Identification of directed interactions in networks

Improved functional connectivity network estimation for brain networks using multivariate partial coherence

OBJECTIVE

Graphical networks and network metrics are widely used to understand and characterise brain networks and brain function. These methods can be applied to a range of electrophysiological data including electroencephalography, local field potential and single unit recordings. Functional networks are often constructed using pair-wise correlation between variables. The objective of this study is to demonstrate that functional networks can be more accurately estimated using partial correlation than with pair-wise correlation.

APPROACH

We compared network metrics derived from unconditional and conditional graphical networks, obtained using coherence and multivariate partial coherence (MVPC), respectively. Graphical networks were constructed using coherence and MVPC estimates, and binary and weighted network metrics derived from these: node degree, path length, clustering coefficients and small-world index.

MAIN RESULTS

Network metrics were applied to simulated and experimental single unit spike train data. Simulated data used a 10x10 grid of simulated cortical neurons with centre-surround connectivity. Conditional network metrics gave a more accurate representation of the known connectivity: Numbers of excitatory connections had range 3-11, unconditional binary node degree had range 6-80, conditional node degree had range 2-13. Experimental data used multi-electrode array recording with 19 single-units from left and right hippocampal brain areas in a rat model for epilepsy. Conditional network analysis showed similar trends to simulated data, with lower binary node degree and longer binary path lengths compared to unconditional networks.

SIGNIFICANCE

We conclude that conditional networks, where common dependencies are removed through partial coherence analysis, give a more accurate representation of the interactions in a graphical network model. These results have important implications for graphical network analyses of brain networks and suggest that functional networks should be derived using partial correlation, based on MVPC estimates, as opposed to the common approach of pair-wise correlation.

Nonparametric directionality measures for time series and point process data

The need to determine the directionality of interactions between neural signals is a key requirement for analysis of multichannel recordings. Approaches most commonly used are parametric, typically relying on autoregressive models. A number of concerns have been expressed regarding parametric approaches, thus there is a need to consider alternatives. We present an alternative nonparametric approach for construction of directionality measures for bivariate random processes. The method combines time and frequency domain representations of bivariate data to decompose the correlation by direction. Our framework generates two sets of complementary measures, a set of scalar measures, which decompose the total product moment correlation coefficient summatively into three terms by direction and a set of functions which decompose the coherence summatively at each frequency into three terms by direction: forward direction, reverse direction and instantaneous interaction. It can be undertaken as an addition to a standard bivariate spectral and coherence analysis, and applied to either time series or point-process (spike train) data or mixtures of the two (hybrid data). In this paper, we demonstrate application to spike train data using simulated cortical neurone networks and application to experimental data from isolated muscle spindle sensory endings subject to random efferent stimulation.

EEG signatures of arm isometric exertions in preparation, planning and execution

The electroencephalographic (EEG) activity patterns in humans during motor behaviour provide insight into normal motor control processes and for diagnostic and rehabilitation applications. While the patterns preceding brisk voluntary movements, and especially movement execution, are well described, there are few EEG studies that address the cortical activation patterns seen in isometric exertions and their planning. In this paper, we report on time and time-frequency EEG signatures in experiments in normal subjects (n=8), using multichannel EEG during motor preparation, planning and execution of directional centre-out arm isometric exertions performed at the wrist in the horizontal plane, in response to instruction-delay visual cues. Our observations suggest that isometric force exertions are accompanied by transient and sustained event-related potentials (ERP) and event-related (de-)synchronisations (ERD/ERS), comparable to those of a movement task. Furthermore, the ERPs and ERD/ERS are also observed during preparation and planning of the isometric task. Comparison of ear-lobe-referenced and surface Laplacian ERPs indicates the contribution of superficial sources in supplementary and pre-motor (FC(z)), parietal (CP(z)) and primary motor cortical areas (C₁ and FC₁) to ERPs (primarily negative peaks in frontal and positive peaks in parietal areas), but contribution of deep sources to sustained time-domain potentials (negativity in planning and positivity in execution). Transient and sustained ERD patterns in μ and β frequency bands of ear-lobe-referenced and surface Laplacian EEG indicate the contribution of both superficial and deep sources to ERD/ERS. As no physical displacement happens during the task, we can infer that the underlying mechanisms of motor-related ERPs and ERD/ERS patterns do not only depend on change in limb coordinate or muscle-length-dependent ascending sensory information and are primary generated by motor preparation, direction-dependent planning and execution of isometric motor tasks. The results contribute to our understanding of the functions of different brain regions during voluntary motor tasks and their activity signatures in EEG can shed light on the relationships between large-scale recordings such as EEG and other recordings such as single unit activity and fMRI in this context.