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


Friston, K J; Bastos, A; Litvak, V; Stephan, K E; Fries, P; Moran, R J (2012). DCM for complex-valued data: Cross-spectra, coherence and phase-delays. NeuroImage, 59(1):439-455.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Institute of Biomedical Engineering
Dewey Decimal Classification:170 Ethics
610 Medicine & health
Language:English
Date:2012
Deposited On:21 Sep 2012 13:08
Last Modified:05 Apr 2016 15:58
Publisher:Elsevier
ISSN:1053-8119
Funders:Wellcome Trust
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.neuroimage.2011.07.048
PubMed ID:21820062

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