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Dynamics on networks: the role of local dynamics and global networks on the emergence of hypersynchronous neural activity.

Schmidt H, Petkov G, Richardson MP, Terry JR - PLoS Comput. Biol. (2014)

Bottom Line: Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3-6 Hz) and low-alpha (6-9 Hz) bands.We further identify left frontal regions as a potential driver of seizure activity within these networks.Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.

View Article: PubMed Central - PubMed

Affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.

ABSTRACT
Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of computational modeling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit, which in the field of complexity sciences is known as dynamics on networks. In this study we describe the development and application of this framework using modular networks of Kuramoto oscillators. We use this framework to understand functional networks inferred from resting state EEG recordings of a cohort of 35 adults with heterogeneous idiopathic generalized epilepsies and 40 healthy adult controls. Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3-6 Hz) and low-alpha (6-9 Hz) bands. We further identify left frontal regions as a potential driver of seizure activity within these networks. We also explore the ability of our method to identify individuals with epilepsy, observing up to 80% predictive power through use of receiver operating characteristic analysis. Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.

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The order parameter on a cycle.A: Illustration of cycles with increasing number of nodes. B: A plot of analytical and numerical results of the order parameter on a cycle of  nodes. The numerical example is obtained for  oscillators per node.
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pcbi-1003947-g006: The order parameter on a cycle.A: Illustration of cycles with increasing number of nodes. B: A plot of analytical and numerical results of the order parameter on a cycle of nodes. The numerical example is obtained for oscillators per node.

Mentions: Strongly connected components are subsets of directed graphs in which there is a path from each node to every other node. Thus, each node in a strongly connected component has an in-degree greater than zero (i.e. it receives input from at least one other node), which is a critical property for enabling network-driven synchrony to emerge. Here, we focus on the example of a strongly connected component as a simple cycle (illustrated in Figure 6), with connectivity matrix having elements and , with all other elements zero. Once more, the intrinsic couplings are chosen arbitrarily with the only restriction of . Using the linearization approach, we thus obtain(22)As for the simple two node system, if all intrinsic couplings are equal (), then the value of the critical coupling is the difference between and . Likewise, if all intrinsic connections are identical, and all connections forming the cycle are equal to one, is simply defined by (21). Further, if any of the connections are removed and the cycle is broken, a zero is introduced into the denominator and becomes infinite, making network-driven synchrony impossible. In real-world networks, a strongly connected component may be formed of more than one cycle, meaning it may be necessary to remove more than one connection to destroy it.


Dynamics on networks: the role of local dynamics and global networks on the emergence of hypersynchronous neural activity.

Schmidt H, Petkov G, Richardson MP, Terry JR - PLoS Comput. Biol. (2014)

The order parameter on a cycle.A: Illustration of cycles with increasing number of nodes. B: A plot of analytical and numerical results of the order parameter on a cycle of  nodes. The numerical example is obtained for  oscillators per node.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230731&req=5

pcbi-1003947-g006: The order parameter on a cycle.A: Illustration of cycles with increasing number of nodes. B: A plot of analytical and numerical results of the order parameter on a cycle of nodes. The numerical example is obtained for oscillators per node.
Mentions: Strongly connected components are subsets of directed graphs in which there is a path from each node to every other node. Thus, each node in a strongly connected component has an in-degree greater than zero (i.e. it receives input from at least one other node), which is a critical property for enabling network-driven synchrony to emerge. Here, we focus on the example of a strongly connected component as a simple cycle (illustrated in Figure 6), with connectivity matrix having elements and , with all other elements zero. Once more, the intrinsic couplings are chosen arbitrarily with the only restriction of . Using the linearization approach, we thus obtain(22)As for the simple two node system, if all intrinsic couplings are equal (), then the value of the critical coupling is the difference between and . Likewise, if all intrinsic connections are identical, and all connections forming the cycle are equal to one, is simply defined by (21). Further, if any of the connections are removed and the cycle is broken, a zero is introduced into the denominator and becomes infinite, making network-driven synchrony impossible. In real-world networks, a strongly connected component may be formed of more than one cycle, meaning it may be necessary to remove more than one connection to destroy it.

Bottom Line: Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3-6 Hz) and low-alpha (6-9 Hz) bands.We further identify left frontal regions as a potential driver of seizure activity within these networks.Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.

View Article: PubMed Central - PubMed

Affiliation: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom.

ABSTRACT
Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of computational modeling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit, which in the field of complexity sciences is known as dynamics on networks. In this study we describe the development and application of this framework using modular networks of Kuramoto oscillators. We use this framework to understand functional networks inferred from resting state EEG recordings of a cohort of 35 adults with heterogeneous idiopathic generalized epilepsies and 40 healthy adult controls. Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3-6 Hz) and low-alpha (6-9 Hz) bands. We further identify left frontal regions as a potential driver of seizure activity within these networks. We also explore the ability of our method to identify individuals with epilepsy, observing up to 80% predictive power through use of receiver operating characteristic analysis. Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.

Show MeSH
Related in: MedlinePlus