On nodes and modes in resting state fMRI.
Bottom Line: We first demonstrate that the eigenmodes of functional connectivity--or covariance among regions or nodes--are the same as the eigenmodes of the underlying effective connectivity, provided we limit ourselves to symmetrical connections.Crucially, the principal modes of functional connectivity correspond to the dynamically unstable modes of effective connectivity that decay slowly and show long term memory.In this model, effective connectivity is parameterised in terms of eigenmodes and their Lyapunov exponents--that can also be interpreted as locations in a multidimensional scaling space.
Affiliation: The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK. Electronic address: email@example.com.Show MeSH
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Mentions: In fact, power law scaling over ranges of frequencies emerges with the superposition of a relatively small number of modes that can be sampled from a finite interval (see also Watanabe (2005)). Fig. 1 shows an example where the time constants were restricted to the range and the integrals above were evaluated numerically. We are not supposing that fMRI signals necessarily show a classical power law scaling behaviour — the aim of this analysis is to show that power law scaling, indicative of nonequilibrium steady-state fluctuations, can be explained by a spectrum of Lyapunov exponents in which there are a small number of exponents that approach zero from below and a large number of large negative exponents λi ≈ − 1/ε, characterising modes of activity that dissipate quickly.
Affiliation: The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK. Electronic address: firstname.lastname@example.org.