Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Temporal evolution and electric potential structure of the auroral acceleration region from multispacecraft measurements

Bright aurorae can be excited by the acceleration of electrons into the atmosphere in violation of ideal magnetohydrodynamics. Modelling studies predict that the accelerating electric potential consists of electric double layers at the boundaries of an acceleration region but observations suggest that particle acceleration occurs throughout this region. Using multi-spacecraft observations from Cluster we have examined two upward current regions on 14 December 2009. Our observations show that the potential difference below C4 and C3 changed by up to 1.7 kV between their respective crossings, which were separated by 150 s. The field-aligned current density observed by C3 was also larger than that observed by C4. The potential drop above C3 and C4 was approximately the same in both crossings. Using a novel technique of quantitatively comparing the electron spectra measured by Cluster 1 and 3, which were separated in altitude, we determine when these spacecraft made effectively magnetically conjugate observations and use these conjugate observations to determine the instantaneous distribution of the potential drop in the AAR. Our observations show that an average of 15% of the potential drop in the AAR was located between C1 at 6235 km and C3 at 4685 km altitude, with a maximum potential drop between the spacecraft of 500~V and that the majority of the potential drop was below C3. By assuming a spatial invariance along the length of the upward current region, we discuss these observations in terms of temporal changes and the vertical structure of the electrostatic potential drop and in the context of existing models and previous observations single- and multi-spacecraft observations.

Long duration stimuli and nonlinearities in the neural–haemodynamic coupling

Recent studies have shown that the haemodynamic responses to brief (<2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (>2 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depth-resolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).

Lord Kelvin’s atmospheric electricity measurements

Lord Kelvin (William Thomson) made important contributions to the study of atmospheric elec- tricity during a brief but productive period from 1859–1861. By 1859 Kelvin had recognised the need for “incessant recording” of atmospheric electrical parameters, and responded by inventing both the water dropper equaliser for measuring the atmospheric potential gradient (PG), and photographic data logging. The water dropper equaliser was widely adopted internationally and is still in use today. Following theoretical consid- erations of electric field distortion by local topography, Kelvin developed a portable electrometer, using it to investigate the PG on the Scottish island of Arran. During these environmental measurements, Kelvin may have unwittingly detected atmospheric PG changes during solar activity in August / September 1859 associated with the “Carrington event”, which is interesting in the context of his later statements that solar magnetic influ- ence on the Earth was impossible. Kelvin’s atmospheric electricity work presents an early representative study in quantitative environmental physics, through the application of mathematical principles to an environmental problem, the design and construction of bespoke instrumentation for real world measurements and recognising the limitations of the original theoretical view revealed by experimental work

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.

Up-gradient eddy fluxes of potential vorticity near the subtropical jet

The role of eddy fluxes in the general circulation is often approached by treating eddies as (macro)turbulence. In this approach, the eddies act to diffuse certain quasiconservative quantities, such as potential vorticity (PV), along isentropic surfaces in the free atmosphere. The eddy fluxes are determined primarily by the eddy diffusivities and are necessarily down-gradient of the basic state PV field. Support for the (macro)turbulence approach stems from the fact that the eddy fluxes of PV in the free atmosphere are generally down-gradient in the long-term mean. Here we call attention to a pronounced and significant region of upgradient eddy PV fluxes on the poleward flank of the jet core in both hemispheres. The region of up-gradient (i.e., notionally “antidiffusive”) eddy PV fluxes is most pronounced during the winter and spring seasons and partially contradicts the turbulence approach described above. Analyses of the PV variance (potential enstrophy) budget suggest that the up-gradient PV fluxes represent local wave decay and are maintained by poleward fluxes of PV variance. Finite-amplitude effects thus represent leading order contributions to the PV variance budget, whereas dissipation is only of secondary importance locally. The appearance of up-gradient PV fluxes in the long-term mean is associated with the poleward shift of the jet—and thus the region of wave decay relative to wave growth—following wave-breaking events.

Within, but not between hands interactions in vibrotactile detection thresholds reflect somatosensory receptive field organization

Detection of a tactile stimulus on one finger is impaired when a concurrent stimulus (masker) is presented on an additional finger of the same or the opposite hand. This phenomenon is known to be finger-specific at the within-hand level. However, whether this specificity is also maintained at the between-hand level is not known. In four experiments, we addressed this issue by combining a Bayesian adaptive staircase procedure (QUEST) with a two-interval forced choice (2IFC) design in order to establish threshold for detecting 200ms, 100Hz sinusoidal vibrations applied to the index or little fingertip of either hand (targets). We systematically varied the masker finger (index, middle, ring, or little finger of either hand), while controlling the spatial location of the target and masker stimuli. Detection thresholds varied consistently as a function of the masker finger when the latter was on the same hand (Experiments 1 and 2), but not when on different hands (Experiments 3 and 4). Within the hand, detection thresholds increased for masker fingers closest to the target finger (i.e., middle>ring when the target was index). Between the hands, detection thresholds were higher only when the masker was present on any finger as compared to when the target was presented in isolation. The within hand effect of masker finger is consistent with the segregation of different fingers at the early stages of somatosensory processing, from the periphery to the primary somatosensory cortex (SI). We propose that detection is finger-specific and reflects the organisation of somatosensory receptive fields in SI within, but not between the hands.

Understanding and representing atmospheric convection across scales: recommendations from the meeting held at Dartington Hall, Devon, UK, 28–30 January 2013

As weather and climate models move toward higher resolution, there is growing excitement about potential future improvements in the understanding and prediction of atmospheric convection and its interaction with larger-scale phenomena. A meeting in January 2013 in Dartington, Devon was convened to address the best way to maximise these improvements, specifically in a UK context but with international relevance. Specific recommendations included increased convective-scale observations, high-resolution virtual laboratories, and a system of parameterization test beds with a range of complexities. The main recommendation was to facilitate the development of physically based convective parameterizations that are scale-aware, non-local, non-equilibrium, and stochastic.

N1 enhancement in synesthesia during visual and audio-visual perception in semantic cross-modal conflict situations: an ERP study

Synesthesia entails a special kind of sensory perception, where stimulation in one sensory modality leads to an internally generated perceptual experience of another, not stimulated sensory modality. This phenomenon can be viewed as an abnormal multisensory integration process as here the synesthetic percept is aberrantly fused with the stimulated modality. Indeed, recent synesthesia research has focused on multimodal processing even outside of the specific synesthesia-inducing context and has revealed changed multimodal integration, thus suggesting perceptual alterations at a global level. Here, we focused on audio-visual processing in synesthesia using a semantic classification task in combination with visually or auditory-visually presented animated and in animated objects in an audio-visual congruent and incongruent manner. Fourteen subjects with auditory-visual and/or grapheme-color synesthesia and 14 control subjects participated in the experiment. During presentation of the stimuli, event-related potentials were recorded from 32 electrodes. The analysis of reaction times and error rates revealed no group differences with best performance for audio-visually congruent stimulation indicating the well-known multimodal facilitation effect. We found enhanced amplitude of the N1 component over occipital electrode sites for synesthetes compared to controls. The differences occurred irrespective of the experimental condition and therefore suggest a global influence on early sensory processing in synesthetes.

Restrictive feeding practices and adiposity are differentially related to P3b cortical responses to food stimuli in children

Across two studies, we examined the association between adiposity, restrictive feeding practices and cortical processing bias to food stimuli in children. We assessed P3b event-related potential (ERP) during visual oddball tasks in which the frequently presented stimulus was non-food and the infrequently presented stimulus was either a food (Study 1) or non-food (Study 2) item. Children responded to the infrequently presented stimulus and accuracy and speed responses were collected. Restrictive feeding practices, children's height and weight were also measured. In Study 1, the difference in P3b amplitude for infrequently presented food stimuli, relative to frequently presented non-food stimuli, was negatively associated with adiposity and positively associated with restrictive feeding practices after controlling for adiposity. There was no association between P3b amplitude difference and adiposity or restriction in Study 2, suggesting that the effects seen in Study 1 were not due to general attentional processes. Taken together, our results suggest that attentional salience, as indexed by the P3b amplitude, may be important for understanding the neural correlates of adiposity and restrictive feeding practices in children.

Field-perpendicular and field-aligned plasma flows observed by EISCAT during a prolonged period of northward IMF

The effect of a prolonged period of strongly northward Interplanetary Magnetic Field (IMF) on the high-latitude F-region is studied using data from the EISCAT Common Programme Zero mode of operation on 11–12 August 1982. The analysis of the raw autocorrelation functions is kept to the directly derived parameters Ne, Te, Ti and velocity, and limits are defined for the errors introduced by assumptions about ion composition and by changes in the transmitted power and system constant. Simple data-cleaning criteria are employed to eliminate problems due to coherent signals and large background noise levels. The observed variations in plasma densities, temperatures and velocities are interpreted in terms of supporting data from ISEE-3 and local riometers and magnetometers. Both field-aligned and field-perpendicular plasma flows at Tromsø showed effects of the northward IMF: convection was slow and irregular and field-aligned flow profiles were characteristic of steady-state polar wind outflow with flux of order 1012 m−2 s−1. This period followed a strongly southward IMF which had triggered a substorm. The substorm gave enhanced convection, with a swing to equatorward flow and large (5 × 1012 m−2 s−1), steady-state field-aligned fluxes, leading to the possibility of O+ escape into the magnetosphere. The apparent influence of the IMF over both field-perpendicular and field-aligned flows is explained in terms of the cross-cap potential difference and the location of the auroral oval.

Satiation attenuates BOLD activity in brain regions involved in reward and increases activity in dorsolateral prefrontal cortex: an fMRI study in healthy volunteers

BACKGROUND: Neural responses to rewarding food cues are significantly different in the fed vs. fasted (>8 h food-deprived) state. However, the effect of eating to satiety after a shorter (more natural) intermeal interval on neural responses to both rewarding and aversive cues has not been examined. OBJECTIVE: With the use of a novel functional magnetic resonance imaging (fMRI) task, we investigated the effect of satiation on neural responses to both rewarding and aversive food tastes and pictures. DESIGN: Sixteen healthy participants (8 men, 8 women) were scanned on 2 separate test days, before and after eating a meal to satiation or after not eating for 4 h (satiated vs. premeal). fMRI blood oxygen level-dependent (BOLD) signals to the sight and/or taste of the stimuli were recorded. RESULTS: A whole-brain cluster-corrected analysis (P < 0.05) showed that satiation attenuated the BOLD response to both stimulus types in the ventromedial prefrontal cortex (vmPFC), orbitofrontal cortex, nucleus accumbens, hypothalamus, and insula but increased BOLD activity in the dorsolateral prefrontal cortex (dlPFC; local maxima corrected to P ≤ 0.001). A psychophysiological interaction analysis showed that the vmPFC was more highly connected to the dlPFC when individuals were exposed to food stimuli when satiated than when not satiated. CONCLUSIONS: These results suggest that natural satiation attenuates activity in reward-related brain regions and increases activity in the dlPFC, which may reflect a "top down" cognitive influence on satiation. This trial was registered at clinicaltrials.gov as NCT02298049.

A palaeoenvironmental context for terminal upper Palaeolithic and Mesolithic activity in the Colne Valley: offsite records contemporary with occupation at three ways Wharf, Uxbridge

Multi-proxy analyses from floodplain deposits in the Colne Valley, southern England, have provided a palaeoenvironmental context for the immediately adjacent Terminal Upper Palaeolithic and Early Mesolithic site of Three Ways Wharf. These deposits show the transition from an open cool environment to fully developed heterogeneous floodplain vegetation during the Early Mesolithic. Several distinct phases of burning are shown to have occurred that are chronologically contemporary with the local archaeological record. The floodplain itself is shown to have supported a number of rare Urwaldrelikt insect species implying human manipulation of the floodplain at this time must have been limited or episodic. By the Late Mesolithic a reed-sedge swamp had developed across much of the floodplain, within which repeated burning of the in situ vegetation took place. This indicates deliberate land management practices utilising fire, comparable with findings from other floodplain sequences in southern Britain. With similar sedimentary sequences known to exist across the Colne Valley, often closely associated with contemporary archaeology, the potential for placing the archaeological record within a spatially explicit palaeoenvironmental context is great.