Information theoretic approaches to functional neuroimaging

Local similarity of activity patterns during auditory and visual processing

Neuroimaging studies have shown that brain activity is variable and changes according to stimuli and the environmental context, reflecting brain coding or information representations at different processing levels. However, little is known about activity organization that reflects coding strategies. Here, we explored and compared two different coding approaches, spatial via cross-correlation and intensity-based coding using mutual information. Using two fMRI datasets and different seeds, we searched for the spatial and intensity-based similarities with the seeds in brain activity. Our results showed that, apart from the seed regions, significant regions detected by intensity-based similarity analysis differ completely from those found using cross-correlation. These findings may indicate that information shared through spatial coding differs from that transmitted via non-spatial coding processes. Our results suggest that brain coding is organized in several different ways to optimize information processing.

Complexity changes in functional state dynamics suggest focal connectivity reductions

The past two decades have seen an explosion in the methods and directions of neuroscience research. Along with many others, complexity research has rapidly gained traction as both an independent research field and a valuable subdiscipline in computational neuroscience. In the past decade alone, several studies have suggested that psychiatric disorders affect the spatiotemporal complexity of both global and region-specific brain activity (Liu et al., 2013; Adhikari et al., 2017; Li et al., 2018). However, many of these studies have not accounted for the distributed nature of cognition in either the global or regional complexity estimates, which may lead to erroneous interpretations of both global and region-specific entropy estimates. To alleviate this concern, we propose a novel method for estimating complexity. This method relies upon projecting dynamic functional connectivity into a low-dimensional space which captures the distributed nature of brain activity. Dimension-specific entropy may be estimated within this space, which in turn allows for a rapid estimate of global signal complexity. Testing this method on a recently acquired obsessive-compulsive disorder dataset reveals substantial increases in the complexity of both global and dimension-specific activity versus healthy controls, suggesting that obsessive-compulsive patients may experience increased disorder in cognition. To probe the potential causes of this alteration, we estimate subject-level effective connectivity via a Hopf oscillator-based model dynamic model, the results of which suggest that obsessive-compulsive patients may experience abnormally high connectivity across a broad network in the cortex. These findings are broadly in line with results from previous studies, suggesting that this method is both robust and sensitive to group-level complexity alterations.

Group-level inference of information-based measures for the analyses of cognitive brain networks from neurophysiological data

The reproducibility crisis in neuroimaging and in particular in the case of underpowered studies has introduced doubts on our ability to reproduce, replicate and generalize findings. As a response, we have seen the emergence of suggested guidelines and principles for neuroscientists known as Good Scientific Practice for conducting more reliable research. Still, every study remains almost unique in its combination of analytical and statistical approaches. While it is understandable considering the diversity of designs and brain data recording, it also represents a striking point against reproducibility. Here, we propose a non-parametric permutation-based statistical framework, primarily designed for neurophysiological data, in order to perform group-level inferences on non-negative measures of information encompassing metrics from information-theory, machine-learning or measures of distances. The framework supports both fixed- and random-effect models to adapt to inter-individuals and inter-sessions variability. Using numerical simulations, we compared the accuracy in ground-truth retrieving of both group models, such as test- and cluster-wise corrections for multiple comparisons. We then reproduced and extended existing results using both spatially uniform MEG and non-uniform intracranial neurophysiological data. We showed how the framework can be used to extract stereotypical task- and behavior-related effects across the population covering scales from the local level of brain regions, inter-areal functional connectivity to measures summarizing network properties. We also present an open-source Python toolbox called Frites¹ that includes the proposed statistical pipeline using information-theoretic metrics such as single-trial functional connectivity estimations for the extraction of cognitive brain networks. Taken together, we believe that this framework deserves careful attention as its robustness and flexibility could be the starting point toward the uniformization of statistical approaches.

Augmenting interictal mapping with neurovascular coupling biomarkers by structured factorization of epileptic EEG and fMRI data

EEG-correlated fMRI analysis is widely used to detect regional BOLD fluctuations that are synchronized to interictal epileptic discharges, which can provide evidence for localizing the ictal onset zone. However, the typical, asymmetrical and mass-univariate approach cannot capture the inherent, higher order structure in the EEG data, nor multivariate relations in the fMRI data, and it is nontrivial to accurately handle varying neurovascular coupling over patients and brain regions. We aim to overcome these drawbacks in a data-driven manner by means of a novel structured matrix-tensor factorization: the single-subject EEG data (represented as a third-order spectrogram tensor) and fMRI data (represented as a spatiotemporal BOLD signal matrix) are jointly decomposed into a superposition of several sources, characterized by space-time-frequency profiles. In the shared temporal mode, Toeplitz-structured factors account for a spatially specific, neurovascular 'bridge' between the EEG and fMRI temporal fluctuations, capturing the hemodynamic response's variability over brain regions. By analyzing interictal data from twelve patients, we show that the extracted source signatures provide a sensitive localization of the ictal onset zone (10/12). Moreover, complementary parts of the IOZ can be uncovered by inspecting those regions with the most deviant neurovascular coupling, as quantified by two entropy-like metrics of the hemodynamic response function waveforms (9/12). Hence, this multivariate, multimodal factorization provides two useful sets of EEG-fMRI biomarkers, which can assist the presurgical evaluation of epilepsy. We make all code required to perform the computations available at https://github.com/svaneynd/structured-cmtf.

Disentangling causal webs in the brain using functional magnetic resonance imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging (fMRI) has been used to relate neuronal network activity to cognitive processing and behavior. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this paper, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, Linear Non-Gaussian Acyclic Models, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area.

EEG-Informed fMRI: A Review of Data Analysis Methods

The simultaneous acquisition of electroencephalography (EEG) with functional magnetic resonance imaging (fMRI) is a very promising non-invasive technique for the study of human brain function. Despite continuous improvements, it remains a challenging technique, and a standard methodology for data analysis is yet to be established. Here we review the methodologies that are currently available to address the challenges at each step of the data analysis pipeline. We start by surveying methods for pre-processing both EEG and fMRI data. On the EEG side, we focus on the correction for several MR-induced artifacts, particularly the gradient and pulse artifacts, as well as other sources of EEG artifacts. On the fMRI side, we consider image artifacts induced by the presence of EEG hardware inside the MR scanner, and the contamination of the fMRI signal by physiological noise of non-neuronal origin, including a review of several approaches to model and remove it. We then provide an overview of the approaches specifically employed for the integration of EEG and fMRI when using EEG to predict the blood oxygenation level dependent (BOLD) fMRI signal, the so-called EEG-informed fMRI integration strategy, the most commonly used strategy in EEG-fMRI research. Finally, we systematically review methods used for the extraction of EEG features reflecting neuronal phenomena of interest.

Functional Semi-Blind Source Separation Identifies Primary Motor Area Without Active Motor Execution

High time resolution techniques are crucial for investigating the brain in action. Here, we propose a method to identify a section of the upper-limb motor area representation (FS_M1) by means of electroencephalographic (EEG) signals recorded during a completely passive condition (FS_M1bySS). We delivered a galvanic stimulation to the median nerve and we applied to EEG the semi-Blind Source Separation (s-BSS) algorithm named Functional Source Separation (FSS). In order to prove that FS_M1bySS is part of FS_M1, we also collected EEG in a motor condition, i.e. during a voluntary movement task (isometric handgrip) and in a rest condition, i.e. at rest with eyes open and closed. In motor condition, we show that the cortico-muscular coherence (CMC) of FS_M1bySS does not differ from FS_ M1 CMC (0.04 for both sources). Moreover, we show that the FS_M1bySS’s ongoing whole band activity during Motor and both rest conditions displays high mutual information and time correlation with FS_M1 (above 0.900 and 0.800, respectively) whereas much smaller ones with the primary somatosensory cortex [Formula: see text] (about 0.300 and 0.500, [Formula: see text]). FS_M1bySS as a marker of the upper-limb FS_M1 representation obtainable without the execution of an active motor task is a great achievement of the FSS algorithm, relevant in most experimental, neurological and psychiatric protocols.

A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula

We begin by reviewing the statistical framework of information theory as applicable to neuroimaging data analysis. A major factor hindering wider adoption of this framework in neuroimaging is the difficulty of estimating information theoretic quantities in practice. We present a novel estimation technique that combines the statistical theory of copulas with the closed form solution for the entropy of Gaussian variables. This results in a general, computationally efficient, flexible, and robust multivariate statistical framework that provides effect sizes on a common meaningful scale, allows for unified treatment of discrete, continuous, unidimensional and multidimensional variables, and enables direct comparisons of representations from behavioral and brain responses across any recording modality. We validate the use of this estimate as a statistical test within a neuroimaging context, considering both discrete stimulus classes and continuous stimulus features. We also present examples of analyses facilitated by these developments, including application of multivariate analyses to MEG planar magnetic field gradients, and pairwise temporal interactions in evoked EEG responses. We show the benefit of considering the instantaneous temporal derivative together with the raw values of M/EEG signals as a multivariate response, how we can separately quantify modulations of amplitude and direction for vector quantities, and how we can measure the emergence of novel information over time in evoked responses. Open-source Matlab and Python code implementing the new methods accompanies this article. Hum Brain Mapp 38:1541-1573, 2017. © 2016 Wiley Periodicals, Inc.

Reliability of information-based integration of EEG and fMRI data: a simulation study

Most studies involving simultaneous electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) data rely on the first-order, affine-linear correlation of EEG and fMRI features within the framework of the general linear model. An alternative is the use of information-based measures such as mutual information and entropy, which can also detect higher-order correlations present in the data. The estimate of information-theoretic quantities might be influenced by several parameters, such as the numerosity of the sample, the amount of correlation between variables, and the discretization (or binning) strategy of choice. While these issues have been investigated for invasive neurophysiological data and a number of bias-correction estimates have been developed, there has been no attempt to systematically examine the accuracy of information estimates for the multivariate distributions arising in the context of EEG-fMRI recordings. This is especially important given the differences between electrophysiological and EEG-fMRI recordings. In this study, we drew random samples from simulated bivariate and trivariate distributions, mimicking the statistical properties of EEG-fMRI data. We compared the estimated information shared by simulated random variables with its numerical value and found that the interaction between the binning strategy and the estimation method influences the accuracy of the estimate. Conditional on the simulation assumptions, we found that the equipopulated binning strategy yields the best and most consistent results across distributions and bias correction methods. We also found that within bias correction techniques, the asymptotically debiased (TPMC), the jackknife debiased (JD), and the best upper bound (BUB) approach give similar results, and those are consistent across distributions.

Mapping interictal epileptic discharges using mutual information between concurrent EEG and fMRI

OBJECTIVE

The mapping of haemodynamic changes related to interictal epileptic discharges (IED) in simultaneous electroencephalography (EEG) and functional MRI (fMRI) studies is usually carried out by means of EEG-correlated fMRI analyses where the EEG information specifies the model to test on the fMRI signal. The sensitivity and specificity critically depend on the accuracy of EEG detection and the validity of the haemodynamic model. In this study we investigated whether an information theoretic analysis based on the mutual information (MI) between the presence of epileptic activity on EEG and the fMRI data can provide further insights into the haemodynamic changes related to interictal epileptic activity. The important features of MI are that: 1) both recording modalities are treated symmetrically; 2) no requirement for a-priori models for the haemodynamic response function, or assumption of a linear relationship between the spiking activity and BOLD responses, and 3) no parametric model for the type of noise or its probability distribution is necessary for the computation of MI.

METHODS

Fourteen patients with pharmaco-resistant focal epilepsy underwent EEG-fMRI and intracranial EEG and/or surgical resection with positive postoperative outcome (seizure freedom or considerable reduction in seizure frequency) was available in 7/14 patients. We used nonparametric statistical assessment of the MI maps based on a four-dimensional wavelet packet resampling method. The results of MI were compared to the statistical parametric maps obtained with two conventional General Linear Model (GLM) analyses based on the informed basis set (canonical HRF and its temporal and dispersion derivatives) and the Finite Impulse Response (FIR) models.

RESULTS

The MI results were concordant with the electro-clinically or surgically defined epileptogenic area in 8/14 patients and showed the same degree of concordance as the results obtained with the GLM-based methods in 12 patients (7 concordant and 5 discordant). In one patient, the information theoretic analysis improved the delineation of the irritative zone compared with the GLM-based methods.

DISCUSSION

Our findings suggest that an information theoretic analysis can provide clinically relevant information about the BOLD signal changes associated with the generation and propagation of interictal epileptic discharges. The concordance between the MI, GLM and FIR maps support the validity of the assumptions adopted in GLM-based analyses of interictal epileptic activity with EEG-fMRI in such a manner that they do not significantly constrain the localization of the epileptogenic zone.

Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.

EEG-fMRI based information theoretic characterization of the human perceptual decision system

The modern metaphor of the brain is that of a dynamic information processing device. In the current study we investigate how a core cognitive network of the human brain, the perceptual decision system, can be characterized regarding its spatiotemporal representation of task-relevant information. We capitalize on a recently developed information theoretic framework for the analysis of simultaneously acquired electroencephalography (EEG) and functional magnetic resonance imaging data (fMRI) (Ostwald et al. (2010), NeuroImage 49: 498-516). We show how this framework naturally extends from previous validations in the sensory to the cognitive domain and how it enables the economic description of neural spatiotemporal information encoding. Specifically, based on simultaneous EEG-fMRI data features from n = 13 observers performing a visual perceptual decision task, we demonstrate how the information theoretic framework is able to reproduce earlier findings on the neurobiological underpinnings of perceptual decisions from the response signal features' marginal distributions. Furthermore, using the joint EEG-fMRI feature distribution, we provide novel evidence for a highly distributed and dynamic encoding of task-relevant information in the human brain.