Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

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

Modelling general anaesthesia as a first-order phase transition in the cortex

Since 1997 we have been developing a theoretical foundation for general anaesthesia. We have been able to demonstrate that the abrupt change in brain state broughton by anaesthetic drugs can be characterized as a first-order phase transition in the population-average membrane voltage of the cortical neurons. The theory predicts that, as the critical point of phase-change into unconsciousness is approached, the electrical fluctuations in cortical activity will grow strongly in amplitude while slowing in frequency, becoming more correlated both in time and in space. Thus the bio-electrical change of brain-state has deep similarities with thermodynamic phase changes of classical physics. The theory further predicts the existence of a second critical point, hysteretically separated from the first, corresponding to the return path from comatose unconsciousness back to normal responsiveness. There is a steadily accumulating body of clinical evidence in support of all of the phasetransition predictions: low-frequency power surge in EEG activity; increased correlation time and correlation length in EEG fluctuations; hysteresis separation, with respect to drug concentration, between the point of induction and the point of emergence

Dark matter, the CMSSM and lattice QCD

Recent lattice measurements have given accurate estimates of the light and strange quark condensates in the proton. We use these new results to significantly improve the dark matter predictions in a set of benchmark models that represent different scenarios in the constrained minimal supersymmetric standard model (CMSSM). Because the predicted cross sections are at least an order of magnitude smaller than previously suggested, our results have significant consequences for dark matter searches.Comment: 4 pages, 4 figure

Instabilities of the cortex during natural sleep

The electrical signals generated by the human cortex during sleep have been widely studied over the last 50 years. The electroencephalogram (EEG) observed during natural sleep exhibits structures with frequencies from 0.5 Hz to over 50 Hz and complicated waveforms such as spindles and K-complexes. Understanding has been enhanced by comprehensive intra-cellular measurements from the cortex and thalamus such as those performed by Steriade et al [1] and Sanchez-Vives and McCormick [2]. Models of the cerebal cortex have been developed in order to explain many of the features observed. These can be classified in terms of individual neuron models or collective models. Since we wish to compare predictions with gross features of the human EEG, we choose a collective model, where we average over a population of neurons in macrocolumns. A number of models of this form have been developed recently; that developed at Waikato draws from a number of different sources to describe the temporal and spatial dynamics of the system

Application of dynamical systems theory to a very low energy transfer

We use lobe dynamics in the restricted three-body problem to design orbits with prescribed itineraries with respect to the resonance regions within a Hill’s region. The application we envision is the design of a low energy trajectory to orbit three of Jupiter’s moons using the patched three-body approximation (P3BA). We introduce the “switching region,” the P3BA analogue to the “sphere of influence.” Numerical results are given for the problem of finding the fastest trajectory from an initial region of phase space (escape orbits from moon A) to a target region (orbits captured by moon B) using small controls

Corn Harvesting Handling Marketing in Ohio

PDF pages: 3

Behavior in normal and reduced gravity of an enclosed liquid/gas system with nonuniform heating from above

The temperature and velocity fields have been investigated for a single-phase gas system and a two-layer gas-and-liquid system enclosed in a circular cylinder being heated suddenly and nonuniformly from above. The transient response of the gas, liquid, and container walls was modelled numerically in normal and reduced gravity (10 to the -5 g). Verification of the model was accomplished via flow visualization experiments in 10 cm high by 10 cm diameter plexiglass cylinders

A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep

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