Development of novel deep brain stimulation techniques: Coordinated reset and Nonlinear delayed feedback

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Development of novel deep brain stimulation techniques: Coordinated reset and Nonlinear delayed feedback Oleksandr Popovych 1, Christian Hauptmann 1, Peter A.

1 Development of novel deep brain stimulation techniques: Coordinated reset and Nonlinear delayed feedback Oleksandr Popovych 1, Christian Hauptmann 1, Peter A. Tass 1,2 1 Institute of Medicine and Virtual Institute of Neuromodulation, Research Center Jülich, D Jülich, Germany 2 Department of Stereotaxic and Functional Neurosurgery, University Hospital, D Cologne, Germany

Deep brain stimulation strong synchronization of neuronal clusters may cause different disease symptoms like peripheral tremor (Morbus Parkinson) or

2 Deep brain stimulation strong synchronization of neuronal clusters may cause different disease symptoms like peripheral tremor (Morbus Parkinson) or epileptic seizures Treatment: strong permanent pulsetrain stimulation signal suppress or over-activate neuronal activity may cause severe side effects

3 Limitations of standard deep brain stimulation: 1. Non-responders: no improvement of tremor (13 %), rigidity (41 %), bradykinesia (58 %), gait (59 %), postural stability (69 %) with bilateral STN (subthalamic nucleus) stimulation Rodriguez-Oroz et al., Brain Adverse effects: in 53 % / 35 % with bilateral STN / bilateral GPi (internal pallidum) stimulation: cognition (memory decline, psychiatric disturbances), depression, speech disturbances (dysphonia, dysarthria), dysequilibrium (falls, balance disturbances) Rodriguez-Oroz et al., Brain Habituation = decrease of therapeutic effect over time: e.g. in patients with essential tremor in % within the first year Allert et al., unpublished data

4 Model-based development of deep brain stimulation Specifically counteract the pathological synchronization processes by demand-controlled desynchronization Tass: Phase Resetting in Medicine and Biology. Springer 1999 Control techniques are designed with methods from statistical physics and nonlinear dynamics in oscillator networks and models of neuronal target populations Exploit dynamical self-organization principles to establish a mild, but effective control by means of 1. Multisite coordinated reset Tass: Biol. Cybern. 2003; Phys. Rev. E 2003; Prog. Theor. Phys Nonlinear delayed feedback Popovych, Hauptmann, Tass: Phys. Rev. Lett. 2005; Int. J. Bif. Chaos, in press

5 Coordinated reset of neuronal sub-populations

6 Effective desynchronization by a multisite coordinated reset 3-cluster state coordinated reset synchronized state Stimulaton sites 1,2,3 spontaneous relaxation (slaving principle, H. Haken) spontaneous resynchronization j / 3 Stimulation site 1 2 uniform desynchronization 2 / 3 Time / 3 stimulation period Tass, Biol. Cybern (2003); Phys. Rev. E 2003; Prog. Theor. Phys. (2003)

7 Multisite coordinated reset Model j j Model neuron = phase oscillator Ermentrout & Kopell 1991, Grannan et al. 1993, Hansel et al. 1993

firing pattern time/period Electrodes 1,.

8 Desynchronizing deep brain stimulation by means of a coordinated reset of neural sub-populations Pattern of pulse trains administered at different stimulation sites Electrode extent of synch. firing pattern time/period Electrodes 1,...,4 no time consuming calibration effective also in case of intermittent epochs of synchronization (epilepsy!) Tass, Biol. Cybern (2003); Prog. Theor. Phys. (2003)

, submitted 3 standard high-frequency stimulation, 133 Hz, 3V 0/3 0/2 coordinated reset 5 Hz, 3V 2 0 1 tremor, acc.

9 Tremor suppression by multisite coordinated reset stimulation (Parkinson s disease, 54 ys., stimulation of the left STN, tremor frequency ~ 4.5 Hz) Tass et al., submitted 3 standard high-frequency stimulation, 133 Hz, 3V 0/3 0/2 coordinated reset 5 Hz, 3V tremor, acc. right hand Time [s] contacts 0 3 f [Hz] / 3 2 / 3 Time / stimulation period 200 ms Time (s) asymmetrical anodic first cathodic second charge balanced biphasic stimulus asymmetrical cathodic first anodic second charge balanced biphasic stimulus

10 Tremor suppression by multisite coordinated reset stimulation (tremor due to multiple sclerosis, 37 ys., stimulation of the right VIM, tremor frequency ~ 4.5 Hz) 2 mm anterior 2 Coordinated reset via 5 electodes medial / 5 2 / 5 3 / 5 4 / 5 Electrodes 1,...,5 electrodes Inomed MER system Time / stimulation period 200 ms

5 Hz) standard high-frequency stimulation 133 Hz, 3V, between electrodes 1 5 (most effective) coordinated reset, 5 Hz, 3V tremor,

11 Tremor suppression by multisite coordinated reset stimulation (tremor due to multiple sclerosis, 37 ys., stimulation of the right VIM, tremor frequency ~ 4.5 Hz) standard high-frequency stimulation 133 Hz, 3V, between electrodes 1 5 (most effective) coordinated reset, 5 Hz, 3V tremor, acc. right hand f [Hz] tremor, acc. right foot f [Hz] Inomed MER system Time (s) asymmetrical anodic first cathodic second charge balanced biphasic stimulus asymmetrical cathodic first anodic second charge balanced biphasic stimulus

Multisite coordinated reset stimulation versus standard high-frequency stimulation First intraoperative study: 100% = prestimulus baseline Mean residual tremor amplitude: 38 % ± 32 % (high-frequency

12 Multisite coordinated reset stimulation versus standard high-frequency stimulation First intraoperative study: 100% = prestimulus baseline Mean residual tremor amplitude: 38 % ± 32 % (high-frequency stimulation) 17 % ± 11 % (coordinated reset stimulation) P = 0.05 (paired one-tailed T-test) Tass et al., submitted Amount of stimulation used: 64% ± 22% (high-frequency stimulation) 16% ± 10% (coordinated reset stimulation) P < (paired one-tailed T-test)

13 Multisite coordinated reset causes a transient desynchronization repetitive stimulus administration is necessary (Parkinson s disease, 71 ys., stimulation of the right VIM) of ACC ACC = accelerometer EMG = electromyogram

14 Desynchronization by nonlinear delayed feedback

15 Stimulation with nonlinear delayed feedback

16 Stimulation with nonlinear delayed feedback Measured signal Z(t): mean field of the ensemble complex signal Z(t) = X(t) + iy (t)

17 Stimulation with nonlinear delayed feedback Measured signal Z(t): mean field of the ensemble complex signal Z(t) = X(t) + iy (t) Stimulation signal: S(t) := KZ 2 (t)z (t τ)

18 Stimulation with nonlinear delayed feedback Measured signal Z(t): mean field of the ensemble complex signal Z(t) = X(t) + iy (t) Stimulation signal: S(t) := KZ 2 (t)z (t τ) [1] M.K.S. Yeung and S.H. Strogatz, Phys. Rev. Lett. 82, 648 (1999) [2] M.G. Rosenblum and A.S. Pikovsky, Phys. Rev. Lett. 92, (2004) [3] O.V. Popovych, C. Hauptmann, and P.A. Tass, Phys. Rev. Lett. 94, (2005)

19 Linear delayed feedback: N coupled oscillators with delay ψ i = ω i + K N NX sin [ψ j (t τ) ψ i (t)] j=1 M.K.S. Yeung and S.H. Strogatz, Phys. Rev. Lett. 82, (1999)

20 Stimulation: coupled limit-cycle oscillators Ż j (t) = (a j +iω j Z j (t) 2 )Z j (t)+cz(t) Z(t) = X(t)+iY (t) = 1 N NX Z j (t) j=1

21 Stimulation: coupled limit-cycle oscillators Ż j (t) = (a j +iω j Z j (t) 2 )Z j (t)+cz(t) Z(t) = X(t)+iY (t) = 1 N NX Z j (t) j=1 + KZ 2 (t)z (t τ) {z } Stimulation Term

22 Stimulation: coupled limit-cycle oscillators Ż j (t) = (a j +iω j Z j (t) 2 )Z j (t)+cz(t) Z(t) = X(t)+iY (t) = 1 N NX Z j (t) j=1 + KZ 2 (t)z (t τ) {z } Stimulation Term N = 100, a j = 1.0, {ω j } Gaussian distributed: mean Ω 0 = 2π/T, T = 5 deviation σ = 0.1

23 Stimulation: coupled limit-cycle oscillators Ż j (t) = (a j +iω j Z j (t) 2 )Z j (t)+cz(t) Z(t) = X(t)+iY (t) = 1 N NX Z j (t) j=1 + KZ 2 (t)z (t τ) {z } Stimulation Term N = 100, a j = 1.0, {ω j } Gaussian distributed: mean Ω 0 = 2π/T, T = 5 deviation σ = 0.1 C = 1 for t > 250 K = 150 for t > 400 delay τ = 5.0 = T

24 Stimulation: coupled relaxation van der Pol and chaotic Rössler oscillators ẋ j = y j ẏ j = µ j (1 x 2 j )y j x j + CY +Im[S(t)] µ = 2.5 ± 0.2, T 8.3, τ = 5

25 Stimulation: coupled relaxation van der Pol and chaotic Rössler oscillators ẋ j = y j ẏ j = µ j (1 x 2 j )y j x j + CY +Im[S(t)] ẋ j = ω j y j z j + CX ẏ j = ω j x j y j +Re[S(t)] ż j = z j (x j 8.0) µ = 2.5 ± 0.2, T 8.3, τ = 5 ω = 1 ± 0.01, T 6, τ = 15

26 Effective desynchronization of coupled limit-cycle oscillators The averaged order parameter: R(t) := D 1 N NP j=1 Z j (t) Z j (t) E 100 K T τ 2T 3T 0.0

27 Effective desynchronization of coupled limit-cycle oscillators The averaged order parameter: R(t) := D 1 N NP j=1 Z j (t) Z j (t) E 100 K T τ 2T 3T 0.0

Effective desynchronization of coupled limit-cycle oscillators The averaged order parameter: R(t) := D 1 N NP j=1 Z j (t) Z j (t) E 100 K 0

28 Effective desynchronization of coupled limit-cycle oscillators The averaged order parameter: R(t) := D 1 N NP j=1 Z j (t) Z j (t) E 100 K T τ 2T 3T 0.0 Decay rate of the order parameter and the amplitude of the stimulation signal R(t) 1 K, S(t) 1 K, as K

29 Desynchronization mechanism Stimulation restores individual frequencies of oscillators to natural frequencies

30 Desynchronization mechanism Stimulation restores individual frequencies of oscillators to natural frequencies

31 Desynchronization mechanism Stimulation restores individual frequencies of oscillators to natural frequencies

32 Desynchronization mechanism Stimulation restores individual frequencies of oscillators to natural frequencies

33 Multistability of stimulation-induced desynchronized states τ = T/2, 3T/2, 5T/2,... mean frequency Ω = Ω τ = T, 2T, 3T,... mean frequency Ω = Ω mean frequency Ω = Ω

Multistability of stimulation-induced desynchronized states τ = T/2, 3T/2, 5T/2,... mean frequency Ω = Ω 0 1.26 τ = T, 2T, 3T,... mean frequency Ω = Ω 1 1.

34 Multistability of stimulation-induced desynchronized states τ = T/2, 3T/2, 5T/2,... mean frequency Ω = Ω τ = T, 2T, 3T,... mean frequency Ω = Ω mean frequency Ω = Ω the individual frequencies of the stimulated oscillators approach the natural frequencies and can slightly be accelerated (Ω = Ω 1 ) or slowed down (Ω = Ω 2 )

35 Dynamics of mean field Model equation for mean field W (t) := R(t)e iθ(t) : Ẇ (t) = C 2 (1 W (t) 2 )W (t) + iω 0 W (t) + K 2 W 2 (t)w (t τ)

36 Dynamics of mean field Model equation for mean field W (t) := R(t)e iθ(t) : Ẇ (t) = C 2 (1 W (t) 2 )W (t) + iω 0 W (t) + K 2 W 2 (t)w (t τ) The trivial solution R(t) 0 is unstable

37 Dynamics of mean field Model equation for mean field W (t) := R(t)e iθ(t) : Ẇ (t) = C 2 (1 W (t) 2 )W (t) + iω 0 W (t) + K 2 W 2 (t)w (t τ) The trivial solution R(t) 0 is unstable Other solutions: R(t) Const 0, Θ(t) = Ωt + Const Ω = Ω 0 + KC sin(ωτ) 2C 2K cos(ωτ), R2 = C C K cos(ωτ)

38 Dynamics of mean field Model equation for mean field W (t) := R(t)e iθ(t) : Ẇ (t) = C 2 (1 W (t) 2 )W (t) + iω 0 W (t) + K 2 W 2 (t)w (t τ) The trivial solution R(t) 0 is unstable Other solutions: R(t) Const 0, Θ(t) = Ωt + Const Ω = Ω 0 + KC sin(ωτ) 2C 2K cos(ωτ), R2 = C C K cos(ωτ) τ = T/2, 3T/2, 5T/2,... = Ω = Ω 0, R 2 = C C + K

39 Dynamics of mean field: Coupled oscillators vs model equation τ = T/2 Frequency of the mean field: Ω = Ω 0 mean natural frequency

40 Dynamics of mean field: Coupled oscillators vs model equation τ = T/2 τ = T Frequency of the mean field: Ω = Ω 0 mean natural frequency Frequency of the mean field: Ω = Ω 1 or Ω = Ω 2 multistability of stimulationinduced desynchronized states

42 1. Title 2. Motivation: deep brain stimulation 3. Limitations of standard deep brain stimulation 4. Model-based development of deep brain stimulation 5. Multisite coordinated reset 6. Tremor suppression: three electrodes 7. Tremor suppression: five electrodes 8. Coordinated reset vs high-frequency stimulation 9. Stimulation with nonlinear delayed feedback 10. Stimulation: coupled limit-cycle oscillators 11. Relaxation van der Pol and chaotic Rössler oscillators 12. Robustness and decay rates 13. Desynchronization mechanism 14. Dynamics of mean field 15. Coupled oscillators vs model equation 16. Co-workers

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