Elsevier

Neurocomputing

Volumes 38–40, June 2001, Pages 983-992
Neurocomputing

Variability and interdependence of local field potentials: Effects of gain modulation and nonstationarity

https://doi.org/10.1016/S0925-2312(01)00433-7Get rights and content

Abstract

Cortical potentials following sensory stimulation are widely analyzed as the linear combination of an invariant evoked response component, time-locked to the stimulus, and an independent, ongoing noise component. We consider two alternative models and compare their predictions with data. In the first model, neuronal populations coupled through nonlinear sigmoid functions have their effective connectivity modulated by the evoked response. This leads to fast changes in the ongoing activity measured by ensemble variance, cross-correlation, spectral power, or coherence time functions. In the second model, trial-to-trial amplitude variability of a stereotyped evoked response leads to similar modulation in ongoing activity. Specific predictions from both models are tested against local field potentials recorded intracortically from monkeys performing a visuomotor task.

Introduction

At least since the time of Dawson [3], cortical potentials following sensory stimulation have been commonly understood as the linear combination of a stimulus-evoked invariant response, which is time-locked to the stimulus onset, and independent, ongoing, broadband noise activity. The trial-to-trial variability of cortical potentials is thus attributed to the variability of the ongoing component. We call this the signal plus noise (SPN) model, which can be formally expressed asZr(t)=E(t)+ηr(t),where Zr(t) is the recorded cortical potential at time t for the rth trial, with the stimulus onset at t=0;E(t) is the stereotyped deterministic stimulus-evoked response, and ηr(t) is a “noise” component reflecting ongoing activity that is independent of the evoked response E(t). In practice, the average 〈Zr(t)〉, taken over an ensemble of trials, is considered an approximate representation of E(t) and is referred to as the average event-related potential (AERP). Accordingly, the ongoing activity can then be estimated by the residual time series computed by subtracting the ensemble mean from each trial: ηr(t)=Zr(t)−〈Zr(t)〉.

The SPN model predicts that statistical quantities computed on the residuals ηr(t) do not display temporal modulations that are event-related. Examples of such quantities are the time-varying ensemble variance 〈(ηr(t))2〉, power spectral density 〈|ηr(f,t)|2〉, lagged cross-correlation 〈η1r(t)η2r(t+τ)〉/(〈[η1r(t)]2〉〈[η2r(t+τ)]2〉)1/2, and coherence, the frequency-domain analogue of the cross-correlation. However, experimental evidence from behaving animals indicates that stimulus-related modulation of these quantities on a time scale of ∼100ms do in fact occur [1]. It is not clear how these temporal modulations arise or whether they relate systematically to different phases of the AERP. In this paper we explore the origins of these modulations by studying models in which the assumptions of the SPN model are no longer maintained. In models of neuronal populations with sigmoid activation functions, such modulatory effects on the ongoing activity can arise from modulations of the input-output gain (local slope of the sigmoid function) that depend on the evoked response. Predictions derived from this nonlinear model are tested on a data set of local field potentials (LFPs) recorded from intracortical electrodes implanted at distributed cortical sites in macaque monkeys performing a visual pattern discrimination task. In another model, the effect of trial-to-trial nonstationarity of the stimulus response amplitude on the referred measures is examined and tested on the same experimental data.

Section snippets

Experiments

All experiments were performed by Dr. Richard Nakamura in the Laboratory of Neuropsychology at the National Institute of Mental Health. Visual evoked responses were sampled at 200Hz from chronically implanted surface-to-depth bipolar electrodes, in four macaque monkeys, at several (11–15) cortical sites in one hemisphere. The monkeys performed a visual pattern discrimination task. The pre-stimulus stage began when the monkey, while viewing a computer screen, depressed a hand lever with the

Event-related gain modulation: nonlinear model perspective

Dynamical models of neuronal population activities [5], [6] relate the field potentials and the pulse density (the number of spikes per unit volume) in a local neuronal population by a nonlinear function of a sigmoid type. A resulting property of networks of such populations is the dynamic modulation of gain and effective connectivity by the network's mean activity level [10]. This modulation can affect both the local population properties and the interactions among local populations. First,

Nonstationarity of evoked responses: Amplitude variability

The frequency specific nature of the observed ongoing activity modulation, coupled with the fact that the modulation frequency is close to that of the AERP, led us to investigate an alternative explanation for the observed modulations in variance and in the ∼12Hz power and coherence. This alternative abandons the assumption in the SPN model that the stimulus-evoked response is invariant over trials. It is known, for example, that the amplitude of evoked responses can vary according to states of

Conclusions

Many computational theories of brain function hypothesize fast transient stimulus- or task-dependent changes in the interdependence between neuronal populations [8], [12]. Usually those changes are thought to be caused by fast transient changes in connectivity strength both at short and long ranges. The common way to search for supporting evidence for these theories is to look for event-related changes in the ensemble variance, power spectral density, and interdependency measures like

Acknowledgements

Supported by grants from CNPq (Brazil), NIMH and ONR.

Wilson A. Truccolo-Filho is a graduate student in the Center for Complex Systems and Brain Sciences at Florida Atlantic University. His main research interests are in the field of theoretical neuroscience and functional specialization and integration in the visual cortex.

References (12)

There are more references available in the full text version of this article.

Cited by (0)

Wilson A. Truccolo-Filho is a graduate student in the Center for Complex Systems and Brain Sciences at Florida Atlantic University. His main research interests are in the field of theoretical neuroscience and functional specialization and integration in the visual cortex.

Mingzhou Ding is Professor in the Center for Complex Systems and Brain Sciences and the Department of Mathematical Sciences at FAU. His research interests are dynamical system theory, random processes, time series analysis and cognitive neurobiology. He has written more than 50 research papers covering a range of topics including Hamiltonian dynamics, nonlinear oscillators, control of chaos, speech perception, and motor coordination.

Steven L. Bressler is Professor in the Center for Complex Systems and Brain Sciences and the Department of Psychology at FAU. He has been investigating the spatial and temporal aspects of information processing in neuronal populations for the past 20 years. He has written more than 40 research articles and books chapters relating to recording and analysis of electrocortical activity, both in animals and humans.

View full text