Guaranteed Stability of Autoregressive Models with Granger Causality Learned from Wald Tests

This paper aims to explain relationships between time series by using the Granger causality (GC) concept through autoregressive (AR) models and to assure the model stability. Examining such GC relationship is performed on the model parameters using the Wald test and the model stability is guaranteed by the infinity-norm constraint on the dynamic matrix of the AR process. The proposed formulation is a least-squares estimation with Granger causality and stability constraints which is a convex program with a quadratic objective subject to linear equality and inequality norm constraints. We show by simulations that various typical factors could lead to unstable estimated models when using an unconstrained method. Estimated models from our approach are guaranteed to be stable but the model fitting error could be conservatively increased due to the selected stability condition

A Review on Dependence Measures in Exploring Brain Networks from fMRI Data

Functional magnetic resonance imaging (fMRI) technique allows us to capture activities occurring in a human brain via signals from blood flow, known as BOLD (blood oxygen level-dependent) signals. Exploring a relationship among brain regions inside human brains from fMRI data is an active and challenging research topic. Relationships or associations between brain regions are commonly referred to as brain connectivity or brain network. This connectivity can be divided into two groups, the functional connectivity which describes the statistical information among brain regions and the effective connectivity which specifies how one region interacts with others by a causal model. This survey paper provides a review on learning brain connectivities via fMRI data, mathematical definitions or dependence measures of such connectivities. These well-known measures include correlation, partial correlation, conditional independence, dynamical causal modeling, Granger causality, and structural equation modeling, which all can be translated in terms of mathematical conditions of model parameters. We also discusses about relevant estimation techniques that have been widely used in the problems of fMRI modeling. Understanding a rigorous definition on relationships in human brain allows us to interpret or compare the results in the context of learning brain network more clearly

Critical comments on EEG sensor space dynamical connectivity analysis

Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because 1) the channel locations cannot be seen as an approximation of a source's anatomical location and 2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing

Critical comments on EEG sensor space dynamical connectivity analysis

any different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because (1) the channel locations cannot be seen as an approximation of a source's anatomical location and (2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing

Alteration in the functional organization of the default mode network following closed non-severe traumatic brain injury

The debilitating effect of traumatic brain injury (TBI) extends years after the initial injury and hampers the recovery process and quality of life. In this study, we explore the functional reorganization of the default mode network (DMN) of those affected with non-severe TBI. Traumatic brain injury (TBI) is a wide-spectrum disease that has heterogeneous effects on its victims and impacts everyday functioning. The functional disruption of the default mode network (DMN) after TBI has been established, but its link to causal effective connectivity remains to be explored. This study investigated the differences in the DMN between healthy participants and mild and moderate TBI, in terms of functional and effective connectivity using resting-state functional magnetic resonance imaging (fMRI). Nineteen non-severe TBI (mean age 30.84 ± 14.56) and twenty-two healthy (HC; mean age 27.23 ± 6.32) participants were recruited for this study. Resting-state fMRI data were obtained at the subacute phase (mean days 40.63 ± 10.14) and analyzed for functional activation and connectivity, independent component analysis, and effective connectivity within and between the DMN. Neuropsychological tests were also performed to assess the cognitive and memory domains. Compared to the HC, the TBI group exhibited lower activation in the thalamus, as well as significant functional hypoconnectivity between DMN and LN. Within the DMN nodes, decreased activations were detected in the left inferior parietal lobule, precuneus, and right superior frontal gyrus. Altered effective connectivities were also observed in the TBI group and were linked to the diminished activation in the left parietal region and precuneus. With regard to intra-DMN connectivity within the TBI group, positive correlations were found in verbal and visual memory with the language network, while a negative correlation was found in the cognitive domain with the visual network. Our results suggested that aberrant activities and functional connectivities within the DMN and with other RSNs were accompanied by the altered effective connectivities in the TBI group. These alterations were associated with impaired cognitive and memory domains in the TBI group, in particular within the language domain. These findings may provide insight for future TBI observational and interventional research