DCM for complex-valued data: cross-spectra, coherence and phase-delays

K J Friston, A Bastos, V Litvak, K E Stephan, P Fries, R J Moran

Research output: Contribution to journalArticle (Academic Journal)peer-review

92 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)439-55
Number of pages17
Issue number1
Publication statusPublished - 2 Jan 2012


  • Algorithms
  • Bayes Theorem
  • Brain
  • Brain Mapping
  • Humans
  • Models, Neurological
  • Models, Theoretical


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