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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

In vitro evidence of critical slowing near onset of a phase transition. (a) Local field potential recordings showing three spontaneous seizure-like events (SLEs) in a slice of mouse-brain tissue. (b) Spectrograms show characteristic “down-chirp” (drift to lower frequencies) in spectral activity as SLE onset is approached (white arrows). Note that the frequency scale increases vertically downwards. (c) The quiescent interval between consecutive events is sampled for 1 s at three representative times (labeled I, II, III) for variance analysis. Bars show the variance distribution across 40 inter-SLE periods. Note the pronounced growth in variance as the moment of seizure onset is approached
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Fig9: In vitro evidence of critical slowing near onset of a phase transition. (a) Local field potential recordings showing three spontaneous seizure-like events (SLEs) in a slice of mouse-brain tissue. (b) Spectrograms show characteristic “down-chirp” (drift to lower frequencies) in spectral activity as SLE onset is approached (white arrows). Note that the frequency scale increases vertically downwards. (c) The quiescent interval between consecutive events is sampled for 1 s at three representative times (labeled I, II, III) for variance analysis. Bars show the variance distribution across 40 inter-SLE periods. Note the pronounced growth in variance as the moment of seizure onset is approached

Mentions: Figure 9(a) shows three consecutive SLEs that are well separated in time: each avalanche lasts ∼20 s, with about 60 s of electrical quiescence between events. Close examination of each quiescent interval reveals a subtle growth in background activity that commences about 30 s prior to avalanche, and that this activity has spectral energy that initially extends to ∼20 Hz, but drops to lower frequencies as onset approaches, forming a characteristic “down-chirp” in the spectrogram of Fig. 9(b). The 1-s fluctuation variances at three representative times (labeled I, II, III in panel (a)) show pronounced growth in background activity as the transition point is approached. Fig. 9


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)

In vitro evidence of critical slowing near onset of a phase transition. (a) Local field potential recordings showing three spontaneous seizure-like events (SLEs) in a slice of mouse-brain tissue. (b) Spectrograms show characteristic “down-chirp” (drift to lower frequencies) in spectral activity as SLE onset is approached (white arrows). Note that the frequency scale increases vertically downwards. (c) The quiescent interval between consecutive events is sampled for 1 s at three representative times (labeled I, II, III) for variance analysis. Bars show the variance distribution across 40 inter-SLE periods. Note the pronounced growth in variance as the moment of seizure onset is approached
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Fig9: In vitro evidence of critical slowing near onset of a phase transition. (a) Local field potential recordings showing three spontaneous seizure-like events (SLEs) in a slice of mouse-brain tissue. (b) Spectrograms show characteristic “down-chirp” (drift to lower frequencies) in spectral activity as SLE onset is approached (white arrows). Note that the frequency scale increases vertically downwards. (c) The quiescent interval between consecutive events is sampled for 1 s at three representative times (labeled I, II, III) for variance analysis. Bars show the variance distribution across 40 inter-SLE periods. Note the pronounced growth in variance as the moment of seizure onset is approached
Mentions: Figure 9(a) shows three consecutive SLEs that are well separated in time: each avalanche lasts ∼20 s, with about 60 s of electrical quiescence between events. Close examination of each quiescent interval reveals a subtle growth in background activity that commences about 30 s prior to avalanche, and that this activity has spectral energy that initially extends to ∼20 Hz, but drops to lower frequencies as onset approaches, forming a characteristic “down-chirp” in the spectrogram of Fig. 9(b). The 1-s fluctuation variances at three representative times (labeled I, II, III in panel (a)) show pronounced growth in background activity as the transition point is approached. Fig. 9

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