Patient-specific measurements of cerebral blood flow provide valuable diagnostic information concerning cerebrovascular diseases rather than visually driven qualitative evaluation. In this paper, we present a quantitative method to estimate blood flow parameters with high temporal resolution from digital subtraction angiography (DSA) image sequences. Using a 3D DSA dataset and a 2D+t DSA sequence, the proposed algorithm employs a 1D Computational Fluid Dynamics (CFD) model for estimation of time-dependent flow values along a cerebral vessel, combined with an additional Advection Diffusion Equation (ADE) for contrast agent propagation. The CFD system, followed by the ADE, is solved with a finite volume approximation, which ensures the conservation of mass. Instead of defining a new imaging protocol to obtain relevant data, our cost function optimizes the bolus arrival time (BAT) of the contrast agent in 2D+t DSA sequences. The visual determination of BAT is common clinical practice and can be easily derived from and be compared to values, generated by a 1D-CFD simulation. Using this strategy, we ensure that our proposed method fits best to clinical practice and does not require any changes to the medical work flow. Synthetic experiments show that the recovered flow estimates match the ground truth values with less than 12% error in the mean flow rates.