Synchronization in Nonlinear Systems and Networks

Transcription

1 Synchronization in Nonlinear Systems and Networks Yuri Maistrenko you can find me in room EW 632 1

2 Lecture SYNCHRONIZATION At the heart of the Universe is a steady, insistent beat: the sound of cycles in sync. It pervades nature at every scale from the nucleus to the cosmos Steven Strogatz, Sync

3 Pathological synchronization in Parkinson s disease Parkinson s disease is characterized by pathological synchronization of neuronal activity in subthalamic nucleus (STN) and external segment of globus pallidus (GPe): Namely, some part of the STN-GPe neurons starts to fires synchronously at some frequency in the beta-band 10-30Hz By contrast, under healthy conditions these neurons fire in an uncorrelated and desynchronized manner. HOW TO DESYNCHRONIZE?

4 Deep Brain Stimulation (Benabid, 1986) permanent high-frequency stimulation >90 Hz Tremor amplitude as a function of DBS frequency electrode target poin generator From : 4

5 Experimental data: beta-band synchronization (~10-30 Hz)

6 Recording individual GPE cells Normal monkey Parkinsonian monkey 6

7 Beta-band synchronization of STN neurons 7

8 Parkinsonian spectrum Healthy spectrum 8

9 Development of deep brain stimulation techniques with methods from nonlinear dynamics or How to desynchronize pathologic neuronal synchrony in the brain National Academy of Sciences of Ukraine Institute of Neuroscience and Medicine Research Center Jülich Pittsburg University Co-workers: R.Levchenko (Kyiv) B.Lysyansky (Juelich-Kyiv) Yu.Maistrenko (Juelich-Kyiv J.Rubin (Pittsburg) O.Sudakov (Kyiv) P.Tass (Juelich)

10 How to switch from pathologic synchronouse to healthy desynchronized state? Intuitively: phenonenon of multistability can help for desirable transitions between the characteristic states If so: one can apply deep brain stimulation (DBS) with a hope to turn from the synchronization to desynchronization by resetting the initial conditions But first: to study the phenomenon, we have to build a model for individual neurons and for connectivity in the network.

11 Why do we need to build the model? I have all these data in the cortex - cell types, their firing properties, dendritic excitability, connectivity, synaptic dynamics,. But I don t Understand it. I need to model it. Why so? Bert Sakmann, 2001 Nobel Prize in Physiology and Medicine, 1991 University of Heidelberg Indeed: we MUST to connect - its structure (connectivity), - its synaptic properties, - its spiking repertoire TO ITS FUNCTION 11

12 How to model an individual neuron? carefully reduce (capture the essence) Kiss - detailed Kiss reduced Rodin Brancusi

13 Hodgkin-Huxley model Alan Lloyd Hodgkin Andrew Fielding Huxley The H&H model; (1) Biophysical, (2) Compact, (3) Predictive I.Segev. Third Vogt-Brodmann Symposium Information Processing in Cortical Networks. Juelich-2009

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15 Network of excitatory (STN) and inhibitory(gpe) neurons STN GPe

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17 Parameters for STN and GPe neurons

18 Network topology Strong connectivity Weak connectivity 18

19 2000 coupled neurons 19

20 2000 coupled neurons 20

21 Four different system parameters to vary Coupling coefficient Coupling coefficient Coupling coefficient External current S G G G G S

22 PARALLEL SOFTWARE FOR NONLINEAR DYNAMICS AND INFORMATION PROCESSING IN LARGE NEURONAL NETWORKS OF THE BRAIN Yu.L.Maistrenko (1,2,4), O.O.Sudakov (2,3), and R.I.Levchenko (2,3) (1) Institute of Mathematics and (2) Centre for Medical and Biotechnical Research, Kiev, Ukraine (3) Medical Radiophysics Department, Kiev University, Ukraine (4) Institute of Neuroscience and Medicine (INM-2), Juelich, Germany Software architecture Config Config Generators Generators Integrator Analyzers Analyzers Creation of config files: Neurons parameters, Links matrix, Initial state Parallel integration of differential equations: Output of dynamic variables time frames based on configuration Analysis of dynamics data: Synchronization, LFP, Power spectrum The software was tested on the model of 2000, and STN-GPe neurons

23 Neurons list Neurons list log(psd) log(psd) 32 Parkinsonian Healthy LFP spectrum frequency, Hz frequency, Hz Regular bursting mode Irregular spiking mode Space-time network activity t, ms t, ms Regular bursting mode Irregular spiking mode

24 Synchronization analysis 24

25 Destruction of the parkinsonian bursting by period doubling and intermittency

26 Parkinsonian bursting GPe cell STN cell

27 Parkinsonian bursting 27

28 Period-double bursting

29 Spike-bursting G S

30 Three-attractors intermittency parkins. bursting spike-bursting period-double bursting

31 Parkinsonian bursting: space-time dynamics Gpe cells STN cells time

32 Chaotic spiking G G 32

33 Periodic spiking G G 33

34 Periodic spiking: space-time dynamics Gpe cells STN cells time

35 Healthy irregular spiking: individual STN dynamics

36 Healthy irregular spiking: space-time dynamics

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40 Low-periodic spiking: space-time dynamics

41 What can we conclude from the modelling study? Network connectivity plays a crucial role for the STN-GPe network dynamics: namely, sparser connectivity provokes appearance of synchronouse bursting Two characteristic regimes, chaotic spiking and regular bursting are confirmed by massive parallel supercomputing (~600 trajectories of ~10000 ms for 2000 neurons) But, both regimes can exist only at distinct coupling configurations How to help parkinsonian patients? Unfortunately, there is no another way to switch from regular bursting (synchronization) to chaotic spiking (desynchronization) except as modifying neuronal connectivity in the network.

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43 Network architecture 43

44 Network architecture 44

45 Excitatory cells Inhibitory cells 45

46 Sodium current 46

47 The main result: synchronized waves 47

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49 - bidirectional connections are more common than one can expected, if the network connections be random - distribution of the connection strength differ significantly from random and characterized by a long tail - synaptic weight is concentrated among few srtong synaptic connections Neuronal connectivity represents a skeleton of stronger connections in the sea of weaker ones! 49

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51 The next UNIT to model (The Neocortical - column ) (1mm 3 ) Size of a pin head

52 Connectivity in cortical column: neuronal microcircuits 52

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