A hands-on tutorial on network and topological neuroscience

Abstract

The brain is an extraordinarily complex system that facilitates the efficient integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pair-wise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks, and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses data from the 1000 Functional Connectomes Project. Moreover, we would like to highlight one part of our notebook that is solely dedicated to realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pair-wise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

Development of the Functional Connectome Topology in Adolescence: evidence from Topological Data Analysis

“…The copyright holder for this preprint this version posted October 5, 2021. ; https://doi.org/10.1101/2021.10.04.463103 doi: bioRxiv preprint to address high-dimensional data such as Topological Data Analysis (TDA) (Sizemore et al, 2018;Expert et al, 2019). TDA models the connectome as a topological space and characterizes its interaction patterns as geometric features, allowing it to simplify complex structures at different scales (Giusti et al, 2016;Santos et al, 2019;Centeno et al, 2021). In particular, TDA applied to functional connectomes is not affected by the potential biases of connectivity thresholding nor brain segmentation (Lee et al, 2012;Gracia-Tabuenca et al, 2020).…”

The expanding horizons of network neuroscience: From description to prediction and control

“…The existence and prevalence of non-dyadic relations could be fruitfully addressed using more advanced mathematical representations, such as hypergraphs and simplicial complexes, where the fundamental units of analysis are not edges between two nodes but larger relational objects ( Torres et al, 2021 ). Such higher-order relations can then be studied using methods from algebraic topology and computer science, including but not limited to topological data analysis ( Centeno et al, 2021 ). The expansion to non-dyadic relations has shown marked utility in addressing open problems of network neuroscience ( Andjelković et al, 2020 ; Billings et al, 2021 ; Guo et al, 2021 ; Helm et al, 2020 ; Patania et al, 2019 ; Saggar et al, 2018 ; Santos et al, 2019 ).…”

Topological conditions for propagation of spatially-distributed neural activity

“…Topological analysis [18] is commonly used to characterize the architecture of data sets. Typically, the Čech or Vietoris-Rips complexes are calculated by increasing the diameter of 'balls' and then constructing simplices and documenting the persistence of Betti numbers [19,20], with the longer lasting Betti numbers being more indicative of the true topology.…”