Partial directed coherence: a new concept in neural structure determination

 This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality. Received: 25 April 2000 / Accepted in revised form: 13 November 2000     

NMR characteristics of intracellular K in the rat salivary gland: a 39K NMR study using double-quantum filtering

Intracellular K of the perfused rat mandibular salivary gland was measured by 39K NMR spectroscopy at 8.45 T. Multiple-quantum NMR arising from multiple-exponential decay was used to eliminate the resonance due to extracellular K in the perfused gland at 25 degrees C. The resonance due to intracellular K consisted of two Lorentzian signals stemming from the [spin 1/2 to -1/2] coherence (sharp resonance) and the [spin -1/2 to -3/2], [spin 3/2 to 1/2] coherences (broad resonance). The transverse relaxation time (T2) corresponding to the [spin 1/2 to -1/2] coherence was ca. 2.5 ms, and that corresponding to the [spin -1/2 to -3/2], [spin 3/2 to 1/2] coherences was ca. 0.4 ms. The relaxation time of the double-quantum coherence of rank 3 (originating from product operators like Ix2Iz) was determined to be ca. 0.2 ms. These results suggest the possibility of the presence of a single homogeneous population of intracellular K with a correlation time of ca. 2.5 x 10(-8) s and a quadrupolar coupling constant of ca. 1.4 MHz.     

Measurement of intracellular Na in the rat salivary gland: a 23Na-NMR study using double quantum filtering

23Na in the prefused rat mandibular salivary gland was measured by spin-echo double quantum filter 23Na-NMR spectroscopy at 8.45 T. Resonances due to the intracellular 23Na and the interstitial 23Na were observed in the perfused gland at 25 degrees C. The resonance due to intracellular 23Na consisted of two Lorentzian signals stemming from the [1/2 mean value of -1/2[ coherence (sharp resonance) and the [-1/2 mean value of -3/2[ and [3/2 mean value of 1/2[ coherences (broad resonance). The transverse relaxation rate constant corresponding to the [1/2 mean value of -1/2[ coherence was 95 +/- 4 s-1 and that corresponding to the [-1/2 mean value of -3/2[ and [3/2 mean value of 1/2[ coherences was 1360 +/- 75 s-1 (mean +/- S.E., n = 5). The resonance due to the interstitial 32Na had longer relaxation rate constants, and disappeared upon administration of dysprosium triethylenetetramine-N,N',N",N",N"'-hexaacetic acid.     

Removal of zero-quantum interference in NOESY spectra of proteins by utilizing the natural inhomogeneity of the radiofrequency field

Summary A single scan method for the suppression of signals arising from zero-quantum coherences (ZQC) is analysed with respect to its application to NMR experiments on proteins. The ZQC are dephased during a spinlock period due to the natural RF inhomogeneity of a commercial probe. A quantitative analysis of a ZQC-compensated NOESY experiment is given. Although the build-up curve for the cross peaks in ZQC-compensated NOESY experiments differ from those in uncompensated experiments, interproton distances in medium-sized proteins can be evaluated with high accuracy. The proposed method is compared with other techniques for ZQC suppression.     

Generation and relaxation of high rank coherences in AX<Subscript>3</Subscript> systems in a selectively methionine labelled SH2 domain

The usefulness of selective isotope labelling patterns is demonstrated using the C-terminal SH2 domain of PLC-γ1 selectively ¹³C labelled at methionine methyl groups. We demonstrate the generation and relaxation of coherences that are second rank in protons and first rank in carbons that derive from quadrupolar order in protons. The decay rates of second rank double quantum proton coherences are measured. These terms exhibit fewer channels for cross-correlated relaxation compared to single quantum coherences. Our results indicate the potential application of the measurement of high order proton coherences to the analysis of dynamics in methyl-bearing side chains.     

Face to phase: pitfalls in time delay estimation from coherency phase

Coherency phase is often interpreted as a time delay reflecting a transmission delay between spatially separated neural populations. However, time delays estimated from corticomuscular coherency are conflicting and often shorter than expected physiologically. Recent work suggests that corticomuscular coherence is influenced by afferent sensory feedback and bidirectional interactions. We investigated how bidirectional interaction affects time delay estimated from coherency, using a feedback model of the corticomuscular system. We also evaluated the effect of bidirectional interaction on two popular directed connectivity measures: directed transfer function (DTF) and partial directed coherence (PDC). The model is able to reproduce the range of time delays found experimentally from coherency phase by varying the strengths of the efferent and afferent pathways and the recording of sensory feedback in the cortical signal. Both coherency phase and DTF phase were affected by sensory feedback, resulting in an underestimation of the transmission delay. Coherency phase was altered by the recording of sensory feedback in the cortical signals and both measures were affected by the presence of a closed loop feedback system. Only PDC phase led to the correct estimation of efferent transmission delay in all simulated model configurations. Coherency and DTF phase should not be used to estimate transmission delays in neural networks as the estimated time delays are meaningless in the presence of sensory feedback and closed feedback loops.     

A new interpretation of P300 responses upon analysis of coherences

Previous studies on cognitive dynamics showed that oscillatory responses of P300 are composed of mainly delta and theta responses. In the present study, for the first time, the long-distance intra-hemispheric event related coherence (auditory oddball paradigm) and evoked coherence (simple sound) were compared in order to evaluate the effects of cognitive tasks on the long-distance coherences. Seventeen healthy subjects (8 female, 9 male) were included in the study. The coherence was analyzed for delta (1–3.5 Hz), theta (4–7.5 Hz) and alpha (8–13 Hz) frequency ranges for (F₃-P₃, F₄-P₄, F₃-T₇, F₄-T₈, F₃-O_1, F₄-O₂) electrode pairs. The coherence to target responses were higher than the non-target and simple auditory response coherence. This difference is significant for the delta coherence for both hemispheres and for theta coherences over the left hemisphere. The highest coherences were recorded at fronto-temporal locations for all frequency bands (delta, theta, alpha). Furthermore, fronto-parietal coherences were higher than the fronto-occipital coherences for all frequency bands (delta, theta, alpha).These results show that the fronto-temporal and fronto-parietal connections are most relevant for the identification of the target signal. This analysis open the way for a new interpretation of dynamic localization results during cognitive tasks.     

On the spectral formulation of Granger causality

Spectral measures of causality are used to explore the role of different rhythms in the causal connectivity between brain regions. We study several spectral measures related to Granger causality, comprising the bivariate and conditional Geweke measures, the directed transfer function, and the partial directed coherence. We derive the formulation of dependence and causality in the spectral domain from the more general formulation in the information-theory framework. We argue that the transfer entropy, the most general measure derived from the concept of Granger causality, lacks a spectral representation in terms of only the processes associated with the recorded signals. For all the spectral measures we show how they are related to mutual information rates when explicitly considering the parametric autoregressive representation of the processes. In this way we express the conditional Geweke spectral measure in terms of a multiple coherence involving innovation variables inherent to the autoregressive representation. We also link partial directed coherence with Sims' criterion of causality. Given our results, we discuss the causal interpretation of the spectral measures related to Granger causality and stress the necessity to explicitly consider their specific formulation based on modeling the signals as linear Gaussian stationary autoregressive processes.     

The use of a multi-channel kalman filter algorithm in structural analysis of the epileptic EEG

An extension of the Kalman filter algorithm to the multi-channel case is presented and its application as a segmenting procedure in the analysis of the epileptic EEG is discussed. An analytical example of structural analysis, using the segments extracted by the proposed filter, is presented for a particular set of 4-channel EEG recordings. This analysis is shown to be especially fruitful if the autoregressive coefficients - a by product of the filtering procedure - are used to estimate the information flow between the channels by the calculation of partial as well as directed coherences for the representative segments.     

Dynamic regulation of IFN-gamma signaling in antigen-specific CD8+ T cells responding to infection

IFN-gamma plays a critical role in the CD8(+) T cell response to infection, but when and if this cytokine directly signals CD8(+) T cells during an immune response is unknown. We show that naive Ag-specific CD8(+) T cells receive IFN-gamma signals within 12 h after in vivo infection with Listeria monocytogenes and then become unresponsive to IFN-gamma throughout the ensuing Ag-driven expansion phase. Ag-specific CD8(+) T cells regain partial IFN-gamma responsiveness throughout the contraction phase, whereas the memory pool exhibits uniform, but reduced, responsiveness that is also modulated during the secondary response. The responsiveness of Ag-specific CD8(+) T cells to IFN-gamma correlated with modulation in the expression of IFN-gammaR2, but not with IFN-gammaR1 or suppressor of cytokine signaling-1. This dynamic regulation suggests that early IFN-gamma signals participate in regulation of the primary CD8(+) T cell response program, but that evading or minimizing IFN-gamma signals during expansion and the memory phase may contribute to appropriate regulation of the CD8(+) T cell response.     

Comparison of different methods of time shift measurement in EEG

Digital signal processing techniques are often used for measurement of small time shifts between EEG signals. In our work we tested properties of linear cross-correlation and phase/coherence method. The last mentioned method was used in two versions. The first version used fast Fourier transform (FFT) algorithm and the second was based on autoregressive modeling with fixed or adaptive model order. Methods were compared on several testing signals mimicking real EEG signals. The accuracy index for each method was computed. Results showed that for long signal segments all methods bring comparably good results. Accuracy of FFT phase/coherence method significantly decreased when very short segments were used and also decreased with an increasing level of the additive noise. The best results were obtained with autoregressive version of phase/coherence. This method is more reliable and may be used with high accuracy even in very short signals segments and it is also resistant to additive noise.     

基于大脑皮层信息传输的脑电信息图示方法

提出一种基于大脑皮层信息传输的脑电地形图示方法—脑电信息图（Ｂｒａｉｎ ＩｎｆｏｒｍａｔｉｏｎＭａｐｐｉｎｇ － ＢＩＭ） 。其原理是从不同导联电极上采集脑电信号经相空间重建构成头皮电位信息传输矩阵, 将各导联信息传输时间序列的信息传输量和复杂度数据绘制成头皮拓扑分布图, 以直观地反映脑电信息传输分布模式在不同时相中的变化进程。该方法不仅是从新的角度观察大脑功能变化, 而且可克服传统的脑电频谱分段地形图不能表达长程脑电模式变化的不足。对局限性癫痫病患者的试用表明,脑电信息图能较好地反映癫痫发作前后的信息传输动向和复杂度（Ｋｃ 、Ｃ１ 、Ｃ２） 的变化趋势。结果提示,脑电信息图（ＢＩＭ） 有可能成为一种新的观察大脑功能活动的图示诊断方法,值得进一步深入研究。     

Parametric and non-parametric modeling of short-term synaptic plasticity. Part I: Computational study

Parametric and non-parametric modeling methods are combined to study the short-term plasticity (STP) of synapses in the central nervous system (CNS). The nonlinear dynamics of STP are modeled by means: (1) previously proposed parametric models based on mechanistic hypotheses and/or specific dynamical processes, and (2) non-parametric models (in the form of Volterra kernels) that transforms the presynaptic signals into postsynaptic signals. In order to synergistically use the two approaches, we estimate the Volterra kernels of the parametric models of STP for four types of synapses using synthetic broadband input–output data. Results show that the non-parametric models accurately and efficiently replicate the input–output transformations of the parametric models. Volterra kernels provide a general and quantitative representation of the STP.     

Spectral analysis of spatial series of oceanographic variables

Time series of fluorescence, temperature, concentration of nitrite, and of nitrate+nitrite, obtained in the upwelling zone of northwest Africa, have been analysed by power spectral techniques, after application of a first difference filter. In three of the runs, coherence between fluorescence and temperature was significant at all frequencies lower than 0.04–0.13 cycles/min, while in another three runs, coherences showed a drop at low frequencies. Coherences between the remaining pairs of variables were significant at the lower frequencies studied in most of the cases. Significant coherences between nitrate+nitrite and temperature were found at wider frequency ranges than for fluorescence and temperature. Nitrite showed higher coherences with fluorescence and lower ones with temperature than nitrate+nitrite, as would be expected from the involvement of phytoplankton in the production of nitrite. In view of the results, some points concerning coherence between fluorescence and physical variables, as represented by temperature, are discussed.     

Exploring the dynamics of collective synchronizations in large ensembles of brain signals.

Developing methods characterizing the dynamics of synchronization in large ensemble of electromagnetic brain signals has become an important issue. In this article, we review a recently introduced method for analyzing multivariate phase synchronization in brain signals. The approach is based on the equivalence between phase locking and frequency locking in narrow band signals, which allows tracking multivariate phase synchronization in the time-frequency domain as periods of common frequency among multiple channels. The method is illustrated with simulations of multivariate phase dynamics in coupled oscillators and real multichannel electro- and magnetoencephalographic data recorded prior and during epileptic seizures. The reviewed results support the relevance of this method in the context of brain synchronization, in particular to track transient collective dynamics fluctuating in time, frequency and space.     

Superbinding: Spatio-temporal oscillatory dynamics

This paper presents superbinding, a concept that represents integrative oscillatory dynamics over the time and space axes. Principle of superposition describes integration over the temporal axis; selectively distributed and selectively coherent oscillatory neural populations describe integration over the spatial axis. Integrative activity is a function of the coherences between spatial locations of the brain; these coherences vary according to the type of sensory and or cognitive event and possibly the consciousness state of the species. Complex percepts and integrative activity in general that is achieved by superbinding supported by the neurons-brain theory may replace the Sherringtonian integrative brain function that is achieved through the single neuron doctrine.

Results of recent experiments related to the percept of the grandmother-face support our concept of super-synergy in the whole brain in order to explain manifestation of Gestalts and Memory-Stages. The strategies of the Grandmother paradigm may open new horizons in search of memories or evolving memories, and possibly provide relevant clinical applications.     

Cellular analysis of ocular circadian pacemaker coupling in Bulla: role of efferent impulses in phase shifting

The eyes of Bulla gouldiana, a marine snail, contain circadian oscillators that are coupled to each other. Obvious candidates for the coupling signals are the optic nerve compound action potentials (CAPs) that express the circadian rhythm and lead to efferent impulses in the contralateral optic nerve. In the present experiments, the role of the CAPs as coupling signals was evaluated. We found that, following desynchronization of the two ocular oscillators by phase-delaying one eye with manganese, subsequent phase shifts in the initially unshifted ocular rhythm only occurred during the time that efferent optic nerve signals were present. In addition, in the absence of ocular desynchrony, phase shifts of the ocular rhythm could still be effected by activation of the efferent pathway. The influence of efferent impulses on identified retinal cells was also evaluated. No effect of efferent signals on receptor layer cells was detected, while it was found that efferent impulses generated depolarizations in basal retinal neurons (BRNs), the putative circadian oscillator cells. Depolarization of the BRNs has been shown previously to be involved in the light entrainment pathway. Depolarization appears to be similarly involved in the coupling pathway, since membrane depolarizations that mimicked the efferent-induced postsynaptic potentials likewise generated phase shifts of the ocular rhythm.     

Partial phase synchronization of neural populations due to random Poisson inputs

We show that populations of identical uncoupled neurons exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. We characterize this partial synchronization using the phase distribution of the population, and consider analytical approximations and numerical simulations of phase-reduced models and the corresponding conductance-based models of typical Type I (Hindmarsh-Rose) and Type II (Hodgkin-Huxley) neurons, showing quantitatively how the extent of the partial phase synchronization depends on the magnitude and mean interspike frequency of the stimulus. Furthermore, we present several simple examples that disprove the notion that phase synchrony must be strongly related to spike synchrony. Instead, the importance of partial phase synchrony is shown to lie in its influence on the response of the population to stimulation, which we illustrate using first spike time histograms.