Investigating directed influences between activated brain areas in a motor-response task using fMRI

Localization of cognitive processes is a strength of functional neuroimaging. However, information about functional interactions between brain areas is crucial for a deeper understanding of brain function. We applied vector autoregressive modeling in the context of Granger causality as a method to analyze directed connectivity in a standard event-related fMRI study using a simple auditory-motor paradigm. The basic idea is to use temporal information in stochastic time series of a brain region in order to predict signal time courses in other brain regions. Thus, we predicted that the method should demonstrate causal influence of the auditory cortex and the supplementary motor area (SMA) on primary motor cortex. Eleven right-handed healthy female subjects were instructed to press a ball with either their left or their right hand when hearing the command "left" or "right" in the scanner. Influence to the left motor cortex was found from bilateral auditory cortex as well as from the SMA in 9 of 11 subjects. Granger causality to the right motor cortex existed from bilateral auditory cortex in 5 and from SMA in 6 subjects. Granger causality to the SMA existed from right auditory cortex in 7 subjects and from left auditory cortex in 8 subjects. Our findings in a simple task show that even under suboptimal circumstances (a relatively long TR of 2440 ms), Granger causality can be a useful tool to explore effective connectivity. Temporally optimized scanning should increase that potential.     

A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging

Granger causality model (GCM) derived from multivariate vector autoregressive models of data has been employed to identify effective connectivity in the human brain with functional magnetic resonance imaging (fMRI) and to reveal complex temporal and spatial dynamics underlying a variety of cognitive processes. In the most recent fMRI effective connectivity measures, pair-wise GCM has commonly been applied based on single-voxel values or average values from special brain areas at the group level. Although a few novel conditional GCM methods have been proposed to quantify the connections between brain areas, our study is the first to propose a viable standardized approach for group analysis of fMRI data with GCM. To compare the effectiveness of our approach with traditional pair-wise GCM models, we applied a well-established conditional GCM to preselected time series of brain regions resulting from general linear model (GLM) and group spatial kernel independent component analysis of an fMRI data set in the temporal domain. Data sets consisting of one task-related and one resting-state fMRI were used to investigate connections among brain areas with the conditional GCM method. With the GLM-detected brain activation regions in the emotion-related cortex during the block design paradigm, the conditional GCM method was proposed to study the causality of the habituation between the left amygdala and pregenual cingulate cortex during emotion processing. For the resting-state data set, it is possible to calculate not only the effective connectivity between networks but also the heterogeneity within a single network. Our results have further shown a particular interacting pattern of default mode network that can be characterized as both afferent and efferent influences on the medial prefrontal cortex and posterior cingulate cortex. These results suggest that the conditional GCM approach based on a linear multivariate vector autoregressive model can achieve greater accuracy in detecting network connectivity than the widely used pair-wise GCM, and this group analysis methodology can be quite useful to extend the information obtainable in fMRI.     

Percolation model, Sherrington-Kirkpatrick model and localization-delocalization model of spin glass transition: A comparative study

We recast the original results of our percolation model of the spin glass transition into alternative forms so as to reveal some apparent “similarities” with the Sherrington-Kirkpatrick model. However, because of the basic difference in the nature of the interactions in the two models, the reason for these “similarities” remains unclear. A close relation between the percolation model of the spin glass transition and the localization-decolization transition is also discussed qualitatively.     

Hemodynamic response (BOLD/fMRI) in focal epilepsy with reference to benzodiazepine effect

We studied a new procedure of BOLD/fMRI acquisition in epilepsy. They use the benzodiazepine effect to achieve a more reliable baseline for statistical analysis. The method works only in the MR domain without EEG correlation. It compares the EPI images during interictal epileptic discharges and the images “inactivated” by benzodiazepine.

The results in five out of eight patients show that this procedure in comparison with the EEG/fMRI method gives a net improvement of spatial definition of BOLD areas. These preliminary results seem to confirm the hypothesis that the better BOLD/fMRI procedure in epilepsy is to make use of physical features of MR that, unlike EEG, is not influenced by the distance of intercerebral sources and consequently allows a more complete and undistorted display of BOLD areas.     

Zigzag wall dynamics in uniaxial in-plane magnetic thin films

An unusual right/left zigzag wall propagation in the bias (transverse) and ac fields applied simultaneously is observed. A dynamic model based on the variable coercivity, effective transverse field, transformation of the walls from asymmetric Bloch into asymmetric Néel type (and vice versa) is proposed. Degeneration of two segments of one “zig” (or “zag”) which “sense” differently the transverse field is one of the crucial point of the zigzag dynamics.     

Real-time MR artifacts filtering during continuous EEG/fMRI acquisition

The purpose of this study was the development of a real-time filtering procedure of MRI artifacts in order to monitor the EEG activity during continuous EEG/fMRI acquisition. The development of a combined EEG and fMRI technique has increased in the past few years. Preliminary “spike-triggered” applications have been possible because in this method, EEG knowledge was only necessary to identify a trigger signal to start a delayed fMRI acquisition. In this way, the two methods were used together but in an interleaved manner. In real simultaneous applications, like event-related fMRI study, artifacts induced by MRI events on EEG traces represent a substantial obstacle for a right analysis. Up until now, the methods proposed to solve this problem are mainly based on procedures to remove post-processing artifacts without the possibility to control electrophysiological behavior of the patient during fMRI scan. Moreover, these methods are not characterized by a strong “prior knowledge” of the artifact, which is an imperative condition to avoid any loss of information on the physiological signals recovered after filtering. In this work, we present a new method to perform simultaneous EEG/fMRI study with real-time artifacts filtering characterized by a procedure based on a preliminary analytical study of EPI sequence parameters-related EEG-artifact shapes. Standard EEG equipment was modified in order to work properly during ultra-fast MRI acquisitions. Changes included: high-performance acquisition device; electrodes/cap/wires/cables materials and geometric design; shielding box for EEG signal receiver; optical fiber link; and software. The effects of the RF pulse and time-varying magnetic fields were minimized by using a correct head cap wires-locked environment montage and then removed during EEG/fMRI acquisition with a subtraction algorithm that takes in account the most significant EPI sequence parameters. The on-line method also allows a further post-processing utilization.     

Acoustic Analyses of Developmental Changes and Emotional Expression in the Preverbal Vocalizations of Infants

The nonverbal vocal utterances of seven normally hearing infants were studied within their first year of life with respect to age- and emotion-related changes. Supported by a multiparametric acoustic analysis it was possible to distinguish one inspiratory and eleven expiratory call types. Most of the call types appeared within the first two months; some emerged in the majority of infants not until the 5th (“laugh”) or 7th month (“babble”). Age-related changes in acoustic structure were found in only 4 call types (“discomfort cry,” “short discomfort cry,” “wail,” “moan”). The acoustic changes were characterized mainly by an increase in harmonic-to-noise ratio and homogeneity of the call, a decrease in frequency range and a downward shift of acoustic energy from higher to lower frequencies. Emotion-related differences were found in the acoustic structure of single call types as well as in the frequency of occurrence of different call types. A change from positive to negative emotional state was accompanied by an increase in call duration, frequency range, and peak frequency (frequency with the highest amplitude within the power spectrum). Negative emotions, in addition, were characterized by a significantly higher rate of “crying,” “hic” and “ingressive vocalizations” than positive emotions, while positive emotions showed a significantly higher rate of “babble,” “laugh,” and “raspberry.”     

Occipital-parietal interactions during shifts of exogenous visuospatial attention: trial-dependent changes of effective connectivity

We studied neural interactions between brain areas involved in exogenous (stimulus-driven) control of visuospatial attention. With event-related functional magnetic resonance imaging (fMRI), we investigated changes of connectivity during shifts of spatial attention from an attended location to a previously unattended target location. Using a 3-T scanner, fMRI data were acquired from three healthy volunteers. According to a central visual cue, participants directed endogenous spatial attention to the left or the right visual hemifield for blocks of 56 s. Peripheral visual targets were presented unpredictably in either the attended hemifield (valid trials, 80%) or in the unattended hemifield (invalid trials, 20%) and participants performed a two-alternative forced-choice discrimination task with the target, irrespective of cue validity. In accordance with previous results, we found that the temporal–parietal junction (TPJ) mediates the shift of spatial attention toward stimuli presented at the unattended side (i.e., invalid trials). We critically studied the interaction between occipital areas responding to the visual stimuli and other brain regions in order to find regions functionally coupled with the occipital cortex during invalid trials. We found that the coupling between occipital areas processing visual stimuli and the TPJ selectively increased during invalid trials. Our results highlight how changes of connectivity between brain areas can describe attentional processes such as stimulus-driven shifts of spatial attention.     

Vulnerability in one-dimensional excitable media

Potentially life-threatening cardiac arrhythmias can be iniated with stimuli timed to occur during the “vulnerable window (VW)”. We defined VW as the time interval between the “conditioning” and “test” stimuli following in sequence, during which the test stimulus response propagates in only one direction. We show that the VW is a generic feature of excitable media and describe the relationship between the properties of an excitable medium and the VW. We present asymptotic results that reveal the sensitivity of the VW to both the propagation velocity of the conditioning wavefront and the recovery process parameters. We also have identified a critical length of medium that must be excited in order to reveal vulnerability. Analytical results are in agreement with numerical studies.     

The role of coincidence experiments in studying the nuclear continuum with high-energy electrons and protons

The Lee model of π-nucleon interactions is very simple, and, in a certain case, an exact solution of the problem of a meson scattering on two “nucleons” can be obtained. However, graphs involving crossed pions are absent in that solution. Because such crossed graphs are crucial in determining the form and character of the physical π-nucleus scattering solution, the Lee model should not be used in testing field theories of the pion-nucleus interaction.     

Participant intimacy : A cluster analysis of the intranuclear cascadet

The intranuclear cascade for relativistic nuclear collisions is analyzed in terms of “clusters” consisting of groups of nucleons which are dynamically linked to each other by violent interactions. The formation cross sections for the different cluster types as well as their intrinsic dynamics are studied and compared with the predictions of the linear cascade model (“rows-on-rows”).     

Electron-muon permutation symmetry and multiplicatively conserved lepton number in gauge theories

The similarity between the weak interactions of electron and muon is extended to the principle that all e and μ interactions in gauge models are invariant under e ↔ μ exchange. This necessitates the existence of two Higgs doublets φ_e and φ_μ, and an extended e ↔ μ permutation invariance. After symmetry-breaking, a multiplicatively conserved “permutation parity” π = ± 1 for all particles naturally emerges, with π_μ = −π_e = 1. The model forbids μ → eγ but predicts e⁻e⁻ → μ⁻μ⁻ mediated by π = −1 Higgs bosons at 10⁻¹¹ times the rate of typical weak cross sections.     

Nonconservation of total lepton number with scalar bosons

The role of scalar bosons is studied in connection with a violation of the number of fermions + antifermions. Some simple estimates of the transitions μ → eλ and μ → 3e are based upon a minimal extension of the “standard” gauge model of weak and electromagnetic interactions.     

Estimation of nonlinear transfer functions for fully developed turbulence

A statistical method for modeling the linear and quadratically nonlinear relationship between fluctuations monitored at two points in space or time in a turbulent medium is presented. This relationship is described with the aid of linear and quadratic transfer functions and the concept of coherency is extended to quantify the goodness of the quadratic model. A unique feature of the approach described in this paper is that it is valid for non-Gaussian “input” and “output” signals. The validity of the approach is demonstrated with simulation data. The method is applied to experimental data taken in the turbulent edge plasma of the TEXT tokamak. The results indicate a three wave process with energy transfer to large scale fluctuations. The estimation of transfer functions is a first step in quantitatively measuring coupling coefficients and the energy transfer.     

Completeness of “good” Bethe ansatz solutions of a quantum-group-invariant Heisenberg model

The sl_q(2) quantum-group-invariant Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into “good” and “bad” states. A “good” state may be described by a path of only “good” representations. It is shown that the “good” states are given by all “good” Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive-parity strings (in the language of Takahashi) are allowed. Applying Bethe's string-counting technique completeness of the “good” Bethe states is proven, i.e. the same number of states is found as the number of all restricted paths on the sl_q(2) Bratteli diagram. It is the first time that a “completeness” proof for an anisotropic quantum-invariant reduced Heisenberg model is performed.     

Diffusion imaging with paired CPMG sequences

We report a method for mapping apparent diffusion coefficients using two interleaved CPMG sequences. Image slice selection is performed prior to each sequence, allowing the use of non-selective “hard” refocussing pulses. Phase cycling of the slice-selection process for each projection minimizes out-of-slice contributions to echo amplitudes. This permits an accurate evaluation of both T₂ and apparent proton self-diffusion coefficients.     

Evaporation of droplets in the two-dimensional Ginzburg–Landau equation

We consider the problem of coarsening in two dimensions for the real (scalar) Ginzburg–Landau equation. This equation has exactly two stable stationary solutions, the constant functions +1 and −1. We assume most of the initial condition is in the “−1” phase with islands of “+1” phase. We use invariant manifold techniques to prove that the boundary of a circular island moves according to Allen–Cahn curvature motion law. We give a criterion for non-interaction of two arbitrary interfaces and a criterion for merging of two nearby interfaces.     

Analysis of the critical behaviour of curved regions in equilibrium shapes of in crystals

Crystal shapes near {111} facets have been analyzed on indium crystals in their equilibrium shape. These measurements are compared with two theoretical concepts of the critical behaviour of curved regions: the “Pokrovsky-Talapov transition” and the “mean field theory”. Taking into account, on the one hand, the inaccuracy of the experimental determination of the origin of the curved region and, on the other hand, the “window” of validity of the Pokrovsky-Talapov transition theory, the choice between the two theories is difficult. Nevertheless the analytical expression of the mean field theory reproduces surprisingly well all the points of the experimental profile.