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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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Related in: MedlinePlus

This figure shows spectral characterisation of the haemodynamic timeseries (shown in Fig. 3) in terms of sampled (dotted lines) and predicted (solid lines) responses, which are largely superimposed. The right and left panels show the imaginary and real parts of the complex cross spectra respectively, superimposed for all pairs of regions. The first half of these functions corresponds to the cross spectra, while the second half reports the associated cross covariance functions (the Fourier transform of the cross spectra).
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f0020: This figure shows spectral characterisation of the haemodynamic timeseries (shown in Fig. 3) in terms of sampled (dotted lines) and predicted (solid lines) responses, which are largely superimposed. The right and left panels show the imaginary and real parts of the complex cross spectra respectively, superimposed for all pairs of regions. The first half of these functions corresponds to the cross spectra, while the second half reports the associated cross covariance functions (the Fourier transform of the cross spectra).

Mentions: The remaining model parameters were set to their usual priors and scaled by a random variate with a standard deviation of about 5%. This simulates regional variation in the haemodynamic response function. The resulting synthetic data were then used for model inversion to produce the predictions of cross spectral responses shown in Fig. 4. The sampled (dotted lines) and predicted (solid lines) cross spectra from this example can be seen in Fig. 4. The right and left panels show the imaginary and real parts of the complex cross spectra respectively, superimposed for all pairs of regions. The first half of these functions corresponds to the cross spectra, while the second half corresponds to the cross covariance functions. Note that the cross covariance functions have only real values. The agreement is self-evident with barely visible differences between the predictions and observations for the real parts. These predictions were based on the effective connectivity estimates shown in Fig. 5.


On nodes and modes in resting state fMRI.

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

This figure shows spectral characterisation of the haemodynamic timeseries (shown in Fig. 3) in terms of sampled (dotted lines) and predicted (solid lines) responses, which are largely superimposed. The right and left panels show the imaginary and real parts of the complex cross spectra respectively, superimposed for all pairs of regions. The first half of these functions corresponds to the cross spectra, while the second half reports the associated cross covariance functions (the Fourier transform of the cross spectra).
© Copyright Policy
Related In: Results  -  Collection

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

f0020: This figure shows spectral characterisation of the haemodynamic timeseries (shown in Fig. 3) in terms of sampled (dotted lines) and predicted (solid lines) responses, which are largely superimposed. The right and left panels show the imaginary and real parts of the complex cross spectra respectively, superimposed for all pairs of regions. The first half of these functions corresponds to the cross spectra, while the second half reports the associated cross covariance functions (the Fourier transform of the cross spectra).
Mentions: The remaining model parameters were set to their usual priors and scaled by a random variate with a standard deviation of about 5%. This simulates regional variation in the haemodynamic response function. The resulting synthetic data were then used for model inversion to produce the predictions of cross spectral responses shown in Fig. 4. The sampled (dotted lines) and predicted (solid lines) cross spectra from this example can be seen in Fig. 4. The right and left panels show the imaginary and real parts of the complex cross spectra respectively, superimposed for all pairs of regions. The first half of these functions corresponds to the cross spectra, while the second half corresponds to the cross covariance functions. Note that the cross covariance functions have only real values. The agreement is self-evident with barely visible differences between the predictions and observations for the real parts. These predictions were based on the effective connectivity estimates shown in Fig. 5.

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