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

Several brain diseases are characterized by abnormalneuronal synchronization. Desynchronization of abnormal neural synchronyis theoretically compelling because of the complex dynamical mechanismsinvolved. We here present a novel type of coordinated reset (CR) stimulation.CR means to deliver phase resetting stimuli at different neuronalsub-populations sequentially, i.e. at times equidistantly distributedin a stimulation cycle. This uniform timing pattern seems to be intuitiveand actually applies to the neural network models used for the studyof CR so far. CR resets the population to an unstable cluster statefrom where it passes through a desynchronized transient, eventuallyresynchronizing if left unperturbed. In contrast, we show that theoptimal stimulation times are nonuniform. Using the model of weaklypulse-coupled neurons with phase response curves, we provide an approachthat enables to determine optimal stimulation timing patterns thatsubstantially maximize the desynchronized transient time followingthe application of CR stimulation. This approach includes an optimizationsearch for clusters in a low-dimensional pulse coupled map. As a consequence,model-specific non-uniformly spaced cluster states cause considerablylonger desynchronization transients. Intriguingly, such a desynchronizationboost with non-uniform CR stimulation can already be achieved by onlyslight modifications of the uniform CR timing pattern. Our resultssuggest that the non-uniformness of the stimulation times can be amedically valuable parameter in the calibration procedure for CR stimulation,where the latter has successfully been used in clinical and pre-clinicalstudies for the treatment of Parkinson's disease and tinnitus