Analysis of Magnetic Resonance Angiography Data

Analysis of magnetic resonance angiography (MRA) brain artery trees to uncover statistically significant trends with age or clustering by gender is performed. A data set of 3D brain artery trees was extracted from MRA images of a group of healthy subjects varying in age (see Aylward and Bullitt (2002) [ 4 ]). More details about the data set can be found in Section 1.4. This research taps into a powerful mathematical basis developed for phylogenetic inference. A phylogenetic tree can be used as a graphical representation of an evolutionary history. The space of phylogenetic trees developed in Billera et al. (2021) [ 25 ] is a geometrically interpretable sample space for phylogenetic trees. That space has the geometric property of global nonpositive curvature under which any two points are connected by a unique shortest path, called a geodesic , and under which any set has a unique Fréchet mean . The Fréchet mean was originally introduced by Fréchet (1948) [ 52 ].