🍩 Database of Original & Non-Theoretical Uses of Topology

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  1. Topological Data Analysis Reveals Robust Alterations in the Whole-Brain and Frontal Lobe Functional Connectomes in Attention-Deficit/Hyperactivity Disorder (2020)

    Zeus Gracia-Tabuenca, Juan Carlos Díaz-Patiño, Isaac Arelio, Sarael Alcauter
    Abstract Visual Abstract \textlessimg class="highwire-fragment fragment-image" alt="Figure" src="https://www.eneuro.org/content/eneuro/7/3/ENEURO.0543-19.2020/F1.medium.gif" width="369" height="440"/\textgreaterDownload figureOpen in new tabDownload powerpoint Attention-deficit/hyperactivity disorder (ADHD) is a developmental disorder characterized by difficulty to control the own behavior. Neuroimaging studies have related ADHD with the interplay of fronto-parietal attention systems with the default mode network (DMN; Castellanos and Aoki, 2016). However, some results have been inconsistent, potentially due to methodological differences in the analytical strategies when defining the brain functional network, i.e., the functional connectivity threshold and/or the brain parcellation scheme. Here, we make use of topological data analysis (TDA) to explore the brain connectome as a function of the filtration value (i.e., the connectivity threshold), instead of using a static connectivity threshold. Specifically, we characterized the transition from all nodes being isolated to being connected into a single component as a function of the filtration value. We explored the utility of such a method to identify differences between 81 children with ADHD (45 male, age: 7.26–17.61 years old) and 96 typically developing children (TDC; 59 male, age: 7.17–17.96 years old), using a public dataset of resting state (rs)fMRI in human subjects. Results were highly congruent when using four different brain segmentations (atlases), and exhibited significant differences for the brain topology of children with ADHD, both at the whole-brain network and the functional subnetwork levels, particularly involving the frontal lobe and the DMN. Therefore, this is a solid approach that complements connectomics-related methods and may contribute to identify the neurophysio-pathology of ADHD.

  2. Development of the Functional Connectome Topology in Adolescence: Evidence From Topological Data Analysis (2021)

    Zeus Gracia-Tabuenca, Juan Carlos Díaz-Patiño, Isaac Arelio, Martha Beatriz Moreno, Fernando A. Barrios, Sarael Alcauter
    Abstract Adolescence is a crucial developmental period in terms of behavior and mental health. Therefore, understanding how the brain develops during this stage is a fundamental challenge for neuroscience. Recent studies have modelled the brain as a network or connectome, mainly applying measures from graph theory, showing a change in its functional organization such as an increase in its segregation and integration. Topological Data Analysis (TDA) complements such modelling by extracting high-dimensional features across the whole range of connectivity values, instead of exploring a fixed set of connections. This study enquiries into the developmental trajectories of such properties using a longitudinal sample of typically developing participants (N = 98; 53/45 F/M; 6.7-18.1 years), applying TDA into their functional connectomes. In addition, we explore the effect of puberty on the individual developmental trajectories. Results showed that compared to random networks, the adolescent brain is more segregated at the global level, but more densely connected at the local level. Furthermore, developmental effects showed nonlinear trajectories for the integration of the whole brain and fronto-parietal networks, with an inflection point and increasing trajectories after puberty onset. These results add to the insights in the development of the functional organization of the adolescent. Significance Statement Topological Data Analysis may be used to explore the topology of the brain along the whole range of connectivity values instead of selecting only a fixed set of connectivity thresholds. Here, we explored some properties of the topology of the brain functional connectome, and how they develop in adolescence. First, we show that developmental trajectories are nonlinear and better explained by the puberty status than chronological age, with an inflection point around the puberty onset. The greatest effect is the increase in functional integration for the whole brain, and particularly for the Fronto-Parietal Network when exploring functional subnetworks.