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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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Model behavior on a two-node network.A: The order parameter  for unidirectional and bidirectional coupling between two nodes plotted against the global coupling parameter , accompanied by numerical results. The slow increase of the numerical result of  with  for unidirectional coupling is due to the finite size of the system with  ocillators. B: The evolution of the signal  of each node with random initial conditions and .
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pcbi-1003947-g005: Model behavior on a two-node network.A: The order parameter for unidirectional and bidirectional coupling between two nodes plotted against the global coupling parameter , accompanied by numerical results. The slow increase of the numerical result of with for unidirectional coupling is due to the finite size of the system with ocillators. B: The evolution of the signal of each node with random initial conditions and .

Mentions: To better understand these different conditions for emergent synchronization, we focus initially on motifs with a small number of nodes. First, we consider the case of two nodes that are either unidirectionally or bidirectionally coupled. In graph-theoretical terms, two bi-directionally coupled nodes are the simplest example of a feedback-loop or cycle, which, in turn, is the simplest form of a strongly connected component. A strongly connected component is a network configuration such that each node can be reached from all other nodes by following directed connections. Hence, a strongly connected component must contain at least one cycle. Conversely, two nodes that are uni-directionally coupled represent the simplest form of a network with a hierarchical flow, such that each node can be assigned its own level of hierarchy. First, we consider two coupled nodes in the most general scenario, where the connectivity matrix has entries and . Then from (17) we obtain the following expression for the critical value of the global coupling parameter , above which both nodes become phase-locked and their order parameters increase:(20)Again, is the critical value of for the onset of synchrony within an individual node. is only real-valued for , verifying that neither node is synchronized in isolation (a prerequisite for network-driven synchronization). In this scenario the value of depends on the distance of the intrinsic coupling parameters from . If both nodes are identical with , and we obtain the simple expression(21)U ni-directional coupling (i.e. either or ) means (20) is undefined, making network-driven synchrony impossible. In this scenario, only node-driven synchrony can arise as a consequence of their intrinsic coupling exceeding the critical value . A comparison of both cases is shown in Figure 5, accompanied by numerical results for oscillators, which leads to an increasing divergence between analytical and numerical results for the uni-directional case with increasing global coupling.


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)

Model behavior on a two-node network.A: The order parameter  for unidirectional and bidirectional coupling between two nodes plotted against the global coupling parameter , accompanied by numerical results. The slow increase of the numerical result of  with  for unidirectional coupling is due to the finite size of the system with  ocillators. B: The evolution of the signal  of each node with random initial conditions and .
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003947-g005: Model behavior on a two-node network.A: The order parameter for unidirectional and bidirectional coupling between two nodes plotted against the global coupling parameter , accompanied by numerical results. The slow increase of the numerical result of with for unidirectional coupling is due to the finite size of the system with ocillators. B: The evolution of the signal of each node with random initial conditions and .
Mentions: To better understand these different conditions for emergent synchronization, we focus initially on motifs with a small number of nodes. First, we consider the case of two nodes that are either unidirectionally or bidirectionally coupled. In graph-theoretical terms, two bi-directionally coupled nodes are the simplest example of a feedback-loop or cycle, which, in turn, is the simplest form of a strongly connected component. A strongly connected component is a network configuration such that each node can be reached from all other nodes by following directed connections. Hence, a strongly connected component must contain at least one cycle. Conversely, two nodes that are uni-directionally coupled represent the simplest form of a network with a hierarchical flow, such that each node can be assigned its own level of hierarchy. First, we consider two coupled nodes in the most general scenario, where the connectivity matrix has entries and . Then from (17) we obtain the following expression for the critical value of the global coupling parameter , above which both nodes become phase-locked and their order parameters increase:(20)Again, is the critical value of for the onset of synchrony within an individual node. is only real-valued for , verifying that neither node is synchronized in isolation (a prerequisite for network-driven synchronization). In this scenario the value of depends on the distance of the intrinsic coupling parameters from . If both nodes are identical with , and we obtain the simple expression(21)U ni-directional coupling (i.e. either or ) means (20) is undefined, making network-driven synchrony impossible. In this scenario, only node-driven synchrony can arise as a consequence of their intrinsic coupling exceeding the critical value . A comparison of both cases is shown in Figure 5, accompanied by numerical results for oscillators, which leads to an increasing divergence between analytical and numerical results for the uni-directional case with increasing global coupling.

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