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

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.