Daniele Marinazzo

Kernel method for nonlinear granger causality.

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Nonlinear connectivity by Granger causality

The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger causality. While DCM models nonlinear couplings, Granger causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger causality. We show the application of the proposed approach on EEG signals and fMRI data.

Small-world directed networks in the human brain: Multivariate Granger causality analysis of resting-state fMRI

Small-world organization is known to be a robust and consistent network architecture, and is a hallmark of the structurally and functionally connected human brain. However, it remains unknown if the same organization is present in directed influence brain networks whose connectivity is inferred by the transfer of information from one node to another. Here, we aimed to reveal the network architecture of the directed influence brain network using multivariate Granger causality analysis and graph theory on resting-state fMRI recordings. We found that some regions acted as pivotal hubs, either being influenced by or influencing other regions, and thus could be considered as information convergence regions. In addition, we observed that an exponentially truncated power law fits the topological distribution for the degree of total incoming and outgoing connectivity. Furthermore, we also found that this directed network has a modular structure. More importantly, according to our data, we suggest that the human brain directed influence network could have a prominent small-world topological property.

Kernel-Granger causality and the analysis of dynamical networks.

We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel-Granger causality to the multivariate case, here presented, shares the following features with the bivariate measures: (i) the nonlinearity of the regression model can be controlled by choosing the kernel function and (ii) the problem of false causalities, arising as the complexity of the model increases, is addressed by a selection strategy of the eigenvectors of a reduced Gram matrix whose range represents the additional features due to the second time series. Moreover, there is no a priori assumption that the network must be a directed acyclic graph. We apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network: it is shown that the underlying topology of the network can be reconstructed from time series of nodes dynamics, provided that a sufficient number of samples is available. Considering a linear dynamical network, built by preferential attachment scheme, we show that for limited data use of the bivariate Granger causality is a better choice than methods using L1 minimization. Finally we consider real expression data from HeLa cells, 94 genes and 48 time points. The analysis of static correlations between genes reveals two modules corresponding to well-known transcription factors; Granger analysis puts in evidence 19 causal relationships, all involving genes related to tumor development.

Altered processing of sensory stimuli in patients with migraine

Migraine is a cyclic disorder, in which functional and morphological brain changes fluctuate over time, culminating periodically in an attack. In the migrainous brain, temporal processing of external stimuli and sequential recruitment of neuronal networks are often dysfunctional. These changes reflect complex CNS dysfunction patterns. Assessment of multimodal evoked potentials and nociceptive reflex responses can reveal altered patterns of the brains electrophysiological activity, thereby aiding our understanding of the pathophysiology of migraine. In this Review, we summarize the most important findings on temporal processing of evoked and reflex responses in migraine. Considering these data, we propose that thalamocortical dysrhythmia may be responsible for the altered synchronicity in migraine. To test this hypothesis in future research, electrophysiological recordings should be combined with neuroimaging studies so that the temporal patterns of sensory processing in patients with migraine can be correlated with the accompanying anatomical and functional changes.

Functional brain connectivity from EEG in epilepsy: Seizure prediction and epileptogenic focus localization

Today, neuroimaging techniques are frequently used to investigate the integration of functionally specialized brain regions in a network. Functional connectivity, which quantifies the statistical dependencies among the dynamics of simultaneously recorded signals, allows to infer the dynamical interactions of segregated brain regions. In this review we discuss how the functional connectivity patterns obtained from intracranial and scalp electroencephalographic (EEG) recordings reveal information about the dynamics of the epileptic brain and can be used to predict upcoming seizures and to localize the seizure onset zone. The added value of extracting information that is not visibly identifiable in the EEG data using functional connectivity analysis is stressed. Despite the fact that many studies have showed promising results, we must conclude that functional connectivity analysis has not made its way into clinical practice yet.

Steady-State Visual Evoked Potentials and Phase Synchronization in Migraine Patients

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in the presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

Accelerated HF-rTMS in treatment-resistant unipolar depression: Insights from subgenual anterior cingulate functional connectivity

Abstract Objectives. Intensified repetitive transcranial magnetic stimulation (rTMS) applied to the left dorsolateral prefrontal cortex (DLPFC) may result in fast clinical responses in treatment resistant depression (TRD). In these kinds of patients, subgenual anterior cingulate cortex (sgACC) functional connectivity (FC) seems to be consistently disturbed. So far, no de novo data on the relationship between sgACC FC changes and clinical efficacy of accelerated rTMS were available. Methods. Twenty unipolar TRD patients, all at least stage III treatment resistant, were recruited in a randomized sham-controlled crossover high-frequency (HF)-rTMS treatment study. Resting-state (rs) functional MRI scans were collected at baseline and at the end of treatment. Results. HF-rTMS responders showed significantly stronger resting-state functional connectivity (rsFC) anti-correlation between the sgACC and parts of the left superior medial prefrontal cortex. After successful treatment an inverted relative strength of the anti-correlations was observed in the perigenual prefrontal cortex (pgPFC). No effects on sgACC rsFC were observed in non-responders. Conclusions. Strong rsFC anti-correlation between the sgACC and parts of the left prefrontal cortex could be indicative of a beneficial outcome. Accelerated HF-rTMS treatment designs have the potential to acutely adjust deregulated sgACC neuronal networks in TRD patients.

Posterior Cingulate Cortex-Related Co-Activation Patterns: A Resting State fMRI Study in Propofol-Induced Loss of Consciousness

Background Recent studies have been shown that functional connectivity of cerebral areas is not a static phenomenon, but exhibits spontaneous fluctuations over time. There is evidence that fluctuating connectivity is an intrinsic phenomenon of brain dynamics that persists during anesthesia. Lately, point process analysis applied on functional data has revealed that much of the information regarding brain connectivity is contained in a fraction of critical time points of a resting state dataset. In the present study we want to extend this methodology for the investigation of resting state fMRI spatial pattern changes during propofol-induced modulation of consciousness, with the aim of extracting new insights on brain networks consciousness-dependent fluctuations. Methods Resting-state fMRI volumes on 18 healthy subjects were acquired in four clinical states during propofol injection: wakefulness, sedation, unconsciousness, and recovery. The dataset was reduced to a spatio-temporal point process by selecting time points in the Posterior Cingulate Cortex (PCC) at which the signal is higher than a given threshold (i.e., BOLD intensity above 1 standard deviation). Spatial clustering on the PCC time frames extracted was then performed (number of clusters = 8), to obtain 8 different PCC co-activation patterns (CAPs) for each level of consciousness. Results The current analysis shows that the core of the PCC-CAPs throughout consciousness modulation seems to be preserved. Nonetheless, this methodology enables to differentiate region-specific propofol-induced reductions in PCC-CAPs, some of them already present in the functional connectivity literature (e.g., disconnections of the prefrontal cortex, thalamus, auditory cortex), some others new (e.g., reduced co-activation in motor cortex and visual area). Conclusion In conclusion, our results indicate that the employed methodology can help in improving and refining the characterization of local functional changes in the brain associated to propofol-induced modulation of consciousness.

MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy.

A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different approaches to evaluate transfer entropy, some of them already proposed, some novel, and present their implementation in a freeware MATLAB toolbox. Applications to simulated and real data are presented.