The current framework for the statistical shape modeling of the aorta involves the parameterization of a mesh of the thoracic aorta onto a periodic rectangular parametric domain defined by the longitudinal and circumferential axes. Through parameterization onto a common parametric domain, dimension reduction techniques such as principal component analysis can be used to study the morphological characteristics of the vessels. The parameterization, however, requires that the mesh be homeomorphic to a cylinder; thus branching vessels cannot be included in the original geometry. This thesis presents a new feature that can be included in addition to the coordinates of each vertex. This new feature is the geodesic signed distance function (a signed distance function defined only on the surface of the mesh) which defines the geodesic distance from each point on the mesh to the boundary where the head vessels branch off on the aortic arch. By creating this new feature, the branching locations for each vessel can be implicitly defined, thus retaining more information on the original geometry. As with the pre-existing framework, principal component analysis can be used to extract the most dominant geometric features of the vessel in addition to the locations at which branching is most likely to occur.