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On nodes and modes in resting state fMRI.

Friston KJ, Kahan J, Razi A, Stephan KE, Sporns O - Neuroimage (2014)

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.

View Article: PubMed Central - PubMed

Affiliation: The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK. Electronic address: k.friston@ucl.ac.uk.

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This figure shows the connectivity matrices corresponding to the proximity graph in the previous figure using an image format. The effective connectivity (upper left) is (proportional to) the inverse of the corresponding functional connectivity (upper right). The middle row shows that the distribution of effective connectivity strengths is sparser than the corresponding distribution of functional connection strengths. If we (arbitrarily) threshold the effective connectivity at 0.3 Hz and the functional connectivity at 0.3, the sparsity structure of the corresponding matrices becomes evident (lower panels). Nearly all the weak effective connections (white elements) become strong functional connections (black elements).
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f0050: This figure shows the connectivity matrices corresponding to the proximity graph in the previous figure using an image format. The effective connectivity (upper left) is (proportional to) the inverse of the corresponding functional connectivity (upper right). The middle row shows that the distribution of effective connectivity strengths is sparser than the corresponding distribution of functional connection strengths. If we (arbitrarily) threshold the effective connectivity at 0.3 Hz and the functional connectivity at 0.3, the sparsity structure of the corresponding matrices becomes evident (lower panels). Nearly all the weak effective connections (white elements) become strong functional connections (black elements).

Mentions: Fig. 10 shows the effective connectivity matrix in image format (upper left) and the corresponding functional connectivity (upper right). This functional connectivity matrix is not the conventional correlation matrix of observations — but the correlation matrix that would be seen if the hidden neuronal states could be observed directly in the absence of observation noise. The key thing to note is that the effective and functional connectivities have a very different form. In fact, as noted above, one is proportional to the inverse of the other. An important difference between effective and functional connectivity is that effective connectivity is generally much sparser. This is intuitively obvious: if there are effective connections from one node to a second — and from the second to third, these will induce functional connectivity or statistical dependencies among all three nodes. This “filling in” of a sparse effective connectivity is shown in the middle row. Here, the distribution of effective connectivity strengths is sparse, with a small number of high connections, in relation to the corresponding distribution of functional connection strengths. If we (arbitrarily) threshold the effective connectivity at 0.3 Hz and the functional connectivity at 0.3, the sparsity structure of the corresponding matrices becomes evident (lower panels). Nearly all the weak effective connections (white elements) become strong functional connections (black elements).


On nodes and modes in resting state fMRI.

Friston KJ, Kahan J, Razi A, Stephan KE, Sporns O - Neuroimage (2014)

This figure shows the connectivity matrices corresponding to the proximity graph in the previous figure using an image format. The effective connectivity (upper left) is (proportional to) the inverse of the corresponding functional connectivity (upper right). The middle row shows that the distribution of effective connectivity strengths is sparser than the corresponding distribution of functional connection strengths. If we (arbitrarily) threshold the effective connectivity at 0.3 Hz and the functional connectivity at 0.3, the sparsity structure of the corresponding matrices becomes evident (lower panels). Nearly all the weak effective connections (white elements) become strong functional connections (black elements).
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4121089&req=5

f0050: This figure shows the connectivity matrices corresponding to the proximity graph in the previous figure using an image format. The effective connectivity (upper left) is (proportional to) the inverse of the corresponding functional connectivity (upper right). The middle row shows that the distribution of effective connectivity strengths is sparser than the corresponding distribution of functional connection strengths. If we (arbitrarily) threshold the effective connectivity at 0.3 Hz and the functional connectivity at 0.3, the sparsity structure of the corresponding matrices becomes evident (lower panels). Nearly all the weak effective connections (white elements) become strong functional connections (black elements).
Mentions: Fig. 10 shows the effective connectivity matrix in image format (upper left) and the corresponding functional connectivity (upper right). This functional connectivity matrix is not the conventional correlation matrix of observations — but the correlation matrix that would be seen if the hidden neuronal states could be observed directly in the absence of observation noise. The key thing to note is that the effective and functional connectivities have a very different form. In fact, as noted above, one is proportional to the inverse of the other. An important difference between effective and functional connectivity is that effective connectivity is generally much sparser. This is intuitively obvious: if there are effective connections from one node to a second — and from the second to third, these will induce functional connectivity or statistical dependencies among all three nodes. This “filling in” of a sparse effective connectivity is shown in the middle row. Here, the distribution of effective connectivity strengths is sparse, with a small number of high connections, in relation to the corresponding distribution of functional connection strengths. If we (arbitrarily) threshold the effective connectivity at 0.3 Hz and the functional connectivity at 0.3, the sparsity structure of the corresponding matrices becomes evident (lower panels). Nearly all the weak effective connections (white elements) become strong functional connections (black elements).

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.

View Article: PubMed Central - PubMed

Affiliation: The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK. Electronic address: k.friston@ucl.ac.uk.

Show MeSH
Related in: MedlinePlus