Lagged and instantaneous dynamical influences related to brain structural connectivity (original) (raw)
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Lagged covariance structure models for studying functional connectivity in the brain
Neuroimage, 2006
Most cognitive processes are supported by large networks of brain regions. To describe the operation of these networks, it is critical to understand how individual areas are functionally connected. Here, we establish a statistical framework for studying effective and functional brain connectivity, using data obtained with a relatively new neuroimaging method, the event-related optical signal (EROS). The novelty of our approach is the use of timing information (in the form of lagged cross-correlations) in interpreting the connections between areas. Interpretation of lagged cross-correlations exploits the combination of spatial and temporal resolution provided by EROS. In this paper, we apply dynamic factor analysis as a method for testing various structural models on the lagged covariance matrices derived from the EROS data. We first illustrate the approach by testing a simple path model of neural activity propagation from area V1 to V3 in a visual stimulation task. We then build more complex structural equation models with latent variables, describing both within-hemisphere integrity, and interactions between the two hemispheres, to interpret data from a second task involving inter-hemispheric competition. The results demonstrate how the integrity of anatomical connections between the two hemispheres explains different patterns of cross-hemispheric interactions. This approach allows for fitting brain imaging data to complex models that capture dynamic cognitive processes as they rapidly evolve over time. D
Connectivity Analysis of Human Functional MRI Data: From Linear to Nonlinear and Static to Dynamic
2006
In this paper, we describe approaches for analyzing functional MRI data to assess brain connectivity. Using phase-space embedding, bivariate embedding dimensions and delta-epsilon methods are introduced to characterize nonlinear connectivity in fMRI data. The nonlinear approaches were applied to resting state data and continuous task data and their results were compared with those obtained from the conventional approach of linear correlation. The nonlinear methods captured couplings not revealed by linear correlation and was found to be more selective in identifying true connectivity. In addition to the nonlinear methods, the concept of Granger causality was applied to infer directional information transfer among the connected brain regions. Finally, we demonstrate the utility of moving window connectivity analysis in understanding temporally evolving neural processes such as motor learning.
NeuroImage, 2010
Increasing interest in understanding dynamic interactions of brain neural networks leads to formulation of sophisticated connectivity analysis methods. Recent studies have applied Granger causality based on standard multivariate autoregressive (MAR) modeling to assess the brain connectivity. Nevertheless, one important flaw of this commonly proposed method is that it requires the analyzed time series to be stationary, whereas such assumption is mostly violated due to the weakly nonstationary nature of functional magnetic resonance imaging (fMRI) time series. Therefore, we propose an approach to dynamic Granger causality in the frequency domain for evaluating functional network connectivity in fMRI data. The effectiveness and robustness of the dynamic approach was significantly improved by combining a forward and backward Kalman filter that improved estimates compared to the standard time-invariant MAR modeling. In our method, the functional networks were first detected by independent component analysis (ICA), a computational method for separating a multivariate signal into maximally independent components. Then the measure of Granger causality was evaluated using generalized partial directed coherence that is suitable for bivariate as well as multivariate data. Moreover, this metric provides identification of causal relation in frequency domain, which allows one to distinguish the frequency components related to the experimental paradigm. The procedure of evaluating Granger causality via dynamic MAR was demonstrated on simulated time series as well as on two sets of group fMRI data collected during an auditory sensorimotor (SM) or auditory oddball discrimination (AOD) tasks. Finally, a comparison with the results obtained from a standard timeinvariant MAR model was provided.
Predicting human resting-state functional connectivity from structural connectivity
Proceedings of the National Academy of Sciences, 2009
In the cerebral cortex, the activity levels of neuronal populations are continuously fluctuating. When neuronal activity, as measured using functional MRI (fMRI), is temporally coherent across 2 populations, those populations are said to be functionally connected. Functional connectivity has previously been shown to correlate with structural (anatomical) connectivity patterns at an aggregate level. In the present study we investigate, with the aid of computational modeling, whether systems-level properties of functional networks-including their spatial statistics and their persistence across time-can be accounted for by properties of the underlying anatomical network. We measured resting state functional connectivity (using fMRI) and structural connectivity (using diffusion spectrum imaging tractography) in the same individuals at high resolution. Structural connectivity then provided the couplings for a model of macroscopic cortical dynamics. In both model and data, we observed (i) that strong functional connections commonly exist between regions with no direct structural connection, rendering the inference of structural connectivity from functional connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity that was unexplained by direct structural connectivity; and (iii) that resting-state functional connectivity exhibits variability within and across both scanning sessions and model runs. These empirical and modeling results demonstrate that although resting state functional connectivity is variable and is frequently present between regions without direct structural linkage, its strength, persistence, and spatial statistics are nevertheless constrained by the large-scale anatomical structure of the human cerebral cortex.
Demonstrating causal links between fMRI time series using time-lagged correlation
Proceedings of the Twenty-sixth International Conference Image and Vision Computing New Zealand, 2011
An autoregressive modelling-based technique, Granger analysis, has increasingly been used for measuring causal connections between brain regions in fundamental magnetic resonance imaging brain imaging (fMRI). This paper summarises the possibilities and limitations of applying Granger analysis to fMRI. It also describes a replication of a previous theoretical study, and an application to spatial working memory currently under way. Previous researchers have described methods for detecting time-lagged correlation between neural activations in brain regions of interest (ROI)-often variants of 'Grangercausality analysis' (GCA). With appropriate caveats, GCA can draw inferences from time-lagged correlation about effective connectivity between ROIs in a way other popular methods do not. We replicated an existing theoretical model using a different non-linear function, and different method of combining a haemodynamic response function. We then examined whether GCA can estimate the direction of causation in brain regions shown to act together in spatial working memory tasks. Independent Component Analysis (ICA) was used to identify independent spatial components. Then, GCA tested the interactions between those components. The method identified causal relationships on replicated, artificially simulated data and in between extracted components in the data. Work is now underway to determine the implications of these relationships.
2011
We propose a model that describes the interactions of several Brain Regions based on Functional Magnetic Resonance Imaging (FMRI) time series to make inferences about functional integration and segregation within the human brain. The method is demonstrated using dynamic causal modelling (DCM) augmented by Granger Causality (GC) using real data to show how such models are able to characterize interregional dependence. We extend estimating and reviewing designed model to characterize the interactions between regions and showing the direction of the signal over regions. A further benefit is to estimate the effective connectivity between these regions. All designs, estimates, reviews are implemented using Statistical Parametric Mapping (SPM) and GCCA toolbox, one of the free best software packages and published toolbox used to design the models and analysis for inferring about FMRI functional magnetic resonance imaging time series.
Mathematical Sciences
Recently, we have witnessed an increase in scientific interest in understanding the dynamic nature of brain networks by evaluating dynamic functional connectivity (FC) using functional magnetic resonance imaging (fMRI). In this work, we introduce two multivariate volatility models, standardized dynamic conditional correlation, and standardized exponentially weighted moving average, both of which are built upon the framework of dynamic conditional correlation and exponentially weighted moving average models, respectively. In these two models, we use standardized residuals with the goal of determining whether the use of standardized residuals reduces the mean square rate error. Moreover, in traditional simulation studies, time series were considered with zero conditional expectation and static conditional variance which do not capture the nature of the real data. This is because of hemodynamic response function in the brain and dynamic functional connectivity of each brain region with itself during the experiment time, respectively. That is why, next, some new simulation studies are introduced which are more similar to blood-oxygen-level-dependent time series of brain regions. Then, methods' proficiency is analyzed using previous and new simulation studies. Results show that, in both former and latter simulations, the new methods work better. Finally, the best model is utilized to model FC in an Iranian resting-state fMRI data.
Granger causality (GC) and dynamic causal modeling (DCM) are the two key approaches used to determine the directed interactions among brain areas. Recent discussions have provided a constructive account of the merits and demerits. GC, on one side, considers dependencies among measured responses, whereas DCM, on the other, models how neuronal activity in one brain area causes dynamics in another. In this study, our objective was to establish construct validity between GC and DCM in the context of resting state functional magnetic resonance imaging (fMRI). We first established the face validity of both approaches using simulated fMRI time series, with endogenous fluctuations in two nodes. Crucially, we tested both unidirectional and bidirectional connections between the two nodes to ensure that both approaches give veridical and consistent results, in terms of model comparison. We then applied both techniques to empirical data and examined their consistency in terms of the (quantitative) in-degree of key nodes of the default mode. Our simulation results suggested a (qualitative) consistency between GC and DCM. Furthermore, by applying nonparametric GC and stochastic DCM to resting-state fMRI data, we confirmed that both GC and DCM infer similar (quantitative) directionality between the posterior cingulate cortex (PCC), the medial prefrontal cortex, the left middle temporal cortex, and the left angular gyrus. These findings suggest that GC and DCM can be used to estimate directed functional and effective connectivity from fMRI measurements in a consistent manner.
NeuroImage, 2015
The relationship between structural connectivity (SC) and functional connectivity (FC) in the human brain can be studied using magnetic resonance imaging (MRI). However many of the underlying physiological mechanisms and parameters cannot be directly observed with MRI. This limitation has motivated the recent use of various computational models meant to bridge the gap. However their absolute and relative explanatory power and the properties that actually drive that power remain insufficiently characterized. We performed an extensive comparison of seven mainstream computational models predicting FC from SC. We investigated the extent to which simulated FC could predict empirical FC. We also applied graph theory to the entire set of simulated and empirical FCs in order to further characterize the relationships between the models and the MRI data. The comparison was performed at three different spatial scales. We found that (i) there were significant effects of scale and model on predictive power; (ii) among all models, the simplest model, the simultaneous autoregressive (SAR) model, was found to consistently perform better than the other models; (iii) the SAR also appeared more 'central' from a graph theory perspective; and (iv) empirical FC only appeared weakly correlated with simulated FCs, and was featured as 'peripheral' in the graph analysis. We conclude that the substantial differences existing between these computational models have little impact on their predictive power for FC and that their capacity to predict FC from SC appears to be both moderate and essentially underlined by a simple core linear process embodied by the SAR model.
Neuroimage, 2006
Functional magnetic resonance imaging (fMRI) is widely used to identify neural correlates of cognitive tasks. However, the analysis of functional connectivity is crucial to understanding neural dynamics. Although many studies of cerebral circuitry have revealed adaptative behavior, which can change during the course of the experiment, most of contemporary connectivity studies are based on correlational analysis or structural equations analysis, assuming a time-invariant connectivity structure. In this paper, a novel method of continuous time-varying connectivity analysis is proposed, based on the wavelet expansion of functions and vector autoregressive model (wavelet dynamic vector autoregressive-DVAR). The model also allows identification of the direction of information flow between brain areas, extending the Granger causality concept to locally stationary processes. Simulation results show a good performance of this approach even using short time intervals. The application of this new approach is illustrated with fMRI data from a simple AB motor task experiment. D