  Vascular networks play a crucial role in understanding brain functionalities.
Brain integrity and function, neuronal activity and plasticity, which are
crucial for learning, are actively modulated by their local environments,
specifically vascular networks. With recent developments in high-resolution 3D
light-sheet microscopy imaging together with tissue processing techniques, it
becomes feasible to obtain and examine large-scale brain vasculature in mice.
To establish a structural foundation for functional study, however, we need
advanced image analysis and structural modeling methods.
  Existing works use geometric features such as thickness, tortuosity, etc.
However, geometric features cannot fully capture structural characteristics
such as the richness of branches, connectivity, etc. In this paper, we study
the morphology of brain vasculature through a topological lens. We extract
topological features based on the theory of topological data analysis.
Comparing of these robust and multi-scale topological structural features
across different brain anatomical structures and between normal and obese
populations sheds light on their promising future in studying neurological
diseases.
