Testing methodologies for the nonlinear analysis of causal relationships in neurovascular coupling

We investigated the use and implementation of a nonlinear methodology for establishing which changes in neurophysiological signals cause changes in the blood oxygenation level-dependent (BOLD) contrast measured in functional magnetic resonance imaging. Unlike previous analytical approaches, which used linear correlation to establish covariations between neural activity and BOLD, we propose a directed information-theoretic measure, the transfer entropy, which can elucidate even highly nonlinear causal relationships between neural activity and BOLD signal. In this study we investigated the practicality of such an analysis given the limited data samples that can be collected experimentally due to the low temporal resolution of BOLD signals. We implemented several algorithms for the estimation of transfer entropy and we tested their effectiveness using simulated local field potentials (LFPs) and BOLD data constructed to match the main statistical properties of real LFP and BOLD signals measured simultaneously in monkey primary visual cortex. We found that using the advanced methods of entropy estimation implemented and described here, a transfer entropy analysis of neurovascular coupling based on experimentally attainable data sets is feasible.     

On the use of information theory for the analysis of the relationship between neural and imaging signals

Functional magnetic resonance imaging (fMRI) is a widely used method for studying the neural basis of cognition and of sensory function. A potential problem in the interpretation of fMRI data is that fMRI measures neural activity only indirectly, as a local change of deoxyhemoglobin concentration due to the metabolic demands of neural function. To build correct sensory and cognitive maps in the human brain, it is thus crucial to understand whether fMRI and neural activity convey the same type of information about external correlates. While a substantial experimental effort has been devoted to the simultaneous recordings of hemodynamic and neural signals, so far, the development of analysis methods that elucidate how neural and hemodynamic signals represent sensory information has received less attention. In this article, we critically review why the analytical framework of information theory, the mathematical theory of communication, is ideally suited to this purpose. We review the principles of information theory and explain how they could be applied to the analysis of fMRI and neural signals. We show that a critical advantage of information theory over more traditional analysis paradigms commonly used in the fMRI literature is that it can elucidate, within a single framework, whether an empirically observed correlation between neural and fMRI signals reflects either a similar stimulus tuning or a common source of variability unrelated to the external stimuli. In addition, information theory determines the extent to which these shared sources of stimulus signal and of variability lead fMRI and neural signals to convey similar information about external correlates. We then illustrate the formalism by applying it to the analysis of the information carried by different bands of the local field potential. We conclude by discussing the current methodological challenges that need to be addressed to make the information-theoretic approach more robustly applicable to the simultaneous recordings of neural and imaging data.     

Non-spherical sources of static gravitational fields: Investigating the boundaries of the no-hair theorem

A new, globally regular model describing a static, non spherical gravitating object in General Relativity is presented. The model is composed by a vacuum Weyl–Levi-Civita special field – the so called gamma metric – generated by a regular static distribution of mass-energy. Standard requirements of physical reasonableness such as, energy, matching and regularity conditions are satisfied. The model is used as a toy in investigating various issues related to the directional behavior of naked singularities in static spacetimes and the black hole (Schwarzschild) limit.     

Coupling of neural activity and fMRI-BOLD in the motion area MT

The fMRI-BOLD contrast is widely used to study the neural basis of sensory perception and cognition. This signal, however, reflects neural activity only indirectly, and the detailed mechanisms of neurovascular coupling and the neurophysiological correlates of the BOLD signal remain debated. Here we investigate the coupling of BOLD and electrophysiological signals in the motion area MT of the macaque monkey by simultaneously recording both signals. Our results demonstrate that a prominent neuronal response property of area MT, so-called motion opponency, can be used to induce dissociations of BOLD and neuronal firing. During the presentation of a stimulus optimally driving the local neurons, both field potentials [local field potentials (LFPs)] and spiking activity [multi-unit activity (MUA)] correlated with the BOLD signal. When introducing the motion opponency stimulus, however, correlations of MUA with BOLD were much reduced, and LFPs were a much better predictor of the BOLD signal than MUA. In addition, for a subset of recording sites we found positive BOLD and LFP responses in the presence of decreases in MUA, regardless of the stimulus used. Together, these results demonstrate that correlations between BOLD and MUA are dependent on the particular site and stimulus paradigm, and foster the notion that the fMRI-BOLD signal reflects local dendrosomatic processing and synaptic activity rather than principal neuron spiking responses.     

Coupling of simultaneously acquired electrophysiological and haemodynamic responses during visual stimulation

We investigate the relationship between the temporal variation in the magnitude of occipital visual evoked potentials (VEPs) and of haemodynamic measures of brain activity obtained using both blood oxygenation level dependent (BOLD) and perfusion sensitive (ASL) functional magnetic resonance imaging (fMRI). Volunteers underwent a continuous BOLD fMRI scan and/or a continuous perfusion-sensitive (gradient and spin echo readout) ASL scan, during which 30 second blocks of contrast reversing visual stimuli (at 4 Hz) were interleaved with 30 second blocks of rest (visual fixation). Electroencephalography (EEG) and fMRI were simultaneously recorded and following EEG artefact cleaning, VEPs were averaged across the whole stimulation block (120 reversals, VEP₁₂₀) and at a finer timescale (15 reversals, VEP₁₅). Both BOLD and ASL time-series were linearly modelled to establish: (1) the mean response to visual stimulation, (2) transient responses at the start and end of each stimulation block, (3) the linear decrease between blocks, (4) the nonlinear between-block variation (covariation with VEP₁₂₀), (5) the linear decrease within block and (6) the nonlinear variation within block (covariation with VEP₁₅).     

Comparison of stochastic resonance in static and dynamical nonlinearities

We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution.     

Regional homogeneity of resting-state fMRI contributes to both neurovascular and task activation variations

The task induced blood oxygenation level dependent signal changes observed using functional magnetic resonance imaging (fMRI) are critically dependent on the relationship between neuronal activity and hemodynamic response. Therefore, understanding the nature of neurovascular coupling is important when interpreting fMRI signal changes evoked via task. In this study, we used regional homogeneity (ReHo), a measure of local synchronization of the BOLD time series, to investigate whether the similarities of one voxel with the surrounding voxels are a property of neurovascular coupling. FMRI scans were obtained from fourteen subjects during bilateral finger tapping (FTAP), digit–symbol substitution (DSST) and periodic breath holding (BH) paradigm. A resting-state scan was also obtained for each of the subjects for 4 min using identical imaging parameters. Inter-voxel correlation analyses were conducted between the resting-state ReHo, resting-state amplitude of low frequency fluctuations (ALFF), BH responses and task activations within the masks related to task activations. There was a reliable mean voxel-wise spatial correlation between ReHo and other neurovascular variables (BH responses and ALFF). We observed a moderate correlation between ReHo and task activations (FTAP: r = 0.32; DSST: r = 0.22) within the task positive network and a small yet reliable correlation within the default mode network (DSST: r = − 0.08). Subsequently, a linear regression was used to estimate the contribution of ReHo, ALFF and BH responses to the task activated voxels. The unique contribution of ReHo was minimal. The results suggest that regional synchrony of the BOLD activity is a property that can explain the variance of neurovascular coupling and task activations; but its contribution to task activations can be accounted for by other neurovascular factors such as the ALFF.     

An investigation of the relationship between BOLD and perfusion signal changes during epileptic generalised spike wave activity

In pathological conditions interpretation of functional magnetic resonance imaging (fMRI) results can be difficult. This is due to a reliance on the assumed coupling between neuronal activity and changes in cerebral blood flow (CBF) and oxygenation. We wanted to investigate the coupling between blood oxygen level dependant contrast (BOLD) and CBF time courses in epilepsy patients with generalised spike wave activity (GSW) to better understand the underlying mechanisms behind the EEG-fMRI signal changes observed, especially in regions of negative BOLD response (NBR). Four patients with frequent GSW were scanned with simultaneous electroencephalographic (EEG)-fMRI with BOLD and arterial spin labeling (ASL) sequences. We examined the relationship between simultaneous CBF and BOLD measurements by looking at the correlation of the two signals in terms of percentage signal change on a voxel-by-voxel basis. This method is not reliant on coincident activation. BOLD and CBF were positively correlated in patients with epilepsy during background EEG activity and GSW. The subject average value of the Delta CBF/Delta BOLD slope lay between +19 and +36 and also showed spatial variation which could indicate areas with altered vascular response. There was not a significant difference between Delta CBF/Delta BOLD during GSW, suggesting that neurovascular coupling to BOLD signal is generally maintained between states and, in particular, within areas of NBR.     

Comparison of dispersion mapping techniques with fiber nonlinearities in carrier suppressed RZ systems

In this paper, the dispersion maps are compared in the presence of fiber nonlinearities in 10 and 40 Gbps carrier suppressed return to zero (CS-RZ) systems. It is observed that the hybrid-compensation is the best dispersion mapping technique, which reduces the BER produced due to the fiber nonlinearities to the more extent than that of pre-compensation and the post-compensation. This technique increases the repeater length almost up to double than that of pre- and post-compensation. The pre-compensation shows the highest BER followed by post-compensation.. It is also observed that with increase in the input bit rate, the BER for all three compensation techniques is also increased. But the still the hybrid-compensation reduce the BER up to more extent. The BER also increases with the increase in input optical power due to nonlinear impairments on the link at high powers.     

Incomplete double frequency sweeps to select small quadrupolar coupling static powder patterns

Difference spectra based on the magnitude of the quadrupolar coupling of a site has been observed under static conditions utilizing a double frequency sweep pulse sequence to enhance the central transition of a small electric field gradient (EFG) environment. Through the use of convergent sweeps that only cover the inner satellite transitions of the smaller EFG site, an echo spectrum results that favors the smaller site, which can then be used in conjunction with normal echo spectra to create a difference spectrum that consists primarily of the smaller site. The simplification of the static lineshape data permits simulation for the extraction of chemical shift anisotropy (CSA) information for the site. The method is demonstrated using ⁹³Nb NMR for samples with multiple niobium environments due to mixtures of compounds, MgNb₂O₆/LiNbO₃, or due to crystallographic structure, KCa₂Nb₃O₁₀.     

On higher order computations in strong coupling

An algorithm which simplifies manipulation of higher order graphs in strong coupling is presented.     

Tesla变压器耦合系数的静磁场解法

 为研究Tesla变压器耦合系数与各参量的关系,采用静磁场分析方法,从柱坐标系磁场Laplace方程出发,推导出磁场级数表达式的系数矩阵方程组,计算出磁芯磁场的轴向分布和间隙磁场的轴向、径向分布。引入了一种平均耦合系数概念——次级绕组每匝线圈具有独立的耦合系数,用全部单匝耦合系数的平均值作为Tesla变压器的耦合系数。重点研究了平均耦合系数与磁芯纵横比、半径比、初级绕组-磁芯长度比、磁芯材料磁导率的相对变化关系。结果表明:增大纵横比、减小半径比是提高Tesla变压器耦合系数的有效方法;增大磁芯材料的磁导率可提高耦合系数,但效果随磁导率增大而降低;初级绕组长度与磁芯长度之比约为0.7时,耦合系数达到最大值。     

Effect of fibre nonlinearities in a WDM transmission system

In this paper the combined effect of major fibre nonlinearities at low data rates like stimulated Raman scattering and four wave mixing has been studied in a WDM transmission system. Analysis has been carried out to evaluate the signal to noise ratio in the presence of amplifier spontaneous emission noise. The system parameters such as interchannel separation, interamplifier separation have been estimated so as to get maximum signal to noise ratio.     

Signal fluctuations in fMRI data acquired with 2D-EPI and 3D-EPI at 7 Tesla

Segmented three-dimensional echo planar imaging (3D-EPI) provides higher image signal-to-noise ratio (SNR) than standard single-shot two-dimensional echo planar imaging (2D-EPI), but is more sensitive to physiological noise. The aim of this study was to compare physiological noise removal efficiency in single-shot 2D-EPI and segmented 3D-EPI acquired at 7 Tesla. Two approaches were investigated based either on physiological regressors (PR) derived from cardiac and respiratory phases, or on principal component analysis (PCA) using additional resting-state data. Results show that, prior to physiological noise removal, 2D-EPI data had higher temporal SNR (tSNR), while spatial SNR was higher in 3D-EPI. Blood oxygen level dependent (BOLD) sensitivity was similar for both methods. The PR-based approach allowed characterization of relative contributions from different noise sources, confirming significant increases in physiological noise from 2D to 3D prior to correction. Both physiological noise removal approaches produced significant increases in tSNR and BOLD sensitivity, and these increases were larger for 3D-EPI, resulting in higher BOLD sensitivity in the 3D-EPI than in the 2D-EPI data. The PCA-based approach was the most effective correction method, yielding higher tSNR values for 3D-EPI than for 2D-EPI postcorrection.     

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.     

The effect of 2.1 T static magnetic field on astrocyte viability and morphology

The viability and a number of morphological properties of in situ astrocytes of rat spinal cord cultures including changes in surface area and migration of both cell body and nucleus were investigated at magnetic field intensities comparable to those currently used for magnetic resonance imaging. Viability of rat spinal astrocytes was studied after up to 72 hours of 2.1T static magnetic field exposure. Surface areas and two-dimensional centroids of both soma and nucleus after 2 hours of magnetic field exposure were determined and compared with those of the same cells before magnetic field exposure. Cell membrane ruffling was quantified using fractal analysis.     

Intra-channel nonlinearities mitigation in pseudo-linear coherent QPSK transmission systems via nonlinear electrical equalizer

A novel nonlinear electrical equalizer (NLEE) based on Volterra theory is proposed for mitigating intra-channel nonlinearities in pseudo-linear coherent optical communication systems. According to the temporal matching condition of intra-channel nonlinear pulse interactions, we just select specific nonlinear terms and reduce the computation complexity considerably. Numerical simulations of 10GBaud coherent quadrature phase-shift keying (QPSK) transmission show that the simplified NLEE can efficiently mitigate intra-channel nonlinearities.     

Assessment of spatial BOLD sensitivity variations in fMRI using gradient-echo field maps

Clinical blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) is becoming increasingly valuable in, e.g., presurgical planning, but the commonly used gradient-echo echo-planar imaging (GE-EPI) technique is sometimes hampered by macroscopic field inhomogeneities. This can affect the degree of signal change that will occur in the GE-EPI images as a response to neural activation and the subsequent blood oxygenation changes, i.e., the BOLD sensitivity (BS). In this study, quantitative BS maps were calculated directly from gradient-echo field maps obtainable on most clinical scanners. In order to validate the accuracy of the calculated BS-maps, known shim gradients were applied and field maps and GE-EPI images of a phantom were acquired. Measured GE-EPI image intensity was then compared with the calculated (predicted) image intensity (pII) which was obtained from the field maps using theoretical expressions for image-intensity loss. The validated expressions for pII were used to calculate the corresponding predicted BOLD sensitivity (pBS) maps in healthy volunteers. Since the field map is assumed to be valid throughout an entire fMRI experiment, the influence of subject motion on the pBS maps was also assessed. To demonstrate the usefulness of such maps, pBS was investigated for clinically important functional areas including hippocampus, Broca's area and primary motor cortex. A systematic left/right pBS difference was observed in Broca's area and in the hippocampus, most likely due to magnetic field inhomogeneity of the particular MRI-system used in this study. For all subjects, the hippocampus showed pBS values above unity with a clear anterior–posterior gradient and with an abrupt drop to zero pBS in the anterior parts of hippocampus. It is concluded that GE field maps can be used to accurately predict BOLD sensitivity and that this parameter is useful to assess spatial variations which will influence fMRI experiments.     

Decreases in ADC observed in tissue areas during activation in the cat visual cortex at 9.4 T using high diffusion sensitization

Recent studies in the human visual cortex using diffusion-weighted functional magnetic resonance imaging (fMRI) have suggested that the apparent diffusion coefficient (ADC) decreases, in contrast to earlier studies that consistently reported ADC increases during neuronal activation. The changes, in either case, are hypothesized to provide the ability to improve the spatial specificity of fMRI over conventional blood-oxygenation-level-dependent (BOLD) methods. Most recently, the ADC decreases have been suggested as originating from transient cell swelling caused by either shrinkage of the extracellular space or some intracellular neuronal process that precedes the hemodynamic response. All of these studies have been conducted in humans and at lower magnetic fields, which can be limited by the signal-to-noise ratio (SNR). The low SNR can lead to significant partial-volume effects because of the lower spatial resolutions required to attain sufficient SNR in diffusion-weighted images. Human studies also have the potential confound of motion. At high magnetic fields and in animal model studies, these limitations are alleviated. At high fields, SNR increases, tissue signals are enhanced and signal changes inside the blood are significantly reduced compared to lower fields. In this work, we were able to measure a small but significant ADC decrease in tissue areas, in conjunction with brain activation in the cat visual cortex at 9.4 T when using highly diffusion-weighted images (b>1200 s/mm2) where intravascular effects are minimal. When using low b-values, delayed increases in the tissue ADC during activation were observed. No significant changes in ADC were observed in surface vessels for any diffusion weighting. Furthermore, we did not observe any temporal differences in the highly diffusion-weighted data compared to BOLD; however, although the changes may likely be vascular in nature, they are highly localized to the tissue areas.     

Recent advances in phase matching of second‐order nonlinearities in monolithic semiconductor waveguides

Techniques used to assist phase matching of second‐order nonlinearities in semiconductor waveguides are reviewed. The salient points of each method are highlighted, with their strengths and weaknesses with regard to various key applications discussed. Recent progress in these techniques is also reviewed. Emphasis is placed on two techniques, namely quasi‐phase matching via domain disordering utilizing quantum well intermixing, and exact phase matching using Bragg reflection waveguides.