Larry B. Sorensen

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 from 80 to 500 Hz. This scaling index, , 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, , increases. We observe a “knee” in the spectra at , implying the existence of a characteristic time scale . Below , 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 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.

Surface speciation of calcite observed in situ by high-resolution X-ray reflectivity

High-resolution, in situ X-ray reflectivity measurements were made of the calcite (104)–water interface in calcite-saturated aqueous solutions at pH values ranging from 6.8 to 12.1 and low PCO2. The X-ray reflectivity data, taken over a momentum transfer range of 6 A−1, indicate that the calcite surface does not vary significantly over this range of experimental conditions. From an analysis of the data at pH 8.3, the best-fit reflectivity model requires the presence of 1.0 ± 0.4 monolayer of a hydroxyl species (OH or OH2) at 2.50 ± 0.12 A above the surface Ca ions and involves rotations of the surface carbonate groups toward the (104) plane. The X-ray reflectivity data for pH 6.8 and 12.1 can be explained without invoking changes other than protonation reactions in the surface speciation of terrace areas. This is consistent with scanning force microscopy studies of calcite growth and dissolution near equilibrium, which show that attachment and detachment of Ca and CO3 ions occurs primarily at step-edge kink sites. These results demonstrate how high-resolution X-ray reflectivity can be used for direct, in situ measurement of mineral surface structure, to provide strong constraints on chemical speciation and reactivity at the mineral-fluid interface.

Distribution of water molecules at Ag(111)/electrolyte interface as studied with surface X-ray scattering

The spatial distribution of water molecules at solid-electrolyte interfaces has received extensive theoretical study, due to the importance of this interface in electrochemistry and other sciences. Such studies suggest that adjacent to the interface water is arranged in several layers, that the molecular arrangements in the inner layer is similar to bulk water, and that the inner-layer molecules have an oxygen-up (oxygen-down) average orientation for negative (positive) electrode charge (or, equivalently, potential). However, little of this has been verified by experimental measurements. In this paper we report surface X-ray scattering measurements of the water distribution perpendicular to a Ag(111)-electrolyte interface in 0.1M NaF at two potentials: +0.52 and −0.23 V from the potential of zero charge (PZC) on the electrode. We find that, first, the water is ordered in layers extending about three molecular diameters from the electrode. Second, the extent of ordering and the distance between the electrode and first water layer depend on potential, the latter being consistent with an oxygen-up (oxygen-down) average molecular orientation for negative (positive) electrode potential. Third, the inner water layer contains 1.55 × 1015 (at −0.23 V) and 2.6 × 1015 (at +0.52 V) water molecules per cm−2, remarkably more than expected from the bulk water density (i.e., ∼ 1.15 × 1015cm−2). Such a large compression shows that the molecular arrangements in the inner layer are significantly different from bulk, which has not been anticipated in current models of charged, aqueous interfaces. We give a qualitative explanation of this large density as resulting from the strong electric field at the charged Ag(111) electrode and present a tentative model of the molecular arrangements.

High gamma mapping using EEG

High gamma (HG) power changes during motor activity, especially at frequencies above 70 Hz, play an important role in functional cortical mapping and as control signals for BCI (brain-computer interface) applications. Most studies of HG activity have used ECoG (electrocorticography) which provides high-quality spatially localized signals, but is an invasive method. Recent studies have shown that non-invasive modalities such as EEG and MEG can also detect task-related HG power changes. We show here that a 27 channel EEG (electroencephalography) montage provides high-quality spatially localized signals non-invasively for HG frequencies ranging from 83 to 101 Hz. We used a generic head model, a weighted minimum norm least squares (MNLS) inverse method, and a self-paced finger movement paradigm. The use of an inverse method enables us to map the EEG onto a generic cortex model. We find the HG activity during the task to be well localized in the contralateral motor area. We find HG power increases prior to finger movement, with average latencies of 462 ms and 82 ms before EMG (electromyogram) onset. We also find significant phase-locking between contra- and ipsilateral motor areas over a similar HG frequency range; here the synchronization onset precedes the EMG by 400 ms. We also compare our results to ECoG data from a similar paradigm and find EEG mapping and ECoG in good agreement. Our findings demonstrate that mapped EEG provides information on two important parameters for functional mapping and BCI which are usually only found in HG of ECoG signals: spatially localized power increases and bihemispheric phase-locking.

Lead adsorption at the calcite-water interface: Synchrotron x-ray standing wave and x-ray reflectivity studies

Abstract By combining synchrotron X-ray standing wave (XSW) measurements with synchrotron X-ray reflectivity measurements, we have determined: (1) the precise three-dimensional location within the calcite unit cell of submonolayer Pb ions adsorbed at the calcite (104) surface from dilute aqueous solutions, and (2) the precise one-dimensional location of these unit cells relative to the calcite surface. Our XSW measurements, using three separate calcite Bragg reflections for triangulation, show that most adsorbed Pb ions occupy Ca sites in the calcite lattice with an ordered coverage of 0.05 equivalent monolayers, while the remaining Pb ions are disordered with a coverage of 0.03 equivalent monolayers. Our X-ray reflectivity measurements show that the ordered Pb ions occur primarily (>70%) in the surface atomic layer of calcite. Atomic force microscopy (AFM) was used to characterize the topography of the calcite (104) surface under conditions similar to the X-ray experiments. The quantitative morphological information obtained by AFM was used to develop realistic models of the calcite surface. The calculated X-ray reflectivities for these model surfaces were compared with the measured X-ray reflectivities. The new combined X-ray method that we have developed can be used to determine the atomic-scale structure of other metals adsorbed at mineral-water interfaces. Such high-resolution structural determinations are essential before detailed conceptual and theoretical models can be further developed to understand and predict the behavior of dissolved metals in mineral-water systems.

Disorder-induced microscopic magnetic memory

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories.

Quasistatic X-Ray Speckle Metrology of Microscopic Magnetic Return-Point Memory

We have used coherent, resonant, x-ray magnetic speckle patterns to measure the statistical evolution of the microscopic magnetic domains in perpendicular magnetic films as a function of the applied magnetic field. Our work constitutes the first direct, ensemble-averaged study of microscopic magnetic return-point memory, and demonstrates the profound impact of interfacial roughness on this phenomenon. At low fields, the microscopic magnetic domains forget their past history with an exponential field dependence.

Quasi-periodic Fluctuations in Default Mode Network Electrophysiology

The study of human brain electrophysiology has extended beyond traditional frequency ranges identified by the classical EEG rhythms, encompassing both higher and lower frequencies. Changes in high-gamma-band (>70 Hz) power have been identified as markers of local cortical activity. Fluctuations at infra-slow (<0.1 Hz) frequencies have been associated with functionally significant cortical networks elucidated using fMRI studies. In this study, we examined infra-slow changes in band-limited power across a range of frequencies (1–120 Hz) in the default mode network (DMN). Measuring the coherence in band-limited power fluctuations between spatially separated electrodes makes it possible to detect small, spatially extended, and temporally coherent fluctuating components in the presence of much larger incoherent fluctuations. We show that the default network is characterized by significant high-gamma-band (65–110 Hz) coherence at infra-slow (<0.1 Hz) frequencies. This coherence occurs over a narrow frequency range, centered at 0.015 Hz, commensurate with the frequency of BOLD signal fluctuations seen by fMRI, suggesting that quasi-periodic, infra-slow changes in local cortical activity form the neurophysiological basis for this network.

Otavite-calcite solid-solution formation at the calcite-water interface studied in situ by synchrotron X-ray scattering

Abstract Synchrotron X-ray scattering measurements were performed in situ during the formation of thin (50–600 A) overgrowths of otavite-calcite solid-solutions at the (10 1 4) cleavage surface of single-crystal calcite. These solid-solutions were precipitated from EDTA-bearing aqueous solutions having varied initial saturation states of otavite and calcite. From repetitive X-ray diffraction scans, the Cd/(Ca + Cd) ratios and the effective thicknesses (average domain size perpendicular to the calcite cleavage surface) of the solid-solutions were determined as a function of time. Additional in-plane X-ray diffraction scans were done to further characterize the relationship between the solid-solutions and the calcite cleavage surface. The solid-solution phase grew epitaxially with a (1014) growth plane oriented parallel to the calcite (10 1 4) cleavage surface. The compositions of the solid-solutions evolved with time, while their growth rates (increases in effective thickness) remained fairly constant (10–54 A/hr). In each experiment, the coverage of the initial surface by the. solid-solution (calculated from the difference between the initial and final Cd concentrations in the aqueous solution) was about 20%. Glancing-incidence X-ray reflectivity scans were also monitored as a function of time. From these scans, we determined that the solid-water interface did not become significantly rougher during the nucleation and growth of the solid-solution phase. These observations indicate that the solid-solution grew by layer spreading and that most growth may have occurred preferentially at macrostep faces produced during cleavage.

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.