A long-time exposure to lack of oxygen (hypoxia) in some regions of the cerebrovascular system is believed to be one of the causes of cerebral neurological disease. Performing {\em in vivo} studies on the human brain is complicated and can be highly risky for patients. In the present study, we show how a combination of Magnetic Resonance Imaging (MRI) and Computational Fluid Dynamics (CFD) can provide a non-invasive alternative for studying blood flow and transport of oxygen within the cerebral vasculature. We perform computer simulations of oxygen mass transfer in the subject-specific geometry of the Circle of Willis. The computational domain and boundary conditions are based on 4D flow MRI measurements. Two different oxygen mass transfer models are considered: passive (where oxygen is treated as a dilute chemical species in plasma) and active (where oxygen is bonded to hemoglobin) models. We show that neglecting hemoglobin transport results in a significant underestimation of the arterial wall-mass transfer of oxygen. We identified the hypoxic regions along the arterial walls by introducing the critical thresholds that are obtained by comparison of the estimated range of Damk\"{o}hler number ($Da\subset\langle9;57\rangle$) with the local Sherwood number. Finally, we recommend additional validations of the combined MRI/CFD approach proposed here for larger groups of subject- or patient-specific brain vasculature systems.

The results obtained are performed by the computational fluid dynamics (CFD) of the blood flow in the subject-specific of the brain vascular system. 

The data are saved in the Tecplot visualization software format (.plt).

The data are saved in the Tecplot visualization software format (.plt) (www.tecplot.com).

The data can be opened directly from Tecplot or by using open-source visualization software ParaView.