A comparison of Granger causality and coherency in fMRI-based analysis of the motor system.
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ABSTRACT:
SUBMITTER: Kayser AS
PROVIDER: S-EPMC2767459 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:The recent interest in the dynamics of networks and the advent, across a range of applications, of measuring modalities that operate on different temporal scales have put the spotlight on some significant gaps in the theory of multivariate time series. Fundamental to the description of network dynamics is the direction of interaction between nodes, accompanied by a measure of the strength of such interactions. Granger causality and its associated frequency domain strength measures (GEMs) (due to Geweke) provide a framework for the formulation and analysis of these issues. In pursuing this setup, three significant unresolved issues emerge. First, computing GEMs involves computing submodels of vector time series models, for which reliable methods do not exist. Second, the impact of filtering on GEMs has never been definitively established. Third, the impact of downsampling on GEMs has never been established. In this work, using state-space methods, we resolve all these issues and illustrate the results with some simulations. Our analysis is motivated by some problems in (fMRI) brain imaging, to which we apply it, but it is of general applicability.
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Project description:The primary motor cortex (M1) is often abnormally recruited in stroke patients with motor disabilities. However, little is known about the alterations in the causal connectivity of M1 following stroke. The purpose of the present study was to investigate whether the effective connectivity of the ipsilesional M1 is disturbed in stroke patients who show different outcomes in hand motor function. 23 patients with left-hemisphere subcortical stroke were selected and divided into two subgroups: partially paralyzed hands (PPH) and completely paralyzed hands (CPH). Further, 24 matched healthy controls (HCs) were recruited. A voxel-wise Granger causality analysis (GCA) on the resting-state fMRI data between the ipsilesional M1 and the whole brain was performed to explore differences between the three groups. Our results showed that the influence from the frontoparietal cortices to ipsilesional M1 was diminished in both stroke subgroups and the influence from ipsilesional M1 to the sensorimotor cortices decreased greater in the CPH group than in the PPH group. Moreover, compared with the PPH group, the decreased influence from ipsilesional M1 to the contralesional cerebellum and from the contralesional superior parietal lobe to ipsilesional M1 were observed in the CPH group, and their GCA values were positively correlated with the FMA scores; Conversely, the increased influence from ipsilesional M1 to the ipsilesional middle frontal gyrus and middle temporal gyrus were observed, whose GCA values were negatively correlated with the FMA scores. This study suggests that the abnormalities of casual flow in the ipsilesional M1 are related to the severity of stroke-hand dysfunction, providing valuable information to understand the deficits in resting-state effective connectivity of motor execution and the frontoparietal motor control network during brain plasticity following stroke.
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Project description:Multivariate neural data provide the basis for assessing interactions in brain networks. Among myriad connectivity measures, Granger causality (GC) has proven to be statistically intuitive, easy to implement, and generate meaningful results. Although its application to functional MRI (fMRI) data is increasing, several factors have been identified that appear to hinder its neural interpretability: (a) latency differences in hemodynamic response function (HRF) across different brain regions, (b) low-sampling rates, and (c) noise. Recognizing that in basic and clinical neuroscience, it is often the change of a dependent variable (e.g., GC) between experimental conditions and between normal and pathology that is of interest, we address the question of whether there exist systematic relationships between GC at the fMRI level and that at the neural level. Simulated neural signals were convolved with a canonical HRF, down-sampled, and noise-added to generate simulated fMRI data. As the coupling parameters in the model were varied, fMRI GC and neural GC were calculated, and their relationship examined. Three main results were found: (1) GC following HRF convolution is a monotonically increasing function of neural GC; (2) this monotonicity can be reliably detected as a positive correlation when realistic fMRI temporal resolution and noise level were used; and (3) although the detectability of monotonicity declined due to the presence of HRF latency differences, substantial recovery of detectability occurred after correcting for latency differences. These results suggest that Granger causality is a viable technique for analyzing fMRI data when the questions are appropriately formulated.
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Project description:While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of nonlinear methods by applying structured multilayer perceptrons (MLPs) or recurrent neural networks (RNNs) combined with sparsity-inducing penalties on the weights. By encouraging specific sets of weights to be zero-in particular, through the use of convex group-lasso penalties-we can extract the Granger causal structure. To further contrast with traditional approaches, our framework naturally enables us to efficiently capture long-range dependencies between series either via our RNNs or through an automatic lag selection in the MLP. We show that our neural Granger causality methods outperform state-of-the-art nonlinear Granger causality methods on the DREAM3 challenge data. This data consists of nonlinear gene expression and regulation time courses with only a limited number of time points. The successes we show in this challenging dataset provide a powerful example of how deep learning can be useful in cases that go beyond prediction on large datasets. We likewise illustrate our methods in detecting nonlinear interactions in a human motion capture dataset.
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Project description:Functional brain network studies using the Blood Oxygen-Level Dependent (BOLD) signal from functional Magnetic Resonance Imaging (fMRI) are becoming increasingly prevalent in research on the neural basis of human cognition. An important problem in functional brain network analysis is to understand directed functional interactions between brain regions during cognitive performance. This problem has important implications for understanding top-down influences from frontal and parietal control regions to visual occipital cortex in visuospatial attention, the goal motivating the present study. A common approach to measuring directed functional interactions between two brain regions is to first create nodal signals by averaging the BOLD signals of all the voxels in each region, and to then measure directed functional interactions between the nodal signals. Another approach, that avoids averaging, is to measure directed functional interactions between all pairwise combinations of voxels in the two regions. Here we employ an alternative approach that avoids the drawbacks of both averaging and pairwise voxel measures. In this approach, we first use the Least Absolute Shrinkage Selection Operator (LASSO) to pre-select voxels for analysis, then compute a Multivariate Vector AutoRegressive (MVAR) model from the time series of the selected voxels, and finally compute summary Granger Causality (GC) statistics from the model to represent directed interregional interactions. We demonstrate the effectiveness of this approach on both simulated and empirical fMRI data. We also show that averaging regional BOLD activity to create a nodal signal may lead to biased GC estimation of directed interregional interactions. The approach presented here makes it feasible to compute GC between brain regions without the need for averaging. Our results suggest that in the analysis of functional brain networks, careful consideration must be given to the way that network nodes and edges are defined because those definitions may have important implications for the validity of the analysis.
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Project description:Major Depressive Disorder (MDD) has been conceptualized as a neural network-level disease. Few studies of the neural bases of depression, however, have used analytical techniques that are capable of testing network-level hypotheses of neural dysfunction in this disorder. Moreover, of those that have, fewer still have attempted to determine the directionality of influence within functionally abnormal networks of structures. We used multivariate GC analysis, a technique that estimates the extent to which preceding neural activity in one or more seed regions predicts subsequent activity in target brain regions, to analyze blood-oxygen-level-dependent (BOLD) data collected during eyes-closed rest from depressed and never-depressed persons. We found that activation in the hippocampus predicted subsequent increases in ventral anterior cingulate cortex (vACC) activity in depression, and that activity in the medial prefrontal cortex and vACC were mutually reinforcing in MDD. Hippocampal and vACC activation in depressed participants predicted subsequent decreases in dorsal cortical activity. This study shows that, on a moment-by-moment basis, there is increased excitatory activity among limbic and paralimbic structures, as well as increased inhibition in the activity of dorsal cortical structures, by limbic structures in depression; these aberrant patterns of effective connectivity implicate disturbances in the mesostriatal dopamine system in depression. These findings advance the neural theory of depression by detailing specific patterns of limbic excitation in MDD, by making explicit the primary role of limbic inhibition of dorsal cortex in the cortico-limbic relation posited to underlie depression, and by presenting an integrated neurofunctional account of altered dopamine function in this disorder.
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Project description:BackgroundThe mechanisms sustaining myocardial fibrillation remain disputed, partly due to a lack of mapping tools that can accurately identify the mechanism with low spatial resolution clinical recordings. Granger causality (GC) analysis, an econometric tool for quantifying causal relationships between complex time-series, was developed as a novel fibrillation mapping tool and adapted to low spatial resolution sequentially acquired data.MethodsVentricular fibrillation (VF) optical mapping was performed in Langendorff-perfused Sprague-Dawley rat hearts (n=18), where novel algorithms were developed using GC-based analysis to (1) quantify causal dependence of neighboring signals and plot GC vectors, (2) quantify global organization with the causality pairing index, a measure of neighboring causal signal pairs, and (3) localize rotational drivers (RDs) by quantifying the circular interdependence of neighboring signals with the circular interdependence value. GC-based mapping tools were optimized for low spatial resolution from downsampled optical mapping data, validated against high-resolution phase analysis and further tested in previous VF optical mapping recordings of coronary perfused donor heart left ventricular wedge preparations (n=12), and adapted for sequentially acquired intracardiac electrograms during human persistent atrial fibrillation mapping (n=16).ResultsGlobal VF organization quantified by causality pairing index showed a negative correlation at progressively lower resolutions (50% resolution: P=0.006, R2=0.38, 12.5% resolution, P=0.004, R2=0.41) with a phase analysis derived measure of disorganization, locations occupied by phase singularities. In organized VF with high causality pairing index values, GC vector mapping characterized dominant propagating patterns and localized stable RDs, with the circular interdependence value showing a significant difference in driver versus nondriver regions (0.91±0.05 versus 0.35±0.06, P=0.0002). These findings were further confirmed in human VF. In persistent atrial fibrillation, a positive correlation was found between the causality pairing index and presence of stable RDs (P=0.0005,R2=0.56). Fifty percent of patients had RDs, with a low incidence of 0.9±0.3 RDs per patient.ConclusionsGC-based fibrillation analysis can measure global fibrillation organization, characterize dominant propagating patterns, and map RDs using low spatial resolution sequentially acquired data.
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Project description:A number of studies have tried to exploit subtle phase differences in BOLD time series to resolve the order of sequential activation of brain regions, or more generally the ability of signal in one region to predict subsequent signal in another region. More recently, such lag-based measures have been applied to investigate directed functional connectivity, although this application has been controversial. We attempted to use large publicly available datasets (FCON 1000, ADHD 200, Human Connectome Project) to determine whether consistent spatial patterns of Granger Causality are observed in typical fMRI data. For BOLD datasets from 1,240 typically developing subjects ages 7-40, we measured Granger causality between time series for every pair of 7,266 spherical ROIs covering the gray matter and 264 seed ROIs at hubs of the brain's functional network architecture. Granger causality estimates were strongly reproducible for connections in a test and replication sample (n=620 subjects for each group), as well as in data from a single subject scanned repeatedly, both during resting and passive video viewing. The same effect was even stronger in high temporal resolution fMRI data from the Human Connectome Project, and was observed independently in data collected during performance of 7 task paradigms. The spatial distribution of Granger causality reflected vascular anatomy with a progression from Granger causality sources, in Circle of Willis arterial inflow distributions, to sinks, near large venous vascular structures such as dural venous sinuses and at the periphery of the brain. Attempts to resolve BOLD phase differences with Granger causality should consider the possibility of reproducible vascular confounds, a problem that is independent of the known regional variability of the hemodynamic response.
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Project description:Quantifying the functional relations between the nodes in a network based on local observations is a key challenge in studying complex systems. Most existing time series analysis techniques for this purpose provide static estimates of the network properties, pertain to stationary Gaussian data, or do not take into account the ubiquitous sparsity in the underlying functional networks. When applied to spike recordings from neuronal ensembles undergoing rapid task-dependent dynamics, they thus hinder a precise statistical characterization of the dynamic neuronal functional networks underlying adaptive behavior. We develop a dynamic estimation and inference paradigm for extracting functional neuronal network dynamics in the sense of Granger, by integrating techniques from adaptive filtering, compressed sensing, point process theory, and high-dimensional statistics. We demonstrate the utility of our proposed paradigm through theoretical analysis, algorithm development, and application to synthetic and real data. Application of our techniques to two-photon Ca2+ imaging experiments from the mouse auditory cortex reveals unique features of the functional neuronal network structures underlying spontaneous activity at unprecedented spatiotemporal resolution. Our analysis of simultaneous recordings from the ferret auditory and prefrontal cortical areas suggests evidence for the role of rapid top-down and bottom-up functional dynamics across these areas involved in robust attentive behavior.
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Project description:BACKGROUND:'Non-parametric directionality' (NPD) is a novel method for estimation of directed functional connectivity (dFC) in neural data. The method has previously been verified in its ability to recover causal interactions in simulated spiking networks in Halliday et al. (2015). METHODS:This work presents a validation of NPD in continuous neural recordings (e.g. local field potentials). Specifically, we use autoregressive models to simulate time delayed correlations between neural signals. We then test for the accurate recovery of networks in the face of several confounds typically encountered in empirical data. We examine the effects of NPD under varying: a) signal-to-noise ratios, b) asymmetries in signal strength, c) instantaneous mixing, d) common drive, e) data length, and f) parallel/convergent signal routing. We also apply NPD to data from a patient who underwent simultaneous magnetoencephalography and deep brain recording. RESULTS:We demonstrate that NPD can accurately recover directed functional connectivity from simulations with known patterns of connectivity. The performance of the NPD measure is compared with non-parametric estimators of Granger causality (NPG), a well-established methodology for model-free estimation of dFC. A series of simulations investigating synthetically imposed confounds demonstrate that NPD provides estimates of connectivity that are equivalent to NPG, albeit with an increased sensitivity to data length. However, we provide evidence that: i) NPD is less sensitive than NPG to degradation by noise; ii) NPD is more robust to the generation of false positive identification of connectivity resulting from SNR asymmetries; iii) NPD is more robust to corruption via moderate amounts of instantaneous signal mixing. CONCLUSIONS:The results in this paper highlight that to be practically applied to neural data, connectivity metrics should not only be accurate in their recovery of causal networks but also resistant to the confounding effects often encountered in experimental recordings of multimodal data. Taken together, these findings position NPD at the state-of-the-art with respect to the estimation of directed functional connectivity in neuroimaging.
| S-EPMC7116477 | biostudies-literature