Modelling the signal propagation through structural connections in the brain: A circuit theory approach

Abstract

The neural function of the brain is characterized by activated brain regions and the connectivities among them. It is still unknown, how a static structural connectivity network affects the occurrence of task-dependent dynamic functional connectivity or why two structurally connected brain regions, are not functionally connected and vice-versa. Studies have shown, the underlying cause for many neurodegenerative diseases is the functional disruptions in neural connections. So understanding the relationship between structural and functional connectivity is important for understanding the impairment characteristics in the brain networks which is in essence depends upon the nature of signal flow through the structural connections in the brain. The purpose of this work is to characterize the signal propagation characteristics through structural connectivity and its influence on functional connectivity of the brain by applying a circuit theory based modelling approach. Modelling structural connections using circuit theory will allow the analysis of signal propagation in both time and frequency domains. So far the studies on the correlation between structural and functional connectivity were done from the time domain perspective of signal propagation. However, the very definition of functional connectivity indicates that the underlying structural connectivity networks has filter like properties and holds the frequency-phase characteristics. In this work, we explore this phenomenon following a step-by-step approach: (1) we develop an automated tool for extracting structural connectivity network from structural MRI image by considering a more general (compared to standard cortical mapping) non-anatomical equal-area parcellation process of the Regions of Interest (ROI) of the brain and extracting the geometrical properties of the white matter tracts between the ROIs, (2) developing circuit-based model for characterising signal propagation through a single myelinated axon fibre and representing it as a simplified transfer function encompassing its time and frequency properties, (3) extending this model for coupled axon fibres and characterising the time and frequency properties of the signal propagation through them under the influence of ephaphtic coupling between them and finally;(4) applying iv the models developed in (2) and (3) for creating an automated tool that is capable to characterising signal propagation through a bundle of axons - the typical scenario of a white matter tract. Our work results in an end-to-end tool taking inputs as the structural and diffusional MRI data and outputting the phase and frequency characteristics of the signal through the axon bundle with a defined geometrical property - the underlying phenomenon for deriving the relationship between structural and functional brain connectivity.

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