are known to be robust compared to synchronous regular
activity and are not easily affected by noise or heterogeneity. We design an appropriate control strategy,
based on delayed state-feedback to quench these stochastic oscillations. We also show that our control
protocol is able to restore the network transfer function thus overcoming the undesired side-effects of
existing methods.
During the last two decades various methods such as
high-frequency deep brain stimulation (DBS) have
been developed for the treatment of oscillations
associated with several pathological conditions, e.g.
in Parkinson's disease (Perlmutter, 2006). These
methods have been traditionally based on open-loop
strategies, that is on fixed, predetermined stimu-
lation parameters. They have been highly effective
in quenching the aberrant oscillations and, thus, in
alleviating the clinical symptoms. At the same time,
however, they introduce undesirable side effects and
in most cases they do not restore the network
transfer function. Recently, adaptive control
strategies have emerged, which promise to increase
the efficacy of the existing stimulation methods to
control and correct the network activity dynamics
(Priori, 2013).
Here, we investigate the effects of closed-loop
control schemes in networks of spiking neurons.
Previous results have shown that delayed feedback
can be used to desynchronizes a network of neurons,
in which the population dynamics results from the
coupling of single neurons modeled themselves as
phase oscillators. In this work, we do not assume
individual neurons to behave as oscillators, i.e. to
fire synchronously and in a regular manner. We
rather fine-tune the network to operate in a
synchronous irregular regime, in which neurons fire
stochastically with frequencies much lower than the
population frequency (Brunel, 1999). These
oscillations are known to be robust compared to
synchronous regular activity (Brunel, 2008) and are
not easily affected by noise or heterogeneity.
We design an appropriate control strategy, based on
delayed state-feedback to quench these sparse or
stochastic oscillations, which resemble a wide range
of pathological conditions. Our control protocol is
able to sufficiently suppress the oscillations and to
drive the network in an asynchronous irregular
regime. Importantly, the network transfer function,
defined as the ratio of the population rate response to
incoming stimuli, is also recovered. Our results thus
suggest that delayed state-feedback control is a
promising strategy to design brain stimulation
protocols to correct stochastic oscillations without
inducing strong side-effects.
ACKNOWLEDGEMENTS
Supported by the German Federal Ministry of
Education and Research (BMBF 01GQ0420 to
BCCN Freiburg) and the Cluster of Excellence
BrainLinks-BrainTools funded by German Research
Foundation (DFG, grant number EXC 1086).
Vlachos I. and Kumar A..
Delayed Feedback Control of Oscillations in a Spiking Neural Network Model of Aberrant Brain Dynamics.
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Effects of closed-loop control on stochastic oscillations. Synchronous irregular activity in a network of one
thousand leaky-integrate-and-fire neurons (left). Delayed state-feedback control is switched on at 100ms. Oscillations are
quenched and the network is driven in an asynchronous irregular regime (right).
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