Computational Models for the Propagation of Spreading Depression Waves

  • Guillem ViaEmail author
  • Jean Faber
  • Esper Abrão Cavalheiro
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 720)


Spreading Depression (SD) consists on a wave of depressed neural, electrical, activity and near complete depolarization of large neuron populations. It is believed to occur both in compromised and healthy tissue from a broad range of animal species and every structure of the gray matter. Glutamate is long been known to be involved in the ignition of SD. Therefore, despite action potentials are not necessary for the wave propagation, one would expect synaptic processes to play a role in initiating the phenomenon if they are functional. Several detailed and phenomenological computational models have been proposed to simulate the ignition and spread of SD, but few considered synaptic mechanisms. Here we briefly review them, emphasizing macroscopic models that reproduce the wave features and the lack of synaptic transmission. We also propose extensions to a popular model for the wave spread to test whether structural connectivity could aid in stopping the wave and preventing it from engulfing larger portions of the brain.


Spreading depression Stroke Migraine Reaction-diffusion model Neural networks 



This work was supported by the Instituto de Ciência e Tecnologia (INCT) grant (88887.137596/2017-00) from the INCT call MCTI/CNPq/CAPES/FAPs nr. 16/2014.


  1. 1.
    Leão, A.A.: Spreading depression of activity in the cerebral cortex. J. Neurophysiol. 7(6), 359–390 (1944)Google Scholar
  2. 2.
    Somjen, G.: Aristides Leao’s discovery of cortical spreading depression. J. Neurophysiol. 94(1), 2–4 (2005)CrossRefGoogle Scholar
  3. 3.
    Somjen, G.G.: Mechanisms of spreading depression and hypoxic spreading depression-like depolarization. Physiol. Rev. 81(3), 1065–1096 (2001)Google Scholar
  4. 4.
    Pietrobon, D., Moskowitz, M.A.: Chaos and commotion in the wake of cortical spreading depression and spreading depolarizations. Nat. Rev. Neurosci. 15(6), 379–393 (2014)CrossRefGoogle Scholar
  5. 5.
    Zandt, B.-J., ten Haken, B., van Putten, M.J., Dahlem, M.A.: How does spreading depression spread? Physiology and modeling. Rev. Neurosci. 26(2), 183–198 (2015)CrossRefGoogle Scholar
  6. 6.
    Sugaya, E., Takato, M., Noda, Y.: Neuronal and glial activity during spreading depression in cerebral cortex of cat. J. Neurophysiol. 38(4), 822–841 (1975)Google Scholar
  7. 7.
    Miura, R.M., Huang, H., Wylie, J.J.: Cortical spreading depression: an enigma. Eur. Phys. J. Spec. Top. 147(1), 287–302 (2007)CrossRefGoogle Scholar
  8. 8.
    Haglund, M.M., Schwartzkroin, P.A.: Role of NA-K pump potassium regulation and IPSPs in seizures and spreading depression in immature rabbit hippocampal slices. J. Neurophysiol. 63(2), 225–239 (1990)Google Scholar
  9. 9.
    Reggia, J.A., Montgomery, D.: A computational model of visual hallucinations in migraine. Comput. Biol. Med. 26(2), 133–141 (1996)CrossRefGoogle Scholar
  10. 10.
    Vecchia, D., Pietrobon, D.: Migraine: a disorder of brain excitatory-inhibitory balance? Trends Neurosci. 35(8), 507–520 (2012)CrossRefGoogle Scholar
  11. 11.
    Tottene, A., Conti, R., Fabbro, A., Vecchia, D., Shapovalova, M., Santello, M., van den Maagdenberg, A.M., Ferrari, M.D., Pietrobon, D.: Enhanced excitatory transmission at cortical synapses as the basis for facilitated spreading depression in Ca V 2.1 knockin migraine mice. Neuron 61(5), 762–773 (2009)CrossRefGoogle Scholar
  12. 12.
    Desroches, M., Faugeras, O., Krupa, M., Mantegazza, M.: Modeling Cortical Spreading Depression Induced by the Hyperactivity of Interneurons (2017)Google Scholar
  13. 13.
    Tuckwell, H.C., Miura, R.M.: A mathematical model for spreading cortical depression. Biophys. J. 23(2), 257–276 (1978)CrossRefGoogle Scholar
  14. 14.
    Shapiro, B.E.: An electrophysiological model of gap-junction mediated cortical spreading depression including osmotic volume changes. Ph.D. thesis, University of California, Los Angeles (2000)Google Scholar
  15. 15.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. physiol. 117(4), 500–544 (1952)CrossRefGoogle Scholar
  16. 16.
    Zandt, B.-J., Stigen, T., ten Haken, B., Netoff, T., van Putten, M.J.: Single neuron dynamics during experimentally induced anoxic depolarization. J. Neurophysiol. 110(7), 1469–1475 (2013)CrossRefGoogle Scholar
  17. 17.
    Somjen, G., Müller, M.: Potassium-induced enhancement of persistent inward current in hippocampal neurons in isolation and in tissue slices. Brain Res. 885(1), 102–110 (2000)CrossRefGoogle Scholar
  18. 18.
    Grafstein, B.: Mechanism of spreading cortical depression. J. Neurophysiol. 19(2), 154–171 (1956)Google Scholar
  19. 19.
    FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445–466 (1961)CrossRefGoogle Scholar
  20. 20.
    Dahlem, M.A., Isele, T.M.: Transient localized wave patterns and their application to migraine. J. Math. Neurosci. 3(1), 1 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Reshodko, L., Bureš, J.: Computer simulation of reverberating spreading depression in a network of cell automata. Biol. Cybern. 18(3), 181–189 (1975)CrossRefzbMATHGoogle Scholar
  22. 22.
    Wiener, N., Rosenblueth, A.: The propagation of impulses in cardial muscle. Arch. Inst. Cardiol. Mex. 16, 3–4 (1946)Google Scholar
  23. 23.
    Revett, K., Ruppin, E., Goodall, S., Reggia, J.A.: Spreading depression in focal ischemia: a computational study. J. Cereb. Blood Flow Metab. 18(9), 998–1007 (1998)CrossRefGoogle Scholar
  24. 24.
    Gerardo-Giorda, L., Kroos, J.M.: A computational multiscale model of cortical spreading depression propagation. Comput. Math. Appl. 74(5), 1076–1090 (2017)CrossRefMathSciNetGoogle Scholar
  25. 25.
    O’Connell, R.A.: A computational study of cortical spreading depression. Ph.D. thesis, University of Minnesota (2016)Google Scholar
  26. 26.
    Causon, D., Mingham, C.: Introductory Finite Difference Methods for PDEs. Bookboon, London (2010)zbMATHGoogle Scholar
  27. 27.
    Renart, A., Brunel, N., Wang, X.-J.: Mean-field theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks. In: Feng, J. (ed.) Computational Neuroscience: A Comprehensive Approach, pp. 431–490. CRC Press (2003)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Guillem Via
    • 1
    Email author
  • Jean Faber
    • 1
  • Esper Abrão Cavalheiro
    • 1
  1. 1.Departamento de Neurologia e NeurocirurgiaUniversidade Federal de São Paulo - UNIFESPSão PauloBrazil

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