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Noise during rest enables the exploration of the brain's dynamic repertoire.

Ghosh A, Rho Y, McIntosh AR, Kötter R, Jirsa VK - PLoS Comput. Biol. (2008)

Bottom Line: Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network.The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging.The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.

View Article: PubMed Central - PubMed

Affiliation: Theoretical Neuroscience Group, Institut des Sciences du Mouvement, Marseille, France. Anandamohan.GHOSH@univmed.fr

ABSTRACT
Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.

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Results of PCA of the network dynamics close to the instability (point B in Figure 3B).(A) The first three dominant areas in the subnetworks as identified by the PCA modes, 1st mode (blue) and 2nd mode (red). The nodes are plotted in the physical space (units in mm) with locations extrapolated for the human. PFCORB, orbital prefrontal cortex; PFCVL, ventrolateral prefrontal cortex; PCM, medial parietal cortex; PCS, superior parietal cortex; CCA, anterior cingulated cortex; PFCDL, dorsolateral prefrontal cortex. (B) The percentile contribution of the first six principal components. The total variance of the first two components is 99.995%. (C) The power of the leading spatial contributions of the first two subnetworks (quantified by PCA) is plotted (normalized per subnetwork). Individual areas are highlighted using the same color coding as in Figure 1C. (D) Time series shown for the rest state subnetwork nodes from a simulation with noise.
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pcbi-1000196-g004: Results of PCA of the network dynamics close to the instability (point B in Figure 3B).(A) The first three dominant areas in the subnetworks as identified by the PCA modes, 1st mode (blue) and 2nd mode (red). The nodes are plotted in the physical space (units in mm) with locations extrapolated for the human. PFCORB, orbital prefrontal cortex; PFCVL, ventrolateral prefrontal cortex; PCM, medial parietal cortex; PCS, superior parietal cortex; CCA, anterior cingulated cortex; PFCDL, dorsolateral prefrontal cortex. (B) The percentile contribution of the first six principal components. The total variance of the first two components is 99.995%. (C) The power of the leading spatial contributions of the first two subnetworks (quantified by PCA) is plotted (normalized per subnetwork). Individual areas are highlighted using the same color coding as in Figure 1C. (D) Time series shown for the rest state subnetwork nodes from a simulation with noise.

Mentions: To perform a spatiotemporal analysis of the network dynamics, we identify the dominating sub-networks involved in the ongoing transient oscillatory dynamics. We implement the network parameter settings according to point B close to the instability in Figure 3A. Results for other representative parameter settings are presented in the supplementary materials. Our challenge here is to extract the network nodes contributing the most variance to the network dynamics, because these nodes will be the most visible in experimental data. Mathematically speaking, we wish to identify a linear vector space spanned by n vectors ψk, where n is the dimension and typically smaller than the total dimension of the network (in the present network the total dimension is 38). These vectors span the directions of a subspace, in which the network is most sensitive to perturbations and noise. Equivalently, these vectors can be considered to be network patterns or network modes of operation. In this subspace most of the variance of the network dynamics is contained and define the dynamic repertoire of the sorts of the behaviors the network is capable to perform following a perturbation. In other words, the activity of the ith network node u(i,t) can be written as , where t is the time and ξk(t) is the time dependent coefficient capturing the dynamics of the kth network pattern ψk. The contribution of the ith network node is given by ψk(i). To identify and quantify the contributions of the subspace, we perform the following procedure (see Methods for details): When the network dynamics relaxes into its equilibrium state, we perform a small parameter change towards the unstable region. A typical time series plot is shown in Figure S1. As a consequence of this minimal parameter change, the previously least stable network modes cross the critical boundary first, become unstable and grow with the fastest growth rate. The mathematical basis thereof is the center manifold theorem [29]. As a consequence, only the unstable network modes are present during the transition. Of course, after the transition the nonlinearities and all the network modes become relevant for the network dynamics. During the transition, though, we use a sliding temporal window analysis and perform a Principal Component Analysis (PCA) to identify the dominant network modes (see Figure 4). We find that only two network modes ψk contribute to the transient dynamics.


Noise during rest enables the exploration of the brain's dynamic repertoire.

Ghosh A, Rho Y, McIntosh AR, Kötter R, Jirsa VK - PLoS Comput. Biol. (2008)

Results of PCA of the network dynamics close to the instability (point B in Figure 3B).(A) The first three dominant areas in the subnetworks as identified by the PCA modes, 1st mode (blue) and 2nd mode (red). The nodes are plotted in the physical space (units in mm) with locations extrapolated for the human. PFCORB, orbital prefrontal cortex; PFCVL, ventrolateral prefrontal cortex; PCM, medial parietal cortex; PCS, superior parietal cortex; CCA, anterior cingulated cortex; PFCDL, dorsolateral prefrontal cortex. (B) The percentile contribution of the first six principal components. The total variance of the first two components is 99.995%. (C) The power of the leading spatial contributions of the first two subnetworks (quantified by PCA) is plotted (normalized per subnetwork). Individual areas are highlighted using the same color coding as in Figure 1C. (D) Time series shown for the rest state subnetwork nodes from a simulation with noise.
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pcbi-1000196-g004: Results of PCA of the network dynamics close to the instability (point B in Figure 3B).(A) The first three dominant areas in the subnetworks as identified by the PCA modes, 1st mode (blue) and 2nd mode (red). The nodes are plotted in the physical space (units in mm) with locations extrapolated for the human. PFCORB, orbital prefrontal cortex; PFCVL, ventrolateral prefrontal cortex; PCM, medial parietal cortex; PCS, superior parietal cortex; CCA, anterior cingulated cortex; PFCDL, dorsolateral prefrontal cortex. (B) The percentile contribution of the first six principal components. The total variance of the first two components is 99.995%. (C) The power of the leading spatial contributions of the first two subnetworks (quantified by PCA) is plotted (normalized per subnetwork). Individual areas are highlighted using the same color coding as in Figure 1C. (D) Time series shown for the rest state subnetwork nodes from a simulation with noise.
Mentions: To perform a spatiotemporal analysis of the network dynamics, we identify the dominating sub-networks involved in the ongoing transient oscillatory dynamics. We implement the network parameter settings according to point B close to the instability in Figure 3A. Results for other representative parameter settings are presented in the supplementary materials. Our challenge here is to extract the network nodes contributing the most variance to the network dynamics, because these nodes will be the most visible in experimental data. Mathematically speaking, we wish to identify a linear vector space spanned by n vectors ψk, where n is the dimension and typically smaller than the total dimension of the network (in the present network the total dimension is 38). These vectors span the directions of a subspace, in which the network is most sensitive to perturbations and noise. Equivalently, these vectors can be considered to be network patterns or network modes of operation. In this subspace most of the variance of the network dynamics is contained and define the dynamic repertoire of the sorts of the behaviors the network is capable to perform following a perturbation. In other words, the activity of the ith network node u(i,t) can be written as , where t is the time and ξk(t) is the time dependent coefficient capturing the dynamics of the kth network pattern ψk. The contribution of the ith network node is given by ψk(i). To identify and quantify the contributions of the subspace, we perform the following procedure (see Methods for details): When the network dynamics relaxes into its equilibrium state, we perform a small parameter change towards the unstable region. A typical time series plot is shown in Figure S1. As a consequence of this minimal parameter change, the previously least stable network modes cross the critical boundary first, become unstable and grow with the fastest growth rate. The mathematical basis thereof is the center manifold theorem [29]. As a consequence, only the unstable network modes are present during the transition. Of course, after the transition the nonlinearities and all the network modes become relevant for the network dynamics. During the transition, though, we use a sliding temporal window analysis and perform a Principal Component Analysis (PCA) to identify the dominant network modes (see Figure 4). We find that only two network modes ψk contribute to the transient dynamics.

Bottom Line: Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network.The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging.The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.

View Article: PubMed Central - PubMed

Affiliation: Theoretical Neuroscience Group, Institut des Sciences du Mouvement, Marseille, France. Anandamohan.GHOSH@univmed.fr

ABSTRACT
Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.

Show MeSH
Related in: MedlinePlus