Understanding the relationships between spike rate and delta/gamma frequency bands of LFPs and EEGs using a local cortical network model
Introduction
Electroencephalography (EEG) is one the most important tools for non-invasively studying brain activity in humans at fine time resolution (Lopes da Silva and Van Rotterdam, 1987, Nunez, 1981). Despite its wide use in clinical applications and in neurophysiological research, the exact relationships between the surface EEG and the underlying physiological events at the cellular and network level remain only partly known. Early studies (Creutzfeldt et al., 1966a, Creutzfeldt et al., 1966b, Klee et al., 1965) demonstrated that a prominent contribution to cortical surface EEGs comes from excitatory and inhibitory synaptic potentials (mostly from pyramidal neurons but perhaps also from spiny and aspiny stellate cells, see (Murakami and Okada, 2006)), and from afterdischarges not directly related to cellular activity (Creutzfeldt et al., 1966a, Creutzfeldt et al., 1966b, Klee et al., 1965). Other studies (Granit et al., 1963, Juergens et al., 1999, Kamondi et al., 1998, Mitzdorf, 1987) showed that these mechanisms also contribute to the generation of the Local Field Potential (LFP), an intracortical signal which shares similarities with the EEG but is more localized (Katzner et al., 2009). However, we still do not know which aspects of the time course and frequency content of the surface EEG allow an estimation of the time course of the spiking activity of cortical projection neurons, i.e. the output of the cortical site. This is clearly an important question to address for several reasons. First, progress in estimating the strength and timing of cortical spike rates from EEGs would greatly increase our understanding of the neural computations underlying the recorded EEG signal. Second, understanding how macroscopic and mesoscopic signals such as EEGs and LFPs relate to the output of a very local neuronal computation (whose results is carried by the spikes of pyramidal neurons) is a fundamental empirical step in constructing models linking large scale dynamics of cortex to computations of local networks.
Recently, we made progress in this direction (Whittingstall and Logothetis, 2009) by showing that, in macaque primary visual cortex, the time course of the spike rate can be predicted by a combination of the instantaneous delta-band (2–4 Hz) phase and gamma-band (30–100 Hz) amplitude of the concurrently recorded surface EEG. This was observed both during visual stimulation with naturalistic movies and during stimulus-free periods. Consistent findings were also obtained when predicting spike rates from intracortical LFPs rather than from EEGs (Rasch et al., 2008, Whittingstall and Logothetis, 2009). Interestingly, the cross-frequency coupling (i.e. the coupling of the phase of a slower frequency with the amplitude of a faster rhythm) which has been shown to determine the strength and timing of spiking activity in visual cortex (Whittingstall and Logothetis, 2009) has also been consistently observed in neocortex (Canolty et al., 2006, Lakatos et al., 2005) and hippocampus (Bragin et al., 1995, Lisman, 2005) and is thought to be central for a number of cognitive and sensory processes (Jensen and Colgin, 2007, Lisman, 2005, Lisman and Idiart, 1995, Schroeder and Lakatos, 2009).
These findings raise the important question of what are the mechanisms which generate cross frequency-coupling, and how cross-frequency coupling correlates to the timing and strength of spiking activity. Answering these questions would not only allow better insights into the mechanism regulating cortical dynamics, but has obvious implications for improving the prediction of spiking activity from EEGs and LFPs.
Here we aim at explaining these empirical findings by hypothesizing that the EEG-LFP delta phase reflects shifts of the cortical excitability arising from low-frequency (delta range) fluctuations in the strength of the input to the local network, and that these changes in excitability modulate both the output spike rate and the engagement of excitatory–inhibitory loops producing gamma-band oscillations, which in turn leads to the observed three-way relationships between spike rate, gamma amplitude and delta phase. Slow (delta range) input fluctuations may be either mediated by thalamocortical connections and arise from slow variations in thalamic firing reflecting responses to the relatively slow and regular changes present in naturalistic stimuli, or may be mediated by cortico-cortical connections and originate from slow and spatially extended fluctuations of ongoing cortical activity.
To test quantitatively this hypothesis, we simulated a recurrent network of integrate-and-fire neurons with excitatory–inhibitory connections stimulated with dynamic inputs with temporal regularities similar to that of thalamic responses during naturalistic visual stimulation and during spontaneous activity; we then carefully studied the dependence between the simulated EEG-LFP frequency bands and the spike rate of the simulated pyramidal neurons and how this dependence is modulated by different biophysical mechanisms; and we compared in detail the spike-EEG/LFP relationships found in the model and in real EEG/LFP recordings of awake and anaesthetized macaques during stimulation with naturalistic movies or in absence of visual stimuli.
Section snippets
Methods
All experiments conducted on macaques were approved by the local authorities (Regierungspräsidium Tübingen) and are in full compliance with the guidelines of the European Community (EUVD 86/609/EEC) for the care and use of laboratory animal.
Summary of relationship between spike rate, gamma amplitude and delta phase in visual cortex
Before analyzing the model of the relationship between the time course of spiking activity and the frequency components of LFPs and EEGs, we present and analyze the basic experimental findings in visual cortex of awake and anaesthetized macaques. The core of these findings was reported by Whittingstall and Logothetis (2009) for the case of the awake monkey. Here we summarize their results by analyzing them in exactly the same way that will be later applied to models, and we extend them by
Discussion
EEG is one of the most important techniques to record brain activity non-invasively and is a fundamental empirical tool to measure the large-scale dynamics of the human brain during cognitive and sensory functions; yet the exact relationship between the dynamics of the EEG signal and the dynamics of the outputs of local neural computations is still not known. Recently, Whittingstall and Logothetis (2009) investigated this question directly, by recording simultaneously EEGs, LFPs and spikes from
Acknowledgments
We thank M. Maravall for useful comments. This research was supported by the Max Planck Society and by the BMI Project of the Department of Robotics, Brain and Cognitive Sciences at the Italian Institute of Technology.
References (63)
- et al.
Dynamic causal modelling of induced responses
NeuroImage
(2008) - et al.
Relations between EEG phenomena and potentials of single cortical cells. I. Evoked responses after thalamic and erpicortical stimulation
Electroencephalogr. Clin. Neurophysiol.
(1966) - et al.
Relations between EEG phenomena and potentials of single cortical cells. II. Spontaneous and convulsoid activity
Electroencephalogr. Clin. Neurophysiol.
(1966) - et al.
Mechanisms of gamma oscillations in the hippocampus of the behaving rat
Neuron
(2003) - et al.
A neural mass model for MEG/EEG: coupling and neuronal dynamics
NeuroImage
(2003) - et al.
Somatosensory integration controlled by dynamic thalamocortical feed-forward inhibition
Neuron
(2005) - et al.
Neurophysiology of the BOLD fMRI signal in awake monkeys
Curr. Biol.
(2008) - et al.
The fMRI signal, slow cortical potential and consciousness
Trends Cogn. Sci.
(2009) - et al.
Cross-frequency coupling between neuronal oscillations
Trends Cogn. Sci.
(2007) - et al.
Local origin of field potentials in visual cortex
Neuron
(2009)