The dataset contains cerebrovascular structures for image-based model and mathematical model to replicate results in a forthcoming paper (PLoS Comput Biol 16(6): e1007943. https://doi.org/10.1371/journal.pcbi.1007943). Data formats: We assume the data will be visualized in ParaView (Kitware Inc, New York, USA). vtp: line edges including additive information (radius, order, level, etc.)/ surface elements including additive information (vascular subregion ID) ply: triangular polygons vti: volume data in a 3-D cubic domain (DAT: values written in a text format) code: fortran programs for running and analyzing the cerebral vasculatures