Cortical activity during motor execution, motor imagery, and imagery-based online feedback.

Imagery of motor movement plays an important role in learning of complex motor skills, from learning to serve in tennis to perfecting a pirouette in ballet. What and where are the neural substrates that underlie motor imagery-based learning? We measured electrocorticographic cortical surface potentials in eight human subjects during overt action and kinesthetic imagery of the same movement, focusing on power in "high frequency" (76-100 Hz) and "low frequency" (8-32 Hz) ranges. We quantitatively establish that the spatial distribution of local neuronal population activity during motor imagery mimics the spatial distribution of activity during actual motor movement. By comparing responses to electrocortical stimulation with imagery-induced cortical surface activity, we demonstrate the role of primary motor areas in movement imagery. The magnitude of imagery-induced cortical activity change was approximately 25% of that associated with actual movement. However, when subjects learned to use this imagery to control a computer cursor in a simple feedback task, the imagery-induced activity change was significantly augmented, even exceeding that of overt movement.

Power-law scaling in the brain surface electric potential.

Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form P(f ) approximately Af(-chi) from 80 to 500 Hz. This scaling index, chi = 4.0+/-0.1, is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, A, increases. We observe a "knee" in the spectra at f(0) approximately 75 Hz, implying the existence of a characteristic time scale tau = (2pif(0))(-1) approximately 2 - 4ms. Below f(0), we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the alpha/beta rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory "asynchronous," scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent "synchronous" rhythm-based paradigm.

Line tensions, correlation lengths, and critical exponents in lipid membranes near critical points.

Membranes containing a wide variety of ternary mixtures of high chain-melting temperature lipids, low chain-melting temperature lipids, and cholesterol undergo lateral phase separation into coexisting liquid phases at a miscibility transition. When membranes are prepared from a ternary lipid mixture at a critical composition, they pass through a miscibility critical point at the transition temperature. Since the critical temperature is typically on the order of room temperature, membranes provide an unusual opportunity in which to perform a quantitative study of biophysical systems that exhibit critical phenomena in the two-dimensional Ising universality class. As a critical point is approached from either high or low temperature, the scale of fluctuations in lipid composition, set by the correlation length, diverges. In addition, as a critical point is approached from low temperature, the line tension between coexisting phases decreases to zero. Here we quantitatively evaluate the temperature dependence of line tension between liquid domains and of fluctuation correlation lengths in lipid membranes to extract a critical exponent, nu. We obtain nu = 1.2 +/- 0.2, consistent with the Ising model prediction nu = 1. We also evaluate the probability distributions of pixel intensities in fluorescence images of membranes. From the temperature dependence of these distributions above the critical temperature, we extract an independent critical exponent of beta = 0.124 +/- 0.03, which is consistent with the Ising prediction of beta = 1/8.

Beyond the gamma band: the role of high-frequency features in movement classification.

Electrocorticographic spectral changes during movement show a behavioral inflection in the classic gamma band (30-70 Hz). We quantify this inflection and demonstrate that it limits classification accuracy. We call for the designation of a functionally defined band above it, which we denote the chi-band.

Dynamic instability transitions in one-dimensional driven diffusive flow with nonlocal hopping.

One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The nonlocal skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk is in control. The first-order transition originates from a turnabout of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.

Dynamic screening in a two-species asymmetric exclusion process.

The dynamic scaling properties of the one-dimensional Burgers equation are expected to change with the inclusion of additional conserved degrees of freedom. We study this by means of one-dimensional (1D) driven lattice gas models that conserve both mass and momentum. The most elementary version of this is the Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two-species diffusion process, with particles of opposite charge hopping in opposite directions and with a variable passing probability. From the hydrodynamics perspective this can be viewed as two coupled Burgers equations, with the number of positive and negative momentum quanta individually conserved. We determine the dynamic scaling dimension of the AHR process from the time evolution of the two-point correlation functions, and find numerically that the dynamic critical exponent is consistent with simple Kardar-Parisi-Zhang- (KPZ) type scaling. We establish that this is the result of perfect screening of fluctuations in the stationary state. The two-point correlations decay exponentially in our simulations and in such a manner that in terms of quasiparticles, fluctuations fully screen each other at coarse grained length scales. We prove this screening rigorously using the analytic matrix product structure of the stationary state. The proof suggests the existence of a topological invariant. The process remains in the KPZ universality class but only in the sense of a factorization, as (KPZ)2. The two Burgers equations decouple at large length scales due to the perfect screening.

Macroscopic car condensation in a parking garage.

An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes macroscopically occupied. The total car density rho(o) and the exit probability alpha from the garage are the two control parameters. At the transition, the number of parked cars N(p) diverges in both cases, with the length of the road N(s), as N(p) approximately N(y(p))(s) with y(p)=1/2. Towards the transition, the number of parked cars vanishes as N(p) approximately epsilon(beta) with beta=1, epsilon=/alpha-alpha(*)/ or epsilon=|rho(*)(o)-rho(o)/ being the distance from the transition. The transition into the normal phase represents also the onset of transmission of information through the garage. This gives rise to unusual parked car autocorrelations and car density profiles near the garage, which depend strongly on the group velocity of the fluctuations along the road.

Directed avalanche processes with underlying interface dynamics.

We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower dimension. In our specific case, the interface growth dynamics belongs to the Kardar-Parisi-Zhang (KPZ) universality class. We formulate relations between the critical exponents of the various avalanche distributions and those of the roughness of the growing interface. The nonlinear nature of the underlying KPZ dynamics provides a nontrivial test of such generic exponent relations. The numerical values of the avalanche exponents are close to the conventional KPZ values, but differ sufficiently to warrant a detailed study of whether avalanche-correlated Monte Carlo sampling changes the scaling exponents of KPZ interfaces. We demonstrate that the exponents remain unchanged, but that the traces left on the surface by previous avalanches give rise to unusually strong finite-size corrections to scaling. This type of slow convergence seems intrinsic to avalanche dynamics.

Two-dimensional equilibrium surface roughness for dissociative dimer dynamics.

Equilibrium crystal surfaces, constrained to equilibrate by means of dissociative dimer deposition and evaporation, have anomalous global surface roughness. We generalize earlier results for one-dimensional interfaces to two dimensions. The global surface width scales with surface size L as W2 approximately equals ln[L/(ln L)(1/4)] instead of the conventional form W2 approximately equal to ln L. The surface roughening transition does not change in nature, but its location is subject to a large and slowly varying logarithmic finite-size-scaling shift.

Interface view of directed sandpile dynamics.

We present a directed unloading sand-box-type avalanche model, driven by slowly lowering the retaining wall at the bottom of the slope. The avalanche propagation in the two-dimensional surface is related to the space-time configurations in one-dimensional Kardar-Parisi-Zhang (KPZ) interface growth. We relate the scaling exponents of the avalanche cluster distribution to those for the growing surface. The numerical results are close but deviate significantly from the exact KPZ values. This might reflect stronger than usual corrections to scaling or be more fundamental, due to correlations between subsequent space-time interface configurations.

Queuing transitions in the asymmetric simple exclusion process.

Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as deltarho approximately x(-nu) with nu=1/3, and x is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent nu=1/3 is universal and independent of the dynamic exponent of the underlying dynamic process. Fast bonds create only power-law shaped depletion queues, and with an exponent that could be equal to nu=2/3, but the numerical results yield consistently somewhat smaller values nu approximately 0.63(3). The implications of these results to faceting of growing interfaces and localization of directed polymers in random media, both in the presence of a columnar defect are pointed out as well.

Brain surface electrode co-registration using MRI and X-ray.

Electrocorticographic recording is now being used in a wide variety of experimental settings. We present a simple method which can be used to estimate electrode position with respect to brain gyral anatomy using a pre-implantation MRI and post-implantation coronal and sagittal x-rays. It is semi-automated, with the user manually rotating and scaling an x-ray to fit brain outline, identifying threshold values for brain surface rendering, and clicking on electrodes on an x-ray. Electrode positions can be rapidly identified and rendered in about 20 minutes from start to finish. This approach is useful when the MRI quality is poor, there is no quality CT, but one would like to understand the relationship between experimental result and brain anatomy.

Dynamic modulation of local population activity by rhythm phase in human occipital cortex during a visual search task.

Brain rhythms are more than just passive phenomena in visual cortex. For the first time, we show that the physiology underlying brain rhythms actively suppresses and releases cortical areas on a second-to-second basis during visual processing. Furthermore, their influence is specific at the scale of individual gyri. We quantified the interaction between broadband spectral change and brain rhythms on a second-to-second basis in electrocorticographic (ECoG) measurement of brain surface potentials in five human subjects during a visual search task. Comparison of visual search epochs with a blank screen baseline revealed changes in the raw potential, the amplitude of rhythmic activity, and in the decoupled broadband spectral amplitude. We present new methods to characterize the intensity and preferred phase of coupling between broadband power and band-limited rhythms, and to estimate the magnitude of rhythm-to-broadband modulation on a trial-by-trial basis. These tools revealed numerous coupling motifs between the phase of low-frequency (δ, θ, α, ß, and γ band) rhythms and the amplitude of broadband spectral change. In the θ and ß ranges, the coupling of phase to broadband change is dynamic during visual processing, decreasing in some occipital areas and increasing in others, in a gyrally specific pattern. Finally, we demonstrate that the rhythms interact with one another across frequency ranges, and across cortical sites.

Detection of spontaneous class-specific visual stimuli with high temporal accuracy in human electrocorticography.

Most brain-computer interface classification experiments from electrical potential recordings have been focused on the identification of classes of stimuli or behavior where the timing of experimental parameters is known or pre-designated. Real world experience, however, is spontaneous, and to this end we describe an experiment predicting the occurrence, timing, and types of visual stimuli perceived by a human subject from electrocorticographic recordings. All 300 of 300 presented stimuli were correctly detected, with a temporal precision of order 20 ms. The type of stimulus (face/house) was correctly identified in 95% of these cases. There were approximately 20 false alarm events, corresponding to a late 2nd neuronal response to a previously identified event.

Three cases of feature correlation in an electrocorticographic BCI.

Three human subjects participated in a closed-loop brain computer interface cursor control experiment mediated by implanted subdural electrocorticographic arrays. The paradigm consisted of several stages: baseline recording, hand and tongue motor tasks as the basis for feature selection, two closed-loop one-dimensional feedback experiments with each of these features, and a two-dimensional feedback experiment using both of the features simultaneously. The two selected features were simple channel and frequency band combinations associated with change during hand and tongue movement. Inter-feature correlation and cross-correlation between features during different epochs of each task were quantified for each stage of the experiment. Our anecdotal, three subject, result suggests that while high correlation between horizontal and vertical control signal can initially preclude successful two-dimensional cursor control, a feedback-based learning strategy can be successfully employed by the subject to overcome this limitation and progressively decorrelate these control signals.