Abstract
Waves are common in cortical networks and may be important for carrying information about a stimulus from one local circuit to another. In a recent study of visually evoked waves in rat cortex, compression and reflection of waves are observed as the activation passes from visual areas V1 to V2. The authors of this study apply bicuculline (BMI) and demonstrate that the reflection disappears. They conclude that inhibition plays a major role in compression and reflection. We present several models for propagating waves in heterogeneous media and show that the velocity and thus compression depends weakly on inhibition. We propose that the main site of action of BMI with respect to wave propagation is on the threshold for firing which we suggest is related to action on potassium channels. We combine numerical and analytic methods to explore both compression and reflection in an excitable system with synaptic coupling.
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References
Bressloff PC (2000) Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire. J Math. Biol. 40: 169–198
Bressloff PC (2001) Traveling fronts and waves propagation failure in an inhomogeneous neural network. Phys D 155: 83–100
Bressloff PC, Folias S, Prat A, Li X (2003) Oscillatory waves in hinomogeneous media. Phys Rev Lett 91: 178101
Coombes S (2005) Waves, bumps and pattern in neural field theories. Biol Cybern 93: 91–108
Coombes S, Laing CR (2011) Pulsating fronts in periodically modulated neural field models. Phys Rev E 83: 011912
Cytrynbaum E, Lewis T (2009) A global bifurcation and the appearance of a one-dimensional spiral wave in excitable media. SIAM J Appl Dyn Syst 8: 348
Ermentrout B, Kleinfeld D (2001) Parabollic bursting in an excitable system coupled with a slow oscillation. Neuron 29: 33–44
Ermentrout B, Kopell N (1986) Parabollic bursting in an excitable system coupled with a slow oscillation. SIAM J Appl Math 46: 233–253
Ermentrout B, Rinzel J (1996) Reflected waves in a inhomogeneous excitable medium. SIAM J Appl Math 56: 1107–1128
Ermentrout G, McLeod J (1991) Existence and uniqueness of travelling waves for a neural network. Proc R Soc Edimb 434: 413–417
Folias S, Bressloff P (2005) Stimulus-locked traveling waves and breathers in an excitatory neural network. SIAM J Appl Math 65: 2067–2092
Golomb D, Ermentrout GB (2001) Bistability in pulse propagation in networks of excitatory and inhibitory populations. Phys Rev Lett 86: 4179–4182
Golomb D, Ermentrout GB (2002) Slow excitation supports propagation of slow pulses in networks of excitatory and inhibitory populations. Phys Rev E Stat Nonlin Soft Matter Phys 65: 061, 911
Hoppensteadt F, Izhikevich E (1997) Weakly connected neural networks, vol 126. Springer Verlag, New York
Hutt A, Atay F (2006) Effect of distributed transmission speeds on propagating activity in neural populations. Phys Rev E 73: 021906
Kilpatrick ZP, Folias SE, Bressloff PC (2008) Traveling pulses and wave propagation failure in inhomogenous neural media. SIAM J Appl Dyn Syst 7: 161–185
Kilpatrick Z, Bressloff P (2010) Spatially structured oscillations in a two dimensional excitatory neuronal network with synaptic depression. J Comput Neurosci 28: 193–209
Osan R, Rubin J, Ermentrout B (2002) Regular traveling waves in a one-dimensional network of theta neurons. SIAM J Appl Math 62(4): 1197–1221 (electronic)
Ozeki H, Finn IM, Schaffer ES, Miller KD, Ferster D (2009) Inhibitory stabilization of the cortical network underlies visual surround suppression. Neuron 62(4): 578–592
Pinto D, Patrick S, Huang W, Connors B (2005) Initiation, propagation, and termination of epileptiform activity in rodent neocortex in vitro involve distinct mechanisms. J Neurosci 25: 8131–8140
Pinto DJ, Ermentrout GB (2001) Spatially structured activity in synaptically coupled neuronal networks. I. Traveling fronts and pulses. SIAM J Appl Math 62(1): 206–225 (electronic)
Prat A, Li YX, Bressloff P (2005) Inhomogeneity-induced bifurcation of stationary and oscillatory pulses. Phys D 202(3–4): 177–199
Rinzel J, Ermentrout B (1998) Analysis of neural exictability and oscillations. In: Koch C, Segev I (eds) Method in neuronal modeling. MIT press, Cambridge, pp 251–291
Shusterman V, Troy W (2008) From baseline to epileptic activity: A path to synchronized rhythmicity in large-scale neural networks. Phys Rev E 77: 061911
Wu J, Huang X, Zhang C (2007) Propagating waves of activity in the neocortex: what they are, what they do. Neuroscientist 55: 119–129
Xu W, Huang X, Takagaki K, Wu J (2008) Compression and reflection of visually evoked cortical waves. Neuron 14: 487–502
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Goulet, J., Ermentrout, G.B. The mechanisms for compression and reflection of cortical waves. Biol Cybern 105, 253–268 (2011). https://doi.org/10.1007/s00422-011-0465-3
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DOI: https://doi.org/10.1007/s00422-011-0465-3