1. ? Dynamical properties of simulated MEG/EEG using a neural mass model
Olivier David, Karl Friston
Functional Imaging Laboratory, 12 Queen Square, London WC1N 3BG, UK
Neural mass models
Functional connectivity: comparison of interdependency measures
The mean activity of interacting neuronal populations within macro-columns, or even cortical areas, is modelled using only one or two state variables per population (membrane potential, firing rate). Such models are classically used to emulate MEG/EEG signals.
This neural mass model has been used to evaluate the sensitivity to coupling and nonlinearity of different interdependency measures that are used to estimate functional networks from MEG/EEG data. Methods based on generalised synchronisation show the best characteristics but are computationally expensive.
Cortical
areas
Neuronal
populations
Brain ?
MEG/EEG
Cross-correlation:
Mutual information:
Jansen’s model
Phase synchronisation:
The Jansen model is a simple model of a macro-column or cortical area. It considers three populations (excitatory pyramidal and stellate cells: time constant te, inhibitory interneurons: time constant ti). In its oscillatory regime, the MEG/EEG frequency range can be reproduced by adjusting [te, ti].
Generalised synchronisation:
Quian-Quiroga et al.
MEG/EEG signal
y(t)
Excitatory output to other cortical areas
Excitatory
pyramidal cells
Solid line: average over 20 realisations (dots).
Dotted line: significance threshold (p<0.01) obtained from a null distribution.
Dashed line: average over 20 realisations after removal of signals’ nonlinear parts.
External input
p(t)
Excitatory
stellate cells
Inhibitory
interneurons
Event-related dynamics
Events are simulated by using impulses as external input p(t). For a given set of parameters, event-related potentials (ERPs) can be estimated, thus generating physiologically motivated basis functions to analyse actual ERPs. Below a somatosensory ERP following a median nerve electrical stimulation (average over 63 channels and about 1000 events) (a) is analysed. The three parameters (w, k, d) of the model (b) are fitted to the data y (a) and single-trials are generated (c). 18 basis functions X (d) are obtained after averaging single-trials for different input time lags (from 10 to 50 ms with 5 ms time step). A linear model of the ERP y=Xb+e is used and the data are fitted (e) by estimating the parameters b (f). This approach will be adopted for statistical parametric mapping (SPM) for ERPs.
Generalisation to two neuronal subpopulations of different kinetics
The Jansen model can be generalised by considering neuronal subpopulations of different kinetics. In the case of two subpopulations of slow (a rhythms) and fast (g rhythms) kinetics, a parameter w balances their relative contribution. Particularly when areas are coupled (coupling 0k1, propagation delay d), a wide range of realistic MEG/EEG signals can be generated.
y(t) y
w w
(a)
(b)
Slow Fast
(a) (g)
(e)
(c)
w w
w w
p(t)
Slow Fast
(a) (g)
Slow Fast
(a) (g)
(d)
(f)
References
David & Friston, NeuroImage, revised.
Jansen & Rit, Biol. Cybern., vol. 73, p , 1995.
Quian-Quiroga et al., Phys. Rev. E, vol. 65, , 2001.