Two-dimensional wave patterns of spreading depolarization: Retracting, re-entrant, and stationary waves

Physica D: Nonlinear Phenomena

Volumn 239, Issue 11, 2010, Pages 889-903

  Dahlem, Markus A ^a,b,c   Graf, Rudolf ^d   Strong, Anthony J ^e   Dreier, Jens P ^f   Dahlem, Yuliya A ^f,g   Sieber, Michaela ^g   Hanke, Wolfgang ^g   Podoll, Klaus ^h   Schöll, Eckehard ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

^c LEIBNIZ INSTITUTE FOR NEUROBIOLOGY   (Germany)

^d MAX PLANCK INSTITUTE FOR NEUROLOGICAL RESEARCH   (Germany)

^e KING'S COLLEGE LONDON   (United Kingdom)

^f CHARITÉ UNIVERSITÄTSMEDIZIN BERLIN   (Germany)

^g UNIVERSITY OF HOHENHEIM   (Germany)

^h RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Migraine; Pattern formation; Reaction diffusion; Spiral waves; Stroke

Indexed keywords

DEPOLARIZATION; SPECKLE;

MIGRAINE; PATTERN FORMATION; REACTION DIFFUSION; SPIRAL WAVES; STROKE;

DIFFUSION IN LIQUIDS;

EID: 77949491283     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2009.08.009     Document Type: Article

References (74)

1. Dodick D.W., and Gargus J.J. Why migraines strike. Sci. Am. 299 (2008) 56
2. Leão A.A.P. Spreading depression of activity in the cerebral cortex. J. Neurophysiol. 7 (1944) 359
3. Milner P.M. Note on a possible correspondence between the scotomas of migraine and spreading depression of Leão. Electroencephalogr. Clin. Neurophysiol. 10 (1958) 705
4. Lauritzen M. Cortical spreading depression as a putative migraine mechanism. Trends Neurosci. 10 (1987) 8
5. Hadjikhani N., Sanchez Del Rio M., Wu O., Schwartz D., Bakker D., Fischl B., Kwong K.K., Cutrer F.M., Rosen B.R., Tootell R.B., Sorensen A.G., and Moskowitz M.A. Mechanisms of migraine aura revealed by functional MRI in human visual cortex. Proc. Natl. Acad. Sci. USA 98 (2001) 4687
6. Moskowitz M.A. The 2006 Thomas Willis lecture: The adventures of a translational researcher in stroke and migraine. Stroke 38 (2007) 1645
7. Hossmann K.A. Periinfarct depolarizations. Cerebrovasc. Brain Metab. Rev. 8 (1996) 195
8. Strong A.J., Fabricius M., Boutelle M.G., Hibbins S.J., Hopwood S.E., Jones R., Parkin M.C., and Lauritzen M. Spreading and synchronous depressions of cortical activity in acutely injured human brain. Stroke 33 (2002) 2738
9. Fabricius M., Fuhr S., Bhatia R., Boutelle M., Hashemi P., Strong A.J., and Lauritzen M. Cortical spreading depression and peri-infarct depolarization in acutely injured human cerebral cortex. Brain 129 (2006) 778
10. Dreier J.P., Woitzik J., Fabricius M., Bhatia R., Major S., Drenckhahn C., Lehmann T.-N., Sarrafzadeh A., Willumsen L., Hartings J.A., Sakowitz O.W., Seemann J.H., Thieme A., Lauritzen M., and Strong A.J. Delayed ischaemic neurological deficits after subarachnoid haemorrhage are associated with clusters of spreading depolarizations. Brain 129 (2006) 3224
11. Dohmen C., Sakowitz O.W., Fabricius M., Bosche B., Reithmeier T., Ernestus R.I., Brinker G., Dreier J.P., Woitzik J., Strong A.J., and Graf R. Spreading depolarizations occur in human ischemic stroke with high incidence. Ann. Neurol. 63 (2008) 720
12. Somjen G.G. Mechanisms of spreading depression and hypoxic spreading depression-like depolarization. Physiol. Rev. 81 (2001) 1065
13. Olesen J., Friberg L., Olsen T.S., Andersen A.R., Lassen N.A., Hansen P.E., and Karle A. Ischaemia-induced (symptomatic) migraine attacks may be more frequent than migraine-induced ischaemic insults. Brain 116 (1993) 187
14. Moskowitz M.A. Defining a pathway to discovery from bench to bedside: The trigeminovascular system and sensitization. Headache 48 (2008) 688
15. Peixoto N.L., Fernandes de Lima V.M., and Hanke W. Correlation of the electrical and intrinsic optical signals in the chicken spreading depression phenomenon. Neurosci. Lett. 299 (2001) 89
16. Dunn A.K., Bolay H., Moskowitz M.A., and Boas D.A. Dynamic imaging of cerebral blood flow using laser speckle. J. Cereb. Blood Flow Metab. 21 (2001) 195
17. Strong A.J., Anderson P.J., Watts H.R., Virley D.J., Lloyd A., Irving E.A., Nagafuji T., Ninomiya M., Nakamura H., Dunn A.K., and Graf R. Peri-infarct depolarizations lead to loss of perfusion in ischaemic gyrencephalic cerebral cortex. Brain 130 (2007) 995
18. de Lima V.M.F., Goldermann M., and Hanke W. The Retinal Spreading Depression (1999), Shaker Verlag, Aachen
19. Dahlem M.A., and Müller S.C. Image processing techniques applied to excitation waves in the chicken retina. Methods 21 (2000) 317
20. Miller R.F. Cell communication mechanisms in the vertebrate retina the proctor lecture. Invest. Ophthalmol. Vis. Sci. 49 (2008) 5184
21. Dahlem M.A., and Hadjikhani N. Migraine aura: Retracting particle-like waves in weakly susceptible cortex. PLoS ONE 4 (2009) e5007
22. Dahlem M.A., and Müller S.C. Self-induced splitting of spiral-shaped spreading depression waves in chicken retina. Exp. Brain Res. 115 (1997) 319
23. Dahlem M.A., Schneider F.M., and Schöll E. Efficient control of transient wave forms to prevent spreading depolarizations. J. Theor. Biol. 251 (2008) 202
24. Dahlem M.A., and Müller S.C. Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex. Biol. Cybern. 88 (2003) 419
25. Shibata M., and Bures J. Reverberation of cortical spreading depression along closed-loop pathways in rat cerebral cortex. J. Neurophysiol. 35 (1972) 381
26. McCulloch J., Edvinsson L., and Watt P. Comparison of the effects of potassium and pH on the calibre of cerebral veins and arteries. Pflugers Arch. 393 (1982) 95
27. Grafstein B. Neural release of potassium during spreading depression. In: Brazier M.A.B. (Ed). Brain Function. Cortical Excitability and Steady Potentials (1963), University of California Press, Berkeley 87-124
28. Tuckwell H.C. Simplified reaction-diffusion equations for potassium and calcium ion concentrations during spreading cortical depression. Int. J. Neurosci. 12 (1981) 95
29. J.A. Reggia, D. Montgomery, Modeling cortical spreading depression, in: Proc. Annu. Symp. Comput. Appl. Med. Care, 1994, pp. 873-877
30. Reggia J.A., and Montgomery D. A computational model of visual hallucinations in migraine. Comput. Biol. Med. 26 (1996) 133
31. Revett K., Ruppin E., Goodall S., and Reggia J.A. Spreading depression in focal ischemia: A computational study. J. Cereb. Blood Flow Metab. 18 (1998) 998
32. Dahlem M.A., and Müller S.C. Reaction-diffusion waves in neuronal tissue and the window of cortical excitability. Ann. Phys. 13 (2004) 442
33. Izhikevich E.M. Neural excitability, spiking and bursting. Int. J. Bifurcation Chaos 10 (2000) 1171
34. Schneider F.M., Schöll E., and Dahlem M.A. Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time delayed feedback. Chaos 19 (2009) 015110
35. Agnati L.F., Zoli M., Strömberg I., and Fuxe K. Intercellular communication in the brain: Wiring versus volume transmission. Neuroscience 69 (1995) 711
36. Syková E., and Nicholson C. Diffusion in brain extracellular space. Physiol. Rev. 88 (2008) 1277
37. Peppiatt C.M., Howarth C., Mobbs P., and Attwell D. Bidirectional control of CNS capillary diameter by pericytes. Nature 443 (2006) 700
38. Wilson H.R. Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience (1999), Oxford University Press, Oxford
39. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1 (1961) 445
40. Nagumo J., Arimoto S., and Yoshizawa S. An active pulse transmission line simulating nerve axon. Proc. IRE 50 (1962) 2061
41. van der Pol B. On relaxation oscillations. Phil. Mag. 2 (1926) 978
42. van der Pol B., and van der Mark J. The heart beat considered as a relaxation oscillation and an electrical model of the heart. Arch. Neerl. Physiol. 14 (1929) 418
43. Bonhoeffer K.F. Activation of passive iron as a model for the excitation of nerve. J. Gen. Physiol. 32 (1948) 69
44. Winfree A.T. Varieties of spiral wave behaviour: An experimentalist's approach to the theory of excitable media. Chaos 1 (1991) 303
45. Dahlem M.A., Schneider F.M., and Schöll E. Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke. Chaos 18 (2008) 026110
46. Wiedemann M., de Lima V.M., and Hanke W. Effects of antimigraine drugs on retinal spreading depression. Naunyn Schmiedebergs Arch. Pharmacol. 353 (1996) 552
47. Brand S., Fernandes de Lima V.M., and Hanke W. Pharmacological modulation of the refractory period of retinal spreading depression. Naunyn Schmiedebergs Arch. Pharmacol. 357 (1998) 419
48. Scheller D., Tegtmeier F., and Schlue W.R. Dose-dependent effects of tetraethylammonium on circling spreading depressions in chicken retina. J. Neurosci. Res. 51 (1998) 85
49. M.A. Dahlem, F.M. Schneider, J.P. Dreier, A.J. Strong, E. Schöll, ECoG-based short-range recurrent functional stimulation techniques to stabilize tissue at risk of progressive damage: Theory based on clinical observations, 2009. Available from Nature Precedings http://dx.doi.org/10.1038/npre.2009.3408.1
50. In: Silberstein S.D., Stiles A., and Young W.B. (Eds). Atlas of Migraine and Other Headaches (2005), Taylor & Francis, London
51. Rebert C.S. Spreading depression in squirrel monkey lissencephalic cortex. Physiology & Behavior 5 (1967) 239
52. Wilkinson F. Auras and other hallucinations: Windows on the visual brain. Prog. Brain Res. 144 (2004) 305
53. Vincent M., and Hadjikhani N. Migraine aura and related phenomena: Beyond scotomata and scintillations. Cephalalgia 27 (2007) 1368
54. James M.F., Smith M.I., Bockhorst K.H., Hall L.D., Houston G.C., Papadakis N.G., Smith J.M., Williams A.J., Xing D., Parsons A.A., Huang C.L., and Carpenter T.A. Cortical spreading depression in the gyrencephalic feline brain studied by magnetic resonance imaging. J. Physiol. (Lond.) 519 Part 2 (1999) 415
55. Krischer K., and Mikhailov A. Bifurcation to traveling spots in reaction-diffusion systems. Phys. Rev. Lett. 73 (1994) 3165
56. Sakurai T., Mihaliuk E., Chirila F., and Showalter K. Design and control of wave propagation patterns in excitable media. Science 296 (2002) 2009
57. Mihaliuk E., Sakurai T., Chirila F., and Showalter K. Feedback stabilization of unstable propagating waves. Phys. Rev. E 65 (2002) 065602
58. Karma A. Universal limit of spiral wave propagation in excitable media. Phys. Rev. Lett. 66 (1991) 2274
59. Hakim V., and Karma A. Theory of spiral wave dynamics in weakly excitable media: Asymptotic reduction to a kinematic model and applications. Phys. Rev. E 60 (1999) 5073
60. Schöll E. Nonlinear Spatio-temporal Dynamics and Chaos in Semiconductors (2001), Cambridge University Press, Cambridge
61. Stegemann G., and Schöll E. Two-dimensional spatiotemporal pattern formation in the double-barrier resonant tunneling diode. New J. Phys. 9 (2007) 55
62. Schöll E. Pattern formation and time-delayed feedback control at the nano-scale. In: Radons G., Rumpf B., and Schuster H.G. (Eds). Nonlinear Dynamics of Nanosystems (2009), Wiley-VCH, Weinheim
63. Dahlem M.A., and Chronicle E.P. A computational perspective on migraine aura. Prog. Neurobiol. 74 (2004) 351
64. Hossmann K.-A. Pathophysiology and therapy of experimental stroke. Cell. Mol. Neurobiol. 26 (2006) 1055
65. Leniger-Follert E., and Lübbers D.W. Regulation of microflow and behaviour of local tissue Po2 during activation and anoxia of the brain cortex. Bibl. Anat. (1977) 345-349
66. Glatt E., Gassel M., and Kaiser F. Variability-induced transition in a net of neural elements: From oscillatory to excitable behavior. Phys. Rev. E 73 (2006) 066230
67. Glatt E., Gassel M., and Kaiser F. Variability-sustained pattern formation in subexcitable media. Phys. Rev. E 75 (2007) 026206
68. Kager H., Wadman W.J., and Somjen G.G. Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J. Neurophysiol. 84 (2000) 495
69. Makarova J., Ibarz J.M., Canals S., and Herreras O. A steady-state model of spreading depression predicts the importance of an unknown conductance in specific dendritic domains. Biophys. J. 92 (2007) 4216
70. Shapiro B.E. Osmotic forces and gap junctions in spreading depression: A computational model. J. Comput. Neurosci. 10 (2001) 99
71. Wilson H.R., and Cowan J.D. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13 (1973) 55
72. Hanyu S., Ito U., Hakamata Y., and Nakano I. Topographical analysis of cortical neuronal loss associated with disseminated selective neuronal necrosis and infarction after repeated ischemia. Brain Res. 767 (1997) 154
73. Liebetanz D., Fregni F., Monte-Silva K.K., Oliveira M.B., Amâncio-dos Santos A., Nitsche M.A., and Guedes R.C. After-effects of transcranial direct current stimulation (tDCS) on cortical spreading depression. Neurosci. Lett. 398 (2006) 85
74. Shepherd A.J. Increased visual after-effects following pattern adaptation in migraine: A lack of intracortical excitation?. Brain 124 (2001) 2310