A MATLAB toolbox for Granger causal connectivity analysis

Prefrontal dynamics underlying rapid instructed task learning reverse with practice

The ability to rapidly reconfigure our minds to perform novel tasks is important for adapting to an ever-changing world, yet little is understood about its basis in the brain. Furthermore, it is unclear how this kind of task preparation changes with practice. Previous research suggests that prefrontal cortex (PFC) is essential when preparing to perform either novel or practiced tasks. Building upon recent evidence that PFC is organized in an anterior-to-posterior hierarchy, we postulated that novel and practiced task preparation would differentiate hierarchically distinct regions within PFC across time. Specifically, we hypothesized and confirmed using functional magnetic resonance imaging and magnetoencephalography with humans that novel task preparation is a bottom-up process that involves lower-level rule representations in dorsolateral PFC (DLPFC) before a higher-level rule-integrating task representation in anterior PFC (aPFC). In contrast, we identified a complete reversal of this activity pattern during practiced task preparation. Specifically, we found that practiced task preparation is a top-down process that involves a higher-level rule-integrating task representation (recalled from long-term memory) in aPFC before lower-level rule representations in DLPFC. These findings reveal two distinct yet highly inter-related mechanisms for task preparation, one involving task set formation from instructions during rapid instructed task learning and the other involving task set retrieval from long-term memory to facilitate familiar task performance. These two mechanisms demonstrate the exceptional flexibility of human PFC as it rapidly reconfigures cognitive brain networks to implement a wide variety of possible tasks.

Multivariate dynamical systems models for estimating causal interactions in fMRI

Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of causal interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data.

Sleep-like states modulate functional connectivity in the rat olfactory system

The present study was an examination of state-dependent functional connectivity during spontaneous activity between the piriform cortex and its upstream and downstream connections. Rats were anesthetized with urethan and allowed to spontaneously cycle between fast- and slow-wave states similar to fast- and slow-wave sleep states. Local field potential recordings were made from the olfactory bulb, piriform cortex, dorsal hippocampus, amygdala, and primary visual cortex. The results demonstrate that during slow-wave sleep-like states, when the piriform cortex shows reduced sensitivity to odor input via the olfactory bulb, there is enhanced coherence with other forebrain structures. Granger causality analyses suggest that the link between piriform cortical and hippocampal activity during slow-wave state is in the direction of the hippocampus to the piriform cortex rather than the reverse. The results suggest that slow-wave sleep-like states may provide an opportunity for the transfer and/or consolidation of information related to odor memories, specifically at a time when the piriform cortex is less sensitive to sensory input.

A cerebellar thalamic cortical circuit for error-related cognitive control

Error detection and behavioral adjustment are core components of cognitive control. Numerous studies have focused on the anterior cingulate cortex (ACC) as a critical locus of this executive function. Our previous work showed greater activation in the dorsal ACC and subcortical structures during error detection, and activation in the ventrolateral prefrontal cortex (VLPFC) during post-error slowing (PES) in a stop signal task (SST). However, the extent of error-related cortical or subcortical activation across subjects was not correlated with VLPFC activity during PES. So then, what causes VLPFC activation during PES? To address this question, we employed Granger causality mapping (GCM) and identified regions that Granger caused VLPFC activation in 54 adults performing the SST during fMRI. These brain regions, including the supplementary motor area (SMA), cerebellum, a pontine region, and medial thalamus, represent potential targets responding to errors in a way that could influence VLPFC activation. In confirmation of this hypothesis, the error-related activity of these regions correlated with VLPFC activation during PES, with the cerebellum showing the strongest association. The finding that cerebellar activation Granger causes prefrontal activity during behavioral adjustment supports a cerebellar function in cognitive control. Furthermore, multivariate GCA described the "flow of information" across these brain regions. Through connectivity with the thalamus and SMA, the cerebellum mediates error and post-error processing in accord with known anatomical projections. Taken together, these new findings highlight the role of the cerebello-thalamo-cortical pathway in an executive function that has heretofore largely been ascribed to the anterior cingulate-prefrontal cortical circuit.

Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data

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 time-invariant MAR model was provided.

Multivariate Granger causality and generalized variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or "ensembles" of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer additional justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy." Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.

Dissociated emergent-response system and fine-processing system in human neural network and a heuristic neural architecture for autonomous humanoid robots

The current study investigated the functional connectivity of the primary sensory system with resting state fMRI and applied such knowledge into the design of the neural architecture of autonomous humanoid robots. Correlation and Granger causality analyses were utilized to reveal the functional connectivity patterns. Dissociation was within the primary sensory system, in that the olfactory cortex and the somatosensory cortex were strongly connected to the amygdala whereas the visual cortex and the auditory cortex were strongly connected with the frontal cortex. The posterior cingulate cortex (PCC) and the anterior cingulate cortex (ACC) were found to maintain constant communication with the primary sensory system, the frontal cortex, and the amygdala. Such neural architecture inspired the design of dissociated emergent-response system and fine-processing system in autonomous humanoid robots, with separate processing units and another consolidation center to coordinate the two systems. Such design can help autonomous robots to detect and respond quickly to danger, so as to maintain their sustainability and independence.

Measuring autonomy and emergence via Granger causality

Concepts of emergence and autonomy are central to artificial life and related cognitive and behavioral sciences. However, quantitative and easy-to-apply measures of these phenomena are mostly lacking. Here, I describe quantitative and practicable measures for both autonomy and emergence, based on the framework of multivariate autoregression and specifically Granger causality. G-autonomy measures the extent to which the knowing the past of a variable helps predict its future, as compared to predictions based on past states of external (environmental) variables. G-emergence measures the extent to which a process is both dependent upon and autonomous from its underlying causal factors. These measures are validated by application to agent-based models of predation (for autonomy) and flocking (for emergence). In the former, evolutionary adaptation enhances autonomy; the latter model illustrates not only emergence but also downward causation. I end with a discussion of relations among autonomy, emergence, and consciousness.