Moira L. Steyn-Ross

The University of Waikato, Hamilton City, Waikato, New Zealand

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Publications (82)124.89 Total impact

  • Alex Bukoski · D A Steyn-Ross · Moira L Steyn-Ross
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    ABSTRACT: The dynamics of a spiking neuron approaching threshold is investigated in the framework of Markov-chain models describing the random state-transitions of the underlying ion-channel proteins. We characterize subthreshold channel-noise-induced transmembrane potential fluctuations in both type-I (integrator) and type-II (resonator) parametrizations of the classic conductance-based Hodgkin-Huxley equations. As each neuron approaches spiking threshold from below, numerical simulations of stochastic trajectories demonstrate pronounced growth in amplitude simultaneous with decay in frequency of membrane voltage fluctuations induced by ion-channel state transitions. To explore this progression of fluctuation statistics, we approximate the exact Markov treatment with a 12-variable channel-based stochastic differential equation (SDE) and its Ornstein-Uhlenbeck (OU) linearization and show excellent agreement between Markov and SDE numerical simulations. Predictions of the OU theory with respect to membrane potential fluctuation variance, autocorrelation, correlation time, and spectral density are also in agreement and illustrate the close connection between the eigenvalue structure of the associated deterministic bifurcations and the observed behavior of the noisy Markov traces on close approach to threshold for both integrator and resonator point-neuron varieties.
    Physical Review E 03/2015; 91(3-1):032708. DOI:10.1103/PhysRevE.91.032708 · 2.33 Impact Factor
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    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.
    01/2015; 5:9. DOI:10.1186/s13408-015-0021-x
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    Kaier Wang · Moira L Steyn-Ross · D A Steyn-Ross · Marcus T Wilson · Jamie W Sleigh
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    ABSTRACT: The electroencephalogram (EEG) patterns recorded during general anesthetic-induced coma are closely similar to those seen during slow-wave sleep, the deepest stage of natural sleep; both states show patterns dominated by large amplitude slow waves. Slow oscillations are believed to be important for memory consolidation during natural sleep. Tracking the emergence of slow-wave oscillations during transition to unconsciousness may help us to identify drug-induced alterations of the underlying brain state, and provide insight into the mechanisms of general anesthesia. Although cellular-based mechanisms have been proposed, the origin of the slow oscillation has not yet been unambiguously established. A recent theoretical study by Steyn-Ross et al. (2013) proposes that the slow oscillation is a network, rather than cellular phenomenon. Modeling anesthesia as a moderate reduction in gap-junction interneuronal coupling, they predict an unconscious state signposted by emergent low-frequency oscillations with chaotic dynamics in space and time. They suggest that anesthetic slow-waves arise from a competitive interaction between symmetry-breaking instabilities in space (Turing) and time (Hopf), modulated by gap-junction coupling strength. A significant prediction of their model is that EEG phase coherence will decrease as the cortex transits from Turing-Hopf balance (wake) to Hopf-dominated chaotic slow-waves (unconsciousness). Here, we investigate changes in phase coherence during induction of general anesthesia. After examining 128-channel EEG traces recorded from five volunteers undergoing propofol anesthesia, we report a significant drop in sub-delta band (0.05-1.5 Hz) slow-wave coherence between frontal, occipital, and frontal-occipital electrode pairs, with the most pronounced wake-vs.-unconscious coherence changes occurring at the frontal cortex.
    Frontiers in Systems Neuroscience 10/2014; 8:215. DOI:10.3389/fnsys.2014.00215
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    ABSTRACT: Characterizing brain dynamics during anesthesia is a main current challenge in anesthesia study. Several single channel Electroencephalogram (EEG) -based commercial monitors like the Bispectral index (BIS) have suggested to examine EEG signal. But, the BIS index has obtained numerous critiques. In this study, we evaluate the concentration-dependent effect of the propofol on long-range frontal-temporal synchronization of EEG signals collected from eight subjects during a controlled induction and recovery design. We used order patterns cross recurrence plot and provide an index named order pattern laminarity (OPL) to assess changes in neuronal synchronization as the mechanism forming the foundation of conscious perception. The prediction probability of 0.9 and 0.84 for OPL and BIS specified that the OPL index correlated more strongly with effect-site propofol concentration. Also, our new index makes faster reaction to transients in EEG recordings based on pharmacokinetic and pharmacodynamic model parameters and demonstrates less variability at the point of loss of consciousness (standard deviation of 0.04 for OPL compared with 0.09 for BIS index). The result show that the OPL index can estimate anesthetic state of patient more efficiently than the BIS index in lightly sedated state with more tolerant of artifacts.
    IEEE Transactions on Neural Systems and Rehabilitation Engineering 08/2014; 23(3). DOI:10.1109/TNSRE.2014.2350537 · 2.82 Impact Factor
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    Moira L Steyn-Ross · Alistair Steyn-Ross · Jamie W Sleigh
    BMC Neuroscience 07/2014; 15(Suppl 1):O19-O19. DOI:10.1186/1471-2202-15-S1-O19 · 2.85 Impact Factor
  • Kaier Wang · Moira L. Steyn-Ross · D. Alistair Steyn-Ross · Marcus T. Wilson
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    ABSTRACT: The amplitude equation describes a reduced form of a reaction-diffusion system, yet still retains its essential dynamical features. By approximating the analytic solution, the amplitude equation allows the examination of mode instability when the system is near a bifurcation point. Multiple-scale expansion (MSE) offers a straightforward way to systematically derive the amplitude equations. The method expresses the single independent variable as an asymptotic power series consisting of newly introduced independent variables with differing time and space scales. The amplitude equations are then formulated under the solvability conditions which remove secular terms. To our knowledge, there is little information in the research literature that explains how the exhaustive workflow of MSE is applied to a reaction-diffusion system. In this paper, detailed mathematical operations underpinning the MSE are elucidated, and the practical ways of encoding these operations using Maple are discussed. A semi-automated MSE computer algorithm Amp_solving is presented for deriving the amplitude equations in this research. Amp_solving has been applied to the classical Brusselator model for the derivation of amplitude equations when the system is in the vicinity of a Turing codimension-1 and a Turing-Hopf codimension-2 bifurcation points. Full open-source Amp_solving codes for the derivation are comprehensively demonstrated and available to the public domain.
    International Journal of Bifurcation and Chaos 07/2014; 24(07):1450101. DOI:10.1142/S0218127414501016 · 1.02 Impact Factor
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    ABSTRACT: Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requiresnumerical solution of the system's set of defining differential equations. Traditionally, this wouldbe done by selecting an appropriate differential equation solver from a library of such solvers, thenwriting computer codes (in a programming language such as C or MATLAB) to access the selectedsolver and display the integrated results as a function of space and time. This "code-based" approachis flexible and powerful, but requires a certain level of programming sophistication. A modernalternative is to use a graphical programming interface such as SIMULINK to construct a data-flowdiagram by assembling and linking appropriate code blocks drawn from a library. The result is avisual representation of the inter-relationships between the state variables whose output can be madecompletely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the SIMULINK data-flow techniqueto the classical van der Pol nonlinear oscillator, and compare MATLAB and SIMULINK coding approaches to solving the van der Pol ordinary differential equations. We then show how to introducespace (in one and two dimensions) by solving numerically the partial differential equations for twodifferent reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuummodel for a two-dimensional sheet of human cortex whose neurons are linked by both chemicaland electrical (diffusive) synapses. We compare the relative performances of the MATLAB andSIMULINK implementations. The pattern simulations by SIMULINK are in good agreement with theoretical predictions. Comparedwith traditional coding approaches, the SIMULINK block-diagram paradigm reduces the time andprogramming burden required to implement a solution for reaction-diffusion systems of equations.Construction of the block-diagram does not require high-level programming skills, and the graphicalinterface lends itself to easy modification and use by non-experts.
    BMC Systems Biology 04/2014; 8(1):45. DOI:10.1186/1752-0509-8-45 · 2.85 Impact Factor
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    ABSTRACT: Low-magnesium hippocampal seizure-like events (hSLE) are well-known in vitro animal models of epilepsy. Although there has been extensive amount of study on the function of ionic channels, single neurons and their communications during hSLEs, less is done about describing these bursts using concepts from dynamical systems. Investigating the applicability of tools such as bifurcation and phase space analysis_which are commonly used in neural modeling studies_to experimental data is the objective of present work. Here we have focused on quantitative analysis of hSLE bursts, specifically their frequency content, how they emerge and terminate. Data was recorded from hippocampal CA1 region of coronal mouse brain slices. Bipolar recording configuration without high-pass filtering, preserved original frequency content of field activity including zero to 10 kHz. Results show capability of CA1 neurons in producing two different patterns of bursting. First pattern shows gradual emergence of burst from quiescence, fixed-amplitude high-frequency oscillations during the burst, and a gradual reduction both in amplitude and frequency toward the end of burst. Second pattern shows instantaneous emergence of burst, fixed-amplitude high frequency bursting phase, and gradual growth in amplitude while reduction of frequency toward the end of hSLE. Phase plots of amplitudes at starting point and tail of each type remind different types of bifurcations responsible for rest-to-spiking and spiking-to-rest transitions. More interesting is the slowing down in the frequency content of hSLEs, along with gradual growth of amplitude toward the end of hSLE that reminds critical slowing down near a bifurcation point. Results show the possibility of existence of fold, saddle-node on invariant circle, Hopf, and subcritical Hopf bifurctions as the mechanisms describing burst initiation and termination. Inter and intraburst frequencies clearly show an undergoing slow-fast system, which is commonly used in theoretical modeling and describing bursting systems. This work shows applicability of theory of dynamical systems to experimentally recorded neural field data. The significance could be making interpretations about genesis of neural state-transitions, investigation of precursors before seizure occurrence, and stimulation-based control of bursting activity based on type of burst.
    2013 Neuroscience Meeting; 11/2013
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    ABSTRACT: When a dynamical system approaches a state transition, the system loses resilience, and critically slowed temporal and spatial patterns can appear. These patterns can be observed in single-neuron and neural population models. Here we examine a simplified mean-field model of cortex, and demonstrate critical fluctuations prior to four distinct classes of bifurcation, including (a) saddle-node, (b) Hopf, (c) Turing, and (d) Turing-Hopf interactions. Our model is a Wilson-Cowan interlinked network of 1500 excitatory (E) and 1500 inhibitory (I) neurons, forming a 3mm-length 1D rod. Neurons have all-to-all connections, with synaptic weights being exponentially-decaying functions of distance. External inputs to the cortical network (such as subcortical drive, gap-junction mediated currents and any applied stimulus) are presented as control parameter P. We use linear stability analysis to extract the Jacobian matrix for the linearized system, locate steady states as a function of P, and identify the stability of the equilibria. We find that the cortical rod supports up to three steady states. The midbranch is always an unstable saddle, and the bottom branch is always a stable node. These two states collide and annihilate via a saddle-node bifurcation, pushing the system to an alternative state on the upper branch. The upper branch consists of stable or unstable spiral points separated by a Hopf bifurcation. If the range of inhibitory connections is made longer than that for excitatory connections, spatial waves can form on the rod through a Turing mechanism. By adjusting the external input to the E neurons and the synaptic range of inhibitory connections, we are able to sweep the system toward temporal (saddle-node, Hopf), spatial (Turing), and spatio-temporal (Turing-Hopf) instabilities without actually crossing the transition threshold. We study critical fluctuations in the firing rate of E neurons in response to white-noise or stepped excitatory stimulus. We use autocorrelation functions in time and space to quantify our analysis. All four classes of bifurcation investigated here show clear evidence of critically-slowed fluctuations on close approach to state transition. Leading indicators show themselves in the form of prolonged correlation time and correlation distance, as well as a profound increase in fluctuation variance, regardless of the type of bifurcation. If the transition from quiescent neural activity to active seizure can be described as a state transition, then we hypothesize that leading indicators in time and space should accompany the state of the neural system prior to this transition. As a model for cortical probing experiments, we also demonstrate spatio-temporal prolongation of excitatory firing rates in response to externally induced excitatory current before emergence of Turing patterns. Our results provide modelling support for experimental attempts to capture pre-seizure leading indicators.
    Sixth International Workshop on Seizure Prediction, San Diego; 11/2013
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    Moira L. Steyn-Ross · J. W. Sleigh
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    ABSTRACT: Slow oscillations in neuronal activity in the human brain are the defining feature of scalp-measured electroencephalography taken under general anesthesia. A theoretical investigation of a model for the human cortex reveals that slow spatiotemporal patterns emerge spontaneously as the result of a chemically modified balancing act between two instabilities in cortical dynamics\char22{}one to spatial organizations and the other to temporal bifurcation. Long-range interneuronal communication across the cortex is shown to be crucial to the pattern formation.
    Physical Review X 05/2013; 3(2). DOI:10.1103/PhysRevX.3.021005 · 8.39 Impact Factor
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    ABSTRACT: Here we present a dynamically rich but computationally efficient model of thalamocortical loop describing the most prominent features of sleep-wake transitions of brain.
    Australian Institute of Physics 20th National Congress; 11/2012
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    Moira L Steyn-Ross · D Alistair Steyn-Ross · Jamie W Sleigh
    BMC Neuroscience 07/2012; 13(1). DOI:10.1186/1471-2202-13-S1-F3 · 2.85 Impact Factor
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    Alex Bukoski · D Alistair Steyn-Ross · Moira L Steyn-Ross
    BMC Neuroscience 07/2012; 13(1). DOI:10.1186/1471-2202-13-S1-P34 · 2.85 Impact Factor
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    ABSTRACT: General anaesthetics have been hypothesised to ablate consciousness by decoupling intracortical neural connectivity. We explored this by investigating the effect of etomidate and ketamine on coupling of neural population activity using the low magnesium neocortical slice model. Four extracellular electrodes (50 μm) were positioned in mouse neocortical slices (400 μm thick) with varying separation. The effect of etomidate (24 μM) and ketamine (16 μM) on the timing of population activity recorded between channels was analysed. No decoupling was observed at the closest electrode separation of 0.2 mm. At 4mm separation, decoupling was observed in 50% and 42% of slices during etomidate and ketamine delivery, respectively (P<0.0001 and P=0.002, compared to 0.2 mm separation). A lower rate of decoupling was observed with 1mm separation (21% and 8%, respectively, P<0.03 for etomidate compared to 0.2mm separation). The data support the hypothesis that mechanistically diverse general anaesthetics disrupt neuronal connectivity across widely distributed intracortical networks.
    European journal of pharmacology 06/2012; 689(1-3):111-7. DOI:10.1016/j.ejphar.2012.06.003 · 2.68 Impact Factor
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    Moira L Steyn-Ross · D Alistair Steyn-Ross · Jamie W Sleigh
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    ABSTRACT: During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (≲8 Hz) oscillatory states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity for seizure and simultaneously an increased sensitivity to GABAergic anesthesia.
    Cognitive Neurodynamics 06/2012; 6(3):215-25. DOI:10.1007/s11571-012-9194-0 · 1.77 Impact Factor
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    ABSTRACT: Clinically, anesthetic drugs show hysteresis in the plasma drug concentrations at induction versus emergence from anesthesia induced unconsciousness. This is assumed to be the result of pharmacokinetic lag between the plasma and brain effect-site and vice versa. However, recent mathematical and experimental studies demonstrate that anesthetic hysteresis might be due in part to lag in the brain physiology, independent of drug transport delay - so-called "neural inertia". The aim of this study was to investigate neural inertia in the reduced neocortical mouse slice model. Seizure-like event (SLE) activity was generated by exposing cortical slices to no-magnesium artificial cerebrospinal fluid (aCSF). Concentration-effect loops were generated by manipulating SLE frequency, using the general anesthetic drug etomidate and by altering the aCSF magnesium concentration. The etomidate (24 μM) concentration-effect relationship showed a clear hysteresis, consistent with the slow diffusion of etomidate into slice tissue. Manipulation of tissue excitability, using either carbachol (50 μM) or elevated potassium (5mM vs 2.5mM) did not significantly alter the size of etomidate hysteresis loops. Hysteresis in the magnesium concentration-effect relationship was evident, but only when the starting condition was magnesium-containing "normal" aCSF. The in vitro cortical slice manifests pathway-dependent "neural inertia" and may be a valuable model for future investigations into the mechanisms of neural inertia in the cerebral cortex.
    European journal of pharmacology 12/2011; 675(1-3):26-31. DOI:10.1016/j.ejphar.2011.11.045 · 2.68 Impact Factor
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    ABSTRACT: The cerebral cortex is responsible for many high-level brain functions. As the outermost part of the brain it has a columnar structure in which each microcolumn is composed of hundreds of excitatory (E) and inhibitory (I) neurons communicating through a complex network of connections. Here we describe the capabilities of a computational model of a cortical microcolumn in predicting some bioelectric phenomena. Each neuron is described by the simple Izhikevich model. As a system of two nonlinear coupled differential equations, this model shows the time evolution of the neural membrane voltage based on some biological characteristics of the neuron and external inputs entering it via E or I synapses. By sparse random connection of 160 E and 40 I neurons via chemical synapses, a network of neurons was constructed. The simulation was performed based on a fourth-order Runge-Kutta method. Result of simulation shows that although individual neurons could not fire beyond a few tens of spikes per second, the average presynaptic currents entering the E neurons has frequency components extending well beyond 30 Hz; these components may be related to gamma range oscillations of a normal behaving brain. Another interesting behaviour is the model prediction of seizure-like activity in patients undergoing anaesthesia or emerging from it. We model the effect of anaesthesia as an increase in the effective time constant of the postsynaptic inhibitory current (GABA A). During induction of, and emergence from, anaesthesia all E neurons fire synchronously, producing sharp discharges in the average network current. This synchronized behaviour can be explained by considering the phase plots of single neurons which will tend to be more in-phase due to the prolongation of GABA A . However further increase in GABA A will force the bistable neurons to enter the attraction domain of quiescent state, and the network collapses into anaesthetic coma. We reduced GABA A to its initial value in order to model the emergence from anaesthesia. The results show re-oscillation of the network with slightly different approach compared with induction phase, making the anaesthetic induction-recovery loop asymmetric and hysteretic, in agreement with clinical findings.
    New Zealand Institute of Physics Conference; 10/2011
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    J. W. Sleigh · L. Voss · M. L. Steyn-Ross · D. A. Steyn-Ross · M. T. Wilson
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    ABSTRACT: A diverse range of modelling approaches have been applied to try and understand some of the neural mechanisms that underlie transitions between wake-sleep (and rapid-eye movement-to-slow-wave sleep) states. There is a strong evolutionary argument that general anaesthesia exists because it is a form of drug-induced harnessing of natural sleep mechanisms. The theoretical models tend to either describe specific interactions between various brain-stem nuclei; or at the other extreme, assume that sleep is a universal property of all neural assemblies, and therefore follow a thalamo-cortico-centric approach Using a general cortex-based mean field model we propose that: (1) Unconsciousness during natural slow wave sleep is caused by blockade of cortical connectivity; which is induced by increased gamma-amino-butyric acid(GABA)-ergic activity and diminished excitatory neuromodulators—and hence relative cortical hyperpolarization. (2) The sleeping subject can be woken because the normal homeostatic effects of arousal neuromodulators are able to depolarize the cortex, and switch off the GABAergic systems. (3) Sedative doses of GABAergic general anaesthetic drugs augment GABAergic systems which then inhibit excitatory neuromodulators and trigger a sleep-like state. However excessive nociceptive activation of the brainstem arousal systems is still able to depolarize the cortex and switch off the GABAergic systems. (4) Larger doses of GABAergic general anaesthetics cause an irreversible global increase in the total charge carried by the inhibitory post synaptic potential. This causes an increased negative feedback loop in the cortex, which is not able to be overcome by intrinsic neuronal currents, and hence the patient cannot be woken up even by the most extreme nociceptive stimuli—the definition of general anaesthesia.
    07/2011: pages 21-41;
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    ABSTRACT: In a hysteretic system the output not only depends on the input, but also depends on the current and previous internal states of the system. In such systems there is no way to predict their output just based on the input level. Hysteresis can be found in electrical, magnetic, mechanical, economical, and biological systems. Reports that patients awaken at lower concentration of anaesthetic than that required to put them to sleep indicate that hysteresis is an important feature of anaesthesia; this clinical finding is supported by a theoretical modelling study of the induction-recovery anaesthesia cycle. Hysteresis may also be an essential component of the transition between slow-wave and REM states of natural sleep. Here we investigate hysteretic behavior of two classes of spiking neuron models, both individually, and as a population aggregate formed from a cluster of excitatory and inhibitory neurons.
    Mathematical Neuroscience; 04/2011
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    Moira L Steyn-Ross · D A Steyn-Ross · J W Sleigh · M T Wilson
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    ABSTRACT: When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated by increases in the strength of the gap-junction coupling between interneurons. We comment on possible implications for slow dendritic computation and information processing.
    Bulletin of Mathematical Biology 02/2011; 73(2):398-416. DOI:10.1007/s11538-010-9565-9 · 1.29 Impact Factor

Publication Stats

1k Citations
124.89 Total Impact Points

Institutions

  • 1970–2015
    • The University of Waikato
      • School of Engineering
      Hamilton City, Waikato, New Zealand
  • 2009
    • University of Auckland
      • Waikato Clinical School
      Окленд, Auckland, New Zealand
  • 2002
    • Charles Sturt University
      Бэтхерст, New South Wales, Australia
  • 1999
    • Waikato Hospital
      Hamilton City, Waikato, New Zealand
  • 1984
    • York University
      Toronto, Ontario, Canada