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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

Growth of zero-lag temporal autocorrelation and slowing of decay-rate prior to phase transition. Biexponential expressions of the form  were fitted to the decay envelopes of the temporal autocorrelations of Fig. 6. Top panels display predicted and measured normalized variance  of the fitted curve; bottom panels are the  slow exponential decay-rates (in (ms)−1)
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Fig7: Growth of zero-lag temporal autocorrelation and slowing of decay-rate prior to phase transition. Biexponential expressions of the form were fitted to the decay envelopes of the temporal autocorrelations of Fig. 6. Top panels display predicted and measured normalized variance of the fitted curve; bottom panels are the slow exponential decay-rates (in (ms)−1)

Mentions: To quantify the growth in correlation times, we fitted biexponential expressions to the envelope of temporal autocorrelation functions of Fig. 6,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ c_{1} \exp(-m_{1} \tau) + c_{2} \exp(-m_{2} \tau), \quad \text{with } m_{1} > m_{2} > 0, $$\end{document}c1exp(−m1τ)+c2exp(−m2τ),with m1>m2>0, representing the sum of fast () and slow () exponential decays. The sum estimates the fluctuation variance (zero-lag autocorrelation), and gives the slow decay-rate (inverse correlation time). Plotted in the top and bottom panels of Fig. 7, respectively, these graphs show the expected indicators of critical slowing: growth of fluctuation variance and duration as bifurcation is approached. Fig. 7


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)

Growth of zero-lag temporal autocorrelation and slowing of decay-rate prior to phase transition. Biexponential expressions of the form  were fitted to the decay envelopes of the temporal autocorrelations of Fig. 6. Top panels display predicted and measured normalized variance  of the fitted curve; bottom panels are the  slow exponential decay-rates (in (ms)−1)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Fig7: Growth of zero-lag temporal autocorrelation and slowing of decay-rate prior to phase transition. Biexponential expressions of the form were fitted to the decay envelopes of the temporal autocorrelations of Fig. 6. Top panels display predicted and measured normalized variance of the fitted curve; bottom panels are the slow exponential decay-rates (in (ms)−1)
Mentions: To quantify the growth in correlation times, we fitted biexponential expressions to the envelope of temporal autocorrelation functions of Fig. 6,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ c_{1} \exp(-m_{1} \tau) + c_{2} \exp(-m_{2} \tau), \quad \text{with } m_{1} > m_{2} > 0, $$\end{document}c1exp(−m1τ)+c2exp(−m2τ),with m1>m2>0, representing the sum of fast () and slow () exponential decays. The sum estimates the fluctuation variance (zero-lag autocorrelation), and gives the slow decay-rate (inverse correlation time). Plotted in the top and bottom panels of Fig. 7, respectively, these graphs show the expected indicators of critical slowing: growth of fluctuation variance and duration as bifurcation is approached. Fig. 7

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