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Kuramoto model simulation of neural hubs and dynamic synchrony in the human cerebral connectome.

Schmidt R, LaFleur KJ, de Reus MA, van den Berg LH, van den Heuvel MP - BMC Neurosci (2015)

Bottom Line: Furthermore, suppressing structural connectivity among hub nodes resulted in an elevated modular state (p < 4.1 × l0(-3), 0.015 < λ < 0.04), indicating that hub-to-hub connections are critical in intermodular synchronization.Finally, perturbing the oscillatory behavior of hub nodes prevented functional modules from synchronizing, implying that synchronization of functional modules is dependent on the hub nodes' behavior.Our results converge on anatomical hubs having a leading role in intermodular synchronization and integration in the human brain.

View Article: PubMed Central - PubMed

Affiliation: Department of Neurology, Brain Center Rudolf Magnus, University Medical Center Utrecht, Heidelberglaan 100, PO Box 85500, 3508 GA, Utrecht, Netherlands. r.schmidt@umcutrecht.nl.

ABSTRACT

Background: The topological structure of the wiring of the mammalian brain cortex plays an important role in shaping the functional dynamics of large-scale neural activity. Due to their central embedding in the network, high degree hub regions and their connections (often referred to as the 'rich club') have been hypothesized to facilitate intermodular neural communication and global integration of information by means of synchronization. Here, we examined the theoretical role of anatomical hubs and their wiring in brain dynamics. The Kuramoto model was used to simulate interaction of cortical brain areas by means of coupled phase oscillators-with anatomical connections between regions derived from diffusion weighted imaging and module assignment of brain regions based on empirically determined resting-state data.

Results: Our findings show that synchrony among hub nodes was higher than any module's intramodular synchrony (p < 10(-4), for cortical coupling strengths, λ, in the range 0.02 < λ < 0.05), suggesting that hub nodes lead the functional modules in the process of synchronization. Furthermore, suppressing structural connectivity among hub nodes resulted in an elevated modular state (p < 4.1 × l0(-3), 0.015 < λ < 0.04), indicating that hub-to-hub connections are critical in intermodular synchronization. Finally, perturbing the oscillatory behavior of hub nodes prevented functional modules from synchronizing, implying that synchronization of functional modules is dependent on the hub nodes' behavior.

Conclusion: Our results converge on anatomical hubs having a leading role in intermodular synchronization and integration in the human brain.

No MeSH data available.


Modular frequency tracking during perturbation. When the internal frequencies of a particular module were perturbed, the evolution of the frequencies towards whole brain synchrony was tracked for each module. Panela shows the case in which the hub nodes had their internal frequencies altered, and the rest of the modules were unable synchronize until the hub nodes’ frequency came down to the range of frequencies of the functional modules. Panelb shows the case in which a random set of nodes equal in number to the rich club has been perturbed. Here, synchronization occurred faster than when the hub nodes were perturbed, and the functional modules were able to synchronize before the random nodes join at a whole brain shared frequency. Panelc shows the case in which the largest functional module (Default Mode) was altered. Note that, in this case too, the rest of the modules are able to synchronize before the Default Mode module joins. The insets in each graph focus on the cortical coupling factors just before the perturbed set of nodes became synchronized with the unperturbed functional modules. From these insets, it is clear that perturbing the hub nodes causes less synchrony among the non-perturbed functional modules
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Fig5: Modular frequency tracking during perturbation. When the internal frequencies of a particular module were perturbed, the evolution of the frequencies towards whole brain synchrony was tracked for each module. Panela shows the case in which the hub nodes had their internal frequencies altered, and the rest of the modules were unable synchronize until the hub nodes’ frequency came down to the range of frequencies of the functional modules. Panelb shows the case in which a random set of nodes equal in number to the rich club has been perturbed. Here, synchronization occurred faster than when the hub nodes were perturbed, and the functional modules were able to synchronize before the random nodes join at a whole brain shared frequency. Panelc shows the case in which the largest functional module (Default Mode) was altered. Note that, in this case too, the rest of the modules are able to synchronize before the Default Mode module joins. The insets in each graph focus on the cortical coupling factors just before the perturbed set of nodes became synchronized with the unperturbed functional modules. From these insets, it is clear that perturbing the hub nodes causes less synchrony among the non-perturbed functional modules

Mentions: Apart from manipulating connectivity through edges as presented in the previous analysis, synchronization dynamics in the Kuramoto model can also be perturbed by offsetting the initial internal frequencies of a set of nodes. As lower levels of synchronization are a trivial consequence of these frequency perturbations, we tracked nodal frequencies along the path towards global synchrony to examine how different sets of nodes affected the synchronization of the entire system. Figure 5a shows that with the frequency of the hub nodes perturbed, the functional modules remained out of synchrony with respect to each other until the hub nodes stabilized at a frequency near the whole brain frequency corresponding to global synchrony. In contrast, in all other simulations where a different set of nodes was perturbed, the frequencies of the unperturbed modules converged to a common global frequency, reflecting global synchronization, even though the perturbed set of nodes were still operating at a markedly higher frequency. For example, when a random set of nodes (equal in number to the hub nodes) had their internal frequencies perturbed, the remaining unperturbed portion of the system was found to synchronize without the perturbed set of nodes (Fig. 5b). Similarly, perturbing the nodes of any of the 11 functional modules did not keep the other modules from synchronizing among one another (see Fig. 5c for an example in which the Default Mode Network module was perturbed). Nearly identical findings for the remaining 10 functional modules are provided in Additional file 6: Figure S6.Fig. 5


Kuramoto model simulation of neural hubs and dynamic synchrony in the human cerebral connectome.

Schmidt R, LaFleur KJ, de Reus MA, van den Berg LH, van den Heuvel MP - BMC Neurosci (2015)

Modular frequency tracking during perturbation. When the internal frequencies of a particular module were perturbed, the evolution of the frequencies towards whole brain synchrony was tracked for each module. Panela shows the case in which the hub nodes had their internal frequencies altered, and the rest of the modules were unable synchronize until the hub nodes’ frequency came down to the range of frequencies of the functional modules. Panelb shows the case in which a random set of nodes equal in number to the rich club has been perturbed. Here, synchronization occurred faster than when the hub nodes were perturbed, and the functional modules were able to synchronize before the random nodes join at a whole brain shared frequency. Panelc shows the case in which the largest functional module (Default Mode) was altered. Note that, in this case too, the rest of the modules are able to synchronize before the Default Mode module joins. The insets in each graph focus on the cortical coupling factors just before the perturbed set of nodes became synchronized with the unperturbed functional modules. From these insets, it is clear that perturbing the hub nodes causes less synchrony among the non-perturbed functional modules
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4556019&req=5

Fig5: Modular frequency tracking during perturbation. When the internal frequencies of a particular module were perturbed, the evolution of the frequencies towards whole brain synchrony was tracked for each module. Panela shows the case in which the hub nodes had their internal frequencies altered, and the rest of the modules were unable synchronize until the hub nodes’ frequency came down to the range of frequencies of the functional modules. Panelb shows the case in which a random set of nodes equal in number to the rich club has been perturbed. Here, synchronization occurred faster than when the hub nodes were perturbed, and the functional modules were able to synchronize before the random nodes join at a whole brain shared frequency. Panelc shows the case in which the largest functional module (Default Mode) was altered. Note that, in this case too, the rest of the modules are able to synchronize before the Default Mode module joins. The insets in each graph focus on the cortical coupling factors just before the perturbed set of nodes became synchronized with the unperturbed functional modules. From these insets, it is clear that perturbing the hub nodes causes less synchrony among the non-perturbed functional modules
Mentions: Apart from manipulating connectivity through edges as presented in the previous analysis, synchronization dynamics in the Kuramoto model can also be perturbed by offsetting the initial internal frequencies of a set of nodes. As lower levels of synchronization are a trivial consequence of these frequency perturbations, we tracked nodal frequencies along the path towards global synchrony to examine how different sets of nodes affected the synchronization of the entire system. Figure 5a shows that with the frequency of the hub nodes perturbed, the functional modules remained out of synchrony with respect to each other until the hub nodes stabilized at a frequency near the whole brain frequency corresponding to global synchrony. In contrast, in all other simulations where a different set of nodes was perturbed, the frequencies of the unperturbed modules converged to a common global frequency, reflecting global synchronization, even though the perturbed set of nodes were still operating at a markedly higher frequency. For example, when a random set of nodes (equal in number to the hub nodes) had their internal frequencies perturbed, the remaining unperturbed portion of the system was found to synchronize without the perturbed set of nodes (Fig. 5b). Similarly, perturbing the nodes of any of the 11 functional modules did not keep the other modules from synchronizing among one another (see Fig. 5c for an example in which the Default Mode Network module was perturbed). Nearly identical findings for the remaining 10 functional modules are provided in Additional file 6: Figure S6.Fig. 5

Bottom Line: Furthermore, suppressing structural connectivity among hub nodes resulted in an elevated modular state (p < 4.1 × l0(-3), 0.015 < λ < 0.04), indicating that hub-to-hub connections are critical in intermodular synchronization.Finally, perturbing the oscillatory behavior of hub nodes prevented functional modules from synchronizing, implying that synchronization of functional modules is dependent on the hub nodes' behavior.Our results converge on anatomical hubs having a leading role in intermodular synchronization and integration in the human brain.

View Article: PubMed Central - PubMed

Affiliation: Department of Neurology, Brain Center Rudolf Magnus, University Medical Center Utrecht, Heidelberglaan 100, PO Box 85500, 3508 GA, Utrecht, Netherlands. r.schmidt@umcutrecht.nl.

ABSTRACT

Background: The topological structure of the wiring of the mammalian brain cortex plays an important role in shaping the functional dynamics of large-scale neural activity. Due to their central embedding in the network, high degree hub regions and their connections (often referred to as the 'rich club') have been hypothesized to facilitate intermodular neural communication and global integration of information by means of synchronization. Here, we examined the theoretical role of anatomical hubs and their wiring in brain dynamics. The Kuramoto model was used to simulate interaction of cortical brain areas by means of coupled phase oscillators-with anatomical connections between regions derived from diffusion weighted imaging and module assignment of brain regions based on empirically determined resting-state data.

Results: Our findings show that synchrony among hub nodes was higher than any module's intramodular synchrony (p < 10(-4), for cortical coupling strengths, λ, in the range 0.02 < λ < 0.05), suggesting that hub nodes lead the functional modules in the process of synchronization. Furthermore, suppressing structural connectivity among hub nodes resulted in an elevated modular state (p < 4.1 × l0(-3), 0.015 < λ < 0.04), indicating that hub-to-hub connections are critical in intermodular synchronization. Finally, perturbing the oscillatory behavior of hub nodes prevented functional modules from synchronizing, implying that synchronization of functional modules is dependent on the hub nodes' behavior.

Conclusion: Our results converge on anatomical hubs having a leading role in intermodular synchronization and integration in the human brain.

No MeSH data available.