Skip to main content
SpringerLink
Log in

Analysis of Cortical Spreading Depression in Brain with Multiscale Mathematical Models

  • Conference paper
  • First Online:
Recent Developments in Mathematical, Statistical and Computational Sciences (AMMCS 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 343))

Abstract

The present study aims at modeling the cortical spreading depression (CSD) propagation in brain considering two different approaches available in the literature: (a) a simplified model consisting of six coupled equations of the reaction-diffusion type in two space dimensions and (b) a one-dimensional, more complex neuronal model comprising of ionic currents and ionic pumps. A study has been conducted to quantify the effects of varying extracellular potassium concentrations on the propagation of CSD in the multiscale reaction-diffusion model by monitoring the respective changes in the extracellular and intracellular concentrations of sodium, chlorine and calcium ions, in addition to evaluating the changes in the generated membrane potentials. In the multiscale neuronal model, the influence of gated conductance on the intracellular and extracellular potassium concentrations of the sodium and potassium and the membrane potential has been reported. The study revealed that the variation in gated conductance results in an increase of the pump currents that leads to the spatio-temporal variations of extracellular potassium.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Le\(\tilde{a}\)o, A.A.: Spreading depression of activity in the cerebral cortex. J. Neurophysiol. 7(6), 359–390 (1944)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Cozzolino, O., Marchese, M., Trovato, F., Pracucci, E., Ratto, G.M., Buzzi, M.G., Santorelli, F.M.: Understanding spreading depression from headache to sudden unexpected death. Front. Neurol. 9(19) (2018)

    Google Scholar 

  4. Chamanzar, A., George, S., Venkatesh, P., Chamanzar, M., Shutter, L., Elmer, J., Grover, P.: An algorithm for automated, noninvasive detection of cortical spreading depolarizations based on EEG simulations. IEEE T. Bio-Med. Eng. 66(4), 1115–1126 (2018)

    Article  Google Scholar 

  5. Tuckwell, H.C.: Stochastic modeling of spreading cortical depression. In: Stochastic Biomathematical Models. Springer, Berlin, Heidelberg, pp. 187–200 (2013)

    Google Scholar 

  6. Tuckwell, H.C., Hermansen, C.L.: Ion and transmitter movements during spreading cortical depression. Int. J. Neurosci. 12(2), 109–135 (1981)

    Article  Google Scholar 

  7. Kager, H., Wadman, W.J., Somjen, G.G.: Conditions for the triggering of spreading depression studied with computer simulations. J. Neurophysiol. 88(5), 2700–2712 (2002)

    Article  Google Scholar 

  8. Shapiro, B.E.: Osmotic forces and gap junctions in spreading depression: a computational model. J. Comput. Neurosci. 10(1), 99–120 (2001)

    Article  Google Scholar 

  9. Huang, H., Miura, R.M., Yao, W.: A continuum neuronal model for the instigation and propagation of cortical spreading depression. Bull. Math. Biol. 73(11), 2773–2790 (2011)

    Article  MathSciNet  Google Scholar 

  10. Huang, H., Miura, R.M., Yao, W.: A simplified neuronal model for the instigation and propagation of cortical spreading depression. Adv. Appl. Math. Mech. 3(6), 759–773 (2011)

    Article  MathSciNet  Google Scholar 

  11. Koch, C., Segev I.: Methods in Neuronal Modeling from Ions to Networks. MIT press (1998)

    Google Scholar 

  12. COMSOL Multiphysics® v. 5.2. www.comsol.com. COMSOL AB, Stockholm

    Google Scholar 

Download references

Acknowledgements

Authors are grateful to the NSERC and the CRC Program for their support. RM is also acknowledging support of the BERC 2018-2021 program and Spanish Ministry of Science, Innovation and Universities through the Agencia Estatal de Investigacion (AEI) BCAM Severo Ochoa excellence accreditation SEV-2017-0718.

Author information

Authors and Affiliations

  1. MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University (WLU), 75 University Avenue West, Waterloo, N2L 3C5, Canada

    Hina Shaheen

  2. MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, Canada

    Roderick Melnik & Sundeep Singh

  3. BCAM—Basque Center for Applied Mathematics, Bilbao, Spain

    Roderick Melnik

Authors
  1. Hina Shaheen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roderick Melnik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sundeep Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hina Shaheen .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    D. Marc Kilgour

  2. Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada

    Herb Kunze

  3. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    Roman Makarov

  4. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    Roderick Melnik

  5. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

    Xu Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Shaheen, H., Melnik, R., Singh, S. (2021). Analysis of Cortical Spreading Depression in Brain with Multiscale Mathematical Models. In: Kilgour, D.M., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Developments in Mathematical, Statistical and Computational Sciences. AMMCS 2019. Springer Proceedings in Mathematics & Statistics, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-030-63591-6_19

Download citation

Publish with us

Policies and ethics

Search

Navigation