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

Siti N Makhtar,Mohd H Senik,Rob Mason,Carl W Stevenson,David M Halliday

doi:10.1088/1741-2552/ab7a50

Siti N Makhtar, Mohd H Senik + Show 3 more

Open Access

https://doi.org/10.1088/1741-2552/ab7a50

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Abstract

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.

Highlights

The ability to infer and characterize interactions between individual neurons and groups of neurons is Current address: Department of Electrical and Electronic Engineering, National Defense University of Malaysia, Malaysia. 7 Current address: Department of Neurosciences, Universiti Sains Malaysia, Malaysia.fundamental to understanding brain function [1]
We describe the calculation of coherence and multivariate partial coherence (MVPC) estimates used to generate the adjacency matrix, describe the construction of network measures
Our hypothesis is that network metrics derived from MVPC should give a more accurate representation of network interactions than those derived from ordinary coherence estimates

Summary

Introduction

Graphical networks and network metrics provide a unified framework for both illustrating and quantifying interactions between multivariate time series. They have been applied to a range of problems including physical networks [2, 3] and biological networks [4, 5]. Their use in characterising the interactions within brain networks is becoming well established [6,7,8,9]. One common approach to determining functional connectivity is through correlation analysis This can use time domain or frequency domain measures of correlation. In the frequency domain a common measure of functional interaction between two neuronal signals, is provided by the coherence function [10]

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