Sparse Estimation of Resting-State Effective Connectivity From fMRI Cross-Spectra.
TL;DR: The presented methodology appears to be well-suited for fMRI, particularly given its lack of explicit dependence on temporal lag structure, and is readily applicable to whole-brain effective connectivity estimation.
Abstract: In functional magnetic resonance imaging (fMRI), functional connectivity is conventionally characterized by correlations between fMRI time series, which are intrinsically undirected measures of connectivity. Yet, some information about the directionality of network connections can nevertheless be extracted from the matrix of pairwise temporal correlations between all considered time series, when expressed in the frequency-domain as a cross-spectral density matrix. Using a sparsity prior, it then becomes possible to determine a unique directed network topology that best explains the observed undirected correlations, without having to rely on temporal precedence relationships that may not be valid in fMRI. Applying this method on simulated data with 100 nodes yielded excellent retrieval of the underlying directed networks under a wide variety of conditions. Importantly, the method did not depend on temporal precedence to establish directionality, thus reducing susceptibility to hemodynamic variability. The computational efficiency of the algorithm was sufficient to enable whole-brain estimations, thus circumventing the problem of missing nodes that otherwise occurs in partial-brain analyses. Applying the method to real resting-state fMRI data acquired with a high temporal resolution, the inferred networks showed good consistency with structural connectivity obtained from diffusion tractography in the same subjects. Interestingly, this agreement could also be seen when considering high-frequency rather than low-frequency connectivity (average correlation: r = 0.26 for f < 0.3 Hz, r = 0.43 for 0.3 < f < 5 Hz). Moreover, this concordance was significantly better (p < 0.05) than for networks obtained with conventional functional connectivity based on correlations (average correlation r = 0.18). The presented methodology thus appears to be well-suited for fMRI, particularly given its lack of explicit dependence on temporal lag structure, and is readily applicable to whole-brain effective connectivity estimation.
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Journal Article•
TL;DR: 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 is introduced.
Abstract: Abstract. 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.
176 citations
Posted Content•
TL;DR: It is argued that mis-inferences of causality from correlation are augmented by an implicit redefinition of words that suggest mechanisms, such as connectivity, causality, and flow, which tell us little about mechanisms.
Abstract: As neuroscientists we want to understand how causal interactions or mechanisms within the brain give rise to perception, cognition, and behavior. It is typical to estimate interaction effects from measured activity using statistical techniques such as functional connectivity, Granger Causality,or information flow, whose outcomes are often falsely treated as revealing mechanistic insight. Since these statistical techniques fit models to low-dimensional measurements from brains, they ignore the fact that brain activity is high-dimensional. Here we focus on the obvious confound of common inputs: the countless unobserved variables likely have more influence than the few observed ones. Any given observed correlation can be explained by an infinite set of causal models that take into account the unobserved variables. Therefore, correlations within massively undersampled measurements tell us little about mechanisms. We argue that these mis-inferences of causality from correlation are augmented by an implicit redefinition of words that suggest mechanisms, such as connectivity, causality, and flow.
33 citations
Cites background from "Sparse Estimation of Resting-State ..."
...Further, estimates of functional network can be validated against known structural network architecture or simulations (Lennartz et al., 2018; Schiefer et al., 2018)....
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TL;DR: In this paper, a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of high-dimensional locally stationary processes using the framework of functional dependence measure is presented.
Abstract: Covariances and spectral density functions play a fundamental role in the theory of time series There is a well-developed asymptotic theory for their estimates for low-dimensional stationary processes For high-dimensional nonstationary processes, however, many important problems on their asymptotic behaviors are still unanswered This paper presents a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of high-dimensional locally stationary processes Using the framework of functional dependence measure, we derive convergence rates of the estimates which depend on the sample size $T$, the dimension $p$, the moment condition and the dependence of the underlying processes
25 citations
Cites background from "Sparse Estimation of Resting-State ..."
...Recently researchers study functional connectivities of brain networks in neuroscience based on inverse of spectral density matrices; see for example, Baccalá and Sameshima (2001), Eichler, Dahlhaus and Sandkühler (2003), Blinowska (2011) and Lennartz et al. (2018)....
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TL;DR: This work proposes a new type of sparse functional connectivity network to precisely describe the relationship of temporal correlations among brain regions and fuse the low-order and the high-order networks using two decision trees for MCI classification.
Abstract: Functional connectivity networks, derived from resting-state fMRI data, have been found as effective biomarkers for identifying mild cognitive impairment (MCI) from healthy elderly. However, the traditional functional connectivity network is essentially a low-order network with the assumption that the brain activity is static over the entire scanning period, ignoring temporal variations among the correlations derived from brain region pairs. To overcome this limitation, we proposed a new type of sparse functional connectivity network to precisely describe the relationship of temporal correlations among brain regions. Specifically, instead of using the simple pairwise Pearson’s correlation coefficient as connectivity, we first estimate the temporal low-order functional connectivity for each region pair based on an ULS Group constrained-UOLS regression algorithm, where a combination of ultra-least squares (ULS) criterion with a Group constrained topology structure detection algorithm is applied to detect the topology of functional connectivity networks, aided by an Ultra-Orthogonal Least Squares (UOLS) algorithm to estimate connectivity strength. Compared to the classical least squares criterion which only measures the discrepancy between the observed signals and the model prediction function, the ULS criterion takes into consideration the discrepancy between the weak derivatives of the observed signals and the model prediction function and thus avoids the overfitting problem. By using a similar approach, we then estimate the high-order functional connectivity from the low-order connectivity to characterize signal flows among the brain regions. We finally fuse the low-order and the high-order networks using two decision trees for MCI classification. Experimental results demonstrate the effectiveness of the proposed method on MCI classification.
19 citations
TL;DR: This review article gives an account of the development of the MR-encephalography (MREG) method, which started as a mere ‘Gedankenexperiment’ in 2005 and gradually developed into a method for ultrafast measurement of physiological activities in the brain.
Abstract: This review article gives an account of the development of the MR-encephalography (MREG) method, which started as a mere ‘Gedankenexperiment’ in 2005 and gradually developed into a method for ultrafast measurement of physiological activities in the brain. After going through different approaches covering k-space with radial, rosette, and concentric shell trajectories we have settled on a stack-of-spiral trajectory, which allows full brain coverage with (nominal) 3 mm isotropic resolution in 100 ms. The very high acceleration factor is facilitated by the near-isotropic k-space coverage, which allows high acceleration in all three spatial dimensions. The methodological section covers the basic sequence design as well as recent advances in image reconstruction including the targeted reconstruction, which allows real-time feedback applications, and—most recently—the time-domain principal component reconstruction (tPCR), which applies a principal component analysis of the acquired time domain data as a sparsifying transformation to improve reconstruction speed as well as quality. Although the BOLD-response is rather slow, the high speed acquisition of MREG allows separation of BOLD-effects from cardiac and breathing related pulsatility. The increased sensitivity enables direct detection of the dynamic variability of resting state networks as well as localization of single interictal events in epilepsy patients. A separate and highly intriguing application is aimed at the investigation of the glymphatic system by assessment of the spatiotemporal patterns of cardiac and breathing related pulsatility. MREG has been developed to push the speed limits of fMRI. Compared to multiband-EPI this allows considerably faster acquisition at the cost of reduced image quality and spatial resolution.
11 citations
References
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TL;DR: It is concluded that correlation of low frequency fluctuations, which may arise from fluctuations in blood oxygenation or flow, is a manifestation of functional connectivity of the brain.
Abstract: An MRI time course of 512 echo-planar images (EPI) in resting human brain obtained every 250 ms reveals fluctuations in signal intensity in each pixel that have a physiologic origin. Regions of the sensorimotor cortex that were activated secondary to hand movement were identified using functional MRI methodology (FMRI). Time courses of low frequency (< 0.1 Hz) fluctuations in resting brain were observed to have a high degree of temporal correlation (P < 10(-3)) within these regions and also with time courses in several other regions that can be associated with motor function. It is concluded that correlation of low frequency fluctuations, which may arise from fluctuations in blood oxygenation or flow, is a manifestation of functional connectivity of the brain.
8,766 citations
"Sparse Estimation of Resting-State ..." refers background in this paper
...In resting state fMRI (rs-fMRI), relationships between intrinsic fluctuations across multiple brain areas are analyzed, giving rise to the concept of the brain as a network (Biswal et al., 1995)....
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TL;DR: As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling, but unlike previous approaches in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.
4,182 citations
"Sparse Estimation of Resting-State ..." refers methods in this paper
...Although several different approaches have been suggested to estimate EC, the most widely used methods for fMRI data are Granger Causality (Bressler and Seth, 2011) and Dynamic Causal Modeling (Friston et al., 2003)....
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TL;DR: This work has developed a graph-theoretical network visualization toolbox, called BrainNet Viewer, to illustrate human connectomes as ball-and-stick models, and helps researchers to visualize brain networks in an easy, flexible and quick manner.
Abstract: The human brain is a complex system whose topological organization can be represented using connectomics. Recent studies have shown that human connectomes can be constructed using various neuroimaging technologies and further characterized using sophisticated analytic strategies, such as graph theory. These methods reveal the intriguing topological architectures of human brain networks in healthy populations and explore the changes throughout normal development and aging and under various pathological conditions. However, given the huge complexity of this methodology, toolboxes for graph-based network visualization are still lacking. Here, using MATLAB with a graphical user interface (GUI), we developed a graph-theoretical network visualization toolbox, called BrainNet Viewer, to illustrate human connectomes as ball-and-stick models. Within this toolbox, several combinations of defined files with connectome information can be loaded to display different combinations of brain surface, nodes and edges. In addition, display properties, such as the color and size of network elements or the layout of the figure, can be adjusted within a comprehensive but easy-to-use settings panel. Moreover, BrainNet Viewer draws the brain surface, nodes and edges in sequence and displays brain networks in multiple views, as required by the user. The figure can be manipulated with certain interaction functions to display more detailed information. Furthermore, the figures can be exported as commonly used image file formats or demonstration video for further use. BrainNet Viewer helps researchers to visualize brain networks in an easy, flexible and quick manner, and this software is freely available on the NITRC website (www.nitrc.org/projects/bnv/).
3,048 citations
TL;DR: The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution and low signal intensities (SNR < 2) are therefore biased due to the noise.
Abstract: The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both, however, is that the noise distributions are nearly Gaussian for SNR larger than two.
2,425 citations
"Sparse Estimation of Resting-State ..." refers background or methods in this paper
...The scanner noise is inherent in all fMRI data and can be modeled by Gaussian white noise (Gudbjartsson and Patz, 1995; Welvaert et al., 2011) given Frontiers in Neuroscience | www.frontiersin.org 4 May 2018 | Volume 12 | Article 287 sufficient signal to noise ratio (SNR)....
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...The scanner noise is inherent in all fMRI data and can be modeled by Gaussian white noise (Gudbjartsson and Patz, 1995; Welvaert et al., 2011) given...
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TL;DR: This article presents one approach that has been used in functional imaging and shows how the integration within and between functionally specialized areas is mediated by functional or effective connectivity.
Abstract: The brain appears to adhere to two principles of functional organization; junctional segregation and functional intryration. The integration within and between functionally specialized areas is mediated by functional or ejectiue connectioity. The characterization of this sort of connectivity is an important theme in many areas of neuroscience. This article presents one approach that has been used in functional imaging. This article reviews the basic distinction between functional and effective connectivity (as the terms are used in neuroimaging) and their role in addressing several aspects of functional organization (e.g. the topography of distributed systems, integration between cortical areas, time-dependent changes in connectivity and nonlinear interactions). Emphasis is placed on the points of contact between the apparently diverse applications of these concepts and in particular the central role of eigenimages or spatial modes. Although the framework that has been developed is inherently linear, it has been extended to assess nonlinear interactions among cortical areas.
2,270 citations
"Sparse Estimation of Resting-State ..." refers background in this paper
...The effective connectivity (EC) describes “the influence one neural system exerts over another” (Friston, 1994), or as Aertsen and Preißl (1991) put it, EC is “the simplest possible circuit diagram that would replicate the observed timing relations” between observed responses and therefore describes directed connectivity....
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...The effective connectivity (EC) describes “the influence one neural system exerts over another” (Friston, 1994), or as Aertsen and Preißl (1991) put it, EC is “the simplest possible circuit diagram that would replicate the observed timing relations” between observed responses and therefore…...
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