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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

Emergence of Turing–Hopf mixed-mode oscillations in 1-D Wilson–Cowan cortex. (a) Steady state distribution with a selected point at  indicated by green circle. The system has a Hopf instability here. (b) Dispersion curve with synaptic range constant set to  (see Table 1 for other parameter values) predicts a Turing instability at spatial frequency  and a temporal instability of frequency  (see the  value at  axis on dispersion curve). (c) Bird’s-eye view and (d) 3-D spatio-temporal graphs demonstrate spatio-temporal evolution of 1-D network and emergence of mixed-mode Turing–Hopf oscillations in space and time
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Fig3: Emergence of Turing–Hopf mixed-mode oscillations in 1-D Wilson–Cowan cortex. (a) Steady state distribution with a selected point at indicated by green circle. The system has a Hopf instability here. (b) Dispersion curve with synaptic range constant set to (see Table 1 for other parameter values) predicts a Turing instability at spatial frequency and a temporal instability of frequency (see the value at axis on dispersion curve). (c) Bird’s-eye view and (d) 3-D spatio-temporal graphs demonstrate spatio-temporal evolution of 1-D network and emergence of mixed-mode Turing–Hopf oscillations in space and time

Mentions: To explore the stability characteristics of the spatially extended 1-D model, we plot the distribution of q-dependent eigenvalues of the matrix. In Figs. 2(a) and 3(b) we plot the real and imaginary parts of eigenvalues at a selected steady state as a function of scaled wavenumber to define the dispersion curve. Expressing the dominant eigenvalue as , we identify the real part Re as the damping rate, and Im as the oscillatory component. Thus instability at a particular wavenumber q is predicted if goes positive, in which case the oscillatory component will have spatial frequency . Fig. 2


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)

Emergence of Turing–Hopf mixed-mode oscillations in 1-D Wilson–Cowan cortex. (a) Steady state distribution with a selected point at  indicated by green circle. The system has a Hopf instability here. (b) Dispersion curve with synaptic range constant set to  (see Table 1 for other parameter values) predicts a Turing instability at spatial frequency  and a temporal instability of frequency  (see the  value at  axis on dispersion curve). (c) Bird’s-eye view and (d) 3-D spatio-temporal graphs demonstrate spatio-temporal evolution of 1-D network and emergence of mixed-mode Turing–Hopf oscillations in space and time
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4388113&req=5

Fig3: Emergence of Turing–Hopf mixed-mode oscillations in 1-D Wilson–Cowan cortex. (a) Steady state distribution with a selected point at indicated by green circle. The system has a Hopf instability here. (b) Dispersion curve with synaptic range constant set to (see Table 1 for other parameter values) predicts a Turing instability at spatial frequency and a temporal instability of frequency (see the value at axis on dispersion curve). (c) Bird’s-eye view and (d) 3-D spatio-temporal graphs demonstrate spatio-temporal evolution of 1-D network and emergence of mixed-mode Turing–Hopf oscillations in space and time
Mentions: To explore the stability characteristics of the spatially extended 1-D model, we plot the distribution of q-dependent eigenvalues of the matrix. In Figs. 2(a) and 3(b) we plot the real and imaginary parts of eigenvalues at a selected steady state as a function of scaled wavenumber to define the dispersion curve. Expressing the dominant eigenvalue as , we identify the real part Re as the damping rate, and Im as the oscillatory component. Thus instability at a particular wavenumber q is predicted if goes positive, in which case the oscillatory component will have spatial frequency . Fig. 2

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