Effective desynchronization with a resetting pulse train followed by a single pulse

Europhysics Letters

Volumn 55, Issue 2, 2001, Pages 171-177

  Tass, P A ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035796133     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2001-00397-8     Document Type: Article

References (26)

1. HAKEN H., Advanced Synergetics (Springer, Berlin) 1983.
2. KURAMOTO Y., Chemical Oscillations, Waves, and Turbulence (Springer, Berlin) 1984.
3. LLINÁS R. and JAHNSEN H., Nature, 297 (1982) 406; VOLKMANN J. et al., Neurology, 46 (1996) 1359: BERGMAN H. et al., Mov. Dis. Suppl. 3, 13 (1998) 29.
4. LLINÁS R. and JAHNSEN H., Nature, 297 (1982) 406; VOLKMANN J. et al., Neurology, 46 (1996) 1359: BERGMAN H. et al., Mov. Dis. Suppl. 3, 13 (1998) 29.
5. LLINÁS R. and JAHNSEN H., Nature, 297 (1982) 406; VOLKMANN J. et al., Neurology, 46 (1996) 1359: BERGMAN H. et al., Mov. Dis. Suppl. 3, 13 (1998) 29.
6. WINFREE A. T., The Geometry of Biological Time (Springer, Berlin) 1980; GLASS L. and MACKEY M. C., From Clocks to Chaos. The Rhythms of Life (Princeton University Press) 1988.
7. WINFREE A. T., The Geometry of Biological Time (Springer, Berlin) 1980; GLASS L. and MACKEY M. C., From Clocks to Chaos. The Rhythms of Life (Princeton University Press) 1988.
8. TASS P. A., J. Biol. Phys., 22 (1996) 27; 125.
9. TASS P. A., Phase Resetting in Medicine and Biology. Stochastic Modelling and Data Analysis (Springer, Berlin) 1999; Prog. Theor. Phys. Suppl. (Kyoto), 139 (2000) 301.
10. TASS P. A., Phase Resetting in Medicine and Biology. Stochastic Modelling and Data Analysis (Springer, Berlin) 1999; Prog. Theor. Phys. Suppl. (Kyoto), 139 (2000) 301.
11. TASS P. A., Europhys. Lett., 53 (2001) 15; to be published in Biol. Cybern.
12. TASS P. A., Europhys. Lett., 53 (2001) 15; to be published in Biol. Cybern.
13. STONEY S. D. et al., J. Neurophysiol, 31 (1968) 659.
14. ERMENTROUT G. B. and KOPELL N., J. Math. Biol., 29 (1991) 195; GRANNAN E. R., Neural Comp., 4 (1992) 550; HANSEL D. et al., Europhys. Lett., 23 (1993) 367.
15. ERMENTROUT G. B. and KOPELL N., J. Math. Biol., 29 (1991) 195; GRANNAN E. R., Neural Comp., 4 (1992) 550; HANSEL D. et al., Europhys. Lett., 23 (1993) 367.
16. ERMENTROUT G. B. and KOPELL N., J. Math. Biol., 29 (1991) 195; GRANNAN E. R., Neural Comp., 4 (1992) 550; HANSEL D. et al., Europhys. Lett., 23 (1993) 367.
17. BEST E. N., Biophys. J., 27 (1979) 87; GUTTMAN R. et al., J. Physiol (London), 305 (1980) 377.
18. BEST E. N., Biophys. J., 27 (1979) 87; GUTTMAN R. et al., J. Physiol (London), 305 (1980) 377.
19. If the coupling Γ is of lowest order noisy in-phase synchronization emerges out of the incoherent state, i.e. n = 1/(2π), due to a decrease of the noise amplitude D [2] or, analogously, if the coupling K exceeds its critical value D [6].
20. m quantifies the extent of synchronization of the m-cluster state and has to be desynchronized as in fig. 1d, f. This is most effectively achieved with a stimulus S containing terms of m-th order, e.g., S(ψ) = I cos(mψ). The composite stimulation works perfectly also if the coupling contains cosine terms.
21. BENABID A. L. et al., The Lancet, 337 (1991) 403; Arch. Med. Res., 31 (2000) 282.
22. BENABID A. L. et al., The Lancet, 337 (1991) 403; Arch. Med. Res., 31 (2000) 282.
23. Parkinsonian resting tremor is an involuntary shaking which predominantely affects the distal portion of the upper limb and has a frequency around 3 to 8 Hz [3]. Its pacemaker-like cluster of neurons is located in the thalamus and the basal ganglia and acts on the muscles via cortical areas [3], where the latter synchronize their activity; TASS P. A. et al., Phys. Rev. Lett., 81 (1998) 3291. Further physiological details of the model are presented in [7]. Standard deep brain stimulation also suppresses the essential tremor, which is caused by a different pacemaker-like cluster of neurons; ELBLE R. J. and KOLLER W. C., Tremor (John Hopkins University Press, Baltimore) 1990.
24. Parkinsonian resting tremor is an involuntary shaking which predominantely affects the distal portion of the upper limb and has a frequency around 3 to 8 Hz [3]. Its pacemaker-like cluster of neurons is located in the thalamus and the basal ganglia and acts on the muscles via cortical areas [3], where the latter synchronize their activity; TASS P. A. et al., Phys. Rev. Lett., 81 (1998) 3291. Further physiological details of the model are presented in [7]. Standard deep brain stimulation also suppresses the essential tremor, which is caused by a different pacemaker-like cluster of neurons; ELBLE R. J. and KOLLER W. C., Tremor (John Hopkins University Press, Baltimore) 1990.
25. NINI A. et al., J. Neurophysiol., 74 (1995) 1800.
26. The right stimulation parameters are experimentally determined in a reliable way with a procedure which was developed for the single-pulse stimulation [6] and works also for the composite stimulation technique: A series of test stimuli is administered, the phase of the dominant mode is extracted out of the experimetal data with bandpass filtering and Hubert transform, and the right parameters are obtained with phase resetting curves.