Self-terminating wave patterns and self-organized pacemakers in a phenomenological model of spreading depression

Brain Research

Volumn 1434, Issue , 2012, Pages 200-211

  Postnov, D E ^a   Postnov, D D ^a   Schimansky Geier, L ^b  

^a SARATOV STATE UNIVERSITY   (Russian Federation)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Autonomous pacemaker; FitzHugh Nagumo; Retracting wave; Spreading depression

Indexed keywords

CONFERENCE PAPER; DYNAMICS; NERVE CELL EXCITABILITY; NERVE CELL STIMULATION; NEUROPHYSIOLOGY; PACEMAKER; PHENOMENOLOGY; PRIORITY JOURNAL; SELF ORGANIZED PACEMAKER; SELF TERMINATING WAVE PATTERN; SPIKE WAVE; SPREADING CORTICAL DEPRESSION; THEORETICAL MODEL;

ACTION POTENTIALS; ANIMALS; CORTICAL SPREADING DEPRESSION; HUMANS; MODELS, NEUROLOGICAL; NEURONS; REACTION TIME;

EID: 84856608121     PISSN: 00068993     EISSN: 18726240     Source Type: Journal    
DOI: 10.1016/j.brainres.2011.10.001     Document Type: Conference Paper

References (52)

1. L.F. Agnati, M. Zoli, I. Strömberg, and K. Fuxe Intercellular communication in the brain: wiring versus volume transmission Neuroscience 69 1995 711 726
2. M. Bär, S. Nettesheim, H.H. Rotermund, M. Eiswirth, and G. Ertl Transition between fronts and spiral waves in a bistable surface reaction Phys. Rev. Lett. 74 1995 1246 1249
3. T.A. Basarsky, S.N. Duffy, R.D. Andrew, and B.A. MacVicar Imaging spreading depression and associated intracellular calcium waves in brain slices J. Neurosci. 18 18 1988 7189 7199
4. M. Bazhenov, I. Timofeev, M. Steriade, and T.J. Sejnowski Potassium model for slow (2-3 Hz) neocortical paroxysmal oscillations in vivo J. Neurophysiol. 92 2004 1116 1132 (Pubitemid 38937044)
5. M.R. Bennett, L. Farnell, and W.G. Gibson A quantitative model of cortical spreading depression due to purinergic and gap-junction transmission in astrocyte networks Biophys. J. 95 2008 5648 5660
6. H. Bolay, U. Reuter, A.K. Dunn, Z. Huang, D.A. Boas, and M.A. Moskowitz Intrinsic brain activity triggers trigeminal meningeal afferents in a migraine model Nat. Med. 8 2002 136 142 (Pubitemid 34155124)
7. G. Chapuisat Discussion of a simple model of spreading depression ESAIM: Proc. 18 2007 87 98
8. G. Chapuisat, M.A. Dronne, E. Grenier, M. Hommel, H. Gilquin, and J.P. Boissel A global phenomenological model of ischemic stroke with stress on spreading depressions Prog. Biophys. Mol. Biol. 97 2008 4 27
9. A.H. Cornell Bell, and S.M. Finkbeiner Ca21 waves in astrocytes Cell Calcium 12 1991 185 204
10. 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 2003 221 228 (Pubitemid 37153643)
11. M.A. Dahlem, and E.P. Chronicle Computational perspective on migraine aura Prog. Neurobiol. 74 2005 351 361
12. M.A. Dahlem, R. Graf, A.J. Strong, J.P. Dreier, Y.A. Dahlem, M. Sieber, W. Hanke, K. Podoll, and E. Schöll Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves Physica D 239 2010 889 903
13. R.A. FitzHugh Impulses and physiological states in theoretical models of nerve Biophys. J. 1 1961 445 466
14. F. Fröhlich, M. Bazhenov, I. Timofeev, M. Steriade, and T.J. Sejnowski Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability J. Neurosci. 26 23 2006 6153 6162
15. F. Fröhlich, M. Bazhenov, V. Iragui-Madoz, and T.J. Sejnowski Potassium dynamics in the epileptic cortex: new insights on an old topic Neuroscientist 14 2008 422 433
16. N.A. Gorelova, and J. Bures Spiral waves of spreading depression in the isolated chicken retina J. Neurobiol. 14 5 1983 353 363
17. B. Grafstein Mechanism of spreading cortical depression J. Neurophysiol. 19 1956 216 227
18. B. Grafstein Neural release of potassium during spreading depression M.A.B. Brazier, Brain Function. Cortical Excitability and Steady Potentials 1963 University of California Press Berkeley 87 124
19. A. Van Harreveld Changes in the diameter of apical dendrites during spreading depression Am. J. Physiol. 192 1958 457 463
20. A. Van Harreveld Compounds in brain extracts causing spreading depression of cerebral cortical activity and contraction of crustacean muscle J. Neurochem. 3 1959 300 315
21. A. Van Harreveld, and F.I. Khattab Changes in cortical extracellular space during spreading depression investigated with the electron microscope J. Neurophysiol. 30 1967 911 929
22. E.M. Izhikevich Neural excitability, spiking, and bursting Int. J. Bifurcation Chaos 10 2000 1171 1266
23. 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 1 2000 495 512 (Pubitemid 30490068)
24. H. Kager, W.J. Wadman, and G.G. Somjen Conditions for the triggering of spreading depression studied with computer simulations J. Neurophysiol. 88 5 2002 2700 2712 (Pubitemid 35346069)
25. L.L. Latour, Y. Hasegawa, J.E. Formato, M. Fisher, and C.H. Sotak Spreading of waves of decreased diffusion coefficient after cortical stimulation in the rat brain Magn. Reson. Med. 32 1994 189 198 (Pubitemid 24243299)
26. M. Lauritzen Pathophysiology of the migraine aura. The spreading depression theory Brain 117 1994 199 210 (Pubitemid 24103394)
27. A.A.P. Leao Spreading depression of activity in the cerebral cortex J. Neurophysiol. 7 1944 359 390
28. A.A.P. Leao On the inferred relationship of migraine andspreading depression Rose F. Clifford, Advances in Headache Research 1987 J. Libbey London 19 24
29. E.S. Lobanova, and F.I. Ataullakhanov Unstable trigger waves induce various intricate dynamic regimes in a reaction-diffusion system of blood clotting Phys. Rev. Lett. 91 2003 138301
30. A.S. Mikhailov Stable autonomous pacemakers in the enlarged Ginzburg-Landau model Physica D 55 1992 99 112
31. R.M. Miura, H. Huang, and J.J. Wylie Cortical spreading depression: an enigma Eur. Phys. J. Spec.Top. 147 2007 287 302
32. M. Nedergaard, A.J. Cooper, and S.A. Goldman Gap junctions are required for the propagation of spreading depression J. Neurobiol. 28 1995 433 444
33. C. Nicholson, G. Bruggencate, R. Steinberg, and H. Stockle Calcium modulation in brain extracellular microenvironment demonstrated with ion-selective micropipette Proc. Natl. Acad. Sci. USA 74 1977 1287 1290 (Pubitemid 8065652)
34. C. Nicholson, and R.P. Kraig The behaviour of extracellular ions during spreading depression T. Zeuthen, The Application of Ion-selective Electrodes 1981 Elsevier Amsterdam 217 238
35. C. Nicholson Diffusion and related transport mechanisms in brain tissue Rep. Prog. Phys. 64 2001 815 884 (Pubitemid 32657274)
36. D.E. Postnov, F. M'uller, R.B. Schuppner, and L. Schimansky-Geier Dynamical structures in binary media of potassium-driven neurons Phys. Rev. E 80 2009 031921
37. C. Radehaus, R. Dohmen, H. Willebrand, and F.-J. Niedernostheide Model for current patterns in physical systems with two charges carriers Phys. Rev. A 42 1990 7426 7446
38. B.E. Shapiro Osmotic forces and gap junctions in spreading depression:a computational model J. Comput. Neurosci. 10 2001 99 120 (Pubitemid 32243556)
39. E. Sugaya, M. Takato, and Y. Noda Neuronal and glial activity during spreading depression in cerebral cortex of cat J. Neurophysiol. 38 1975 822 841
40. M. Shibata, and J. Bures Reverberation of cortical spreading depression along closed-loop pathways in rat cerebral cortex J. Neurophysiol. 35 1972 381 388
41. G.G. Somjen Mechanisms of spreading depression and hypoxic spreading depression-like depolarization Physiol. Rev. 81 2001 1065 1096 (Pubitemid 32606666)
42. M. Stich, A.S. Mikhailov, and Y. Kuramoto Self-organized pacemakers and bistability of pulses in an excitable medium Phys. Rev. E 79 2009 026110
43. T. Teramoto, X. Yuan, M. Br, and Y. Nishiura Onset of unidirectional pulse propagation in an excitable medium with asymmetric heterogeneity Phys. Rev. E 79 2009 046205
44. H.C. Tuckwell, and R.M. Miura A mathematical model for spreading cortical depression Biophys. J. 23 1978 257 276
45. H.C. Tuckwell Predictions and properties of a model of potassium and calcium ion movements during spreading cortical depressions Int. J. Neurosci. 10 1980 145 164 (Pubitemid 10168640)
46. H.C. Tuckwell Simplified reaction-diffusion equations for potassium and calcium ion concentrations during spreading cortical depression Int. J. Neurosci. 12 1981 95 107 (Pubitemid 11142210)
47. H.C. Tuckwell, and C.L. Hermansen Ion and transmitter movements during spreading cortical depression Int. J. Neurosci. 12 1981 109 135 (Pubitemid 11142211)
48. H.C. Tuckwell Mathematical modeling of spreading cortical depression: spiral and reverberating waves Am. Inst. Phys. Conf. Proc. 1028 2008 46 64
49. W. Yao, H. Huang, and R.M. Miura A continuum neuronal model for the instigation and propagation of cortical spreading depression Bull. Math. Biol 2011 10.1007/s11538-011-9647-3
50. X. Yuan, T. Teramoto, and Y. Nishiura Heterogeneity-induced defect bifurcation and pulse dynamics for a three-component reaction-diffusion system Phys. Rev. E 75 2007 036220
51. Zhou, N., 2010. Cellular mechanisms underlying cortical spreading depression. PhD thesis, The University of British Columbia, Canada.
52. C. Zülicke, A.S. Mikhailov, and L. Schimansky-Geier Dynamic bistability of front propagation and stable localized domains in systems with first-order phase transition Physica A 163 1990 559 583