Biological Cybernetics

, Volume 111, Issue 1, pp 91–103 | Cite as

Macroscopic neural mass model constructed from a current-based network model of spiking neurons

  • Hiroaki Umehara
  • Masato Okada
  • Jun-nosuke Teramae
  • Yasushi Naruse
Original Article


Neural mass models (NMMs) are efficient frameworks for describing macroscopic cortical dynamics including electroencephalogram and magnetoencephalogram signals. Originally, these models were formulated on an empirical basis of synaptic dynamics with relatively long time constants. By clarifying the relations between NMMs and the dynamics of microscopic structures such as neurons and synapses, we can better understand cortical and neural mechanisms from a multi-scale perspective. In a previous study, the NMMs were analytically derived by averaging the equations of synaptic dynamics over the neurons in the population and further averaging the equations of the membrane-potential dynamics. However, the averaging of synaptic current assumes that the neuron membrane potentials are nearly time invariant and that they remain at sub-threshold levels to retain the conductance-based model. This approximation limits the NMM to the non-firing state. In the present study, we newly propose a derivation of a NMM by alternatively approximating the synaptic current which is assumed to be independent of the membrane potential, thus adopting a current-based model. Our proposed model releases the constraint of the nearly constant membrane potential. We confirm that the obtained model is reducible to the previous model in the non-firing situation and that it reproduces the temporal mean values and relative power spectrum densities of the average membrane potentials for the spiking neurons. It is further ensured that the existing NMM properly models the averaged dynamics over individual neurons even if they are spiking in the populations.


Recurrent network Integrate-and-fire neuron Spike train Mean field 



This work was supported by JSPS KAKENHI Grant Number 26330293.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Center for Information and Neural Networks (CiNet)National Institute of Information and Communications Technology (NICT) and Osaka UniversityKobeJapan
  2. 2.Graduate School of Frontier SciencesThe University of TokyoKashiwaJapan
  3. 3.Graduate School of Information Science and TechnologyOsaka UniversitySuitaJapan

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