Content area
Full Text
J Comput Neurosci (2014) 37:549568 DOI 10.1007/s10827-014-0517-5
A neural mass model based on single cell dynamics to model pathophysiology
Bas-Jan Zandt Sid Visser
Michel J. A. M. van Putten
Bennie ten Haken
Received: 9 January 2014 / Revised: 24 June 2014 / Accepted: 21 July 2014 / Published online: 19 August 2014 Springer Science+Business Media New York 2014
Abstract Neural mass models are successful in modeling brain rhythms as observed in macroscopic measurements such as the electroencephalogram (EEG). While the synaptic current is explicitly modeled in current models, the single cell electrophysiology is not taken into account. To allow for investigations of the effects of channel pathologies, channel blockers and ion concentrations on macroscopic activity, we formulate neural mass equations explicitly incorporating the single cell dynamics by using a bottom-up approach. The mean and variance of the firing rate and synaptic input distributions are modeled. The firing rate curve (F(I)-curve) is used as link between the single cell and macroscopic dynamics. We show that this model accurately reproduces the behavior of two populations of synaptically connected Hodgkin-Huxley neurons, also in non-steady state.
Keywords Mean field Neural mass Recurring
network Firing rate curve Pathology Hodgkin-Huxley
Variance Channel blockers
1 Introduction
Neural mass models (NMM) are very successful in describing brain rhythms as measured with electroencephalogram
Action Editor: Michael Breakspear
B. -J. Zandt ([envelopeback]) M. J. A. M. van Putten B. ten Haken
MIRA - Institute for Biomedical Technology and Technical Medicine, University of Twente, P.O. Box 217, 7500, AE Enschede, The Netherlandse-mail: mailto:[email protected]
Web End [email protected]
S. VisserSchool of Mathematical Sciences, University of Nottingham, University Park, NG7 2RD, Nottingham, UK
(EEG) (Bhattacharya et al. 2011; Victor et al. 2011; van Putten M.J. and Zandt B.J. 2013), electrocorticogram (ECoG) (Hocepied et al. 2013), magnetoencephalogram (MEG) (Moran et al. 2013) and functional magnetic resonance imaging (fMRI) (Grefkes and Fink 2011). The main advantage of these models is that they can be mathematically analyzed due to their low dimensionality and that they are computationally inexpensive. In short, a NMM produces the average activity (firing rates) of populations of neurons. A NMM for cortex typically includes two populations, one modeling the excitatory pyramidal cells, and one the inhibitory interneurons (Wilson and Cowan 1972). If desired, NMMs can be extended with...