Elsevier

NeuroImage

Volume 19, Issue 1, May 2003, Pages 200-207
NeuroImage

Technical note
Modeling regional and psychophysiologic interactions in fMRI: the importance of hemodynamic deconvolution

https://doi.org/10.1016/S1053-8119(03)00058-2Get rights and content

Abstract

The analysis of functional magnetic resonance imaging (fMRI) time-series data can provide information not only about task-related activity, but also about the connectivity (functional or effective) among regions and the influences of behavioral or physiologic states on that connectivity. Similar analyses have been performed in other imaging modalities, such as positron emission tomography. However, fMRI is unique because the information about the underlying neuronal activity is filtered or convolved with a hemodynamic response function. Previous studies of regional connectivity in fMRI have overlooked this convolution and have assumed that the observed hemodynamic response approximates the neuronal response. In this article, this assumption is revisited using estimates of underlying neuronal activity. These estimates use a parametric empirical Bayes formulation for hemodynamic deconvolution.

Introduction

A common objective in functional imaging is to characterize the activity in a particular brain region in terms of the interactions among inputs from other regions or by the interaction between inputs from another region’s activity and a behavioral state. Examples of analyses modeling these interactions include psychophysiologic interactions (PPI), physiophysiologic interactions, and the incorporation of moderator variables in structural equation modeling (SEM) Friston et al 1997, Büchel et al 1999. Analyzing functional magnetic resonance imaging (fMRI) data presents a unique challenge to these techniques because the experimenter is presented with a time series that represents the neural signal convolved with some hemodynamic response function (HRF). However, interactions in the brain are expressed, not at the level of hemodynamic responses, but at a neural level. Therefore, veridical models of neuronal interactions require the neural signal or at least a well-constrained approximation to it. Given the blood oxygen level-dependent (BOLD) signal in fMRI, the appropriate approximation can be obtained by deconvolution using an assumed hemodynamic response. The need for robust deconvolution is motivated neurobiologically (because brain interactions take place at a neural level) and mathematically (because modeling interactions at a hemodynamic level is not equivalent to modeling them neuronally).

Only a few previous articles have commented on the role of deconvolution when analyzing fMRI data. Glover used Wiener deconvolution and noted that the deconvolved BOLD signal more closely tracked the experimental design (Glover, 1999). However, Wiener filtering requires independent measurement of the noise spectral density, and it will be shown represents a special and limited case of the approach we describe. Zarahn outlined a number of pitfalls in deconvolution and applied a least-squares deconvolution method to particular time periods in a trial (Zarahn, 2000). This procedure also represents a special case of the technique we describe and required the assumption of specific noise estimates.

This note reviews the mathematical theory, presents a simple method for constrained deconvolution, and demonstrates the method using simulated and empirical data sets.

Section snippets

Theory

Brain interactions occur at a neuronal level, yet the signal observed in fMRI is the hemodynamic response engendered by that neuronal activity. The problem is how to construct regressors, based on hemodynamic observations, which model neuronal influences. The hemodynamic response to neural activity can be modeled by convolution with a finite impulse response function yt=τhτxt−τ, where yt is the measured BOLD signal at time t, hτ is the hemodynamic (impulse) response function defined at times

Examples

To illustrate the importance of deconvolving prior to forming interactions we will use the interaction between two simulated event-related responses. When using the empirical Bayesian approach, the basis set for deconvolution can be complete or indeed overcomplete. In this work we have used a full rank discrete cosine set (as the explanatory variables) and a white noise form for the prior constraints on Cβ. The examples described in this article used the standard HRF, consisting of two gamma

Discussion and conclusion

This article has illustrated the distinction between interactions among BOLD signals as opposed to interactions occurring at a neuronal level. When modeling neural networks, interactions occur at a neuronal level; thus, it is essential to generate the proper form of the interaction term. The distinction between BOLD and neuronal interactions appears to be even more prominent in the setting of high noise, further demonstrating the importance of deconvolution for generally noisy fMRI data.

Acknowledgements

D.R.G. was supported by a grant from the NIA (K23 00940-03). W.B.P., J.A., and K.J.F. were supported by the Wellcome Trust. We also thank two anonymous reviewers for their helpful comments.

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