Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

Chaos

Volumn 18, Issue 2, 2008, Pages

  Dahlem, Markus A ^a   Schneider, Felix M ^a   Schöll, Eckehard ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46449099873     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2937120     Document Type: Article

References (65)

1. N. Hadjikhani, M. Sanchez Del. Rio, O. Wu, D. Schwartz, D. Bakker, B. Fischl, K. K. Kwong, F. M. Cutrer, B. R. Rosen, R. B. Tootell, A. G. Sorensen, and M. A. Moskowitz, " Mechanisms of migraine aura revealed by functional MRI in human visual cortex.," Proc. Natl. Acad. Sci. U.S.A. 98, 4687 (2001).
2. M. Fabricius, S. Fuhr, R. Bhatia, M. Boutelle, P. Hashemi, A. J. Strong, and M. Lauritzen, " Cortical spreading depression and peri-infarct depolarization in acutely injured human cerebral cortex.," Brain 129, 778 (2006).
3. A. T. Winfree, " Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media.," Chaos 1, 303 (1991).
4. A. S. Mikhailov and K. Showalter, " Control of waves, patterns and turbulence in chemical systems.," Phys. Rep. 425, 79 (2006).
5. M. G. Bousser and K. M. Welch, " Relation between migraine and stroke.," Lancet Neurol. 4, 533 (2005).
6. A. A. P. Leão, " Spreading depression of activity in the cerebral cortex.," J. Neurophysiol. 7, 359 (1944).
7. B. Grafstein, " Neural release of potassium during spreading depression.," in Brain Function, Cortical Excitability, and Steady Potentials, edited by, M. A. B. Brazier, (University of California Press, Berkely, 1963), pp. 87-124.
8. A. R. Gardner-Medwin, " Possible roles of vertebrate neuroglia in potassium dynamics, spreading depression and migraine.," J. Exp. Biol. 95, 111 (1981).
9. M. Lauritzen, " Pathophysiology of the migraine aura. The spreading depression theory.," Brain 117, 199 (1994).
10. H. Martins-Ferreira, M. Nedergaard, and C. Nicholson, " Perspectives on spreading depression.," Brain Res. Rev. 32, 215 (2000).
11. M. A. Dahlem and E. P. Chronicle, " A computational perspective on migraine aura.," Prog. Neurobiol. 74, 351 (2004).
12. M. A. Dahlem and S. C. Müller, " Reaction-diffusion waves in neuronal tissue and the window of cortical excitability.," Ann. Phys. (Paris) 13, 442 (2004).
13. J. P. Dreier, J. Woitzik, M. Fabricius, R. Bhatia, S. Major, C. Drenckhahn, T.-N. Lehmann, A. Sarrafzadeh, L. Willumsen, J. A. Hartings, O. W. Sakowitz, J. H. Seemann, A. Thieme, M. Lauritzen, and A. J. Strong, " Delayed ischemic neurological deficits after subarachnoid haemorrhage are associated with clusters of spreading depolarizations.," Brain 129, 3224 (2006).
14. K. A. Hossmann, " Periinfarct depolarizations.," Cerebrovasc Brain Metab. Rev. 8, 195 (1996).
15. Handbook of Chaos Control, 2nd completely revised and enlarged edition, edited by, E. Schöll, and, H. G. Schuster, (Wiley-VCH, Weinheim, 2008).
16. K. M. Welch, " Brain hyperexcitability: The basis for antiepileptic drugs in migraine prevention.," Headache 45, 25 (2005).
17. O. Herreras, C. Largo, J. M. Ibarz, G. G. Somjen, and R. Martin del Rio, " Role of neuronal synchronizing mechanisms in the propagation of spreading depression in the in vivo hippocampus.," J. Neurosci. 14, 7087 (1994).
18. B. Larrosa, J. Pastor, L. Lopez-Aguado, and O. Herreras, " A role for glutamate and glia in the fast network oscillations preceding spreading depression.," Neuroscience 141, 1057 (2006).
19. H. C. Tuckwell and R. M. Miura, " A mathematical model for spreading cortical depression.," Biophys. J. 23, 257 (1978).
20. H. Kager, W. J. Wadman, and G. G. Somjen, " Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations.," J. Neurophysiol. 84, 495 (2000).
21. B. E. Shapiro, " Osmotic forces and gap junctions in spreading depression: a computational model.," J. Comput. Neurosci. 10, 99 (2001).
22. J. A. Reggia and D. Montgomery, " A computational model of visual hallucinations in migraine.," Comput. Biol. Med. 26, 133 (1996).
23. K. Revett, E. Ruppin, S. Goodall, and J. A. Reggia, " Spreading depression in focal ischemia: A computational study.," J. Cereb. Blood Flow Metab. 18, 998 (1998).
24. E. Ruppin, K. Revett, E. Ofer, S. Goodall, and J. A. Reggia, " Penumbral tissue damage following acute stroke: A computational investigation.," Prog. Brain Res. 121, 243 (1999).
25. R. FitzHugh, " Impulses and physiological states in theoretical models of nerve membrane.," Biophys. J. 1, 445 (1961).
26. J. Nagumo, S. Arimoto, and S. Yoshizawa., " An active pulse transmission line simulating nerve axon..," Proc. IRE 50, 2061 (1962).
27. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, " Effects of noise in excitable systems.," Phys. Rep. 392, 321 (2004).
28. K. Pyragas, " Continuous control of chaos by self-controlling feedback.," Phys. Lett. A 170, 421 (1992).
29. O. Beck, A. Amann, E. Schöll, J. E. S. Socolar, and W. Just, " Comparison of time-delayed feedback schemes for spatio-temporal control of chaos in a reaction-diffusion system with global coupling.," Phys. Rev. E 66, 016213 (2002).
30. N. Baba, A. Amann, E. Schöll, and W. Just, " Giant improvement of time-delayed feedback control by spatio-temporal filtering.," Phys. Rev. Lett. 89, 074101 (2002).
31. J. Unkelbach, A. Amann, W. Just, and E. Schöll, " Time-delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes.," Phys. Rev. E 68, 026204 (2003).
32. J. Schlesner, A. Amann, N. B. Janson, W. Just, and E. Schöll, " Self-stabilization of high frequency oscillations in semiconductor superlattices by time-delay autosynchronization.," Phys. Rev. E 68, 066208 (2003).
33. J. Schlesner, V. Zykov, H. Engel, and E. Schöll, " Stabilization of unstable rigid rotation of spiral waves in excitable media.," Phys. Rev. E 74, 046215 (2006).
34. N. B. Janson, A. G. Balanov, and E. Schöll, " Delayed feedback as a means of control of noise-induced motion.," Phys. Rev. Lett. 93, 010601 (2004).
35. A. G. Balanov, N. B. Janson, and E. Schöll, " Control of noise-induced oscillations by delayed feedback.," Physica D 199, 1 (2004).
36. T. Prager, H. P. Lerch, L. Schimansky-Geier, and E. Schöll, " Increase of coherence in excitable systems by delayed feedback.," J. Phys. A 40, 11045 (2007).
37. B. Hauschildt, N. B. Janson, A. G. Balanov, and E. Schöll, " Noise-induced cooperative dynamics and its control in coupled neuron models.," Phys. Rev. E 74, 051906 (2006).
38. P. Hövel, M. A. Dahlem, and E. Schöll, " Synchronization of noise-induced oscillations by time-delayed feedback.," in Proceedings of the 19th International Conference on Noise and Fluctuations (ICNF-2007) (American Institute of Physics, College Park, Maryland, 2007), pp. 2074-3843.
39. G. Stegemann, A. G. Balanov, and E. Schöll, " Noise-induced pattern formation in a semiconductor nanostructure.," Phys. Rev. E 71, 016221 (2005).
40. G. Stegemann, A. G. Balanov, and E. Schöll, " Delayed feedback control of stochastic spatiotemporal dynamics in a resonant tunneling diode.," Phys. Rev. E 73, 016203 (2006).
41. J. Hizanidis, A. G. Balanov, A. Amann, and E. Schöll, " Noise-induced front motion: Signature of a global bifurcation.," Phys. Rev. Lett. 96, 244104 (2006).
42. J. Hizanidis and E. Schöll, " Control of noise-induced spatiotemporal patterns in superlattices.," Phys. Status Solidi C 5, 207 (2008).
43. A. G. Balanov, V. Beato, N. B. Janson, H. Engel, and E. Schöll, " Delayed feedback control of noise-induced patterns in excitable media.," Phys. Rev. E 74, 016214 (2006).
44. M. Gassel, E. Glatt, and F. Kaiser, " Time-delayed feedback in a net of neural elements: Transitions from oscillatory to excitable dynamics.," Fluct. Noise Lett. 7, L225 (2007).
45. C. M. Peppiatt, C. Howarth, P. Mobbs, and D. Attwell, " Bidirectional control of CNS capillary diameter by pericytes.," Nature (London) 443, 700 (2006).
46. C. Iadecola, G. Yang, T. J. Ebner, and G. Chen, " Local and propagated vascular responses evoked by focal synaptic activity in cerebellar cortex.," J. Neurophysiol. 78, 651 (1997).
47. P. Hövel and E. Schöll, " Control of unstable steady states by time-delayed feedback methods.," Phys. Rev. E 72, 046203 (2005).
48. S. Schikora, P. Hövel, H. J. Wünsche, E. Schöll, and F. Henneberger, " All-optical noninvasive control of unstable steady states in a semiconductor laser.," Phys. Rev. Lett. 97, 213902 (2006).
49. T. Dahms, P. Hövel, and E. Schöll, " Control of unstable steady states by extended time-delayed feedback.," Phys. Rev. E 76, 056201 (2007).
50. A. S. Mikhailov and V. S. Zykov, " Kinematical theory of spiral waves in excitable media: comparison with numerical simulations.," Physica D 52, 379 (1991).
51. V. Hakim and A. Karma, " Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications.," Phys. Rev. E 60, 5073 (1999).
52. E. Mihaliuk, T. Sakurai, F. Chirila, and K. Showalter, " Feedback stabilization of unstable propagating waves.," Phys. Rev. E 65, 065602 (2002).
53. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory (Springer, New York, 1995).
54. E. J. Doedel, R. C. Pfaffenroth, A. R. Chambodut, T. F. Fairgrieve, Y. A. Kuznetsov, B. E. Oldeman, B. Sandstede, and X. Wang, " AUTO 2000: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont). " (2006).
55. C. Nicholson and J. D. Phillips, " Ion diffusion modified by tortuosity and volume fraction in the extracellular microenvironment of the rat cerebellum.," J. Physiol. (London) 321, 225 (1981).
56. H. R. Wilson, Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience (Oxford University Press, Oxford, 1999).
57. M. A. Dahlem, F. M. Schneider, and E. Schöll, " Efficient control of transient wave forms to prevent spreading depolarizations.," J. Theor. Biol. 251, 202 (2008).
58. G. B. Ermentrout, " Neural networks as spatio-temporal pattern-forming systems.," Rep. Prog. Phys. 61, 353 (1998).
59. H. R. Wilson, " Simplified dynamics of human and mammalian neocortical neurons.," J. Theor. Biol. 200, 375 (1999).
60. J. Hizanidis, R. Aust, and E. Schöll, " Delay-induced multistability near a global bifurcation.," arXiv:nlin-sys/0702002 (in press).
61. Y. A. Dahlem, M. A. Dahlem, T. Mair, K. Braun, and S. C. Müller, " Extracellular potassium alters frequency and profile of retinal spreading depression waves.," Exp. Brain Res. 152, 221 (2003).
62. U. Heinemann and H. D. Lux, " Ceiling of stimulus induced rises in extracellular potassium concentration in the cerebral cortex of cat.," Brain Res. 120, 231 (1977).
63. F. Schlögl, " Chemical reaction models for nonequilibrium phase transitions.," Z. Phys. 253, 147 (1972).
64. E. Schöll, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors, Nonlinear Science Series (Cambridge University Press, Cambridge, 2001), Vol. 10.
65. R. H. Stokes, " The diffusion coefficients of eight uni-univalent electrolytes in aqueous solution at 25.," J. Am. Chem. Soc. 72, 2243 (1950).