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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 Kuramoto model with varying coupling strength to demonstrate the ictal (synchronized) and interictal (unsynchronized) behavior of the model.A: For  below a critical value  (red, dotted line) the signal  is irregular and the order parameter representing the degree of synchronicity is low. If  is above the critical value,  is sinusoidal with large amplitude, and the order parameter is large. B: At the onset of synchronization, the oscillators start forming a cluster resulting in an increase of the order parameter. Bars around the circles indicate the phase density of oscillators. The internal frequencies  are drawn from a normal distribution with mean  and standard deviation . Here we use  oscillators.
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pcbi-1003947-g003: The Kuramoto model with varying coupling strength to demonstrate the ictal (synchronized) and interictal (unsynchronized) behavior of the model.A: For below a critical value (red, dotted line) the signal is irregular and the order parameter representing the degree of synchronicity is low. If is above the critical value, is sinusoidal with large amplitude, and the order parameter is large. B: At the onset of synchronization, the oscillators start forming a cluster resulting in an increase of the order parameter. Bars around the circles indicate the phase density of oscillators. The internal frequencies are drawn from a normal distribution with mean and standard deviation . Here we use oscillators.

Mentions: The degree of synchrony between oscillators within a single node and across the global network is controlled by the coupling parameters and . Focussing first on an individual node, Figure 3 demonstrates how the dynamic behavior of the Kuramoto model depends on the coupling constant . When this coupling constant is below a critical value, each oscillator behaves incoherently (i.e. they are uniformly spread around the unit circle) and the emergent signal is apparently stochastic and of low amplitude. However, when the coupling reaches a critical value, a phase transition occurs and oscillators become phase-locked (which in this context is synonymous to synchronized), resulting in emergent large amplitude oscillations; analogous to the transition between background and spike-wave activity seen in the onset of seizures.


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 Kuramoto model with varying coupling strength to demonstrate the ictal (synchronized) and interictal (unsynchronized) behavior of the model.A: For  below a critical value  (red, dotted line) the signal  is irregular and the order parameter representing the degree of synchronicity is low. If  is above the critical value,  is sinusoidal with large amplitude, and the order parameter is large. B: At the onset of synchronization, the oscillators start forming a cluster resulting in an increase of the order parameter. Bars around the circles indicate the phase density of oscillators. The internal frequencies  are drawn from a normal distribution with mean  and standard deviation . Here we use  oscillators.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003947-g003: The Kuramoto model with varying coupling strength to demonstrate the ictal (synchronized) and interictal (unsynchronized) behavior of the model.A: For below a critical value (red, dotted line) the signal is irregular and the order parameter representing the degree of synchronicity is low. If is above the critical value, is sinusoidal with large amplitude, and the order parameter is large. B: At the onset of synchronization, the oscillators start forming a cluster resulting in an increase of the order parameter. Bars around the circles indicate the phase density of oscillators. The internal frequencies are drawn from a normal distribution with mean and standard deviation . Here we use oscillators.
Mentions: The degree of synchrony between oscillators within a single node and across the global network is controlled by the coupling parameters and . Focussing first on an individual node, Figure 3 demonstrates how the dynamic behavior of the Kuramoto model depends on the coupling constant . When this coupling constant is below a critical value, each oscillator behaves incoherently (i.e. they are uniformly spread around the unit circle) and the emergent signal is apparently stochastic and of low amplitude. However, when the coupling reaches a critical value, a phase transition occurs and oscillators become phase-locked (which in this context is synonymous to synchronized), resulting in emergent large amplitude oscillations; analogous to the transition between background and spike-wave activity seen in the onset of seizures.

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