Selective internal radiation therapy (SIRT) using Yttrium-90 loaded glass microspheres injected in the hepatic artery is an emerging, minimally invasive therapy of liver cancer. A personalized intervention can lead to high concentration dose in the tumor, while sparing the surrounding parenchyma. We propose a computational model for patient-specific simulation of entire hepatic arterial tree, based on liver, tumors, and arteries segmentation on patient's tomography. Segmentation of hepatic arteries down to a diameter of 0.5 mm is semi-automatically performed on 3D cone-beam CT angiography. The liver and tumors are extracted from CT-scan at portal phase by an active surface method. Once the images are registered through an automatic multimodal registration, extracted data are used to initialize a numerical model simulating liver vascular network. The model creates successive bifurcations from given principal vessels, observing Poiseuille's and matter conservation laws. Simulations provide a coherent reconstruction of global hepatic arterial tree until vessel diameter of 0.05 mm. Microspheres distribution under simple hypotheses is also quantified, depending on injection site. The patient-specific character of this model may allow a personalized numerical approximation of microspheres final distribution, opening the way to clinical optimization of catheter placement for tumor targeting.