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Spirals and Vortices pp 225–235Cite as

Yet More Spirals

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Abstract

Having presented several systems in which biologically and medically relevant processes induce rotating spiral waves, we add several more examples of comparable nature: glycolytic waves in yeast, calcium waves in egg cells, wave-like patterns during spreading depression, and spiral waves in the epileptic neocortex.

T. Mair, Deceased author

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References

  1. B. Hess, A. Boiteux, Oscillatory phenomena in glycolysis. Annu. Rev. Biochem. 40, 237–258 (1971)

    Article  Google Scholar 

  2. T. Mair, Private communication

    Google Scholar 

  3. T. Shinjyo, Y. Nakagawa, T. Ueda, Hierarchic spatio-temporal dynamics in glycolysis. Physica D 84, 212–219 (1995)

    Article  ADS  Google Scholar 

  4. T. Mair, C. Warnke, S.C. Müller, Spatio-temporal dynamics in glycolysis. Faraday Discuss. 120, 249–259 (2001)

    Article  ADS  Google Scholar 

  5. E. Meléndez-Hevia, T.G. Waddell, R. Heinrich, F. Montero, Theoretical approaches to the evolutionary optimization of glycolysis: chemical analysis. Eur. J. Biochem. 244, 527–543 (1997)

    Article  Google Scholar 

  6. A. Goldbeter, La Vie Oscillatoire au Coeur des Rythmes du Vivant (Odile Jacob, Paris, 2010)

    Google Scholar 

  7. J. Lechleiter, S. Girard, D. Clapham, E. Peralta, Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science 252, 123–126 (1991)

    Google Scholar 

  8. J.D. Lechleiter, D.E. Clapham, Molecular mechanisms of intracellular calcium excitability in Xenopus laevis oocytes. Cell 69, 283–294 (1992)

    Google Scholar 

  9. A.A.P. Leão, Spreading depression of activity in the cerebral cortex. J. Neurophysiol. 7, 359–390 (1944)

    Google Scholar 

  10. M.A. Dahlem, T. Mair, S.C. Müller, Spatio-temporal aspects of a dynamical disease: waves of spreading depression, in Function and Regulation of Cellular Systems: Experiments and Models, ed. by A. Deutsch, J. Howard, M. Falke, W. Zimmermann, (Birkhäuser, Basel, 2004)

    Google Scholar 

  11. M. Lauritzen, Pathophysiology of the migraine aura: the spreading depression therapy. Brain 117, 199–210 (1994)

    Article  Google Scholar 

  12. M. Avoli, C. Drapeau, J. Loevel, R. Pumain, A. Olivier, J.Q. Villemure, Epileptiform activity induced by low extracellular magnesium in the human cortex maintained in vitro. Ann. Neurol. 30, 580–596 (1991)

    Article  Google Scholar 

  13. H. Martins-Ferreira, G. Oliveira de Castro, Light-scattering changes accompanying spreading depression in isolated retina. J. Neurophysiol. 29, 715–726 (1966)

    Article  Google Scholar 

  14. M.A. Dahlem, R. Graf, A.J. Strong, J.P. Dreier, Y.A. Dahlem, M. Sieber, W. Hanke, K. Podoll, E. Schöll, Two-dimensional wave patterns of spreading depression. Physica D 239, 889–903 (2010)

    Article  ADS  Google Scholar 

  15. S.D. Silberstein, A. Stiles, W.B. Young (eds.), Atlas of Migraine and Other Headaches (Taylor and Francis, London, 2005)

    Google Scholar 

  16. K. Lashley, Patterns of cerebral integration indicated by the scotomas of migraine. Arch. Neurol. Psychiatry 46, 331–341 (1941)

    Article  Google Scholar 

  17. P.M. Milner, Note on a possible correspondence between the scotomas of migraine and the spreading depression of Leão Electroencephalography. Clin. Neurophysiol. 10, 705–706 (1958)

    Google Scholar 

  18. T. Bonhoeffer, A. Grinvald, Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns. Nature 353, 420–431 (1991)

    Article  ADS  Google Scholar 

  19. M.A. Dahlem, R. Engelmann, S. Löwel, S.C. Müller, Does the migraine aura reflect cortical organization? Eur. J. Neurosci. 12, 767–770 (2000)

    Article  Google Scholar 

  20. O. Steinbock, S.C. Müller, Control of spiral waves in excitable media by external perturbation, in Handbook of Chaos Control, ed. by H.G. Schuster (Wiley VCH, Weinheim, 1999), pp. 591–614

    MATH  Google Scholar 

  21. V.K. Jirsa, W.C. Stacey, P.P. Quilichini, A.I. Ivanov, On the nature of seizure dynamics. Brain 137, 2210–2230 (2014)

    Article  Google Scholar 

  22. W.J. Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics (Springer, New York, 2000)

    Book  Google Scholar 

  23. K. Takagaki, F.W. Ohl, Coarse-graining to investigate cerebral cortex dynamics, in Complexity and Synergetics, ed. by S.C. Müller, P.J. Plath, G. Radons, A. Fuchs (Springer, Cham, 2018), pp. 289–299

    Chapter  Google Scholar 

  24. K. Takagaki, C. Zhang, J.-Y. Wu, F.W. Ohl, Flow detection of propagating waves with temporospatial correlation of activity. J. Neurosci. Methods 200, 207–218 (2011)

    Article  Google Scholar 

  25. W. Lytton, Computer modelling of epilepsy. Nat. Rev. Neurosci. 9, 626–637 (2008)

    Article  Google Scholar 

  26. Y. Wang, M. Goodfellow, P. Taylor, G. Baier, Phase space approach for modelling of epileptic dynamic activity. Epilepsis 44, 72–83 (2003)

    Article  Google Scholar 

  27. P.N. Taylor, M. Goodfellow, Y. Wang, G. Baier, Towards a large-scale model of patient-specific epileptic spike-wave discharges. Biol. Cybern. 107, 83–94 (2013)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Medical Affairs, Newsenselab GmbH, Blücherstraße, 10961, Berlin, Germany

    Markus A. Dahlem

  2. Institute of Physics, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Stefan C. Müller

Authors
  1. Thomas Mair
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  2. Markus A. Dahlem
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  3. Stefan C. Müller
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Corresponding author

Correspondence to Stefan C. Müller .

Editor information

Editors and Affiliations

  1. Shimadzu Europa GmbH, Duisburg, Germany

    Kinko Tsuji

  2. Institute of Physics, Otto von Guericke University Magdeburg, Magdeburg, Germany

    Stefan C. Müller

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Mair, T., Dahlem, M.A., Müller, S.C. (2019). Yet More Spirals. In: Tsuji, K., Müller, S.C. (eds) Spirals and Vortices. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-030-05798-5_13

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