Journal of Mathematical Imaging and Vision

, Volume 50, Issue 1–2, pp 126–143 | Cite as

Tree-Oriented Analysis of Brain Artery Structure

  • Sean SkwererEmail author
  • Elizabeth Bullitt
  • Stephan Huckemann
  • Ezra Miller
  • Ipek Oguz
  • Megan Owen
  • Vic Patrangenaru
  • Scott Provan
  • J. S. Marron


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.


Tree Brain-anatomy Treespace Object-oriented data analysis Stratified space Statistics 



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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Sean Skwerer
    • 1
    Email author
  • Elizabeth Bullitt
    • 2
  • Stephan Huckemann
    • 3
  • Ezra Miller
    • 4
  • Ipek Oguz
    • 5
  • Megan Owen
    • 6
  • Vic Patrangenaru
    • 7
  • Scott Provan
    • 1
  • J. S. Marron
    • 1
  1. 1.Department of Statistics and Operations ResearchUniversity of North CarolinaChapel HillUSA
  2. 2.Department of NeurosurgeryUniversity of North Carolina School of MedicineChapel HillUSA
  3. 3.Felix Bernstein Institute for Mathematical Statistics in the BiosciencesUniversity of GöttingenGöttingenGermany
  4. 4.Mathematics DepartmentDuke UniversityDurhamUSA
  5. 5.Department of Computer ScienceUniversity of North CarolinaChapel HillUSA
  6. 6.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  7. 7.Department of StatisticsFlorida State UniversityTallahasseeUSA

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