title: DCM for complex-valued data: cross-spectra, coherence and phase-delays.
abstract: This note describes an extension of Bayesian model inversion procedures for the Dynamic Causal Modeling (DCM) of complex-valued data. Modeling complex data can be particularly useful in the analysis of multivariate ergodic (stationary) time-series. We illustrate this with a generalization of DCM for steady-state responses that models both the real and imaginary parts of sample cross-spectra. DCM allows one to infer underlying biophysical parameters generating data (like synaptic time constants, connection strengths and conduction delays). Because transfer functions and complex cross-spectra can be generated from these parameters, one can also describe the implicit system architecture in terms of conventional (linear systems) measures; like coherence, phase-delay or cross-correlation functions. Crucially, these measures can be derived in both sensor and source-space. In other words, one can examine the cross-correlation or phase-delay functions between hidden neuronal sources using non-invasive data and relate these functions to synaptic parameters and neuronal conduction delays. We illustrate these points using local field potential recordings from the subthalamic nucleus and globus pallidus, with a special focus on the relationship between conduction delays and the ensuing phase relationships and cross-correlation time lags between population activities.
authors.affiliation: The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK.
authors.forename: K J
authors.initials: KJ
authors.lastname: Friston
authors.forename: A
authors.initials: A
authors.lastname: Bastos
authors.forename: V
authors.initials: V
authors.lastname: Litvak
authors.forename: K E
authors.initials: KE
authors.lastname: Stephan
authors.forename: P
authors.initials: P
authors.lastname: Fries
authors.forename: R J
authors.initials: RJ
authors.lastname: Moran
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D006801:Humans; D008959:Models, Neurological; D008962:Models, Theoretical