[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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; · 2.82 Impact Factor
[Show abstract][Hide abstract] 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. · 2.85 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] ABSTRACT: Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1 Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning.
Physical Review X 05/2013; 3(2). · 8.39 Impact Factor
[Show abstract][Hide abstract] 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
[Show abstract][Hide abstract] 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. · 2.59 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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. · 2.59 Impact Factor
[Show abstract][Hide abstract] 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
[Show abstract][Hide abstract] 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:
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.
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.
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.
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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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. · 2.02 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: It is a well established clinical observation that, at low concentrations, most anesthetic agents produce a surge in brain
activity that occurs around the time of loss of consciousness. At higher concentrations, brain activity slows, and eventually
tends towards electrical silence. Asecond surge in EEG power occurs during the return to consciousness. These induction and
recovery biphasic power surges were first explained in terms of a first-order switching transition between distinct active
and quiescent neural states, but subsequent modeling by other researchers has demonstrated that biphasic surges can also be
generated by a smooth, graduated transition between normal and suppressed levels of cortical activity. In this chapter we
examine the contrasting predictions of the switching model versus the continuous model for anesthetic induction. If the continuous
non-switching picture is correct, then the return path to recovery will retrace the trajectory for induction, so the biphasic
peaks should occur at identical drug concentrations. In contrast, the switching model predicts that there must be a hysteresis
separation between the entry and recovery EEG power maxima, and that the patient will awaken at a lower drug concentration
than that required to put her to sleep.
[Show abstract][Hide abstract] ABSTRACT: Large-scale synchronous firing of neurons during seizures is modulated by electrotonic coupling between neurons via gap junctions. To explore roles for connexin36 (Cx36) gap junctions in seizures, we examined the seizure threshold of connexin36 knockout (Cx36KO) mice using a pentylenetetrazol (PTZ) model.
Mice (2-3months old) with Cx36 wildtype (WT) or Cx36KO genotype were treated with vehicle or 10-40mg/kg of the convulsant PTZ by intraperitoneal injection. Seizure and seizure-like behaviors were scored by examination of video collected for 20min. Quantitative real-time PCR (QPCR) was performed to measure potential compensatory neuronal connexin (Cx30.2, Cx37, Cx43 and Cx45), pannexin (PANX1 and PANX2) and gamma-aminobutyric acid type A (GABA(A)) receptor α1 subunit gene expression.
Cx36KO animals exhibited considerably more severe seizures; 40mg/kg of PTZ caused severe generalized (≥grade III) seizures in 78% of KO, but just 5% of WT mice. A lower dose of PTZ (20mg/kg) induced grade II seizure-like behaviors in 40% KO vs. 0% of WT animals. There was no significant difference in either connexin, pannexin or GABA(A) α1 gene expression between WT and KO animals.
Increased sensitivity of Cx36KO animals to PTZ-induced seizure suggests that Cx36 gap junctional communication functions as a physiological anti-convulsant mechanism, and identifies the Cx36 gap junction as a potential therapeutic target in epilepsy.
Brain research 11/2010; 1360:198-204. · 2.83 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Epilepsy affects nearly 3 million people in the United States alone. Given the fact that many people suffer from seizures that are intractable to pharmacological intervention, research groups are investigating the use of electrical stimulation to interact with and ameliorate symptoms of epileptic seizures. In mouse cortical slices made seizuregenic through chemical means, we applied precision controlled current pulses and measured local field potentials through a four point probe system to investigate the response of seizing tissue to electrical stimulation. We have determined that the frequency of the spontaneous seizure-like events may be modified by low amplitude, current controlled stimulation (0.5 μA). Differently from previously thought, this change in frequency is however not accompanied by any alteration of the tissue permittivity or conductivity during the inter-seizure interval.
Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE; 10/2010
[Show abstract][Hide abstract] ABSTRACT: Previous studies have shown that activated cortical states (awake and rapid eye-movement (REM) sleep), are associated with
increased cholinergic input into the cerebral cortex. However, the mechanisms that underlie the detailed dynamics of the cortical
transition from slow-wave to REM sleep have not been quantitatively modeled. How does the sequence of abrupt changes in the
cortical dynamics (as detected in the electrocorticogram) result from the more gradual change in subcortical cholinergic input?
We compare the output from a continuum model of cortical neuronal dynamics with experimentally-derived rat electrocorticogram
data. The output from the computer model was consistent with experimental observations. In slow-wave sleep, 0.5–2-Hz oscillations
arise from the cortex jumping between “up” and “down” states on the stationary-state manifold. As cholinergic input increases,
the upper state undergoes a bifurcation to an 8-Hz oscillation. The coexistence of both oscillations is similar to that found
in the intermediate stage of sleep of the rat. Further cholinergic input moves the trajectory to a point where the lower part
of the manifold in not available, and thus the slow oscillation abruptly ceases (REM sleep). The model provides a natural
basis to explain neuromodulator-induced changes in cortical activity, and indicates that a cortical phase change, rather than
a brainstem “flip-flop”, may describe the transition from slow-wave sleep to REM.
Keywords and phrasesSWS-REM-intermediate sleep-EEG-ECoG-theta oscillation-delta oscillation-rat-mean-field model