A Stepwise Multivariate Granger Causality Method for Constructing Hierarchical Directed Brain Functional Network

Efficient Estimation of Directed Connectivity in Nonlinear and Nonstationary Spiking Neuron Networks

OBJECTIVE

Studying directed connectivity within spiking neuron networks can help understand neural mechanisms. Existing methods assume linear time-invariant neural dynamics with a fixed time lag in information transmission, while spiking networks usually involve complex dynamics that are nonlinear and nonstationary, and have varying time lags.

METHODS

We develop a Gated Recurrent Unit (GRU)-Point Process (PP) method to estimate directed connectivity within spiking networks. We use a GRU to describe the dependency of the target neuron's current firing rate on the source neurons' past spiking events and a PP to relate the target neuron's firing rate to its current 0-1 spiking event. The GRU model uses recurrent states and gate/activation functions to deal with varying time lags, nonlinearity, and nonstationarity in a parameter-efficient manner. We estimate the model using maximum likelihood and compute directed information as our measure of directed connectivity.

RESULTS

We conduct simulations using artificial spiking networks and a biophysical model of Parkinson's disease to show that GRU-PP systematically addresses varying time lags, nonlinearity, and nonstationarity, and estimates directed connectivity with high accuracy and data efficiency. We also use a non-human-primate dataset to show that GRU-PP correctly identifies the biophysically-plausible stronger PMd-to-M1 connectivity than M1-to-PMd connectivity during reaching. In all experiments, the GRU-PP consistently outperforms state-of-the-art methods.

CONCLUSION

The GRU-PP method efficiently estimates directed connectivity in varying time lag, nonlinear, and nonstationary spiking neuron networks.

SIGNIFICANCE

The proposed method can serve as a directed connectivity analysis tool for investigating complex spiking neuron network dynamics.

Depression mediated the relationships between precentral-subcortical causal links and motor recovery in spinal cord injury patients

Depression after brain damage may impede the motivation and consequently influence the motor recovery after spinal cord injury (SCI); however, the neural mechanism underlying the psychological effects remains unclear. This study aimed to examine the casual connectivity changes of the emotion-motivation-motor circuit and the potential mediating effects of depression on motor recovery after SCI. Using the resting-state functional magnetic resonance imaging data of 35 SCI patients (24 good recoverers, GR and 11 poor recoverers, PR) and 32 healthy controls (HC), the results from the conditional Granger causality (GC) analysis demonstrated that the GR group exhibited sparser emotion-motivation-motor GC network compared with the HC and PR groups, though the in-/out-degrees of the emotion subnetwork and the motor subnetwork were relatively balanced in the HC and GR group. The PR group showed significantly inhibitory causal links from amygdala to supplementary motor area and from precentral gyrus to nucleus accumbens compared with GR group. Further mediation analysis revealed the indirect effect of the 2 causal connections on motor function recovery via depression severity. Our findings provide further evidence of abnormal causal connectivity in emotion-motivation-motor circuit in SCI patients and highlight the importance of emotion intervention for motor function recovery after SCI.