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A Simplified Neuronal Model for the Instigation and Propagation of Cortical Spreading Depression

Published online by Cambridge University Press:  03 June 2015

Huaxiong Huang ,
Robert M. Miura  and
Wei Yao
Huaxiong Huang*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
Robert M. Miura*
Affiliation:
Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
Wei Yao*
Affiliation:
Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China
*
Corresponding author. URL: www.math.yorku.ca/∼hhuang Email: hhuang@yorku.ca
Email: miura@njit.edu
Email: weiyao@fudan.edu.cn
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Abstract

In this paper, we construct a simplified neuronal model that is capable of simulating the instigation of cortical spreading depression (CSD) and propagation of a CSD wave. Our model is a simplification and extension of a single neuron model proposed in the literature for studying the instigation of CSD. Using the simplified neuronal model, we construct a network of these simplified neurons. This network model shows that the propagation of a CSD wave occurs naturally after it is instigated electrically or chemically. Although the model is simple, the speed of the CSD wave predicted by our model is consistent with experimentally observed values. Finally, our model allows us to investigate the effects of specific ion channels on the spread of a CSD wave.

Keywords

34A3334A3492C2092C4297M60Cortical spreading depressionneuronal modelnetworknumerical simulation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 6 , December 2011 , pp. 759 - 773
Copyright
Copyright © Global-Science Press 2011

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References

[1] Bennett, M. R., Farnell, L. and Gibson, W. G., A quantitative model of cortical spreading depression due to purinergic and gap-junction transmission in astrocyte networks, Biophys. J., 95 (2008), pp. 5648–5660.Google Scholar
[2] Bureš, J., Burešová, O. and Krřivánek, J., The Mechanism and Applications of Leao’s Spreading Depression of Electroencephalographic Activity, Prague, Academia, 1974.Google Scholar
[3] Brennan, K. C., Reyes, M. R., Valdés, H. E. L., Arnold, A. P. and Charles, A. C., Reduced threshold for cortical spreading depression in female mice, Ann. Neurol., 61 (2007), pp. 603–606.CrossRefGoogle ScholarPubMed
[4] Grafstein, B., Mechanism of spreading depression, J. Neurophys., 19 (1965), pp. 154–171.CrossRefGoogle Scholar
[5] Hadjikhane, N., M. Rio, S. Del, Wu, O., Schwartz, D., Bakker, D., Fischi, B., Kwong, K. K., Cutrer, F. M., Rosen, B. R., Tootell, R. B. H., Sorensen, A. G. and Moskowitz, M. A., Mechanisms of migraine aura revealed by functional MRI in human visual cortex, Proc. Natl. Acad. Sci., 98 (2001), pp. 4687–4692.CrossRefGoogle Scholar
[6] Howard, C. V., Cruz-Orive, L. M. and Yaegashi, H., Estimating neuron dendritic length in 3D from total vertical projections and from vertical slices, Acta Neurol Scand., 137 (1990), pp. 14–19.Google Scholar
[7] Kager, H., Wadman, W. J. and Somjen, G. G., Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations, J. Neurophys., 84 (2000), pp. 495–512.Google Scholar
[8] Kager, H., Wadman, W. J. and Somjen, G. G., Conditions for the triggering of spreading depression studied with computer simulations, J. Neurophys., 88 (2002), pp. 2700–2712.Google Scholar
[9] Koch, C. and Segev, I., Methods in Neuronal Modeling: From Ions to Networks, MIT Press, Cambridge, MA, 1998.Google Scholar
[10] Läuger, P., Electrogenic Ion Pumps, Sinauer, Sunderland MA, 1991.Google Scholar
[11] Leão, A. A. P., Spreading depression of activity in the cerebral cortex, Neurophys., 7 (1944), pp. 359–390.CrossRefGoogle Scholar
[12] Martins-Ferreira, H., Nedergaard, M. and Nicolson, C., Perspective on spreading depression, Brain Res. Rev., 32 (2000), pp. 215–234.Google Scholar
[13] Nagumo, J., Arimoto, S. and Yoshizawa, S., An active pulse transmission line simulating nerve axon, Proc. IRE, 50 (1962), pp. 2061–2070.CrossRefGoogle Scholar
[14] Shapiro, B. E., An Elecrophysiological Model of Gap-Junction Mediated Cortical Spreading Depression Including Osmotic Volume Changes, PhD Dissertation, Biomath-ematics, UCLA, 2000.Google Scholar
[15] Shapiro, B. E., Osmotic forces and gap junctions in spreading depression: a computational model, J. Comput. Neurosci., 10 (2001), pp. 99–120.Google Scholar
[16] Shibata, M. and Bures, J., Techniques for termination of reverberating spreading depression in rats, J. Neurophys., 38 (1975), pp. 158.CrossRefGoogle ScholarPubMed
[17] Somjen, G. G., Mechanisms of spreading depression and hypoxic spreading depression-like depolarization, Phys. Rev., 81 (2001), pp. 1065–1096.Google ScholarPubMed
[18] Sugaya, E., Takato, M. and Noda, Y., Neuronal and glial activity during spreading depression in cerebral cortex of cat, J. Neurophys., 38 (1975), pp. 822–841.Google Scholar
[19] Takano, T., Tian, G. F., Peng, W., Lou, N., Lovatt, D., Hansen, A. J., Kasis-Chke, K. A. and Nedergaard, M., Cortical spreading depression causes and coincides with tissue hypoxia, Nature Neurosci., 10 (2006), pp. 754–762.Google Scholar
[20] Tuckwell, H. C. and Miura, R. M., A mathematical model for spreading cortical depression, Biophys. J., 23 (1978), pp. 257–276.Google Scholar
[21] Wiener, N. and Rosenblueth, A., The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle, Arch. Inst. Cardiol. Mex., 16 (1946), pp. 205–265.Google Scholar