Desynchronization boost by non-uniform coordinated reset stimulation in ensembles of pulse-coupled neurons

Leonhard Lücken,Oleksandr V Popovych,Serhiy Yanchuk,Peter A Tass

doi:10.3389/fncom.2013.00063

Abstract

Several brain diseases are characterized by abnormal neuronal synchronization. Desynchronization of abnormal neural synchrony is theoretically compelling because of the complex dynamical mechanisms involved. We here present a novel type of coordinated reset (CR) stimulation. CR means to deliver phase resetting stimuli at different neuronal sub-populations sequentially, i.e., at times equidistantly distributed in a stimulation cycle. This uniform timing pattern seems to be intuitive and actually applies to the neural network models used for the study of CR so far. CR resets the population to an unstable cluster state from where it passes through a desynchronized transient, eventually resynchronizing if left unperturbed. In contrast, we show that the optimal stimulation times are non-uniform. Using the model of weakly pulse-coupled neurons with phase response curves, we provide an approach that enables to determine optimal stimulation timing patterns that substantially maximize the desynchronized transient time following the application of CR stimulation. This approach includes an optimization search for clusters in a low-dimensional pulse coupled map. As a consequence, model-specific non-uniformly spaced cluster states cause considerably longer desynchronization transients. Intriguingly, such a desynchronization boost with non-uniform CR stimulation can already be achieved by only slight modifications of the uniform CR timing pattern. Our results suggest that the non-uniformness of the stimulation times can be a medically valuable parameter in the calibration procedure for CR stimulation, where the latter has successfully been used in clinical and pre-clinical studies for the treatment of Parkinson's disease and tinnitus.

Highlights

IntroductionPathological neuronal synchronization is a hallmark of several neurological disorders like Parkinson’s disease (PD), essential tremor, tinnitus, or epilepsy (Lenz et al, 1994; Nini et al, 1995; Mormann et al, 2000; Weisz et al, 2005, 2007; Kane et al, 2009; Schnitzler et al, 2009; Roberts et al, 2010), whereas the neuronal firing is uncorrelated in the normal state (Nini et al, 1995; Wilson et al, 2004) such that the abnormal synchronization is associated with pathology and symptoms (Levy et al, 2000)
In order to further optimize the therapeutic benefit of coordinated reset (CR) stimulation, in this paper we investigate the impact of the stimulation parameters and the stimulation protocol on the stimulationinduced desynchronization
A number of pulsatile stimulation techniques have been developed which enable to directly shift a synchronized neuronal population into a desynchronized state, irrespective of the initial state at which the stimulus is delivered (Tass, 2001a,b, 2002a,b). Less favorably, these techniques require careful calibration of the stimulation parameters and their continuous adaptation to varying model parameters. To overcome this limitation and provide a desynchronizing stimulation technique which is robust and does not require time-consuming or technically involved calibration procedures, CR’s indirect approach to desynchronization was developed (Tass, 2003a,b): Inducing a cluster state by means of time-shifted phase resetting stimuli delivered to different neuronal sub-populations can robustly be achieved and does not require relevant calibration (Tass, 2003a,b)

Summary

Introduction

Pathological neuronal synchronization is a hallmark of several neurological disorders like Parkinson’s disease (PD), essential tremor, tinnitus, or epilepsy (Lenz et al, 1994; Nini et al, 1995; Mormann et al, 2000; Weisz et al, 2005, 2007; Kane et al, 2009; Schnitzler et al, 2009; Roberts et al, 2010), whereas the neuronal firing is uncorrelated in the normal state (Nini et al, 1995; Wilson et al, 2004) such that the abnormal synchronization is associated with pathology and symptoms (Levy et al, 2000). Along the lines of a model-based approach (Tass, 1999) novel stimulation techniques have been developed (Tass, 2001a, 2003a,b; Rosenblum and Pikovsky, 2004; Hauptmann et al, 2005; Popovych et al, 2005, 2006; Pyragas et al, 2007; Popovych and Tass, 2010), which selectively counteract the pathological synchronization and restore uncorrelated neuronal firing. They are based on either phase resetting or feedback approaches, where from a theoretical standpoint the latter might have a great potential in controlling pathological synchronization, but so far have not been technically realized

Methods

Results

Conclusion