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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Leão, A.A.: Spreading depression of activity in the cerebral cortex. J. Neurophysiol. 7(6), 359–390 (1944)
Somjen, G.: Aristides Leao’s discovery of cortical spreading depression. J. Neurophysiol. 94(1), 2–4 (2005)
Somjen, G.G.: Mechanisms of spreading depression and hypoxic spreading depression-like depolarization. Physiol. Rev. 81(3), 1065–1096 (2001)
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)
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)
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)
Miura, R.M., Huang, H., Wylie, J.J.: Cortical spreading depression: an enigma. Eur. Phys. J. Spec. Top. 147(1), 287–302 (2007)
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)
Reggia, J.A., Montgomery, D.: A computational model of visual hallucinations in migraine. Comput. Biol. Med. 26(2), 133–141 (1996)
Vecchia, D., Pietrobon, D.: Migraine: a disorder of brain excitatory-inhibitory balance? Trends Neurosci. 35(8), 507–520 (2012)
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)
Desroches, M., Faugeras, O., Krupa, M., Mantegazza, M.: Modeling Cortical Spreading Depression Induced by the Hyperactivity of Interneurons (2017)
Tuckwell, H.C., Miura, R.M.: A mathematical model for spreading cortical depression. Biophys. J. 23(2), 257–276 (1978)
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)
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)
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)
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)
Grafstein, B.: Mechanism of spreading cortical depression. J. Neurophysiol. 19(2), 154–171 (1956)
FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445–466 (1961)
Dahlem, M.A., Isele, T.M.: Transient localized wave patterns and their application to migraine. J. Math. Neurosci. 3(1), 1 (2013)
Reshodko, L., Bureš, J.: Computer simulation of reverberating spreading depression in a network of cell automata. Biol. Cybern. 18(3), 181–189 (1975)
Wiener, N., Rosenblueth, A.: The propagation of impulses in cardial muscle. Arch. Inst. Cardiol. Mex. 16, 3–4 (1946)
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)
Gerardo-Giorda, L., Kroos, J.M.: A computational multiscale model of cortical spreading depression propagation. Comput. Math. Appl. 74(5), 1076–1090 (2017)
O’Connell, R.A.: A computational study of cortical spreading depression. Ph.D. thesis, University of Minnesota (2016)
Causon, D., Mingham, C.: Introductory Finite Difference Methods for PDEs. Bookboon, London (2010)
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)
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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
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)