Experimental fMRI Data Research Articles

A Bayesian complex-valued latent variable model applied to functional magnetic resonance imaging

Abstract In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data.

A new transfer entropy method for measuring directed connectivity from complex-valued fMRI data.

Inferring directional connectivity of brain regions from functional magnetic resonance imaging (fMRI) data has been shown to provide additional insights into predicting mental disorders such as schizophrenia. However, existing research has focused on the magnitude data from complex-valued fMRI data without considering the informative phase data, thus ignoring potentially important information. We propose a new complex-valued transfer entropy (CTE) method to measure causal links among brain regions in complex-valued fMRI data. We use the transfer entropy to model a general non-linear magnitude-magnitude and phase-phase directed connectivity and utilize partial transfer entropy to measure the complementary phase and magnitude effects on magnitude-phase and phase-magnitude causality. We also define the significance of the causality based on a statistical test and the shuffling strategy of the two complex-valued signals. Simulated results verified higher accuracy of CTE than four causal analysis methods, including a simplified complex-valued approach and three real-valued approaches. Using experimental fMRI data from schizophrenia and controls, CTE yields results consistent with previous findings but with more significant group differences. The proposed method detects new directed connectivity related to the right frontal parietal regions and achieves 10.2-20.9% higher SVM classification accuracy when inferring directed connectivity using anatomical automatic labeling (AAL) regions as features. The proposed CTE provides a new general method for fully detecting highly predictive directed connectivity from complex-valued fMRI data, with magnitude-only fMRI data as a specific case.

Causalized Convergent Cross Mapping and Its Implementation in Causality Analysis.

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications.

Denoising brain networks using a fixed mathematical phase change in independent component analysis of magnitude-only fMRI data.

Brain networks extracted by independent component analysis (ICA) from magnitude-only fMRI data are usually denoised using various amplitude-based thresholds. By contrast, spatial source phase (SSP) or the phase information of ICA brain networks extracted from complex-valued fMRI data, has provided a simple yet effective way to perform the denoising using a fixed phase change. In this work, we extend the approach to magnitude-only fMRI data to avoid testing various amplitude thresholds for denoising magnitude maps extracted by ICA, as most studies do not save the complex-valued data. The main idea is to generate a mathematical SSP map for a magnitude map using a mapping framework, and the mapping framework is built using complex-valued fMRI data with a known SSP map. Here we leverage the fact that the phase map derived from phase fMRI data has similar phase information to the SSP map. After verifying the use of the magnitude data of complex-valued fMRI, this framework is generalized to work with magnitude-only data, allowing use of our approach even without the availability of the corresponding phase fMRI datasets. We test the proposed method using both simulated and experimental fMRI data including complex-valued data from University of New Mexico and magnitude-only data from Human Connectome Project. The results provide evidence that the mathematical SSP denoising with a fixed phase change is effective for denoising spatial maps from magnitude-only fMRI data in terms of retaining more BOLD-related activity and fewer unwanted voxels, compared with amplitude-based thresholding. The proposed method provides a unified and efficient SSP approach to denoise ICA brain networks in fMRI data.

Hemodynamic Deconvolution Demystified: Sparsity-Driven Regularization at Work

Deconvolution of the hemodynamic response is an important step to access short timescales of brain activity recorded by functional magnetic resonance imaging (fMRI). Albeit conventional deconvolution algorithms have been around for a long time (e.g., Wiener deconvolution), recent state-of-the-art methods based on sparsity-pursuing regularization are attracting increasing interest to investigate brain dynamics and connectivity with fMRI. This technical note revisits the main concepts underlying two main methods, paradigm free mapping and total activation, in the most accessible way. Despite their apparent differences in the formulation, these methods are theoretically equivalent as they represent the synthesis and analysis sides of the same problem, respectively. We demonstrate this equivalence in practice with their best-available implementations using both simulations, with different signal-to-noise ratios, and experimental fMRI data acquired during a motor task and resting state. We evaluate the parameter settings that lead to equivalent results and showcase the potential of these algorithms compared to other common approaches. This note is useful for practitioners interested in gaining a better understanding of state-of-the-art hemodynamic deconvolution and aims to answer questions that practitioners often have regarding the differences between the two methods.

Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition With Spatial Sparsity Constraint.

Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI data. More precisely, we propose to impose a sparsity constraint on spatial maps by using an ℓp norm (0 < p ≤ 1), in addition to adding low-rank constraints on factor matrices via the Frobenius norm. We solve the constrained Tucker-2 model using alternating direction method of multipliers, and propose to update both sparsity and low-rank constrained spatial maps using half quadratic splitting. Moreover, we extract new spatial and temporal features in addition to subject-specific intensities from the core tensor, and use these features to classify multiple subjects. The results from both simulated and experimental fMRI data verify the improvement of the proposed method, compared with four related algorithms including robust Kronecker component analysis, Tucker decomposition with orthogonality constraints, canonical polyadic decomposition, and block term decomposition in extracting common spatial and temporal components across subjects. The spatial and temporal features extracted from the core tensor show promise for characterizing subjects within the same group of patients or healthy controls as well.

Technologies for studying functional neural networks of the human brain based on data of nuclear functional magnetic tomography

Nuclear functional magnetic resonance imaging (fMRI) is one of the most popular methods for studying the functional activity of the human brain. In particular, this method is used in medicine to obtain information about the state of the functional networks of the patient’s brain. However, the process of processing and analysis of experimental fMRI data is complex and requires the selection of the correct technique, depending on the specific task. Practice has shown that different processing methods can give slightly different results for the same set of fMRI data. There are a number of alternative specialized software packages for processing and analysis, but the methodology still needs improvement and development. We are working in this direction: we analyze the effectiveness of existing methods; we develop our own methods; we create software services for processing and analysis of fMRI data on the basis of the distributed modular platform “Digital Laboratory”, with the involvement of the supercomputer NRC “Kurchatov Institute”. For research we use experimental fMRI data obtained on the scanner Siemens Verio Magnetom 3T at the Kurchatov Institute. One of our tasks within the framework of this project is to improve the technology for studying large-scale functional areas of the cerebral cortex at rest. To build a hierarchical model of interaction of large-scale neural networks, a verified binding of functional areas to anatomy is required. Today, there are a number of generally accepted atlases of the functional areas of the human cerebral cortex, which, nevertheless, are constantly being finalized and refined. This article presents the results of our study of the Glasser atlas for the consistency of voxels within one region and the connectivity metrics of voxel dynamics.

Influence of sample size and analytic approach on stability and interpretation of brain-behavior correlations in task-related fMRI data.

Limited statistical power due to small sample sizes is a problem in fMRI research. Most of the work to date has examined the impact of sample size on task‐related activation, with less attention paid to the influence of sample size on brain‐behavior correlations, especially in actual experimental fMRI data. We addressed this issue using two large data sets (a working memory task, N = 171, and a relational processing task, N = 865) and both univariate and multivariate approaches to voxel‐wise correlations. We created subsamples of different sizes and calculated correlations between task‐related activity at each voxel and task performance. Across both data sets the magnitude of the brain‐behavior correlations decreased and similarity across spatial maps increased with larger sample sizes. The multivariate technique identified more extensive correlated areas and more similarity across spatial maps, suggesting that a multivariate approach would provide a consistent advantage over univariate approaches in the stability of brain‐behavior correlations. In addition, the multivariate analyses showed that a sample size of roughly 80 or more participants would be needed for stable estimates of correlation magnitude in these data sets. Importantly, a number of additional factors would likely influence the choice of sample size for assessing such correlations in any given experiment, including the cognitive task of interest and the amount of data collected per participant. Our results provide novel experimental evidence in two independent data sets that the sample size commonly used in fMRI studies of 20–30 participants is very unlikely to be sufficient for obtaining reproducible brain‐behavior correlations, regardless of analytic approach.

Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data With a Phase Sparsity Constraint.

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed l0 norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

Mutual connectivity analysis of resting-state functional MRI data with local models

Functional connectivity analysis of functional MRI (fMRI) can represent brain networks and reveal insights into interactions amongst different brain regions. However, most connectivity analysis approaches adopted in practice are linear and non-directional. In this paper, we demonstrate the advantage of a data-driven, directed connectivity analysis approach called Mutual Connectivity Analysis using Local Models (MCA-LM) that approximates connectivity by modeling nonlinear dependencies of signal interaction, over more conventionally used approaches, such as Pearson's and partial correlation, Patel's conditional dependence measures, etcetera. We demonstrate on realistic simulations of fMRI data that, at long sampling intervals, i.e. high repetition time (TR) of fMRI signals, MCA-LM performs better than or comparable to correlation-based methods and Patel's measures. However, at fast image acquisition rates corresponding to low TR, MCA-LM significantly outperforms these methods. This insight is particularly useful in the light of recent advances in fast fMRI acquisition techniques. Methods that can capture the complex dynamics of brain activity, such as MCA-LM, should be adopted to extract as much information as possible from the improved representation. Furthermore, MCA-LM works very well for simulations generated at weak neuronal interaction strengths, and simulations modeling inhibitory and excitatory connections as it disentangles the two opposing effects between pairs of regions/voxels. Additionally, we demonstrate that MCA-LM is capable of capturing meaningful directed connectivity on experimental fMRI data. Such results suggest that it introduces sufficient complexity into modeling fMRI time-series interactions that simple, linear approaches cannot, while being data-driven, computationally practical and easy to use. In conclusion, MCA-LM can provide valuable insights towards better understanding brain activity.

Variational Bayesian Parameter Estimation Techniques for the General Linear Model.

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that a theoretical treatment of their relationships and their application in a basic modeling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation.

The dynamic programming high-order Dynamic Bayesian Networks learning for identifying effective connectivity in human brain from fMRI

BackgroundDetermination of effective connectivity (EC) among brain regions using fMRI is helpful in understanding the underlying neural mechanisms. Dynamic Bayesian Networks (DBNs) are an appropriate class of probabilistic graphical temporal-models that have been used in past to model EC from fMRI, specifically order-one. New-methodHigh-order DBNs (HO-DBNs) have still not been explored for fMRI data. A fundamental problem faced in the structure-learning of HO-DBN is high computational-burden and low accuracy by the existing heuristic search techniques used for EC detection from fMRI. In this paper, we propose using dynamic programming (DP) principle along with integration of properties of scoring-function in a way to reduce search space for structure-learning of HO-DBNs and finally, for identifying EC from fMRI which has not been done yet to the best of our knowledge. The proposed exact search-&-score learning approach HO-DBN-DP is an extension of the technique which was originally devised for learning a BN’s structure from static data (Singh and Moore, 2005). ResultsThe effectiveness in structure-learning is shown on synthetic fMRI dataset. The algorithm reaches globally-optimal solution in appreciably reduced time-complexity than the static counterpart due to integration of properties. The proof of optimality is provided. ComparisonThe results demonstrate that HO-DBN-DP is comparably more accurate and faster than currently used structure-learning algorithms used for identifying EC from fMRI. The real data EC from HO-DBN-DP shows consistency with previous literature than the classical Granger Causality method. ConclusionHence, the DP algorithm can be employed for reliable EC estimates from experimental fMRI data.

Adaptive independent vector analysis for multi-subject complex-valued fMRI data

BackgroundComplex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. New methodTo address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV distributions in which the MGGD shape parameter was estimated using maximum likelihood estimation. To achieve our de-noising goal, we updated the MGGD-based nonlinearity in the dominant SCV subspace, and employed a post-IVA de-noising strategy based on phase information in the IVA estimates. We also incorporated the pseudo-covariance matrix of fMRI data into the algorithm to emphasize the noncircularity of complex-valued fMRI sources. ResultsResults from simulated and experimental fMRI data demonstrated the efficacy of our method. Comparison with existing method(s)Our approach exhibited significant improvements over typical complex-valued IVA algorithms, especially during higher noise levels and larger spatial and temporal changes. As expected, the proposed complex-valued IVA algorithm detected more contiguous and reasonable activations than the magnitude-only method for task-related (393%) and default mode (301%) spatial maps. ConclusionsThe proposed approach is suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability.

Can Patel's τ accurately estimate directionality of connections in brain networks from fMRI?

Investigating directional interactions between brain regions plays a critical role in fully understanding brain function. Consequently, multiple methods have been developed for noninvasively inferring directional connectivity in human brain networks using functional MRI (fMRI). Recent simulations by Smith et al. showed that Patel's τ, a method based on higher-order statistics, was the best approach for inferring directional interactions from fMRI. Because simulations make restrictive assumptions about reality, we set out to verify this finding using experimental fMRI data obtained from a three-region network in a rat model with electrophysiological validation. Previous studies have shown that dynamic causal modeling can correctly estimate the directionality of this three-region network; Granger causality can also work after the deconvolution of the hemodynamic response. Therefore, we set out to test the hypothesis that Patel's τ obtained from either raw or deconvolved fMRI data should correctly estimate the directionality of neuronal influences obtained from intracerebral electroencephalogram in this network. Our results indicate that the accuracy of network directionality estimated using Patel's τ was not better than chance. First, our results highlight the necessity of experimental validation of simulation results. Second, it is unclear which brain mechanism is modeled by a directionality inferred from Patel's τ. Third, this study shows that a directional connection ascertained by different methods may mean different things and more experimental studies are needed for investigating the neuronal mechanisms underlying the direction of a connection in the brain ascertained by fMRI using different methods. M Magn Reson Med 78:2003-2010, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Reconstructing multivariate causal structure between functional brain networks through a Laguerre-Volterra based Granger causality approach.

Classical multivariate approaches based on Granger causality (GC) which estimate functional connectivity in the brain are almost exclusively based on autoregressive models. Nevertheless, information available from past samples is limited due to both signal autocorrelation and necessarily low model orders. Consequently, multiple time-scales interactions are usually unaccounted for. To overcome these limitations, in this study we propose the use of discrete-time orthogonal Laguerre basis functions within a Wiener-Volterra decomposition of the BOLD signals to perform effective GC assessments of brain functional connectivity. We validate our method in synthetic noisy oscillator networks, and analyze experimental fMRI data from 30 healthy subjects publicly available within the Human Connectome Project (HCP). Synthetic results demonstrate that our Laguerre-Volterra based GC estimates outperform classical approaches in terms of accuracy in detecting true causal links while rejecting false causal links in complex nonlinear networks. Human data analysis shows for the first time that the default mode network modulates both the salience network as well as fronto-temporal circuits in a causal fashion.

Multivariate dynamical systems-based estimation of causal brain interactions in fMRI: Group-level validation using benchmark data, neurophysiological models and human connectome project data

BackgroundCausal estimation methods are increasingly being used to investigate functional brain networks in fMRI, but there are continuing concerns about the validity of these methods. New methodMultivariate dynamical systems (MDS) is a state-space method for estimating dynamic causal interactions in fMRI data. Here we validate MDS using benchmark simulations as well as simulations from a more realistic stochastic neurophysiological model. Finally, we applied MDS to investigate dynamic casual interactions in a fronto-cingulate-parietal control network using human connectome project (HCP) data acquired during performance of a working memory task. Crucially, since the ground truth in experimental data is unknown, we conducted novel stability analysis to determine robust causal interactions within this network. ResultsMDS accurately recovered dynamic causal interactions with an area under receiver operating characteristic (AUC) above 0.7 for benchmark datasets and AUC above 0.9 for datasets generated using the neurophysiological model. In experimental fMRI data, bootstrap procedures revealed a stable pattern of causal influences from the anterior insula to other nodes of the fronto-cingulate-parietal network. Comparison with existing methodsMDS is effective in estimating dynamic causal interactions in both the benchmark and neurophysiological model based datasets in terms of AUC, sensitivity and false positive rates. ConclusionsOur findings demonstrate that MDS can accurately estimate causal interactions in fMRI data. Neurophysiological models and stability analysis provide a general framework for validating computational methods designed to estimate causal interactions in fMRI. The right anterior insula functions as a causal hub during working memory.

Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome.

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.

Select and Cluster: A Method for Finding Functional Networks of Clustered Voxels in fMRI.

Extracting functional connectivity patterns among cortical regions in fMRI datasets is a challenge stimulating the development of effective data-driven or model based techniques. Here, we present a novel data-driven method for the extraction of significantly connected functional ROIs directly from the preprocessed fMRI data without relying on a priori knowledge of the expected activations. This method finds spatially compact groups of voxels which show a homogeneous pattern of significant connectivity with other regions in the brain. The method, called Select and Cluster (S&C), consists of two steps: first, a dimensionality reduction step based on a blind multiresolution pairwise correlation by which the subset of all cortical voxels with significant mutual correlation is selected and the second step in which the selected voxels are grouped into spatially compact and functionally homogeneous ROIs by means of a Support Vector Clustering (SVC) algorithm. The S&C method is described in detail. Its performance assessed on simulated and experimental fMRI data is compared to other methods commonly used in functional connectivity analyses, such as Independent Component Analysis (ICA) or clustering. S&C method simplifies the extraction of functional networks in fMRI by identifying automatically spatially compact groups of voxels (ROIs) involved in whole brain scale activation networks.

Dynamic model of whole cortex reveals disassortative hub structure in the intracortical connectome

The brain exhibits complex spatio-temporal patterns of activity. In particular, its baseline neural activity for idle subjects or animals has a specific structure, also called functional connectivity (FC): cortical areas experience correlated fluctuations at rest as revealed by imaging techniques (e.g., fMRI, EEG and MEG). Moreover, these correlation patterns become more expressed or suppressed depending on the engaged task. The putative function for this stereotypical background activity has been actively questioned by the neuroscience community. A Bayesian hypothesis is that it reflects the variety of possible coactivations of cortical areas for usual tasks, forming a prior representation of the environment and interactions wherewith. The present study relies on our recently developed model [1] in which noise diffusion is constrained by intracortical white-matter projections to reproduce FC observed in experimental data (fMRI BOLD signal). In this model, noise has a functional role and represents the variability of neural activity during tasks. This model allows us to explore the role of various parameters in shaping FC, such as the local nonlinear dynamics of cortical areas. More importantly, we can infer the efficacies of intracortical projections, also called effective connectivity (EC), from experimental data. EC plays a crucial role in shaping FC and differs from the structural connectivity (SC) that is typically obtained using diffusion tensor imaging (DTI), which estimates the density of white-matter fibers. It is important to notice that the efficacies of these fibers may differ from their density, due to the concentration of synapses formed at their end, the type of neurotransmitters associated and the excitability of target neural populations. In the end, our model combines anatomical SC and activity FC to evaluate what drives the neural dynamics, embodied in EC. Practically, directed EC can be estimated using two matrices of empirical FC, namely FC0 for correlations with zero time shift and FCτ for correlations with a given time shift τ>0. We apply our method to infer the intracortical EC from experimental fMRI data that consists of ~20 minutes of recording for 25 idle subjects. The model reproduces both empirical FC0 and FCτ matrices with a Pearson correlation coefficient of 0.65. The recovered EC connectivity is significantly asymmetric, with a value of 0.3 for an index that scales from 0 for symmetric matrices to 1 for asymmetric matrices. Moreover, EC exhibits hubs that have either strong incoming or outgoing weights, but not both. This disassortative property is expected to exert a strong influence in shaping the whole network dynamics.

Causality Analysis of fMRI Data Based on the Directed Information Theory Framework

This paper aims to conduct fMRI-based causality analysis in brain connectivity by exploiting the directed information (DI) theory framework. Unlike the well-known Granger causality (GC) analysis, which relies on the linear prediction technique, the DI theory framework does not have any modeling constraints on the sequences to be evaluated and ensures estimation convergence. Moreover, it can be used to generate the GC graphs. In this paper, first, we introduce the core concepts in the DI framework. Second, we present how to conduct causality analysis using DI measures between two time series. We provide the detailed procedure on how to calculate the DI for two finite-time series. The two major steps involved here are optimal bin size selection for data digitization and probability estimation. Finally, we demonstrate the applicability of DI-based causality analysis using both the simulated data and experimental fMRI data, and compare the results with that of the GC analysis. Our analysis indicates that GC analysis is effective in detecting linear or nearly linear causal relationship, but may have difficulty in capturing nonlinear causal relationships. On the other hand, DI-based causality analysis is more effective in capturing both linear and nonlinear causal relationships. Moreover, it is observed that brain connectivity among different regions generally involves dynamic two-way information transmissions between them. Our results show that when bidirectional information flow is present, DI is more effective than GC to quantify the overall causal relationship.