Skip to main content

Computational Models for the Propagation of Spreading Depression Waves

  • Conference paper
  • First Online:
  • 905 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 720))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Leão, A.A.: Spreading depression of activity in the cerebral cortex. J. Neurophysiol. 7(6), 359–390 (1944)

    Google Scholar 

  2. Somjen, G.: Aristides Leao’s discovery of cortical spreading depression. J. Neurophysiol. 94(1), 2–4 (2005)

    Article  Google Scholar 

  3. Somjen, G.G.: Mechanisms of spreading depression and hypoxic spreading depression-like depolarization. Physiol. Rev. 81(3), 1065–1096 (2001)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Miura, R.M., Huang, H., Wylie, J.J.: Cortical spreading depression: an enigma. Eur. Phys. J. Spec. Top. 147(1), 287–302 (2007)

    Article  Google Scholar 

  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. Reggia, J.A., Montgomery, D.: A computational model of visual hallucinations in migraine. Comput. Biol. Med. 26(2), 133–141 (1996)

    Article  Google Scholar 

  10. Vecchia, D., Pietrobon, D.: Migraine: a disorder of brain excitatory-inhibitory balance? Trends Neurosci. 35(8), 507–520 (2012)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  12. Desroches, M., Faugeras, O., Krupa, M., Mantegazza, M.: Modeling Cortical Spreading Depression Induced by the Hyperactivity of Interneurons (2017)

    Google Scholar 

  13. Tuckwell, H.C., Miura, R.M.: A mathematical model for spreading cortical depression. Biophys. J. 23(2), 257–276 (1978)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  18. Grafstein, B.: Mechanism of spreading cortical depression. J. Neurophysiol. 19(2), 154–171 (1956)

    Google Scholar 

  19. FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445–466 (1961)

    Article  Google Scholar 

  20. Dahlem, M.A., Isele, T.M.: Transient localized wave patterns and their application to migraine. J. Math. Neurosci. 3(1), 1 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Reshodko, L., Bureš, J.: Computer simulation of reverberating spreading depression in a network of cell automata. Biol. Cybern. 18(3), 181–189 (1975)

    Article  MATH  Google Scholar 

  22. Wiener, N., Rosenblueth, A.: The propagation of impulses in cardial muscle. Arch. Inst. Cardiol. Mex. 16, 3–4 (1946)

    Google Scholar 

  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)

    Article  Google Scholar 

  24. Gerardo-Giorda, L., Kroos, J.M.: A computational multiscale model of cortical spreading depression propagation. Comput. Math. Appl. 74(5), 1076–1090 (2017)

    Article  MathSciNet  Google Scholar 

  25. O’Connell, R.A.: A computational study of cortical spreading depression. Ph.D. thesis, University of Minnesota (2016)

    Google Scholar 

  26. Causon, D., Mingham, C.: Introductory Finite Difference Methods for PDEs. Bookboon, London (2010)

    MATH  Google Scholar 

  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 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guillem Via .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Via, G., Faber, J., Cavalheiro, E.A. (2017). Computational Models for the Propagation of Spreading Depression Waves. In: Barone, D., Teles, E., Brackmann, C. (eds) Computational Neuroscience. LAWCN 2017. Communications in Computer and Information Science, vol 720. Springer, Cham. https://doi.org/10.1007/978-3-319-71011-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71011-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71010-5

  • Online ISBN: 978-3-319-71011-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics