Limits...
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.


Related in: MedlinePlus

Global synchrony progression. The order parameters, r, reflecting global phase synchronization, and rlink, reflecting the synchronized node fraction, increase with the coupling factor, λ (a). The critical regime, highlighted in blue, is the domain during which the system quickly transitions from the modular state to whole brain synchrony. Panelb shows the simulated functional synchrony output of the model at several different cortical coupling factors. A notable change from synchrony within the modules (along the diagonal) to whole brain synchrony occurs as the coupling factor is increased. Note that for illustrative purposes color scales vary among the three realizations of simulated functional synchrony
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig2: Global synchrony progression. The order parameters, r, reflecting global phase synchronization, and rlink, reflecting the synchronized node fraction, increase with the coupling factor, λ (a). The critical regime, highlighted in blue, is the domain during which the system quickly transitions from the modular state to whole brain synchrony. Panelb shows the simulated functional synchrony output of the model at several different cortical coupling factors. A notable change from synchrony within the modules (along the diagonal) to whole brain synchrony occurs as the coupling factor is increased. Note that for illustrative purposes color scales vary among the three realizations of simulated functional synchrony

Mentions: Figure 2a shows how levels of global synchronization progress with respect to cortical coupling strength. The order parameter r has been shown to follow a square-root function of the coupling strength λ [21], therefore the shape of the curve results from a square-root curve smoothed out by the heterogeneity in the intrinsic frequencies and by the network topology of the oscillators. A critical regime was observed between λ = 0.02 and λ = 0.04, indicated in blue in Fig. 2a, during which the network abruptly switches from brain regions being synchronized locally to a state of global synchrony, consistent with previous work on the cat cerebral cortex [3]. Figure 2b shows three panels of synchronization levels, or simulated functional connectivity, illustrating the modular state (small clusters of synchronized nodes), transition state (widespread synchrony arising) and global synchrony state (nearly all nodes in synchrony), evaluated by the Kuramoto model at cortical coupling factors λ = 0.02, λ = 0.03 and λ = 0.04, respectively.Fig. 2


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)

Global synchrony progression. The order parameters, r, reflecting global phase synchronization, and rlink, reflecting the synchronized node fraction, increase with the coupling factor, λ (a). The critical regime, highlighted in blue, is the domain during which the system quickly transitions from the modular state to whole brain synchrony. Panelb shows the simulated functional synchrony output of the model at several different cortical coupling factors. A notable change from synchrony within the modules (along the diagonal) to whole brain synchrony occurs as the coupling factor is increased. Note that for illustrative purposes color scales vary among the three realizations of simulated functional synchrony
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig2: Global synchrony progression. The order parameters, r, reflecting global phase synchronization, and rlink, reflecting the synchronized node fraction, increase with the coupling factor, λ (a). The critical regime, highlighted in blue, is the domain during which the system quickly transitions from the modular state to whole brain synchrony. Panelb shows the simulated functional synchrony output of the model at several different cortical coupling factors. A notable change from synchrony within the modules (along the diagonal) to whole brain synchrony occurs as the coupling factor is increased. Note that for illustrative purposes color scales vary among the three realizations of simulated functional synchrony
Mentions: Figure 2a shows how levels of global synchronization progress with respect to cortical coupling strength. The order parameter r has been shown to follow a square-root function of the coupling strength λ [21], therefore the shape of the curve results from a square-root curve smoothed out by the heterogeneity in the intrinsic frequencies and by the network topology of the oscillators. A critical regime was observed between λ = 0.02 and λ = 0.04, indicated in blue in Fig. 2a, during which the network abruptly switches from brain regions being synchronized locally to a state of global synchrony, consistent with previous work on the cat cerebral cortex [3]. Figure 2b shows three panels of synchronization levels, or simulated functional connectivity, illustrating the modular state (small clusters of synchronized nodes), transition state (widespread synchrony arising) and global synchrony state (nearly all nodes in synchrony), evaluated by the Kuramoto model at cortical coupling factors λ = 0.02, λ = 0.03 and λ = 0.04, respectively.Fig. 2

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.


Related in: MedlinePlus