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Noise-induced precursors of state transitions in the stochastic Wilson-cowan model.

Negahbani E, Steyn-Ross DA, Steyn-Ross ML, Wilson MT, Sleigh JW - J Math Neurosci (2015)

Bottom Line: In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex.We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue.This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

View Article: PubMed Central - PubMed

Affiliation: School of Engineering, The University of Waikato, Hamilton, 3200 New Zealand.

ABSTRACT
The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

No MeSH data available.


Related in: MedlinePlus

Approach to state transition in 1-D Wilson–Cowan cortex. The cortex is placed in subthreshold mode I, close to one of four bifurcation types, then driven toward instability in two steps (II, III) using one of two control parameters or a combination of both (red arrows). The resulting dispersion curves predict the spatial or temporal frequency of upcoming instabilities, determined by value of  at the peak of α-curve (blue) and the  value (green) at the  axis, respectively
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Fig4: Approach to state transition in 1-D Wilson–Cowan cortex. The cortex is placed in subthreshold mode I, close to one of four bifurcation types, then driven toward instability in two steps (II, III) using one of two control parameters or a combination of both (red arrows). The resulting dispersion curves predict the spatial or temporal frequency of upcoming instabilities, determined by value of at the peak of α-curve (blue) and the value (green) at the axis, respectively

Mentions: The results of theoretical and numerical examination of the stochastic 1-D Wilson–Cowan model prior to onset of its four bifurcation types are presented in this section. We sample the fluctuation characteristics of the model at three distinct steady-state coordinates, labeled I, II, III in Figs. 4–6, representing a closer and closer approach to instability threshold. Fig. 4


Noise-induced precursors of state transitions in the stochastic Wilson-cowan model.

Negahbani E, Steyn-Ross DA, Steyn-Ross ML, Wilson MT, Sleigh JW - J Math Neurosci (2015)

Approach to state transition in 1-D Wilson–Cowan cortex. The cortex is placed in subthreshold mode I, close to one of four bifurcation types, then driven toward instability in two steps (II, III) using one of two control parameters or a combination of both (red arrows). The resulting dispersion curves predict the spatial or temporal frequency of upcoming instabilities, determined by value of  at the peak of α-curve (blue) and the  value (green) at the  axis, respectively
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4388113&req=5

Fig4: Approach to state transition in 1-D Wilson–Cowan cortex. The cortex is placed in subthreshold mode I, close to one of four bifurcation types, then driven toward instability in two steps (II, III) using one of two control parameters or a combination of both (red arrows). The resulting dispersion curves predict the spatial or temporal frequency of upcoming instabilities, determined by value of at the peak of α-curve (blue) and the value (green) at the axis, respectively
Mentions: The results of theoretical and numerical examination of the stochastic 1-D Wilson–Cowan model prior to onset of its four bifurcation types are presented in this section. We sample the fluctuation characteristics of the model at three distinct steady-state coordinates, labeled I, II, III in Figs. 4–6, representing a closer and closer approach to instability threshold. Fig. 4

Bottom Line: In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex.We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue.This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

View Article: PubMed Central - PubMed

Affiliation: School of Engineering, The University of Waikato, Hamilton, 3200 New Zealand.

ABSTRACT
The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum of excitatory and inhibitory cortical neural aggregates, using a pair of coupled integro-differential equations. Here we use bifurcation theory and small-noise linear stochastics to study the range of a phase transitions-sudden qualitative changes in the state of a dynamical system emerging from a bifurcation-accessible to the Wilson-Cowan network. Specifically, we examine saddle-node, Hopf, Turing, and Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, and analyze the resulting subthreshold fluctuations using an Ornstein-Uhlenbeck linearization. This analysis predicts divergent changes in correlation and spectral characteristics of neural activity during close approach to bifurcation from below. We validate these theoretical predictions using numerical simulations. The results demonstrate the role of noise in the emergence of critically slowed precursors in both space and time, and suggest that these early-warning signals are a universal feature of a neural system close to bifurcation. In particular, these precursor signals are likely to have neurobiological significance as early warnings of impending state change in the cortex. We support this claim with an analysis of the in vitro local field potentials recorded from slices of mouse-brain tissue. We show that in the period leading up to emergence of spontaneous seizure-like events, the mouse field potentials show a characteristic spectral focusing toward lower frequencies concomitant with a growth in fluctuation variance, consistent with critical slowing near a bifurcation point. This observation of biological criticality has clear implications regarding the feasibility of seizure prediction.

No MeSH data available.


Related in: MedlinePlus