Scale-Free and Multifractal Time Dynamics of fMRI Signals during Rest and Task

Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain networks and to be modulated between rest and task (He, 2011): notably, Hurst exponent, quantifying long memory, decreases under task in activating and deactivating brain regions. In most cases, such results were obtained: First, from univariate (voxelwise or regionwise) analysis, hence focusing on specific cognitive systems such as Resting-State Networks (RSNs) and raising the issue of the specificity of this scale-free dynamics modulation in RSNs. Second, using analysis tools designed to measure a single scaling exponent related to the second order statistics of the data, thus relying on models that either implicitly or explicitly assume Gaussianity and (asymptotic) self-similarity, while fMRI signals may significantly depart from those either of those two assumptions (Ciuciu et al., 2008; Wink et al., 2008). To address these issues, the present contribution elaborates on the analysis of the scaling properties of fMRI temporal dynamics by proposing two significant variations. First, scaling properties are technically investigated using the recently introduced Wavelet Leader-based Multifractal formalism (WLMF; Wendt et al., 2007). This measures a collection of scaling exponents, thus enables a richer and more versatile description of scale invariance (beyond correlation and Gaussianity), referred to as multifractality. Also, it benefits from improved estimation performance compared to tools previously used in the literature. Second, scaling properties are investigated in both RSN and non-RSN structures (e.g., artifacts), at a broader spatial scale than the voxel one, using a multivariate approach, namely the Multi-Subject Dictionary Learning (MSDL) algorithm (Varoquaux et al., 2011) that produces a set of spatial components that appear more sparse than their Independent Component Analysis (ICA) counterpart. These tools are combined and applied to a fMRI dataset comprising 12 subjects with resting-state and activation runs (Sadaghiani et al., 2009). Results stemming from those analysis confirm the already reported task-related decrease of long memory in functional networks, but also show that it occurs in artifacts, thus making this feature not specific to functional networks. Further, results indicate that most fMRI signals appear multifractal at rest except in non-cortical regions. Task-related modulation of multifractality appears only significant in functional networks and thus can be considered as the key property disentangling functional networks from artifacts. These finding are discussed in the light of the recent literature reporting scaling dynamics of EEG microstate sequences at rest and addressing non-stationarity issues in temporally independent fMRI modes

Selective attention and speech processing in the cortex

In noisy and complex environments, human listeners must segregate the mixture of sound sources arriving at their ears and selectively attend a single source, thereby solving a computationally difficult problem called the cocktail party problem. However, the neural mechanisms underlying these computations are still largely a mystery. Oscillatory synchronization of neuronal activity between cortical areas is thought to provide a crucial role in facilitating information transmission between spatially separated populations of neurons, enabling the formation of functional networks. In this thesis, we seek to analyze and model the functional neuronal networks underlying attention to speech stimuli and find that the Frontal Eye Fields play a central 'hub' role in the auditory spatial attention network in a cocktail party experiment. We use magnetoencephalography (MEG) to measure neural signals with high temporal precision, while sampling from the whole cortex. However, several methodological issues arise when undertaking functional connectivity analysis with MEG data. Specifically, volume conduction of electrical and magnetic fields in the brain complicates interpretation of results. We compare several approaches through simulations, and analyze the trade-offs among various measures of neural phase-locking in the presence of volume conduction. We use these insights to study functional networks in a cocktail party experiment. We then construct a linear dynamical system model of neural responses to ongoing speech. Using this model, we are able to correctly predict which of two speakers is being attended by a listener. We then apply this model to data from a task where people were attending to stories with synchronous and scrambled videos of the speakers' faces to explore how the presence of visual information modifies the underlying neuronal mechanisms of speech perception. This model allows us to probe neural processes as subjects listen to long stimuli, without the need for a trial-based experimental design. We model the neural activity with latent states, and model the neural noise spectrum and functional connectivity with multivariate autoregressive dynamics, along with impulse responses for external stimulus processing. We also develop a new regularized Expectation-Maximization (EM) algorithm to fit this model to electroencephalography (EEG) data

Brain source imaging: from sparse to tensor models

International audienceA number of application areas such as biomedical engineering require solving an underdetermined linear inverse problem. In such a case, it is necessary to make assumptions on the sources to restore identifiability. This problem is encountered in brain source imaging when identifying the source signals from noisy electroencephalographic or magnetoencephalographic measurements. This inverse problem has been widely studied during the last decades, giving rise to an impressive number of methods using different priors. Nevertheless, a thorough study of the latter, including especially sparse and tensor-based approaches, is still missing. In this paper, we propose i) a taxonomy of the algorithms based on methodological considerations, ii) a discussion of identifiability and convergence properties, advantages, drawbacks, and application domains of various techniques, and iii) an illustration of the performance of selected methods on identical data sets. Directions for future research in the area of biomedical imaging are eventually provided

Advances in Spectral Learning with Applications to Text Analysis and Brain Imaging

Spectral learning algorithms are becoming increasingly popular in data-rich domains, driven in part by recent advances in large scale randomized SVD, and in spectral estimation of Hidden Markov Models. Extensions of these methods lead to statistical estimation algorithms which are not only fast, scalable, and useful on real data sets, but are also provably correct. Following this line of research, we make two contributions. First, we propose a set of spectral algorithms for text analysis and natural language processing. In particular, we propose fast and scalable spectral algorithms for learning word embeddings -- low dimensional real vectors (called Eigenwords) that capture the “meaning” of words from their context. Second, we show how similar spectral methods can be applied to analyzing brain images. State-of-the-art approaches to learning word embeddings are slow to train or lack theoretical grounding; We propose three spectral algorithms that overcome these limitations. All three algorithms harness the multi-view nature of text data i.e. the left and right context of each word, and share three characteristics: 1). They are fast to train and are scalable. 2). They have strong theoretical properties. 3). They can induce context-specific embeddings i.e. different embedding for “river bank” or “Bank of America”. \end{enumerate} They also have lower sample complexity and hence higher statistical power for rare words. We provide theory which establishes relationships between these algorithms and optimality criteria for the estimates they provide. We also perform thorough qualitative and quantitative evaluation of Eigenwords and demonstrate their superior performance over state-of-the-art approaches. Next, we turn to the task of using spectral learning methods for brain imaging data. Methods like Sparse Principal Component Analysis (SPCA), Non-negative Matrix Factorization (NMF) and Independent Component Analysis (ICA) have been used to obtain state-of-the-art accuracies in a variety of problems in machine learning. However, their usage in brain imaging, though increasing, is limited by the fact that they are used as out-of-the-box techniques and are seldom tailored to the domain specific constraints and knowledge pertaining to medical imaging, which leads to difficulties in interpretation of results. In order to address the above shortcomings, we propose Eigenanatomy (EANAT), a general framework for sparse matrix factorization. Its goal is to statistically learn the boundaries of and connections between brain regions by weighing both the data and prior neuroanatomical knowledge. Although EANAT incorporates some neuroanatomical prior knowledge in the form of connectedness and smoothness constraints, it can still be difficult for clinicians to interpret the results in specific domains where network-specific hypotheses exist. We thus extend EANAT and present a novel framework for prior-constrained sparse decomposition of matrices derived from brain imaging data, called Prior Based Eigenanatomy (p-Eigen). We formulate our solution in terms of a prior-constrained l1 penalized (sparse) principal component analysis. Experimental evaluation confirms that p-Eigen extracts biologically-relevant, patient-specific functional parcels and that it significantly aids classification of Mild Cognitive Impairment when compared to state-of-the-art competing approaches

The SURE-LET approach to image denoising

Denoising is an essential step prior to any higher-level image-processing tasks such as segmentation or object tracking, because the undesirable corruption by noise is inherent to any physical acquisition device. When the measurements are performed by photosensors, one usually distinguish between two main regimes: in the first scenario, the measured intensities are sufficiently high and the noise is assumed to be signal-independent. In the second scenario, only few photons are detected, which leads to a strong signal-dependent degradation. When the noise is considered as signal-independent, it is often modeled as an additive independent (typically Gaussian) random variable, whereas, otherwise, the measurements are commonly assumed to follow independent Poisson laws, whose underlying intensities are the unknown noise-free measures. We first consider the reduction of additive white Gaussian noise (AWGN). Contrary to most existing denoising algorithms, our approach does not require an explicit prior statistical modeling of the unknown data. Our driving principle is the minimization of a purely data-adaptive unbiased estimate of the mean-squared error (MSE) between the processed and the noise-free data. In the AWGN case, such a MSE estimate was first proposed by Stein, and is known as "Stein's unbiased risk estimate" (SURE). We further develop the original SURE theory and propose a general methodology for fast and efficient multidimensional image denoising, which we call the SURE-LET approach. While SURE allows the quantitative monitoring of the denoising quality, the flexibility and the low computational complexity of our approach are ensured by a linear parameterization of the denoising process, expressed as a linear expansion of thresholds (LET).We propose several pointwise, multivariate, and multichannel thresholding functions applied to arbitrary (in particular, redundant) linear transformations of the input data, with a special focus on multiscale signal representations. We then transpose the SURE-LET approach to the estimation of Poisson intensities degraded by AWGN. The signal-dependent specificity of the Poisson statistics leads to the derivation of a new unbiased MSE estimate that we call "Poisson's unbiased risk estimate" (PURE) and requires more adaptive transform-domain thresholding rules. In a general PURE-LET framework, we first devise a fast interscale thresholding method restricted to the use of the (unnormalized) Haar wavelet transform. We then lift this restriction and show how the PURE-LET strategy can be used to design and optimize a wide class of nonlinear processing applied in an arbitrary (in particular, redundant) transform domain. We finally apply some of the proposed denoising algorithms to real multidimensional fluorescence microscopy images. Such in vivo imaging modality often operates under low-illumination conditions and short exposure time; consequently, the random fluctuations of the measured fluorophore radiations are well described by a Poisson process degraded (or not) by AWGN. We validate experimentally this statistical measurement model, and we assess the performance of the PURE-LET algorithms in comparison with some state-of-the-art denoising methods. Our solution turns out to be very competitive both qualitatively and computationally, allowing for a fast and efficient denoising of the huge volumes of data that are nowadays routinely produced in biomedical imaging

Data-Based And Theory-Based Network Models Of Perturbations To Neural Dynamics

Much of neuroscience is centered on uncovering simple principles that constrain the behavior of the brain. When considering the formation of neural architectures, similar structures can be recreated following the principles of minimizing wiring and maximizing topological complexity. However, a similar understanding of neural dynamics on top of these structural connections has not yet been achieved. One promising strategy for identifying underlying principles of neural dynamics is quantifying and modeling the response of neural systems to perturbation. Here, we use a spectrum of data- and theory-based network models to characterize the response of neural systems to different types of perturbations. We report how functional networks change in the context of pathological epileptic activity and brain-computer interface control. We also specifically test one possible principle: that activity is constrained to spread along connections in both the context of brain-computer interfaces and direct electrical stimulation. In the first study, we demonstrate across a wide variety of functional connectivity metrics and frequency bands that epileptic activity increases amplitude-based functional interactions, an observation that can now be incorporated into future theory-based models. In a second study, we determine that modeling activity that is constrained to spread along connections suggests why certain connections are important for brain-computer interface learning; specifically, these connections support sustained activity in attention regions. In our third study, we demonstrate that modeling activity changes from direct electrical stimulation using white matter connectivity explains more variance than models with rewired connections. This model generates testable predictions about which individuals, regions, and time points would lead to successful applications of direct electrical stimulation. Overall, this work demonstrates the potential uses of a range of data- and theory-based models for uncovering simple guiding principles that determine the behavior of a system. It also uses one specific principle - that activity is constrained to spread along connections - to understand the role of specific connections that may support learning, and provide a method to optimize individually tailored stimulation therapies for a specific outcome

Magnetoencephalography

This is a practical book on MEG that covers a wide range of topics. The book begins with a series of reviews on the use of MEG for clinical applications, the study of cognitive functions in various diseases, and one chapter focusing specifically on studies of memory with MEG. There are sections with chapters that describe source localization issues, the use of beamformers and dipole source methods, as well as phase-based analyses, and a step-by-step guide to using dipoles for epilepsy spike analyses. The book ends with a section describing new innovations in MEG systems, namely an on-line real-time MEG data acquisition system, novel applications for MEG research, and a proposal for a helium re-circulation system. With such breadth of topics, there will be a chapter that is of interest to every MEG researcher or clinician