Models of Effective Connectivity in Neural Systems

Klaas Enno Stephan and Karl J Friston

Wellcome Dept. of Imaging Neuroscience, Institute of Neurology, University College London, 12 Queen Square, WC1N 3BG, London, UK.

It is a longstanding scientific insight that understanding processes that result from the interaction of multiple elements require mathematical models of system dynamics (von Bertalanffy 1969). This notion is an increasingly important theme in neuroscience, particularly in neuroimaging, where causal mechanisms in neural systems are described in terms of effective connectivity. Here, we review established models of effective connectivity that are applied to data acquired with positron emission tomography (PET), functional magnetic resonance imaging (fMRI), electroencephalography (EEG) or magnetoencephalog-raphy (MEG). We start with an outline of general systems theory, a very general framework for formalizing the description of systems. This framework will guide the subsequent description of various establishd models of effective connectivity, including structural equation modeling (SEM), multivariate autoregressive modeling (MAR) and dynamic causal modeling (DCM). We focus particularly on DCM which distinguishes between neural state equations and a biophysical forward model that translates neural activity into a measured signal. After presenting some examples of applications of DCM to fMRI and EEG data, we conclude with some thoughts on pharmacological and clinical applications of models of effective connectivity.

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