Persistent Homology Analysis of Brain Artery Trees

By Paul Bendich, James Stephen Marron, Ezra Miller, Alex Pieloch, Sean Skwerer. Annals of Applied Statistics, 2014

298 citations recorded by the source corpus.

New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries.

Subfields: Biophysics, Computational Theory and Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/869263162d6dde4a56c8688ebbffa41a47fe3b6e

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In Biophysics

In Computational Theory and Mathematics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Two’s company, three (or more) is a simplex (2016, methodology): “…have been applied to uncover structure in the space of natural images (Carls-son et al, 2008), to detect subject gender from the shape of brain artery trees (Bendich et al, 2014), and to identify statistically anomolous multi-region activation patterns in fMRI recordings (Ellis and Klein, 2014).”
A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology (2019, background): “PH has found applications in neuroscience [21], studying phase transitions [22], analysis of tree-structured data [23], and in measuring image artefacts [24].”
Persistence Images: A Stable Vector Representation of Persistent Homology (2015, methodology): “To resolve these issues, considerable effort (which we review in §2) has been made to map PDs into spaces which are suitable for other ML tools (Bubenik, 2015; Reininghaus et al., 2015; Rouse et al., 2015; Adcock et al., 2016; Donatini et al., 1998; Ferri et al., 1997; Chung et al., 2009; Pachauri e”
Topological Data Analysis (2016, background): “There is now a substantial literature on TDA in neuroscience including Arai et al. (2014); Babichev & Dabaghian (2016); Basso et al. (2016); Bendich et al. (2014); Brown & Gedeon (2012); Cassidy et al. (2015); Chen et al. (2014); Choi et al. (2014); Chung et al. (2009); Curto & Itskov (2008); Curto…”
What are higher-order networks? (2021, background): “Higher-order networks have also proven useful in genomics and evolutionary biology [63, 242], structural biology [301], as well as for the analysis of structures such as vascular networks [28, 53, 279].”