Subject: Modeling & Analysis
Abstract
Introduction
We propose the use of Multivariate Autoregressive (MAR) models of fMRI time series to measure effective connectivity. The method is demonstrated with synthetic and real data, showing how such models are able to differentiate the degree of dependence between cortical regions. We consider first and second order interactions by introducing moderator variables (1) and the method is compared with Structural Equation Modelling (SEM) (2).
Methods
Given a univariate time series an Autoregressive (AR) model makes a prediction of the next observation based on a weighted sum of those preceding it. The AR coefficients (weights) then characterise the time series. Extending these ideas to many variables enables predictions of future observations in the same way, but based on all other variables in the model. The MAR coefficients are a measure of the association between variables based on their recent history and, within the context of neuroimaging time series, can be considered as characterising effective connection strengths among cortical regions. MAR models are linear and as such standard Multiple Linear Regression techniques can be used to estimate their coefficients. We estimate these using a Bayesian framework (3) and calculate their significance using F-contrasts.
Data
Time series from a fMRI study demonstrating attentional modulation of dorsal visual motion pathways were modelled. The experiment involved subjects viewing radial motion while the attentional set was alternated between attending to potential change in the motion to just observing the screen. Categorical comparisons demonstrated differential activations dependent on the attentional set in primary visual cortex (V1), motion cortex (V5), and regions associated with attentional networks, Posterior Parietal Cortex (PPC) and Prefrontal Cortex (PFC). Three MAR models were used to measure first and second order interactions among these regions.
Results
First order interactions produced significant MAR coefficients for ascending connections from V1 to V5 and V5 to PPC, and for descending connections from PFC to the dorsal stream. Significant second order interactions were found in which PPC modulated the connectivity between V1 and V5 and PFC modulated that between V5 and PPC.
Discussion
The MAR method is interesting in that intercortical dependence is measured using each regions recent history. This is in contradistinction to SEM, which does not take the time series nature of the signals into account and assumes only instantaneous interactions. A further benefit of the MAR approach is that connectivity maps may contain loops, yet exact inference can proceed within a linear framework.
References
1. K.J.Friston et al. Psychophysiological and modulatory interactions in neuroimaging. Neuroimage 6, 218-229 (1997)
2. C.Buchel and K.J.Friston. Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. Cerebral Cortex 7, 768-778 (1997)
3. W.D.Penny and S.J.Roberts. Bayesian multivariate autoregressive models with structured priors. To appear in IEE Proceedings in Vision, Image and Signal Processing (2002).