Intraoperative management of bleeding is a critical skill all surgeons must possess. It is, however, very challenging to create a safe and realistic learning environment for its acquisition. In this paper, we propose a simple and efficient approach to integrate blood circulation to computerized surgical simulation systems and allow for real-time processing of punctures, ruptures, and cauterization of blood vessels. Blood pressures and flows are calculated using a system of ordinary differential equations, which can be simulated very efficiently. The equation system itself is constructed using a graph of the vessels' connectivity extracted from magnetic resonance angiograms (MRA) and completed with virtual vessels deduced from the principle of minimum work. Real-time performances of the method are assessed and results are demonstrated on ten patients who underwent a MRA before removal of a brain tumor.