Synchronization control of interacting oscillatory ensembles by mixed nonlinear delayed feedback.

We propose a method for the control of synchronization in two oscillator populations interacting according to a drive-response coupling scheme. The response ensemble of oscillators, which gets synchronized because of a strong forcing by the intrinsically synchronized driving ensemble, is controlled by mixed nonlinear delayed feedback. The stimulation signal is constructed from the mixed macroscopic activities of both ensembles. We show that the suggested method can effectively decouple the interacting ensembles from each other, where the natural desynchronous dynamics can be recovered in a demand-controlled way either in the stimulated ensemble, or, intriguingly, in both stimulated and not stimulated populations. We discuss possible therapeutic applications in the context of the control of abnormal brain synchrony in loops of affected neuronal populations.

[1]  Peter A. Tass,et al.  Control of Neuronal Synchrony by Nonlinear Delayed Feedback , 2006, Biological Cybernetics.

[2]  P. Brown.  Oscillatory nature of human basal ganglia activity: Relationship to the pathophysiology of Parkinson's disease , 2003, Movement disorders : official journal of the Movement Disorder Society.

[3]  Scott T. Grafton,et al.  Normalizing motor-related brain activity , 2006, Neurology.

[4]  Peter A. Tass,et al.  A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations , 2003, Biological Cybernetics.

[5]  P. Gatev,et al.  Oscillations in the basal ganglia under normal conditions and in movement disorders , 2006, Movement disorders : official journal of the Movement Disorder Society.

[6]  J. Vitek,et al.  Stimulation of the Subthalamic Nucleus Changes the Firing Pattern of Pallidal Neurons , 2003, The Journal of Neuroscience.

[7]  J. Dostrovsky,et al.  High-frequency Synchronization of Neuronal Activity in the Subthalamic Nucleus of Parkinsonian Patients with Limb Tremor , 2000, The Journal of Neuroscience.

[8]  E. Vaadia,et al.  Physiological aspects of information processing in the basal ganglia of normal and parkinsonian primates , 1998, Trends in Neurosciences.

[9]  H. Bergman,et al.  Neurons in the globus pallidus do not show correlated activity in the normal monkey, but phase-locked oscillations appear in the MPTP model of parkinsonism. , 1995, Journal of neurophysiology.

[10]  H. Freund,et al.  The causal relationship between subcortical local field potential oscillations and Parkinsonian resting tremor , 2010, Journal of neural engineering.

[11]  C Hauptmann,et al.  Control of spatially patterned synchrony with multisite delayed feedback. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Peter A. Tass,et al.  Long-term anti-kindling effects of desynchronizing brain stimulation: a theoretical study , 2005, Biological Cybernetics.

[13]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[14]  Peter A. Tass,et al.  Delayed feedback control of synchronization in locally coupled neuronal networks , 2005, Neurocomputing.

[15]  J. Dostrovsky,et al.  Stimulation-induced inhibition of neuronal firing in human subthalamic nucleus , 2004, Experimental Brain Research.

[16]  C. Wilson,et al.  Overwhelmingly asynchronous firing of rat subthalamic nucleus neurones in brain slices provides little evidence for intrinsic interconnectivity , 2004, Neuroscience.

[17]  Christian Hauptmann,et al.  Effective desynchronization by nonlinear delayed feedback. , 2005, Physical review letters.

[18]  G. Deuschl,et al.  Neuronal activity of the human subthalamic nucleus in the parkinsonian and nonparkinsonian state. , 2008, Journal of neurophysiology.

[19]  A. Benabid,et al.  Long-term suppression of tremor by chronic stimulation of the ventral intermediate thalamic nucleus , 1991, The Lancet.

[20]  C. McIntyre,et al.  Uncovering the mechanism(s) of action of deep brain stimulation: activation, inhibition, or both , 2004, Clinical Neurophysiology.

[21]  P. Brown,et al.  Different functional loops between cerebral cortex and the subthalmic area in Parkinson's disease. , 2006, Cerebral cortex.

[22]  A. Schnitzler,et al.  Normal and pathological oscillatory communication in the brain , 2005, Nature Reviews Neuroscience.

[23]  J. Volkmann.  DEEP BRAIN STIMULATION II Deep Brain Stimulation for the Treatment of Parkinson’s Disease , 2004 .

[24]  H. Freund,et al.  The cerebral oscillatory network of parkinsonian resting tremor. , 2003, Brain : a journal of neurology.

[25]  M. Delong,et al.  Deep Brain Stimulation for Neurologic and Neuropsychiatric Disorders , 2006, Neuron.

[26]  M. Rosenblum,et al.  Controlling synchronization in an ensemble of globally coupled oscillators. , 2004, Physical review letters.

[27]  P. Brown,et al.  Cortico-cortical coupling in Parkinson's disease and its modulation by therapy. , 2005, Brain : a journal of neurology.

[28]  J. Bolam,et al.  Dopamine regulates the impact of the cerebral cortex on the subthalamic nucleus–globus pallidus network , 2001, Neuroscience.

[29]  Peter A. Tass,et al.  Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study , 2005, Biological Cybernetics.

[30]  G. Deuschl,et al.  Pathophysiology of Parkinson's disease: From clinical neurology to basic neuroscience and back , 2002, Movement disorders : official journal of the Movement Disorder Society.

[31]  W Singer,et al.  Visual feature integration and the temporal correlation hypothesis. , 1995, Annual review of neuroscience.

[32]  Peter A. Tass,et al.  Controlling synchrony in oscillatory networks with a separate stimulation-registration setup , 2007 .

[33]  C. Gray,et al.  Dynamics of tremor-related oscillations in the human globus pallidus: a single case study. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Balth van der Pol Jun Docts. Sc.,et al.  LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart , 1928 .

[35]  J. Obeso,et al.  Bilateral deep brain stimulation in Parkinson's disease: a multicentre study with 4 years follow-up. , 2005, Brain : a journal of neurology.

[36]  Peter A. Tass,et al.  Desynchronization and Decoupling of Interacting oscillators by Nonlinear Delayed Feedback , 2006, Int. J. Bifurc. Chaos.

[37]  R. Ilmoniemi,et al.  Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain , 1993 .

[38]  P. Tass.  Phase Resetting in Medicine and Biology , 1999 .

[39]  F. Ritort,et al.  A moment-based approach to the dynamical solution of the Kuramoto model , 1997 .

[40]  Thomas Wichmann,et al.  Circuits and circuit disorders of the basal ganglia. , 2007, Archives of neurology.

[41]  P. Brown,et al.  Reduction in subthalamic 8–35 Hz oscillatory activity correlates with clinical improvement in Parkinson's disease , 2006, The European journal of neuroscience.

[42]  J. Timmer,et al.  Tremor-correlated neuronal activity in the subthalamic nucleus of Parkinsonian patients , 2008, Neuroscience Letters.

[43]  Peter A Tass,et al.  Response clustering in transient stochastic synchronization and desynchronization of coupled neuronal bursters. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  P. Bossuyt,et al.  A comparison of continuous thalamic stimulation and thalamotomy for suppression of severe tremor. , 2000, The New England journal of medicine.

[45]  H. Freund,et al.  The generation of Parkinsonian tremor as revealed by directional coupling analysis , 2008 .

[46]  Hiroshi Kori,et al.  Engineering Complex Dynamical Structures: Sequential Patterns and Desynchronization , 2007, Science.

[47]  S. Groiss,et al.  Characterisation of tremor‐associated local field potentials in the subthalamic nucleus in Parkinson’s disease , 2009, The European journal of neuroscience.

[48]  P. Tass.  Desynchronization by Means of a Coordinated Reset of Neural Sub-Populations A Novel Technique for Demand-Controlled Deep Brain Stimulation , 2003 .

[49]  Balth. van der Pol,et al.  VII. Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode) , 1927 .

[50]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[51]  A. Lang,et al.  Long-term follow-up of thalamic deep brain stimulation for essential and parkinsonian tremor , 2003, Neurology.

[52]  P. Gatev,et al.  Interactions between cortical rhythms and spiking activity of single basal ganglia neurons in the normal and parkinsonian state. , 2009, Cerebral cortex.