Andreas Daffertshofer — Move Research Institute and Department of Human Movement Sciences - Vrije Universiteit Amsterdam #
Synchrony in the nervous system – from spikes via neural masses to phase oscillators #

The interplay between structural and functional networks is an urgent topic in neuroscientific research. The discrepancy in the respective topologies may help to unravel details how network structure facilitates or constrains function, i.e. information transfer. In a combined neural mass and graph theoretical model, it was found that patterns of functional connectivity are influenced by the corresponding structural level [1]. Functional connectivity is often being defined through the synchronization between activities at different nodes. These activities are considered to stem from meso-scale neural populations that oscillate at certain frequencies with certain amplitudes. The amplitude of a local neural population reflects the degree of synchronization across its members.


It will be illustrated how this amplitude can affect the phase dynamics in neural networks by approximating the node dynamics as self-sustaining, weakly non-linear oscillators. The dynamics of these populations can be derived from networks of spiking neurons in mean-field approximation. The resulting neural mass models allow for deducing the corresponding phase dynamics proper [2,3]. Dependent on the type of neural mass, the phase dynamics may be influenced by the amplitudes of the individual oscillators. The corresponding phases obeys the form of a Kuramoto-like network [4]. It will be discussed how the functional connectivity between phases depends on the structural connectivity but also on the oscillators’ amplitudes. In consequence, phase dynamics and, hence, synchrony patterns should always be analyzed in conjunction with the corresponding changes in amplitude [4]. These results will be extended to the case of two or more coupled networks [5] to bring the theoretical findings closer to neuro-imaging data and corresponding numerical studies.


References

[1]  Ponten, Daffertshofer, Hillebrand, Stam (2010) The relationship between structural and functional connectivity: Graph theoretical analysis of an EEG neural mass model. NeuroImage, 52(3):985.

[2]  Ton, Deco, Daffertshofer (2014). Structure-function discrepancy: inhomogeneity and delays in synchronized neural networks. PLoS Comp. Biol., 10(7): e1003736.

[3]  Daffertshofer, van Wijk (2011). On the influence of amplitude on the connectivity between phases. Frontiers in Neuroinf., 5, art. 6.

[4]  Breakspear, Heitmann, Daffertshofer (2010) Generative models of cortical oscillations: From Kuramoto to the nonlinear Fokker–Planck equation, Frontiers Human Neurosci., 4, art. 190.

[5] Pietras, Deschle, Daffertshofer (2016) Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case, Phys. Rev. E 94, 052211.