Autoregulation of blood flow drives early hypotension in a rat model of systemic inflammation induced by bacterial lipopolysaccharide.

Uncontrolled vasodilation is known to account for hypotension in the advanced stages of sepsis and other systemic inflammatory conditions, but the mechanisms of hypotension in earlier stages of such conditions are not clear. By monitoring hemodynamics with the highest temporal resolution in unanesthetized rats, in combination with ex-vivo assessment of vascular function, we found that early development of hypotension following injection of bacterial lipopolysaccharide is brought about by a fall in vascular resistance when arterioles are still fully responsive to vasoactive agents. This approach further uncovered that the early development of hypotension stabilized blood flow. We thus hypothesized that prioritization of the local mechanisms of blood flow regulation (tissue autoregulation) over the brain-driven mechanisms of pressure regulation (baroreflex) underscored the early development of hypotension in this model. Consistent with this hypothesis, an assessment of squared coherence and partial-directed coherence revealed that, at the onset of hypotension, the flow-pressure relationship was strengthened at frequencies (<0.2 Hz) known to be associated with autoregulation. The autoregulatory escape to phenylephrine-induced vasoconstriction, another proxy of autoregulation, was also strengthened in this phase. The competitive demand that drives prioritization of flow over pressure regulation could be edema-associated hypovolemia, as this became detectable at the onset of hypotension. Accordingly, blood transfusion aimed at preventing hypovolemia brought the autoregulation proxies back to normal and prevented the fall in vascular resistance. This novel hypothesis opens a new avenue of investigation into the mechanisms that can drive hypotension in systemic inflammation.

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat.

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

Frequency Domain Repercussions of Instantaneous Granger Causality.

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC's repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected.

Partial directed coherence: twenty years on some history and an appraisal.

Here while we reminisce about how partial directed coherence was proposed, its motivation and evolution, we take the opportunity to relate it to some of its kin quantities and some of its offspring. Emphasis is placed on our development of asymptotic criteria to place it as a reliable investigation tool, where the connectivity detection problem is completely solved as opposed to what we call the characterization problem. We end by musing over some points now on our wishlist.

Kernel Methods for Nonlinear Connectivity Detection.

In this paper, we show that the presence of nonlinear coupling between time series may be detected using kernel feature space F representations while dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. This is done by showing that the kernelized auto/cross sequences in F can be computed from the model rather than from prediction residuals in the original data space X . Furthermore, this allows for reducing the connectivity inference problem to that of fitting a consistent linear model in F that works even in the case of nonlinear interactions in the X -space which ordinary linear models may fail to capture. We further illustrate the fact that the resulting F -space parameter asymptotics provide reliable means of space model diagnostics in this space, and provide straightforward Granger connectivity inference tools even for relatively short time series records as opposed to other kernel based methods available in the literature.

Backward renormalization-group inference of cortical dipole sources and neural connectivity efficacy.

Proper neural connectivity inference has become essential for understanding cognitive processes associated with human brain function. Its efficacy is often hampered by the curse of dimensionality. In the electroencephalogram case, which is a noninvasive electrophysiological monitoring technique to record electrical activity of the brain, a possible way around this is to replace multichannel electrode information with dipole reconstructed data. We use a method based on maximum entropy and the renormalization group to infer the position of the sources, whose success hinges on transmitting information from low- to high-resolution representations of the cortex. The performance of this method compares favorably to other available source inference algorithms, which are ranked here in terms of their performance with respect to directed connectivity inference by using artificially generated dynamic data. We examine some representative scenarios comprising different numbers of dynamically connected dipoles over distinct cortical surface positions and under different sensor noise impairment levels. The overall conclusion is that inverse problem solutions do not affect the correct inference of the direction of the flow of information as long as the equivalent dipole sources are correctly found.

Directed Transfer Function: Unified Asymptotic Theory and Some of Its Implications.

OBJECTIVE: To present a unified mathematical derivation of the frequency-dependent asymptotic behavior of the three main forms of directed transfer function (DTF). METHODS: A synthesis of the results (proved in an extended Appendix) is followed by a series of Monte Carlo simulations of representative examples. RESULTS: DTF estimators are asymptotically normal when the true values are different from zero. Under the null hypothesis H0: DTF=0, the estimator is distributed as a linear combination of independent χ21 variables. CONCLUSIONS: Null DTF rejection is shown to be achievable with identical performance irrespective of which DTF form is adopted. SIGNIFICANCE: Together with recent allied partial directed coherence results, this paper rounds up connectivity inference tools for a class of frequency-domain connectivity estimators.

Source and sink nodes in absence seizures.

As opposed to focal epilepsy, absence seizures do not exhibit a clear seizure onset zone or focus since its ictal activity rapidly engages both brain hemispheres. Yet recent graph theoretical analysis applied to absence seizures EEG suggests the cortical focal presence, an unexpected feature for this type of epilepsy. In this study, we explore the characteristics of absence seizure by classifying the nodes as to their source/sink natures via weighted directed graph analysis based on connectivity direction and strength estimation using information partial directed coherence (iPDC). By segmenting the EEG signals into relatively short 5-sec-long time windows we studied the evolution of coupling strengths from both sink and source nodes, and the network dynamics of absence seizures in eight patients.

Statistically significant time-varying neural connectivity estimation using generalized partial directed coherence.

This paper illustrates the effectiveness of generalized partial directed coherence (gPDC) in characterizing time-varying neural connectivity by properly extrapolating its single trial asymptotic statistical results to a multi trial setting. Time-varying estimation is performed with a sliding-window procedure based on the proposal in [1], whereby a time-frequency map of the connectivity between channels is built. The technique is validated on a non-linear toy model generating simulated EEG and then applied to a publicly available real EEG dataset for benchmarking purposes.

Independent Component versus Local Sparse Component Analysis in Resting State fMRI.

Independent Component Analysis (ICA) algorithms are potentially powerful ways of localizing sources of cerebral activity in resting state functional Magnetic Resonance Imaging (fMRI). But the assumptions underling the nature of identified sources limits this tool. By creating local one-dimensional approximations, Local Sparse Component Analysis (LSCA) can separate contiguous sources on the basis of their sparse representation into smoothness spaces via the 3D wavelet transformation. In this paper we systematically compare Probabilistic ICA (PICA) and LSCA for analyzing resting state fMRI across healthy participants. We show that the PICA sources usually representing biologically plausible components can in fact be decomposed into several LSCA sources that are not necessarily independent from each other. In addition, we show that LSCA identifies sources that approximate much better the local variations of the blood oxygenation level-dependent (BOLD) signal than PICA sources.

Kernel-nonlinear-PDC extends Partial Directed Coherence to detecting nonlinear causal coupling.

Here we investigate a new concept, kernel-nonlinear-Partial Directed Coherence, whereby a kernel feature space representation of the data allows detecting nonlinear causal links that are otherwise undetectable through linear modeling. We show that adequate connectivity detection is achievable by applying asympotic decision criteria similar to the ones developed for linear models.

A new algorithm for neural connectivity estimation of EEG event related potentials.

We propose a new algorithm for estimating neural connectivity during event related potentials (ERP) in EEG. It is composed of two steps: the estimation of a time-varying multivariate-autoregressive (MVAR) model and the calculation of the generalized partial directed coherence (gPDC) for assessing the connectivities between channels where MVAR estimation is done via an adapted version of the Nuttall-Strand algorithm, a multivariate generalization of Burg's spectral estimation algorithm. Successful algorithm validation was performed through simulations using toys model with physiologically ERP inspired features.

On neural connectivity estimation problems.

After briefly recapping and reframing the problem of neural connectivity and its implications for today's brain mapping efforts, we argue that supplementing/replacing traditional conservative correlation based analysis methods requires active user understanding of the aims and limitations of the newly proposed multivariate analysis frameworks before the new methods can gain general acceptance and full profit can be made from the expanded descriptive opportunities they offer.

Local dimension-reduced dynamical spatio-temporal models for resting state network estimation.

To overcome the limitations of independent component analysis (ICA), today's most popular analysis tool for investigating whole-brain spatial activation in resting state functional magnetic resonance imaging (fMRI), we present a new class of local dimension-reduced dynamical spatio-temporal model which dispenses the independence assumptions that severely limit deeper connectivity descriptions between spatial components. The new method combines novel concepts of group sparsity with contiguity-constrained clusterization to produce physiologically consistent regions of interest in illustrative fMRI data whose causal interactions may then be easily estimated, something impossible under the usual ICA assumptions.

On the statistical performance of Granger-causal connectivity estimators.

In this article, we extend the statistical detection performance evaluation of linear connectivity from Sameshima et al. (in: Slezak et al. (eds.) Lecture Notes in Computer Science, 2014) via brand new Monte Carlo simulations of three widely used toy models under different data record lengths for a classic time domain multivariate Granger causality test, information partial directed coherence, information directed transfer function, and include conditional multivariate Granger causality whose behaviour was found to be anomalous.

Canonical information flow decomposition among neural structure subsets.

Partial directed coherence (PDC) and directed coherence (DC) which describe complementary aspects of the directed information flow between pairs of univariate components that belong to a vector of simultaneously observed time series have recently been generalized as bPDC/bDC, respectively, to portray the relationship between subsets of component vectors (Takahashi, 2009; Faes and Nollo, 2013). This generalization is specially important for neuroscience applications as one often wishes to address the link between the set of time series from an observed ROI (region of interest) with respect to series from some other physiologically relevant ROI. bPDC/bDC are limited, however, in that several time series within a given subset may be irrelevant or may even interact opposingly with respect to one another leading to interpretation difficulties. To address this, we propose an alternative measure, termed cPDC/cDC, employing canonical decomposition to reveal the main frequency domain modes of interaction between the vector subsets. We also show bPDC/bDC and cPDC/cDC are related and possess mutual information rate interpretations. Numerical examples and a real data set illustrate the concepts. The present contribution provides what is seemingly the first canonical decomposition of information flow in the frequency domain.

Local sparse component analysis for blind source separation: an application to resting state FMRI.

We propose a new Blind Source Separation technique for whole-brain activity estimation that best profits from FMRI's intrinsic spatial sparsity. The Local Sparse Component Analysis (LSCA) combines wavelet analysis, group-separable regularizers, contiguity-constrained clusterization and principal components analysis (PCA) into a unique spatial sparse representation of FMRI images towards efficient dimensionality reduction without sacrificing physiological characteristics by avoiding artificial stochastic model constraints. The LSCA outperforms classical PCA source reconstruction for artificial data sets over many noise levels. A real FMRI data illustration reveals resting-state activities in regions hard to observe, such as thalamus and basal ganglia, because of their small spatial scale.

Information theoretic interpretation of frequency domain connectivity measures.

In order to provide adequate multivariate measures of information flow between neural structures, modified expressions of partial directed coherence (PDC) and directed transfer function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.

Frequency domain connectivity: an information theoretic perspective.

This paper addresses the relationship between Partial Directed Coherence (PDC) and Directed Transfer Function (DTF), popular multivariate connectivity measures employed in neuroscience, and information flow as quantified by mutual information rate.