Abstract
Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. In this chapter we consider the \(\theta \)-neuron model that has recently been shown to admit to an exact mean-field description for instantaneous pulsatile interactions. We show that the inclusion of a more realistic synapse model leads to a mean-field model that has many of the features of a neural mass model coupled to a further dynamical equation that describes the evolution of network synchrony. A bifurcation analysis is used to uncover the primary mechanism for generating oscillations at the single and two population level. Numerical simulations also show that the phenomena of event related synchronisation and desynchronisation are easily realised. Importantly unlike its phenomenological counterpart this next generation neural mass model is an exact macroscopic description of an underlying microscopic spiking neurodynamics, and is a natural candidate for use in future large scale human brain simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1–24 (1972)
Zetterberg, L.H., Kristiansson, L., Mossberg, K.: Performance of a model for a local neuron population. Biol. Cybern. 31, 15–26 (1978)
Lopes da Silva, F.H., Hoeks, A., Smits, H., Zetterberg, L.H.: Model of brain rhythmic activity: the alpha-rhythm of the thalamus. Kybernetik 15, 27–37 (1974)
Lopes da Silva, F.H., van Rotterdam, A., Barts, P., van Heusden, E., Burr, W.: Models of neuronal populations: the basic mechanisms of rhythmicity. Prog. Brain Res. 45, 281–308 (1976)
Jansen, B.H., Rit, V.G.: Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol. Cyber. 73, 357–366 (1995)
Wendling, F., Benquet, P., Bartolomei, F., Jirsa, V.: Computational models of epileptiform activity. J. Neurosci. Methods 260, 233–251 (2016)
Dafilis, M.P., Frascoli, F., Cadusch, P.J., Liley, D.T.J.: Chaos and generalised multistability in a mesoscopic model of the electroencephalogram. Phys. D 238, 1056–1060 (2009)
Freeman, W.J.: Tutorial on neurobiology: from single neurons to brain chaos. Int. J. Bifurc. Chaos 2, 451–482 (1992)
Sotero, R.C., Trujillo-Barreto, N.J., Iturria-Medina, Y., Carbonell, F., Jimenez, J.C.: Realistically coupled neural mass models can generate EEG rhythms. Neural Comput. 19, 478–512 (2007)
Spiegler, A., Knösche, T.R., Schwab, K., Haueisen, J., Atay, F.M.: Modeling brain resonance phenomena using a neural mass model. PLoS Comput. Biol. 7(12), e1002298 (2011)
Deco, G., Jirsa, V.K., McIntosh, A.R.: Emerging concepts for the dynamical organization of resting-state activity in the brain. Nature Rev. Neurosci. 12, 43–56 (2011)
Valdes-Sosa, P., Sanchez-Bornot, J.M., Sotero, R.C., Iturria-Medina, Y., Aleman-Gomez, Y., Bosch-Bayard, J., Carbonell, F., Ozaki, T.: Model driven EEG/fMRI fusion of brain oscillations. Hum. Brain Mapp. 30, 2701–2721 (2009)
Moran, R., Pinotsis, D.A., Friston, K.: Neural masses and fields in dynamic causal modeling. Front. Comput. Neurosci. 7(57), 1–12 (2013)
Sanz-Leon, P., Knock, S.A., Spiegler, A., Jirsa, V.K.: Mathematical framework for large-scale brain network modeling in the virtual brain. NeuroImage 111, 385–430 (2015)
Bhattacharya, B.S., Chowdhury, F.N (eds.): Validating Neuro-Computational Models of Neurological and Psychiatric Disorders. Springer, Berlin (2015)
Pfurtscheller, G., Lopes da Silva, F.H.: Event-related EEG/MEG synchronization and desynchronization: basic principles. Clin. Neurophys. 110, 1842–1857 (1999)
Ashwin, P., Coombes, S., Nicks, R.: Mathematical frameworks for oscillatory network dynamics in neuroscience. J. Math. Neurosci. 6(2), (2016)
Luke, T.B., Barreto, E., So, P.: Complete classification of the macroscopic behaviour of a heterogeneous network of theta neurons. Neural Comput. 25, 3207–3234 (2013)
Montbrió, E., Pazó, D., Roxin, A.: Macroscopic description for networks of spiking neurons. Phys. Rev. X 5, 021028 (2015)
Spiegler, A., Kiebel, S.J., Atay, F.M., Knösche, T.R.: Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. NeuroImage 52, 1041–1058 (2010)
Touboul, J., Wendling, F., Chauvel, P., Faugeras, O.: Neural mass activity, bifurcations, and epilepsy. Neural Comput. 23, 3232–3286 (2011)
Ermentrout, G.B., Kopell, N.: Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM J. Appl. Math. 46, 233–253 (1986)
Latham, P.E., Richmond, B.J., Nelson, P.G., Nirenberg, S.: Intrinsic dynamics in neuronal networks I theory. J. Neurophysiol. 83, 808–827 (2000)
Pazó, D., Montbrió, E.: Low-dimensional dynamics of populations of pulse-coupled oscillators. Phys. Rev. X 4, 011009 (2014)
Kuramoto, Y.: Collective synchronization of pulse-coupled oscillators and excitable units. Phys. D 50, 15–30 (1991)
Ott, E., Antonsen, T.M.: Low dimensional behavior of large systems of globally coupled oscillators. Chaos 18, 037113 (2008)
Laing, C.R : Phase oscillator network models of brain dynamics. In: Computational Models of Brain and Behavior. Wiley-Blackwell (2016)
Ermentrout, G.B.: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM Books, Philadelphia (2002)
Börgers, C., Kopell, N.: Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comput. 15, 509–538 (2003)
Byrne, Á., Brookes, M.J., Coombes, S.: A mean field model for movement induced changes in the \(\beta \) rhythm. J. Comput. Neurosci. 43, 143–158 (2017)
Bojak, I., Breakspear, M.: Neuroimaging, neural population models for. In: Encyclopedia of Computational Neuroscience, pp. 1–29. Springer, Berlin (2014)
Baladron, J., Fasoli, D., Faugeras, O., Touboul, J.: Mean field description of and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons. J. Math. Neurosci. 2(10), (2012)
Coombes, S., beim Graben, P., Potthast, R., Wright, J.J. (eds). Neural Field Theory. Springer, Berlin (2014)
Laing, C.R.: Exact neural fields incorporating gap junctions. SIAM J. Appl. Dyn. Syst. 14, 1899–1929 (2015)
Acknowledgements
SC was supported by the European Commission through the FP7 Marie Curie Initial Training Network 289146, NETT: Neural Engineering Transformative Technologies.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Coombes, S., Byrne, Á. (2019). Next Generation Neural Mass Models. In: Corinto, F., Torcini, A. (eds) Nonlinear Dynamics in Computational Neuroscience. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-319-71048-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-71048-8_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71047-1
Online ISBN: 978-3-319-71048-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)