Abstract
Statistical analysis of magnetic resonance angiography (MRA) brain artery trees is performed using two methods for mapping brain artery trees to points in phylogenetic treespace: cortical landmark correspondence and descendant correspondence. The differences in end-results based on these mappings are highlighted to emphasize the importance of correspondence in tree-oriented data analysis. Representation of brain artery systems as points in phylogenetic treespace, a mathematical space developed in (Billera et al. Adv. Appl. Math 27:733–767, 2001), facilitates this analysis. The phylogenetic treespace is a rich setting for tree-oriented data analysis. The Fréchet sample mean or an approximation is reported. Multidimensional scaling is used to explore structure in the data set based on pairwise distances between data points. This analysis of MRA data shows a statistically significant effect of age and sex on brain artery structure. Variation in the proximity of brain arteries to the cortical surface results in strong statistical difference between sexes and statistically significant age effect. That particular observation is possible with cortical correspondence but did not show up in the descendant correspondence.
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The MR brain images form healthy volunteers used in this paper were collected and made available by the CASILab at The University of North Carolina at Chapel Hill and were distributed by the MIDAS Data Server at Kitware, Inc.
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We are grateful to SAMSI, for sponsoring the authors’ visits to the Research Triangle and for facilitating net meetings, as part of the Analysis of Object Data program in 2010–2011, that helped advance this research. SH acknowledges support from DFG HU 1575/2-1 as well as the Niedersachsen Vorab of the Volkswagen Foundation. IO acknowledges support from UNC Neurodevelopment Disorders Research Center HD 03110. MO acknowledges the support of the Fields Institute VP acknowledges support from NSF grants DMS-0805977 and DMS-1106935.
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Skwerer, S., Bullitt, E., Huckemann, S. et al. Tree-Oriented Analysis of Brain Artery Structure. J Math Imaging Vis 50, 126–143 (2014). https://doi.org/10.1007/s10851-013-0473-0
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DOI: https://doi.org/10.1007/s10851-013-0473-0