Brain Artery Tree Data

This is a set of tree structured data objects collected by the CASILab of Dr. Elizabeth Bullitt.

Various analyses of this data set, using a variety of different representations, have been published as listed below.

Here are versions of this data maintained by J. S. Marron:

Data Descriptors and Covariates

Raw MRA Images (from which the trees were derived with tube tracking algorithms, plus two levels of manual post-processing)

Terms of Use

This database is provided without charge for use in research, teaching, and commercial developments that advance the medical field.  Uses outside of the medical field require prior written approval from Dr. Elizabeth Bullitt.  These data may not be redistributed except when a few cases are distributed as part of an electronic publication in which the author of the publication has added significant value to the publication, beyond the value of the cases being redistributed.  In all other situations, citations and links to this webpage should be used.

We request that any publication or project that uses this data do the following:

a) Cite the following paper
Bullitt E, Zeng D, Gerig G, Aylward S, Joshi S, Smith JK, Lin W, Ewend MG (2005) Vessel tortuosity and brain tumor malignancy: A blinded study. Academic Radiology 12:1232-1240
as an example of how this kind of healthy image database can be used,

b) Include the following text (or something similar) in your acknowledgements
“The MR brain images from 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.”


Matlab workspaces of tree versions (one for each case) by Sean Skwerer

Notes on Those


Persistent Homology Analysis Files (including input trees and persistence diagrams) from Sean Skwerer


Other Repositories of Brain Artery Tree Data:

Raw MRA Images (hosted by MIDAS):

Sean Skwerer’s Dropbox of Matlab workspaces:

Sean Skwerer’s Dropbox of material from persistent homology analysis:


Brain Artery Tree Analysis Publications with Marron as co-author:

Topology Only:

“Object oriented data analysis: sets of trees”, Wang, H. and Marron, J. S. (2007) Annals of Statistics, 35, 1849-1873.

“A principal component analysis for trees”, Aydin, B., Pataki, G., Wang, H., Bullitt, E. and Marron, J. S., (2009) Annals of Applied Statistics, 3, 1597-1615.

“Visualizing the Structure of Large Trees”, Aydin, B., Pataki, G., Wang, H., Ladha, A., Bullitt, E. Marron, J. S. (2011) Electronic Journal of Statistics, 5, 405-420.

“New approaches to principal component analysis for trees”, Aydin B, and Pataki G, Wang H, Ladha A, Bullitt E, Marron JS (2012) Statistics in Biosciences, 4, 132-156.

“A Nonparametric Regression Model with Tree-structured Response”, Wang, Y., Marron, J. S.,  Aydin, B., Ladha, A., Bullitt, E., and Wang, H. (2012) Journal of the American Statistical Association, 107, 1272-1285.


Phylogenetic Trees Approach:

“Sticky Central Limit Theorems On Open Books”, T. Hotz, S. Huckemann, H. Le, J. S. Marron, J. C. Mattingly, Ezra Miller, J. Nolen, M. Owen, V. Patrangenaru, and S. Skwerer. (2013) Annals of Applied Probability, 23, 2238–2258, DOI: 10.1214/12-AAP899.

“Tree-oriented analysis of brain artery structure”, S. Skwerer, E. Bullitt, S. Huckemann, E. Miller, I. Oguz, M. Owen, J. S. Marron (2014). Journal of Mathematical Imaging and Vision, 1-18. DOI 10.1007/s10851-013-0473-0.

“Relative Optimality Conditions and Algorithms for Treespace Fréchet Means”, S. Skwerer, S. Provan & J. S. Marron (2018). SIAM Journal on Optimization, 28(2), 959-988, DOI: 10.1137/15M1050914.


Dyck Path Approach:

“Functional data analysis of tree data objects”, D. Shen, H. Shen, S. Bhamidi, Y. Muñoz Maldonado, Y. Kim, and J. S. Marron (2014). Journal of Computational and Graphical Statistics, 23, 418-438.


Persistent Homology (Topological Data Analysis) Approach:

“Persistent homology analysis of brain artery trees”, P. Bendich, J. S. Marron, E. Miller, A. Pieloch, S. Skwerer (2016) The Annals of Applied Statistics, 10, 198-218.


Other publications:

“Symbolic description of intracerebral vessels segmented from magnetic resonance angiograms and evaluation by comparison with X-ray angiograms”, Bullitt, E., Aylward, S., Smith, K., Mukherji, S., Jiroutek, M. and Muller, K. (2001) Medical Image Analysis, 5, 157-169.

“Initialization, noise, singularities, and scale in height ridge traversal for tubular object centerline extraction”,  Aylward, S.R. and Bullitt, E. (2002) IEEE transactions on medical imaging, 21, 61-75.

“Measuring tortuosity of the intracerebral vasculature from MRA images”, Bullitt, E., Gerig, G., Pizer, S.M., Lin, W. and Aylward, S.R. (2003) IEEE transactions on medical imaging, 22, 1163-1171.

“Analyzing attributes of vessel populations”, Bullitt, E., Muller, K.E., Jung, I., Lin, W. and Aylward, S. (2005)  Medical image analysis, 9(1), pp.39-49.

“Dimension reduction in principal component analysis for trees”, Alfaro, C. A., Aydın, B., Valencia, C. E., Bullitt, E. and Ladha, A. (2014)  Computational Statistics & Data Analysis, 74, 157–179.

“Branch order regression for modeling brain vasculature”, Roy Choudhury, K. and Skwerer, S. (2018) Medical physics, 45(3), pp.1123-1134.